zlib1g-dev
# Workaround missing libmpdec-dev on ubuntu 24.04 by building mpdecimal
-# from source. ppa:ondrej/php (launchpad.net) are unreliable
+# from source. ppa:ondrej/php (launchpad.net) are unreliable
# (https://status.canonical.com) so fetch the tarball directly
# from the upstream host.
# https://www.bytereef.org/mpdecimal/
library/asyncio-task.html: terminating-a-task-group
+# Removed libmpdec
+using/configure.html: cmdoption-with-system-libmpdec
+
# Removed APIs
library/symtable.html: symtable.Class.get_methods
-library/sys.html: sys._enablelegacywindowsfsencoding
\ No newline at end of file
+library/sys.html: sys._enablelegacywindowsfsencoding
.. [1] If *libmpdec* is not available, the :mod:`decimal` module will use
a pure-Python implementation.
- See :option:`--with-system-libmpdec` for details.
.. [2] See :option:`--with-readline` for choosing the backend for the
:mod:`readline` module.
.. [3] The :mod:`uuid` module uses ``_uuid`` to generate "safe" UUIDs.
C compiler and linker flags for ``libmpdec``, used by :mod:`decimal` module,
overriding ``pkg-config``.
- .. note::
-
- These environment variables have no effect unless
- :option:`--with-system-libmpdec` is specified.
-
.. option:: LIBLZMA_CFLAGS
.. option:: LIBLZMA_LIBS
Build the :mod:`!pyexpat` module using an installed ``expat`` library
(default is no).
-.. option:: --with-system-libmpdec
-
- Build the ``_decimal`` extension module using an installed ``mpdecimal``
- library, see the :mod:`decimal` module (default is yes).
-
- .. versionadded:: 3.3
-
- .. versionchanged:: 3.13
- Default to using the installed ``mpdecimal`` library.
-
- .. versionchanged:: 3.15
-
- A bundled copy of the library will no longer be selected
- implicitly if an installed ``mpdecimal`` library is not found.
- In Python 3.15 only, it can still be selected explicitly using
- ``--with-system-libmpdec=no`` or ``--without-system-libmpdec``.
-
- .. deprecated-removed:: 3.13 3.16
- A copy of the ``mpdecimal`` library sources will no longer be distributed
- with Python 3.16.
-
- .. seealso:: :option:`LIBMPDEC_CFLAGS` and :option:`LIBMPDEC_LIBS`.
-
.. option:: --with-readline=readline|editline
Designate a backend library for the :mod:`readline` module.
.. _mimalloc library: https://github.com/microsoft/mimalloc/
-* The :file:`configure` option :option:`--with-system-libmpdec`
+* The :file:`configure` option :option:`!--with-system-libmpdec`
now defaults to ``yes``.
The bundled copy of ``libmpdec`` will be removed in Python 3.16.
=============
* Removed implicit fallback to the bundled copy of the ``libmpdec`` library.
- Now this should be explicitly enabled with :option:`--with-system-libmpdec`
+ Now this should be explicitly enabled with :option:`!--with-system-libmpdec`
set to ``no`` or with :option:`!--without-system-libmpdec`.
(Contributed by Sergey B Kirpichev in :gh:`115119`.)
Build changes
=============
+* Remove the bundled copy of the libmpdec_ decimal library from the CPython source tree
+ to simplify maintenence and updates. The :mod:`decimal` module will now
+ unconditionally use the system's libmpdec decimal library. Also remove the
+ now unused :option:`!--with-system-libmpdec` :program:`configure` flag.
+ This change has no impact on binary releases of Python, which have been
+ built against a separate copy of libmpdec for the past several releases.
+
+ (Contributed by Sergey B Kirpichev in :gh:`115119`.)
+
+ .. _libmpdec: https://www.bytereef.org/mpdecimal/
+
C API changes
=============
print(" NOTE: --with-mimalloc=no pending resolution of weak linking issues")
runCommand("%s -C --enable-framework --enable-universalsdk=/ "
"--with-mimalloc=no "
- "--with-system-libmpdec "
"--with-universal-archs=%s "
"%s "
"%s "
ENSUREPIP= @ENSUREPIP@
# Internal static libraries
-LIBMPDEC_A= Modules/_decimal/libmpdec/libmpdec.a
LIBEXPAT_A= Modules/expat/libexpat.a
# HACL* build configuration
DTRACE_DEPS = \
Python/ceval.o Python/gc.o Python/import.o Python/sysmodule.o
-##########################################################################
-# decimal's libmpdec
-
-LIBMPDEC_OBJS= \
- Modules/_decimal/libmpdec/basearith.o \
- Modules/_decimal/libmpdec/constants.o \
- Modules/_decimal/libmpdec/context.o \
- Modules/_decimal/libmpdec/convolute.o \
- Modules/_decimal/libmpdec/crt.o \
- Modules/_decimal/libmpdec/difradix2.o \
- Modules/_decimal/libmpdec/fnt.o \
- Modules/_decimal/libmpdec/fourstep.o \
- Modules/_decimal/libmpdec/io.o \
- Modules/_decimal/libmpdec/mpalloc.o \
- Modules/_decimal/libmpdec/mpdecimal.o \
- Modules/_decimal/libmpdec/numbertheory.o \
- Modules/_decimal/libmpdec/sixstep.o \
- Modules/_decimal/libmpdec/transpose.o
- # _decimal does not use signaling API
- # Modules/_decimal/libmpdec/mpsignal.o
-
-LIBMPDEC_HEADERS= \
- $(srcdir)/Modules/_decimal/libmpdec/basearith.h \
- $(srcdir)/Modules/_decimal/libmpdec/bits.h \
- $(srcdir)/Modules/_decimal/libmpdec/constants.h \
- $(srcdir)/Modules/_decimal/libmpdec/convolute.h \
- $(srcdir)/Modules/_decimal/libmpdec/crt.h \
- $(srcdir)/Modules/_decimal/libmpdec/difradix2.h \
- $(srcdir)/Modules/_decimal/libmpdec/fnt.h \
- $(srcdir)/Modules/_decimal/libmpdec/fourstep.h \
- $(srcdir)/Modules/_decimal/libmpdec/io.h \
- $(srcdir)/Modules/_decimal/libmpdec/mpalloc.h \
- $(srcdir)/Modules/_decimal/libmpdec/mpdecimal.h \
- $(srcdir)/Modules/_decimal/libmpdec/numbertheory.h \
- $(srcdir)/Modules/_decimal/libmpdec/sixstep.h \
- $(srcdir)/Modules/_decimal/libmpdec/transpose.h \
- $(srcdir)/Modules/_decimal/libmpdec/typearith.h \
- $(srcdir)/Modules/_decimal/libmpdec/umodarith.h
-
##########################################################################
# pyexpat's expat library
@lcov $(COVERAGE_LCOV_OPTIONS) --remove $(COVERAGE_INFO) \
'*/Modules/_hacl/*' \
'*/Modules/_ctypes/libffi*/*' \
- '*/Modules/_decimal/libmpdec/*' \
'*/Modules/expat/*' \
'*/Modules/xx*.c' \
'*/Python/pyfpe.c' \
\
$(srcdir)/Python/stdlib_module_names.h
-##########################################################################
-# Build static libmpdec.a
-LIBMPDEC_CFLAGS=@LIBMPDEC_CFLAGS@ $(PY_STDMODULE_CFLAGS) $(CCSHARED)
-
-# "%.o: %c" is not portable
-Modules/_decimal/libmpdec/basearith.o: $(srcdir)/Modules/_decimal/libmpdec/basearith.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/basearith.c
-
-Modules/_decimal/libmpdec/constants.o: $(srcdir)/Modules/_decimal/libmpdec/constants.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/constants.c
-
-Modules/_decimal/libmpdec/context.o: $(srcdir)/Modules/_decimal/libmpdec/context.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/context.c
-
-Modules/_decimal/libmpdec/convolute.o: $(srcdir)/Modules/_decimal/libmpdec/convolute.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/convolute.c
-
-Modules/_decimal/libmpdec/crt.o: $(srcdir)/Modules/_decimal/libmpdec/crt.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/crt.c
-
-Modules/_decimal/libmpdec/difradix2.o: $(srcdir)/Modules/_decimal/libmpdec/difradix2.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/difradix2.c
-
-Modules/_decimal/libmpdec/fnt.o: $(srcdir)/Modules/_decimal/libmpdec/fnt.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/fnt.c
-
-Modules/_decimal/libmpdec/fourstep.o: $(srcdir)/Modules/_decimal/libmpdec/fourstep.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/fourstep.c
-
-Modules/_decimal/libmpdec/io.o: $(srcdir)/Modules/_decimal/libmpdec/io.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/io.c
-
-Modules/_decimal/libmpdec/mpalloc.o: $(srcdir)/Modules/_decimal/libmpdec/mpalloc.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/mpalloc.c
-
-Modules/_decimal/libmpdec/mpdecimal.o: $(srcdir)/Modules/_decimal/libmpdec/mpdecimal.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/mpdecimal.c
-
-Modules/_decimal/libmpdec/mpsignal.o: $(srcdir)/Modules/_decimal/libmpdec/mpsignal.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/mpsignal.c
-
-Modules/_decimal/libmpdec/numbertheory.o: $(srcdir)/Modules/_decimal/libmpdec/numbertheory.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/numbertheory.c
-
-Modules/_decimal/libmpdec/sixstep.o: $(srcdir)/Modules/_decimal/libmpdec/sixstep.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/sixstep.c
-
-Modules/_decimal/libmpdec/transpose.o: $(srcdir)/Modules/_decimal/libmpdec/transpose.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS)
- $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/transpose.c
-
-$(LIBMPDEC_A): $(LIBMPDEC_OBJS)
- -rm -f $@
- $(AR) $(ARFLAGS) $@ $(LIBMPDEC_OBJS)
-
##########################################################################
# Build static libexpat.a
LIBEXPAT_CFLAGS=@LIBEXPAT_CFLAGS@ $(PY_STDMODULE_CFLAGS) $(CCSHARED)
MODULE__CTYPES_DEPS=$(srcdir)/Modules/_ctypes/ctypes.h
MODULE__CTYPES_TEST_DEPS=$(srcdir)/Modules/_ctypes/_ctypes_test_generated.c.h
MODULE__CTYPES_MALLOC_CLOSURE=@MODULE__CTYPES_MALLOC_CLOSURE@
-MODULE__DECIMAL_DEPS=@LIBMPDEC_INTERNAL@
MODULE__ELEMENTTREE_DEPS=$(srcdir)/Modules/pyexpat.c @LIBEXPAT_INTERNAL@
MODULE__HASHLIB_DEPS=$(srcdir)/Modules/hashlib.h
MODULE__IO_DEPS=$(srcdir)/Modules/_io/_iomodule.h
.. nonce: eVXGEx
.. section: Build
-Don't use vendored ``libmpdec`` headers if :option:`--with-system-libmpdec`
+Don't use vendored ``libmpdec`` headers if :option:`!--with-system-libmpdec`
is passed to :program:`configure`. Don't use vendored ``libexpat`` headers
if :option:`--with-system-expat` is passed to :program:`configure`.
.. nonce: LT27pF
.. section: Build
-The :file:`configure` option :option:`--with-system-libmpdec` now defaults
+The :file:`configure` option :option:`!--with-system-libmpdec` now defaults
to ``yes``. The bundled copy of ``libmpdecimal`` will be removed in Python
3.15.
.. section: Build
:program:`configure` now uses :program:`pkg-config` to detect :mod:`decimal`
-dependencies if the :option:`--with-system-libmpdec` option is given.
+dependencies if the :option:`!--with-system-libmpdec` option is given.
..
.. section: Build
Removed implicit fallback to the bundled copy of the ``libmpdec`` library.
-Now this should be explicitly enabled via :option:`--with-system-libmpdec`
+Now this should be explicitly enabled via :option:`!--with-system-libmpdec`
set to ``no`` or :option:`!--without-system-libmpdec`. Patch by Sergey B
Kirpichev.
--- /dev/null
+Removed bundled copy of the libmpdec, use system library if it's available.
+Patch by Sergey B Kirpichev.
}
],
"fileName": "Lib/ctypes/macholib/framework.py"
- },
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@MODULE_CMATH_TRUE@cmath cmathmodule.c
@MODULE__STATISTICS_TRUE@_statistics _statisticsmodule.c
-# _decimal uses libmpdec
-# either static libmpdec.a from Modules/_decimal/libmpdec or libmpdec.so
-# with ./configure --with-system-libmpdec
+# _decimal uses the system's libmpdec.so
@MODULE__DECIMAL_TRUE@_decimal _decimal/_decimal.c
# compression libs and binascii (optional CRC32 from zlib)
-
-
About
=====
library for correctly-rounded arbitrary precision decimal floating point
arithmetic. It is a complete implementation of Mike Cowlishaw/IBM's
General Decimal Arithmetic Specification.
-
-
-Build process for the module
-============================
-
-As usual, the build process for _decimal.so is driven by setup.py in the top
-level directory. setup.py autodetects the following build configurations:
-
- 1) x64 - 64-bit Python, x86_64 processor (AMD, Intel)
-
- 2) uint128 - 64-bit Python, compiler provides __uint128_t (gcc)
-
- 3) ansi64 - 64-bit Python, ANSI C
-
- 4) ppro - 32-bit Python, x86 CPU, PentiumPro or later
-
- 5) ansi32 - 32-bit Python, ANSI C
-
- 6) ansi-legacy - 32-bit Python, compiler without uint64_t
-
- 7) universal - Mac OS only (multi-arch)
-
-
-It is possible to override autodetection by exporting:
-
- PYTHON_DECIMAL_WITH_MACHINE=value, where value is one of the above options.
-
-
-NOTE
-====
-
-decimal.so is not built from a static libmpdec.a since doing so led to
-failures on AIX (user report) and Windows (mixing static and dynamic CRTs
-causes locale problems and more).
-
-
-
+++ /dev/null
-
-
-libmpdec
-========
-
-libmpdec is a fast C/C++ library for correctly-rounded arbitrary precision
-decimal floating point arithmetic. It is a complete implementation of
-Mike Cowlishaw/IBM's General Decimal Arithmetic Specification.
-
-
-Files required for the Python _decimal module
-=============================================
-
- Core files for small and medium precision arithmetic
- ----------------------------------------------------
-
- basearith.{c,h} -> Core arithmetic in base 10**9 or 10**19.
- bits.h -> Portable detection of least/most significant one-bit.
- constants.{c,h} -> Constants that are used in multiple files.
- context.c -> Context functions.
- io.{c,h} -> Conversions between mpd_t and ASCII strings,
- mpd_t formatting (allows UTF-8 fill character).
- mpalloc.{c,h} -> Allocation handlers with overflow detection
- and functions for switching between static
- and dynamic mpd_t.
- mpdecimal.{c,h} -> All (quiet) functions of the specification.
- typearith.h -> Fast primitives for double word multiplication,
- division etc.
-
- Visual Studio only:
- ~~~~~~~~~~~~~~~~~~~
- vcdiv64.asm -> Double word division used in typearith.h. VS 2008 does
- not allow inline asm for x64. Also, it does not provide
- an intrinsic for double word division.
-
- Files for bignum arithmetic:
- ----------------------------
-
- The following files implement the Fast Number Theoretic Transform
- used for multiplying coefficients with more than 1024 words (see
- mpdecimal.c: _mpd_fntmul()).
-
- umodarith.h -> Fast low level routines for unsigned modular arithmetic.
- numbertheory.{c,h} -> Routines for setting up the Number Theoretic Transform.
- difradix2.{c,h} -> Decimation in frequency transform, used as the
- "base case" by the following three files:
-
- fnt.{c,h} -> Transform arrays up to 4096 words.
- sixstep.{c,h} -> Transform larger arrays of length 2**n.
- fourstep.{c,h} -> Transform larger arrays of length 3 * 2**n.
-
- convolute.{c,h} -> Fast convolution using one of the three transform
- functions.
- transpose.{c,h} -> Transpositions needed for the sixstep algorithm.
- crt.{c,h} -> Chinese Remainder Theorem: use information from three
- transforms modulo three different primes to get the
- final result.
-
-
-Pointers to literature, proofs and more
-=======================================
-
- literature/
- -----------
-
- REFERENCES.txt -> List of relevant papers.
- bignum.txt -> Explanation of the Fast Number Theoretic Transform (FNT).
- fnt.py -> Verify constants used in the FNT; Python demo for the
- O(N**2) discrete transform.
-
- matrix-transform.txt -> Proof for the Matrix Fourier Transform used in
- fourstep.c.
- six-step.txt -> Show that the algorithm used in sixstep.c is
- a variant of the Matrix Fourier Transform.
- mulmod-64.txt -> Proof for the mulmod64 algorithm from
- umodarith.h.
- mulmod-ppro.txt -> Proof for the x87 FPU modular multiplication
- from umodarith.h.
- umodarith.lisp -> ACL2 proofs for many functions from umodarith.h.
-
-
-Library Author
-==============
-
- Stefan Krah <skrah@bytereef.org>
-
-
-
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <assert.h>
-#include <stdio.h>
-
-#include "basearith.h"
-#include "constants.h"
-#include "typearith.h"
-
-
-/*********************************************************************/
-/* Calculations in base MPD_RADIX */
-/*********************************************************************/
-
-
-/*
- * Knuth, TAOCP, Volume 2, 4.3.1:
- * w := sum of u (len m) and v (len n)
- * n > 0 and m >= n
- * The calling function has to handle a possible final carry.
- */
-mpd_uint_t
-_mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
- mpd_size_t m, mpd_size_t n)
-{
- mpd_uint_t s;
- mpd_uint_t carry = 0;
- mpd_size_t i;
-
- assert(n > 0 && m >= n);
-
- /* add n members of u and v */
- for (i = 0; i < n; i++) {
- s = u[i] + (v[i] + carry);
- carry = (s < u[i]) | (s >= MPD_RADIX);
- w[i] = carry ? s-MPD_RADIX : s;
- }
- /* if there is a carry, propagate it */
- for (; carry && i < m; i++) {
- s = u[i] + carry;
- carry = (s == MPD_RADIX);
- w[i] = carry ? 0 : s;
- }
- /* copy the rest of u */
- for (; i < m; i++) {
- w[i] = u[i];
- }
-
- return carry;
-}
-
-/*
- * Add the contents of u to w. Carries are propagated further. The caller
- * has to make sure that w is big enough.
- */
-void
-_mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n)
-{
- mpd_uint_t s;
- mpd_uint_t carry = 0;
- mpd_size_t i;
-
- if (n == 0) return;
-
- /* add n members of u to w */
- for (i = 0; i < n; i++) {
- s = w[i] + (u[i] + carry);
- carry = (s < w[i]) | (s >= MPD_RADIX);
- w[i] = carry ? s-MPD_RADIX : s;
- }
- /* if there is a carry, propagate it */
- for (; carry; i++) {
- s = w[i] + carry;
- carry = (s == MPD_RADIX);
- w[i] = carry ? 0 : s;
- }
-}
-
-/*
- * Add v to w (len m). The calling function has to handle a possible
- * final carry. Assumption: m > 0.
- */
-mpd_uint_t
-_mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v)
-{
- mpd_uint_t s;
- mpd_uint_t carry;
- mpd_size_t i;
-
- assert(m > 0);
-
- /* add v to w */
- s = w[0] + v;
- carry = (s < v) | (s >= MPD_RADIX);
- w[0] = carry ? s-MPD_RADIX : s;
-
- /* if there is a carry, propagate it */
- for (i = 1; carry && i < m; i++) {
- s = w[i] + carry;
- carry = (s == MPD_RADIX);
- w[i] = carry ? 0 : s;
- }
-
- return carry;
-}
-
-/* Increment u. The calling function has to handle a possible carry. */
-mpd_uint_t
-_mpd_baseincr(mpd_uint_t *u, mpd_size_t n)
-{
- mpd_uint_t s;
- mpd_uint_t carry = 1;
- mpd_size_t i;
-
- assert(n > 0);
-
- /* if there is a carry, propagate it */
- for (i = 0; carry && i < n; i++) {
- s = u[i] + carry;
- carry = (s == MPD_RADIX);
- u[i] = carry ? 0 : s;
- }
-
- return carry;
-}
-
-/*
- * Knuth, TAOCP, Volume 2, 4.3.1:
- * w := difference of u (len m) and v (len n).
- * number in u >= number in v;
- */
-void
-_mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
- mpd_size_t m, mpd_size_t n)
-{
- mpd_uint_t d;
- mpd_uint_t borrow = 0;
- mpd_size_t i;
-
- assert(m > 0 && n > 0);
-
- /* subtract n members of v from u */
- for (i = 0; i < n; i++) {
- d = u[i] - (v[i] + borrow);
- borrow = (u[i] < d);
- w[i] = borrow ? d + MPD_RADIX : d;
- }
- /* if there is a borrow, propagate it */
- for (; borrow && i < m; i++) {
- d = u[i] - borrow;
- borrow = (u[i] == 0);
- w[i] = borrow ? MPD_RADIX-1 : d;
- }
- /* copy the rest of u */
- for (; i < m; i++) {
- w[i] = u[i];
- }
-}
-
-/*
- * Subtract the contents of u from w. w is larger than u. Borrows are
- * propagated further, but eventually w can absorb the final borrow.
- */
-void
-_mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n)
-{
- mpd_uint_t d;
- mpd_uint_t borrow = 0;
- mpd_size_t i;
-
- if (n == 0) return;
-
- /* subtract n members of u from w */
- for (i = 0; i < n; i++) {
- d = w[i] - (u[i] + borrow);
- borrow = (w[i] < d);
- w[i] = borrow ? d + MPD_RADIX : d;
- }
- /* if there is a borrow, propagate it */
- for (; borrow; i++) {
- d = w[i] - borrow;
- borrow = (w[i] == 0);
- w[i] = borrow ? MPD_RADIX-1 : d;
- }
-}
-
-/* w := product of u (len n) and v (single word) */
-void
-_mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v)
-{
- mpd_uint_t hi, lo;
- mpd_uint_t carry = 0;
- mpd_size_t i;
-
- assert(n > 0);
-
- for (i=0; i < n; i++) {
-
- _mpd_mul_words(&hi, &lo, u[i], v);
- lo = carry + lo;
- if (lo < carry) hi++;
-
- _mpd_div_words_r(&carry, &w[i], hi, lo);
- }
- w[i] = carry;
-}
-
-/*
- * Knuth, TAOCP, Volume 2, 4.3.1:
- * w := product of u (len m) and v (len n)
- * w must be initialized to zero
- */
-void
-_mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
- mpd_size_t m, mpd_size_t n)
-{
- mpd_uint_t hi, lo;
- mpd_uint_t carry;
- mpd_size_t i, j;
-
- assert(m > 0 && n > 0);
-
- for (j=0; j < n; j++) {
- carry = 0;
- for (i=0; i < m; i++) {
-
- _mpd_mul_words(&hi, &lo, u[i], v[j]);
- lo = w[i+j] + lo;
- if (lo < w[i+j]) hi++;
- lo = carry + lo;
- if (lo < carry) hi++;
-
- _mpd_div_words_r(&carry, &w[i+j], hi, lo);
- }
- w[j+m] = carry;
- }
-}
-
-/*
- * Knuth, TAOCP Volume 2, 4.3.1, exercise 16:
- * w := quotient of u (len n) divided by a single word v
- */
-mpd_uint_t
-_mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v)
-{
- mpd_uint_t hi, lo;
- mpd_uint_t rem = 0;
- mpd_size_t i;
-
- assert(n > 0);
-
- for (i=n-1; i != MPD_SIZE_MAX; i--) {
-
- _mpd_mul_words(&hi, &lo, rem, MPD_RADIX);
- lo = u[i] + lo;
- if (lo < u[i]) hi++;
-
- _mpd_div_words(&w[i], &rem, hi, lo, v);
- }
-
- return rem;
-}
-
-/*
- * Knuth, TAOCP Volume 2, 4.3.1:
- * q, r := quotient and remainder of uconst (len nplusm)
- * divided by vconst (len n)
- * nplusm >= n
- *
- * If r is not NULL, r will contain the remainder. If r is NULL, the
- * return value indicates if there is a remainder: 1 for true, 0 for
- * false. A return value of -1 indicates an error.
- */
-int
-_mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r,
- const mpd_uint_t *uconst, const mpd_uint_t *vconst,
- mpd_size_t nplusm, mpd_size_t n)
-{
- mpd_uint_t ustatic[MPD_MINALLOC_MAX];
- mpd_uint_t vstatic[MPD_MINALLOC_MAX];
- mpd_uint_t *u = ustatic;
- mpd_uint_t *v = vstatic;
- mpd_uint_t d, qhat, rhat, w2[2];
- mpd_uint_t hi, lo, x;
- mpd_uint_t carry;
- mpd_size_t i, j, m;
- int retval = 0;
-
- assert(n > 1 && nplusm >= n);
- m = sub_size_t(nplusm, n);
-
- /* D1: normalize */
- d = MPD_RADIX / (vconst[n-1] + 1);
-
- if (nplusm >= MPD_MINALLOC_MAX) {
- if ((u = mpd_alloc(nplusm+1, sizeof *u)) == NULL) {
- return -1;
- }
- }
- if (n >= MPD_MINALLOC_MAX) {
- if ((v = mpd_alloc(n+1, sizeof *v)) == NULL) {
- mpd_free(u);
- return -1;
- }
- }
-
- _mpd_shortmul(u, uconst, nplusm, d);
- _mpd_shortmul(v, vconst, n, d);
-
- /* D2: loop */
- for (j=m; j != MPD_SIZE_MAX; j--) {
- assert(2 <= j+n && j+n <= nplusm); /* annotation for scan-build */
-
- /* D3: calculate qhat and rhat */
- rhat = _mpd_shortdiv(w2, u+j+n-1, 2, v[n-1]);
- qhat = w2[1] * MPD_RADIX + w2[0];
-
- while (1) {
- if (qhat < MPD_RADIX) {
- _mpd_singlemul(w2, qhat, v[n-2]);
- if (w2[1] <= rhat) {
- if (w2[1] != rhat || w2[0] <= u[j+n-2]) {
- break;
- }
- }
- }
- qhat -= 1;
- rhat += v[n-1];
- if (rhat < v[n-1] || rhat >= MPD_RADIX) {
- break;
- }
- }
- /* D4: multiply and subtract */
- carry = 0;
- for (i=0; i <= n; i++) {
-
- _mpd_mul_words(&hi, &lo, qhat, v[i]);
-
- lo = carry + lo;
- if (lo < carry) hi++;
-
- _mpd_div_words_r(&hi, &lo, hi, lo);
-
- x = u[i+j] - lo;
- carry = (u[i+j] < x);
- u[i+j] = carry ? x+MPD_RADIX : x;
- carry += hi;
- }
- q[j] = qhat;
- /* D5: test remainder */
- if (carry) {
- q[j] -= 1;
- /* D6: add back */
- (void)_mpd_baseadd(u+j, u+j, v, n+1, n);
- }
- }
-
- /* D8: unnormalize */
- if (r != NULL) {
- _mpd_shortdiv(r, u, n, d);
- /* we are not interested in the return value here */
- retval = 0;
- }
- else {
- retval = !_mpd_isallzero(u, n);
- }
-
-
-if (u != ustatic) mpd_free(u);
-if (v != vstatic) mpd_free(v);
-return retval;
-}
-
-/*
- * Left shift of src by 'shift' digits; src may equal dest.
- *
- * dest := area of n mpd_uint_t with space for srcdigits+shift digits.
- * src := coefficient with length m.
- *
- * The case splits in the function are non-obvious. The following
- * equations might help:
- *
- * Let msdigits denote the number of digits in the most significant
- * word of src. Then 1 <= msdigits <= rdigits.
- *
- * 1) shift = q * rdigits + r
- * 2) srcdigits = qsrc * rdigits + msdigits
- * 3) destdigits = shift + srcdigits
- * = q * rdigits + r + qsrc * rdigits + msdigits
- * = q * rdigits + (qsrc * rdigits + (r + msdigits))
- *
- * The result has q zero words, followed by the coefficient that
- * is left-shifted by r. The case r == 0 is trivial. For r > 0, it
- * is important to keep in mind that we always read m source words,
- * but write m+1 destination words if r + msdigits > rdigits, m words
- * otherwise.
- */
-void
-_mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n, mpd_size_t m,
- mpd_size_t shift)
-{
-#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__)
- /* spurious uninitialized warnings */
- mpd_uint_t l=l, lprev=lprev, h=h;
-#else
- mpd_uint_t l, lprev, h;
-#endif
- mpd_uint_t q, r;
- mpd_uint_t ph;
-
- assert(m > 0 && n >= m);
-
- _mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS);
-
- if (r != 0) {
-
- ph = mpd_pow10[r];
-
- --m; --n;
- _mpd_divmod_pow10(&h, &lprev, src[m--], MPD_RDIGITS-r);
- if (h != 0) { /* r + msdigits > rdigits <==> h != 0 */
- dest[n--] = h;
- }
- /* write m-1 shifted words */
- for (; m != MPD_SIZE_MAX; m--,n--) {
- _mpd_divmod_pow10(&h, &l, src[m], MPD_RDIGITS-r);
- dest[n] = ph * lprev + h;
- lprev = l;
- }
- /* write least significant word */
- dest[q] = ph * lprev;
- }
- else {
- while (--m != MPD_SIZE_MAX) {
- dest[m+q] = src[m];
- }
- }
-
- mpd_uint_zero(dest, q);
-}
-
-/*
- * Right shift of src by 'shift' digits; src may equal dest.
- * Assumption: srcdigits-shift > 0.
- *
- * dest := area with space for srcdigits-shift digits.
- * src := coefficient with length 'slen'.
- *
- * The case splits in the function rely on the following equations:
- *
- * Let msdigits denote the number of digits in the most significant
- * word of src. Then 1 <= msdigits <= rdigits.
- *
- * 1) shift = q * rdigits + r
- * 2) srcdigits = qsrc * rdigits + msdigits
- * 3) destdigits = srcdigits - shift
- * = qsrc * rdigits + msdigits - (q * rdigits + r)
- * = (qsrc - q) * rdigits + msdigits - r
- *
- * Since destdigits > 0 and 1 <= msdigits <= rdigits:
- *
- * 4) qsrc >= q
- * 5) qsrc == q ==> msdigits > r
- *
- * The result has slen-q words if msdigits > r, slen-q-1 words otherwise.
- */
-mpd_uint_t
-_mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen,
- mpd_size_t shift)
-{
-#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__)
- /* spurious uninitialized warnings */
- mpd_uint_t l=l, h=h, hprev=hprev; /* low, high, previous high */
-#else
- mpd_uint_t l, h, hprev; /* low, high, previous high */
-#endif
- mpd_uint_t rnd, rest; /* rounding digit, rest */
- mpd_uint_t q, r;
- mpd_size_t i, j;
- mpd_uint_t ph;
-
- assert(slen > 0);
-
- _mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS);
-
- rnd = rest = 0;
- if (r != 0) {
-
- ph = mpd_pow10[MPD_RDIGITS-r];
-
- _mpd_divmod_pow10(&hprev, &rest, src[q], r);
- _mpd_divmod_pow10(&rnd, &rest, rest, r-1);
-
- if (rest == 0 && q > 0) {
- rest = !_mpd_isallzero(src, q);
- }
- /* write slen-q-1 words */
- for (j=0,i=q+1; i<slen; i++,j++) {
- _mpd_divmod_pow10(&h, &l, src[i], r);
- dest[j] = ph * l + hprev;
- hprev = h;
- }
- /* write most significant word */
- if (hprev != 0) { /* always the case if slen==q-1 */
- dest[j] = hprev;
- }
- }
- else {
- if (q > 0) {
- _mpd_divmod_pow10(&rnd, &rest, src[q-1], MPD_RDIGITS-1);
- /* is there any non-zero digit below rnd? */
- if (rest == 0) rest = !_mpd_isallzero(src, q-1);
- }
- for (j = 0; j < slen-q; j++) {
- dest[j] = src[q+j];
- }
- }
-
- /* 0-4 ==> rnd+rest < 0.5 */
- /* 5 ==> rnd+rest == 0.5 */
- /* 6-9 ==> rnd+rest > 0.5 */
- return (rnd == 0 || rnd == 5) ? rnd + !!rest : rnd;
-}
-
-
-/*********************************************************************/
-/* Calculations in base b */
-/*********************************************************************/
-
-/*
- * Add v to w (len m). The calling function has to handle a possible
- * final carry. Assumption: m > 0.
- */
-mpd_uint_t
-_mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v, mpd_uint_t b)
-{
- mpd_uint_t s;
- mpd_uint_t carry;
- mpd_size_t i;
-
- assert(m > 0);
-
- /* add v to w */
- s = w[0] + v;
- carry = (s < v) | (s >= b);
- w[0] = carry ? s-b : s;
-
- /* if there is a carry, propagate it */
- for (i = 1; carry && i < m; i++) {
- s = w[i] + carry;
- carry = (s == b);
- w[i] = carry ? 0 : s;
- }
-
- return carry;
-}
-
-/* w := product of u (len n) and v (single word). Return carry. */
-mpd_uint_t
-_mpd_shortmul_c(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v)
-{
- mpd_uint_t hi, lo;
- mpd_uint_t carry = 0;
- mpd_size_t i;
-
- assert(n > 0);
-
- for (i=0; i < n; i++) {
-
- _mpd_mul_words(&hi, &lo, u[i], v);
- lo = carry + lo;
- if (lo < carry) hi++;
-
- _mpd_div_words_r(&carry, &w[i], hi, lo);
- }
-
- return carry;
-}
-
-/* w := product of u (len n) and v (single word) */
-mpd_uint_t
-_mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
- mpd_uint_t v, mpd_uint_t b)
-{
- mpd_uint_t hi, lo;
- mpd_uint_t carry = 0;
- mpd_size_t i;
-
- assert(n > 0);
-
- for (i=0; i < n; i++) {
-
- _mpd_mul_words(&hi, &lo, u[i], v);
- lo = carry + lo;
- if (lo < carry) hi++;
-
- _mpd_div_words(&carry, &w[i], hi, lo, b);
- }
-
- return carry;
-}
-
-/*
- * Knuth, TAOCP Volume 2, 4.3.1, exercise 16:
- * w := quotient of u (len n) divided by a single word v
- */
-mpd_uint_t
-_mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
- mpd_uint_t v, mpd_uint_t b)
-{
- mpd_uint_t hi, lo;
- mpd_uint_t rem = 0;
- mpd_size_t i;
-
- assert(n > 0);
-
- for (i=n-1; i != MPD_SIZE_MAX; i--) {
-
- _mpd_mul_words(&hi, &lo, rem, b);
- lo = u[i] + lo;
- if (lo < u[i]) hi++;
-
- _mpd_div_words(&w[i], &rem, hi, lo, v);
- }
-
- return rem;
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_BASEARITH_H_
-#define LIBMPDEC_BASEARITH_H_
-
-
-#include "mpdecimal.h"
-#include "typearith.h"
-
-
-/* Internal header file: all symbols have local scope in the DSO */
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
-
-
-mpd_uint_t _mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
- mpd_size_t m, mpd_size_t n);
-void _mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
-mpd_uint_t _mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v);
-mpd_uint_t _mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v,
- mpd_uint_t b);
-mpd_uint_t _mpd_baseincr(mpd_uint_t *u, mpd_size_t n);
-void _mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
- mpd_size_t m, mpd_size_t n);
-void _mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
-void _mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
- mpd_size_t m, mpd_size_t n);
-void _mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
- mpd_uint_t v);
-mpd_uint_t _mpd_shortmul_c(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
- mpd_uint_t v);
-mpd_uint_t _mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
- mpd_uint_t v, mpd_uint_t b);
-mpd_uint_t _mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
- mpd_uint_t v);
-mpd_uint_t _mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
- mpd_uint_t v, mpd_uint_t b);
-int _mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r, const mpd_uint_t *uconst,
- const mpd_uint_t *vconst, mpd_size_t nplusm, mpd_size_t n);
-void _mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n,
- mpd_size_t m, mpd_size_t shift);
-mpd_uint_t _mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen,
- mpd_size_t shift);
-
-
-
-#ifdef CONFIG_64
-extern const mpd_uint_t mprime_rdx;
-
-/*
- * Algorithm from: Division by Invariant Integers using Multiplication,
- * T. Granlund and P. L. Montgomery, Proceedings of the SIGPLAN '94
- * Conference on Programming Language Design and Implementation.
- *
- * http://gmplib.org/~tege/divcnst-pldi94.pdf
- *
- * Variables from the paper and their translations (See section 8):
- *
- * N := 64
- * d := MPD_RADIX
- * l := 64
- * m' := floor((2**(64+64) - 1)/MPD_RADIX) - 2**64
- *
- * Since N-l == 0:
- *
- * dnorm := d
- * n2 := hi
- * n10 := lo
- *
- * ACL2 proof: mpd-div-words-r-correct
- */
-static inline void
-_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
-{
- mpd_uint_t n_adj, h, l, t;
- mpd_uint_t n1_neg;
-
- /* n1_neg = if lo >= 2**63 then MPD_UINT_MAX else 0 */
- n1_neg = (lo & (1ULL<<63)) ? MPD_UINT_MAX : 0;
- /* n_adj = if lo >= 2**63 then lo+MPD_RADIX else lo */
- n_adj = lo + (n1_neg & MPD_RADIX);
-
- /* (h, l) = if lo >= 2**63 then m'*(hi+1) else m'*hi */
- _mpd_mul_words(&h, &l, mprime_rdx, hi-n1_neg);
- l = l + n_adj;
- if (l < n_adj) h++;
- t = h + hi;
- /* At this point t == qest, with q == qest or q == qest+1:
- * 1) 0 <= 2**64*hi + lo - qest*MPD_RADIX < 2*MPD_RADIX
- */
-
- /* t = 2**64-1 - qest = 2**64 - (qest+1) */
- t = MPD_UINT_MAX - t;
-
- /* (h, l) = 2**64*MPD_RADIX - (qest+1)*MPD_RADIX */
- _mpd_mul_words(&h, &l, t, MPD_RADIX);
- l = l + lo;
- if (l < lo) h++;
- h += hi;
- h -= MPD_RADIX;
- /* (h, l) = 2**64*hi + lo - (qest+1)*MPD_RADIX (mod 2**128)
- * Case q == qest+1:
- * a) h == 0, l == r
- * b) q := h - t == qest+1
- * c) r := l
- * Case q == qest:
- * a) h == MPD_UINT_MAX, l == 2**64-(MPD_RADIX-r)
- * b) q := h - t == qest
- * c) r := l + MPD_RADIX = r
- */
-
- *q = (h - t);
- *r = l + (MPD_RADIX & h);
-}
-#else
-static inline void
-_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
-{
- _mpd_div_words(q, r, hi, lo, MPD_RADIX);
-}
-#endif
-
-
-/* Multiply two single base MPD_RADIX words, store result in array w[2]. */
-static inline void
-_mpd_singlemul(mpd_uint_t w[2], mpd_uint_t u, mpd_uint_t v)
-{
- mpd_uint_t hi, lo;
-
- _mpd_mul_words(&hi, &lo, u, v);
- _mpd_div_words_r(&w[1], &w[0], hi, lo);
-}
-
-/* Multiply u (len 2) and v (len m, 1 <= m <= 2). */
-static inline void
-_mpd_mul_2_le2(mpd_uint_t w[4], mpd_uint_t u[2], mpd_uint_t v[2], mpd_ssize_t m)
-{
- mpd_uint_t hi, lo;
-
- _mpd_mul_words(&hi, &lo, u[0], v[0]);
- _mpd_div_words_r(&w[1], &w[0], hi, lo);
-
- _mpd_mul_words(&hi, &lo, u[1], v[0]);
- lo = w[1] + lo;
- if (lo < w[1]) hi++;
- _mpd_div_words_r(&w[2], &w[1], hi, lo);
- if (m == 1) return;
-
- _mpd_mul_words(&hi, &lo, u[0], v[1]);
- lo = w[1] + lo;
- if (lo < w[1]) hi++;
- _mpd_div_words_r(&w[3], &w[1], hi, lo);
-
- _mpd_mul_words(&hi, &lo, u[1], v[1]);
- lo = w[2] + lo;
- if (lo < w[2]) hi++;
- lo = w[3] + lo;
- if (lo < w[3]) hi++;
- _mpd_div_words_r(&w[3], &w[2], hi, lo);
-}
-
-
-/*
- * Test if all words from data[len-1] to data[0] are zero. If len is 0, nothing
- * is tested and the coefficient is regarded as "all zero".
- */
-static inline int
-_mpd_isallzero(const mpd_uint_t *data, mpd_ssize_t len)
-{
- while (--len >= 0) {
- if (data[len] != 0) return 0;
- }
- return 1;
-}
-
-/*
- * Test if all full words from data[len-1] to data[0] are MPD_RADIX-1
- * (all nines). Return true if len == 0.
- */
-static inline int
-_mpd_isallnine(const mpd_uint_t *data, mpd_ssize_t len)
-{
- while (--len >= 0) {
- if (data[len] != MPD_RADIX-1) return 0;
- }
- return 1;
-}
-
-
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
-
-
-#endif /* LIBMPDEC_BASEARITH_H_ */
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <stdint.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <time.h>
-
-
-static void
-err_exit(const char *msg)
-{
- fprintf(stderr, "%s\n", msg);
- exit(1);
-}
-
-static mpd_t *
-new_mpd(void)
-{
- mpd_t *x = mpd_qnew();
- if (x == NULL) {
- err_exit("out of memory");
- }
-
- return x;
-}
-
-/* Nonsense version of escape-time algorithm for calculating a mandelbrot
- * set. Just for benchmarking. */
-static void
-color_point(mpd_t *x0, mpd_t *y0, long maxiter, mpd_context_t *ctx)
-{
- mpd_t *x, *y, *sq_x, *sq_y;
- mpd_t *two;
-
- x = new_mpd();
- y = new_mpd();
- mpd_set_u32(x, 0, ctx);
- mpd_set_u32(y, 0, ctx);
-
- sq_x = new_mpd();
- sq_y = new_mpd();
- mpd_set_u32(sq_x, 0, ctx);
- mpd_set_u32(sq_y, 0, ctx);
-
- two = new_mpd();
- mpd_set_u32(two, 2, ctx);
-
- for (long i = 0; i < maxiter; i++) {
- mpd_mul(y, x, y, ctx);
- mpd_mul(y, y, two, ctx);
- mpd_add(y, y, y0, ctx);
-
- mpd_sub(x, sq_x, sq_y, ctx);
- mpd_add(x, x, x0, ctx);
-
- mpd_mul(sq_x, x, x, ctx);
- mpd_mul(sq_y, y, y, ctx);
- }
-
- mpd_copy(x0, x, ctx);
-
- mpd_del(two);
- mpd_del(sq_y);
- mpd_del(sq_x);
- mpd_del(y);
- mpd_del(x);
-}
-
-
-int
-main(int argc, char **argv)
-{
- mpd_context_t ctx;
- mpd_t *x0, *y0;
- uint32_t prec = 19;
- long iter = 10000000;
- clock_t start_clock, end_clock;
-
- if (argc != 3) {
- err_exit("usage: bench prec iter\n");
- }
- prec = strtoul(argv[1], NULL, 10);
- iter = strtol(argv[2], NULL, 10);
-
- mpd_init(&ctx, prec);
- /* no more MPD_MINALLOC changes after here */
-
- x0 = new_mpd();
- y0 = new_mpd();
- mpd_set_string(x0, "0.222", &ctx);
- mpd_set_string(y0, "0.333", &ctx);
- if (ctx.status & MPD_Errors) {
- mpd_del(y0);
- mpd_del(x0);
- err_exit("unexpected error during conversion");
- }
-
- start_clock = clock();
- color_point(x0, y0, iter, &ctx);
- end_clock = clock();
-
- mpd_print(x0);
- fprintf(stderr, "time: %f\n\n", (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC);
-
- mpd_del(y0);
- mpd_del(x0);
-
- return 0;
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <stdint.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <time.h>
-
-
-static void
-err_exit(const char *msg)
-{
- fprintf(stderr, "%s\n", msg);
- exit(1);
-}
-
-static mpd_t *
-new_mpd(void)
-{
- mpd_t *x = mpd_qnew();
- if (x == NULL) {
- err_exit("out of memory");
- }
-
- return x;
-}
-
-/*
- * Example from: http://en.wikipedia.org/wiki/Mandelbrot_set
- *
- * Escape time algorithm for drawing the set:
- *
- * Point x0, y0 is deemed to be in the Mandelbrot set if the return
- * value is maxiter. Lower return values indicate how quickly points
- * escaped and can be used for coloring.
- */
-static int
-color_point(const mpd_t *x0, const mpd_t *y0, const long maxiter, mpd_context_t *ctx)
-{
- mpd_t *x, *y, *sq_x, *sq_y;
- mpd_t *two, *four, *c;
- long i;
-
- x = new_mpd();
- y = new_mpd();
- mpd_set_u32(x, 0, ctx);
- mpd_set_u32(y, 0, ctx);
-
- sq_x = new_mpd();
- sq_y = new_mpd();
- mpd_set_u32(sq_x, 0, ctx);
- mpd_set_u32(sq_y, 0, ctx);
-
- two = new_mpd();
- four = new_mpd();
- mpd_set_u32(two, 2, ctx);
- mpd_set_u32(four, 4, ctx);
-
- c = new_mpd();
- mpd_set_u32(c, 0, ctx);
-
- for (i = 0; i < maxiter && mpd_cmp(c, four, ctx) <= 0; i++) {
- mpd_mul(y, x, y, ctx);
- mpd_mul(y, y, two, ctx);
- mpd_add(y, y, y0, ctx);
-
- mpd_sub(x, sq_x, sq_y, ctx);
- mpd_add(x, x, x0, ctx);
-
- mpd_mul(sq_x, x, x, ctx);
- mpd_mul(sq_y, y, y, ctx);
- mpd_add(c, sq_x, sq_y, ctx);
- }
-
- mpd_del(c);
- mpd_del(four);
- mpd_del(two);
- mpd_del(sq_y);
- mpd_del(sq_x);
- mpd_del(y);
- mpd_del(x);
-
- return i;
-}
-
-int
-main(int argc, char **argv)
-{
- mpd_context_t ctx;
- mpd_t *x0, *y0;
- mpd_t *sqrt_2, *xstep, *ystep;
- mpd_ssize_t prec = 19;
-
- long iter = 1000;
- int points[40][80];
- int i, j;
- clock_t start_clock, end_clock;
-
-
- if (argc != 3) {
- fprintf(stderr, "usage: ./bench prec iter\n");
- exit(1);
- }
- prec = strtoll(argv[1], NULL, 10);
- iter = strtol(argv[2], NULL, 10);
-
- mpd_init(&ctx, prec);
- /* no more MPD_MINALLOC changes after here */
-
- sqrt_2 = new_mpd();
- xstep = new_mpd();
- ystep = new_mpd();
- x0 = new_mpd();
- y0 = new_mpd();
-
- mpd_set_u32(sqrt_2, 2, &ctx);
- mpd_sqrt(sqrt_2, sqrt_2, &ctx);
- mpd_div_u32(xstep, sqrt_2, 40, &ctx);
- mpd_div_u32(ystep, sqrt_2, 20, &ctx);
-
- start_clock = clock();
- mpd_copy(y0, sqrt_2, &ctx);
- for (i = 0; i < 40; i++) {
- mpd_copy(x0, sqrt_2, &ctx);
- mpd_set_negative(x0);
- for (j = 0; j < 80; j++) {
- points[i][j] = color_point(x0, y0, iter, &ctx);
- mpd_add(x0, x0, xstep, &ctx);
- }
- mpd_sub(y0, y0, ystep, &ctx);
- }
- end_clock = clock();
-
-#ifdef BENCH_VERBOSE
- for (i = 0; i < 40; i++) {
- for (j = 0; j < 80; j++) {
- if (points[i][j] == iter) {
- putchar('*');
- }
- else if (points[i][j] >= 10) {
- putchar('+');
- }
- else if (points[i][j] >= 5) {
- putchar('.');
- }
- else {
- putchar(' ');
- }
- }
- putchar('\n');
- }
- putchar('\n');
-#else
- (void)points; /* suppress gcc warning */
-#endif
-
- printf("time: %f\n\n", (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC);
-
- mpd_del(y0);
- mpd_del(x0);
- mpd_del(ystep);
- mpd_del(xstep);
- mpd_del(sqrt_2);
-
- return 0;
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_BITS_H_
-#define LIBMPDEC_BITS_H_
-
-
-#include "mpdecimal.h"
-
-
-/* Check if n is a power of 2. */
-static inline int
-ispower2(mpd_size_t n)
-{
- return n != 0 && (n & (n-1)) == 0;
-}
-
-#if defined(ANSI)
-/*
- * Return the most significant bit position of n from 0 to 31 (63).
- * Assumptions: n != 0.
- */
-static inline int
-mpd_bsr(mpd_size_t n)
-{
- int pos = 0;
- mpd_size_t tmp;
-
-#ifdef CONFIG_64
- tmp = n >> 32;
- if (tmp != 0) { n = tmp; pos += 32; }
-#endif
- tmp = n >> 16;
- if (tmp != 0) { n = tmp; pos += 16; }
- tmp = n >> 8;
- if (tmp != 0) { n = tmp; pos += 8; }
- tmp = n >> 4;
- if (tmp != 0) { n = tmp; pos += 4; }
- tmp = n >> 2;
- if (tmp != 0) { n = tmp; pos += 2; }
- tmp = n >> 1;
- if (tmp != 0) { n = tmp; pos += 1; }
-
- return pos + (int)n - 1;
-}
-
-/*
- * Return the least significant bit position of n from 0 to 31 (63).
- * Assumptions: n != 0.
- */
-static inline int
-mpd_bsf(mpd_size_t n)
-{
- int pos;
-
-#ifdef CONFIG_64
- pos = 63;
- if (n & 0x00000000FFFFFFFFULL) { pos -= 32; } else { n >>= 32; }
- if (n & 0x000000000000FFFFULL) { pos -= 16; } else { n >>= 16; }
- if (n & 0x00000000000000FFULL) { pos -= 8; } else { n >>= 8; }
- if (n & 0x000000000000000FULL) { pos -= 4; } else { n >>= 4; }
- if (n & 0x0000000000000003ULL) { pos -= 2; } else { n >>= 2; }
- if (n & 0x0000000000000001ULL) { pos -= 1; }
-#else
- pos = 31;
- if (n & 0x000000000000FFFFUL) { pos -= 16; } else { n >>= 16; }
- if (n & 0x00000000000000FFUL) { pos -= 8; } else { n >>= 8; }
- if (n & 0x000000000000000FUL) { pos -= 4; } else { n >>= 4; }
- if (n & 0x0000000000000003UL) { pos -= 2; } else { n >>= 2; }
- if (n & 0x0000000000000001UL) { pos -= 1; }
-#endif
- return pos;
-}
-/* END ANSI */
-
-#elif defined(ASM)
-/*
- * Bit scan reverse. Assumptions: a != 0.
- */
-static inline int
-mpd_bsr(mpd_size_t a)
-{
- mpd_size_t retval;
-
- __asm__ (
-#ifdef CONFIG_64
- "bsrq %1, %0\n\t"
-#else
- "bsr %1, %0\n\t"
-#endif
- :"=r" (retval)
- :"r" (a)
- :"cc"
- );
-
- return (int)retval;
-}
-
-/*
- * Bit scan forward. Assumptions: a != 0.
- */
-static inline int
-mpd_bsf(mpd_size_t a)
-{
- mpd_size_t retval;
-
- __asm__ (
-#ifdef CONFIG_64
- "bsfq %1, %0\n\t"
-#else
- "bsf %1, %0\n\t"
-#endif
- :"=r" (retval)
- :"r" (a)
- :"cc"
- );
-
- return (int)retval;
-}
-/* END ASM */
-
-#elif defined(MASM)
-#include <intrin.h>
-/*
- * Bit scan reverse. Assumptions: a != 0.
- */
-static inline int __cdecl
-mpd_bsr(mpd_size_t a)
-{
- unsigned long retval;
-
-#ifdef CONFIG_64
- _BitScanReverse64(&retval, a);
-#else
- _BitScanReverse(&retval, a);
-#endif
-
- return (int)retval;
-}
-
-/*
- * Bit scan forward. Assumptions: a != 0.
- */
-static inline int __cdecl
-mpd_bsf(mpd_size_t a)
-{
- unsigned long retval;
-
-#ifdef CONFIG_64
- _BitScanForward64(&retval, a);
-#else
- _BitScanForward(&retval, a);
-#endif
-
- return (int)retval;
-}
-/* END MASM (_MSC_VER) */
-#else
- #error "missing preprocessor definitions"
-#endif /* BSR/BSF */
-
-
-#endif /* LIBMPDEC_BITS_H_ */
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-#include "basearith.h"
-#include "constants.h"
-
-
-#if defined(CONFIG_64)
-
- /* number-theory.c */
- const mpd_uint_t mpd_moduli[3] = {
- 18446744069414584321ULL, 18446744056529682433ULL, 18446742974197923841ULL
- };
- const mpd_uint_t mpd_roots[3] = {7ULL, 10ULL, 19ULL};
-
- /* crt.c */
- const mpd_uint_t INV_P1_MOD_P2 = 18446744055098026669ULL;
- const mpd_uint_t INV_P1P2_MOD_P3 = 287064143708160ULL;
- const mpd_uint_t LH_P1P2 = 18446744052234715137ULL; /* (P1*P2) % 2^64 */
- const mpd_uint_t UH_P1P2 = 18446744052234715141ULL; /* (P1*P2) / 2^64 */
-
- /* transpose.c */
- const mpd_size_t mpd_bits[64] = {
- 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384,
- 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608,
- 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824,
- 2147483648ULL, 4294967296ULL, 8589934592ULL, 17179869184ULL, 34359738368ULL,
- 68719476736ULL, 137438953472ULL, 274877906944ULL, 549755813888ULL,
- 1099511627776ULL, 2199023255552ULL, 4398046511104, 8796093022208ULL,
- 17592186044416ULL, 35184372088832ULL, 70368744177664ULL, 140737488355328ULL,
- 281474976710656ULL, 562949953421312ULL, 1125899906842624ULL,
- 2251799813685248ULL, 4503599627370496ULL, 9007199254740992ULL,
- 18014398509481984ULL, 36028797018963968ULL, 72057594037927936ULL,
- 144115188075855872ULL, 288230376151711744ULL, 576460752303423488ULL,
- 1152921504606846976ULL, 2305843009213693952ULL, 4611686018427387904ULL,
- 9223372036854775808ULL
- };
-
- /* mpdecimal.c */
- const mpd_uint_t mpd_pow10[MPD_RDIGITS+1] = {
- 1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000,
- 10000000000ULL,100000000000ULL,1000000000000ULL,10000000000000ULL,
- 100000000000000ULL,1000000000000000ULL,10000000000000000ULL,
- 100000000000000000ULL,1000000000000000000ULL,10000000000000000000ULL
- };
-
- /* magic number for constant division by MPD_RADIX */
- const mpd_uint_t mprime_rdx = 15581492618384294730ULL;
-
-#elif defined(CONFIG_32)
-
- /* number-theory.c */
- const mpd_uint_t mpd_moduli[3] = {2113929217UL, 2013265921UL, 1811939329UL};
- const mpd_uint_t mpd_roots[3] = {5UL, 31UL, 13UL};
-
- /* PentiumPro modular multiplication: These constants have to be loaded as
- * 80 bit long doubles, which are not supported by certain compilers. */
- const uint32_t mpd_invmoduli[3][3] = {
- {4293885170U, 2181570688U, 16352U}, /* ((long double) 1 / 2113929217UL) */
- {1698898177U, 2290649223U, 16352U}, /* ((long double) 1 / 2013265921UL) */
- {2716021846U, 2545165803U, 16352U} /* ((long double) 1 / 1811939329UL) */
- };
-
- const float MPD_TWO63 = 9223372036854775808.0; /* 2^63 */
-
- /* crt.c */
- const mpd_uint_t INV_P1_MOD_P2 = 2013265901UL;
- const mpd_uint_t INV_P1P2_MOD_P3 = 54UL;
- const mpd_uint_t LH_P1P2 = 4127195137UL; /* (P1*P2) % 2^32 */
- const mpd_uint_t UH_P1P2 = 990904320UL; /* (P1*P2) / 2^32 */
-
- /* transpose.c */
- const mpd_size_t mpd_bits[32] = {
- 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384,
- 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608,
- 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824,
- 2147483648UL
- };
-
- /* mpdecimal.c */
- const mpd_uint_t mpd_pow10[MPD_RDIGITS+1] = {
- 1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000
- };
-
-#else
- #error "CONFIG_64 or CONFIG_32 must be defined."
-#endif
-
-const char * const mpd_round_string[MPD_ROUND_GUARD] = {
- "ROUND_UP", /* round away from 0 */
- "ROUND_DOWN", /* round toward 0 (truncate) */
- "ROUND_CEILING", /* round toward +infinity */
- "ROUND_FLOOR", /* round toward -infinity */
- "ROUND_HALF_UP", /* 0.5 is rounded up */
- "ROUND_HALF_DOWN", /* 0.5 is rounded down */
- "ROUND_HALF_EVEN", /* 0.5 is rounded to even */
- "ROUND_05UP", /* round zero or five away from 0 */
- "ROUND_TRUNC", /* truncate, but set infinity */
-};
-
-const char * const mpd_clamp_string[MPD_CLAMP_GUARD] = {
- "CLAMP_DEFAULT",
- "CLAMP_IEEE_754"
-};
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_CONSTANTS_H_
-#define LIBMPDEC_CONSTANTS_H_
-
-
-#include "mpdecimal.h"
-
-#include <stdint.h>
-
-
-/* Internal header file: all symbols have local scope in the DSO */
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
-
-
-/* choice of optimized functions */
-#if defined(CONFIG_64)
-/* x64 */
- #define MULMOD(a, b) x64_mulmod(a, b, umod)
- #define MULMOD2C(a0, a1, w) x64_mulmod2c(a0, a1, w, umod)
- #define MULMOD2(a0, b0, a1, b1) x64_mulmod2(a0, b0, a1, b1, umod)
- #define POWMOD(base, exp) x64_powmod(base, exp, umod)
- #define SETMODULUS(modnum) std_setmodulus(modnum, &umod)
- #define SIZE3_NTT(x0, x1, x2, w3table) std_size3_ntt(x0, x1, x2, w3table, umod)
-#elif defined(PPRO)
-/* PentiumPro (or later) gcc inline asm */
- #define MULMOD(a, b) ppro_mulmod(a, b, &dmod, dinvmod)
- #define MULMOD2C(a0, a1, w) ppro_mulmod2c(a0, a1, w, &dmod, dinvmod)
- #define MULMOD2(a0, b0, a1, b1) ppro_mulmod2(a0, b0, a1, b1, &dmod, dinvmod)
- #define POWMOD(base, exp) ppro_powmod(base, exp, &dmod, dinvmod)
- #define SETMODULUS(modnum) ppro_setmodulus(modnum, &umod, &dmod, dinvmod)
- #define SIZE3_NTT(x0, x1, x2, w3table) ppro_size3_ntt(x0, x1, x2, w3table, umod, &dmod, dinvmod)
-#else
- /* ANSI C99 */
- #define MULMOD(a, b) std_mulmod(a, b, umod)
- #define MULMOD2C(a0, a1, w) std_mulmod2c(a0, a1, w, umod)
- #define MULMOD2(a0, b0, a1, b1) std_mulmod2(a0, b0, a1, b1, umod)
- #define POWMOD(base, exp) std_powmod(base, exp, umod)
- #define SETMODULUS(modnum) std_setmodulus(modnum, &umod)
- #define SIZE3_NTT(x0, x1, x2, w3table) std_size3_ntt(x0, x1, x2, w3table, umod)
-#endif
-
-/* PentiumPro (or later) gcc inline asm */
-extern const float MPD_TWO63;
-extern const uint32_t mpd_invmoduli[3][3];
-
-enum {P1, P2, P3};
-
-extern const mpd_uint_t mpd_moduli[];
-extern const mpd_uint_t mpd_roots[];
-extern const mpd_size_t mpd_bits[];
-extern const mpd_uint_t mpd_pow10[];
-
-extern const mpd_uint_t INV_P1_MOD_P2;
-extern const mpd_uint_t INV_P1P2_MOD_P3;
-extern const mpd_uint_t LH_P1P2;
-extern const mpd_uint_t UH_P1P2;
-
-
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
-
-
-#endif /* LIBMPDEC_CONSTANTS_H_ */
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <signal.h>
-#include <stdio.h>
-#include <string.h>
-
-
-void
-mpd_dflt_traphandler(mpd_context_t *ctx)
-{
- (void)ctx;
- raise(SIGFPE);
-}
-
-void (* mpd_traphandler)(mpd_context_t *) = mpd_dflt_traphandler;
-
-
-/* Set guaranteed minimum number of coefficient words. The function may
- be used once at program start. Setting MPD_MINALLOC to out-of-bounds
- values is a catastrophic error, so in that case the function exits rather
- than relying on the user to check a return value. */
-void
-mpd_setminalloc(mpd_ssize_t n)
-{
- static int minalloc_is_set = 0;
-
- if (minalloc_is_set) {
- mpd_err_warn("mpd_setminalloc: ignoring request to set "
- "MPD_MINALLOC a second time\n");
- return;
- }
- if (n < MPD_MINALLOC_MIN || n > MPD_MINALLOC_MAX) {
- mpd_err_fatal("illegal value for MPD_MINALLOC"); /* GCOV_NOT_REACHED */
- }
- MPD_MINALLOC = n;
- minalloc_is_set = 1;
-}
-
-void
-mpd_init(mpd_context_t *ctx, mpd_ssize_t prec)
-{
- mpd_ssize_t ideal_minalloc;
-
- mpd_defaultcontext(ctx);
-
- if (!mpd_qsetprec(ctx, prec)) {
- mpd_addstatus_raise(ctx, MPD_Invalid_context);
- return;
- }
-
- ideal_minalloc = 2 * ((prec+MPD_RDIGITS-1) / MPD_RDIGITS);
- if (ideal_minalloc < MPD_MINALLOC_MIN) ideal_minalloc = MPD_MINALLOC_MIN;
- if (ideal_minalloc > MPD_MINALLOC_MAX) ideal_minalloc = MPD_MINALLOC_MAX;
-
- mpd_setminalloc(ideal_minalloc);
-}
-
-void
-mpd_maxcontext(mpd_context_t *ctx)
-{
- ctx->prec=MPD_MAX_PREC;
- ctx->emax=MPD_MAX_EMAX;
- ctx->emin=MPD_MIN_EMIN;
- ctx->round=MPD_ROUND_HALF_EVEN;
- ctx->traps=MPD_Traps;
- ctx->status=0;
- ctx->newtrap=0;
- ctx->clamp=0;
- ctx->allcr=1;
-}
-
-void
-mpd_defaultcontext(mpd_context_t *ctx)
-{
- ctx->prec=2*MPD_RDIGITS;
- ctx->emax=MPD_MAX_EMAX;
- ctx->emin=MPD_MIN_EMIN;
- ctx->round=MPD_ROUND_HALF_UP;
- ctx->traps=MPD_Traps;
- ctx->status=0;
- ctx->newtrap=0;
- ctx->clamp=0;
- ctx->allcr=1;
-}
-
-void
-mpd_basiccontext(mpd_context_t *ctx)
-{
- ctx->prec=9;
- ctx->emax=MPD_MAX_EMAX;
- ctx->emin=MPD_MIN_EMIN;
- ctx->round=MPD_ROUND_HALF_UP;
- ctx->traps=MPD_Traps|MPD_Clamped;
- ctx->status=0;
- ctx->newtrap=0;
- ctx->clamp=0;
- ctx->allcr=1;
-}
-
-int
-mpd_ieee_context(mpd_context_t *ctx, int bits)
-{
- if (bits <= 0 || bits > MPD_IEEE_CONTEXT_MAX_BITS || bits % 32) {
- return -1;
- }
-
- ctx->prec = 9 * (bits/32) - 2;
- ctx->emax = 3 * ((mpd_ssize_t)1<<(bits/16+3));
- ctx->emin = 1 - ctx->emax;
- ctx->round=MPD_ROUND_HALF_EVEN;
- ctx->traps=0;
- ctx->status=0;
- ctx->newtrap=0;
- ctx->clamp=1;
- ctx->allcr=1;
-
- return 0;
-}
-
-mpd_ssize_t
-mpd_getprec(const mpd_context_t *ctx)
-{
- return ctx->prec;
-}
-
-mpd_ssize_t
-mpd_getemax(const mpd_context_t *ctx)
-{
- return ctx->emax;
-}
-
-mpd_ssize_t
-mpd_getemin(const mpd_context_t *ctx)
-{
- return ctx->emin;
-}
-
-int
-mpd_getround(const mpd_context_t *ctx)
-{
- return ctx->round;
-}
-
-uint32_t
-mpd_gettraps(const mpd_context_t *ctx)
-{
- return ctx->traps;
-}
-
-uint32_t
-mpd_getstatus(const mpd_context_t *ctx)
-{
- return ctx->status;
-}
-
-int
-mpd_getclamp(const mpd_context_t *ctx)
-{
- return ctx->clamp;
-}
-
-int
-mpd_getcr(const mpd_context_t *ctx)
-{
- return ctx->allcr;
-}
-
-
-int
-mpd_qsetprec(mpd_context_t *ctx, mpd_ssize_t prec)
-{
- if (prec <= 0 || prec > MPD_MAX_PREC) {
- return 0;
- }
- ctx->prec = prec;
- return 1;
-}
-
-int
-mpd_qsetemax(mpd_context_t *ctx, mpd_ssize_t emax)
-{
- if (emax < 0 || emax > MPD_MAX_EMAX) {
- return 0;
- }
- ctx->emax = emax;
- return 1;
-}
-
-int
-mpd_qsetemin(mpd_context_t *ctx, mpd_ssize_t emin)
-{
- if (emin > 0 || emin < MPD_MIN_EMIN) {
- return 0;
- }
- ctx->emin = emin;
- return 1;
-}
-
-int
-mpd_qsetround(mpd_context_t *ctx, int round)
-{
- if (!(0 <= round && round < MPD_ROUND_GUARD)) {
- return 0;
- }
- ctx->round = round;
- return 1;
-}
-
-int
-mpd_qsettraps(mpd_context_t *ctx, uint32_t flags)
-{
- if (flags > MPD_Max_status) {
- return 0;
- }
- ctx->traps = flags;
- return 1;
-}
-
-int
-mpd_qsetstatus(mpd_context_t *ctx, uint32_t flags)
-{
- if (flags > MPD_Max_status) {
- return 0;
- }
- ctx->status = flags;
- return 1;
-}
-
-int
-mpd_qsetclamp(mpd_context_t *ctx, int c)
-{
- if (c != 0 && c != 1) {
- return 0;
- }
- ctx->clamp = c;
- return 1;
-}
-
-int
-mpd_qsetcr(mpd_context_t *ctx, int c)
-{
- if (c != 0 && c != 1) {
- return 0;
- }
- ctx->allcr = c;
- return 1;
-}
-
-
-void
-mpd_addstatus_raise(mpd_context_t *ctx, uint32_t flags)
-{
- ctx->status |= flags;
- if (flags&ctx->traps) {
- ctx->newtrap = (flags&ctx->traps);
- mpd_traphandler(ctx);
- }
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-#include "bits.h"
-#include "constants.h"
-#include "convolute.h"
-#include "fnt.h"
-#include "fourstep.h"
-#include "numbertheory.h"
-#include "sixstep.h"
-#include "umodarith.h"
-
-
-/* Bignum: Fast convolution using the Number Theoretic Transform. Used for
- the multiplication of very large coefficients. */
-
-
-/* Convolute the data in c1 and c2. Result is in c1. */
-int
-fnt_convolute(mpd_uint_t *c1, mpd_uint_t *c2, mpd_size_t n, int modnum)
-{
- int (*fnt)(mpd_uint_t *, mpd_size_t, int);
- int (*inv_fnt)(mpd_uint_t *, mpd_size_t, int);
-#ifdef PPRO
- double dmod;
- uint32_t dinvmod[3];
-#endif
- mpd_uint_t n_inv, umod;
- mpd_size_t i;
-
-
- SETMODULUS(modnum);
- n_inv = POWMOD(n, (umod-2));
-
- if (ispower2(n)) {
- if (n > SIX_STEP_THRESHOLD) {
- fnt = six_step_fnt;
- inv_fnt = inv_six_step_fnt;
- }
- else {
- fnt = std_fnt;
- inv_fnt = std_inv_fnt;
- }
- }
- else {
- fnt = four_step_fnt;
- inv_fnt = inv_four_step_fnt;
- }
-
- if (!fnt(c1, n, modnum)) {
- return 0;
- }
- if (!fnt(c2, n, modnum)) {
- return 0;
- }
- for (i = 0; i < n-1; i += 2) {
- mpd_uint_t x0 = c1[i];
- mpd_uint_t y0 = c2[i];
- mpd_uint_t x1 = c1[i+1];
- mpd_uint_t y1 = c2[i+1];
- MULMOD2(&x0, y0, &x1, y1);
- c1[i] = x0;
- c1[i+1] = x1;
- }
-
- if (!inv_fnt(c1, n, modnum)) {
- return 0;
- }
- for (i = 0; i < n-3; i += 4) {
- mpd_uint_t x0 = c1[i];
- mpd_uint_t x1 = c1[i+1];
- mpd_uint_t x2 = c1[i+2];
- mpd_uint_t x3 = c1[i+3];
- MULMOD2C(&x0, &x1, n_inv);
- MULMOD2C(&x2, &x3, n_inv);
- c1[i] = x0;
- c1[i+1] = x1;
- c1[i+2] = x2;
- c1[i+3] = x3;
- }
-
- return 1;
-}
-
-/* Autoconvolute the data in c1. Result is in c1. */
-int
-fnt_autoconvolute(mpd_uint_t *c1, mpd_size_t n, int modnum)
-{
- int (*fnt)(mpd_uint_t *, mpd_size_t, int);
- int (*inv_fnt)(mpd_uint_t *, mpd_size_t, int);
-#ifdef PPRO
- double dmod;
- uint32_t dinvmod[3];
-#endif
- mpd_uint_t n_inv, umod;
- mpd_size_t i;
-
-
- SETMODULUS(modnum);
- n_inv = POWMOD(n, (umod-2));
-
- if (ispower2(n)) {
- if (n > SIX_STEP_THRESHOLD) {
- fnt = six_step_fnt;
- inv_fnt = inv_six_step_fnt;
- }
- else {
- fnt = std_fnt;
- inv_fnt = std_inv_fnt;
- }
- }
- else {
- fnt = four_step_fnt;
- inv_fnt = inv_four_step_fnt;
- }
-
- if (!fnt(c1, n, modnum)) {
- return 0;
- }
- for (i = 0; i < n-1; i += 2) {
- mpd_uint_t x0 = c1[i];
- mpd_uint_t x1 = c1[i+1];
- MULMOD2(&x0, x0, &x1, x1);
- c1[i] = x0;
- c1[i+1] = x1;
- }
-
- if (!inv_fnt(c1, n, modnum)) {
- return 0;
- }
- for (i = 0; i < n-3; i += 4) {
- mpd_uint_t x0 = c1[i];
- mpd_uint_t x1 = c1[i+1];
- mpd_uint_t x2 = c1[i+2];
- mpd_uint_t x3 = c1[i+3];
- MULMOD2C(&x0, &x1, n_inv);
- MULMOD2C(&x2, &x3, n_inv);
- c1[i] = x0;
- c1[i+1] = x1;
- c1[i+2] = x2;
- c1[i+3] = x3;
- }
-
- return 1;
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_CONVOLUTE_H_
-#define LIBMPDEC_CONVOLUTE_H_
-
-
-#include "mpdecimal.h"
-
-
-/* Internal header file: all symbols have local scope in the DSO */
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
-
-
-#define SIX_STEP_THRESHOLD 4096
-
-int fnt_convolute(mpd_uint_t *c1, mpd_uint_t *c2, mpd_size_t n, int modnum);
-int fnt_autoconvolute(mpd_uint_t *c1, mpd_size_t n, int modnum);
-
-
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
-
-
-#endif /* LIBMPDEC_CONVOLUTE_H_ */
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <assert.h>
-
-#include "constants.h"
-#include "crt.h"
-#include "numbertheory.h"
-#include "typearith.h"
-#include "umodarith.h"
-
-
-/* Bignum: Chinese Remainder Theorem, extends the maximum transform length. */
-
-
-/* Multiply P1P2 by v, store result in w. */
-static inline void
-_crt_mulP1P2_3(mpd_uint_t w[3], mpd_uint_t v)
-{
- mpd_uint_t hi1, hi2, lo;
-
- _mpd_mul_words(&hi1, &lo, LH_P1P2, v);
- w[0] = lo;
-
- _mpd_mul_words(&hi2, &lo, UH_P1P2, v);
- lo = hi1 + lo;
- if (lo < hi1) hi2++;
-
- w[1] = lo;
- w[2] = hi2;
-}
-
-/* Add 3 words from v to w. The result is known to fit in w. */
-static inline void
-_crt_add3(mpd_uint_t w[3], mpd_uint_t v[3])
-{
- mpd_uint_t carry;
-
- w[0] = w[0] + v[0];
- carry = (w[0] < v[0]);
-
- w[1] = w[1] + v[1];
- if (w[1] < v[1]) w[2]++;
-
- w[1] = w[1] + carry;
- if (w[1] < carry) w[2]++;
-
- w[2] += v[2];
-}
-
-/* Divide 3 words in u by v, store result in w, return remainder. */
-static inline mpd_uint_t
-_crt_div3(mpd_uint_t *w, const mpd_uint_t *u, mpd_uint_t v)
-{
- mpd_uint_t r1 = u[2];
- mpd_uint_t r2;
-
- if (r1 < v) {
- w[2] = 0;
- }
- else {
- _mpd_div_word(&w[2], &r1, u[2], v); /* GCOV_NOT_REACHED */
- }
-
- _mpd_div_words(&w[1], &r2, r1, u[1], v);
- _mpd_div_words(&w[0], &r1, r2, u[0], v);
-
- return r1;
-}
-
-
-/*
- * Chinese Remainder Theorem:
- * Algorithm from Joerg Arndt, "Matters Computational",
- * Chapter 37.4.1 [http://www.jjj.de/fxt/]
- *
- * See also Knuth, TAOCP, Volume 2, 4.3.2, exercise 7.
- */
-
-/*
- * CRT with carry: x1, x2, x3 contain numbers modulo p1, p2, p3. For each
- * triple of members of the arrays, find the unique z modulo p1*p2*p3, with
- * zmax = p1*p2*p3 - 1.
- *
- * In each iteration of the loop, split z into result[i] = z % MPD_RADIX
- * and carry = z / MPD_RADIX. Let N be the size of carry[] and cmax the
- * maximum carry.
- *
- * Limits for the 32-bit build:
- *
- * N = 2**96
- * cmax = 7711435591312380274
- *
- * Limits for the 64 bit build:
- *
- * N = 2**192
- * cmax = 627710135393475385904124401220046371710
- *
- * The following statements hold for both versions:
- *
- * 1) cmax + zmax < N, so the addition does not overflow.
- *
- * 2) (cmax + zmax) / MPD_RADIX == cmax.
- *
- * 3) If c <= cmax, then c_next = (c + zmax) / MPD_RADIX <= cmax.
- */
-void
-crt3(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_size_t rsize)
-{
- mpd_uint_t p1 = mpd_moduli[P1];
- mpd_uint_t umod;
-#ifdef PPRO
- double dmod;
- uint32_t dinvmod[3];
-#endif
- mpd_uint_t a1, a2, a3;
- mpd_uint_t s;
- mpd_uint_t z[3], t[3];
- mpd_uint_t carry[3] = {0,0,0};
- mpd_uint_t hi, lo;
- mpd_size_t i;
-
- for (i = 0; i < rsize; i++) {
-
- a1 = x1[i];
- a2 = x2[i];
- a3 = x3[i];
-
- SETMODULUS(P2);
- s = ext_submod(a2, a1, umod);
- s = MULMOD(s, INV_P1_MOD_P2);
-
- _mpd_mul_words(&hi, &lo, s, p1);
- lo = lo + a1;
- if (lo < a1) hi++;
-
- SETMODULUS(P3);
- s = dw_submod(a3, hi, lo, umod);
- s = MULMOD(s, INV_P1P2_MOD_P3);
-
- z[0] = lo;
- z[1] = hi;
- z[2] = 0;
-
- _crt_mulP1P2_3(t, s);
- _crt_add3(z, t);
- _crt_add3(carry, z);
-
- x1[i] = _crt_div3(carry, carry, MPD_RADIX);
- }
-
- assert(carry[0] == 0 && carry[1] == 0 && carry[2] == 0);
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_CRT_H_
-#define LIBMPDEC_CRT_H_
-
-
-#include "mpdecimal.h"
-
-
-/* Internal header file: all symbols have local scope in the DSO */
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
-
-
-void crt3(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_size_t rsize);
-
-
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
-
-
-#endif /* LIBMPDEC_CRT_H_ */
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <assert.h>
-
-#include "bits.h"
-#include "constants.h"
-#include "difradix2.h"
-#include "numbertheory.h"
-#include "umodarith.h"
-
-
-/* Bignum: The actual transform routine (decimation in frequency). */
-
-
-/*
- * Generate index pairs (x, bitreverse(x)) and carry out the permutation.
- * n must be a power of two.
- * Algorithm due to Brent/Lehmann, see Joerg Arndt, "Matters Computational",
- * Chapter 1.14.4. [http://www.jjj.de/fxt/]
- */
-static inline void
-bitreverse_permute(mpd_uint_t a[], mpd_size_t n)
-{
- mpd_size_t x = 0;
- mpd_size_t r = 0;
- mpd_uint_t t;
-
- do { /* Invariant: r = bitreverse(x) */
- if (r > x) {
- t = a[x];
- a[x] = a[r];
- a[r] = t;
- }
- /* Flip trailing consecutive 1 bits and the first zero bit
- * that absorbs a possible carry. */
- x += 1;
- /* Mirror the operation on r: Flip n_trailing_zeros(x)+1
- high bits of r. */
- r ^= (n - (n >> (mpd_bsf(x)+1)));
- /* The loop invariant is preserved. */
- } while (x < n);
-}
-
-
-/* Fast Number Theoretic Transform, decimation in frequency. */
-void
-fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams)
-{
- mpd_uint_t *wtable = tparams->wtable;
- mpd_uint_t umod;
-#ifdef PPRO
- double dmod;
- uint32_t dinvmod[3];
-#endif
- mpd_uint_t u0, u1, v0, v1;
- mpd_uint_t w, w0, w1, wstep;
- mpd_size_t m, mhalf;
- mpd_size_t j, r;
-
-
- assert(ispower2(n));
- assert(n >= 4);
-
- SETMODULUS(tparams->modnum);
-
- /* m == n */
- mhalf = n / 2;
- for (j = 0; j < mhalf; j += 2) {
-
- w0 = wtable[j];
- w1 = wtable[j+1];
-
- u0 = a[j];
- v0 = a[j+mhalf];
-
- u1 = a[j+1];
- v1 = a[j+1+mhalf];
-
- a[j] = addmod(u0, v0, umod);
- v0 = submod(u0, v0, umod);
-
- a[j+1] = addmod(u1, v1, umod);
- v1 = submod(u1, v1, umod);
-
- MULMOD2(&v0, w0, &v1, w1);
-
- a[j+mhalf] = v0;
- a[j+1+mhalf] = v1;
-
- }
-
- wstep = 2;
- for (m = n/2; m >= 2; m>>=1, wstep<<=1) {
-
- mhalf = m / 2;
-
- /* j == 0 */
- for (r = 0; r < n; r += 2*m) {
-
- u0 = a[r];
- v0 = a[r+mhalf];
-
- u1 = a[m+r];
- v1 = a[m+r+mhalf];
-
- a[r] = addmod(u0, v0, umod);
- v0 = submod(u0, v0, umod);
-
- a[m+r] = addmod(u1, v1, umod);
- v1 = submod(u1, v1, umod);
-
- a[r+mhalf] = v0;
- a[m+r+mhalf] = v1;
- }
-
- for (j = 1; j < mhalf; j++) {
-
- w = wtable[j*wstep];
-
- for (r = 0; r < n; r += 2*m) {
-
- u0 = a[r+j];
- v0 = a[r+j+mhalf];
-
- u1 = a[m+r+j];
- v1 = a[m+r+j+mhalf];
-
- a[r+j] = addmod(u0, v0, umod);
- v0 = submod(u0, v0, umod);
-
- a[m+r+j] = addmod(u1, v1, umod);
- v1 = submod(u1, v1, umod);
-
- MULMOD2C(&v0, &v1, w);
-
- a[r+j+mhalf] = v0;
- a[m+r+j+mhalf] = v1;
- }
-
- }
-
- }
-
- bitreverse_permute(a, n);
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_DIFRADIX2_H_
-#define LIBMPDEC_DIFRADIX2_H_
-
-
-#include "mpdecimal.h"
-#include "numbertheory.h"
-
-
-/* Internal header file: all symbols have local scope in the DSO */
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
-
-
-void fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams);
-
-
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
-
-
-#endif /* LIBMPDEC_DIFRADIX2_H_ */
+++ /dev/null
-
-
-This directory contains a number of examples. In order to compile, run
-(for example):
-
-gcc -Wall -W -O2 -o powmod powmod.c -lmpdec -lm
-
-
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <time.h>
-#include <mpdecimal.h>
-
-
-int
-main(int argc, char **argv)
-{
- mpd_context_t ctx;
- mpd_t *a, *b;
- mpd_t *result;
- char *rstring;
- char status_str[MPD_MAX_FLAG_STRING];
- clock_t start_clock, end_clock;
-
- if (argc != 3) {
- fprintf(stderr, "compare: usage: ./compare x y\n");
- exit(1);
- }
-
- mpd_init(&ctx, 38);
- ctx.traps = 0;
-
- result = mpd_new(&ctx);
- a = mpd_new(&ctx);
- b = mpd_new(&ctx);
- mpd_set_string(a, argv[1], &ctx);
- mpd_set_string(b, argv[2], &ctx);
-
- start_clock = clock();
- mpd_compare(result, a, b, &ctx);
- end_clock = clock();
- fprintf(stderr, "time: %f\n\n",
- (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC);
-
- rstring = mpd_to_sci(result, 1);
- mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status);
- printf("%s %s\n", rstring, status_str);
-
- mpd_del(a);
- mpd_del(b);
- mpd_del(result);
- mpd_free(rstring);
-
- return 0;
-}
-
-
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <time.h>
-#include <mpdecimal.h>
-
-
-int
-main(int argc, char **argv)
-{
- mpd_context_t ctx;
- mpd_t *a, *b;
- mpd_t *result;
- char *rstring;
- char status_str[MPD_MAX_FLAG_STRING];
- clock_t start_clock, end_clock;
-
- if (argc != 3) {
- fprintf(stderr, "div: usage: ./div x y\n");
- exit(1);
- }
-
- mpd_init(&ctx, 38);
- ctx.traps = 0;
-
- result = mpd_new(&ctx);
- a = mpd_new(&ctx);
- b = mpd_new(&ctx);
- mpd_set_string(a, argv[1], &ctx);
- mpd_set_string(b, argv[2], &ctx);
-
- start_clock = clock();
- mpd_div(result, a, b, &ctx);
- end_clock = clock();
- fprintf(stderr, "time: %f\n\n",
- (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC);
-
- rstring = mpd_to_sci(result, 1);
- mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status);
- printf("%s %s\n", rstring, status_str);
-
- mpd_del(a);
- mpd_del(b);
- mpd_del(result);
- mpd_free(rstring);
-
- return 0;
-}
-
-
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <time.h>
-#include <mpdecimal.h>
-
-
-int
-main(int argc, char **argv)
-{
- mpd_context_t ctx;
- mpd_t *a, *b;
- mpd_t *q, *r;
- char *qs, *rs;
- char status_str[MPD_MAX_FLAG_STRING];
- clock_t start_clock, end_clock;
-
- if (argc != 3) {
- fprintf(stderr, "divmod: usage: ./divmod x y\n");
- exit(1);
- }
-
- mpd_init(&ctx, 38);
- ctx.traps = 0;
-
- q = mpd_new(&ctx);
- r = mpd_new(&ctx);
- a = mpd_new(&ctx);
- b = mpd_new(&ctx);
- mpd_set_string(a, argv[1], &ctx);
- mpd_set_string(b, argv[2], &ctx);
-
- start_clock = clock();
- mpd_divmod(q, r, a, b, &ctx);
- end_clock = clock();
- fprintf(stderr, "time: %f\n\n",
- (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC);
-
- qs = mpd_to_sci(q, 1);
- rs = mpd_to_sci(r, 1);
-
- mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status);
- printf("%s %s %s\n", qs, rs, status_str);
-
- mpd_del(q);
- mpd_del(r);
- mpd_del(a);
- mpd_del(b);
- mpd_free(qs);
- mpd_free(rs);
-
- return 0;
-}
-
-
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <time.h>
-#include <mpdecimal.h>
-
-
-int
-main(int argc, char **argv)
-{
- mpd_context_t ctx;
- mpd_t *a, *b;
- mpd_t *result;
- char *rstring;
- char status_str[MPD_MAX_FLAG_STRING];
- clock_t start_clock, end_clock;
-
- if (argc != 3) {
- fprintf(stderr, "multiply: usage: ./multiply x y\n");
- exit(1);
- }
-
- mpd_init(&ctx, 38);
- ctx.traps = 0;
-
- result = mpd_new(&ctx);
- a = mpd_new(&ctx);
- b = mpd_new(&ctx);
- mpd_set_string(a, argv[1], &ctx);
- mpd_set_string(b, argv[2], &ctx);
-
- start_clock = clock();
- mpd_mul(result, a, b, &ctx);
- end_clock = clock();
- fprintf(stderr, "time: %f\n\n",
- (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC);
-
- rstring = mpd_to_sci(result, 1);
- mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status);
- printf("%s %s\n", rstring, status_str);
-
- mpd_del(a);
- mpd_del(b);
- mpd_del(result);
- mpd_free(rstring);
-
- return 0;
-}
-
-
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <time.h>
-#include <mpdecimal.h>
-
-
-int
-main(int argc, char **argv)
-{
- mpd_context_t ctx;
- mpd_t *a, *b;
- mpd_t *result;
- char *rstring;
- char status_str[MPD_MAX_FLAG_STRING];
- clock_t start_clock, end_clock;
-
- if (argc != 3) {
- fprintf(stderr, "pow: usage: ./pow x y\n");
- exit(1);
- }
-
- mpd_init(&ctx, 38);
- ctx.traps = 0;
-
- result = mpd_new(&ctx);
- a = mpd_new(&ctx);
- b = mpd_new(&ctx);
- mpd_set_string(a, argv[1], &ctx);
- mpd_set_string(b, argv[2], &ctx);
-
- start_clock = clock();
- mpd_pow(result, a, b, &ctx);
- end_clock = clock();
- fprintf(stderr, "time: %f\n\n",
- (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC);
-
- rstring = mpd_to_sci(result, 1);
- mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status);
- printf("%s %s\n", rstring, status_str);
-
- mpd_del(a);
- mpd_del(b);
- mpd_del(result);
- mpd_free(rstring);
-
- return 0;
-}
-
-
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <time.h>
-#include <mpdecimal.h>
-
-
-int
-main(int argc, char **argv)
-{
- mpd_context_t ctx;
- mpd_t *a, *b, *c;
- mpd_t *result;
- char *rstring;
- char status_str[MPD_MAX_FLAG_STRING];
- clock_t start_clock, end_clock;
-
- if (argc != 4) {
- fprintf(stderr, "powmod: usage: ./powmod x y z\n");
- exit(1);
- }
-
- mpd_init(&ctx, 38);
- ctx.traps = 0;
-
- result = mpd_new(&ctx);
- a = mpd_new(&ctx);
- b = mpd_new(&ctx);
- c = mpd_new(&ctx);
- mpd_set_string(a, argv[1], &ctx);
- mpd_set_string(b, argv[2], &ctx);
- mpd_set_string(c, argv[3], &ctx);
-
- start_clock = clock();
- mpd_powmod(result, a, b, c, &ctx);
- end_clock = clock();
- fprintf(stderr, "time: %f\n\n",
- (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC);
-
- rstring = mpd_to_sci(result, 1);
- mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status);
- printf("%s %s\n", rstring, status_str);
-
- mpd_del(a);
- mpd_del(b);
- mpd_del(c);
- mpd_del(result);
- mpd_free(rstring);
-
- return 0;
-}
-
-
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <time.h>
-#include <mpdecimal.h>
-
-
-int
-main(int argc, char **argv)
-{
- mpd_context_t ctx;
- mpd_t *a, *b;
- mpd_t *result;
- char *rstring;
- char status_str[MPD_MAX_FLAG_STRING];
- clock_t start_clock, end_clock;
-
- if (argc != 3) {
- fprintf(stderr, "shift: usage: ./shift x y\n");
- exit(1);
- }
-
- mpd_init(&ctx, 38);
- ctx.traps = 0;
-
- result = mpd_new(&ctx);
- a = mpd_new(&ctx);
- b = mpd_new(&ctx);
- mpd_set_string(a, argv[1], &ctx);
- mpd_set_string(b, argv[2], &ctx);
-
- start_clock = clock();
- mpd_shift(result, a, b, &ctx);
- end_clock = clock();
- fprintf(stderr, "time: %f\n\n",
- (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC);
-
- rstring = mpd_to_sci(result, 1);
- mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status);
- printf("%s %s\n", rstring, status_str);
-
- mpd_del(a);
- mpd_del(b);
- mpd_del(result);
- mpd_free(rstring);
-
- return 0;
-}
-
-
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <time.h>
-#include <mpdecimal.h>
-
-
-int
-main(int argc, char **argv)
-{
- mpd_context_t ctx;
- mpd_t *a;
- mpd_t *result;
- char *rstring;
- char status_str[MPD_MAX_FLAG_STRING];
- clock_t start_clock, end_clock;
-
- if (argc != 2) {
- fprintf(stderr, "sqrt: usage: ./sqrt x\n");
- exit(1);
- }
-
- mpd_init(&ctx, 38);
- ctx.traps = 0;
-
- result = mpd_new(&ctx);
- a = mpd_new(&ctx);
- mpd_set_string(a, argv[1], &ctx);
-
- start_clock = clock();
- mpd_sqrt(result, a, &ctx);
- end_clock = clock();
- fprintf(stderr, "time: %f\n\n",
- (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC);
-
- rstring = mpd_to_sci(result, 1);
- mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status);
- printf("%s %s\n", rstring, status_str);
-
- mpd_del(a);
- mpd_del(result);
- mpd_free(rstring);
-
- return 0;
-}
-
-
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <assert.h>
-#include <stdio.h>
-
-#include "bits.h"
-#include "difradix2.h"
-#include "fnt.h"
-#include "numbertheory.h"
-
-
-/* Bignum: Fast transform for medium-sized coefficients. */
-
-
-/* forward transform, sign = -1 */
-int
-std_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
-{
- struct fnt_params *tparams;
-
- assert(ispower2(n));
- assert(n >= 4);
- assert(n <= 3*MPD_MAXTRANSFORM_2N);
-
- if ((tparams = _mpd_init_fnt_params(n, -1, modnum)) == NULL) {
- return 0;
- }
- fnt_dif2(a, n, tparams);
-
- mpd_free(tparams);
- return 1;
-}
-
-/* reverse transform, sign = 1 */
-int
-std_inv_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
-{
- struct fnt_params *tparams;
-
- assert(ispower2(n));
- assert(n >= 4);
- assert(n <= 3*MPD_MAXTRANSFORM_2N);
-
- if ((tparams = _mpd_init_fnt_params(n, 1, modnum)) == NULL) {
- return 0;
- }
- fnt_dif2(a, n, tparams);
-
- mpd_free(tparams);
- return 1;
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_FNT_H_
-#define LIBMPDEC_FNT_H_
-
-
-#include "mpdecimal.h"
-
-
-/* Internal header file: all symbols have local scope in the DSO */
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
-
-
-int std_fnt(mpd_uint_t a[], mpd_size_t n, int modnum);
-int std_inv_fnt(mpd_uint_t a[], mpd_size_t n, int modnum);
-
-
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
-
-
-#endif /* LIBMPDEC_FNT_H_ */
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <assert.h>
-
-#include "constants.h"
-#include "fourstep.h"
-#include "numbertheory.h"
-#include "sixstep.h"
-#include "umodarith.h"
-
-
-/* Bignum: Cache efficient Matrix Fourier Transform for arrays of the
- form 3 * 2**n (See literature/matrix-transform.txt). */
-
-
-#ifndef PPRO
-static inline void
-std_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3,
- mpd_uint_t w3table[3], mpd_uint_t umod)
-{
- mpd_uint_t r1, r2;
- mpd_uint_t w;
- mpd_uint_t s, tmp;
-
-
- /* k = 0 -> w = 1 */
- s = *x1;
- s = addmod(s, *x2, umod);
- s = addmod(s, *x3, umod);
-
- r1 = s;
-
- /* k = 1 */
- s = *x1;
-
- w = w3table[1];
- tmp = MULMOD(*x2, w);
- s = addmod(s, tmp, umod);
-
- w = w3table[2];
- tmp = MULMOD(*x3, w);
- s = addmod(s, tmp, umod);
-
- r2 = s;
-
- /* k = 2 */
- s = *x1;
-
- w = w3table[2];
- tmp = MULMOD(*x2, w);
- s = addmod(s, tmp, umod);
-
- w = w3table[1];
- tmp = MULMOD(*x3, w);
- s = addmod(s, tmp, umod);
-
- *x3 = s;
- *x2 = r2;
- *x1 = r1;
-}
-#else /* PPRO */
-static inline void
-ppro_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_uint_t w3table[3],
- mpd_uint_t umod, double *dmod, uint32_t dinvmod[3])
-{
- mpd_uint_t r1, r2;
- mpd_uint_t w;
- mpd_uint_t s, tmp;
-
-
- /* k = 0 -> w = 1 */
- s = *x1;
- s = addmod(s, *x2, umod);
- s = addmod(s, *x3, umod);
-
- r1 = s;
-
- /* k = 1 */
- s = *x1;
-
- w = w3table[1];
- tmp = ppro_mulmod(*x2, w, dmod, dinvmod);
- s = addmod(s, tmp, umod);
-
- w = w3table[2];
- tmp = ppro_mulmod(*x3, w, dmod, dinvmod);
- s = addmod(s, tmp, umod);
-
- r2 = s;
-
- /* k = 2 */
- s = *x1;
-
- w = w3table[2];
- tmp = ppro_mulmod(*x2, w, dmod, dinvmod);
- s = addmod(s, tmp, umod);
-
- w = w3table[1];
- tmp = ppro_mulmod(*x3, w, dmod, dinvmod);
- s = addmod(s, tmp, umod);
-
- *x3 = s;
- *x2 = r2;
- *x1 = r1;
-}
-#endif
-
-
-/* forward transform, sign = -1; transform length = 3 * 2**n */
-int
-four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
-{
- mpd_size_t R = 3; /* number of rows */
- mpd_size_t C = n / 3; /* number of columns */
- mpd_uint_t w3table[3];
- mpd_uint_t kernel, w0, w1, wstep;
- mpd_uint_t *s, *p0, *p1, *p2;
- mpd_uint_t umod;
-#ifdef PPRO
- double dmod;
- uint32_t dinvmod[3];
-#endif
- mpd_size_t i, k;
-
-
- assert(n >= 48);
- assert(n <= 3*MPD_MAXTRANSFORM_2N);
-
-
- /* Length R transform on the columns. */
- SETMODULUS(modnum);
- _mpd_init_w3table(w3table, -1, modnum);
- for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) {
-
- SIZE3_NTT(p0, p1, p2, w3table);
- }
-
- /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
- kernel = _mpd_getkernel(n, -1, modnum);
- for (i = 1; i < R; i++) {
- w0 = 1; /* r**(i*0): initial value for k=0 */
- w1 = POWMOD(kernel, i); /* r**(i*1): initial value for k=1 */
- wstep = MULMOD(w1, w1); /* r**(2*i) */
- for (k = 0; k < C-1; k += 2) {
- mpd_uint_t x0 = a[i*C+k];
- mpd_uint_t x1 = a[i*C+k+1];
- MULMOD2(&x0, w0, &x1, w1);
- MULMOD2C(&w0, &w1, wstep); /* r**(i*(k+2)) = r**(i*k) * r**(2*i) */
- a[i*C+k] = x0;
- a[i*C+k+1] = x1;
- }
- }
-
- /* Length C transform on the rows. */
- for (s = a; s < a+n; s += C) {
- if (!six_step_fnt(s, C, modnum)) {
- return 0;
- }
- }
-
-#if 0
- /* An unordered transform is sufficient for convolution. */
- /* Transpose the matrix. */
- #include "transpose.h"
- transpose_3xpow2(a, R, C);
-#endif
-
- return 1;
-}
-
-/* backward transform, sign = 1; transform length = 3 * 2**n */
-int
-inv_four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
-{
- mpd_size_t R = 3; /* number of rows */
- mpd_size_t C = n / 3; /* number of columns */
- mpd_uint_t w3table[3];
- mpd_uint_t kernel, w0, w1, wstep;
- mpd_uint_t *s, *p0, *p1, *p2;
- mpd_uint_t umod;
-#ifdef PPRO
- double dmod;
- uint32_t dinvmod[3];
-#endif
- mpd_size_t i, k;
-
-
- assert(n >= 48);
- assert(n <= 3*MPD_MAXTRANSFORM_2N);
-
-
-#if 0
- /* An unordered transform is sufficient for convolution. */
- /* Transpose the matrix, producing an R*C matrix. */
- #include "transpose.h"
- transpose_3xpow2(a, C, R);
-#endif
-
- /* Length C transform on the rows. */
- for (s = a; s < a+n; s += C) {
- if (!inv_six_step_fnt(s, C, modnum)) {
- return 0;
- }
- }
-
- /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
- SETMODULUS(modnum);
- kernel = _mpd_getkernel(n, 1, modnum);
- for (i = 1; i < R; i++) {
- w0 = 1;
- w1 = POWMOD(kernel, i);
- wstep = MULMOD(w1, w1);
- for (k = 0; k < C; k += 2) {
- mpd_uint_t x0 = a[i*C+k];
- mpd_uint_t x1 = a[i*C+k+1];
- MULMOD2(&x0, w0, &x1, w1);
- MULMOD2C(&w0, &w1, wstep);
- a[i*C+k] = x0;
- a[i*C+k+1] = x1;
- }
- }
-
- /* Length R transform on the columns. */
- _mpd_init_w3table(w3table, 1, modnum);
- for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) {
-
- SIZE3_NTT(p0, p1, p2, w3table);
- }
-
- return 1;
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_FOURSTEP_H_
-#define LIBMPDEC_FOURSTEP_H_
-
-
-#include "mpdecimal.h"
-
-
-/* Internal header file: all symbols have local scope in the DSO */
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
-
-
-int four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum);
-int inv_four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum);
-
-
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
-
-
-#endif /* LIBMPDEC_FOURSTEP_H_ */
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <assert.h>
-#include <ctype.h>
-#include <errno.h>
-#include <limits.h>
-#include <locale.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-
-#include "io.h"
-#include "typearith.h"
-
-
-/* This file contains functions for decimal <-> string conversions, including
- PEP-3101 formatting for numeric types. */
-
-
-#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && __GNUC__ >= 7
- #pragma GCC diagnostic ignored "-Wimplicit-fallthrough"
- #pragma GCC diagnostic ignored "-Wmisleading-indentation"
- #pragma GCC diagnostic ignored "-Warray-bounds"
-#endif
-
-
-/*
- * Work around the behavior of tolower() and strcasecmp() in certain
- * locales. For example, in tr_TR.utf8:
- *
- * tolower((unsigned char)'I') == 'I'
- *
- * u is the exact uppercase version of l; n is strlen(l) or strlen(l)+1
- */
-static inline int
-_mpd_strneq(const char *s, const char *l, const char *u, size_t n)
-{
- while (--n != SIZE_MAX) {
- if (*s != *l && *s != *u) {
- return 0;
- }
- s++; u++; l++;
- }
-
- return 1;
-}
-
-static mpd_ssize_t
-strtoexp(const char *s)
-{
- char *end;
- mpd_ssize_t retval;
-
- errno = 0;
- retval = mpd_strtossize(s, &end, 10);
- if (errno == 0 && !(*s != '\0' && *end == '\0'))
- errno = EINVAL;
-
- return retval;
-}
-
-/*
- * Scan 'len' words. The most significant word contains 'r' digits,
- * the remaining words are full words. Skip dpoint. The string 's' must
- * consist of digits and an optional single decimal point at 'dpoint'.
- */
-static void
-string_to_coeff(mpd_uint_t *data, const char *s, const char *dpoint, int r,
- size_t len)
-{
- int j;
-
- if (r > 0) {
- data[--len] = 0;
- for (j = 0; j < r; j++, s++) {
- if (s == dpoint) s++;
- data[len] = 10 * data[len] + (*s - '0');
- }
- }
-
- while (--len != SIZE_MAX) {
- data[len] = 0;
- for (j = 0; j < MPD_RDIGITS; j++, s++) {
- if (s == dpoint) s++;
- data[len] = 10 * data[len] + (*s - '0');
- }
- }
-}
-
-/*
- * Partially verify a numeric string of the form:
- *
- * [cdigits][.][cdigits][eE][+-][edigits]
- *
- * If successful, return a pointer to the location of the first
- * relevant coefficient digit. This digit is either non-zero or
- * part of one of the following patterns:
- *
- * ["0\x00", "0.\x00", "0.E", "0.e", "0E", "0e"]
- *
- * The locations of a single optional dot or indicator are stored
- * in 'dpoint' and 'exp'.
- *
- * The end of the string is stored in 'end'. If an indicator [eE]
- * occurs without trailing [edigits], the condition is caught
- * later by strtoexp().
- */
-static const char *
-scan_dpoint_exp(const char *s, const char **dpoint, const char **exp,
- const char **end)
-{
- const char *coeff = NULL;
-
- *dpoint = NULL;
- *exp = NULL;
- for (; *s != '\0'; s++) {
- switch (*s) {
- case '.':
- if (*dpoint != NULL || *exp != NULL)
- return NULL;
- *dpoint = s;
- break;
- case 'E': case 'e':
- if (*exp != NULL)
- return NULL;
- *exp = s;
- if (*(s+1) == '+' || *(s+1) == '-')
- s++;
- break;
- default:
- if (!isdigit((unsigned char)*s))
- return NULL;
- if (coeff == NULL && *exp == NULL) {
- if (*s == '0') {
- if (!isdigit((unsigned char)*(s+1)))
- if (!(*(s+1) == '.' &&
- isdigit((unsigned char)*(s+2))))
- coeff = s;
- }
- else {
- coeff = s;
- }
- }
- break;
-
- }
- }
-
- *end = s;
- return coeff;
-}
-
-/* scan the payload of a NaN */
-static const char *
-scan_payload(const char *s, const char **end)
-{
- const char *coeff;
-
- while (*s == '0')
- s++;
- coeff = s;
-
- while (isdigit((unsigned char)*s))
- s++;
- *end = s;
-
- return (*s == '\0') ? coeff : NULL;
-}
-
-/* convert a character string to a decimal */
-void
-mpd_qset_string(mpd_t *dec, const char *s, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_ssize_t q, r, len;
- const char *coeff, *end;
- const char *dpoint = NULL, *exp = NULL;
- size_t digits;
- uint8_t sign = MPD_POS;
-
- mpd_set_flags(dec, 0);
- dec->len = 0;
- dec->exp = 0;
-
- /* sign */
- if (*s == '+') {
- s++;
- }
- else if (*s == '-') {
- mpd_set_negative(dec);
- sign = MPD_NEG;
- s++;
- }
-
- if (_mpd_strneq(s, "nan", "NAN", 3)) { /* NaN */
- s += 3;
- mpd_setspecial(dec, sign, MPD_NAN);
- if (*s == '\0')
- return;
- /* validate payload: digits only */
- if ((coeff = scan_payload(s, &end)) == NULL)
- goto conversion_error;
- /* payload consists entirely of zeros */
- if (*coeff == '\0')
- return;
- digits = end - coeff;
- /* prec >= 1, clamp is 0 or 1 */
- if (digits > (size_t)(ctx->prec-ctx->clamp))
- goto conversion_error;
- } /* sNaN */
- else if (_mpd_strneq(s, "snan", "SNAN", 4)) {
- s += 4;
- mpd_setspecial(dec, sign, MPD_SNAN);
- if (*s == '\0')
- return;
- /* validate payload: digits only */
- if ((coeff = scan_payload(s, &end)) == NULL)
- goto conversion_error;
- /* payload consists entirely of zeros */
- if (*coeff == '\0')
- return;
- digits = end - coeff;
- if (digits > (size_t)(ctx->prec-ctx->clamp))
- goto conversion_error;
- }
- else if (_mpd_strneq(s, "inf", "INF", 3)) {
- s += 3;
- if (*s == '\0' || _mpd_strneq(s, "inity", "INITY", 6)) {
- /* numeric-value: infinity */
- mpd_setspecial(dec, sign, MPD_INF);
- return;
- }
- goto conversion_error;
- }
- else {
- /* scan for start of coefficient, decimal point, indicator, end */
- if ((coeff = scan_dpoint_exp(s, &dpoint, &exp, &end)) == NULL)
- goto conversion_error;
-
- /* numeric-value: [exponent-part] */
- if (exp) {
- /* exponent-part */
- end = exp; exp++;
- dec->exp = strtoexp(exp);
- if (errno) {
- if (!(errno == ERANGE &&
- (dec->exp == MPD_SSIZE_MAX ||
- dec->exp == MPD_SSIZE_MIN)))
- goto conversion_error;
- }
- }
-
- digits = end - coeff;
- if (dpoint) {
- size_t fracdigits = end-dpoint-1;
- if (dpoint > coeff) digits--;
-
- if (fracdigits > MPD_MAX_PREC) {
- goto conversion_error;
- }
- if (dec->exp < MPD_SSIZE_MIN+(mpd_ssize_t)fracdigits) {
- dec->exp = MPD_SSIZE_MIN;
- }
- else {
- dec->exp -= (mpd_ssize_t)fracdigits;
- }
- }
- if (digits > MPD_MAX_PREC) {
- goto conversion_error;
- }
- if (dec->exp > MPD_EXP_INF) {
- dec->exp = MPD_EXP_INF;
- }
- if (dec->exp == MPD_SSIZE_MIN) {
- dec->exp = MPD_SSIZE_MIN+1;
- }
- }
-
- _mpd_idiv_word(&q, &r, (mpd_ssize_t)digits, MPD_RDIGITS);
-
- len = (r == 0) ? q : q+1;
- if (len == 0) {
- goto conversion_error; /* GCOV_NOT_REACHED */
- }
- if (!mpd_qresize(dec, len, status)) {
- mpd_seterror(dec, MPD_Malloc_error, status);
- return;
- }
- dec->len = len;
-
- string_to_coeff(dec->data, coeff, dpoint, (int)r, len);
-
- mpd_setdigits(dec);
- mpd_qfinalize(dec, ctx, status);
- return;
-
-conversion_error:
- /* standard wants a positive NaN */
- mpd_seterror(dec, MPD_Conversion_syntax, status);
-}
-
-/* convert a character string to a decimal, use a maxcontext for conversion */
-void
-mpd_qset_string_exact(mpd_t *dec, const char *s, uint32_t *status)
-{
- mpd_context_t maxcontext;
-
- mpd_maxcontext(&maxcontext);
- mpd_qset_string(dec, s, &maxcontext, status);
-
- if (*status & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) {
- /* we want exact results */
- mpd_seterror(dec, MPD_Invalid_operation, status);
- }
- *status &= MPD_Errors;
-}
-
-/* Print word x with n decimal digits to string s. dot is either NULL
- or the location of a decimal point. */
-#define EXTRACT_DIGIT(s, x, d, dot) \
- if (s == dot) *s++ = '.'; *s++ = '0' + (char)(x / d); x %= d
-#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && __GNUC__ >= 12
- #pragma GCC diagnostic push
- #pragma GCC diagnostic ignored "-Wstringop-overflow"
-#endif
-static inline char *
-word_to_string(char *s, mpd_uint_t x, int n, char *dot)
-{
- switch(n) {
-#ifdef CONFIG_64
- case 20: EXTRACT_DIGIT(s, x, 10000000000000000000ULL, dot); /* GCOV_NOT_REACHED */
- case 19: EXTRACT_DIGIT(s, x, 1000000000000000000ULL, dot);
- case 18: EXTRACT_DIGIT(s, x, 100000000000000000ULL, dot);
- case 17: EXTRACT_DIGIT(s, x, 10000000000000000ULL, dot);
- case 16: EXTRACT_DIGIT(s, x, 1000000000000000ULL, dot);
- case 15: EXTRACT_DIGIT(s, x, 100000000000000ULL, dot);
- case 14: EXTRACT_DIGIT(s, x, 10000000000000ULL, dot);
- case 13: EXTRACT_DIGIT(s, x, 1000000000000ULL, dot);
- case 12: EXTRACT_DIGIT(s, x, 100000000000ULL, dot);
- case 11: EXTRACT_DIGIT(s, x, 10000000000ULL, dot);
-#endif
- case 10: EXTRACT_DIGIT(s, x, 1000000000UL, dot);
- case 9: EXTRACT_DIGIT(s, x, 100000000UL, dot);
- case 8: EXTRACT_DIGIT(s, x, 10000000UL, dot);
- case 7: EXTRACT_DIGIT(s, x, 1000000UL, dot);
- case 6: EXTRACT_DIGIT(s, x, 100000UL, dot);
- case 5: EXTRACT_DIGIT(s, x, 10000UL, dot);
- case 4: EXTRACT_DIGIT(s, x, 1000UL, dot);
- case 3: EXTRACT_DIGIT(s, x, 100UL, dot);
- case 2: EXTRACT_DIGIT(s, x, 10UL, dot);
- default: if (s == dot) *s++ = '.'; *s++ = '0' + (char)x;
- }
-
- *s = '\0';
- return s;
-}
-#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && __GNUC__ >= 12
- #pragma GCC diagnostic pop
-#endif
-
-/* Print exponent x to string s. Undefined for MPD_SSIZE_MIN. */
-static inline char *
-exp_to_string(char *s, mpd_ssize_t x)
-{
- char sign = '+';
-
- if (x < 0) {
- sign = '-';
- x = -x;
- }
- *s++ = sign;
-
- return word_to_string(s, x, mpd_word_digits(x), NULL);
-}
-
-/* Print the coefficient of dec to string s. len(dec) > 0. */
-static inline char *
-coeff_to_string(char *s, const mpd_t *dec)
-{
- mpd_uint_t x;
- mpd_ssize_t i;
-
- /* most significant word */
- x = mpd_msword(dec);
- s = word_to_string(s, x, mpd_word_digits(x), NULL);
-
- /* remaining full words */
- for (i=dec->len-2; i >= 0; --i) {
- x = dec->data[i];
- s = word_to_string(s, x, MPD_RDIGITS, NULL);
- }
-
- return s;
-}
-
-/* Print the coefficient of dec to string s. len(dec) > 0. dot is either
- NULL or a pointer to the location of a decimal point. */
-static inline char *
-coeff_to_string_dot(char *s, char *dot, const mpd_t *dec)
-{
- mpd_uint_t x;
- mpd_ssize_t i;
-
- /* most significant word */
- x = mpd_msword(dec);
- s = word_to_string(s, x, mpd_word_digits(x), dot);
-
- /* remaining full words */
- for (i=dec->len-2; i >= 0; --i) {
- x = dec->data[i];
- s = word_to_string(s, x, MPD_RDIGITS, dot);
- }
-
- return s;
-}
-
-/* Format type */
-#define MPD_FMT_LOWER 0x00000000
-#define MPD_FMT_UPPER 0x00000001
-#define MPD_FMT_TOSCI 0x00000002
-#define MPD_FMT_TOENG 0x00000004
-#define MPD_FMT_EXP 0x00000008
-#define MPD_FMT_FIXED 0x00000010
-#define MPD_FMT_PERCENT 0x00000020
-#define MPD_FMT_SIGN_SPACE 0x00000040
-#define MPD_FMT_SIGN_PLUS 0x00000080
-
-/* Default place of the decimal point for MPD_FMT_TOSCI, MPD_FMT_EXP */
-#define MPD_DEFAULT_DOTPLACE 1
-
-/*
- * Set *result to the string representation of a decimal. Return the length
- * of *result, not including the terminating '\0' character.
- *
- * Formatting is done according to 'flags'. A return value of -1 with *result
- * set to NULL indicates MPD_Malloc_error.
- *
- * 'dplace' is the default place of the decimal point. It is always set to
- * MPD_DEFAULT_DOTPLACE except for zeros in combination with MPD_FMT_EXP.
- */
-static mpd_ssize_t
-_mpd_to_string(char **result, const mpd_t *dec, int flags, mpd_ssize_t dplace)
-{
- char *decstring = NULL, *cp = NULL;
- mpd_ssize_t ldigits;
- mpd_ssize_t mem = 0, k;
-
- if (mpd_isspecial(dec)) {
-
- mem = sizeof "-Infinity%";
- if (mpd_isnan(dec) && dec->len > 0) {
- /* diagnostic code */
- mem += dec->digits;
- }
- cp = decstring = mpd_alloc(mem, sizeof *decstring);
- if (cp == NULL) {
- *result = NULL;
- return -1;
- }
-
- if (mpd_isnegative(dec)) {
- *cp++ = '-';
- }
- else if (flags&MPD_FMT_SIGN_SPACE) {
- *cp++ = ' ';
- }
- else if (flags&MPD_FMT_SIGN_PLUS) {
- *cp++ = '+';
- }
-
- if (mpd_isnan(dec)) {
- if (mpd_isqnan(dec)) {
- strcpy(cp, "NaN");
- cp += 3;
- }
- else {
- strcpy(cp, "sNaN");
- cp += 4;
- }
- if (dec->len > 0) { /* diagnostic code */
- cp = coeff_to_string(cp, dec);
- }
- }
- else if (mpd_isinfinite(dec)) {
- strcpy(cp, "Infinity");
- cp += 8;
- }
- else { /* debug */
- abort(); /* GCOV_NOT_REACHED */
- }
- }
- else {
- assert(dec->len > 0);
-
- /*
- * For easier manipulation of the decimal point's location
- * and the exponent that is finally printed, the number is
- * rescaled to a virtual representation with exp = 0. Here
- * ldigits denotes the number of decimal digits to the left
- * of the decimal point and remains constant once initialized.
- *
- * dplace is the location of the decimal point relative to
- * the start of the coefficient. Note that 3) always holds
- * when dplace is shifted.
- *
- * 1) ldigits := dec->digits - dec->exp
- * 2) dplace := ldigits (initially)
- * 3) exp := ldigits - dplace (initially exp = 0)
- *
- * 0.00000_.____._____000000.
- * ^ ^ ^ ^
- * | | | |
- * | | | `- dplace >= digits
- * | | `- dplace in the middle of the coefficient
- * | ` dplace = 1 (after the first coefficient digit)
- * `- dplace <= 0
- */
-
- ldigits = dec->digits + dec->exp;
-
- if (flags&MPD_FMT_EXP) {
- ;
- }
- else if (flags&MPD_FMT_FIXED || (dec->exp <= 0 && ldigits > -6)) {
- /* MPD_FMT_FIXED: always use fixed point notation.
- * MPD_FMT_TOSCI, MPD_FMT_TOENG: for a certain range,
- * override exponent notation. */
- dplace = ldigits;
- }
- else if (flags&MPD_FMT_TOENG) {
- if (mpd_iszero(dec)) {
- /* If the exponent is divisible by three,
- * dplace = 1. Otherwise, move dplace one
- * or two places to the left. */
- dplace = -1 + mod_mpd_ssize_t(dec->exp+2, 3);
- }
- else { /* ldigits-1 is the adjusted exponent, which
- * should be divisible by three. If not, move
- * dplace one or two places to the right. */
- dplace += mod_mpd_ssize_t(ldigits-1, 3);
- }
- }
-
- /*
- * Basic space requirements:
- *
- * [-][.][coeffdigits][E][-][expdigits+1][%]['\0']
- *
- * If the decimal point lies outside of the coefficient digits,
- * space is adjusted accordingly.
- */
- if (dplace <= 0) {
- mem = -dplace + dec->digits + 2;
- }
- else if (dplace >= dec->digits) {
- mem = dplace;
- }
- else {
- mem = dec->digits;
- }
- mem += (MPD_EXPDIGITS+1+6);
-
- cp = decstring = mpd_alloc(mem, sizeof *decstring);
- if (cp == NULL) {
- *result = NULL;
- return -1;
- }
-
-
- if (mpd_isnegative(dec)) {
- *cp++ = '-';
- }
- else if (flags&MPD_FMT_SIGN_SPACE) {
- *cp++ = ' ';
- }
- else if (flags&MPD_FMT_SIGN_PLUS) {
- *cp++ = '+';
- }
-
- if (dplace <= 0) {
- /* space: -dplace+dec->digits+2 */
- *cp++ = '0';
- *cp++ = '.';
- for (k = 0; k < -dplace; k++) {
- *cp++ = '0';
- }
- cp = coeff_to_string(cp, dec);
- }
- else if (dplace >= dec->digits) {
- /* space: dplace */
- cp = coeff_to_string(cp, dec);
- for (k = 0; k < dplace-dec->digits; k++) {
- *cp++ = '0';
- }
- }
- else {
- /* space: dec->digits+1 */
- cp = coeff_to_string_dot(cp, cp+dplace, dec);
- }
-
- /*
- * Conditions for printing an exponent:
- *
- * MPD_FMT_TOSCI, MPD_FMT_TOENG: only if ldigits != dplace
- * MPD_FMT_FIXED: never (ldigits == dplace)
- * MPD_FMT_EXP: always
- */
- if (ldigits != dplace || flags&MPD_FMT_EXP) {
- /* space: expdigits+2 */
- *cp++ = (flags&MPD_FMT_UPPER) ? 'E' : 'e';
- cp = exp_to_string(cp, ldigits-dplace);
- }
- }
-
- if (flags&MPD_FMT_PERCENT) {
- *cp++ = '%';
- }
-
- assert(cp < decstring+mem);
- assert(cp-decstring < MPD_SSIZE_MAX);
-
- *cp = '\0';
- *result = decstring;
- return (mpd_ssize_t)(cp-decstring);
-}
-
-char *
-mpd_to_sci(const mpd_t *dec, int fmt)
-{
- char *res;
- int flags = MPD_FMT_TOSCI;
-
- flags |= fmt ? MPD_FMT_UPPER : MPD_FMT_LOWER;
- (void)_mpd_to_string(&res, dec, flags, MPD_DEFAULT_DOTPLACE);
- return res;
-}
-
-char *
-mpd_to_eng(const mpd_t *dec, int fmt)
-{
- char *res;
- int flags = MPD_FMT_TOENG;
-
- flags |= fmt ? MPD_FMT_UPPER : MPD_FMT_LOWER;
- (void)_mpd_to_string(&res, dec, flags, MPD_DEFAULT_DOTPLACE);
- return res;
-}
-
-mpd_ssize_t
-mpd_to_sci_size(char **res, const mpd_t *dec, int fmt)
-{
- int flags = MPD_FMT_TOSCI;
-
- flags |= fmt ? MPD_FMT_UPPER : MPD_FMT_LOWER;
- return _mpd_to_string(res, dec, flags, MPD_DEFAULT_DOTPLACE);
-}
-
-mpd_ssize_t
-mpd_to_eng_size(char **res, const mpd_t *dec, int fmt)
-{
- int flags = MPD_FMT_TOENG;
-
- flags |= fmt ? MPD_FMT_UPPER : MPD_FMT_LOWER;
- return _mpd_to_string(res, dec, flags, MPD_DEFAULT_DOTPLACE);
-}
-
-/* Copy a single UTF-8 char to dest. See: The Unicode Standard, version 5.2,
- chapter 3.9: Well-formed UTF-8 byte sequences. */
-static int
-_mpd_copy_utf8(char dest[5], const char *s)
-{
- const unsigned char *cp = (const unsigned char *)s;
- unsigned char lb, ub;
- int count, i;
-
-
- if (*cp == 0) {
- /* empty string */
- dest[0] = '\0';
- return 0;
- }
- else if (*cp <= 0x7f) {
- /* ascii */
- dest[0] = *cp;
- dest[1] = '\0';
- return 1;
- }
- else if (0xc2 <= *cp && *cp <= 0xdf) {
- lb = 0x80; ub = 0xbf;
- count = 2;
- }
- else if (*cp == 0xe0) {
- lb = 0xa0; ub = 0xbf;
- count = 3;
- }
- else if (*cp <= 0xec) {
- lb = 0x80; ub = 0xbf;
- count = 3;
- }
- else if (*cp == 0xed) {
- lb = 0x80; ub = 0x9f;
- count = 3;
- }
- else if (*cp <= 0xef) {
- lb = 0x80; ub = 0xbf;
- count = 3;
- }
- else if (*cp == 0xf0) {
- lb = 0x90; ub = 0xbf;
- count = 4;
- }
- else if (*cp <= 0xf3) {
- lb = 0x80; ub = 0xbf;
- count = 4;
- }
- else if (*cp == 0xf4) {
- lb = 0x80; ub = 0x8f;
- count = 4;
- }
- else {
- /* invalid */
- goto error;
- }
-
- dest[0] = *cp++;
- if (*cp < lb || ub < *cp) {
- goto error;
- }
- dest[1] = *cp++;
- for (i = 2; i < count; i++) {
- if (*cp < 0x80 || 0xbf < *cp) {
- goto error;
- }
- dest[i] = *cp++;
- }
- dest[i] = '\0';
-
- return count;
-
-error:
- dest[0] = '\0';
- return -1;
-}
-
-int
-mpd_validate_lconv(mpd_spec_t *spec)
-{
- size_t n;
-#if CHAR_MAX == SCHAR_MAX
- const char *cp = spec->grouping;
- while (*cp != '\0') {
- if (*cp++ < 0) {
- return -1;
- }
- }
-#endif
- n = strlen(spec->dot);
- if (n == 0 || n > 4) {
- return -1;
- }
- if (strlen(spec->sep) > 4) {
- return -1;
- }
-
- return 0;
-}
-
-int
-mpd_parse_fmt_str(mpd_spec_t *spec, const char *fmt, int caps)
-{
- char *cp = (char *)fmt;
- int have_align = 0, n;
-
- /* defaults */
- spec->min_width = 0;
- spec->prec = -1;
- spec->type = caps ? 'G' : 'g';
- spec->align = '>';
- spec->sign = '-';
- spec->dot = "";
- spec->sep = "";
- spec->grouping = "";
-
-
- /* presume that the first character is a UTF-8 fill character */
- if ((n = _mpd_copy_utf8(spec->fill, cp)) < 0) {
- return 0;
- }
-
- /* alignment directive, prefixed by a fill character */
- if (*cp && (*(cp+n) == '<' || *(cp+n) == '>' ||
- *(cp+n) == '=' || *(cp+n) == '^')) {
- cp += n;
- spec->align = *cp++;
- have_align = 1;
- } /* alignment directive */
- else {
- /* default fill character */
- spec->fill[0] = ' ';
- spec->fill[1] = '\0';
- if (*cp == '<' || *cp == '>' ||
- *cp == '=' || *cp == '^') {
- spec->align = *cp++;
- have_align = 1;
- }
- }
-
- /* sign formatting */
- if (*cp == '+' || *cp == '-' || *cp == ' ') {
- spec->sign = *cp++;
- }
-
- /* zero padding */
- if (*cp == '0') {
- /* zero padding implies alignment, which should not be
- * specified twice. */
- if (have_align) {
- return 0;
- }
- spec->align = 'z';
- spec->fill[0] = *cp++;
- spec->fill[1] = '\0';
- }
-
- /* minimum width */
- if (isdigit((unsigned char)*cp)) {
- if (*cp == '0') {
- return 0;
- }
- errno = 0;
- spec->min_width = mpd_strtossize(cp, &cp, 10);
- if (errno == ERANGE || errno == EINVAL) {
- return 0;
- }
- }
-
- /* thousands separator */
- if (*cp == ',') {
- spec->dot = ".";
- spec->sep = ",";
- spec->grouping = "\003\003";
- cp++;
- }
-
- /* fraction digits or significant digits */
- if (*cp == '.') {
- cp++;
- if (!isdigit((unsigned char)*cp)) {
- return 0;
- }
- errno = 0;
- spec->prec = mpd_strtossize(cp, &cp, 10);
- if (errno == ERANGE || errno == EINVAL) {
- return 0;
- }
- }
-
- /* type */
- if (*cp == 'E' || *cp == 'e' || *cp == 'F' || *cp == 'f' ||
- *cp == 'G' || *cp == 'g' || *cp == '%') {
- spec->type = *cp++;
- }
- else if (*cp == 'N' || *cp == 'n') {
- /* locale specific conversion */
- struct lconv *lc;
- /* separator has already been specified */
- if (*spec->sep) {
- return 0;
- }
- spec->type = *cp++;
- spec->type = (spec->type == 'N') ? 'G' : 'g';
- lc = localeconv();
- spec->dot = lc->decimal_point;
- spec->sep = lc->thousands_sep;
- spec->grouping = lc->grouping;
- if (mpd_validate_lconv(spec) < 0) {
- return 0; /* GCOV_NOT_REACHED */
- }
- }
-
- /* check correctness */
- if (*cp != '\0') {
- return 0;
- }
-
- return 1;
-}
-
-/*
- * The following functions assume that spec->min_width <= MPD_MAX_PREC, which
- * is made sure in mpd_qformat_spec. Then, even with a spec that inserts a
- * four-byte separator after each digit, nbytes in the following struct
- * cannot overflow.
- */
-
-/* Multibyte string */
-typedef struct {
- mpd_ssize_t nbytes; /* length in bytes */
- mpd_ssize_t nchars; /* length in chars */
- mpd_ssize_t cur; /* current write index */
- char *data;
-} mpd_mbstr_t;
-
-static inline void
-_mpd_bcopy(char *dest, const char *src, mpd_ssize_t n)
-{
- while (--n >= 0) {
- dest[n] = src[n];
- }
-}
-
-static inline void
-_mbstr_copy_char(mpd_mbstr_t *dest, const char *src, mpd_ssize_t n)
-{
- dest->nbytes += n;
- dest->nchars += (n > 0 ? 1 : 0);
- dest->cur -= n;
-
- if (dest->data != NULL) {
- _mpd_bcopy(dest->data+dest->cur, src, n);
- }
-}
-
-static inline void
-_mbstr_copy_ascii(mpd_mbstr_t *dest, const char *src, mpd_ssize_t n)
-{
- dest->nbytes += n;
- dest->nchars += n;
- dest->cur -= n;
-
- if (dest->data != NULL) {
- _mpd_bcopy(dest->data+dest->cur, src, n);
- }
-}
-
-static inline void
-_mbstr_copy_pad(mpd_mbstr_t *dest, mpd_ssize_t n)
-{
- dest->nbytes += n;
- dest->nchars += n;
- dest->cur -= n;
-
- if (dest->data != NULL) {
- char *cp = dest->data + dest->cur;
- while (--n >= 0) {
- cp[n] = '0';
- }
- }
-}
-
-/*
- * Copy a numeric string to dest->data, adding separators in the integer
- * part according to spec->grouping. If leading zero padding is enabled
- * and the result is smaller than spec->min_width, continue adding zeros
- * and separators until the minimum width is reached.
- *
- * The final length of dest->data is stored in dest->nbytes. The number
- * of UTF-8 characters is stored in dest->nchars.
- *
- * First run (dest->data == NULL): determine the length of the result
- * string and store it in dest->nbytes.
- *
- * Second run (write to dest->data): data is written in chunks and in
- * reverse order, starting with the rest of the numeric string.
- */
-static void
-_mpd_add_sep_dot(mpd_mbstr_t *dest,
- const char *sign, /* location of optional sign */
- const char *src, mpd_ssize_t n_src, /* integer part and length */
- const char *dot, /* location of optional decimal point */
- const char *rest, mpd_ssize_t n_rest, /* remaining part and length */
- const mpd_spec_t *spec)
-{
- mpd_ssize_t n_sep, n_sign, consume;
- const char *g;
- int pad = 0;
-
- n_sign = sign ? 1 : 0;
- n_sep = (mpd_ssize_t)strlen(spec->sep);
- /* Initial write index: set to location of '\0' in the output string.
- * Irrelevant for the first run. */
- dest->cur = dest->nbytes;
- dest->nbytes = dest->nchars = 0;
-
- _mbstr_copy_ascii(dest, rest, n_rest);
-
- if (dot) {
- _mbstr_copy_char(dest, dot, (mpd_ssize_t)strlen(dot));
- }
-
- g = spec->grouping;
- consume = *g;
- while (1) {
- /* If the group length is 0 or CHAR_MAX or greater than the
- * number of source bytes, consume all remaining bytes. */
- if (*g == 0 || *g == CHAR_MAX || consume > n_src) {
- consume = n_src;
- }
- n_src -= consume;
- if (pad) {
- _mbstr_copy_pad(dest, consume);
- }
- else {
- _mbstr_copy_ascii(dest, src+n_src, consume);
- }
-
- if (n_src == 0) {
- /* Either the real source of intpart digits or the virtual
- * source of padding zeros is exhausted. */
- if (spec->align == 'z' &&
- dest->nchars + n_sign < spec->min_width) {
- /* Zero padding is set and length < min_width:
- * Generate n_src additional characters. */
- n_src = spec->min_width - (dest->nchars + n_sign);
- /* Next iteration:
- * case *g == 0 || *g == CHAR_MAX:
- * consume all padding characters
- * case consume < g*:
- * fill remainder of current group
- * case consume == g*
- * copying is a no-op */
- consume = *g - consume;
- /* Switch on virtual source of zeros. */
- pad = 1;
- continue;
- }
- break;
- }
-
- if (n_sep > 0) {
- /* If padding is switched on, separators are counted
- * as padding characters. This rule does not apply if
- * the separator would be the first character of the
- * result string. */
- if (pad && n_src > 1) n_src -= 1;
- _mbstr_copy_char(dest, spec->sep, n_sep);
- }
-
- /* If non-NUL, use the next value for grouping. */
- if (*g && *(g+1)) g++;
- consume = *g;
- }
-
- if (sign) {
- _mbstr_copy_ascii(dest, sign, 1);
- }
-
- if (dest->data) {
- dest->data[dest->nbytes] = '\0';
- }
-}
-
-/*
- * Convert a numeric-string to its locale-specific appearance.
- * The string must have one of these forms:
- *
- * 1) [sign] digits [exponent-part]
- * 2) [sign] digits '.' [digits] [exponent-part]
- *
- * Not allowed, since _mpd_to_string() never returns this form:
- *
- * 3) [sign] '.' digits [exponent-part]
- *
- * Input: result->data := original numeric string (ASCII)
- * result->bytes := strlen(result->data)
- * result->nchars := strlen(result->data)
- *
- * Output: result->data := modified or original string
- * result->bytes := strlen(result->data)
- * result->nchars := number of characters (possibly UTF-8)
- */
-static int
-_mpd_apply_lconv(mpd_mbstr_t *result, const mpd_spec_t *spec, uint32_t *status)
-{
- const char *sign = NULL, *intpart = NULL, *dot = NULL;
- const char *rest, *dp;
- char *decstring;
- mpd_ssize_t n_int, n_rest;
-
- /* original numeric string */
- dp = result->data;
-
- /* sign */
- if (*dp == '+' || *dp == '-' || *dp == ' ') {
- sign = dp++;
- }
- /* integer part */
- assert(isdigit((unsigned char)*dp));
- intpart = dp++;
- while (isdigit((unsigned char)*dp)) {
- dp++;
- }
- n_int = (mpd_ssize_t)(dp-intpart);
- /* decimal point */
- if (*dp == '.') {
- dp++; dot = spec->dot;
- }
- /* rest */
- rest = dp;
- n_rest = result->nbytes - (mpd_ssize_t)(dp-result->data);
-
- if (dot == NULL && (*spec->sep == '\0' || *spec->grouping == '\0')) {
- /* _mpd_add_sep_dot() would not change anything */
- return 1;
- }
-
- /* Determine the size of the new decimal string after inserting the
- * decimal point, optional separators and optional padding. */
- decstring = result->data;
- result->data = NULL;
- _mpd_add_sep_dot(result, sign, intpart, n_int, dot,
- rest, n_rest, spec);
-
- result->data = mpd_alloc(result->nbytes+1, 1);
- if (result->data == NULL) {
- *status |= MPD_Malloc_error;
- mpd_free(decstring);
- return 0;
- }
-
- /* Perform actual writes. */
- _mpd_add_sep_dot(result, sign, intpart, n_int, dot,
- rest, n_rest, spec);
-
- mpd_free(decstring);
- return 1;
-}
-
-/* Add padding to the formatted string if necessary. */
-static int
-_mpd_add_pad(mpd_mbstr_t *result, const mpd_spec_t *spec, uint32_t *status)
-{
- if (result->nchars < spec->min_width) {
- mpd_ssize_t add_chars, add_bytes;
- size_t lpad = 0, rpad = 0;
- size_t n_fill, len, i, j;
- char align = spec->align;
- uint8_t err = 0;
- char *cp;
-
- n_fill = strlen(spec->fill);
- add_chars = (spec->min_width - result->nchars);
- /* max value: MPD_MAX_PREC * 4 */
- add_bytes = add_chars * (mpd_ssize_t)n_fill;
-
- cp = result->data = mpd_realloc(result->data,
- result->nbytes+add_bytes+1,
- sizeof *result->data, &err);
- if (err) {
- *status |= MPD_Malloc_error;
- mpd_free(result->data);
- return 0;
- }
-
- if (align == 'z') {
- align = '=';
- }
-
- if (align == '<') {
- rpad = add_chars;
- }
- else if (align == '>' || align == '=') {
- lpad = add_chars;
- }
- else { /* align == '^' */
- lpad = add_chars/2;
- rpad = add_chars-lpad;
- }
-
- len = result->nbytes;
- if (align == '=' && (*cp == '-' || *cp == '+' || *cp == ' ')) {
- /* leave sign in the leading position */
- cp++; len--;
- }
-
- memmove(cp+n_fill*lpad, cp, len);
- for (i = 0; i < lpad; i++) {
- for (j = 0; j < n_fill; j++) {
- cp[i*n_fill+j] = spec->fill[j];
- }
- }
- cp += (n_fill*lpad + len);
- for (i = 0; i < rpad; i++) {
- for (j = 0; j < n_fill; j++) {
- cp[i*n_fill+j] = spec->fill[j];
- }
- }
-
- result->nbytes += add_bytes;
- result->nchars += add_chars;
- result->data[result->nbytes] = '\0';
- }
-
- return 1;
-}
-
-/* Round a number to prec digits. The adjusted exponent stays the same
- or increases by one if rounding up crosses a power of ten boundary.
- If result->digits would exceed MPD_MAX_PREC+1, MPD_Invalid_operation
- is set and the result is NaN. */
-static inline void
-_mpd_round(mpd_t *result, const mpd_t *a, mpd_ssize_t prec,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_ssize_t exp = a->exp + a->digits - prec;
-
- if (prec <= 0) {
- mpd_seterror(result, MPD_Invalid_operation, status); /* GCOV_NOT_REACHED */
- return; /* GCOV_NOT_REACHED */
- }
- if (mpd_isspecial(a) || mpd_iszero(a)) {
- mpd_qcopy(result, a, status); /* GCOV_NOT_REACHED */
- return; /* GCOV_NOT_REACHED */
- }
-
- mpd_qrescale_fmt(result, a, exp, ctx, status);
- if (result->digits > prec) {
- mpd_qrescale_fmt(result, result, exp+1, ctx, status);
- }
-}
-
-/*
- * Return the string representation of an mpd_t, formatted according to 'spec'.
- * The format specification is assumed to be valid. Memory errors are indicated
- * as usual. This function is quiet.
- */
-char *
-mpd_qformat_spec(const mpd_t *dec, const mpd_spec_t *spec,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_uint_t dt[MPD_MINALLOC_MAX];
- mpd_t tmp = {MPD_STATIC|MPD_STATIC_DATA,0,0,0,MPD_MINALLOC_MAX,dt};
- mpd_ssize_t dplace = MPD_DEFAULT_DOTPLACE;
- mpd_mbstr_t result;
- mpd_spec_t stackspec;
- char type = spec->type;
- int flags = 0;
-
-
- if (spec->min_width > MPD_MAX_PREC) {
- *status |= MPD_Invalid_operation;
- return NULL;
- }
-
- if (isupper((unsigned char)type)) {
- type = (char)tolower((unsigned char)type);
- flags |= MPD_FMT_UPPER;
- }
- if (spec->sign == ' ') {
- flags |= MPD_FMT_SIGN_SPACE;
- }
- else if (spec->sign == '+') {
- flags |= MPD_FMT_SIGN_PLUS;
- }
-
- if (mpd_isspecial(dec)) {
- if (spec->align == 'z') {
- stackspec = *spec;
- stackspec.fill[0] = ' ';
- stackspec.fill[1] = '\0';
- stackspec.align = '>';
- spec = &stackspec;
- }
- assert(strlen(spec->fill) == 1); /* annotation for scan-build */
- if (type == '%') {
- flags |= MPD_FMT_PERCENT;
- }
- }
- else {
- uint32_t workstatus = 0;
- mpd_ssize_t prec;
-
- switch (type) {
- case 'g': flags |= MPD_FMT_TOSCI; break;
- case 'e': flags |= MPD_FMT_EXP; break;
- case '%': flags |= MPD_FMT_PERCENT;
- if (!mpd_qcopy(&tmp, dec, status)) {
- return NULL;
- }
- tmp.exp += 2;
- dec = &tmp;
- type = 'f'; /* fall through */
- case 'f': flags |= MPD_FMT_FIXED; break;
- default: abort(); /* debug: GCOV_NOT_REACHED */
- }
-
- if (spec->prec >= 0) {
- if (spec->prec > MPD_MAX_PREC) {
- *status |= MPD_Invalid_operation;
- goto error;
- }
-
- switch (type) {
- case 'g':
- prec = (spec->prec == 0) ? 1 : spec->prec;
- if (dec->digits > prec) {
- _mpd_round(&tmp, dec, prec, ctx,
- &workstatus);
- dec = &tmp;
- }
- break;
- case 'e':
- if (mpd_iszero(dec)) {
- dplace = 1-spec->prec;
- }
- else {
- _mpd_round(&tmp, dec, spec->prec+1, ctx,
- &workstatus);
- dec = &tmp;
- }
- break;
- case 'f':
- mpd_qrescale(&tmp, dec, -spec->prec, ctx,
- &workstatus);
- dec = &tmp;
- break;
- }
- }
-
- if (type == 'f') {
- if (mpd_iszero(dec) && dec->exp > 0) {
- mpd_qrescale(&tmp, dec, 0, ctx, &workstatus);
- dec = &tmp;
- }
- }
-
- if (workstatus&MPD_Errors) {
- *status |= (workstatus&MPD_Errors);
- goto error;
- }
- }
-
- /*
- * At this point, for all scaled or non-scaled decimals:
- * 1) 1 <= digits <= MAX_PREC+1
- * 2) adjexp(scaled) = adjexp(orig) [+1]
- * 3) case 'g': MIN_ETINY <= exp <= MAX_EMAX+1
- * case 'e': MIN_ETINY-MAX_PREC <= exp <= MAX_EMAX+1
- * case 'f': MIN_ETINY <= exp <= MAX_EMAX+1
- * 4) max memory alloc in _mpd_to_string:
- * case 'g': MAX_PREC+36
- * case 'e': MAX_PREC+36
- * case 'f': 2*MPD_MAX_PREC+30
- */
- result.nbytes = _mpd_to_string(&result.data, dec, flags, dplace);
- result.nchars = result.nbytes;
- if (result.nbytes < 0) {
- *status |= MPD_Malloc_error;
- goto error;
- }
-
- if (*spec->dot != '\0' && !mpd_isspecial(dec)) {
- if (result.nchars > MPD_MAX_PREC+36) {
- /* Since a group length of one is not explicitly
- * disallowed, ensure that it is always possible to
- * insert a four byte separator after each digit. */
- *status |= MPD_Invalid_operation;
- mpd_free(result.data);
- goto error;
- }
- if (!_mpd_apply_lconv(&result, spec, status)) {
- goto error;
- }
- }
-
- if (spec->min_width) {
- if (!_mpd_add_pad(&result, spec, status)) {
- goto error;
- }
- }
-
- mpd_del(&tmp);
- return result.data;
-
-error:
- mpd_del(&tmp);
- return NULL;
-}
-
-char *
-mpd_qformat(const mpd_t *dec, const char *fmt, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_spec_t spec;
-
- if (!mpd_parse_fmt_str(&spec, fmt, 1)) {
- *status |= MPD_Invalid_operation;
- return NULL;
- }
-
- return mpd_qformat_spec(dec, &spec, ctx, status);
-}
-
-/*
- * The specification has a *condition* called Invalid_operation and an
- * IEEE *signal* called Invalid_operation. The former corresponds to
- * MPD_Invalid_operation, the latter to MPD_IEEE_Invalid_operation.
- * MPD_IEEE_Invalid_operation comprises the following conditions:
- *
- * [MPD_Conversion_syntax, MPD_Division_impossible, MPD_Division_undefined,
- * MPD_Fpu_error, MPD_Invalid_context, MPD_Invalid_operation,
- * MPD_Malloc_error]
- *
- * In the following functions, 'flag' denotes the condition, 'signal'
- * denotes the IEEE signal.
- */
-
-static const char *mpd_flag_string[MPD_NUM_FLAGS] = {
- "Clamped",
- "Conversion_syntax",
- "Division_by_zero",
- "Division_impossible",
- "Division_undefined",
- "Fpu_error",
- "Inexact",
- "Invalid_context",
- "Invalid_operation",
- "Malloc_error",
- "Not_implemented",
- "Overflow",
- "Rounded",
- "Subnormal",
- "Underflow",
-};
-
-static const char *mpd_signal_string[MPD_NUM_FLAGS] = {
- "Clamped",
- "IEEE_Invalid_operation",
- "Division_by_zero",
- "IEEE_Invalid_operation",
- "IEEE_Invalid_operation",
- "IEEE_Invalid_operation",
- "Inexact",
- "IEEE_Invalid_operation",
- "IEEE_Invalid_operation",
- "IEEE_Invalid_operation",
- "Not_implemented",
- "Overflow",
- "Rounded",
- "Subnormal",
- "Underflow",
-};
-
-/* print conditions to buffer, separated by spaces */
-int
-mpd_snprint_flags(char *dest, int nmemb, uint32_t flags)
-{
- char *cp;
- int n, j;
-
- assert(nmemb >= MPD_MAX_FLAG_STRING);
-
- *dest = '\0'; cp = dest;
- for (j = 0; j < MPD_NUM_FLAGS; j++) {
- if (flags & (1U<<j)) {
- n = snprintf(cp, nmemb, "%s ", mpd_flag_string[j]);
- if (n < 0 || n >= nmemb) return -1;
- cp += n; nmemb -= n;
- }
- }
-
- if (cp != dest) {
- *(--cp) = '\0';
- }
-
- return (int)(cp-dest);
-}
-
-/* print conditions to buffer, in list form */
-int
-mpd_lsnprint_flags(char *dest, int nmemb, uint32_t flags, const char *flag_string[])
-{
- char *cp;
- int n, j;
-
- assert(nmemb >= MPD_MAX_FLAG_LIST);
- if (flag_string == NULL) {
- flag_string = mpd_flag_string;
- }
-
- *dest = '[';
- *(dest+1) = '\0';
- cp = dest+1;
- --nmemb;
-
- for (j = 0; j < MPD_NUM_FLAGS; j++) {
- if (flags & (1U<<j)) {
- n = snprintf(cp, nmemb, "%s, ", flag_string[j]);
- if (n < 0 || n >= nmemb) return -1;
- cp += n; nmemb -= n;
- }
- }
-
- /* erase the last ", " */
- if (cp != dest+1) {
- cp -= 2;
- }
-
- *cp++ = ']';
- *cp = '\0';
-
- return (int)(cp-dest); /* strlen, without NUL terminator */
-}
-
-/* print signals to buffer, in list form */
-int
-mpd_lsnprint_signals(char *dest, int nmemb, uint32_t flags, const char *signal_string[])
-{
- char *cp;
- int n, j;
- int ieee_invalid_done = 0;
-
- assert(nmemb >= MPD_MAX_SIGNAL_LIST);
- if (signal_string == NULL) {
- signal_string = mpd_signal_string;
- }
-
- *dest = '[';
- *(dest+1) = '\0';
- cp = dest+1;
- --nmemb;
-
- for (j = 0; j < MPD_NUM_FLAGS; j++) {
- uint32_t f = flags & (1U<<j);
- if (f) {
- if (f&MPD_IEEE_Invalid_operation) {
- if (ieee_invalid_done) {
- continue;
- }
- ieee_invalid_done = 1;
- }
- n = snprintf(cp, nmemb, "%s, ", signal_string[j]);
- if (n < 0 || n >= nmemb) return -1;
- cp += n; nmemb -= n;
- }
- }
-
- /* erase the last ", " */
- if (cp != dest+1) {
- cp -= 2;
- }
-
- *cp++ = ']';
- *cp = '\0';
-
- return (int)(cp-dest); /* strlen, without NUL terminator */
-}
-
-/* The following two functions are mainly intended for debugging. */
-void
-mpd_fprint(FILE *file, const mpd_t *dec)
-{
- char *decstring;
-
- decstring = mpd_to_sci(dec, 1);
- if (decstring != NULL) {
- fprintf(file, "%s\n", decstring);
- mpd_free(decstring);
- }
- else {
- fputs("mpd_fprint: output error\n", file); /* GCOV_NOT_REACHED */
- }
-}
-
-void
-mpd_print(const mpd_t *dec)
-{
- char *decstring;
-
- decstring = mpd_to_sci(dec, 1);
- if (decstring != NULL) {
- printf("%s\n", decstring);
- mpd_free(decstring);
- }
- else {
- fputs("mpd_fprint: output error\n", stderr); /* GCOV_NOT_REACHED */
- }
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_IO_H_
-#define LIBMPDEC_IO_H_
-
-
-#include "mpdecimal.h"
-
-#include <stdint.h>
-
-
-#if SIZE_MAX == MPD_SIZE_MAX
- #define mpd_strtossize _mpd_strtossize
-#else
-#include <errno.h>
-
-static inline mpd_ssize_t
-mpd_strtossize(const char *s, char **end, int base)
-{
- int64_t retval;
-
- errno = 0;
- retval = _mpd_strtossize(s, end, base);
- if (errno == 0 && (retval > MPD_SSIZE_MAX || retval < MPD_SSIZE_MIN)) {
- errno = ERANGE;
- }
- if (errno == ERANGE) {
- return (retval < 0) ? MPD_SSIZE_MIN : MPD_SSIZE_MAX;
- }
-
- return (mpd_ssize_t)retval;
-}
-#endif
-
-
-#endif /* LIBMPDEC_IO_H_ */
+++ /dev/null
-
-
-This document contains links to the literature used in the process of
-creating the library. The list is probably not complete.
-
-
-Mike Cowlishaw: General Decimal Arithmetic Specification
-http://speleotrove.com/decimal/decarith.html
-
-
-Jean-Michel Muller: On the definition of ulp (x)
-lara.inist.fr/bitstream/2332/518/1/LIP-RR2005-09.pdf
-
-
-T. E. Hull, A. Abrham: Properly rounded variable precision square root
-http://portal.acm.org/citation.cfm?id=214413
-
-
-T. E. Hull, A. Abrham: Variable precision exponential function
-http://portal.acm.org/citation.cfm?id=6498
-
-
-Roman E. Maeder: Storage allocation for the Karatsuba integer multiplication
-algorithm. http://www.springerlink.com/content/w15058mj6v59t565/
-
-
-J. M. Pollard: The fast Fourier transform in a finite field
-http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0301966-0/home.html
-
-
-David H. Bailey: FFTs in External or Hierarchical Memory
-http://crd.lbl.gov/~dhbailey/dhbpapers/
-
-
-W. Morven Gentleman: Matrix Multiplication and Fast Fourier Transforms
-http://www.alcatel-lucent.com/bstj/vol47-1968/articles/bstj47-6-1099.pdf
-
-
-Mikko Tommila: Apfloat documentation
-http://www.apfloat.org/apfloat/2.41/apfloat.pdf
-
-
-Joerg Arndt: "Matters Computational"
-http://www.jjj.de/fxt/
-
-
-Karl Hasselstrom: Fast Division of Large Integers
-www.treskal.com/kalle/exjobb/original-report.pdf
-
-
-
+++ /dev/null
-
-
-Bignum support (Fast Number Theoretic Transform or FNT):
-========================================================
-
-Bignum arithmetic in libmpdec uses the scheme for fast convolution
-of integer sequences from:
-
-J. M. Pollard: The fast Fourier transform in a finite field
-http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0301966-0/home.html
-
-
-The transform in a finite field can be used for convolution in the same
-way as the Fourier Transform. The main advantages of the Number Theoretic
-Transform are that it is both exact and very memory efficient.
-
-
-Convolution in pseudo-code:
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
- fnt_convolute(a, b):
- x = fnt(a) # forward transform of a
- y = fnt(b) # forward transform of b
- z = pairwise multiply x[i] and y[i]
- result = inv_fnt(z) # backward transform of z.
-
-
-Extending the maximum transform length (Chinese Remainder Theorem):
--------------------------------------------------------------------
-
-The maximum transform length is quite limited when using a single
-prime field. However, it is possible to use multiple primes and
-recover the result using the Chinese Remainder Theorem.
-
-
-Multiplication in pseudo-code:
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
- _mpd_fntmul(u, v):
- c1 = fnt_convolute(u, v, P1) # convolute modulo prime1
- c2 = fnt_convolute(u, v, P2) # convolute modulo prime2
- c3 = fnt_convolute(u, v, P3) # convolute modulo prime3
- result = crt3(c1, c2, c3) # Chinese Remainder Theorem
-
-
-Optimized transform functions:
-------------------------------
-
-There are three different fnt() functions:
-
- std_fnt: "standard" decimation in frequency transform for array lengths
- of 2**n. Performs well up to 1024 words.
-
- sixstep: Cache-friendly algorithm for array lengths of 2**n. Outperforms
- std_fnt for large arrays.
-
- fourstep: Algorithm for array lengths of 3 * 2**n. Also cache friendly
- in large parts.
-
-
-List of bignum-only files:
---------------------------
-
-Functions from these files are only used in _mpd_fntmul().
-
- umodarith.h -> fast low level routines for unsigned modular arithmetic
- numbertheory.c -> routines for setting up the FNT
- difradix2.c -> decimation in frequency transform, used as the
- "base case" by the following three files:
-
- fnt.c -> standard transform for smaller arrays
- sixstep.c -> transform large arrays of length 2**n
- fourstep.c -> transform arrays of length 3 * 2**n
-
- convolute.c -> do the actual fast convolution, using one of
- the three transform functions.
- transpose.c -> transpositions needed for the sixstep algorithm.
- crt.c -> Chinese Remainder Theorem: use information from three
- transforms modulo three different primes to get the
- final result.
-
-
-
+++ /dev/null
-#
-# Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
-#
-# Redistribution and use in source and binary forms, with or without
-# modification, are permitted provided that the following conditions
-# are met:
-#
-# 1. Redistributions of source code must retain the above copyright
-# notice, this list of conditions and the following disclaimer.
-#
-# 2. Redistributions in binary form must reproduce the above copyright
-# notice, this list of conditions and the following disclaimer in the
-# documentation and/or other materials provided with the distribution.
-#
-# THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
-# ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
-# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
-# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
-# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
-# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
-# OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
-# HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
-# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
-# OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
-# SUCH DAMAGE.
-#
-
-
-######################################################################
-# This file lists and checks some of the constants and limits used #
-# in libmpdec's Number Theoretic Transform. At the end of the file #
-# there is an example function for the plain DFT transform. #
-######################################################################
-
-
-#
-# Number theoretic transforms are done in subfields of F(p). P[i]
-# are the primes, D[i] = P[i] - 1 are highly composite and w[i]
-# are the respective primitive roots of F(p).
-#
-# The strategy is to convolute two coefficients modulo all three
-# primes, then use the Chinese Remainder Theorem on the three
-# result arrays to recover the result in the usual base RADIX
-# form.
-#
-
-# ======================================================================
-# Primitive roots
-# ======================================================================
-
-#
-# Verify primitive roots:
-#
-# For a prime field, r is a primitive root if and only if for all prime
-# factors f of p-1, r**((p-1)/f) =/= 1 (mod p).
-#
-def prod(F, E):
- """Check that the factorization of P-1 is correct. F is the list of
- factors of P-1, E lists the number of occurrences of each factor."""
- x = 1
- for y, z in zip(F, E):
- x *= y**z
- return x
-
-def is_primitive_root(r, p, factors, exponents):
- """Check if r is a primitive root of F(p)."""
- if p != prod(factors, exponents) + 1:
- return False
- for f in factors:
- q, control = divmod(p-1, f)
- if control != 0:
- return False
- if pow(r, q, p) == 1:
- return False
- return True
-
-
-# =================================================================
-# Constants and limits for the 64-bit version
-# =================================================================
-
-RADIX = 10**19
-
-# Primes P1, P2 and P3:
-P = [2**64-2**32+1, 2**64-2**34+1, 2**64-2**40+1]
-
-# P-1, highly composite. The transform length d is variable and
-# must divide D = P-1. Since all D are divisible by 3 * 2**32,
-# transform lengths can be 2**n or 3 * 2**n (where n <= 32).
-D = [2**32 * 3 * (5 * 17 * 257 * 65537),
- 2**34 * 3**2 * (7 * 11 * 31 * 151 * 331),
- 2**40 * 3**2 * (5 * 7 * 13 * 17 * 241)]
-
-# Prime factors of P-1 and their exponents:
-F = [(2,3,5,17,257,65537), (2,3,7,11,31,151,331), (2,3,5,7,13,17,241)]
-E = [(32,1,1,1,1,1), (34,2,1,1,1,1,1), (40,2,1,1,1,1,1)]
-
-# Maximum transform length for 2**n. Above that only 3 * 2**31
-# or 3 * 2**32 are possible.
-MPD_MAXTRANSFORM_2N = 2**32
-
-
-# Limits in the terminology of Pollard's paper:
-m2 = (MPD_MAXTRANSFORM_2N * 3) // 2 # Maximum length of the smaller array.
-M1 = M2 = RADIX-1 # Maximum value per single word.
-L = m2 * M1 * M2
-P[0] * P[1] * P[2] > 2 * L
-
-
-# Primitive roots of F(P1), F(P2) and F(P3):
-w = [7, 10, 19]
-
-# The primitive roots are correct:
-for i in range(3):
- if not is_primitive_root(w[i], P[i], F[i], E[i]):
- print("FAIL")
-
-
-# =================================================================
-# Constants and limits for the 32-bit version
-# =================================================================
-
-RADIX = 10**9
-
-# Primes P1, P2 and P3:
-P = [2113929217, 2013265921, 1811939329]
-
-# P-1, highly composite. All D = P-1 are divisible by 3 * 2**25,
-# allowing for transform lengths up to 3 * 2**25 words.
-D = [2**25 * 3**2 * 7,
- 2**27 * 3 * 5,
- 2**26 * 3**3]
-
-# Prime factors of P-1 and their exponents:
-F = [(2,3,7), (2,3,5), (2,3)]
-E = [(25,2,1), (27,1,1), (26,3)]
-
-# Maximum transform length for 2**n. Above that only 3 * 2**24 or
-# 3 * 2**25 are possible.
-MPD_MAXTRANSFORM_2N = 2**25
-
-
-# Limits in the terminology of Pollard's paper:
-m2 = (MPD_MAXTRANSFORM_2N * 3) // 2 # Maximum length of the smaller array.
-M1 = M2 = RADIX-1 # Maximum value per single word.
-L = m2 * M1 * M2
-P[0] * P[1] * P[2] > 2 * L
-
-
-# Primitive roots of F(P1), F(P2) and F(P3):
-w = [5, 31, 13]
-
-# The primitive roots are correct:
-for i in range(3):
- if not is_primitive_root(w[i], P[i], F[i], E[i]):
- print("FAIL")
-
-
-# ======================================================================
-# Example transform using a single prime
-# ======================================================================
-
-def ntt(lst, dir):
- """Perform a transform on the elements of lst. len(lst) must
- be 2**n or 3 * 2**n, where n <= 25. This is the slow DFT."""
- p = 2113929217 # prime
- d = len(lst) # transform length
- d_prime = pow(d, (p-2), p) # inverse of d
- xi = (p-1)//d
- w = 5 # primitive root of F(p)
- r = pow(w, xi, p) # primitive root of the subfield
- r_prime = pow(w, (p-1-xi), p) # inverse of r
- if dir == 1: # forward transform
- a = lst # input array
- A = [0] * d # transformed values
- for i in range(d):
- s = 0
- for j in range(d):
- s += a[j] * pow(r, i*j, p)
- A[i] = s % p
- return A
- elif dir == -1: # backward transform
- A = lst # input array
- a = [0] * d # transformed values
- for j in range(d):
- s = 0
- for i in range(d):
- s += A[i] * pow(r_prime, i*j, p)
- a[j] = (d_prime * s) % p
- return a
-
-def ntt_convolute(a, b):
- """convolute arrays a and b."""
- assert(len(a) == len(b))
- x = ntt(a, 1)
- y = ntt(b, 1)
- for i in range(len(a)):
- y[i] = y[i] * x[i]
- r = ntt(y, -1)
- return r
-
-
-# Example: Two arrays representing 21 and 81 in little-endian:
-a = [1, 2, 0, 0]
-b = [1, 8, 0, 0]
-
-assert(ntt_convolute(a, b) == [1, 10, 16, 0])
-assert(21 * 81 == (1*10**0 + 10*10**1 + 16*10**2 + 0*10**3))
+++ /dev/null
-
-
-(* Copyright (c) 2011-2020 Stefan Krah. All rights reserved. *)
-
-
-The Matrix Fourier Transform:
-=============================
-
-In libmpdec, the Matrix Fourier Transform [1] is called four-step transform
-after a variant that appears in [2]. The algorithm requires that the input
-array can be viewed as an R*C matrix.
-
-All operations are done modulo p. For readability, the proofs drop all
-instances of (mod p).
-
-
-Algorithm four-step (forward transform):
-----------------------------------------
-
- a := input array
- d := len(a) = R * C
- p := prime
- w := primitive root of unity of the prime field
- r := w**((p-1)/d)
- A := output array
-
- 1) Apply a length R FNT to each column.
-
- 2) Multiply each matrix element (addressed by j*C+m) by r**(j*m).
-
- 3) Apply a length C FNT to each row.
-
- 4) Transpose the matrix.
-
-
-Proof (forward transform):
---------------------------
-
- The algorithm can be derived starting from the regular definition of
- the finite-field transform of length d:
-
- d-1
- ,----
- \
- A[k] = | a[l] * r**(k * l)
- /
- `----
- l = 0
-
-
- The sum can be rearranged into the sum of the sums of columns:
-
- C-1 R-1
- ,---- ,----
- \ \
- = | | a[i * C + j] * r**(k * (i * C + j))
- / /
- `---- `----
- j = 0 i = 0
-
-
- Extracting a constant from the inner sum:
-
- C-1 R-1
- ,---- ,----
- \ \
- = | r**k*j * | a[i * C + j] * r**(k * i * C)
- / /
- `---- `----
- j = 0 i = 0
-
-
- Without any loss of generality, let k = n * R + m,
- where n < C and m < R:
-
- C-1 R-1
- ,---- ,----
- \ \
- A[n*R+m] = | r**(R*n*j) * r**(m*j) * | a[i*C+j] * r**(R*C*n*i) * r**(C*m*i)
- / /
- `---- `----
- j = 0 i = 0
-
-
- Since r = w ** ((p-1) / (R*C)):
-
- a) r**(R*C*n*i) = w**((p-1)*n*i) = 1
-
- b) r**(C*m*i) = w**((p-1) / R) ** (m*i) = r_R ** (m*i)
-
- c) r**(R*n*j) = w**((p-1) / C) ** (n*j) = r_C ** (n*j)
-
- r_R := root of the subfield of length R.
- r_C := root of the subfield of length C.
-
-
- C-1 R-1
- ,---- ,----
- \ \
- A[n*R+m] = | r_C**(n*j) * [ r**(m*j) * | a[i*C+j] * r_R**(m*i) ]
- / ^ /
- `---- | `---- 1) transform the columns
- j = 0 | i = 0
- ^ |
- | `-- 2) multiply
- |
- `-- 3) transform the rows
-
-
- Note that the entire RHS is a function of n and m and that the results
- for each pair (n, m) are stored in Fortran order.
-
- Let the term in square brackets be f(m, j). Step 1) and 2) precalculate
- the term for all (m, j). After that, the original matrix is now a lookup
- table with the mth element in the jth column at location m * C + j.
-
- Let the complete RHS be g(m, n). Step 3) does an in-place transform of
- length n on all rows. After that, the original matrix is now a lookup
- table with the mth element in the nth column at location m * C + n.
-
- But each (m, n) pair should be written to location n * R + m. Therefore,
- step 4) transposes the result of step 3).
-
-
-
-Algorithm four-step (inverse transform):
-----------------------------------------
-
- A := input array
- d := len(A) = R * C
- p := prime
- d' := d**(p-2) # inverse of d
- w := primitive root of unity of the prime field
- r := w**((p-1)/d) # root of the subfield
- r' := w**((p-1) - (p-1)/d) # inverse of r
- a := output array
-
- 0) View the matrix as a C*R matrix.
-
- 1) Transpose the matrix, producing an R*C matrix.
-
- 2) Apply a length C FNT to each row.
-
- 3) Multiply each matrix element (addressed by i*C+n) by r**(i*n).
-
- 4) Apply a length R FNT to each column.
-
-
-Proof (inverse transform):
---------------------------
-
- The algorithm can be derived starting from the regular definition of
- the finite-field inverse transform of length d:
-
- d-1
- ,----
- \
- a[k] = d' * | A[l] * r' ** (k * l)
- /
- `----
- l = 0
-
-
- The sum can be rearranged into the sum of the sums of columns. Note
- that at this stage we still have a C*R matrix, so C denotes the number
- of rows:
-
- R-1 C-1
- ,---- ,----
- \ \
- = d' * | | a[j * R + i] * r' ** (k * (j * R + i))
- / /
- `---- `----
- i = 0 j = 0
-
-
- Extracting a constant from the inner sum:
-
- R-1 C-1
- ,---- ,----
- \ \
- = d' * | r' ** (k*i) * | a[j * R + i] * r' ** (k * j * R)
- / /
- `---- `----
- i = 0 j = 0
-
-
- Without any loss of generality, let k = m * C + n,
- where m < R and n < C:
-
- R-1 C-1
- ,---- ,----
- \ \
- A[m*C+n] = d' * | r' ** (C*m*i) * r' ** (n*i) * | a[j*R+i] * r' ** (R*C*m*j) * r' ** (R*n*j)
- / /
- `---- `----
- i = 0 j = 0
-
-
- Since r' = w**((p-1) - (p-1)/d) and d = R*C:
-
- a) r' ** (R*C*m*j) = w**((p-1)*R*C*m*j - (p-1)*m*j) = 1
-
- b) r' ** (C*m*i) = w**((p-1)*C - (p-1)/R) ** (m*i) = r_R' ** (m*i)
-
- c) r' ** (R*n*j) = r_C' ** (n*j)
-
- d) d' = d**(p-2) = (R*C) ** (p-2) = R**(p-2) * C**(p-2) = R' * C'
-
- r_R' := inverse of the root of the subfield of length R.
- r_C' := inverse of the root of the subfield of length C.
- R' := inverse of R
- C' := inverse of C
-
-
- R-1 C-1
- ,---- ,---- 2) transform the rows of a^T
- \ \
- A[m*C+n] = R' * | r_R' ** (m*i) * [ r' ** (n*i) * C' * | a[j*R+i] * r_C' ** (n*j) ]
- / ^ / ^
- `---- | `---- |
- i = 0 | j = 0 |
- ^ | `-- 1) Transpose input matrix
- | `-- 3) multiply to address elements by
- | i * C + j
- `-- 3) transform the columns
-
-
-
- Note that the entire RHS is a function of m and n and that the results
- for each pair (m, n) are stored in C order.
-
- Let the term in square brackets be f(n, i). Without step 1), the sum
- would perform a length C transform on the columns of the input matrix.
- This is a) inefficient and b) the results are needed in C order, so
- step 1) exchanges rows and columns.
-
- Step 2) and 3) precalculate f(n, i) for all (n, i). After that, the
- original matrix is now a lookup table with the ith element in the nth
- column at location i * C + n.
-
- Let the complete RHS be g(m, n). Step 4) does an in-place transform of
- length m on all columns. After that, the original matrix is now a lookup
- table with the mth element in the nth column at location m * C + n,
- which means that all A[k] = A[m * C + n] are in the correct order.
-
-
---
-
- [1] Joerg Arndt: "Matters Computational"
- http://www.jjj.de/fxt/
- [2] David H. Bailey: FFTs in External or Hierarchical Memory
- http://crd.lbl.gov/~dhbailey/dhbpapers/
-
-
-
+++ /dev/null
-
-
-(* Copyright (c) 2011-2020 Stefan Krah. All rights reserved. *)
-
-
-==========================================================================
- Calculate (a * b) % p using special primes
-==========================================================================
-
-A description of the algorithm can be found in the apfloat manual by
-Tommila [1].
-
-
-Definitions:
-------------
-
-In the whole document, "==" stands for "is congruent with".
-
-Result of a * b in terms of high/low words:
-
- (1) hi * 2**64 + lo = a * b
-
-Special primes:
-
- (2) p = 2**64 - z + 1, where z = 2**n
-
-Single step modular reduction:
-
- (3) R(hi, lo) = hi * z - hi + lo
-
-
-Strategy:
----------
-
- a) Set (hi, lo) to the result of a * b.
-
- b) Set (hi', lo') to the result of R(hi, lo).
-
- c) Repeat step b) until 0 <= hi' * 2**64 + lo' < 2*p.
-
- d) If the result is less than p, return lo'. Otherwise return lo' - p.
-
-
-The reduction step b) preserves congruence:
--------------------------------------------
-
- hi * 2**64 + lo == hi * z - hi + lo (mod p)
-
- Proof:
- ~~~~~~
-
- hi * 2**64 + lo = (2**64 - z + 1) * hi + z * hi - hi + lo
-
- = p * hi + z * hi - hi + lo
-
- == z * hi - hi + lo (mod p)
-
-
-Maximum numbers of step b):
----------------------------
-
-# To avoid unnecessary formalism, define:
-
-def R(hi, lo, z):
- return divmod(hi * z - hi + lo, 2**64)
-
-# For simplicity, assume hi=2**64-1, lo=2**64-1 after the
-# initial multiplication a * b. This is of course impossible
-# but certainly covers all cases.
-
-# Then, for p1:
-hi=2**64-1; lo=2**64-1; z=2**32
-p1 = 2**64 - z + 1
-
-hi, lo = R(hi, lo, z) # First reduction
-hi, lo = R(hi, lo, z) # Second reduction
-hi * 2**64 + lo < 2 * p1 # True
-
-# For p2:
-hi=2**64-1; lo=2**64-1; z=2**34
-p2 = 2**64 - z + 1
-
-hi, lo = R(hi, lo, z) # First reduction
-hi, lo = R(hi, lo, z) # Second reduction
-hi, lo = R(hi, lo, z) # Third reduction
-hi * 2**64 + lo < 2 * p2 # True
-
-# For p3:
-hi=2**64-1; lo=2**64-1; z=2**40
-p3 = 2**64 - z + 1
-
-hi, lo = R(hi, lo, z) # First reduction
-hi, lo = R(hi, lo, z) # Second reduction
-hi, lo = R(hi, lo, z) # Third reduction
-hi * 2**64 + lo < 2 * p3 # True
-
-
-Step d) preserves congruence and yields a result < p:
------------------------------------------------------
-
- Case hi = 0:
-
- Case lo < p: trivial.
-
- Case lo >= p:
-
- lo == lo - p (mod p) # result is congruent
-
- p <= lo < 2*p -> 0 <= lo - p < p # result is in the correct range
-
- Case hi = 1:
-
- p < 2**64 /\ 2**64 + lo < 2*p -> lo < p # lo is always less than p
-
- 2**64 + lo == 2**64 + (lo - p) (mod p) # result is congruent
-
- = lo - p # exactly the same value as the previous RHS
- # in uint64_t arithmetic.
-
- p < 2**64 + lo < 2*p -> 0 < 2**64 + (lo - p) < p # correct range
-
-
-
-[1] http://www.apfloat.org/apfloat/2.40/apfloat.pdf
-
-
-
+++ /dev/null
-
-
-(* Copyright (c) 2011-2020 Stefan Krah. All rights reserved. *)
-
-
-========================================================================
- Calculate (a * b) % p using the 80-bit x87 FPU
-========================================================================
-
-A description of the algorithm can be found in the apfloat manual by
-Tommila [1].
-
-The proof follows an argument made by Granlund/Montgomery in [2].
-
-
-Definitions and assumptions:
-----------------------------
-
-The 80-bit extended precision format uses 64 bits for the significand:
-
- (1) F = 64
-
-The modulus is prime and less than 2**31:
-
- (2) 2 <= p < 2**31
-
-The factors are less than p:
-
- (3) 0 <= a < p
- (4) 0 <= b < p
-
-The product a * b is less than 2**62 and is thus exact in 64 bits:
-
- (5) n = a * b
-
-The product can be represented in terms of quotient and remainder:
-
- (6) n = q * p + r
-
-Using (3), (4) and the fact that p is prime, the remainder is always
-greater than zero:
-
- (7) 0 <= q < p /\ 1 <= r < p
-
-
-Strategy:
----------
-
-Precalculate the 80-bit long double inverse of p, with a maximum
-relative error of 2**(1-F):
-
- (8) pinv = (long double)1.0 / p
-
-Calculate an estimate for q = floor(n/p). The multiplication has another
-maximum relative error of 2**(1-F):
-
- (9) qest = n * pinv
-
-If we can show that q < qest < q+1, then trunc(qest) = q. It is then
-easy to recover the remainder r. The complete algorithm is:
-
- a) Set the control word to 64-bit precision and truncation mode.
-
- b) n = a * b # Calculate exact product.
-
- c) qest = n * pinv # Calculate estimate for the quotient.
-
- d) q = (qest+2**63)-2**63 # Truncate qest to the exact quotient.
-
- f) r = n - q * p # Calculate remainder.
-
-
-Proof for q < qest < q+1:
--------------------------
-
-Using the cumulative error, the error bounds for qest are:
-
- n n * (1 + 2**(1-F))**2
- (9) --------------------- <= qest <= ---------------------
- p * (1 + 2**(1-F))**2 p
-
-
- Lemma 1:
- --------
- n q * p + r
- (10) q < --------------------- = ---------------------
- p * (1 + 2**(1-F))**2 p * (1 + 2**(1-F))**2
-
-
- Proof:
- ~~~~~~
-
- (I) q * p * (1 + 2**(1-F))**2 < q * p + r
-
- (II) q * p * 2**(2-F) + q * p * 2**(2-2*F) < r
-
- Using (1) and (7), it is sufficient to show that:
-
- (III) q * p * 2**(-62) + q * p * 2**(-126) < 1 <= r
-
- (III) can easily be verified by substituting the largest possible
- values p = 2**31-1 and q = 2**31-2.
-
- The critical cases occur when r = 1, n = m * p + 1. These cases
- can be exhaustively verified with a test program.
-
-
- Lemma 2:
- --------
-
- n * (1 + 2**(1-F))**2 (q * p + r) * (1 + 2**(1-F))**2
- (11) --------------------- = ------------------------------- < q + 1
- p p
-
- Proof:
- ~~~~~~
-
- (I) (q * p + r) + (q * p + r) * 2**(2-F) + (q * p + r) * 2**(2-2*F) < q * p + p
-
- (II) (q * p + r) * 2**(2-F) + (q * p + r) * 2**(2-2*F) < p - r
-
- Using (1) and (7), it is sufficient to show that:
-
- (III) (q * p + r) * 2**(-62) + (q * p + r) * 2**(-126) < 1 <= p - r
-
- (III) can easily be verified by substituting the largest possible
- values p = 2**31-1, q = 2**31-2 and r = 2**31-2.
-
- The critical cases occur when r = (p - 1), n = m * p - 1. These cases
- can be exhaustively verified with a test program.
-
-
-[1] http://www.apfloat.org/apfloat/2.40/apfloat.pdf
-[2] http://gmplib.org/~tege/divcnst-pldi94.pdf
- [Section 7: "Use of floating point"]
-
-
-
-(* Coq proof for (10) and (11) *)
-
-Require Import ZArith.
-Require Import QArith.
-Require Import Qpower.
-Require Import Qabs.
-Require Import Psatz.
-
-Open Scope Q_scope.
-
-
-Ltac qreduce T :=
- rewrite <- (Qred_correct (T)); simpl (Qred (T)).
-
-Theorem Qlt_move_right :
- forall x y z:Q, x + z < y <-> x < y - z.
-Proof.
- intros.
- split.
- intros.
- psatzl Q.
- intros.
- psatzl Q.
-Qed.
-
-Theorem Qlt_mult_by_z :
- forall x y z:Q, 0 < z -> (x < y <-> x * z < y * z).
-Proof.
- intros.
- split.
- intros.
- apply Qmult_lt_compat_r. trivial. trivial.
- intros.
- rewrite <- (Qdiv_mult_l x z). rewrite <- (Qdiv_mult_l y z).
- apply Qmult_lt_compat_r.
- apply Qlt_shift_inv_l.
- trivial. psatzl Q. trivial. psatzl Q. psatzl Q.
-Qed.
-
-Theorem Qle_mult_quad :
- forall (a b c d:Q),
- 0 <= a -> a <= c ->
- 0 <= b -> b <= d ->
- a * b <= c * d.
- intros.
- psatz Q.
-Qed.
-
-
-Theorem q_lt_qest:
- forall (p q r:Q),
- (0 < p) -> (p <= (2#1)^31 - 1) ->
- (0 <= q) -> (q <= p - 1) ->
- (1 <= r) -> (r <= p - 1) ->
- q < (q * p + r) / (p * (1 + (2#1)^(-63))^2).
-Proof.
- intros.
- rewrite Qlt_mult_by_z with (z := (p * (1 + (2#1)^(-63))^2)).
-
- unfold Qdiv.
- rewrite <- Qmult_assoc.
- rewrite (Qmult_comm (/ (p * (1 + (2 # 1) ^ (-63)) ^ 2)) (p * (1 + (2 # 1) ^ (-63)) ^ 2)).
- rewrite Qmult_inv_r.
- rewrite Qmult_1_r.
-
- assert (q * (p * (1 + (2 # 1) ^ (-63)) ^ 2) == q * p + (q * p) * ((2 # 1) ^ (-62) + (2 # 1) ^ (-126))).
- qreduce ((1 + (2 # 1) ^ (-63)) ^ 2).
- qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)).
- ring_simplify.
- reflexivity.
- rewrite H5.
-
- rewrite Qplus_comm.
- rewrite Qlt_move_right.
- ring_simplify (q * p + r - q * p).
- qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)).
-
- apply Qlt_le_trans with (y := 1).
- rewrite Qlt_mult_by_z with (z := 85070591730234615865843651857942052864 # 18446744073709551617).
- ring_simplify.
-
- apply Qle_lt_trans with (y := ((2 # 1) ^ 31 - (2#1)) * ((2 # 1) ^ 31 - 1)).
- apply Qle_mult_quad.
- assumption. psatzl Q. psatzl Q. psatzl Q. psatzl Q. psatzl Q. assumption. psatzl Q. psatzl Q.
-Qed.
-
-Theorem qest_lt_qplus1:
- forall (p q r:Q),
- (0 < p) -> (p <= (2#1)^31 - 1) ->
- (0 <= q) -> (q <= p - 1) ->
- (1 <= r) -> (r <= p - 1) ->
- ((q * p + r) * (1 + (2#1)^(-63))^2) / p < q + 1.
-Proof.
- intros.
- rewrite Qlt_mult_by_z with (z := p).
-
- unfold Qdiv.
- rewrite <- Qmult_assoc.
- rewrite (Qmult_comm (/ p) p).
- rewrite Qmult_inv_r.
- rewrite Qmult_1_r.
-
- assert ((q * p + r) * (1 + (2 # 1) ^ (-63)) ^ 2 == q * p + r + (q * p + r) * ((2 # 1) ^ (-62) + (2 # 1) ^ (-126))).
- qreduce ((1 + (2 # 1) ^ (-63)) ^ 2).
- qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)).
- ring_simplify. reflexivity.
- rewrite H5.
-
- rewrite <- Qplus_assoc. rewrite <- Qplus_comm. rewrite Qlt_move_right.
- ring_simplify ((q + 1) * p - q * p).
-
- rewrite <- Qplus_comm. rewrite Qlt_move_right.
-
- apply Qlt_le_trans with (y := 1).
- qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)).
-
- rewrite Qlt_mult_by_z with (z := 85070591730234615865843651857942052864 # 18446744073709551617).
- ring_simplify.
-
- ring_simplify in H0.
- apply Qle_lt_trans with (y := (2147483646 # 1) * (2147483647 # 1) + (2147483646 # 1)).
-
- apply Qplus_le_compat.
- apply Qle_mult_quad.
- assumption. psatzl Q. auto with qarith. assumption. psatzl Q.
- auto with qarith. auto with qarith.
- psatzl Q. psatzl Q. assumption.
-Qed.
-
-
-
+++ /dev/null
-
-
-(* Copyright (c) 2011-2020 Stefan Krah. All rights reserved. *)
-
-
-The Six Step Transform:
-=======================
-
-In libmpdec, the six-step transform is the Matrix Fourier Transform (See
-matrix-transform.txt) in disguise. It is called six-step transform after
-a variant that appears in [1]. The algorithm requires that the input
-array can be viewed as an R*C matrix.
-
-
-Algorithm six-step (forward transform):
----------------------------------------
-
- 1a) Transpose the matrix.
-
- 1b) Apply a length R FNT to each row.
-
- 1c) Transpose the matrix.
-
- 2) Multiply each matrix element (addressed by j*C+m) by r**(j*m).
-
- 3) Apply a length C FNT to each row.
-
- 4) Transpose the matrix.
-
-Note that steps 1a) - 1c) are exactly equivalent to step 1) of the Matrix
-Fourier Transform. For large R, it is faster to transpose twice and do
-a transform on the rows than to perform a column transpose directly.
-
-
-
-Algorithm six-step (inverse transform):
----------------------------------------
-
- 0) View the matrix as a C*R matrix.
-
- 1) Transpose the matrix, producing an R*C matrix.
-
- 2) Apply a length C FNT to each row.
-
- 3) Multiply each matrix element (addressed by i*C+n) by r**(i*n).
-
- 4a) Transpose the matrix.
-
- 4b) Apply a length R FNT to each row.
-
- 4c) Transpose the matrix.
-
-Again, steps 4a) - 4c) are equivalent to step 4) of the Matrix Fourier
-Transform.
-
-
-
---
-
- [1] David H. Bailey: FFTs in External or Hierarchical Memory
- http://crd.lbl.gov/~dhbailey/dhbpapers/
-
-
+++ /dev/null
-;
-; Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
-;
-; Redistribution and use in source and binary forms, with or without
-; modification, are permitted provided that the following conditions
-; are met:
-;
-; 1. Redistributions of source code must retain the above copyright
-; notice, this list of conditions and the following disclaimer.
-;
-; 2. Redistributions in binary form must reproduce the above copyright
-; notice, this list of conditions and the following disclaimer in the
-; documentation and/or other materials provided with the distribution.
-;
-; THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
-; ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
-; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
-; ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
-; FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
-; DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
-; OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
-; HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
-; LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
-; OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
-; SUCH DAMAGE.
-;
-
-
-(in-package "ACL2")
-
-(include-book "arithmetic/top-with-meta" :dir :system)
-(include-book "arithmetic-2/floor-mod/floor-mod" :dir :system)
-
-
-;; =====================================================================
-;; Proofs for several functions in umodarith.h
-;; =====================================================================
-
-
-
-;; =====================================================================
-;; Helper theorems
-;; =====================================================================
-
-(defthm elim-mod-m<x<2*m
- (implies (and (<= m x)
- (< x (* 2 m))
- (rationalp x) (rationalp m))
- (equal (mod x m)
- (+ x (- m)))))
-
-(defthm modaux-1a
- (implies (and (< x m) (< 0 x) (< 0 m)
- (rationalp x) (rationalp m))
- (equal (mod (- x) m)
- (+ (- x) m))))
-
-(defthm modaux-1b
- (implies (and (< (- x) m) (< x 0) (< 0 m)
- (rationalp x) (rationalp m))
- (equal (mod x m)
- (+ x m)))
- :hints (("Goal" :use ((:instance modaux-1a
- (x (- x)))))))
-
-(defthm modaux-1c
- (implies (and (< x m) (< 0 x) (< 0 m)
- (rationalp x) (rationalp m))
- (equal (mod x m)
- x)))
-
-(defthm modaux-2a
- (implies (and (< 0 b) (< b m)
- (natp x) (natp b) (natp m)
- (< (mod (+ b x) m) b))
- (equal (mod (+ (- m) b x) m)
- (+ (- m) b (mod x m)))))
-
-(defthm modaux-2b
- (implies (and (< 0 b) (< b m)
- (natp x) (natp b) (natp m)
- (< (mod (+ b x) m) b))
- (equal (mod (+ b x) m)
- (+ (- m) b (mod x m))))
- :hints (("Goal" :use (modaux-2a))))
-
-(defthm linear-mod-1
- (implies (and (< x m) (< b m)
- (natp x) (natp b)
- (rationalp m))
- (equal (< x (mod (+ (- b) x) m))
- (< x b)))
- :hints (("Goal" :use ((:instance modaux-1a
- (x (+ b (- x))))))))
-
-(defthm linear-mod-2
- (implies (and (< 0 b) (< b m)
- (natp x) (natp b)
- (natp m))
- (equal (< (mod x m)
- (mod (+ (- b) x) m))
- (< (mod x m) b))))
-
-(defthm linear-mod-3
- (implies (and (< x m) (< b m)
- (natp x) (natp b)
- (rationalp m))
- (equal (<= b (mod (+ b x) m))
- (< (+ b x) m)))
- :hints (("Goal" :use ((:instance elim-mod-m<x<2*m
- (x (+ b x)))))))
-
-(defthm modaux-2c
- (implies (and (< 0 b) (< b m)
- (natp x) (natp b) (natp m)
- (<= b (mod (+ b x) m)))
- (equal (mod (+ b x) m)
- (+ b (mod x m))))
- :hints (("Subgoal *1/8''" :use (linear-mod-3))))
-
-(defthmd modaux-2d
- (implies (and (< x m) (< 0 x) (< 0 m)
- (< (- m) b) (< b 0) (rationalp m)
- (<= x (mod (+ b x) m))
- (rationalp x) (rationalp b))
- (equal (+ (- m) (mod (+ b x) m))
- (+ b x)))
- :hints (("Goal" :cases ((<= 0 (+ b x))))
- ("Subgoal 2'" :use ((:instance modaux-1b
- (x (+ b x)))))))
-
-(defthm mod-m-b
- (implies (and (< 0 x) (< 0 b) (< 0 m)
- (< x b) (< b m)
- (natp x) (natp b) (natp m))
- (equal (mod (+ (mod (- x) m) b) m)
- (mod (- x) b))))
-
-
-;; =====================================================================
-;; addmod, submod
-;; =====================================================================
-
-(defun addmod (a b m base)
- (let* ((s (mod (+ a b) base))
- (s (if (< s a) (mod (- s m) base) s))
- (s (if (>= s m) (mod (- s m) base) s)))
- s))
-
-(defthmd addmod-correct
- (implies (and (< 0 m) (< m base)
- (< a m) (<= b m)
- (natp m) (natp base)
- (natp a) (natp b))
- (equal (addmod a b m base)
- (mod (+ a b) m)))
- :hints (("Goal" :cases ((<= base (+ a b))))
- ("Subgoal 2.1'" :use ((:instance elim-mod-m<x<2*m
- (x (+ a b)))))))
-
-(defun submod (a b m base)
- (let* ((d (mod (- a b) base))
- (d (if (< a d) (mod (+ d m) base) d)))
- d))
-
-(defthmd submod-aux1
- (implies (and (< a (mod (+ a (- b)) base))
- (< 0 base) (< a base) (<= b base)
- (natp base) (natp a) (natp b))
- (< a b))
- :rule-classes :forward-chaining)
-
-(defthmd submod-aux2
- (implies (and (<= (mod (+ a (- b)) base) a)
- (< 0 base) (< a base) (< b base)
- (natp base) (natp a) (natp b))
- (<= b a))
- :rule-classes :forward-chaining)
-
-(defthmd submod-correct
- (implies (and (< 0 m) (< m base)
- (< a m) (<= b m)
- (natp m) (natp base)
- (natp a) (natp b))
- (equal (submod a b m base)
- (mod (- a b) m)))
- :hints (("Goal" :cases ((<= base (+ a b))))
- ("Subgoal 2.2" :use ((:instance submod-aux1)))
- ("Subgoal 2.2'''" :cases ((and (< 0 (+ a (- b) m))
- (< (+ a (- b) m) m))))
- ("Subgoal 2.1" :use ((:instance submod-aux2)))
- ("Subgoal 1.2" :use ((:instance submod-aux1)))
- ("Subgoal 1.1" :use ((:instance submod-aux2)))))
-
-
-(defun submod-2 (a b m base)
- (let* ((d (mod (- a b) base))
- (d (if (< a b) (mod (+ d m) base) d)))
- d))
-
-(defthm submod-2-correct
- (implies (and (< 0 m) (< m base)
- (< a m) (<= b m)
- (natp m) (natp base)
- (natp a) (natp b))
- (equal (submod-2 a b m base)
- (mod (- a b) m)))
- :hints (("Subgoal 2'" :cases ((and (< 0 (+ a (- b) m))
- (< (+ a (- b) m) m))))))
-
-
-;; =========================================================================
-;; ext-submod is correct
-;; =========================================================================
-
-; a < 2*m, b < 2*m
-(defun ext-submod (a b m base)
- (let* ((a (if (>= a m) (- a m) a))
- (b (if (>= b m) (- b m) b))
- (d (mod (- a b) base))
- (d (if (< a b) (mod (+ d m) base) d)))
- d))
-
-; a < 2*m, b < 2*m
-(defun ext-submod-2 (a b m base)
- (let* ((a (mod a m))
- (b (mod b m))
- (d (mod (- a b) base))
- (d (if (< a b) (mod (+ d m) base) d)))
- d))
-
-(defthmd ext-submod-ext-submod-2-equal
- (implies (and (< 0 m) (< m base)
- (< a (* 2 m)) (< b (* 2 m))
- (natp m) (natp base)
- (natp a) (natp b))
- (equal (ext-submod a b m base)
- (ext-submod-2 a b m base))))
-
-(defthmd ext-submod-2-correct
- (implies (and (< 0 m) (< m base)
- (< a (* 2 m)) (< b (* 2 m))
- (natp m) (natp base)
- (natp a) (natp b))
- (equal (ext-submod-2 a b m base)
- (mod (- a b) m))))
-
-
-;; =========================================================================
-;; dw-reduce is correct
-;; =========================================================================
-
-(defun dw-reduce (hi lo m base)
- (let* ((r1 (mod hi m))
- (r2 (mod (+ (* r1 base) lo) m)))
- r2))
-
-(defthmd dw-reduce-correct
- (implies (and (< 0 m) (< m base)
- (< hi base) (< lo base)
- (natp m) (natp base)
- (natp hi) (natp lo))
- (equal (dw-reduce hi lo m base)
- (mod (+ (* hi base) lo) m))))
-
-(defthmd <=-multiply-both-sides-by-z
- (implies (and (rationalp x) (rationalp y)
- (< 0 z) (rationalp z))
- (equal (<= x y)
- (<= (* z x) (* z y)))))
-
-(defthmd dw-reduce-aux1
- (implies (and (< 0 m) (< m base)
- (natp m) (natp base)
- (< lo base) (natp lo)
- (< x m) (natp x))
- (< (+ lo (* base x)) (* base m)))
- :hints (("Goal" :cases ((<= (+ x 1) m)))
- ("Subgoal 1''" :cases ((<= (* base (+ x 1)) (* base m))))
- ("subgoal 1.2" :use ((:instance <=-multiply-both-sides-by-z
- (x (+ 1 x))
- (y m)
- (z base))))))
-
-(defthm dw-reduce-aux2
- (implies (and (< x (* base m))
- (< 0 m) (< m base)
- (natp m) (natp base) (natp x))
- (< (floor x m) base)))
-
-;; This is the necessary condition for using _mpd_div_words().
-(defthmd dw-reduce-second-quotient-fits-in-single-word
- (implies (and (< 0 m) (< m base)
- (< hi base) (< lo base)
- (natp m) (natp base)
- (natp hi) (natp lo)
- (equal r1 (mod hi m)))
- (< (floor (+ (* r1 base) lo) m)
- base))
- :hints (("Goal" :cases ((< r1 m)))
- ("Subgoal 1''" :cases ((< (+ lo (* base (mod hi m))) (* base m))))
- ("Subgoal 1.2" :use ((:instance dw-reduce-aux1
- (x (mod hi m)))))))
-
-
-;; =========================================================================
-;; dw-submod is correct
-;; =========================================================================
-
-(defun dw-submod (a hi lo m base)
- (let* ((r (dw-reduce hi lo m base))
- (d (mod (- a r) base))
- (d (if (< a r) (mod (+ d m) base) d)))
- d))
-
-(defthmd dw-submod-aux1
- (implies (and (natp a) (< 0 m) (natp m)
- (natp x) (equal r (mod x m)))
- (equal (mod (- a x) m)
- (mod (- a r) m))))
-
-(defthmd dw-submod-correct
- (implies (and (< 0 m) (< m base)
- (natp a) (< a m)
- (< hi base) (< lo base)
- (natp m) (natp base)
- (natp hi) (natp lo))
- (equal (dw-submod a hi lo m base)
- (mod (- a (+ (* base hi) lo)) m)))
- :hints (("Goal" :in-theory (disable dw-reduce)
- :use ((:instance dw-submod-aux1
- (x (+ lo (* base hi)))
- (r (dw-reduce hi lo m base)))
- (:instance dw-reduce-correct)))))
-
-
-;; =========================================================================
-;; ANSI C arithmetic for uint64_t
-;; =========================================================================
-
-(defun add (a b)
- (mod (+ a b)
- (expt 2 64)))
-
-(defun sub (a b)
- (mod (- a b)
- (expt 2 64)))
-
-(defun << (w n)
- (mod (* w (expt 2 n))
- (expt 2 64)))
-
-(defun >> (w n)
- (floor w (expt 2 n)))
-
-;; join upper and lower half of a double word, yielding a 128 bit number
-(defun join (hi lo)
- (+ (* (expt 2 64) hi) lo))
-
-
-;; =============================================================================
-;; Fast modular reduction
-;; =============================================================================
-
-;; These are the three primes used in the Number Theoretic Transform.
-;; A fast modular reduction scheme exists for all of them.
-(defmacro p1 ()
- (+ (expt 2 64) (- (expt 2 32)) 1))
-
-(defmacro p2 ()
- (+ (expt 2 64) (- (expt 2 34)) 1))
-
-(defmacro p3 ()
- (+ (expt 2 64) (- (expt 2 40)) 1))
-
-
-;; reduce the double word number hi*2**64 + lo (mod p1)
-(defun simple-mod-reduce-p1 (hi lo)
- (+ (* (expt 2 32) hi) (- hi) lo))
-
-;; reduce the double word number hi*2**64 + lo (mod p2)
-(defun simple-mod-reduce-p2 (hi lo)
- (+ (* (expt 2 34) hi) (- hi) lo))
-
-;; reduce the double word number hi*2**64 + lo (mod p3)
-(defun simple-mod-reduce-p3 (hi lo)
- (+ (* (expt 2 40) hi) (- hi) lo))
-
-
-; ----------------------------------------------------------
-; The modular reductions given above are correct
-; ----------------------------------------------------------
-
-(defthmd congruence-p1-aux
- (equal (* (expt 2 64) hi)
- (+ (* (p1) hi)
- (* (expt 2 32) hi)
- (- hi))))
-
-(defthmd congruence-p2-aux
- (equal (* (expt 2 64) hi)
- (+ (* (p2) hi)
- (* (expt 2 34) hi)
- (- hi))))
-
-(defthmd congruence-p3-aux
- (equal (* (expt 2 64) hi)
- (+ (* (p3) hi)
- (* (expt 2 40) hi)
- (- hi))))
-
-(defthmd mod-augment
- (implies (and (rationalp x)
- (rationalp y)
- (rationalp m))
- (equal (mod (+ x y) m)
- (mod (+ x (mod y m)) m))))
-
-(defthmd simple-mod-reduce-p1-congruent
- (implies (and (integerp hi)
- (integerp lo))
- (equal (mod (simple-mod-reduce-p1 hi lo) (p1))
- (mod (join hi lo) (p1))))
- :hints (("Goal''" :use ((:instance congruence-p1-aux)
- (:instance mod-augment
- (m (p1))
- (x (+ (- hi) lo (* (expt 2 32) hi)))
- (y (* (p1) hi)))))))
-
-(defthmd simple-mod-reduce-p2-congruent
- (implies (and (integerp hi)
- (integerp lo))
- (equal (mod (simple-mod-reduce-p2 hi lo) (p2))
- (mod (join hi lo) (p2))))
- :hints (("Goal''" :use ((:instance congruence-p2-aux)
- (:instance mod-augment
- (m (p2))
- (x (+ (- hi) lo (* (expt 2 34) hi)))
- (y (* (p2) hi)))))))
-
-(defthmd simple-mod-reduce-p3-congruent
- (implies (and (integerp hi)
- (integerp lo))
- (equal (mod (simple-mod-reduce-p3 hi lo) (p3))
- (mod (join hi lo) (p3))))
- :hints (("Goal''" :use ((:instance congruence-p3-aux)
- (:instance mod-augment
- (m (p3))
- (x (+ (- hi) lo (* (expt 2 40) hi)))
- (y (* (p3) hi)))))))
-
-
-; ---------------------------------------------------------------------
-; We need a number less than 2*p, so that we can use the trick from
-; elim-mod-m<x<2*m for the final reduction.
-; For p1, two modular reductions are sufficient, for p2 and p3 three.
-; ---------------------------------------------------------------------
-
-;; p1: the first reduction is less than 2**96
-(defthmd simple-mod-reduce-p1-<-2**96
- (implies (and (< hi (expt 2 64))
- (< lo (expt 2 64))
- (natp hi) (natp lo))
- (< (simple-mod-reduce-p1 hi lo)
- (expt 2 96))))
-
-;; p1: the second reduction is less than 2*p1
-(defthmd simple-mod-reduce-p1-<-2*p1
- (implies (and (< hi (expt 2 64))
- (< lo (expt 2 64))
- (< (join hi lo) (expt 2 96))
- (natp hi) (natp lo))
- (< (simple-mod-reduce-p1 hi lo)
- (* 2 (p1)))))
-
-
-;; p2: the first reduction is less than 2**98
-(defthmd simple-mod-reduce-p2-<-2**98
- (implies (and (< hi (expt 2 64))
- (< lo (expt 2 64))
- (natp hi) (natp lo))
- (< (simple-mod-reduce-p2 hi lo)
- (expt 2 98))))
-
-;; p2: the second reduction is less than 2**69
-(defthmd simple-mod-reduce-p2-<-2*69
- (implies (and (< hi (expt 2 64))
- (< lo (expt 2 64))
- (< (join hi lo) (expt 2 98))
- (natp hi) (natp lo))
- (< (simple-mod-reduce-p2 hi lo)
- (expt 2 69))))
-
-;; p3: the third reduction is less than 2*p2
-(defthmd simple-mod-reduce-p2-<-2*p2
- (implies (and (< hi (expt 2 64))
- (< lo (expt 2 64))
- (< (join hi lo) (expt 2 69))
- (natp hi) (natp lo))
- (< (simple-mod-reduce-p2 hi lo)
- (* 2 (p2)))))
-
-
-;; p3: the first reduction is less than 2**104
-(defthmd simple-mod-reduce-p3-<-2**104
- (implies (and (< hi (expt 2 64))
- (< lo (expt 2 64))
- (natp hi) (natp lo))
- (< (simple-mod-reduce-p3 hi lo)
- (expt 2 104))))
-
-;; p3: the second reduction is less than 2**81
-(defthmd simple-mod-reduce-p3-<-2**81
- (implies (and (< hi (expt 2 64))
- (< lo (expt 2 64))
- (< (join hi lo) (expt 2 104))
- (natp hi) (natp lo))
- (< (simple-mod-reduce-p3 hi lo)
- (expt 2 81))))
-
-;; p3: the third reduction is less than 2*p3
-(defthmd simple-mod-reduce-p3-<-2*p3
- (implies (and (< hi (expt 2 64))
- (< lo (expt 2 64))
- (< (join hi lo) (expt 2 81))
- (natp hi) (natp lo))
- (< (simple-mod-reduce-p3 hi lo)
- (* 2 (p3)))))
-
-
-; -------------------------------------------------------------------------
-; The simple modular reductions, adapted for compiler friendly C
-; -------------------------------------------------------------------------
-
-(defun mod-reduce-p1 (hi lo)
- (let* ((y hi)
- (x y)
- (hi (>> hi 32))
- (x (sub lo x))
- (hi (if (> x lo) (+ hi -1) hi))
- (y (<< y 32))
- (lo (add y x))
- (hi (if (< lo y) (+ hi 1) hi)))
- (+ (* hi (expt 2 64)) lo)))
-
-(defun mod-reduce-p2 (hi lo)
- (let* ((y hi)
- (x y)
- (hi (>> hi 30))
- (x (sub lo x))
- (hi (if (> x lo) (+ hi -1) hi))
- (y (<< y 34))
- (lo (add y x))
- (hi (if (< lo y) (+ hi 1) hi)))
- (+ (* hi (expt 2 64)) lo)))
-
-(defun mod-reduce-p3 (hi lo)
- (let* ((y hi)
- (x y)
- (hi (>> hi 24))
- (x (sub lo x))
- (hi (if (> x lo) (+ hi -1) hi))
- (y (<< y 40))
- (lo (add y x))
- (hi (if (< lo y) (+ hi 1) hi)))
- (+ (* hi (expt 2 64)) lo)))
-
-
-; -------------------------------------------------------------------------
-; The compiler friendly versions are equal to the simple versions
-; -------------------------------------------------------------------------
-
-(defthm mod-reduce-aux1
- (implies (and (<= 0 a) (natp a) (natp m)
- (< (- m) b) (<= b 0)
- (integerp b)
- (< (mod (+ b a) m)
- (mod a m)))
- (equal (mod (+ b a) m)
- (+ b (mod a m))))
- :hints (("Subgoal 2" :use ((:instance modaux-1b
- (x (+ a b)))))))
-
-(defthm mod-reduce-aux2
- (implies (and (<= 0 a) (natp a) (natp m)
- (< b m) (natp b)
- (< (mod (+ b a) m)
- (mod a m)))
- (equal (+ m (mod (+ b a) m))
- (+ b (mod a m)))))
-
-
-(defthm mod-reduce-aux3
- (implies (and (< 0 a) (natp a) (natp m)
- (< (- m) b) (< b 0)
- (integerp b)
- (<= (mod a m)
- (mod (+ b a) m)))
- (equal (+ (- m) (mod (+ b a) m))
- (+ b (mod a m))))
- :hints (("Subgoal 1.2'" :use ((:instance modaux-1b
- (x b))))
- ("Subgoal 1''" :use ((:instance modaux-2d
- (x I))))))
-
-
-(defthm mod-reduce-aux4
- (implies (and (< 0 a) (natp a) (natp m)
- (< b m) (natp b)
- (<= (mod a m)
- (mod (+ b a) m)))
- (equal (mod (+ b a) m)
- (+ b (mod a m)))))
-
-
-(defthm mod-reduce-p1==simple-mod-reduce-p1
- (implies (and (< hi (expt 2 64))
- (< lo (expt 2 64))
- (natp hi) (natp lo))
- (equal (mod-reduce-p1 hi lo)
- (simple-mod-reduce-p1 hi lo)))
- :hints (("Goal" :in-theory (disable expt)
- :cases ((< 0 hi)))
- ("Subgoal 1.2.2'" :use ((:instance mod-reduce-aux1
- (m (expt 2 64))
- (b (+ (- HI) LO))
- (a (* (expt 2 32) hi)))))
- ("Subgoal 1.2.1'" :use ((:instance mod-reduce-aux3
- (m (expt 2 64))
- (b (+ (- HI) LO))
- (a (* (expt 2 32) hi)))))
- ("Subgoal 1.1.2'" :use ((:instance mod-reduce-aux2
- (m (expt 2 64))
- (b (+ (- HI) LO))
- (a (* (expt 2 32) hi)))))
- ("Subgoal 1.1.1'" :use ((:instance mod-reduce-aux4
- (m (expt 2 64))
- (b (+ (- HI) LO))
- (a (* (expt 2 32) hi)))))))
-
-
-(defthm mod-reduce-p2==simple-mod-reduce-p2
- (implies (and (< hi (expt 2 64))
- (< lo (expt 2 64))
- (natp hi) (natp lo))
- (equal (mod-reduce-p2 hi lo)
- (simple-mod-reduce-p2 hi lo)))
- :hints (("Goal" :cases ((< 0 hi)))
- ("Subgoal 1.2.2'" :use ((:instance mod-reduce-aux1
- (m (expt 2 64))
- (b (+ (- HI) LO))
- (a (* (expt 2 34) hi)))))
- ("Subgoal 1.2.1'" :use ((:instance mod-reduce-aux3
- (m (expt 2 64))
- (b (+ (- HI) LO))
- (a (* (expt 2 34) hi)))))
- ("Subgoal 1.1.2'" :use ((:instance mod-reduce-aux2
- (m (expt 2 64))
- (b (+ (- HI) LO))
- (a (* (expt 2 34) hi)))))
- ("Subgoal 1.1.1'" :use ((:instance mod-reduce-aux4
- (m (expt 2 64))
- (b (+ (- HI) LO))
- (a (* (expt 2 34) hi)))))))
-
-
-(defthm mod-reduce-p3==simple-mod-reduce-p3
- (implies (and (< hi (expt 2 64))
- (< lo (expt 2 64))
- (natp hi) (natp lo))
- (equal (mod-reduce-p3 hi lo)
- (simple-mod-reduce-p3 hi lo)))
- :hints (("Goal" :cases ((< 0 hi)))
- ("Subgoal 1.2.2'" :use ((:instance mod-reduce-aux1
- (m (expt 2 64))
- (b (+ (- HI) LO))
- (a (* (expt 2 40) hi)))))
- ("Subgoal 1.2.1'" :use ((:instance mod-reduce-aux3
- (m (expt 2 64))
- (b (+ (- HI) LO))
- (a (* (expt 2 40) hi)))))
- ("Subgoal 1.1.2'" :use ((:instance mod-reduce-aux2
- (m (expt 2 64))
- (b (+ (- HI) LO))
- (a (* (expt 2 40) hi)))))
- ("Subgoal 1.1.1'" :use ((:instance mod-reduce-aux4
- (m (expt 2 64))
- (b (+ (- HI) LO))
- (a (* (expt 2 40) hi)))))))
-
-
-
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <assert.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-
-#include "mpalloc.h"
-#include "typearith.h"
-
-
-#if defined(_MSC_VER)
- #pragma warning(disable : 4232)
-#endif
-
-
-/* Guaranteed minimum allocation for a coefficient. May be changed once
- at program start using mpd_setminalloc(). */
-mpd_ssize_t MPD_MINALLOC = MPD_MINALLOC_MIN;
-
-/* Custom allocation and free functions */
-void *(* mpd_mallocfunc)(size_t size) = malloc;
-void *(* mpd_reallocfunc)(void *ptr, size_t size) = realloc;
-void *(* mpd_callocfunc)(size_t nmemb, size_t size) = calloc;
-void (* mpd_free)(void *ptr) = free;
-
-
-/* emulate calloc if it is not available */
-void *
-mpd_callocfunc_em(size_t nmemb, size_t size)
-{
- void *ptr;
- size_t req;
- mpd_size_t overflow;
-
- req = mul_size_t_overflow((mpd_size_t)nmemb, (mpd_size_t)size,
- &overflow);
- if (overflow) {
- return NULL;
- }
-
- ptr = mpd_mallocfunc(req);
- if (ptr == NULL) {
- return NULL;
- }
- /* used on uint32_t or uint64_t */
- memset(ptr, 0, req);
-
- return ptr;
-}
-
-
-/* malloc with overflow checking */
-void *
-mpd_alloc(mpd_size_t nmemb, mpd_size_t size)
-{
- mpd_size_t req, overflow;
-
- req = mul_size_t_overflow(nmemb, size, &overflow);
- if (overflow) {
- return NULL;
- }
-
- return mpd_mallocfunc(req);
-}
-
-/* calloc with overflow checking */
-void *
-mpd_calloc(mpd_size_t nmemb, mpd_size_t size)
-{
- mpd_size_t overflow;
-
- (void)mul_size_t_overflow(nmemb, size, &overflow);
- if (overflow) {
- return NULL;
- }
-
- return mpd_callocfunc(nmemb, size);
-}
-
-/* realloc with overflow checking */
-void *
-mpd_realloc(void *ptr, mpd_size_t nmemb, mpd_size_t size, uint8_t *err)
-{
- void *new;
- mpd_size_t req, overflow;
-
- req = mul_size_t_overflow(nmemb, size, &overflow);
- if (overflow) {
- *err = 1;
- return ptr;
- }
-
- new = mpd_reallocfunc(ptr, req);
- if (new == NULL) {
- *err = 1;
- return ptr;
- }
-
- return new;
-}
-
-/* struct hack malloc with overflow checking */
-void *
-mpd_sh_alloc(mpd_size_t struct_size, mpd_size_t nmemb, mpd_size_t size)
-{
- mpd_size_t req, overflow;
-
- req = mul_size_t_overflow(nmemb, size, &overflow);
- if (overflow) {
- return NULL;
- }
-
- req = add_size_t_overflow(req, struct_size, &overflow);
- if (overflow) {
- return NULL;
- }
-
- return mpd_mallocfunc(req);
-}
-
-
-/* Allocate a new decimal with a coefficient of length 'nwords'. In case
- of an error the return value is NULL. */
-mpd_t *
-mpd_qnew_size(mpd_ssize_t nwords)
-{
- mpd_t *result;
-
- nwords = (nwords < MPD_MINALLOC) ? MPD_MINALLOC : nwords;
-
- result = mpd_alloc(1, sizeof *result);
- if (result == NULL) {
- return NULL;
- }
-
- result->data = mpd_alloc(nwords, sizeof *result->data);
- if (result->data == NULL) {
- mpd_free(result);
- return NULL;
- }
-
- result->flags = 0;
- result->exp = 0;
- result->digits = 0;
- result->len = 0;
- result->alloc = nwords;
-
- return result;
-}
-
-/* Allocate a new decimal with a coefficient of length MPD_MINALLOC.
- In case of an error the return value is NULL. */
-mpd_t *
-mpd_qnew(void)
-{
- return mpd_qnew_size(MPD_MINALLOC);
-}
-
-/* Allocate new decimal. Caller can check for NULL or MPD_Malloc_error.
- Raises on error. */
-mpd_t *
-mpd_new(mpd_context_t *ctx)
-{
- mpd_t *result;
-
- result = mpd_qnew();
- if (result == NULL) {
- mpd_addstatus_raise(ctx, MPD_Malloc_error);
- }
- return result;
-}
-
-/*
- * Input: 'result' is a static mpd_t with a static coefficient.
- * Assumption: 'nwords' >= result->alloc.
- *
- * Resize the static coefficient to a larger dynamic one and copy the
- * existing data. If successful, the value of 'result' is unchanged.
- * Otherwise, set 'result' to NaN and update 'status' with MPD_Malloc_error.
- */
-int
-mpd_switch_to_dyn(mpd_t *result, mpd_ssize_t nwords, uint32_t *status)
-{
- mpd_uint_t *p = result->data;
-
- assert(nwords >= result->alloc);
-
- result->data = mpd_alloc(nwords, sizeof *result->data);
- if (result->data == NULL) {
- result->data = p;
- mpd_set_qnan(result);
- mpd_set_positive(result);
- result->exp = result->digits = result->len = 0;
- *status |= MPD_Malloc_error;
- return 0;
- }
-
- memcpy(result->data, p, result->alloc * (sizeof *result->data));
- result->alloc = nwords;
- mpd_set_dynamic_data(result);
- return 1;
-}
-
-/*
- * Input: 'result' is a static mpd_t with a static coefficient.
- *
- * Convert the coefficient to a dynamic one that is initialized to zero. If
- * malloc fails, set 'result' to NaN and update 'status' with MPD_Malloc_error.
- */
-int
-mpd_switch_to_dyn_zero(mpd_t *result, mpd_ssize_t nwords, uint32_t *status)
-{
- mpd_uint_t *p = result->data;
-
- result->data = mpd_calloc(nwords, sizeof *result->data);
- if (result->data == NULL) {
- result->data = p;
- mpd_set_qnan(result);
- mpd_set_positive(result);
- result->exp = result->digits = result->len = 0;
- *status |= MPD_Malloc_error;
- return 0;
- }
-
- result->alloc = nwords;
- mpd_set_dynamic_data(result);
-
- return 1;
-}
-
-/*
- * Input: 'result' is a static or a dynamic mpd_t with a dynamic coefficient.
- * Resize the coefficient to length 'nwords':
- * Case nwords > result->alloc:
- * If realloc is successful:
- * 'result' has a larger coefficient but the same value. Return 1.
- * Otherwise:
- * Set 'result' to NaN, update status with MPD_Malloc_error and return 0.
- * Case nwords < result->alloc:
- * If realloc is successful:
- * 'result' has a smaller coefficient. result->len is undefined. Return 1.
- * Otherwise (unlikely):
- * 'result' is unchanged. Reuse the now oversized coefficient. Return 1.
- */
-int
-mpd_realloc_dyn(mpd_t *result, mpd_ssize_t nwords, uint32_t *status)
-{
- uint8_t err = 0;
-
- result->data = mpd_realloc(result->data, nwords, sizeof *result->data, &err);
- if (!err) {
- result->alloc = nwords;
- }
- else if (nwords > result->alloc) {
- mpd_set_qnan(result);
- mpd_set_positive(result);
- result->exp = result->digits = result->len = 0;
- *status |= MPD_Malloc_error;
- return 0;
- }
-
- return 1;
-}
-
-/*
- * Input: 'result' is a static mpd_t with a static coefficient.
- * Assumption: 'nwords' >= result->alloc.
- *
- * Resize the static coefficient to a larger dynamic one and copy the
- * existing data.
- *
- * On failure the value of 'result' is unchanged.
- */
-int
-mpd_switch_to_dyn_cxx(mpd_t *result, mpd_ssize_t nwords)
-{
- assert(nwords >= result->alloc);
-
- mpd_uint_t *data = mpd_alloc(nwords, sizeof *result->data);
- if (data == NULL) {
- return 0;
- }
-
- memcpy(data, result->data, result->alloc * (sizeof *result->data));
- result->data = data;
- result->alloc = nwords;
- mpd_set_dynamic_data(result);
- return 1;
-}
-
-/*
- * Input: 'result' is a static or a dynamic mpd_t with a dynamic coefficient.
- * Resize the coefficient to length 'nwords':
- * Case nwords > result->alloc:
- * If realloc is successful:
- * 'result' has a larger coefficient but the same value. Return 1.
- * Otherwise:
- * 'result' has a the same coefficient. Return 0.
- * Case nwords < result->alloc:
- * If realloc is successful:
- * 'result' has a smaller coefficient. result->len is undefined. Return 1.
- * Otherwise (unlikely):
- * 'result' is unchanged. Reuse the now oversized coefficient. Return 1.
- */
-int
-mpd_realloc_dyn_cxx(mpd_t *result, mpd_ssize_t nwords)
-{
- uint8_t err = 0;
-
- mpd_uint_t *p = mpd_realloc(result->data, nwords, sizeof *result->data, &err);
- if (!err) {
- result->data = p;
- result->alloc = nwords;
- }
- else if (nwords > result->alloc) {
- return 0;
- }
-
- return 1;
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_MPALLOC_H_
-#define LIBMPDEC_MPALLOC_H_
-
-
-#include "mpdecimal.h"
-
-#include <stdint.h>
-
-
-/* Internal header file: all symbols have local scope in the DSO */
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
-
-
-int mpd_switch_to_dyn(mpd_t *result, mpd_ssize_t nwords, uint32_t *status);
-int mpd_switch_to_dyn_zero(mpd_t *result, mpd_ssize_t nwords, uint32_t *status);
-int mpd_realloc_dyn(mpd_t *result, mpd_ssize_t nwords, uint32_t *status);
-
-int mpd_switch_to_dyn_cxx(mpd_t *result, mpd_ssize_t nwords);
-int mpd_realloc_dyn_cxx(mpd_t *result, mpd_ssize_t nwords);
-
-
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
-
-
-#endif /* LIBMPDEC_MPALLOC_H_ */
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <assert.h>
-#include <limits.h>
-#include <math.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-
-#include "basearith.h"
-#include "bits.h"
-#include "constants.h"
-#include "convolute.h"
-#include "crt.h"
-#include "mpalloc.h"
-#include "typearith.h"
-
-#ifdef PPRO
- #if defined(_MSC_VER)
- #include <float.h>
- #pragma float_control(precise, on)
- #pragma fenv_access(on)
- #elif !defined(__OpenBSD__) && !defined(__NetBSD__)
- /* C99 */
- #include <fenv.h>
- #pragma STDC FENV_ACCESS ON
- #endif
-#endif
-
-
-/* Disable warning that is part of -Wextra since gcc 7.0. */
-#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && __GNUC__ >= 7
- #pragma GCC diagnostic ignored "-Wimplicit-fallthrough"
-#endif
-
-
-#if defined(_MSC_VER)
- #define ALWAYS_INLINE __forceinline
-#elif defined (__IBMC__) || defined(LEGACY_COMPILER)
- #define ALWAYS_INLINE
- #undef inline
- #define inline
-#else
- #ifdef TEST_COVERAGE
- #define ALWAYS_INLINE
- #else
- #define ALWAYS_INLINE inline __attribute__ ((always_inline))
- #endif
-#endif
-
-/* ClangCL claims to support 128-bit int, but doesn't */
-#if defined(__SIZEOF_INT128__) && defined(__clang__) && defined(_MSC_VER)
-#undef __SIZEOF_INT128__
-#endif
-
-
-
-#define MPD_NEWTONDIV_CUTOFF 1024L
-
-#define MPD_NEW_STATIC(name, flags, exp, digits, len) \
- mpd_uint_t name##_data[MPD_MINALLOC_MAX]; \
- mpd_t name = {flags|MPD_STATIC|MPD_STATIC_DATA, exp, digits, \
- len, MPD_MINALLOC_MAX, name##_data}
-
-#define MPD_NEW_CONST(name, flags, exp, digits, len, alloc, initval) \
- mpd_uint_t name##_data[alloc] = {initval}; \
- mpd_t name = {flags|MPD_STATIC|MPD_CONST_DATA, exp, digits, \
- len, alloc, name##_data}
-
-#define MPD_NEW_SHARED(name, a) \
- mpd_t name = {(a->flags&~MPD_DATAFLAGS)|MPD_STATIC|MPD_SHARED_DATA, \
- a->exp, a->digits, a->len, a->alloc, a->data}
-
-
-static mpd_uint_t data_one[1] = {1};
-static mpd_uint_t data_zero[1] = {0};
-static const mpd_t one = {MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, data_one};
-static const mpd_t minus_one = {MPD_NEG|MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1,
- data_one};
-static const mpd_t zero = {MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, data_zero};
-
-static inline void _mpd_check_exp(mpd_t *dec, const mpd_context_t *ctx,
- uint32_t *status);
-static void _settriple(mpd_t *result, uint8_t sign, mpd_uint_t a,
- mpd_ssize_t exp);
-static inline mpd_ssize_t _mpd_real_size(mpd_uint_t *data, mpd_ssize_t size);
-
-static int _mpd_cmp_abs(const mpd_t *a, const mpd_t *b);
-
-static void _mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status);
-static inline void _mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status);
-static void _mpd_base_ndivmod(mpd_t *q, mpd_t *r, const mpd_t *a,
- const mpd_t *b, uint32_t *status);
-static inline void _mpd_qpow_uint(mpd_t *result, const mpd_t *base,
- mpd_uint_t exp, uint8_t resultsign,
- const mpd_context_t *ctx, uint32_t *status);
-
-static mpd_uint_t mpd_qsshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n);
-
-
-/******************************************************************************/
-/* Version */
-/******************************************************************************/
-
-const char *
-mpd_version(void)
-{
- return MPD_VERSION;
-}
-
-
-/******************************************************************************/
-/* Performance critical inline functions */
-/******************************************************************************/
-
-#ifdef CONFIG_64
-/* Digits in a word, primarily useful for the most significant word. */
-ALWAYS_INLINE int
-mpd_word_digits(mpd_uint_t word)
-{
- if (word < mpd_pow10[9]) {
- if (word < mpd_pow10[4]) {
- if (word < mpd_pow10[2]) {
- return (word < mpd_pow10[1]) ? 1 : 2;
- }
- return (word < mpd_pow10[3]) ? 3 : 4;
- }
- if (word < mpd_pow10[6]) {
- return (word < mpd_pow10[5]) ? 5 : 6;
- }
- if (word < mpd_pow10[8]) {
- return (word < mpd_pow10[7]) ? 7 : 8;
- }
- return 9;
- }
- if (word < mpd_pow10[14]) {
- if (word < mpd_pow10[11]) {
- return (word < mpd_pow10[10]) ? 10 : 11;
- }
- if (word < mpd_pow10[13]) {
- return (word < mpd_pow10[12]) ? 12 : 13;
- }
- return 14;
- }
- if (word < mpd_pow10[18]) {
- if (word < mpd_pow10[16]) {
- return (word < mpd_pow10[15]) ? 15 : 16;
- }
- return (word < mpd_pow10[17]) ? 17 : 18;
- }
-
- return (word < mpd_pow10[19]) ? 19 : 20;
-}
-#else
-ALWAYS_INLINE int
-mpd_word_digits(mpd_uint_t word)
-{
- if (word < mpd_pow10[4]) {
- if (word < mpd_pow10[2]) {
- return (word < mpd_pow10[1]) ? 1 : 2;
- }
- return (word < mpd_pow10[3]) ? 3 : 4;
- }
- if (word < mpd_pow10[6]) {
- return (word < mpd_pow10[5]) ? 5 : 6;
- }
- if (word < mpd_pow10[8]) {
- return (word < mpd_pow10[7]) ? 7 : 8;
- }
-
- return (word < mpd_pow10[9]) ? 9 : 10;
-}
-#endif
-
-
-/* Adjusted exponent */
-ALWAYS_INLINE mpd_ssize_t
-mpd_adjexp(const mpd_t *dec)
-{
- return (dec->exp + dec->digits) - 1;
-}
-
-/* Etiny */
-ALWAYS_INLINE mpd_ssize_t
-mpd_etiny(const mpd_context_t *ctx)
-{
- return ctx->emin - (ctx->prec - 1);
-}
-
-/* Etop: used for folding down in IEEE clamping */
-ALWAYS_INLINE mpd_ssize_t
-mpd_etop(const mpd_context_t *ctx)
-{
- return ctx->emax - (ctx->prec - 1);
-}
-
-/* Most significant word */
-ALWAYS_INLINE mpd_uint_t
-mpd_msword(const mpd_t *dec)
-{
- assert(dec->len > 0);
- return dec->data[dec->len-1];
-}
-
-/* Most significant digit of a word */
-inline mpd_uint_t
-mpd_msd(mpd_uint_t word)
-{
- int n;
-
- n = mpd_word_digits(word);
- return word / mpd_pow10[n-1];
-}
-
-/* Least significant digit of a word */
-ALWAYS_INLINE mpd_uint_t
-mpd_lsd(mpd_uint_t word)
-{
- return word % 10;
-}
-
-/* Coefficient size needed to store 'digits' */
-mpd_ssize_t
-mpd_digits_to_size(mpd_ssize_t digits)
-{
- mpd_ssize_t q, r;
-
- _mpd_idiv_word(&q, &r, digits, MPD_RDIGITS);
- return (r == 0) ? q : q+1;
-}
-
-/* Number of digits in the exponent. Not defined for MPD_SSIZE_MIN. */
-inline int
-mpd_exp_digits(mpd_ssize_t exp)
-{
- exp = (exp < 0) ? -exp : exp;
- return mpd_word_digits(exp);
-}
-
-/* Canonical */
-ALWAYS_INLINE int
-mpd_iscanonical(const mpd_t *dec)
-{
- (void)dec;
- return 1;
-}
-
-/* Finite */
-ALWAYS_INLINE int
-mpd_isfinite(const mpd_t *dec)
-{
- return !(dec->flags & MPD_SPECIAL);
-}
-
-/* Infinite */
-ALWAYS_INLINE int
-mpd_isinfinite(const mpd_t *dec)
-{
- return dec->flags & MPD_INF;
-}
-
-/* NaN */
-ALWAYS_INLINE int
-mpd_isnan(const mpd_t *dec)
-{
- return dec->flags & (MPD_NAN|MPD_SNAN);
-}
-
-/* Negative */
-ALWAYS_INLINE int
-mpd_isnegative(const mpd_t *dec)
-{
- return dec->flags & MPD_NEG;
-}
-
-/* Positive */
-ALWAYS_INLINE int
-mpd_ispositive(const mpd_t *dec)
-{
- return !(dec->flags & MPD_NEG);
-}
-
-/* qNaN */
-ALWAYS_INLINE int
-mpd_isqnan(const mpd_t *dec)
-{
- return dec->flags & MPD_NAN;
-}
-
-/* Signed */
-ALWAYS_INLINE int
-mpd_issigned(const mpd_t *dec)
-{
- return dec->flags & MPD_NEG;
-}
-
-/* sNaN */
-ALWAYS_INLINE int
-mpd_issnan(const mpd_t *dec)
-{
- return dec->flags & MPD_SNAN;
-}
-
-/* Special */
-ALWAYS_INLINE int
-mpd_isspecial(const mpd_t *dec)
-{
- return dec->flags & MPD_SPECIAL;
-}
-
-/* Zero */
-ALWAYS_INLINE int
-mpd_iszero(const mpd_t *dec)
-{
- return !mpd_isspecial(dec) && mpd_msword(dec) == 0;
-}
-
-/* Test for zero when specials have been ruled out already */
-ALWAYS_INLINE int
-mpd_iszerocoeff(const mpd_t *dec)
-{
- return mpd_msword(dec) == 0;
-}
-
-/* Normal */
-inline int
-mpd_isnormal(const mpd_t *dec, const mpd_context_t *ctx)
-{
- if (mpd_isspecial(dec)) return 0;
- if (mpd_iszerocoeff(dec)) return 0;
-
- return mpd_adjexp(dec) >= ctx->emin;
-}
-
-/* Subnormal */
-inline int
-mpd_issubnormal(const mpd_t *dec, const mpd_context_t *ctx)
-{
- if (mpd_isspecial(dec)) return 0;
- if (mpd_iszerocoeff(dec)) return 0;
-
- return mpd_adjexp(dec) < ctx->emin;
-}
-
-/* Odd word */
-ALWAYS_INLINE int
-mpd_isoddword(mpd_uint_t word)
-{
- return word & 1;
-}
-
-/* Odd coefficient */
-ALWAYS_INLINE int
-mpd_isoddcoeff(const mpd_t *dec)
-{
- return mpd_isoddword(dec->data[0]);
-}
-
-/* 0 if dec is positive, 1 if dec is negative */
-ALWAYS_INLINE uint8_t
-mpd_sign(const mpd_t *dec)
-{
- return dec->flags & MPD_NEG;
-}
-
-/* 1 if dec is positive, -1 if dec is negative */
-ALWAYS_INLINE int
-mpd_arith_sign(const mpd_t *dec)
-{
- return 1 - 2 * mpd_isnegative(dec);
-}
-
-/* Radix */
-ALWAYS_INLINE long
-mpd_radix(void)
-{
- return 10;
-}
-
-/* Dynamic decimal */
-ALWAYS_INLINE int
-mpd_isdynamic(const mpd_t *dec)
-{
- return !(dec->flags & MPD_STATIC);
-}
-
-/* Static decimal */
-ALWAYS_INLINE int
-mpd_isstatic(const mpd_t *dec)
-{
- return dec->flags & MPD_STATIC;
-}
-
-/* Data of decimal is dynamic */
-ALWAYS_INLINE int
-mpd_isdynamic_data(const mpd_t *dec)
-{
- return !(dec->flags & MPD_DATAFLAGS);
-}
-
-/* Data of decimal is static */
-ALWAYS_INLINE int
-mpd_isstatic_data(const mpd_t *dec)
-{
- return dec->flags & MPD_STATIC_DATA;
-}
-
-/* Data of decimal is shared */
-ALWAYS_INLINE int
-mpd_isshared_data(const mpd_t *dec)
-{
- return dec->flags & MPD_SHARED_DATA;
-}
-
-/* Data of decimal is const */
-ALWAYS_INLINE int
-mpd_isconst_data(const mpd_t *dec)
-{
- return dec->flags & MPD_CONST_DATA;
-}
-
-
-/******************************************************************************/
-/* Inline memory handling */
-/******************************************************************************/
-
-/* Fill destination with zeros */
-ALWAYS_INLINE void
-mpd_uint_zero(mpd_uint_t *dest, mpd_size_t len)
-{
- mpd_size_t i;
-
- for (i = 0; i < len; i++) {
- dest[i] = 0;
- }
-}
-
-/* Free a decimal */
-ALWAYS_INLINE void
-mpd_del(mpd_t *dec)
-{
- if (mpd_isdynamic_data(dec)) {
- mpd_free(dec->data);
- }
- if (mpd_isdynamic(dec)) {
- mpd_free(dec);
- }
-}
-
-/*
- * Resize the coefficient. Existing data up to 'nwords' is left untouched.
- * Return 1 on success, 0 otherwise.
- *
- * Input invariant: MPD_MINALLOC <= result->alloc.
- *
- * Case nwords == result->alloc:
- * 'result' is unchanged. Return 1.
- *
- * Case nwords > result->alloc:
- * Case realloc success:
- * The value of 'result' does not change. Return 1.
- * Case realloc failure:
- * 'result' is NaN, status is updated with MPD_Malloc_error. Return 0.
- *
- * Case nwords < result->alloc:
- * Case is_static_data or realloc failure [1]:
- * 'result' is unchanged. Return 1.
- * Case realloc success:
- * The value of result is undefined (expected). Return 1.
- *
- *
- * [1] In that case the old (now oversized) area is still valid.
- */
-ALWAYS_INLINE int
-mpd_qresize(mpd_t *result, mpd_ssize_t nwords, uint32_t *status)
-{
- assert(!mpd_isconst_data(result)); /* illegal operation for a const */
- assert(!mpd_isshared_data(result)); /* illegal operation for a shared */
- assert(MPD_MINALLOC <= result->alloc);
-
- nwords = (nwords <= MPD_MINALLOC) ? MPD_MINALLOC : nwords;
- if (nwords == result->alloc) {
- return 1;
- }
- if (mpd_isstatic_data(result)) {
- if (nwords > result->alloc) {
- return mpd_switch_to_dyn(result, nwords, status);
- }
- return 1;
- }
-
- return mpd_realloc_dyn(result, nwords, status);
-}
-
-/* Same as mpd_qresize, but do not set the result no NaN on failure. */
-static ALWAYS_INLINE int
-mpd_qresize_cxx(mpd_t *result, mpd_ssize_t nwords)
-{
- assert(!mpd_isconst_data(result)); /* illegal operation for a const */
- assert(!mpd_isshared_data(result)); /* illegal operation for a shared */
- assert(MPD_MINALLOC <= result->alloc);
-
- nwords = (nwords <= MPD_MINALLOC) ? MPD_MINALLOC : nwords;
- if (nwords == result->alloc) {
- return 1;
- }
- if (mpd_isstatic_data(result)) {
- if (nwords > result->alloc) {
- return mpd_switch_to_dyn_cxx(result, nwords);
- }
- return 1;
- }
-
- return mpd_realloc_dyn_cxx(result, nwords);
-}
-
-/* Same as mpd_qresize, but the complete coefficient (including the old
- * memory area!) is initialized to zero. */
-ALWAYS_INLINE int
-mpd_qresize_zero(mpd_t *result, mpd_ssize_t nwords, uint32_t *status)
-{
- assert(!mpd_isconst_data(result)); /* illegal operation for a const */
- assert(!mpd_isshared_data(result)); /* illegal operation for a shared */
- assert(MPD_MINALLOC <= result->alloc);
-
- nwords = (nwords <= MPD_MINALLOC) ? MPD_MINALLOC : nwords;
- if (nwords != result->alloc) {
- if (mpd_isstatic_data(result)) {
- if (nwords > result->alloc) {
- return mpd_switch_to_dyn_zero(result, nwords, status);
- }
- }
- else if (!mpd_realloc_dyn(result, nwords, status)) {
- return 0;
- }
- }
-
- mpd_uint_zero(result->data, nwords);
- return 1;
-}
-
-/*
- * Reduce memory size for the coefficient to MPD_MINALLOC. In theory,
- * realloc may fail even when reducing the memory size. But in that case
- * the old memory area is always big enough, so checking for MPD_Malloc_error
- * is not imperative.
- */
-ALWAYS_INLINE void
-mpd_minalloc(mpd_t *result)
-{
- assert(!mpd_isconst_data(result)); /* illegal operation for a const */
- assert(!mpd_isshared_data(result)); /* illegal operation for a shared */
-
- if (!mpd_isstatic_data(result) && result->alloc > MPD_MINALLOC) {
- uint8_t err = 0;
- result->data = mpd_realloc(result->data, MPD_MINALLOC,
- sizeof *result->data, &err);
- if (!err) {
- result->alloc = MPD_MINALLOC;
- }
- }
-}
-
-int
-mpd_resize(mpd_t *result, mpd_ssize_t nwords, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- if (!mpd_qresize(result, nwords, &status)) {
- mpd_addstatus_raise(ctx, status);
- return 0;
- }
- return 1;
-}
-
-int
-mpd_resize_zero(mpd_t *result, mpd_ssize_t nwords, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- if (!mpd_qresize_zero(result, nwords, &status)) {
- mpd_addstatus_raise(ctx, status);
- return 0;
- }
- return 1;
-}
-
-
-/******************************************************************************/
-/* Set attributes of a decimal */
-/******************************************************************************/
-
-/* Set digits. Assumption: result->len is initialized and > 0. */
-inline void
-mpd_setdigits(mpd_t *result)
-{
- mpd_ssize_t wdigits = mpd_word_digits(mpd_msword(result));
- result->digits = wdigits + (result->len-1) * MPD_RDIGITS;
-}
-
-/* Set sign */
-ALWAYS_INLINE void
-mpd_set_sign(mpd_t *result, uint8_t sign)
-{
- result->flags &= ~MPD_NEG;
- result->flags |= sign;
-}
-
-/* Copy sign from another decimal */
-ALWAYS_INLINE void
-mpd_signcpy(mpd_t *result, const mpd_t *a)
-{
- uint8_t sign = a->flags&MPD_NEG;
-
- result->flags &= ~MPD_NEG;
- result->flags |= sign;
-}
-
-/* Set infinity */
-ALWAYS_INLINE void
-mpd_set_infinity(mpd_t *result)
-{
- result->flags &= ~MPD_SPECIAL;
- result->flags |= MPD_INF;
-}
-
-/* Set qNaN */
-ALWAYS_INLINE void
-mpd_set_qnan(mpd_t *result)
-{
- result->flags &= ~MPD_SPECIAL;
- result->flags |= MPD_NAN;
-}
-
-/* Set sNaN */
-ALWAYS_INLINE void
-mpd_set_snan(mpd_t *result)
-{
- result->flags &= ~MPD_SPECIAL;
- result->flags |= MPD_SNAN;
-}
-
-/* Set to negative */
-ALWAYS_INLINE void
-mpd_set_negative(mpd_t *result)
-{
- result->flags |= MPD_NEG;
-}
-
-/* Set to positive */
-ALWAYS_INLINE void
-mpd_set_positive(mpd_t *result)
-{
- result->flags &= ~MPD_NEG;
-}
-
-/* Set to dynamic */
-ALWAYS_INLINE void
-mpd_set_dynamic(mpd_t *result)
-{
- result->flags &= ~MPD_STATIC;
-}
-
-/* Set to static */
-ALWAYS_INLINE void
-mpd_set_static(mpd_t *result)
-{
- result->flags |= MPD_STATIC;
-}
-
-/* Set data to dynamic */
-ALWAYS_INLINE void
-mpd_set_dynamic_data(mpd_t *result)
-{
- result->flags &= ~MPD_DATAFLAGS;
-}
-
-/* Set data to static */
-ALWAYS_INLINE void
-mpd_set_static_data(mpd_t *result)
-{
- result->flags &= ~MPD_DATAFLAGS;
- result->flags |= MPD_STATIC_DATA;
-}
-
-/* Set data to shared */
-ALWAYS_INLINE void
-mpd_set_shared_data(mpd_t *result)
-{
- result->flags &= ~MPD_DATAFLAGS;
- result->flags |= MPD_SHARED_DATA;
-}
-
-/* Set data to const */
-ALWAYS_INLINE void
-mpd_set_const_data(mpd_t *result)
-{
- result->flags &= ~MPD_DATAFLAGS;
- result->flags |= MPD_CONST_DATA;
-}
-
-/* Clear flags, preserving memory attributes. */
-ALWAYS_INLINE void
-mpd_clear_flags(mpd_t *result)
-{
- result->flags &= (MPD_STATIC|MPD_DATAFLAGS);
-}
-
-/* Set flags, preserving memory attributes. */
-ALWAYS_INLINE void
-mpd_set_flags(mpd_t *result, uint8_t flags)
-{
- result->flags &= (MPD_STATIC|MPD_DATAFLAGS);
- result->flags |= flags;
-}
-
-/* Copy flags, preserving memory attributes of result. */
-ALWAYS_INLINE void
-mpd_copy_flags(mpd_t *result, const mpd_t *a)
-{
- uint8_t aflags = a->flags;
- result->flags &= (MPD_STATIC|MPD_DATAFLAGS);
- result->flags |= (aflags & ~(MPD_STATIC|MPD_DATAFLAGS));
-}
-
-/* Initialize a workcontext from ctx. Set traps, flags and newtrap to 0. */
-static inline void
-mpd_workcontext(mpd_context_t *workctx, const mpd_context_t *ctx)
-{
- workctx->prec = ctx->prec;
- workctx->emax = ctx->emax;
- workctx->emin = ctx->emin;
- workctx->round = ctx->round;
- workctx->traps = 0;
- workctx->status = 0;
- workctx->newtrap = 0;
- workctx->clamp = ctx->clamp;
- workctx->allcr = ctx->allcr;
-}
-
-
-/******************************************************************************/
-/* Getting and setting parts of decimals */
-/******************************************************************************/
-
-/* Flip the sign of a decimal */
-static inline void
-_mpd_negate(mpd_t *dec)
-{
- dec->flags ^= MPD_NEG;
-}
-
-/* Set coefficient to zero */
-void
-mpd_zerocoeff(mpd_t *result)
-{
- mpd_minalloc(result);
- result->digits = 1;
- result->len = 1;
- result->data[0] = 0;
-}
-
-/* Set the coefficient to all nines. */
-void
-mpd_qmaxcoeff(mpd_t *result, const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_ssize_t len, r;
-
- _mpd_idiv_word(&len, &r, ctx->prec, MPD_RDIGITS);
- len = (r == 0) ? len : len+1;
-
- if (!mpd_qresize(result, len, status)) {
- return;
- }
-
- result->len = len;
- result->digits = ctx->prec;
-
- --len;
- if (r > 0) {
- result->data[len--] = mpd_pow10[r]-1;
- }
- for (; len >= 0; --len) {
- result->data[len] = MPD_RADIX-1;
- }
-}
-
-/*
- * Cut off the most significant digits so that the rest fits in ctx->prec.
- * Cannot fail.
- */
-static void
-_mpd_cap(mpd_t *result, const mpd_context_t *ctx)
-{
- uint32_t dummy;
- mpd_ssize_t len, r;
-
- if (result->len > 0 && result->digits > ctx->prec) {
- _mpd_idiv_word(&len, &r, ctx->prec, MPD_RDIGITS);
- len = (r == 0) ? len : len+1;
-
- if (r != 0) {
- result->data[len-1] %= mpd_pow10[r];
- }
-
- len = _mpd_real_size(result->data, len);
- /* resize to fewer words cannot fail */
- mpd_qresize(result, len, &dummy);
- result->len = len;
- mpd_setdigits(result);
- }
- if (mpd_iszero(result)) {
- _settriple(result, mpd_sign(result), 0, result->exp);
- }
-}
-
-/*
- * Cut off the most significant digits of a NaN payload so that the rest
- * fits in ctx->prec - ctx->clamp. Cannot fail.
- */
-static void
-_mpd_fix_nan(mpd_t *result, const mpd_context_t *ctx)
-{
- uint32_t dummy;
- mpd_ssize_t prec;
- mpd_ssize_t len, r;
-
- prec = ctx->prec - ctx->clamp;
- if (result->len > 0 && result->digits > prec) {
- if (prec == 0) {
- mpd_minalloc(result);
- result->len = result->digits = 0;
- }
- else {
- _mpd_idiv_word(&len, &r, prec, MPD_RDIGITS);
- len = (r == 0) ? len : len+1;
-
- if (r != 0) {
- result->data[len-1] %= mpd_pow10[r];
- }
-
- len = _mpd_real_size(result->data, len);
- /* resize to fewer words cannot fail */
- mpd_qresize(result, len, &dummy);
- result->len = len;
- mpd_setdigits(result);
- if (mpd_iszerocoeff(result)) {
- /* NaN0 is not a valid representation */
- result->len = result->digits = 0;
- }
- }
- }
-}
-
-/*
- * Get n most significant digits from a decimal, where 0 < n <= MPD_UINT_DIGITS.
- * Assumes MPD_UINT_DIGITS == MPD_RDIGITS+1, which is true for 32 and 64 bit
- * machines.
- *
- * The result of the operation will be in lo. If the operation is impossible,
- * hi will be nonzero. This is used to indicate an error.
- */
-static inline void
-_mpd_get_msdigits(mpd_uint_t *hi, mpd_uint_t *lo, const mpd_t *dec,
- unsigned int n)
-{
- mpd_uint_t r, tmp;
-
- assert(0 < n && n <= MPD_RDIGITS+1);
-
- _mpd_div_word(&tmp, &r, dec->digits, MPD_RDIGITS);
- r = (r == 0) ? MPD_RDIGITS : r; /* digits in the most significant word */
-
- *hi = 0;
- *lo = dec->data[dec->len-1];
- if (n <= r) {
- *lo /= mpd_pow10[r-n];
- }
- else if (dec->len > 1) {
- /* at this point 1 <= r < n <= MPD_RDIGITS+1 */
- _mpd_mul_words(hi, lo, *lo, mpd_pow10[n-r]);
- tmp = dec->data[dec->len-2] / mpd_pow10[MPD_RDIGITS-(n-r)];
- *lo = *lo + tmp;
- if (*lo < tmp) (*hi)++;
- }
-}
-
-
-/******************************************************************************/
-/* Gathering information about a decimal */
-/******************************************************************************/
-
-/* The real size of the coefficient without leading zero words. */
-static inline mpd_ssize_t
-_mpd_real_size(mpd_uint_t *data, mpd_ssize_t size)
-{
- while (size > 1 && data[size-1] == 0) {
- size--;
- }
-
- return size;
-}
-
-/* Return number of trailing zeros. No errors are possible. */
-mpd_ssize_t
-mpd_trail_zeros(const mpd_t *dec)
-{
- mpd_uint_t word;
- mpd_ssize_t i, tz = 0;
-
- for (i=0; i < dec->len; ++i) {
- if (dec->data[i] != 0) {
- word = dec->data[i];
- tz = i * MPD_RDIGITS;
- while (word % 10 == 0) {
- word /= 10;
- tz++;
- }
- break;
- }
- }
-
- return tz;
-}
-
-/* Integer: Undefined for specials */
-static int
-_mpd_isint(const mpd_t *dec)
-{
- mpd_ssize_t tz;
-
- if (mpd_iszerocoeff(dec)) {
- return 1;
- }
-
- tz = mpd_trail_zeros(dec);
- return (dec->exp + tz >= 0);
-}
-
-/* Integer */
-int
-mpd_isinteger(const mpd_t *dec)
-{
- if (mpd_isspecial(dec)) {
- return 0;
- }
- return _mpd_isint(dec);
-}
-
-/* Word is a power of 10 */
-static int
-mpd_word_ispow10(mpd_uint_t word)
-{
- int n;
-
- n = mpd_word_digits(word);
- if (word == mpd_pow10[n-1]) {
- return 1;
- }
-
- return 0;
-}
-
-/* Coefficient is a power of 10 */
-static int
-mpd_coeff_ispow10(const mpd_t *dec)
-{
- if (mpd_word_ispow10(mpd_msword(dec))) {
- if (_mpd_isallzero(dec->data, dec->len-1)) {
- return 1;
- }
- }
-
- return 0;
-}
-
-/* All digits of a word are nines */
-static int
-mpd_word_isallnine(mpd_uint_t word)
-{
- int n;
-
- n = mpd_word_digits(word);
- if (word == mpd_pow10[n]-1) {
- return 1;
- }
-
- return 0;
-}
-
-/* All digits of the coefficient are nines */
-static int
-mpd_coeff_isallnine(const mpd_t *dec)
-{
- if (mpd_word_isallnine(mpd_msword(dec))) {
- if (_mpd_isallnine(dec->data, dec->len-1)) {
- return 1;
- }
- }
-
- return 0;
-}
-
-/* Odd decimal: Undefined for non-integers! */
-int
-mpd_isodd(const mpd_t *dec)
-{
- mpd_uint_t q, r;
- assert(mpd_isinteger(dec));
- if (mpd_iszerocoeff(dec)) return 0;
- if (dec->exp < 0) {
- _mpd_div_word(&q, &r, -dec->exp, MPD_RDIGITS);
- q = dec->data[q] / mpd_pow10[r];
- return mpd_isoddword(q);
- }
- return dec->exp == 0 && mpd_isoddword(dec->data[0]);
-}
-
-/* Even: Undefined for non-integers! */
-int
-mpd_iseven(const mpd_t *dec)
-{
- return !mpd_isodd(dec);
-}
-
-/******************************************************************************/
-/* Getting and setting decimals */
-/******************************************************************************/
-
-/* Internal function: Set a static decimal from a triple, no error checking. */
-static void
-_ssettriple(mpd_t *result, uint8_t sign, mpd_uint_t a, mpd_ssize_t exp)
-{
- mpd_set_flags(result, sign);
- result->exp = exp;
- _mpd_div_word(&result->data[1], &result->data[0], a, MPD_RADIX);
- result->len = (result->data[1] == 0) ? 1 : 2;
- mpd_setdigits(result);
-}
-
-/* Internal function: Set a decimal from a triple, no error checking. */
-static void
-_settriple(mpd_t *result, uint8_t sign, mpd_uint_t a, mpd_ssize_t exp)
-{
- mpd_minalloc(result);
- mpd_set_flags(result, sign);
- result->exp = exp;
- _mpd_div_word(&result->data[1], &result->data[0], a, MPD_RADIX);
- result->len = (result->data[1] == 0) ? 1 : 2;
- mpd_setdigits(result);
-}
-
-/* Set a special number from a triple */
-void
-mpd_setspecial(mpd_t *result, uint8_t sign, uint8_t type)
-{
- mpd_minalloc(result);
- result->flags &= ~(MPD_NEG|MPD_SPECIAL);
- result->flags |= (sign|type);
- result->exp = result->digits = result->len = 0;
-}
-
-/* Set result of NaN with an error status */
-void
-mpd_seterror(mpd_t *result, uint32_t flags, uint32_t *status)
-{
- mpd_minalloc(result);
- mpd_set_qnan(result);
- mpd_set_positive(result);
- result->exp = result->digits = result->len = 0;
- *status |= flags;
-}
-
-/* quietly set a static decimal from an mpd_ssize_t */
-void
-mpd_qsset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_uint_t u;
- uint8_t sign = MPD_POS;
-
- if (a < 0) {
- if (a == MPD_SSIZE_MIN) {
- u = (mpd_uint_t)MPD_SSIZE_MAX +
- (-(MPD_SSIZE_MIN+MPD_SSIZE_MAX));
- }
- else {
- u = -a;
- }
- sign = MPD_NEG;
- }
- else {
- u = a;
- }
- _ssettriple(result, sign, u, 0);
- mpd_qfinalize(result, ctx, status);
-}
-
-/* quietly set a static decimal from an mpd_uint_t */
-void
-mpd_qsset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- _ssettriple(result, MPD_POS, a, 0);
- mpd_qfinalize(result, ctx, status);
-}
-
-/* quietly set a static decimal from an int32_t */
-void
-mpd_qsset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_qsset_ssize(result, a, ctx, status);
-}
-
-/* quietly set a static decimal from a uint32_t */
-void
-mpd_qsset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_qsset_uint(result, a, ctx, status);
-}
-
-#ifdef CONFIG_64
-/* quietly set a static decimal from an int64_t */
-void
-mpd_qsset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_qsset_ssize(result, a, ctx, status);
-}
-
-/* quietly set a static decimal from a uint64_t */
-void
-mpd_qsset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_qsset_uint(result, a, ctx, status);
-}
-#endif
-
-/* quietly set a decimal from an mpd_ssize_t */
-void
-mpd_qset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_minalloc(result);
- mpd_qsset_ssize(result, a, ctx, status);
-}
-
-/* quietly set a decimal from an mpd_uint_t */
-void
-mpd_qset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- _settriple(result, MPD_POS, a, 0);
- mpd_qfinalize(result, ctx, status);
-}
-
-/* quietly set a decimal from an int32_t */
-void
-mpd_qset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_qset_ssize(result, a, ctx, status);
-}
-
-/* quietly set a decimal from a uint32_t */
-void
-mpd_qset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_qset_uint(result, a, ctx, status);
-}
-
-#if defined(CONFIG_32) && !defined(LEGACY_COMPILER)
-/* set a decimal from a uint64_t */
-static void
-_c32setu64(mpd_t *result, uint64_t u, uint8_t sign, uint32_t *status)
-{
- mpd_uint_t w[3];
- uint64_t q;
- int i, len;
-
- len = 0;
- do {
- q = u / MPD_RADIX;
- w[len] = (mpd_uint_t)(u - q * MPD_RADIX);
- u = q; len++;
- } while (u != 0);
-
- if (!mpd_qresize(result, len, status)) {
- return;
- }
- for (i = 0; i < len; i++) {
- result->data[i] = w[i];
- }
-
- mpd_set_flags(result, sign);
- result->exp = 0;
- result->len = len;
- mpd_setdigits(result);
-}
-
-static void
-_c32_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- _c32setu64(result, a, MPD_POS, status);
- mpd_qfinalize(result, ctx, status);
-}
-
-/* set a decimal from an int64_t */
-static void
-_c32_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- uint64_t u;
- uint8_t sign = MPD_POS;
-
- if (a < 0) {
- if (a == INT64_MIN) {
- u = (uint64_t)INT64_MAX + (-(INT64_MIN+INT64_MAX));
- }
- else {
- u = -a;
- }
- sign = MPD_NEG;
- }
- else {
- u = a;
- }
- _c32setu64(result, u, sign, status);
- mpd_qfinalize(result, ctx, status);
-}
-#endif /* CONFIG_32 && !LEGACY_COMPILER */
-
-#ifndef LEGACY_COMPILER
-/* quietly set a decimal from an int64_t */
-void
-mpd_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx,
- uint32_t *status)
-{
-#ifdef CONFIG_64
- mpd_qset_ssize(result, a, ctx, status);
-#else
- _c32_qset_i64(result, a, ctx, status);
-#endif
-}
-
-/* quietly set a decimal from an int64_t, use a maxcontext for conversion */
-void
-mpd_qset_i64_exact(mpd_t *result, int64_t a, uint32_t *status)
-{
- mpd_context_t maxcontext;
-
- mpd_maxcontext(&maxcontext);
-#ifdef CONFIG_64
- mpd_qset_ssize(result, a, &maxcontext, status);
-#else
- _c32_qset_i64(result, a, &maxcontext, status);
-#endif
-
- if (*status & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) {
- /* we want exact results */
- mpd_seterror(result, MPD_Invalid_operation, status);
- }
- *status &= MPD_Errors;
-}
-
-/* quietly set a decimal from a uint64_t */
-void
-mpd_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx,
- uint32_t *status)
-{
-#ifdef CONFIG_64
- mpd_qset_uint(result, a, ctx, status);
-#else
- _c32_qset_u64(result, a, ctx, status);
-#endif
-}
-
-/* quietly set a decimal from a uint64_t, use a maxcontext for conversion */
-void
-mpd_qset_u64_exact(mpd_t *result, uint64_t a, uint32_t *status)
-{
- mpd_context_t maxcontext;
-
- mpd_maxcontext(&maxcontext);
-#ifdef CONFIG_64
- mpd_qset_uint(result, a, &maxcontext, status);
-#else
- _c32_qset_u64(result, a, &maxcontext, status);
-#endif
-
- if (*status & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) {
- /* we want exact results */
- mpd_seterror(result, MPD_Invalid_operation, status);
- }
- *status &= MPD_Errors;
-}
-#endif /* !LEGACY_COMPILER */
-
-/*
- * Quietly get an mpd_uint_t from a decimal. Assumes
- * MPD_UINT_DIGITS == MPD_RDIGITS+1, which is true for
- * 32 and 64 bit machines.
- *
- * If the operation is impossible, MPD_Invalid_operation is set.
- */
-static mpd_uint_t
-_mpd_qget_uint(int use_sign, const mpd_t *a, uint32_t *status)
-{
- mpd_t tmp;
- mpd_uint_t tmp_data[2];
- mpd_uint_t lo, hi;
-
- if (mpd_isspecial(a)) {
- *status |= MPD_Invalid_operation;
- return MPD_UINT_MAX;
- }
- if (mpd_iszero(a)) {
- return 0;
- }
- if (use_sign && mpd_isnegative(a)) {
- *status |= MPD_Invalid_operation;
- return MPD_UINT_MAX;
- }
-
- if (a->digits+a->exp > MPD_RDIGITS+1) {
- *status |= MPD_Invalid_operation;
- return MPD_UINT_MAX;
- }
-
- if (a->exp < 0) {
- if (!_mpd_isint(a)) {
- *status |= MPD_Invalid_operation;
- return MPD_UINT_MAX;
- }
- /* At this point a->digits+a->exp <= MPD_RDIGITS+1,
- * so the shift fits. */
- tmp.data = tmp_data;
- tmp.flags = MPD_STATIC|MPD_STATIC_DATA;
- tmp.alloc = 2;
- mpd_qsshiftr(&tmp, a, -a->exp);
- tmp.exp = 0;
- a = &tmp;
- }
-
- _mpd_get_msdigits(&hi, &lo, a, MPD_RDIGITS+1);
- if (hi) {
- *status |= MPD_Invalid_operation;
- return MPD_UINT_MAX;
- }
-
- if (a->exp > 0) {
- _mpd_mul_words(&hi, &lo, lo, mpd_pow10[a->exp]);
- if (hi) {
- *status |= MPD_Invalid_operation;
- return MPD_UINT_MAX;
- }
- }
-
- return lo;
-}
-
-/*
- * Sets Invalid_operation for:
- * - specials
- * - negative numbers (except negative zero)
- * - non-integers
- * - overflow
- */
-mpd_uint_t
-mpd_qget_uint(const mpd_t *a, uint32_t *status)
-{
- return _mpd_qget_uint(1, a, status);
-}
-
-/* Same as above, but gets the absolute value, i.e. the sign is ignored. */
-mpd_uint_t
-mpd_qabs_uint(const mpd_t *a, uint32_t *status)
-{
- return _mpd_qget_uint(0, a, status);
-}
-
-/* quietly get an mpd_ssize_t from a decimal */
-mpd_ssize_t
-mpd_qget_ssize(const mpd_t *a, uint32_t *status)
-{
- uint32_t workstatus = 0;
- mpd_uint_t u;
- int isneg;
-
- u = mpd_qabs_uint(a, &workstatus);
- if (workstatus&MPD_Invalid_operation) {
- *status |= workstatus;
- return MPD_SSIZE_MAX;
- }
-
- isneg = mpd_isnegative(a);
- if (u <= MPD_SSIZE_MAX) {
- return isneg ? -((mpd_ssize_t)u) : (mpd_ssize_t)u;
- }
- else if (isneg && u+(MPD_SSIZE_MIN+MPD_SSIZE_MAX) == MPD_SSIZE_MAX) {
- return MPD_SSIZE_MIN;
- }
-
- *status |= MPD_Invalid_operation;
- return MPD_SSIZE_MAX;
-}
-
-#if defined(CONFIG_32) && !defined(LEGACY_COMPILER)
-/*
- * Quietly get a uint64_t from a decimal. If the operation is impossible,
- * MPD_Invalid_operation is set.
- */
-static uint64_t
-_c32_qget_u64(int use_sign, const mpd_t *a, uint32_t *status)
-{
- MPD_NEW_STATIC(tmp,0,0,20,3);
- mpd_context_t maxcontext;
- uint64_t ret;
-
- tmp_data[0] = 709551615;
- tmp_data[1] = 446744073;
- tmp_data[2] = 18;
-
- if (mpd_isspecial(a)) {
- *status |= MPD_Invalid_operation;
- return UINT64_MAX;
- }
- if (mpd_iszero(a)) {
- return 0;
- }
- if (use_sign && mpd_isnegative(a)) {
- *status |= MPD_Invalid_operation;
- return UINT64_MAX;
- }
- if (!_mpd_isint(a)) {
- *status |= MPD_Invalid_operation;
- return UINT64_MAX;
- }
-
- if (_mpd_cmp_abs(a, &tmp) > 0) {
- *status |= MPD_Invalid_operation;
- return UINT64_MAX;
- }
-
- mpd_maxcontext(&maxcontext);
- mpd_qrescale(&tmp, a, 0, &maxcontext, &maxcontext.status);
- maxcontext.status &= ~MPD_Rounded;
- if (maxcontext.status != 0) {
- *status |= (maxcontext.status|MPD_Invalid_operation); /* GCOV_NOT_REACHED */
- return UINT64_MAX; /* GCOV_NOT_REACHED */
- }
-
- ret = 0;
- switch (tmp.len) {
- case 3:
- ret += (uint64_t)tmp_data[2] * 1000000000000000000ULL;
- case 2:
- ret += (uint64_t)tmp_data[1] * 1000000000ULL;
- case 1:
- ret += tmp_data[0];
- break;
- default:
- abort(); /* GCOV_NOT_REACHED */
- }
-
- return ret;
-}
-
-static int64_t
-_c32_qget_i64(const mpd_t *a, uint32_t *status)
-{
- uint64_t u;
- int isneg;
-
- u = _c32_qget_u64(0, a, status);
- if (*status&MPD_Invalid_operation) {
- return INT64_MAX;
- }
-
- isneg = mpd_isnegative(a);
- if (u <= INT64_MAX) {
- return isneg ? -((int64_t)u) : (int64_t)u;
- }
- else if (isneg && u+(INT64_MIN+INT64_MAX) == INT64_MAX) {
- return INT64_MIN;
- }
-
- *status |= MPD_Invalid_operation;
- return INT64_MAX;
-}
-#endif /* CONFIG_32 && !LEGACY_COMPILER */
-
-#ifdef CONFIG_64
-/* quietly get a uint64_t from a decimal */
-uint64_t
-mpd_qget_u64(const mpd_t *a, uint32_t *status)
-{
- return mpd_qget_uint(a, status);
-}
-
-/* quietly get an int64_t from a decimal */
-int64_t
-mpd_qget_i64(const mpd_t *a, uint32_t *status)
-{
- return mpd_qget_ssize(a, status);
-}
-
-/* quietly get a uint32_t from a decimal */
-uint32_t
-mpd_qget_u32(const mpd_t *a, uint32_t *status)
-{
- uint32_t workstatus = 0;
- uint64_t x = mpd_qget_uint(a, &workstatus);
-
- if (workstatus&MPD_Invalid_operation) {
- *status |= workstatus;
- return UINT32_MAX;
- }
- if (x > UINT32_MAX) {
- *status |= MPD_Invalid_operation;
- return UINT32_MAX;
- }
-
- return (uint32_t)x;
-}
-
-/* quietly get an int32_t from a decimal */
-int32_t
-mpd_qget_i32(const mpd_t *a, uint32_t *status)
-{
- uint32_t workstatus = 0;
- int64_t x = mpd_qget_ssize(a, &workstatus);
-
- if (workstatus&MPD_Invalid_operation) {
- *status |= workstatus;
- return INT32_MAX;
- }
- if (x < INT32_MIN || x > INT32_MAX) {
- *status |= MPD_Invalid_operation;
- return INT32_MAX;
- }
-
- return (int32_t)x;
-}
-#else
-#ifndef LEGACY_COMPILER
-/* quietly get a uint64_t from a decimal */
-uint64_t
-mpd_qget_u64(const mpd_t *a, uint32_t *status)
-{
- uint32_t workstatus = 0;
- uint64_t x = _c32_qget_u64(1, a, &workstatus);
- *status |= workstatus;
- return x;
-}
-
-/* quietly get an int64_t from a decimal */
-int64_t
-mpd_qget_i64(const mpd_t *a, uint32_t *status)
-{
- uint32_t workstatus = 0;
- int64_t x = _c32_qget_i64(a, &workstatus);
- *status |= workstatus;
- return x;
-}
-#endif
-
-/* quietly get a uint32_t from a decimal */
-uint32_t
-mpd_qget_u32(const mpd_t *a, uint32_t *status)
-{
- return mpd_qget_uint(a, status);
-}
-
-/* quietly get an int32_t from a decimal */
-int32_t
-mpd_qget_i32(const mpd_t *a, uint32_t *status)
-{
- return mpd_qget_ssize(a, status);
-}
-#endif
-
-
-/******************************************************************************/
-/* Filtering input of functions, finalizing output of functions */
-/******************************************************************************/
-
-/*
- * Check if the operand is NaN, copy to result and return 1 if this is
- * the case. Copying can fail since NaNs are allowed to have a payload that
- * does not fit in MPD_MINALLOC.
- */
-int
-mpd_qcheck_nan(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- if (mpd_isnan(a)) {
- *status |= mpd_issnan(a) ? MPD_Invalid_operation : 0;
- mpd_qcopy(result, a, status);
- mpd_set_qnan(result);
- _mpd_fix_nan(result, ctx);
- return 1;
- }
- return 0;
-}
-
-/*
- * Check if either operand is NaN, copy to result and return 1 if this
- * is the case. Copying can fail since NaNs are allowed to have a payload
- * that does not fit in MPD_MINALLOC.
- */
-int
-mpd_qcheck_nans(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- if ((a->flags|b->flags)&(MPD_NAN|MPD_SNAN)) {
- const mpd_t *choice = b;
- if (mpd_issnan(a)) {
- choice = a;
- *status |= MPD_Invalid_operation;
- }
- else if (mpd_issnan(b)) {
- *status |= MPD_Invalid_operation;
- }
- else if (mpd_isqnan(a)) {
- choice = a;
- }
- mpd_qcopy(result, choice, status);
- mpd_set_qnan(result);
- _mpd_fix_nan(result, ctx);
- return 1;
- }
- return 0;
-}
-
-/*
- * Check if one of the operands is NaN, copy to result and return 1 if this
- * is the case. Copying can fail since NaNs are allowed to have a payload
- * that does not fit in MPD_MINALLOC.
- */
-static int
-mpd_qcheck_3nans(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c,
- const mpd_context_t *ctx, uint32_t *status)
-{
- if ((a->flags|b->flags|c->flags)&(MPD_NAN|MPD_SNAN)) {
- const mpd_t *choice = c;
- if (mpd_issnan(a)) {
- choice = a;
- *status |= MPD_Invalid_operation;
- }
- else if (mpd_issnan(b)) {
- choice = b;
- *status |= MPD_Invalid_operation;
- }
- else if (mpd_issnan(c)) {
- *status |= MPD_Invalid_operation;
- }
- else if (mpd_isqnan(a)) {
- choice = a;
- }
- else if (mpd_isqnan(b)) {
- choice = b;
- }
- mpd_qcopy(result, choice, status);
- mpd_set_qnan(result);
- _mpd_fix_nan(result, ctx);
- return 1;
- }
- return 0;
-}
-
-/* Check if rounding digit 'rnd' leads to an increment. */
-static inline int
-_mpd_rnd_incr(const mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx)
-{
- int ld;
-
- switch (ctx->round) {
- case MPD_ROUND_DOWN: case MPD_ROUND_TRUNC:
- return 0;
- case MPD_ROUND_HALF_UP:
- return (rnd >= 5);
- case MPD_ROUND_HALF_EVEN:
- return (rnd > 5) || ((rnd == 5) && mpd_isoddcoeff(dec));
- case MPD_ROUND_CEILING:
- return !(rnd == 0 || mpd_isnegative(dec));
- case MPD_ROUND_FLOOR:
- return !(rnd == 0 || mpd_ispositive(dec));
- case MPD_ROUND_HALF_DOWN:
- return (rnd > 5);
- case MPD_ROUND_UP:
- return !(rnd == 0);
- case MPD_ROUND_05UP:
- ld = (int)mpd_lsd(dec->data[0]);
- return (!(rnd == 0) && (ld == 0 || ld == 5));
- default:
- /* Without a valid context, further results will be undefined. */
- return 0; /* GCOV_NOT_REACHED */
- }
-}
-
-/*
- * Apply rounding to a decimal that has been right-shifted into a full
- * precision decimal. If an increment leads to an overflow of the precision,
- * adjust the coefficient and the exponent and check the new exponent for
- * overflow.
- */
-static inline void
-_mpd_apply_round(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx,
- uint32_t *status)
-{
- if (_mpd_rnd_incr(dec, rnd, ctx)) {
- /* We have a number with exactly ctx->prec digits. The increment
- * can only lead to an overflow if the decimal is all nines. In
- * that case, the result is a power of ten with prec+1 digits.
- *
- * If the precision is a multiple of MPD_RDIGITS, this situation is
- * detected by _mpd_baseincr returning a carry.
- * If the precision is not a multiple of MPD_RDIGITS, we have to
- * check if the result has one digit too many.
- */
- mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len);
- if (carry) {
- dec->data[dec->len-1] = mpd_pow10[MPD_RDIGITS-1];
- dec->exp += 1;
- _mpd_check_exp(dec, ctx, status);
- return;
- }
- mpd_setdigits(dec);
- if (dec->digits > ctx->prec) {
- mpd_qshiftr_inplace(dec, 1);
- dec->exp += 1;
- dec->digits = ctx->prec;
- _mpd_check_exp(dec, ctx, status);
- }
- }
-}
-
-/*
- * Apply rounding to a decimal. Allow overflow of the precision.
- */
-static inline void
-_mpd_apply_round_excess(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx,
- uint32_t *status)
-{
- if (_mpd_rnd_incr(dec, rnd, ctx)) {
- mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len);
- if (carry) {
- if (!mpd_qresize(dec, dec->len+1, status)) {
- return;
- }
- dec->data[dec->len] = 1;
- dec->len += 1;
- }
- mpd_setdigits(dec);
- }
-}
-
-/*
- * Apply rounding to a decimal that has been right-shifted into a decimal
- * with full precision or less. Return failure if an increment would
- * overflow the precision.
- */
-static inline int
-_mpd_apply_round_fit(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx,
- uint32_t *status)
-{
- if (_mpd_rnd_incr(dec, rnd, ctx)) {
- mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len);
- if (carry) {
- if (!mpd_qresize(dec, dec->len+1, status)) {
- return 0;
- }
- dec->data[dec->len] = 1;
- dec->len += 1;
- }
- mpd_setdigits(dec);
- if (dec->digits > ctx->prec) {
- mpd_seterror(dec, MPD_Invalid_operation, status);
- return 0;
- }
- }
- return 1;
-}
-
-/* Check a normal number for overflow, underflow, clamping. If the operand
- is modified, it will be zero, special or (sub)normal with a coefficient
- that fits into the current context precision. */
-static inline void
-_mpd_check_exp(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_ssize_t adjexp, etiny, shift;
- int rnd;
-
- adjexp = mpd_adjexp(dec);
- if (adjexp > ctx->emax) {
-
- if (mpd_iszerocoeff(dec)) {
- dec->exp = ctx->emax;
- if (ctx->clamp) {
- dec->exp -= (ctx->prec-1);
- }
- mpd_zerocoeff(dec);
- *status |= MPD_Clamped;
- return;
- }
-
- switch (ctx->round) {
- case MPD_ROUND_HALF_UP: case MPD_ROUND_HALF_EVEN:
- case MPD_ROUND_HALF_DOWN: case MPD_ROUND_UP:
- case MPD_ROUND_TRUNC:
- mpd_setspecial(dec, mpd_sign(dec), MPD_INF);
- break;
- case MPD_ROUND_DOWN: case MPD_ROUND_05UP:
- mpd_qmaxcoeff(dec, ctx, status);
- dec->exp = ctx->emax - ctx->prec + 1;
- break;
- case MPD_ROUND_CEILING:
- if (mpd_isnegative(dec)) {
- mpd_qmaxcoeff(dec, ctx, status);
- dec->exp = ctx->emax - ctx->prec + 1;
- }
- else {
- mpd_setspecial(dec, MPD_POS, MPD_INF);
- }
- break;
- case MPD_ROUND_FLOOR:
- if (mpd_ispositive(dec)) {
- mpd_qmaxcoeff(dec, ctx, status);
- dec->exp = ctx->emax - ctx->prec + 1;
- }
- else {
- mpd_setspecial(dec, MPD_NEG, MPD_INF);
- }
- break;
- default: /* debug */
- abort(); /* GCOV_NOT_REACHED */
- }
-
- *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded;
-
- } /* fold down */
- else if (ctx->clamp && dec->exp > mpd_etop(ctx)) {
- /* At this point adjexp=exp+digits-1 <= emax and exp > etop=emax-prec+1:
- * (1) shift = exp -emax+prec-1 > 0
- * (2) digits+shift = exp+digits-1 - emax + prec <= prec */
- shift = dec->exp - mpd_etop(ctx);
- if (!mpd_qshiftl(dec, dec, shift, status)) {
- return;
- }
- dec->exp -= shift;
- *status |= MPD_Clamped;
- if (!mpd_iszerocoeff(dec) && adjexp < ctx->emin) {
- /* Underflow is impossible, since exp < etiny=emin-prec+1
- * and exp > etop=emax-prec+1 would imply emax < emin. */
- *status |= MPD_Subnormal;
- }
- }
- else if (adjexp < ctx->emin) {
-
- etiny = mpd_etiny(ctx);
-
- if (mpd_iszerocoeff(dec)) {
- if (dec->exp < etiny) {
- dec->exp = etiny;
- mpd_zerocoeff(dec);
- *status |= MPD_Clamped;
- }
- return;
- }
-
- *status |= MPD_Subnormal;
- if (dec->exp < etiny) {
- /* At this point adjexp=exp+digits-1 < emin and exp < etiny=emin-prec+1:
- * (1) shift = emin-prec+1 - exp > 0
- * (2) digits-shift = exp+digits-1 - emin + prec < prec */
- shift = etiny - dec->exp;
- rnd = (int)mpd_qshiftr_inplace(dec, shift);
- dec->exp = etiny;
- /* We always have a spare digit in case of an increment. */
- _mpd_apply_round_excess(dec, rnd, ctx, status);
- *status |= MPD_Rounded;
- if (rnd) {
- *status |= (MPD_Inexact|MPD_Underflow);
- if (mpd_iszerocoeff(dec)) {
- mpd_zerocoeff(dec);
- *status |= MPD_Clamped;
- }
- }
- }
- /* Case exp >= etiny=emin-prec+1:
- * (1) adjexp=exp+digits-1 < emin
- * (2) digits < emin-exp+1 <= prec */
- }
-}
-
-/* Transcendental functions do not always set Underflow reliably,
- * since they only use as much precision as is necessary for correct
- * rounding. If a result like 1.0000000000e-101 is finalized, there
- * is no rounding digit that would trigger Underflow. But we can
- * assume Inexact, so a short check suffices. */
-static inline void
-mpd_check_underflow(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status)
-{
- if (mpd_adjexp(dec) < ctx->emin && !mpd_iszero(dec) &&
- dec->exp < mpd_etiny(ctx)) {
- *status |= MPD_Underflow;
- }
-}
-
-/* Check if a normal number must be rounded after the exponent has been checked. */
-static inline void
-_mpd_check_round(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_uint_t rnd;
- mpd_ssize_t shift;
-
- /* must handle specials: _mpd_check_exp() can produce infinities or NaNs */
- if (mpd_isspecial(dec)) {
- return;
- }
-
- if (dec->digits > ctx->prec) {
- shift = dec->digits - ctx->prec;
- rnd = mpd_qshiftr_inplace(dec, shift);
- dec->exp += shift;
- _mpd_apply_round(dec, rnd, ctx, status);
- *status |= MPD_Rounded;
- if (rnd) {
- *status |= MPD_Inexact;
- }
- }
-}
-
-/* Finalize all operations. */
-void
-mpd_qfinalize(mpd_t *result, const mpd_context_t *ctx, uint32_t *status)
-{
- if (mpd_isspecial(result)) {
- if (mpd_isnan(result)) {
- _mpd_fix_nan(result, ctx);
- }
- return;
- }
-
- _mpd_check_exp(result, ctx, status);
- _mpd_check_round(result, ctx, status);
-}
-
-
-/******************************************************************************/
-/* Copying */
-/******************************************************************************/
-
-/* Internal function: Copy a decimal, share data with src: USE WITH CARE! */
-static inline void
-_mpd_copy_shared(mpd_t *dest, const mpd_t *src)
-{
- dest->flags = src->flags;
- dest->exp = src->exp;
- dest->digits = src->digits;
- dest->len = src->len;
- dest->alloc = src->alloc;
- dest->data = src->data;
-
- mpd_set_shared_data(dest);
-}
-
-/*
- * Copy a decimal. In case of an error, status is set to MPD_Malloc_error.
- */
-int
-mpd_qcopy(mpd_t *result, const mpd_t *a, uint32_t *status)
-{
- if (result == a) return 1;
-
- if (!mpd_qresize(result, a->len, status)) {
- return 0;
- }
-
- mpd_copy_flags(result, a);
- result->exp = a->exp;
- result->digits = a->digits;
- result->len = a->len;
- memcpy(result->data, a->data, a->len * (sizeof *result->data));
-
- return 1;
-}
-
-/* Same as mpd_qcopy, but do not set the result to NaN on failure. */
-int
-mpd_qcopy_cxx(mpd_t *result, const mpd_t *a)
-{
- if (result == a) return 1;
-
- if (!mpd_qresize_cxx(result, a->len)) {
- return 0;
- }
-
- mpd_copy_flags(result, a);
- result->exp = a->exp;
- result->digits = a->digits;
- result->len = a->len;
- memcpy(result->data, a->data, a->len * (sizeof *result->data));
-
- return 1;
-}
-
-/*
- * Copy to a decimal with a static buffer. The caller has to make sure that
- * the buffer is big enough. Cannot fail.
- */
-static void
-mpd_qcopy_static(mpd_t *result, const mpd_t *a)
-{
- if (result == a) return;
-
- memcpy(result->data, a->data, a->len * (sizeof *result->data));
-
- mpd_copy_flags(result, a);
- result->exp = a->exp;
- result->digits = a->digits;
- result->len = a->len;
-}
-
-/*
- * Return a newly allocated copy of the operand. In case of an error,
- * status is set to MPD_Malloc_error and the return value is NULL.
- */
-mpd_t *
-mpd_qncopy(const mpd_t *a)
-{
- mpd_t *result;
-
- if ((result = mpd_qnew_size(a->len)) == NULL) {
- return NULL;
- }
- memcpy(result->data, a->data, a->len * (sizeof *result->data));
- mpd_copy_flags(result, a);
- result->exp = a->exp;
- result->digits = a->digits;
- result->len = a->len;
-
- return result;
-}
-
-/*
- * Copy a decimal and set the sign to positive. In case of an error, the
- * status is set to MPD_Malloc_error.
- */
-int
-mpd_qcopy_abs(mpd_t *result, const mpd_t *a, uint32_t *status)
-{
- if (!mpd_qcopy(result, a, status)) {
- return 0;
- }
- mpd_set_positive(result);
- return 1;
-}
-
-/*
- * Copy a decimal and negate the sign. In case of an error, the
- * status is set to MPD_Malloc_error.
- */
-int
-mpd_qcopy_negate(mpd_t *result, const mpd_t *a, uint32_t *status)
-{
- if (!mpd_qcopy(result, a, status)) {
- return 0;
- }
- _mpd_negate(result);
- return 1;
-}
-
-/*
- * Copy a decimal, setting the sign of the first operand to the sign of the
- * second operand. In case of an error, the status is set to MPD_Malloc_error.
- */
-int
-mpd_qcopy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status)
-{
- uint8_t sign_b = mpd_sign(b); /* result may equal b! */
-
- if (!mpd_qcopy(result, a, status)) {
- return 0;
- }
- mpd_set_sign(result, sign_b);
- return 1;
-}
-
-
-/******************************************************************************/
-/* Comparisons */
-/******************************************************************************/
-
-/*
- * For all functions that compare two operands and return an int the usual
- * convention applies to the return value:
- *
- * -1 if op1 < op2
- * 0 if op1 == op2
- * 1 if op1 > op2
- *
- * INT_MAX for error
- */
-
-
-/* Convenience macro. If a and b are not equal, return from the calling
- * function with the correct comparison value. */
-#define CMP_EQUAL_OR_RETURN(a, b) \
- if (a != b) { \
- if (a < b) { \
- return -1; \
- } \
- return 1; \
- }
-
-/*
- * Compare the data of big and small. This function does the equivalent
- * of first shifting small to the left and then comparing the data of
- * big and small, except that no allocation for the left shift is needed.
- */
-static int
-_mpd_basecmp(mpd_uint_t *big, mpd_uint_t *small, mpd_size_t n, mpd_size_t m,
- mpd_size_t shift)
-{
-#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__)
- /* spurious uninitialized warnings */
- mpd_uint_t l=l, lprev=lprev, h=h;
-#else
- mpd_uint_t l, lprev, h;
-#endif
- mpd_uint_t q, r;
- mpd_uint_t ph, x;
-
- assert(m > 0 && n >= m && shift > 0);
-
- _mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS);
-
- if (r != 0) {
-
- ph = mpd_pow10[r];
-
- --m; --n;
- _mpd_divmod_pow10(&h, &lprev, small[m--], MPD_RDIGITS-r);
- if (h != 0) {
- CMP_EQUAL_OR_RETURN(big[n], h)
- --n;
- }
- for (; m != MPD_SIZE_MAX; m--,n--) {
- _mpd_divmod_pow10(&h, &l, small[m], MPD_RDIGITS-r);
- x = ph * lprev + h;
- CMP_EQUAL_OR_RETURN(big[n], x)
- lprev = l;
- }
- x = ph * lprev;
- CMP_EQUAL_OR_RETURN(big[q], x)
- }
- else {
- while (--m != MPD_SIZE_MAX) {
- CMP_EQUAL_OR_RETURN(big[m+q], small[m])
- }
- }
-
- return !_mpd_isallzero(big, q);
-}
-
-/* Compare two decimals with the same adjusted exponent. */
-static int
-_mpd_cmp_same_adjexp(const mpd_t *a, const mpd_t *b)
-{
- mpd_ssize_t shift, i;
-
- if (a->exp != b->exp) {
- /* Cannot wrap: a->exp + a->digits = b->exp + b->digits, so
- * a->exp - b->exp = b->digits - a->digits. */
- shift = a->exp - b->exp;
- if (shift > 0) {
- return -1 * _mpd_basecmp(b->data, a->data, b->len, a->len, shift);
- }
- else {
- return _mpd_basecmp(a->data, b->data, a->len, b->len, -shift);
- }
- }
-
- /*
- * At this point adjexp(a) == adjexp(b) and a->exp == b->exp,
- * so a->digits == b->digits, therefore a->len == b->len.
- */
- for (i = a->len-1; i >= 0; --i) {
- CMP_EQUAL_OR_RETURN(a->data[i], b->data[i])
- }
-
- return 0;
-}
-
-/* Compare two numerical values. */
-static int
-_mpd_cmp(const mpd_t *a, const mpd_t *b)
-{
- mpd_ssize_t adjexp_a, adjexp_b;
-
- /* equal pointers */
- if (a == b) {
- return 0;
- }
-
- /* infinities */
- if (mpd_isinfinite(a)) {
- if (mpd_isinfinite(b)) {
- return mpd_isnegative(b) - mpd_isnegative(a);
- }
- return mpd_arith_sign(a);
- }
- if (mpd_isinfinite(b)) {
- return -mpd_arith_sign(b);
- }
-
- /* zeros */
- if (mpd_iszerocoeff(a)) {
- if (mpd_iszerocoeff(b)) {
- return 0;
- }
- return -mpd_arith_sign(b);
- }
- if (mpd_iszerocoeff(b)) {
- return mpd_arith_sign(a);
- }
-
- /* different signs */
- if (mpd_sign(a) != mpd_sign(b)) {
- return mpd_sign(b) - mpd_sign(a);
- }
-
- /* different adjusted exponents */
- adjexp_a = mpd_adjexp(a);
- adjexp_b = mpd_adjexp(b);
- if (adjexp_a != adjexp_b) {
- if (adjexp_a < adjexp_b) {
- return -1 * mpd_arith_sign(a);
- }
- return mpd_arith_sign(a);
- }
-
- /* same adjusted exponents */
- return _mpd_cmp_same_adjexp(a, b) * mpd_arith_sign(a);
-}
-
-/* Compare the absolutes of two numerical values. */
-static int
-_mpd_cmp_abs(const mpd_t *a, const mpd_t *b)
-{
- mpd_ssize_t adjexp_a, adjexp_b;
-
- /* equal pointers */
- if (a == b) {
- return 0;
- }
-
- /* infinities */
- if (mpd_isinfinite(a)) {
- if (mpd_isinfinite(b)) {
- return 0;
- }
- return 1;
- }
- if (mpd_isinfinite(b)) {
- return -1;
- }
-
- /* zeros */
- if (mpd_iszerocoeff(a)) {
- if (mpd_iszerocoeff(b)) {
- return 0;
- }
- return -1;
- }
- if (mpd_iszerocoeff(b)) {
- return 1;
- }
-
- /* different adjusted exponents */
- adjexp_a = mpd_adjexp(a);
- adjexp_b = mpd_adjexp(b);
- if (adjexp_a != adjexp_b) {
- if (adjexp_a < adjexp_b) {
- return -1;
- }
- return 1;
- }
-
- /* same adjusted exponents */
- return _mpd_cmp_same_adjexp(a, b);
-}
-
-/* Compare two values and return an integer result. */
-int
-mpd_qcmp(const mpd_t *a, const mpd_t *b, uint32_t *status)
-{
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_isnan(a) || mpd_isnan(b)) {
- *status |= MPD_Invalid_operation;
- return INT_MAX;
- }
- }
-
- return _mpd_cmp(a, b);
-}
-
-/*
- * Compare a and b, convert the usual integer result to a decimal and
- * store it in 'result'. For convenience, the integer result of the comparison
- * is returned. Comparisons involving NaNs return NaN/INT_MAX.
- */
-int
-mpd_qcompare(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- int c;
-
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_qcheck_nans(result, a, b, ctx, status)) {
- return INT_MAX;
- }
- }
-
- c = _mpd_cmp(a, b);
- _settriple(result, (c < 0), (c != 0), 0);
- return c;
-}
-
-/* Same as mpd_compare(), but signal for all NaNs, i.e. also for quiet NaNs. */
-int
-mpd_qcompare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- int c;
-
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_qcheck_nans(result, a, b, ctx, status)) {
- *status |= MPD_Invalid_operation;
- return INT_MAX;
- }
- }
-
- c = _mpd_cmp(a, b);
- _settriple(result, (c < 0), (c != 0), 0);
- return c;
-}
-
-/* Compare the operands using a total order. */
-int
-mpd_cmp_total(const mpd_t *a, const mpd_t *b)
-{
- mpd_t aa, bb;
- int nan_a, nan_b;
- int c;
-
- if (mpd_sign(a) != mpd_sign(b)) {
- return mpd_sign(b) - mpd_sign(a);
- }
-
-
- if (mpd_isnan(a)) {
- c = 1;
- if (mpd_isnan(b)) {
- nan_a = (mpd_isqnan(a)) ? 1 : 0;
- nan_b = (mpd_isqnan(b)) ? 1 : 0;
- if (nan_b == nan_a) {
- if (a->len > 0 && b->len > 0) {
- _mpd_copy_shared(&aa, a);
- _mpd_copy_shared(&bb, b);
- aa.exp = bb.exp = 0;
- /* compare payload */
- c = _mpd_cmp_abs(&aa, &bb);
- }
- else {
- c = (a->len > 0) - (b->len > 0);
- }
- }
- else {
- c = nan_a - nan_b;
- }
- }
- }
- else if (mpd_isnan(b)) {
- c = -1;
- }
- else {
- c = _mpd_cmp_abs(a, b);
- if (c == 0 && a->exp != b->exp) {
- c = (a->exp < b->exp) ? -1 : 1;
- }
- }
-
- return c * mpd_arith_sign(a);
-}
-
-/*
- * Compare a and b according to a total order, convert the usual integer result
- * to a decimal and store it in 'result'. For convenience, the integer result
- * of the comparison is returned.
- */
-int
-mpd_compare_total(mpd_t *result, const mpd_t *a, const mpd_t *b)
-{
- int c;
-
- c = mpd_cmp_total(a, b);
- _settriple(result, (c < 0), (c != 0), 0);
- return c;
-}
-
-/* Compare the magnitude of the operands using a total order. */
-int
-mpd_cmp_total_mag(const mpd_t *a, const mpd_t *b)
-{
- mpd_t aa, bb;
-
- _mpd_copy_shared(&aa, a);
- _mpd_copy_shared(&bb, b);
-
- mpd_set_positive(&aa);
- mpd_set_positive(&bb);
-
- return mpd_cmp_total(&aa, &bb);
-}
-
-/*
- * Compare the magnitude of a and b according to a total order, convert the
- * the usual integer result to a decimal and store it in 'result'.
- * For convenience, the integer result of the comparison is returned.
- */
-int
-mpd_compare_total_mag(mpd_t *result, const mpd_t *a, const mpd_t *b)
-{
- int c;
-
- c = mpd_cmp_total_mag(a, b);
- _settriple(result, (c < 0), (c != 0), 0);
- return c;
-}
-
-/* Determine an ordering for operands that are numerically equal. */
-static inline int
-_mpd_cmp_numequal(const mpd_t *a, const mpd_t *b)
-{
- int sign_a, sign_b;
- int c;
-
- sign_a = mpd_sign(a);
- sign_b = mpd_sign(b);
- if (sign_a != sign_b) {
- c = sign_b - sign_a;
- }
- else {
- c = (a->exp < b->exp) ? -1 : 1;
- c *= mpd_arith_sign(a);
- }
-
- return c;
-}
-
-
-/******************************************************************************/
-/* Shifting the coefficient */
-/******************************************************************************/
-
-/*
- * Shift the coefficient of the operand to the left, no check for specials.
- * Both operands may be the same pointer. If the result length has to be
- * increased, mpd_qresize() might fail with MPD_Malloc_error.
- */
-int
-mpd_qshiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status)
-{
- mpd_ssize_t size;
-
- assert(!mpd_isspecial(a));
- assert(n >= 0);
-
- if (mpd_iszerocoeff(a) || n == 0) {
- return mpd_qcopy(result, a, status);
- }
-
- size = mpd_digits_to_size(a->digits+n);
- if (!mpd_qresize(result, size, status)) {
- return 0; /* result is NaN */
- }
-
- _mpd_baseshiftl(result->data, a->data, size, a->len, n);
-
- mpd_copy_flags(result, a);
- result->exp = a->exp;
- result->digits = a->digits+n;
- result->len = size;
-
- return 1;
-}
-
-/* Determine the rounding indicator if all digits of the coefficient are shifted
- * out of the picture. */
-static mpd_uint_t
-_mpd_get_rnd(const mpd_uint_t *data, mpd_ssize_t len, int use_msd)
-{
- mpd_uint_t rnd = 0, rest = 0, word;
-
- word = data[len-1];
- /* special treatment for the most significant digit if shift == digits */
- if (use_msd) {
- _mpd_divmod_pow10(&rnd, &rest, word, mpd_word_digits(word)-1);
- if (len > 1 && rest == 0) {
- rest = !_mpd_isallzero(data, len-1);
- }
- }
- else {
- rest = !_mpd_isallzero(data, len);
- }
-
- return (rnd == 0 || rnd == 5) ? rnd + !!rest : rnd;
-}
-
-/*
- * Same as mpd_qshiftr(), but 'result' is an mpd_t with a static coefficient.
- * It is the caller's responsibility to ensure that the coefficient is big
- * enough. The function cannot fail.
- */
-static mpd_uint_t
-mpd_qsshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n)
-{
- mpd_uint_t rnd;
- mpd_ssize_t size;
-
- assert(!mpd_isspecial(a));
- assert(n >= 0);
-
- if (mpd_iszerocoeff(a) || n == 0) {
- mpd_qcopy_static(result, a);
- return 0;
- }
-
- if (n >= a->digits) {
- rnd = _mpd_get_rnd(a->data, a->len, (n==a->digits));
- mpd_zerocoeff(result);
- }
- else {
- result->digits = a->digits-n;
- size = mpd_digits_to_size(result->digits);
- rnd = _mpd_baseshiftr(result->data, a->data, a->len, n);
- result->len = size;
- }
-
- mpd_copy_flags(result, a);
- result->exp = a->exp;
-
- return rnd;
-}
-
-/*
- * Inplace shift of the coefficient to the right, no check for specials.
- * Returns the rounding indicator for mpd_rnd_incr().
- * The function cannot fail.
- */
-mpd_uint_t
-mpd_qshiftr_inplace(mpd_t *result, mpd_ssize_t n)
-{
- uint32_t dummy;
- mpd_uint_t rnd;
- mpd_ssize_t size;
-
- assert(!mpd_isspecial(result));
- assert(n >= 0);
-
- if (mpd_iszerocoeff(result) || n == 0) {
- return 0;
- }
-
- if (n >= result->digits) {
- rnd = _mpd_get_rnd(result->data, result->len, (n==result->digits));
- mpd_zerocoeff(result);
- }
- else {
- rnd = _mpd_baseshiftr(result->data, result->data, result->len, n);
- result->digits -= n;
- size = mpd_digits_to_size(result->digits);
- /* reducing the size cannot fail */
- mpd_qresize(result, size, &dummy);
- result->len = size;
- }
-
- return rnd;
-}
-
-/*
- * Shift the coefficient of the operand to the right, no check for specials.
- * Both operands may be the same pointer. Returns the rounding indicator to
- * be used by mpd_rnd_incr(). If the result length has to be increased,
- * mpd_qcopy() or mpd_qresize() might fail with MPD_Malloc_error. In those
- * cases, MPD_UINT_MAX is returned.
- */
-mpd_uint_t
-mpd_qshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status)
-{
- mpd_uint_t rnd;
- mpd_ssize_t size;
-
- assert(!mpd_isspecial(a));
- assert(n >= 0);
-
- if (mpd_iszerocoeff(a) || n == 0) {
- if (!mpd_qcopy(result, a, status)) {
- return MPD_UINT_MAX;
- }
- return 0;
- }
-
- if (n >= a->digits) {
- rnd = _mpd_get_rnd(a->data, a->len, (n==a->digits));
- mpd_zerocoeff(result);
- }
- else {
- result->digits = a->digits-n;
- size = mpd_digits_to_size(result->digits);
- if (result == a) {
- rnd = _mpd_baseshiftr(result->data, a->data, a->len, n);
- /* reducing the size cannot fail */
- mpd_qresize(result, size, status);
- }
- else {
- if (!mpd_qresize(result, size, status)) {
- return MPD_UINT_MAX;
- }
- rnd = _mpd_baseshiftr(result->data, a->data, a->len, n);
- }
- result->len = size;
- }
-
- mpd_copy_flags(result, a);
- result->exp = a->exp;
-
- return rnd;
-}
-
-
-/******************************************************************************/
-/* Miscellaneous operations */
-/******************************************************************************/
-
-/* Logical And */
-void
-mpd_qand(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- const mpd_t *big = a, *small = b;
- mpd_uint_t x, y, z, xbit, ybit;
- int k, mswdigits;
- mpd_ssize_t i;
-
- if (mpd_isspecial(a) || mpd_isspecial(b) ||
- mpd_isnegative(a) || mpd_isnegative(b) ||
- a->exp != 0 || b->exp != 0) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- if (b->digits > a->digits) {
- big = b;
- small = a;
- }
- if (!mpd_qresize(result, big->len, status)) {
- return;
- }
-
-
- /* full words */
- for (i = 0; i < small->len-1; i++) {
- x = small->data[i];
- y = big->data[i];
- z = 0;
- for (k = 0; k < MPD_RDIGITS; k++) {
- xbit = x % 10;
- x /= 10;
- ybit = y % 10;
- y /= 10;
- if (xbit > 1 || ybit > 1) {
- goto invalid_operation;
- }
- z += (xbit&ybit) ? mpd_pow10[k] : 0;
- }
- result->data[i] = z;
- }
- /* most significant word of small */
- x = small->data[i];
- y = big->data[i];
- z = 0;
- mswdigits = mpd_word_digits(x);
- for (k = 0; k < mswdigits; k++) {
- xbit = x % 10;
- x /= 10;
- ybit = y % 10;
- y /= 10;
- if (xbit > 1 || ybit > 1) {
- goto invalid_operation;
- }
- z += (xbit&ybit) ? mpd_pow10[k] : 0;
- }
- result->data[i++] = z;
-
- /* scan the rest of y for digits > 1 */
- for (; k < MPD_RDIGITS; k++) {
- ybit = y % 10;
- y /= 10;
- if (ybit > 1) {
- goto invalid_operation;
- }
- }
- /* scan the rest of big for digits > 1 */
- for (; i < big->len; i++) {
- y = big->data[i];
- for (k = 0; k < MPD_RDIGITS; k++) {
- ybit = y % 10;
- y /= 10;
- if (ybit > 1) {
- goto invalid_operation;
- }
- }
- }
-
- mpd_clear_flags(result);
- result->exp = 0;
- result->len = _mpd_real_size(result->data, small->len);
- mpd_qresize(result, result->len, status);
- mpd_setdigits(result);
- _mpd_cap(result, ctx);
- return;
-
-invalid_operation:
- mpd_seterror(result, MPD_Invalid_operation, status);
-}
-
-/* Class of an operand. Returns a pointer to the constant name. */
-const char *
-mpd_class(const mpd_t *a, const mpd_context_t *ctx)
-{
- if (mpd_isnan(a)) {
- if (mpd_isqnan(a))
- return "NaN";
- else
- return "sNaN";
- }
- else if (mpd_ispositive(a)) {
- if (mpd_isinfinite(a))
- return "+Infinity";
- else if (mpd_iszero(a))
- return "+Zero";
- else if (mpd_isnormal(a, ctx))
- return "+Normal";
- else
- return "+Subnormal";
- }
- else {
- if (mpd_isinfinite(a))
- return "-Infinity";
- else if (mpd_iszero(a))
- return "-Zero";
- else if (mpd_isnormal(a, ctx))
- return "-Normal";
- else
- return "-Subnormal";
- }
-}
-
-/* Logical Xor */
-void
-mpd_qinvert(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_uint_t x, z, xbit;
- mpd_ssize_t i, digits, len;
- mpd_ssize_t q, r;
- int k;
-
- if (mpd_isspecial(a) || mpd_isnegative(a) || a->exp != 0) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- digits = (a->digits < ctx->prec) ? ctx->prec : a->digits;
- _mpd_idiv_word(&q, &r, digits, MPD_RDIGITS);
- len = (r == 0) ? q : q+1;
- if (!mpd_qresize(result, len, status)) {
- return;
- }
-
- for (i = 0; i < len; i++) {
- x = (i < a->len) ? a->data[i] : 0;
- z = 0;
- for (k = 0; k < MPD_RDIGITS; k++) {
- xbit = x % 10;
- x /= 10;
- if (xbit > 1) {
- goto invalid_operation;
- }
- z += !xbit ? mpd_pow10[k] : 0;
- }
- result->data[i] = z;
- }
-
- mpd_clear_flags(result);
- result->exp = 0;
- result->len = _mpd_real_size(result->data, len);
- mpd_qresize(result, result->len, status);
- mpd_setdigits(result);
- _mpd_cap(result, ctx);
- return;
-
-invalid_operation:
- mpd_seterror(result, MPD_Invalid_operation, status);
-}
-
-/* Exponent of the magnitude of the most significant digit of the operand. */
-void
-mpd_qlogb(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- if (mpd_isspecial(a)) {
- if (mpd_qcheck_nan(result, a, ctx, status)) {
- return;
- }
- mpd_setspecial(result, MPD_POS, MPD_INF);
- }
- else if (mpd_iszerocoeff(a)) {
- mpd_setspecial(result, MPD_NEG, MPD_INF);
- *status |= MPD_Division_by_zero;
- }
- else {
- mpd_qset_ssize(result, mpd_adjexp(a), ctx, status);
- }
-}
-
-/* Logical Or */
-void
-mpd_qor(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- const mpd_t *big = a, *small = b;
- mpd_uint_t x, y, z, xbit, ybit;
- int k, mswdigits;
- mpd_ssize_t i;
-
- if (mpd_isspecial(a) || mpd_isspecial(b) ||
- mpd_isnegative(a) || mpd_isnegative(b) ||
- a->exp != 0 || b->exp != 0) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- if (b->digits > a->digits) {
- big = b;
- small = a;
- }
- if (!mpd_qresize(result, big->len, status)) {
- return;
- }
-
-
- /* full words */
- for (i = 0; i < small->len-1; i++) {
- x = small->data[i];
- y = big->data[i];
- z = 0;
- for (k = 0; k < MPD_RDIGITS; k++) {
- xbit = x % 10;
- x /= 10;
- ybit = y % 10;
- y /= 10;
- if (xbit > 1 || ybit > 1) {
- goto invalid_operation;
- }
- z += (xbit|ybit) ? mpd_pow10[k] : 0;
- }
- result->data[i] = z;
- }
- /* most significant word of small */
- x = small->data[i];
- y = big->data[i];
- z = 0;
- mswdigits = mpd_word_digits(x);
- for (k = 0; k < mswdigits; k++) {
- xbit = x % 10;
- x /= 10;
- ybit = y % 10;
- y /= 10;
- if (xbit > 1 || ybit > 1) {
- goto invalid_operation;
- }
- z += (xbit|ybit) ? mpd_pow10[k] : 0;
- }
-
- /* scan for digits > 1 and copy the rest of y */
- for (; k < MPD_RDIGITS; k++) {
- ybit = y % 10;
- y /= 10;
- if (ybit > 1) {
- goto invalid_operation;
- }
- z += ybit*mpd_pow10[k];
- }
- result->data[i++] = z;
- /* scan for digits > 1 and copy the rest of big */
- for (; i < big->len; i++) {
- y = big->data[i];
- for (k = 0; k < MPD_RDIGITS; k++) {
- ybit = y % 10;
- y /= 10;
- if (ybit > 1) {
- goto invalid_operation;
- }
- }
- result->data[i] = big->data[i];
- }
-
- mpd_clear_flags(result);
- result->exp = 0;
- result->len = _mpd_real_size(result->data, big->len);
- mpd_qresize(result, result->len, status);
- mpd_setdigits(result);
- _mpd_cap(result, ctx);
- return;
-
-invalid_operation:
- mpd_seterror(result, MPD_Invalid_operation, status);
-}
-
-/*
- * Rotate the coefficient of 'a' by 'b' digits. 'b' must be an integer with
- * exponent 0.
- */
-void
-mpd_qrotate(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- uint32_t workstatus = 0;
- MPD_NEW_STATIC(tmp,0,0,0,0);
- MPD_NEW_STATIC(big,0,0,0,0);
- MPD_NEW_STATIC(small,0,0,0,0);
- mpd_ssize_t n, lshift, rshift;
-
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_qcheck_nans(result, a, b, ctx, status)) {
- return;
- }
- }
- if (b->exp != 0 || mpd_isinfinite(b)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- n = mpd_qget_ssize(b, &workstatus);
- if (workstatus&MPD_Invalid_operation) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- if (n > ctx->prec || n < -ctx->prec) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- if (mpd_isinfinite(a)) {
- mpd_qcopy(result, a, status);
- return;
- }
-
- if (n >= 0) {
- lshift = n;
- rshift = ctx->prec-n;
- }
- else {
- lshift = ctx->prec+n;
- rshift = -n;
- }
-
- if (a->digits > ctx->prec) {
- if (!mpd_qcopy(&tmp, a, status)) {
- mpd_seterror(result, MPD_Malloc_error, status);
- goto finish;
- }
- _mpd_cap(&tmp, ctx);
- a = &tmp;
- }
-
- if (!mpd_qshiftl(&big, a, lshift, status)) {
- mpd_seterror(result, MPD_Malloc_error, status);
- goto finish;
- }
- _mpd_cap(&big, ctx);
-
- if (mpd_qshiftr(&small, a, rshift, status) == MPD_UINT_MAX) {
- mpd_seterror(result, MPD_Malloc_error, status);
- goto finish;
- }
- _mpd_qadd(result, &big, &small, ctx, status);
-
-
-finish:
- mpd_del(&tmp);
- mpd_del(&big);
- mpd_del(&small);
-}
-
-/*
- * b must be an integer with exponent 0 and in the range +-2*(emax + prec).
- * XXX: In my opinion +-(2*emax + prec) would be more sensible.
- * The result is a with the value of b added to its exponent.
- */
-void
-mpd_qscaleb(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- uint32_t workstatus = 0;
- mpd_uint_t n, maxjump;
-#ifndef LEGACY_COMPILER
- int64_t exp;
-#else
- mpd_uint_t x;
- int x_sign, n_sign;
- mpd_ssize_t exp;
-#endif
-
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_qcheck_nans(result, a, b, ctx, status)) {
- return;
- }
- }
- if (b->exp != 0 || mpd_isinfinite(b)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- n = mpd_qabs_uint(b, &workstatus);
- /* the spec demands this */
- maxjump = 2 * (mpd_uint_t)(ctx->emax + ctx->prec);
-
- if (n > maxjump || workstatus&MPD_Invalid_operation) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- if (mpd_isinfinite(a)) {
- mpd_qcopy(result, a, status);
- return;
- }
-
-#ifndef LEGACY_COMPILER
- exp = a->exp + (int64_t)n * mpd_arith_sign(b);
- exp = (exp > MPD_EXP_INF) ? MPD_EXP_INF : exp;
- exp = (exp < MPD_EXP_CLAMP) ? MPD_EXP_CLAMP : exp;
-#else
- x = (a->exp < 0) ? -a->exp : a->exp;
- x_sign = (a->exp < 0) ? 1 : 0;
- n_sign = mpd_isnegative(b) ? 1 : 0;
-
- if (x_sign == n_sign) {
- x = x + n;
- if (x < n) x = MPD_UINT_MAX;
- }
- else {
- x_sign = (x >= n) ? x_sign : n_sign;
- x = (x >= n) ? x - n : n - x;
- }
- if (!x_sign && x > MPD_EXP_INF) x = MPD_EXP_INF;
- if (x_sign && x > -MPD_EXP_CLAMP) x = -MPD_EXP_CLAMP;
- exp = x_sign ? -((mpd_ssize_t)x) : (mpd_ssize_t)x;
-#endif
-
- mpd_qcopy(result, a, status);
- result->exp = (mpd_ssize_t)exp;
-
- mpd_qfinalize(result, ctx, status);
-}
-
-/*
- * Shift the coefficient by n digits, positive n is a left shift. In the case
- * of a left shift, the result is decapitated to fit the context precision. If
- * you don't want that, use mpd_shiftl().
- */
-void
-mpd_qshiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, const mpd_context_t *ctx,
- uint32_t *status)
-{
- if (mpd_isspecial(a)) {
- if (mpd_qcheck_nan(result, a, ctx, status)) {
- return;
- }
- mpd_qcopy(result, a, status);
- return;
- }
-
- if (n >= 0 && n <= ctx->prec) {
- mpd_qshiftl(result, a, n, status);
- _mpd_cap(result, ctx);
- }
- else if (n < 0 && n >= -ctx->prec) {
- if (!mpd_qcopy(result, a, status)) {
- return;
- }
- _mpd_cap(result, ctx);
- mpd_qshiftr_inplace(result, -n);
- }
- else {
- mpd_seterror(result, MPD_Invalid_operation, status);
- }
-}
-
-/*
- * Same as mpd_shiftn(), but the shift is specified by the decimal b, which
- * must be an integer with a zero exponent. Infinities remain infinities.
- */
-void
-mpd_qshift(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx,
- uint32_t *status)
-{
- uint32_t workstatus = 0;
- mpd_ssize_t n;
-
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_qcheck_nans(result, a, b, ctx, status)) {
- return;
- }
- }
- if (b->exp != 0 || mpd_isinfinite(b)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- n = mpd_qget_ssize(b, &workstatus);
- if (workstatus&MPD_Invalid_operation) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- if (n > ctx->prec || n < -ctx->prec) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- if (mpd_isinfinite(a)) {
- mpd_qcopy(result, a, status);
- return;
- }
-
- if (n >= 0) {
- mpd_qshiftl(result, a, n, status);
- _mpd_cap(result, ctx);
- }
- else {
- if (!mpd_qcopy(result, a, status)) {
- return;
- }
- _mpd_cap(result, ctx);
- mpd_qshiftr_inplace(result, -n);
- }
-}
-
-/* Logical Xor */
-void
-mpd_qxor(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- const mpd_t *big = a, *small = b;
- mpd_uint_t x, y, z, xbit, ybit;
- int k, mswdigits;
- mpd_ssize_t i;
-
- if (mpd_isspecial(a) || mpd_isspecial(b) ||
- mpd_isnegative(a) || mpd_isnegative(b) ||
- a->exp != 0 || b->exp != 0) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- if (b->digits > a->digits) {
- big = b;
- small = a;
- }
- if (!mpd_qresize(result, big->len, status)) {
- return;
- }
-
-
- /* full words */
- for (i = 0; i < small->len-1; i++) {
- x = small->data[i];
- y = big->data[i];
- z = 0;
- for (k = 0; k < MPD_RDIGITS; k++) {
- xbit = x % 10;
- x /= 10;
- ybit = y % 10;
- y /= 10;
- if (xbit > 1 || ybit > 1) {
- goto invalid_operation;
- }
- z += (xbit^ybit) ? mpd_pow10[k] : 0;
- }
- result->data[i] = z;
- }
- /* most significant word of small */
- x = small->data[i];
- y = big->data[i];
- z = 0;
- mswdigits = mpd_word_digits(x);
- for (k = 0; k < mswdigits; k++) {
- xbit = x % 10;
- x /= 10;
- ybit = y % 10;
- y /= 10;
- if (xbit > 1 || ybit > 1) {
- goto invalid_operation;
- }
- z += (xbit^ybit) ? mpd_pow10[k] : 0;
- }
-
- /* scan for digits > 1 and copy the rest of y */
- for (; k < MPD_RDIGITS; k++) {
- ybit = y % 10;
- y /= 10;
- if (ybit > 1) {
- goto invalid_operation;
- }
- z += ybit*mpd_pow10[k];
- }
- result->data[i++] = z;
- /* scan for digits > 1 and copy the rest of big */
- for (; i < big->len; i++) {
- y = big->data[i];
- for (k = 0; k < MPD_RDIGITS; k++) {
- ybit = y % 10;
- y /= 10;
- if (ybit > 1) {
- goto invalid_operation;
- }
- }
- result->data[i] = big->data[i];
- }
-
- mpd_clear_flags(result);
- result->exp = 0;
- result->len = _mpd_real_size(result->data, big->len);
- mpd_qresize(result, result->len, status);
- mpd_setdigits(result);
- _mpd_cap(result, ctx);
- return;
-
-invalid_operation:
- mpd_seterror(result, MPD_Invalid_operation, status);
-}
-
-
-/******************************************************************************/
-/* Arithmetic operations */
-/******************************************************************************/
-
-/*
- * The absolute value of a. If a is negative, the result is the same
- * as the result of the minus operation. Otherwise, the result is the
- * result of the plus operation.
- */
-void
-mpd_qabs(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- if (mpd_isspecial(a)) {
- if (mpd_qcheck_nan(result, a, ctx, status)) {
- return;
- }
- }
-
- if (mpd_isnegative(a)) {
- mpd_qminus(result, a, ctx, status);
- }
- else {
- mpd_qplus(result, a, ctx, status);
- }
-}
-
-static inline void
-_mpd_ptrswap(const mpd_t **a, const mpd_t **b)
-{
- const mpd_t *t = *a;
- *a = *b;
- *b = t;
-}
-
-/* Add or subtract infinities. */
-static void
-_mpd_qaddsub_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, uint8_t sign_b,
- uint32_t *status)
-{
- if (mpd_isinfinite(a)) {
- if (mpd_sign(a) != sign_b && mpd_isinfinite(b)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- }
- else {
- mpd_setspecial(result, mpd_sign(a), MPD_INF);
- }
- return;
- }
- assert(mpd_isinfinite(b));
- mpd_setspecial(result, sign_b, MPD_INF);
-}
-
-/* Add or subtract non-special numbers. */
-static void
-_mpd_qaddsub(mpd_t *result, const mpd_t *a, const mpd_t *b, uint8_t sign_b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- const mpd_t *big, *small;
- MPD_NEW_STATIC(big_aligned,0,0,0,0);
- MPD_NEW_CONST(tiny,0,0,1,1,1,1);
- mpd_uint_t carry;
- mpd_ssize_t newsize, shift;
- mpd_ssize_t exp, i;
- int swap = 0;
-
-
- /* compare exponents */
- big = a; small = b;
- if (big->exp != small->exp) {
- if (small->exp > big->exp) {
- _mpd_ptrswap(&big, &small);
- swap++;
- }
- /* align the coefficients */
- if (!mpd_iszerocoeff(big)) {
- exp = big->exp - 1;
- exp += (big->digits > ctx->prec) ? 0 : big->digits-ctx->prec-1;
- if (mpd_adjexp(small) < exp) {
- /*
- * Avoid huge shifts by substituting a value for small that is
- * guaranteed to produce the same results.
- *
- * adjexp(small) < exp if and only if:
- *
- * bdigits <= prec AND
- * bdigits+shift >= prec+2+sdigits AND
- * exp = bexp+bdigits-prec-2
- *
- * 1234567000000000 -> bdigits + shift
- * ----------XX1234 -> sdigits
- * ----------X1 -> tiny-digits
- * |- prec -|
- *
- * OR
- *
- * bdigits > prec AND
- * shift > sdigits AND
- * exp = bexp-1
- *
- * 1234567892100000 -> bdigits + shift
- * ----------XX1234 -> sdigits
- * ----------X1 -> tiny-digits
- * |- prec -|
- *
- * If tiny is zero, adding or subtracting is a no-op.
- * Otherwise, adding tiny generates a non-zero digit either
- * below the rounding digit or the least significant digit
- * of big. When subtracting, tiny is in the same position as
- * the carry that would be generated by subtracting sdigits.
- */
- mpd_copy_flags(&tiny, small);
- tiny.exp = exp;
- tiny.digits = 1;
- tiny.len = 1;
- tiny.data[0] = mpd_iszerocoeff(small) ? 0 : 1;
- small = &tiny;
- }
- /* This cannot wrap: the difference is positive and <= maxprec */
- shift = big->exp - small->exp;
- if (!mpd_qshiftl(&big_aligned, big, shift, status)) {
- mpd_seterror(result, MPD_Malloc_error, status);
- goto finish;
- }
- big = &big_aligned;
- }
- }
- result->exp = small->exp;
-
-
- /* compare length of coefficients */
- if (big->len < small->len) {
- _mpd_ptrswap(&big, &small);
- swap++;
- }
-
- newsize = big->len;
- if (!mpd_qresize(result, newsize, status)) {
- goto finish;
- }
-
- if (mpd_sign(a) == sign_b) {
-
- carry = _mpd_baseadd(result->data, big->data, small->data,
- big->len, small->len);
-
- if (carry) {
- newsize = big->len + 1;
- if (!mpd_qresize(result, newsize, status)) {
- goto finish;
- }
- result->data[newsize-1] = carry;
- }
-
- result->len = newsize;
- mpd_set_flags(result, sign_b);
- }
- else {
- if (big->len == small->len) {
- for (i=big->len-1; i >= 0; --i) {
- if (big->data[i] != small->data[i]) {
- if (big->data[i] < small->data[i]) {
- _mpd_ptrswap(&big, &small);
- swap++;
- }
- break;
- }
- }
- }
-
- _mpd_basesub(result->data, big->data, small->data,
- big->len, small->len);
- newsize = _mpd_real_size(result->data, big->len);
- /* resize to smaller cannot fail */
- (void)mpd_qresize(result, newsize, status);
-
- result->len = newsize;
- sign_b = (swap & 1) ? sign_b : mpd_sign(a);
- mpd_set_flags(result, sign_b);
-
- if (mpd_iszerocoeff(result)) {
- mpd_set_positive(result);
- if (ctx->round == MPD_ROUND_FLOOR) {
- mpd_set_negative(result);
- }
- }
- }
-
- mpd_setdigits(result);
-
-finish:
- mpd_del(&big_aligned);
-}
-
-/* Add a and b. No specials, no finalizing. */
-static void
-_mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- _mpd_qaddsub(result, a, b, mpd_sign(b), ctx, status);
-}
-
-/* Subtract b from a. No specials, no finalizing. */
-static void
-_mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- _mpd_qaddsub(result, a, b, !mpd_sign(b), ctx, status);
-}
-
-/* Add a and b. */
-void
-mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_qcheck_nans(result, a, b, ctx, status)) {
- return;
- }
- _mpd_qaddsub_inf(result, a, b, mpd_sign(b), status);
- return;
- }
-
- _mpd_qaddsub(result, a, b, mpd_sign(b), ctx, status);
- mpd_qfinalize(result, ctx, status);
-}
-
-/* Add a and b. Set NaN/Invalid_operation if the result is inexact. */
-static void
-_mpd_qadd_exact(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- uint32_t workstatus = 0;
-
- mpd_qadd(result, a, b, ctx, &workstatus);
- *status |= workstatus;
- if (workstatus & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- }
-}
-
-/* Subtract b from a. */
-void
-mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_qcheck_nans(result, a, b, ctx, status)) {
- return;
- }
- _mpd_qaddsub_inf(result, a, b, !mpd_sign(b), status);
- return;
- }
-
- _mpd_qaddsub(result, a, b, !mpd_sign(b), ctx, status);
- mpd_qfinalize(result, ctx, status);
-}
-
-/* Subtract b from a. Set NaN/Invalid_operation if the result is inexact. */
-static void
-_mpd_qsub_exact(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- uint32_t workstatus = 0;
-
- mpd_qsub(result, a, b, ctx, &workstatus);
- *status |= workstatus;
- if (workstatus & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- }
-}
-
-/* Add decimal and mpd_ssize_t. */
-void
-mpd_qadd_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qsset_ssize(&bb, b, &maxcontext, status);
- mpd_qadd(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-
-/* Add decimal and mpd_uint_t. */
-void
-mpd_qadd_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qsset_uint(&bb, b, &maxcontext, status);
- mpd_qadd(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-
-/* Subtract mpd_ssize_t from decimal. */
-void
-mpd_qsub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qsset_ssize(&bb, b, &maxcontext, status);
- mpd_qsub(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-
-/* Subtract mpd_uint_t from decimal. */
-void
-mpd_qsub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qsset_uint(&bb, b, &maxcontext, status);
- mpd_qsub(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-
-/* Add decimal and int32_t. */
-void
-mpd_qadd_i32(mpd_t *result, const mpd_t *a, int32_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qadd_ssize(result, a, b, ctx, status);
-}
-
-/* Add decimal and uint32_t. */
-void
-mpd_qadd_u32(mpd_t *result, const mpd_t *a, uint32_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qadd_uint(result, a, b, ctx, status);
-}
-
-#ifdef CONFIG_64
-/* Add decimal and int64_t. */
-void
-mpd_qadd_i64(mpd_t *result, const mpd_t *a, int64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qadd_ssize(result, a, b, ctx, status);
-}
-
-/* Add decimal and uint64_t. */
-void
-mpd_qadd_u64(mpd_t *result, const mpd_t *a, uint64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qadd_uint(result, a, b, ctx, status);
-}
-#elif !defined(LEGACY_COMPILER)
-/* Add decimal and int64_t. */
-void
-mpd_qadd_i64(mpd_t *result, const mpd_t *a, int64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qset_i64(&bb, b, &maxcontext, status);
- mpd_qadd(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-
-/* Add decimal and uint64_t. */
-void
-mpd_qadd_u64(mpd_t *result, const mpd_t *a, uint64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qset_u64(&bb, b, &maxcontext, status);
- mpd_qadd(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-#endif
-
-/* Subtract int32_t from decimal. */
-void
-mpd_qsub_i32(mpd_t *result, const mpd_t *a, int32_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qsub_ssize(result, a, b, ctx, status);
-}
-
-/* Subtract uint32_t from decimal. */
-void
-mpd_qsub_u32(mpd_t *result, const mpd_t *a, uint32_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qsub_uint(result, a, b, ctx, status);
-}
-
-#ifdef CONFIG_64
-/* Subtract int64_t from decimal. */
-void
-mpd_qsub_i64(mpd_t *result, const mpd_t *a, int64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qsub_ssize(result, a, b, ctx, status);
-}
-
-/* Subtract uint64_t from decimal. */
-void
-mpd_qsub_u64(mpd_t *result, const mpd_t *a, uint64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qsub_uint(result, a, b, ctx, status);
-}
-#elif !defined(LEGACY_COMPILER)
-/* Subtract int64_t from decimal. */
-void
-mpd_qsub_i64(mpd_t *result, const mpd_t *a, int64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qset_i64(&bb, b, &maxcontext, status);
- mpd_qsub(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-
-/* Subtract uint64_t from decimal. */
-void
-mpd_qsub_u64(mpd_t *result, const mpd_t *a, uint64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qset_u64(&bb, b, &maxcontext, status);
- mpd_qsub(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-#endif
-
-
-/* Divide infinities. */
-static void
-_mpd_qdiv_inf(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- if (mpd_isinfinite(a)) {
- if (mpd_isinfinite(b)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF);
- return;
- }
- assert(mpd_isinfinite(b));
- _settriple(result, mpd_sign(a)^mpd_sign(b), 0, mpd_etiny(ctx));
- *status |= MPD_Clamped;
-}
-
-enum {NO_IDEAL_EXP, SET_IDEAL_EXP};
-/* Divide a by b. */
-static void
-_mpd_qdiv(int action, mpd_t *q, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- MPD_NEW_STATIC(aligned,0,0,0,0);
- mpd_uint_t ld;
- mpd_ssize_t shift, exp, tz;
- mpd_ssize_t newsize;
- mpd_ssize_t ideal_exp;
- mpd_uint_t rem;
- uint8_t sign_a = mpd_sign(a);
- uint8_t sign_b = mpd_sign(b);
-
-
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_qcheck_nans(q, a, b, ctx, status)) {
- return;
- }
- _mpd_qdiv_inf(q, a, b, ctx, status);
- return;
- }
- if (mpd_iszerocoeff(b)) {
- if (mpd_iszerocoeff(a)) {
- mpd_seterror(q, MPD_Division_undefined, status);
- }
- else {
- mpd_setspecial(q, sign_a^sign_b, MPD_INF);
- *status |= MPD_Division_by_zero;
- }
- return;
- }
- if (mpd_iszerocoeff(a)) {
- exp = a->exp - b->exp;
- _settriple(q, sign_a^sign_b, 0, exp);
- mpd_qfinalize(q, ctx, status);
- return;
- }
-
- shift = (b->digits - a->digits) + ctx->prec + 1;
- ideal_exp = a->exp - b->exp;
- exp = ideal_exp - shift;
- if (shift > 0) {
- if (!mpd_qshiftl(&aligned, a, shift, status)) {
- mpd_seterror(q, MPD_Malloc_error, status);
- goto finish;
- }
- a = &aligned;
- }
- else if (shift < 0) {
- shift = -shift;
- if (!mpd_qshiftl(&aligned, b, shift, status)) {
- mpd_seterror(q, MPD_Malloc_error, status);
- goto finish;
- }
- b = &aligned;
- }
-
-
- newsize = a->len - b->len + 1;
- if ((q != b && q != a) || (q == b && newsize > b->len)) {
- if (!mpd_qresize(q, newsize, status)) {
- mpd_seterror(q, MPD_Malloc_error, status);
- goto finish;
- }
- }
-
-
- if (b->len == 1) {
- rem = _mpd_shortdiv(q->data, a->data, a->len, b->data[0]);
- }
- else if (b->len <= MPD_NEWTONDIV_CUTOFF) {
- int ret = _mpd_basedivmod(q->data, NULL, a->data, b->data,
- a->len, b->len);
- if (ret < 0) {
- mpd_seterror(q, MPD_Malloc_error, status);
- goto finish;
- }
- rem = ret;
- }
- else {
- MPD_NEW_STATIC(r,0,0,0,0);
- _mpd_base_ndivmod(q, &r, a, b, status);
- if (mpd_isspecial(q) || mpd_isspecial(&r)) {
- mpd_setspecial(q, MPD_POS, MPD_NAN);
- mpd_del(&r);
- goto finish;
- }
- rem = !mpd_iszerocoeff(&r);
- mpd_del(&r);
- newsize = q->len;
- }
-
- newsize = _mpd_real_size(q->data, newsize);
- /* resize to smaller cannot fail */
- mpd_qresize(q, newsize, status);
- mpd_set_flags(q, sign_a^sign_b);
- q->len = newsize;
- mpd_setdigits(q);
-
- shift = ideal_exp - exp;
- if (rem) {
- ld = mpd_lsd(q->data[0]);
- if (ld == 0 || ld == 5) {
- q->data[0] += 1;
- }
- }
- else if (action == SET_IDEAL_EXP && shift > 0) {
- tz = mpd_trail_zeros(q);
- shift = (tz > shift) ? shift : tz;
- mpd_qshiftr_inplace(q, shift);
- exp += shift;
- }
-
- q->exp = exp;
-
-
-finish:
- mpd_del(&aligned);
- mpd_qfinalize(q, ctx, status);
-}
-
-/* Divide a by b. */
-void
-mpd_qdiv(mpd_t *q, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- MPD_NEW_STATIC(aa,0,0,0,0);
- MPD_NEW_STATIC(bb,0,0,0,0);
- uint32_t xstatus = 0;
-
- if (q == a) {
- if (!mpd_qcopy(&aa, a, status)) {
- mpd_seterror(q, MPD_Malloc_error, status);
- goto out;
- }
- a = &aa;
- }
-
- if (q == b) {
- if (!mpd_qcopy(&bb, b, status)) {
- mpd_seterror(q, MPD_Malloc_error, status);
- goto out;
- }
- b = &bb;
- }
-
- _mpd_qdiv(SET_IDEAL_EXP, q, a, b, ctx, &xstatus);
-
- if (xstatus & (MPD_Malloc_error|MPD_Division_impossible)) {
- /* Inexact quotients (the usual case) fill the entire context precision,
- * which can lead to the above errors for very high precisions. Retry
- * the operation with a lower precision in case the result is exact.
- *
- * We need an upper bound for the number of digits of a_coeff / b_coeff
- * when the result is exact. If a_coeff' * 1 / b_coeff' is in lowest
- * terms, then maxdigits(a_coeff') + maxdigits(1 / b_coeff') is a suitable
- * bound.
- *
- * 1 / b_coeff' is exact iff b_coeff' exclusively has prime factors 2 or 5.
- * The largest amount of digits is generated if b_coeff' is a power of 2 or
- * a power of 5 and is less than or equal to log5(b_coeff') <= log2(b_coeff').
- *
- * We arrive at a total upper bound:
- *
- * maxdigits(a_coeff') + maxdigits(1 / b_coeff') <=
- * log10(a_coeff) + log2(b_coeff) =
- * log10(a_coeff) + log10(b_coeff) / log10(2) <=
- * a->digits + b->digits * 4;
- */
- mpd_context_t workctx = *ctx;
- uint32_t ystatus = 0;
-
- workctx.prec = a->digits + b->digits * 4;
- if (workctx.prec >= ctx->prec) {
- *status |= (xstatus&MPD_Errors);
- goto out; /* No point in retrying, keep the original error. */
- }
-
- _mpd_qdiv(SET_IDEAL_EXP, q, a, b, &workctx, &ystatus);
- if (ystatus != 0) {
- ystatus = *status | ((ystatus|xstatus)&MPD_Errors);
- mpd_seterror(q, ystatus, status);
- }
- }
- else {
- *status |= xstatus;
- }
-
-
-out:
- mpd_del(&aa);
- mpd_del(&bb);
-}
-
-/* Internal function. */
-static void
-_mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- MPD_NEW_STATIC(aligned,0,0,0,0);
- mpd_ssize_t qsize, rsize;
- mpd_ssize_t ideal_exp, expdiff, shift;
- uint8_t sign_a = mpd_sign(a);
- uint8_t sign_ab = mpd_sign(a)^mpd_sign(b);
-
-
- ideal_exp = (a->exp > b->exp) ? b->exp : a->exp;
- if (mpd_iszerocoeff(a)) {
- if (!mpd_qcopy(r, a, status)) {
- goto nanresult; /* GCOV_NOT_REACHED */
- }
- r->exp = ideal_exp;
- _settriple(q, sign_ab, 0, 0);
- return;
- }
-
- expdiff = mpd_adjexp(a) - mpd_adjexp(b);
- if (expdiff < 0) {
- if (a->exp > b->exp) {
- /* positive and less than b->digits - a->digits */
- shift = a->exp - b->exp;
- if (!mpd_qshiftl(r, a, shift, status)) {
- goto nanresult;
- }
- r->exp = ideal_exp;
- }
- else {
- if (!mpd_qcopy(r, a, status)) {
- goto nanresult;
- }
- }
- _settriple(q, sign_ab, 0, 0);
- return;
- }
- if (expdiff > ctx->prec) {
- *status |= MPD_Division_impossible;
- goto nanresult;
- }
-
-
- /*
- * At this point we have:
- * (1) 0 <= a->exp + a->digits - b->exp - b->digits <= prec
- * (2) a->exp - b->exp >= b->digits - a->digits
- * (3) a->exp - b->exp <= prec + b->digits - a->digits
- */
- if (a->exp != b->exp) {
- shift = a->exp - b->exp;
- if (shift > 0) {
- /* by (3), after the shift a->digits <= prec + b->digits */
- if (!mpd_qshiftl(&aligned, a, shift, status)) {
- goto nanresult;
- }
- a = &aligned;
- }
- else {
- shift = -shift;
- /* by (2), after the shift b->digits <= a->digits */
- if (!mpd_qshiftl(&aligned, b, shift, status)) {
- goto nanresult;
- }
- b = &aligned;
- }
- }
-
-
- qsize = a->len - b->len + 1;
- if (!(q == a && qsize < a->len) && !(q == b && qsize < b->len)) {
- if (!mpd_qresize(q, qsize, status)) {
- goto nanresult;
- }
- }
-
- rsize = b->len;
- if (!(r == a && rsize < a->len)) {
- if (!mpd_qresize(r, rsize, status)) {
- goto nanresult;
- }
- }
-
- if (b->len == 1) {
- assert(b->data[0] != 0); /* annotation for scan-build */
- if (a->len == 1) {
- _mpd_div_word(&q->data[0], &r->data[0], a->data[0], b->data[0]);
- }
- else {
- r->data[0] = _mpd_shortdiv(q->data, a->data, a->len, b->data[0]);
- }
- }
- else if (b->len <= MPD_NEWTONDIV_CUTOFF) {
- int ret;
- ret = _mpd_basedivmod(q->data, r->data, a->data, b->data,
- a->len, b->len);
- if (ret == -1) {
- *status |= MPD_Malloc_error;
- goto nanresult;
- }
- }
- else {
- _mpd_base_ndivmod(q, r, a, b, status);
- if (mpd_isspecial(q) || mpd_isspecial(r)) {
- goto nanresult;
- }
- qsize = q->len;
- rsize = r->len;
- }
-
- qsize = _mpd_real_size(q->data, qsize);
- /* resize to smaller cannot fail */
- mpd_qresize(q, qsize, status);
- q->len = qsize;
- mpd_setdigits(q);
- mpd_set_flags(q, sign_ab);
- q->exp = 0;
- if (q->digits > ctx->prec) {
- *status |= MPD_Division_impossible;
- goto nanresult;
- }
-
- rsize = _mpd_real_size(r->data, rsize);
- /* resize to smaller cannot fail */
- mpd_qresize(r, rsize, status);
- r->len = rsize;
- mpd_setdigits(r);
- mpd_set_flags(r, sign_a);
- r->exp = ideal_exp;
-
-out:
- mpd_del(&aligned);
- return;
-
-nanresult:
- mpd_setspecial(q, MPD_POS, MPD_NAN);
- mpd_setspecial(r, MPD_POS, MPD_NAN);
- goto out;
-}
-
-/* Integer division with remainder. */
-void
-mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- uint8_t sign = mpd_sign(a)^mpd_sign(b);
-
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_qcheck_nans(q, a, b, ctx, status)) {
- mpd_qcopy(r, q, status);
- return;
- }
- if (mpd_isinfinite(a)) {
- if (mpd_isinfinite(b)) {
- mpd_setspecial(q, MPD_POS, MPD_NAN);
- }
- else {
- mpd_setspecial(q, sign, MPD_INF);
- }
- mpd_setspecial(r, MPD_POS, MPD_NAN);
- *status |= MPD_Invalid_operation;
- return;
- }
- if (mpd_isinfinite(b)) {
- if (!mpd_qcopy(r, a, status)) {
- mpd_seterror(q, MPD_Malloc_error, status);
- return;
- }
- mpd_qfinalize(r, ctx, status);
- _settriple(q, sign, 0, 0);
- return;
- }
- /* debug */
- abort(); /* GCOV_NOT_REACHED */
- }
- if (mpd_iszerocoeff(b)) {
- if (mpd_iszerocoeff(a)) {
- mpd_setspecial(q, MPD_POS, MPD_NAN);
- mpd_setspecial(r, MPD_POS, MPD_NAN);
- *status |= MPD_Division_undefined;
- }
- else {
- mpd_setspecial(q, sign, MPD_INF);
- mpd_setspecial(r, MPD_POS, MPD_NAN);
- *status |= (MPD_Division_by_zero|MPD_Invalid_operation);
- }
- return;
- }
-
- _mpd_qdivmod(q, r, a, b, ctx, status);
- mpd_qfinalize(q, ctx, status);
- mpd_qfinalize(r, ctx, status);
-}
-
-void
-mpd_qdivint(mpd_t *q, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- MPD_NEW_STATIC(r,0,0,0,0);
- uint8_t sign = mpd_sign(a)^mpd_sign(b);
-
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_qcheck_nans(q, a, b, ctx, status)) {
- return;
- }
- if (mpd_isinfinite(a) && mpd_isinfinite(b)) {
- mpd_seterror(q, MPD_Invalid_operation, status);
- return;
- }
- if (mpd_isinfinite(a)) {
- mpd_setspecial(q, sign, MPD_INF);
- return;
- }
- if (mpd_isinfinite(b)) {
- _settriple(q, sign, 0, 0);
- return;
- }
- /* debug */
- abort(); /* GCOV_NOT_REACHED */
- }
- if (mpd_iszerocoeff(b)) {
- if (mpd_iszerocoeff(a)) {
- mpd_seterror(q, MPD_Division_undefined, status);
- }
- else {
- mpd_setspecial(q, sign, MPD_INF);
- *status |= MPD_Division_by_zero;
- }
- return;
- }
-
-
- _mpd_qdivmod(q, &r, a, b, ctx, status);
- mpd_del(&r);
- mpd_qfinalize(q, ctx, status);
-}
-
-/* Divide decimal by mpd_ssize_t. */
-void
-mpd_qdiv_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qsset_ssize(&bb, b, &maxcontext, status);
- mpd_qdiv(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-
-/* Divide decimal by mpd_uint_t. */
-void
-mpd_qdiv_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qsset_uint(&bb, b, &maxcontext, status);
- mpd_qdiv(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-
-/* Divide decimal by int32_t. */
-void
-mpd_qdiv_i32(mpd_t *result, const mpd_t *a, int32_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qdiv_ssize(result, a, b, ctx, status);
-}
-
-/* Divide decimal by uint32_t. */
-void
-mpd_qdiv_u32(mpd_t *result, const mpd_t *a, uint32_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qdiv_uint(result, a, b, ctx, status);
-}
-
-#ifdef CONFIG_64
-/* Divide decimal by int64_t. */
-void
-mpd_qdiv_i64(mpd_t *result, const mpd_t *a, int64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qdiv_ssize(result, a, b, ctx, status);
-}
-
-/* Divide decimal by uint64_t. */
-void
-mpd_qdiv_u64(mpd_t *result, const mpd_t *a, uint64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qdiv_uint(result, a, b, ctx, status);
-}
-#elif !defined(LEGACY_COMPILER)
-/* Divide decimal by int64_t. */
-void
-mpd_qdiv_i64(mpd_t *result, const mpd_t *a, int64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qset_i64(&bb, b, &maxcontext, status);
- mpd_qdiv(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-
-/* Divide decimal by uint64_t. */
-void
-mpd_qdiv_u64(mpd_t *result, const mpd_t *a, uint64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qset_u64(&bb, b, &maxcontext, status);
- mpd_qdiv(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-#endif
-
-/* Pad the result with trailing zeros if it has fewer digits than prec. */
-static void
-_mpd_zeropad(mpd_t *result, const mpd_context_t *ctx, uint32_t *status)
-{
- if (!mpd_isspecial(result) && !mpd_iszero(result) &&
- result->digits < ctx->prec) {
- mpd_ssize_t shift = ctx->prec - result->digits;
- mpd_qshiftl(result, result, shift, status);
- result->exp -= shift;
- }
-}
-
-/* Check if the result is guaranteed to be one. */
-static int
-_mpd_qexp_check_one(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- MPD_NEW_CONST(lim,0,-(ctx->prec+1),1,1,1,9);
- MPD_NEW_SHARED(aa, a);
-
- mpd_set_positive(&aa);
-
- /* abs(a) <= 9 * 10**(-prec-1) */
- if (_mpd_cmp(&aa, &lim) <= 0) {
- _settriple(result, 0, 1, 0);
- *status |= MPD_Rounded|MPD_Inexact;
- return 1;
- }
-
- return 0;
-}
-
-/*
- * Get the number of iterations for the Horner scheme in _mpd_qexp().
- */
-static inline mpd_ssize_t
-_mpd_get_exp_iterations(const mpd_t *r, mpd_ssize_t p)
-{
- mpd_ssize_t log10pbyr; /* lower bound for log10(p / abs(r)) */
- mpd_ssize_t n;
-
- assert(p >= 10);
- assert(!mpd_iszero(r));
- assert(-p < mpd_adjexp(r) && mpd_adjexp(r) <= -1);
-
-#ifdef CONFIG_64
- if (p > (mpd_ssize_t)(1ULL<<52)) {
- return MPD_SSIZE_MAX;
- }
-#endif
-
- /*
- * Lower bound for log10(p / abs(r)): adjexp(p) - (adjexp(r) + 1)
- * At this point (for CONFIG_64, CONFIG_32 is not problematic):
- * 1) 10 <= p <= 2**52
- * 2) -p < adjexp(r) <= -1
- * 3) 1 <= log10pbyr <= 2**52 + 14
- */
- log10pbyr = (mpd_word_digits(p)-1) - (mpd_adjexp(r)+1);
-
- /*
- * The numerator in the paper is 1.435 * p - 1.182, calculated
- * exactly. We compensate for rounding errors by using 1.43503.
- * ACL2 proofs:
- * 1) exp-iter-approx-lower-bound: The term below evaluated
- * in 53-bit floating point arithmetic is greater than or
- * equal to the exact term used in the paper.
- * 2) exp-iter-approx-upper-bound: The term below is less than
- * or equal to 3/2 * p <= 3/2 * 2**52.
- */
- n = (mpd_ssize_t)ceil((1.43503*(double)p - 1.182) / (double)log10pbyr);
- return n >= 3 ? n : 3;
-}
-
-/*
- * Internal function, specials have been dealt with. Apart from Overflow
- * and Underflow, two cases must be considered for the error of the result:
- *
- * 1) abs(a) <= 9 * 10**(-prec-1) ==> result == 1
- *
- * Absolute error: abs(1 - e**x) < 10**(-prec)
- * -------------------------------------------
- *
- * 2) abs(a) > 9 * 10**(-prec-1)
- *
- * Relative error: abs(result - e**x) < 0.5 * 10**(-prec) * e**x
- * -------------------------------------------------------------
- *
- * The algorithm is from Hull&Abrham, Variable Precision Exponential Function,
- * ACM Transactions on Mathematical Software, Vol. 12, No. 2, June 1986.
- *
- * Main differences:
- *
- * - The number of iterations for the Horner scheme is calculated using
- * 53-bit floating point arithmetic.
- *
- * - In the error analysis for ER (relative error accumulated in the
- * evaluation of the truncated series) the reduced operand r may
- * have any number of digits.
- * ACL2 proof: exponent-relative-error
- *
- * - The analysis for early abortion has been adapted for the mpd_t
- * ranges.
- */
-static void
-_mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_context_t workctx;
- MPD_NEW_STATIC(tmp,0,0,0,0);
- MPD_NEW_STATIC(sum,0,0,0,0);
- MPD_NEW_CONST(word,0,0,1,1,1,1);
- mpd_ssize_t j, n, t;
-
- assert(!mpd_isspecial(a));
-
- if (mpd_iszerocoeff(a)) {
- _settriple(result, MPD_POS, 1, 0);
- return;
- }
-
- /*
- * We are calculating e^x = e^(r*10^t) = (e^r)^(10^t), where abs(r) < 1 and t >= 0.
- *
- * If t > 0, we have:
- *
- * (1) 0.1 <= r < 1, so e^0.1 <= e^r. If t > MAX_T, overflow occurs:
- *
- * MAX-EMAX+1 < log10(e^(0.1*10*t)) <= log10(e^(r*10^t)) < adjexp(e^(r*10^t))+1
- *
- * (2) -1 < r <= -0.1, so e^r <= e^-0.1. If t > MAX_T, underflow occurs:
- *
- * adjexp(e^(r*10^t)) <= log10(e^(r*10^t)) <= log10(e^(-0.1*10^t)) < MIN-ETINY
- */
-#if defined(CONFIG_64)
- #define MPD_EXP_MAX_T 19
-#elif defined(CONFIG_32)
- #define MPD_EXP_MAX_T 10
-#endif
- t = a->digits + a->exp;
- t = (t > 0) ? t : 0;
- if (t > MPD_EXP_MAX_T) {
- if (mpd_ispositive(a)) {
- mpd_setspecial(result, MPD_POS, MPD_INF);
- *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded;
- }
- else {
- _settriple(result, MPD_POS, 0, mpd_etiny(ctx));
- *status |= (MPD_Inexact|MPD_Rounded|MPD_Subnormal|
- MPD_Underflow|MPD_Clamped);
- }
- return;
- }
-
- /* abs(a) <= 9 * 10**(-prec-1) */
- if (_mpd_qexp_check_one(result, a, ctx, status)) {
- return;
- }
-
- mpd_maxcontext(&workctx);
- workctx.prec = ctx->prec + t + 2;
- workctx.prec = (workctx.prec < 10) ? 10 : workctx.prec;
- workctx.round = MPD_ROUND_HALF_EVEN;
-
- if (!mpd_qcopy(result, a, status)) {
- return;
- }
- result->exp -= t;
-
- /*
- * At this point:
- * 1) 9 * 10**(-prec-1) < abs(a)
- * 2) 9 * 10**(-prec-t-1) < abs(r)
- * 3) log10(9) - prec - t - 1 < log10(abs(r)) < adjexp(abs(r)) + 1
- * 4) - prec - t - 2 < adjexp(abs(r)) <= -1
- */
- n = _mpd_get_exp_iterations(result, workctx.prec);
- if (n == MPD_SSIZE_MAX) {
- mpd_seterror(result, MPD_Invalid_operation, status); /* GCOV_UNLIKELY */
- return; /* GCOV_UNLIKELY */
- }
-
- _settriple(&sum, MPD_POS, 1, 0);
-
- for (j = n-1; j >= 1; j--) {
- word.data[0] = j;
- mpd_setdigits(&word);
- mpd_qdiv(&tmp, result, &word, &workctx, &workctx.status);
- mpd_qfma(&sum, &sum, &tmp, &one, &workctx, &workctx.status);
- }
-
-#ifdef CONFIG_64
- _mpd_qpow_uint(result, &sum, mpd_pow10[t], MPD_POS, &workctx, status);
-#else
- if (t <= MPD_MAX_POW10) {
- _mpd_qpow_uint(result, &sum, mpd_pow10[t], MPD_POS, &workctx, status);
- }
- else {
- t -= MPD_MAX_POW10;
- _mpd_qpow_uint(&tmp, &sum, mpd_pow10[MPD_MAX_POW10], MPD_POS,
- &workctx, status);
- _mpd_qpow_uint(result, &tmp, mpd_pow10[t], MPD_POS, &workctx, status);
- }
-#endif
-
- mpd_del(&tmp);
- mpd_del(&sum);
- *status |= (workctx.status&MPD_Errors);
- *status |= (MPD_Inexact|MPD_Rounded);
-}
-
-/* exp(a) */
-void
-mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_context_t workctx;
-
- if (mpd_isspecial(a)) {
- if (mpd_qcheck_nan(result, a, ctx, status)) {
- return;
- }
- if (mpd_isnegative(a)) {
- _settriple(result, MPD_POS, 0, 0);
- }
- else {
- mpd_setspecial(result, MPD_POS, MPD_INF);
- }
- return;
- }
- if (mpd_iszerocoeff(a)) {
- _settriple(result, MPD_POS, 1, 0);
- return;
- }
-
- workctx = *ctx;
- workctx.round = MPD_ROUND_HALF_EVEN;
-
- if (ctx->allcr) {
- MPD_NEW_STATIC(t1, 0,0,0,0);
- MPD_NEW_STATIC(t2, 0,0,0,0);
- MPD_NEW_STATIC(ulp, 0,0,0,0);
- MPD_NEW_STATIC(aa, 0,0,0,0);
- mpd_ssize_t prec;
- mpd_ssize_t ulpexp;
- uint32_t workstatus;
-
- if (result == a) {
- if (!mpd_qcopy(&aa, a, status)) {
- mpd_seterror(result, MPD_Malloc_error, status);
- return;
- }
- a = &aa;
- }
-
- workctx.clamp = 0;
- prec = ctx->prec + 3;
- while (1) {
- workctx.prec = prec;
- workstatus = 0;
-
- _mpd_qexp(result, a, &workctx, &workstatus);
- *status |= workstatus;
-
- ulpexp = result->exp + result->digits - workctx.prec;
- if (workstatus & MPD_Underflow) {
- /* The effective work precision is result->digits. */
- ulpexp = result->exp;
- }
- _ssettriple(&ulp, MPD_POS, 1, ulpexp);
-
- /*
- * At this point [1]:
- * 1) abs(result - e**x) < 0.5 * 10**(-prec) * e**x
- * 2) result - ulp < e**x < result + ulp
- * 3) result - ulp < result < result + ulp
- *
- * If round(result-ulp)==round(result+ulp), then
- * round(result)==round(e**x). Therefore the result
- * is correctly rounded.
- *
- * [1] If abs(a) <= 9 * 10**(-prec-1), use the absolute
- * error for a similar argument.
- */
- workctx.prec = ctx->prec;
- mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status);
- mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status);
- if (mpd_isspecial(result) || mpd_iszerocoeff(result) ||
- mpd_qcmp(&t1, &t2, status) == 0) {
- workctx.clamp = ctx->clamp;
- _mpd_zeropad(result, &workctx, status);
- mpd_check_underflow(result, &workctx, status);
- mpd_qfinalize(result, &workctx, status);
- break;
- }
- prec += MPD_RDIGITS;
- }
- mpd_del(&t1);
- mpd_del(&t2);
- mpd_del(&ulp);
- mpd_del(&aa);
- }
- else {
- _mpd_qexp(result, a, &workctx, status);
- _mpd_zeropad(result, &workctx, status);
- mpd_check_underflow(result, &workctx, status);
- mpd_qfinalize(result, &workctx, status);
- }
-}
-
-/* Fused multiply-add: (a * b) + c, with a single final rounding. */
-void
-mpd_qfma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c,
- const mpd_context_t *ctx, uint32_t *status)
-{
- uint32_t workstatus = 0;
- mpd_t *cc = NULL;
-
- if (result == c) {
- if ((cc = mpd_qncopy(c)) == NULL) {
- mpd_seterror(result, MPD_Malloc_error, status);
- return;
- }
- c = cc;
- }
-
- _mpd_qmul(result, a, b, ctx, &workstatus);
- if (!(workstatus&MPD_Invalid_operation)) {
- mpd_qadd(result, result, c, ctx, &workstatus);
- }
-
- if (cc) mpd_del(cc);
- *status |= workstatus;
-}
-
-/*
- * Schedule the optimal precision increase for the Newton iteration.
- * v := input operand
- * z_0 := initial approximation
- * initprec := natural number such that abs(log(v) - z_0) < 10**-initprec
- * maxprec := target precision
- *
- * For convenience the output klist contains the elements in reverse order:
- * klist := [k_n-1, ..., k_0], where
- * 1) k_0 <= initprec and
- * 2) abs(log(v) - result) < 10**(-2*k_n-1 + 1) <= 10**-maxprec.
- */
-static inline int
-ln_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2], mpd_ssize_t maxprec,
- mpd_ssize_t initprec)
-{
- mpd_ssize_t k;
- int i;
-
- assert(maxprec >= 2 && initprec >= 2);
- if (maxprec <= initprec) return -1;
-
- i = 0; k = maxprec;
- do {
- k = (k+2) / 2;
- klist[i++] = k;
- } while (k > initprec);
-
- return i-1;
-}
-
-/* The constants have been verified with both decimal.py and mpfr. */
-#ifdef CONFIG_64
-#if MPD_RDIGITS != 19
- #error "mpdecimal.c: MPD_RDIGITS must be 19."
-#endif
-static const mpd_uint_t mpd_ln10_data[MPD_MINALLOC_MAX] = {
- 6983716328982174407ULL, 9089704281976336583ULL, 1515961135648465461ULL,
- 4416816335727555703ULL, 2900988039194170265ULL, 2307925037472986509ULL,
- 107598438319191292ULL, 3466624107184669231ULL, 4450099781311469159ULL,
- 9807828059751193854ULL, 7713456862091670584ULL, 1492198849978748873ULL,
- 6528728696511086257ULL, 2385392051446341972ULL, 8692180205189339507ULL,
- 6518769751037497088ULL, 2375253577097505395ULL, 9095610299291824318ULL,
- 982748238504564801ULL, 5438635917781170543ULL, 7547331541421808427ULL,
- 752371033310119785ULL, 3171643095059950878ULL, 9785265383207606726ULL,
- 2932258279850258550ULL, 5497347726624257094ULL, 2976979522110718264ULL,
- 9221477656763693866ULL, 1979650047149510504ULL, 6674183485704422507ULL,
- 9702766860595249671ULL, 9278096762712757753ULL, 9314848524948644871ULL,
- 6826928280848118428ULL, 754403708474699401ULL, 230105703089634572ULL,
- 1929203337658714166ULL, 7589402567763113569ULL, 4208241314695689016ULL,
- 2922455440575892572ULL, 9356734206705811364ULL, 2684916746550586856ULL,
- 644507064800027750ULL, 9476834636167921018ULL, 5659121373450747856ULL,
- 2835522011480466371ULL, 6470806855677432162ULL, 7141748003688084012ULL,
- 9619404400222105101ULL, 5504893431493939147ULL, 6674744042432743651ULL,
- 2287698219886746543ULL, 7773262884616336622ULL, 1985283935053089653ULL,
- 4680843799894826233ULL, 8168948290720832555ULL, 8067566662873690987ULL,
- 6248633409525465082ULL, 9829834196778404228ULL, 3524802359972050895ULL,
- 3327900967572609677ULL, 110148862877297603ULL, 179914546843642076ULL,
- 2302585092994045684ULL
-};
-#else
-#if MPD_RDIGITS != 9
- #error "mpdecimal.c: MPD_RDIGITS must be 9."
-#endif
-static const mpd_uint_t mpd_ln10_data[MPD_MINALLOC_MAX] = {
- 401682692UL, 708474699UL, 720754403UL, 30896345UL, 602301057UL, 765871416UL,
- 192920333UL, 763113569UL, 589402567UL, 956890167UL, 82413146UL, 589257242UL,
- 245544057UL, 811364292UL, 734206705UL, 868569356UL, 167465505UL, 775026849UL,
- 706480002UL, 18064450UL, 636167921UL, 569476834UL, 734507478UL, 156591213UL,
- 148046637UL, 283552201UL, 677432162UL, 470806855UL, 880840126UL, 417480036UL,
- 210510171UL, 940440022UL, 939147961UL, 893431493UL, 436515504UL, 440424327UL,
- 654366747UL, 821988674UL, 622228769UL, 884616336UL, 537773262UL, 350530896UL,
- 319852839UL, 989482623UL, 468084379UL, 720832555UL, 168948290UL, 736909878UL,
- 675666628UL, 546508280UL, 863340952UL, 404228624UL, 834196778UL, 508959829UL,
- 23599720UL, 967735248UL, 96757260UL, 603332790UL, 862877297UL, 760110148UL,
- 468436420UL, 401799145UL, 299404568UL, 230258509UL
-};
-#endif
-/* _mpd_ln10 is used directly for precisions smaller than MINALLOC_MAX*RDIGITS.
- Otherwise, it serves as the initial approximation for calculating ln(10). */
-static const mpd_t _mpd_ln10 = {
- MPD_STATIC|MPD_CONST_DATA, -(MPD_MINALLOC_MAX*MPD_RDIGITS-1),
- MPD_MINALLOC_MAX*MPD_RDIGITS, MPD_MINALLOC_MAX, MPD_MINALLOC_MAX,
- (mpd_uint_t *)mpd_ln10_data
-};
-
-/*
- * Set 'result' to log(10).
- * Ulp error: abs(result - log(10)) < ulp(log(10))
- * Relative error: abs(result - log(10)) < 5 * 10**-prec * log(10)
- *
- * NOTE: The relative error is not derived from the ulp error, but
- * calculated separately using the fact that 23/10 < log(10) < 24/10.
- */
-void
-mpd_qln10(mpd_t *result, mpd_ssize_t prec, uint32_t *status)
-{
- mpd_context_t varcontext, maxcontext;
- MPD_NEW_STATIC(tmp, 0,0,0,0);
- MPD_NEW_CONST(static10, 0,0,2,1,1,10);
- mpd_ssize_t klist[MPD_MAX_PREC_LOG2];
- mpd_uint_t rnd;
- mpd_ssize_t shift;
- int i;
-
- assert(prec >= 1);
-
- shift = MPD_MINALLOC_MAX*MPD_RDIGITS-prec;
- shift = shift < 0 ? 0 : shift;
-
- rnd = mpd_qshiftr(result, &_mpd_ln10, shift, status);
- if (rnd == MPD_UINT_MAX) {
- mpd_seterror(result, MPD_Malloc_error, status);
- return;
- }
- result->exp = -(result->digits-1);
-
- mpd_maxcontext(&maxcontext);
- if (prec < MPD_MINALLOC_MAX*MPD_RDIGITS) {
- maxcontext.prec = prec;
- _mpd_apply_round_excess(result, rnd, &maxcontext, status);
- *status |= (MPD_Inexact|MPD_Rounded);
- return;
- }
-
- mpd_maxcontext(&varcontext);
- varcontext.round = MPD_ROUND_TRUNC;
-
- i = ln_schedule_prec(klist, prec+2, -result->exp);
- for (; i >= 0; i--) {
- varcontext.prec = 2*klist[i]+3;
- result->flags ^= MPD_NEG;
- _mpd_qexp(&tmp, result, &varcontext, status);
- result->flags ^= MPD_NEG;
- mpd_qmul(&tmp, &static10, &tmp, &varcontext, status);
- mpd_qsub(&tmp, &tmp, &one, &maxcontext, status);
- mpd_qadd(result, result, &tmp, &maxcontext, status);
- if (mpd_isspecial(result)) {
- break;
- }
- }
-
- mpd_del(&tmp);
- maxcontext.prec = prec;
- mpd_qfinalize(result, &maxcontext, status);
-}
-
-/*
- * Initial approximations for the ln() iteration. The values have the
- * following properties (established with both decimal.py and mpfr):
- *
- * Index 0 - 400, logarithms of x in [1.00, 5.00]:
- * abs(lnapprox[i] * 10**-3 - log((i+100)/100)) < 10**-2
- * abs(lnapprox[i] * 10**-3 - log((i+1+100)/100)) < 10**-2
- *
- * Index 401 - 899, logarithms of x in (0.500, 0.999]:
- * abs(-lnapprox[i] * 10**-3 - log((i+100)/1000)) < 10**-2
- * abs(-lnapprox[i] * 10**-3 - log((i+1+100)/1000)) < 10**-2
- */
-static const uint16_t lnapprox[900] = {
- /* index 0 - 400: log((i+100)/100) * 1000 */
- 0, 10, 20, 30, 39, 49, 58, 68, 77, 86, 95, 104, 113, 122, 131, 140, 148, 157,
- 166, 174, 182, 191, 199, 207, 215, 223, 231, 239, 247, 255, 262, 270, 278,
- 285, 293, 300, 308, 315, 322, 329, 336, 344, 351, 358, 365, 372, 378, 385,
- 392, 399, 406, 412, 419, 425, 432, 438, 445, 451, 457, 464, 470, 476, 482,
- 489, 495, 501, 507, 513, 519, 525, 531, 536, 542, 548, 554, 560, 565, 571,
- 577, 582, 588, 593, 599, 604, 610, 615, 621, 626, 631, 637, 642, 647, 652,
- 658, 663, 668, 673, 678, 683, 688, 693, 698, 703, 708, 713, 718, 723, 728,
- 732, 737, 742, 747, 751, 756, 761, 766, 770, 775, 779, 784, 788, 793, 798,
- 802, 806, 811, 815, 820, 824, 829, 833, 837, 842, 846, 850, 854, 859, 863,
- 867, 871, 876, 880, 884, 888, 892, 896, 900, 904, 908, 912, 916, 920, 924,
- 928, 932, 936, 940, 944, 948, 952, 956, 959, 963, 967, 971, 975, 978, 982,
- 986, 990, 993, 997, 1001, 1004, 1008, 1012, 1015, 1019, 1022, 1026, 1030,
- 1033, 1037, 1040, 1044, 1047, 1051, 1054, 1058, 1061, 1065, 1068, 1072, 1075,
- 1078, 1082, 1085, 1089, 1092, 1095, 1099, 1102, 1105, 1109, 1112, 1115, 1118,
- 1122, 1125, 1128, 1131, 1135, 1138, 1141, 1144, 1147, 1151, 1154, 1157, 1160,
- 1163, 1166, 1169, 1172, 1176, 1179, 1182, 1185, 1188, 1191, 1194, 1197, 1200,
- 1203, 1206, 1209, 1212, 1215, 1218, 1221, 1224, 1227, 1230, 1233, 1235, 1238,
- 1241, 1244, 1247, 1250, 1253, 1256, 1258, 1261, 1264, 1267, 1270, 1273, 1275,
- 1278, 1281, 1284, 1286, 1289, 1292, 1295, 1297, 1300, 1303, 1306, 1308, 1311,
- 1314, 1316, 1319, 1322, 1324, 1327, 1330, 1332, 1335, 1338, 1340, 1343, 1345,
- 1348, 1351, 1353, 1356, 1358, 1361, 1364, 1366, 1369, 1371, 1374, 1376, 1379,
- 1381, 1384, 1386, 1389, 1391, 1394, 1396, 1399, 1401, 1404, 1406, 1409, 1411,
- 1413, 1416, 1418, 1421, 1423, 1426, 1428, 1430, 1433, 1435, 1437, 1440, 1442,
- 1445, 1447, 1449, 1452, 1454, 1456, 1459, 1461, 1463, 1466, 1468, 1470, 1472,
- 1475, 1477, 1479, 1482, 1484, 1486, 1488, 1491, 1493, 1495, 1497, 1500, 1502,
- 1504, 1506, 1509, 1511, 1513, 1515, 1517, 1520, 1522, 1524, 1526, 1528, 1530,
- 1533, 1535, 1537, 1539, 1541, 1543, 1545, 1548, 1550, 1552, 1554, 1556, 1558,
- 1560, 1562, 1564, 1567, 1569, 1571, 1573, 1575, 1577, 1579, 1581, 1583, 1585,
- 1587, 1589, 1591, 1593, 1595, 1597, 1599, 1601, 1603, 1605, 1607, 1609,
- /* index 401 - 899: -log((i+100)/1000) * 1000 */
- 691, 689, 687, 685, 683, 681, 679, 677, 675, 673, 671, 669, 668, 666, 664,
- 662, 660, 658, 656, 654, 652, 650, 648, 646, 644, 642, 641, 639, 637, 635,
- 633, 631, 629, 627, 626, 624, 622, 620, 618, 616, 614, 612, 611, 609, 607,
- 605, 603, 602, 600, 598, 596, 594, 592, 591, 589, 587, 585, 583, 582, 580,
- 578, 576, 574, 573, 571, 569, 567, 566, 564, 562, 560, 559, 557, 555, 553,
- 552, 550, 548, 546, 545, 543, 541, 540, 538, 536, 534, 533, 531, 529, 528,
- 526, 524, 523, 521, 519, 518, 516, 514, 512, 511, 509, 508, 506, 504, 502,
- 501, 499, 498, 496, 494, 493, 491, 489, 488, 486, 484, 483, 481, 480, 478,
- 476, 475, 473, 472, 470, 468, 467, 465, 464, 462, 460, 459, 457, 456, 454,
- 453, 451, 449, 448, 446, 445, 443, 442, 440, 438, 437, 435, 434, 432, 431,
- 429, 428, 426, 425, 423, 422, 420, 419, 417, 416, 414, 412, 411, 410, 408,
- 406, 405, 404, 402, 400, 399, 398, 396, 394, 393, 392, 390, 389, 387, 386,
- 384, 383, 381, 380, 378, 377, 375, 374, 372, 371, 370, 368, 367, 365, 364,
- 362, 361, 360, 358, 357, 355, 354, 352, 351, 350, 348, 347, 345, 344, 342,
- 341, 340, 338, 337, 336, 334, 333, 331, 330, 328, 327, 326, 324, 323, 322,
- 320, 319, 318, 316, 315, 313, 312, 311, 309, 308, 306, 305, 304, 302, 301,
- 300, 298, 297, 296, 294, 293, 292, 290, 289, 288, 286, 285, 284, 282, 281,
- 280, 278, 277, 276, 274, 273, 272, 270, 269, 268, 267, 265, 264, 263, 261,
- 260, 259, 258, 256, 255, 254, 252, 251, 250, 248, 247, 246, 245, 243, 242,
- 241, 240, 238, 237, 236, 234, 233, 232, 231, 229, 228, 227, 226, 224, 223,
- 222, 221, 219, 218, 217, 216, 214, 213, 212, 211, 210, 208, 207, 206, 205,
- 203, 202, 201, 200, 198, 197, 196, 195, 194, 192, 191, 190, 189, 188, 186,
- 185, 184, 183, 182, 180, 179, 178, 177, 176, 174, 173, 172, 171, 170, 168,
- 167, 166, 165, 164, 162, 161, 160, 159, 158, 157, 156, 154, 153, 152, 151,
- 150, 148, 147, 146, 145, 144, 143, 142, 140, 139, 138, 137, 136, 135, 134,
- 132, 131, 130, 129, 128, 127, 126, 124, 123, 122, 121, 120, 119, 118, 116,
- 115, 114, 113, 112, 111, 110, 109, 108, 106, 105, 104, 103, 102, 101, 100,
- 99, 98, 97, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 84, 83, 82, 81, 80, 79,
- 78, 77, 76, 75, 74, 73, 72, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59,
- 58, 57, 56, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39,
- 38, 37, 36, 35, 34, 33, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19,
- 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
-};
-
-/*
- * Internal ln() function that does not check for specials, zero or one.
- * Relative error: abs(result - log(a)) < 0.1 * 10**-prec * abs(log(a))
- */
-static void
-_mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_context_t varcontext, maxcontext;
- mpd_t *z = result;
- MPD_NEW_STATIC(v,0,0,0,0);
- MPD_NEW_STATIC(vtmp,0,0,0,0);
- MPD_NEW_STATIC(tmp,0,0,0,0);
- mpd_ssize_t klist[MPD_MAX_PREC_LOG2];
- mpd_ssize_t maxprec, shift, t;
- mpd_ssize_t a_digits, a_exp;
- mpd_uint_t dummy, x;
- int i;
-
- assert(!mpd_isspecial(a) && !mpd_iszerocoeff(a));
-
- /*
- * We are calculating ln(a) = ln(v * 10^t) = ln(v) + t*ln(10),
- * where 0.5 < v <= 5.
- */
- if (!mpd_qcopy(&v, a, status)) {
- mpd_seterror(result, MPD_Malloc_error, status);
- goto finish;
- }
-
- /* Initial approximation: we have at least one non-zero digit */
- _mpd_get_msdigits(&dummy, &x, &v, 3);
- if (x < 10) x *= 10;
- if (x < 100) x *= 10;
- x -= 100;
-
- /* a may equal z */
- a_digits = a->digits;
- a_exp = a->exp;
-
- mpd_minalloc(z);
- mpd_clear_flags(z);
- z->data[0] = lnapprox[x];
- z->len = 1;
- z->exp = -3;
- mpd_setdigits(z);
-
- if (x <= 400) {
- /* Reduce the input operand to 1.00 <= v <= 5.00. Let y = x + 100,
- * so 100 <= y <= 500. Since y contains the most significant digits
- * of v, y/100 <= v < (y+1)/100 and abs(z - log(v)) < 10**-2. */
- v.exp = -(a_digits - 1);
- t = a_exp + a_digits - 1;
- }
- else {
- /* Reduce the input operand to 0.500 < v <= 0.999. Let y = x + 100,
- * so 500 < y <= 999. Since y contains the most significant digits
- * of v, y/1000 <= v < (y+1)/1000 and abs(z - log(v)) < 10**-2. */
- v.exp = -a_digits;
- t = a_exp + a_digits;
- mpd_set_negative(z);
- }
-
- mpd_maxcontext(&maxcontext);
- mpd_maxcontext(&varcontext);
- varcontext.round = MPD_ROUND_TRUNC;
-
- maxprec = ctx->prec + 2;
- if (t == 0 && (x <= 15 || x >= 800)) {
- /* 0.900 <= v <= 1.15: Estimate the magnitude of the logarithm.
- * If ln(v) will underflow, skip the loop. Otherwise, adjust the
- * precision upwards in order to obtain a sufficient number of
- * significant digits.
- *
- * Case v > 1:
- * abs((v-1)/10) < abs((v-1)/v) < abs(ln(v)) < abs(v-1)
- * Case v < 1:
- * abs(v-1) < abs(ln(v)) < abs((v-1)/v) < abs((v-1)*10)
- */
- int cmp = _mpd_cmp(&v, &one);
-
- /* Upper bound (assume v > 1): abs(v-1), unrounded */
- _mpd_qsub(&tmp, &v, &one, &maxcontext, &maxcontext.status);
- if (maxcontext.status & MPD_Errors) {
- mpd_seterror(result, MPD_Malloc_error, status);
- goto finish;
- }
-
- if (cmp < 0) {
- /* v < 1: abs((v-1)*10) */
- tmp.exp += 1;
- }
- if (mpd_adjexp(&tmp) < mpd_etiny(ctx)) {
- /* The upper bound is less than etiny: Underflow to zero */
- _settriple(result, (cmp<0), 1, mpd_etiny(ctx)-1);
- goto finish;
- }
- /* Lower bound: abs((v-1)/10) or abs(v-1) */
- tmp.exp -= 1;
- if (mpd_adjexp(&tmp) < 0) {
- /* Absolute error of the loop: abs(z - log(v)) < 10**-p. If
- * p = ctx->prec+2-adjexp(lower), then the relative error of
- * the result is (using 10**adjexp(x) <= abs(x)):
- *
- * abs(z - log(v)) / abs(log(v)) < 10**-p / abs(log(v))
- * <= 10**(-ctx->prec-2)
- */
- maxprec = maxprec - mpd_adjexp(&tmp);
- }
- }
-
- i = ln_schedule_prec(klist, maxprec, 2);
- for (; i >= 0; i--) {
- varcontext.prec = 2*klist[i]+3;
- z->flags ^= MPD_NEG;
- _mpd_qexp(&tmp, z, &varcontext, status);
- z->flags ^= MPD_NEG;
-
- if (v.digits > varcontext.prec) {
- shift = v.digits - varcontext.prec;
- mpd_qshiftr(&vtmp, &v, shift, status);
- vtmp.exp += shift;
- mpd_qmul(&tmp, &vtmp, &tmp, &varcontext, status);
- }
- else {
- mpd_qmul(&tmp, &v, &tmp, &varcontext, status);
- }
-
- mpd_qsub(&tmp, &tmp, &one, &maxcontext, status);
- mpd_qadd(z, z, &tmp, &maxcontext, status);
- if (mpd_isspecial(z)) {
- break;
- }
- }
-
- /*
- * Case t == 0:
- * t * log(10) == 0, the result does not change and the analysis
- * above applies. If v < 0.900 or v > 1.15, the relative error is
- * less than 10**(-ctx.prec-1).
- * Case t != 0:
- * z := approx(log(v))
- * y := approx(log(10))
- * p := maxprec = ctx->prec + 2
- * Absolute errors:
- * 1) abs(z - log(v)) < 10**-p
- * 2) abs(y - log(10)) < 10**-p
- * The multiplication is exact, so:
- * 3) abs(t*y - t*log(10)) < t*10**-p
- * The sum is exact, so:
- * 4) abs((z + t*y) - (log(v) + t*log(10))) < (abs(t) + 1) * 10**-p
- * Bounds for log(v) and log(10):
- * 5) -7/10 < log(v) < 17/10
- * 6) 23/10 < log(10) < 24/10
- * Using 4), 5), 6) and t != 0, the relative error is:
- *
- * 7) relerr < ((abs(t) + 1)*10**-p) / abs(log(v) + t*log(10))
- * < 0.5 * 10**(-p + 1) = 0.5 * 10**(-ctx->prec-1)
- */
- mpd_qln10(&v, maxprec+1, status);
- mpd_qmul_ssize(&tmp, &v, t, &maxcontext, status);
- mpd_qadd(result, &tmp, z, &maxcontext, status);
-
-
-finish:
- *status |= (MPD_Inexact|MPD_Rounded);
- mpd_del(&v);
- mpd_del(&vtmp);
- mpd_del(&tmp);
-}
-
-/* ln(a) */
-void
-mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_context_t workctx;
- mpd_ssize_t adjexp, t;
-
- if (mpd_isspecial(a)) {
- if (mpd_qcheck_nan(result, a, ctx, status)) {
- return;
- }
- if (mpd_isnegative(a)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- mpd_setspecial(result, MPD_POS, MPD_INF);
- return;
- }
- if (mpd_iszerocoeff(a)) {
- mpd_setspecial(result, MPD_NEG, MPD_INF);
- return;
- }
- if (mpd_isnegative(a)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- if (_mpd_cmp(a, &one) == 0) {
- _settriple(result, MPD_POS, 0, 0);
- return;
- }
- /*
- * Check if the result will overflow (0 < x, x != 1):
- * 1) log10(x) < 0 iff adjexp(x) < 0
- * 2) 0 < x /\ x <= y ==> adjexp(x) <= adjexp(y)
- * 3) 0 < x /\ x != 1 ==> 2 * abs(log10(x)) < abs(log(x))
- * 4) adjexp(x) <= log10(x) < adjexp(x) + 1
- *
- * Case adjexp(x) >= 0:
- * 5) 2 * adjexp(x) < abs(log(x))
- * Case adjexp(x) > 0:
- * 6) adjexp(2 * adjexp(x)) <= adjexp(abs(log(x)))
- * Case adjexp(x) == 0:
- * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered)
- *
- * Case adjexp(x) < 0:
- * 7) 2 * (-adjexp(x) - 1) < abs(log(x))
- * Case adjexp(x) < -1:
- * 8) adjexp(2 * (-adjexp(x) - 1)) <= adjexp(abs(log(x)))
- * Case adjexp(x) == -1:
- * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered)
- */
- adjexp = mpd_adjexp(a);
- t = (adjexp < 0) ? -adjexp-1 : adjexp;
- t *= 2;
- if (mpd_exp_digits(t)-1 > ctx->emax) {
- *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded;
- mpd_setspecial(result, (adjexp<0), MPD_INF);
- return;
- }
-
- workctx = *ctx;
- workctx.round = MPD_ROUND_HALF_EVEN;
-
- if (ctx->allcr) {
- MPD_NEW_STATIC(t1, 0,0,0,0);
- MPD_NEW_STATIC(t2, 0,0,0,0);
- MPD_NEW_STATIC(ulp, 0,0,0,0);
- MPD_NEW_STATIC(aa, 0,0,0,0);
- mpd_ssize_t prec;
-
- if (result == a) {
- if (!mpd_qcopy(&aa, a, status)) {
- mpd_seterror(result, MPD_Malloc_error, status);
- return;
- }
- a = &aa;
- }
-
- workctx.clamp = 0;
- prec = ctx->prec + 3;
- while (1) {
- workctx.prec = prec;
- _mpd_qln(result, a, &workctx, status);
- _ssettriple(&ulp, MPD_POS, 1,
- result->exp + result->digits-workctx.prec);
-
- workctx.prec = ctx->prec;
- mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status);
- mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status);
- if (mpd_isspecial(result) || mpd_iszerocoeff(result) ||
- mpd_qcmp(&t1, &t2, status) == 0) {
- workctx.clamp = ctx->clamp;
- mpd_check_underflow(result, &workctx, status);
- mpd_qfinalize(result, &workctx, status);
- break;
- }
- prec += MPD_RDIGITS;
- }
- mpd_del(&t1);
- mpd_del(&t2);
- mpd_del(&ulp);
- mpd_del(&aa);
- }
- else {
- _mpd_qln(result, a, &workctx, status);
- mpd_check_underflow(result, &workctx, status);
- mpd_qfinalize(result, &workctx, status);
- }
-}
-
-/*
- * Internal log10() function that does not check for specials, zero or one.
- * Case SKIP_FINALIZE:
- * Relative error: abs(result - log10(a)) < 0.1 * 10**-prec * abs(log10(a))
- * Case DO_FINALIZE:
- * Ulp error: abs(result - log10(a)) < ulp(log10(a))
- */
-enum {SKIP_FINALIZE, DO_FINALIZE};
-static void
-_mpd_qlog10(int action, mpd_t *result, const mpd_t *a,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t workctx;
- MPD_NEW_STATIC(ln10,0,0,0,0);
-
- mpd_maxcontext(&workctx);
- workctx.prec = ctx->prec + 3;
- /* relative error: 0.1 * 10**(-p-3). The specific underflow shortcut
- * in _mpd_qln() does not change the final result. */
- _mpd_qln(result, a, &workctx, status);
- /* relative error: 5 * 10**(-p-3) */
- mpd_qln10(&ln10, workctx.prec, status);
-
- if (action == DO_FINALIZE) {
- workctx = *ctx;
- workctx.round = MPD_ROUND_HALF_EVEN;
- }
- /* SKIP_FINALIZE: relative error: 5 * 10**(-p-3) */
- _mpd_qdiv(NO_IDEAL_EXP, result, result, &ln10, &workctx, status);
-
- mpd_del(&ln10);
-}
-
-/* log10(a) */
-void
-mpd_qlog10(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_context_t workctx;
- mpd_ssize_t adjexp, t;
-
- workctx = *ctx;
- workctx.round = MPD_ROUND_HALF_EVEN;
-
- if (mpd_isspecial(a)) {
- if (mpd_qcheck_nan(result, a, ctx, status)) {
- return;
- }
- if (mpd_isnegative(a)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- mpd_setspecial(result, MPD_POS, MPD_INF);
- return;
- }
- if (mpd_iszerocoeff(a)) {
- mpd_setspecial(result, MPD_NEG, MPD_INF);
- return;
- }
- if (mpd_isnegative(a)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- if (mpd_coeff_ispow10(a)) {
- uint8_t sign = 0;
- adjexp = mpd_adjexp(a);
- if (adjexp < 0) {
- sign = 1;
- adjexp = -adjexp;
- }
- _settriple(result, sign, adjexp, 0);
- mpd_qfinalize(result, &workctx, status);
- return;
- }
- /*
- * Check if the result will overflow (0 < x, x != 1):
- * 1) log10(x) < 0 iff adjexp(x) < 0
- * 2) 0 < x /\ x <= y ==> adjexp(x) <= adjexp(y)
- * 3) adjexp(x) <= log10(x) < adjexp(x) + 1
- *
- * Case adjexp(x) >= 0:
- * 4) adjexp(x) <= abs(log10(x))
- * Case adjexp(x) > 0:
- * 5) adjexp(adjexp(x)) <= adjexp(abs(log10(x)))
- * Case adjexp(x) == 0:
- * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered)
- *
- * Case adjexp(x) < 0:
- * 6) -adjexp(x) - 1 < abs(log10(x))
- * Case adjexp(x) < -1:
- * 7) adjexp(-adjexp(x) - 1) <= adjexp(abs(log(x)))
- * Case adjexp(x) == -1:
- * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered)
- */
- adjexp = mpd_adjexp(a);
- t = (adjexp < 0) ? -adjexp-1 : adjexp;
- if (mpd_exp_digits(t)-1 > ctx->emax) {
- *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded;
- mpd_setspecial(result, (adjexp<0), MPD_INF);
- return;
- }
-
- if (ctx->allcr) {
- MPD_NEW_STATIC(t1, 0,0,0,0);
- MPD_NEW_STATIC(t2, 0,0,0,0);
- MPD_NEW_STATIC(ulp, 0,0,0,0);
- MPD_NEW_STATIC(aa, 0,0,0,0);
- mpd_ssize_t prec;
-
- if (result == a) {
- if (!mpd_qcopy(&aa, a, status)) {
- mpd_seterror(result, MPD_Malloc_error, status);
- return;
- }
- a = &aa;
- }
-
- workctx.clamp = 0;
- prec = ctx->prec + 3;
- while (1) {
- workctx.prec = prec;
- _mpd_qlog10(SKIP_FINALIZE, result, a, &workctx, status);
- _ssettriple(&ulp, MPD_POS, 1,
- result->exp + result->digits-workctx.prec);
-
- workctx.prec = ctx->prec;
- mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status);
- mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status);
- if (mpd_isspecial(result) || mpd_iszerocoeff(result) ||
- mpd_qcmp(&t1, &t2, status) == 0) {
- workctx.clamp = ctx->clamp;
- mpd_check_underflow(result, &workctx, status);
- mpd_qfinalize(result, &workctx, status);
- break;
- }
- prec += MPD_RDIGITS;
- }
- mpd_del(&t1);
- mpd_del(&t2);
- mpd_del(&ulp);
- mpd_del(&aa);
- }
- else {
- _mpd_qlog10(DO_FINALIZE, result, a, &workctx, status);
- mpd_check_underflow(result, &workctx, status);
- }
-}
-
-/*
- * Maximum of the two operands. Attention: If one operand is a quiet NaN and the
- * other is numeric, the numeric operand is returned. This may not be what one
- * expects.
- */
-void
-mpd_qmax(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- int c;
-
- if (mpd_isqnan(a) && !mpd_isnan(b)) {
- mpd_qcopy(result, b, status);
- }
- else if (mpd_isqnan(b) && !mpd_isnan(a)) {
- mpd_qcopy(result, a, status);
- }
- else if (mpd_qcheck_nans(result, a, b, ctx, status)) {
- return;
- }
- else {
- c = _mpd_cmp(a, b);
- if (c == 0) {
- c = _mpd_cmp_numequal(a, b);
- }
-
- if (c < 0) {
- mpd_qcopy(result, b, status);
- }
- else {
- mpd_qcopy(result, a, status);
- }
- }
-
- mpd_qfinalize(result, ctx, status);
-}
-
-/*
- * Maximum magnitude: Same as mpd_max(), but compares the operands with their
- * sign ignored.
- */
-void
-mpd_qmax_mag(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- int c;
-
- if (mpd_isqnan(a) && !mpd_isnan(b)) {
- mpd_qcopy(result, b, status);
- }
- else if (mpd_isqnan(b) && !mpd_isnan(a)) {
- mpd_qcopy(result, a, status);
- }
- else if (mpd_qcheck_nans(result, a, b, ctx, status)) {
- return;
- }
- else {
- c = _mpd_cmp_abs(a, b);
- if (c == 0) {
- c = _mpd_cmp_numequal(a, b);
- }
-
- if (c < 0) {
- mpd_qcopy(result, b, status);
- }
- else {
- mpd_qcopy(result, a, status);
- }
- }
-
- mpd_qfinalize(result, ctx, status);
-}
-
-/*
- * Minimum of the two operands. Attention: If one operand is a quiet NaN and the
- * other is numeric, the numeric operand is returned. This may not be what one
- * expects.
- */
-void
-mpd_qmin(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- int c;
-
- if (mpd_isqnan(a) && !mpd_isnan(b)) {
- mpd_qcopy(result, b, status);
- }
- else if (mpd_isqnan(b) && !mpd_isnan(a)) {
- mpd_qcopy(result, a, status);
- }
- else if (mpd_qcheck_nans(result, a, b, ctx, status)) {
- return;
- }
- else {
- c = _mpd_cmp(a, b);
- if (c == 0) {
- c = _mpd_cmp_numequal(a, b);
- }
-
- if (c < 0) {
- mpd_qcopy(result, a, status);
- }
- else {
- mpd_qcopy(result, b, status);
- }
- }
-
- mpd_qfinalize(result, ctx, status);
-}
-
-/*
- * Minimum magnitude: Same as mpd_min(), but compares the operands with their
- * sign ignored.
- */
-void
-mpd_qmin_mag(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- int c;
-
- if (mpd_isqnan(a) && !mpd_isnan(b)) {
- mpd_qcopy(result, b, status);
- }
- else if (mpd_isqnan(b) && !mpd_isnan(a)) {
- mpd_qcopy(result, a, status);
- }
- else if (mpd_qcheck_nans(result, a, b, ctx, status)) {
- return;
- }
- else {
- c = _mpd_cmp_abs(a, b);
- if (c == 0) {
- c = _mpd_cmp_numequal(a, b);
- }
-
- if (c < 0) {
- mpd_qcopy(result, a, status);
- }
- else {
- mpd_qcopy(result, b, status);
- }
- }
-
- mpd_qfinalize(result, ctx, status);
-}
-
-/* Minimum space needed for the result array in _karatsuba_rec(). */
-static inline mpd_size_t
-_kmul_resultsize(mpd_size_t la, mpd_size_t lb)
-{
- mpd_size_t n, m;
-
- n = add_size_t(la, lb);
- n = add_size_t(n, 1);
-
- m = (la+1)/2 + 1;
- m = mul_size_t(m, 3);
-
- return (m > n) ? m : n;
-}
-
-/* Work space needed in _karatsuba_rec(). lim >= 4 */
-static inline mpd_size_t
-_kmul_worksize(mpd_size_t n, mpd_size_t lim)
-{
- mpd_size_t m;
-
- if (n <= lim) {
- return 0;
- }
-
- m = (n+1)/2 + 1;
-
- return add_size_t(mul_size_t(m, 2), _kmul_worksize(m, lim));
-}
-
-
-#define MPD_KARATSUBA_BASECASE 16 /* must be >= 4 */
-
-/*
- * Add the product of a and b to c.
- * c must be _kmul_resultsize(la, lb) in size.
- * w is used as a work array and must be _kmul_worksize(a, lim) in size.
- * Roman E. Maeder, Storage Allocation for the Karatsuba Integer Multiplication
- * Algorithm. In "Design and implementation of symbolic computation systems",
- * Springer, 1993, ISBN 354057235X, 9783540572350.
- */
-static void
-_karatsuba_rec(mpd_uint_t *c, const mpd_uint_t *a, const mpd_uint_t *b,
- mpd_uint_t *w, mpd_size_t la, mpd_size_t lb)
-{
- mpd_size_t m, lt;
-
- assert(la >= lb && lb > 0);
- assert(la <= MPD_KARATSUBA_BASECASE || w != NULL);
-
- if (la <= MPD_KARATSUBA_BASECASE) {
- _mpd_basemul(c, a, b, la, lb);
- return;
- }
-
- m = (la+1)/2; /* ceil(la/2) */
-
- /* lb <= m < la */
- if (lb <= m) {
-
- /* lb can now be larger than la-m */
- if (lb > la-m) {
- lt = lb + lb + 1; /* space needed for result array */
- mpd_uint_zero(w, lt); /* clear result array */
- _karatsuba_rec(w, b, a+m, w+lt, lb, la-m); /* b*ah */
- }
- else {
- lt = (la-m) + (la-m) + 1; /* space needed for result array */
- mpd_uint_zero(w, lt); /* clear result array */
- _karatsuba_rec(w, a+m, b, w+lt, la-m, lb); /* ah*b */
- }
- _mpd_baseaddto(c+m, w, (la-m)+lb); /* add ah*b*B**m */
-
- lt = m + m + 1; /* space needed for the result array */
- mpd_uint_zero(w, lt); /* clear result array */
- _karatsuba_rec(w, a, b, w+lt, m, lb); /* al*b */
- _mpd_baseaddto(c, w, m+lb); /* add al*b */
-
- return;
- }
-
- /* la >= lb > m */
- memcpy(w, a, m * sizeof *w);
- w[m] = 0;
- _mpd_baseaddto(w, a+m, la-m);
-
- memcpy(w+(m+1), b, m * sizeof *w);
- w[m+1+m] = 0;
- _mpd_baseaddto(w+(m+1), b+m, lb-m);
-
- _karatsuba_rec(c+m, w, w+(m+1), w+2*(m+1), m+1, m+1);
-
- lt = (la-m) + (la-m) + 1;
- mpd_uint_zero(w, lt);
-
- _karatsuba_rec(w, a+m, b+m, w+lt, la-m, lb-m);
-
- _mpd_baseaddto(c+2*m, w, (la-m) + (lb-m));
- _mpd_basesubfrom(c+m, w, (la-m) + (lb-m));
-
- lt = m + m + 1;
- mpd_uint_zero(w, lt);
-
- _karatsuba_rec(w, a, b, w+lt, m, m);
- _mpd_baseaddto(c, w, m+m);
- _mpd_basesubfrom(c+m, w, m+m);
-
- return;
-}
-
-/*
- * Multiply u and v, using Karatsuba multiplication. Returns a pointer
- * to the result or NULL in case of failure (malloc error).
- * Conditions: ulen >= vlen, ulen >= 4
- */
-static mpd_uint_t *
-_mpd_kmul(const mpd_uint_t *u, const mpd_uint_t *v,
- mpd_size_t ulen, mpd_size_t vlen,
- mpd_size_t *rsize)
-{
- mpd_uint_t *result = NULL, *w = NULL;
- mpd_size_t m;
-
- assert(ulen >= 4);
- assert(ulen >= vlen);
-
- *rsize = _kmul_resultsize(ulen, vlen);
- if ((result = mpd_calloc(*rsize, sizeof *result)) == NULL) {
- return NULL;
- }
-
- m = _kmul_worksize(ulen, MPD_KARATSUBA_BASECASE);
- if (m && ((w = mpd_calloc(m, sizeof *w)) == NULL)) {
- mpd_free(result);
- return NULL;
- }
-
- _karatsuba_rec(result, u, v, w, ulen, vlen);
-
-
- if (w) mpd_free(w);
- return result;
-}
-
-
-/*
- * Determine the minimum length for the number theoretic transform. Valid
- * transform lengths are 2**n or 3*2**n, where 2**n <= MPD_MAXTRANSFORM_2N.
- * The function finds the shortest length m such that rsize <= m.
- */
-static inline mpd_size_t
-_mpd_get_transform_len(mpd_size_t rsize)
-{
- mpd_size_t log2rsize;
- mpd_size_t x, step;
-
- assert(rsize >= 4);
- log2rsize = mpd_bsr(rsize);
-
- if (rsize <= 1024) {
- /* 2**n is faster in this range. */
- x = ((mpd_size_t)1)<<log2rsize;
- return (rsize == x) ? x : x<<1;
- }
- else if (rsize <= MPD_MAXTRANSFORM_2N) {
- x = ((mpd_size_t)1)<<log2rsize;
- if (rsize == x) return x;
- step = x>>1;
- x += step;
- return (rsize <= x) ? x : x + step;
- }
- else if (rsize <= MPD_MAXTRANSFORM_2N+MPD_MAXTRANSFORM_2N/2) {
- return MPD_MAXTRANSFORM_2N+MPD_MAXTRANSFORM_2N/2;
- }
- else if (rsize <= 3*MPD_MAXTRANSFORM_2N) {
- return 3*MPD_MAXTRANSFORM_2N;
- }
- else {
- return MPD_SIZE_MAX;
- }
-}
-
-#ifdef PPRO
-#ifndef _MSC_VER
-static inline unsigned short
-_mpd_get_control87(void)
-{
- unsigned short cw;
-
- __asm__ __volatile__ ("fnstcw %0" : "=m" (cw));
- return cw;
-}
-
-static inline void
-_mpd_set_control87(unsigned short cw)
-{
- __asm__ __volatile__ ("fldcw %0" : : "m" (cw));
-}
-#endif
-
-static unsigned int
-mpd_set_fenv(void)
-{
- unsigned int cw;
-#ifdef _MSC_VER
- unsigned int flags =
- _EM_INVALID|_EM_DENORMAL|_EM_ZERODIVIDE|_EM_OVERFLOW|
- _EM_UNDERFLOW|_EM_INEXACT|_RC_CHOP|_PC_64;
- unsigned int mask = _MCW_EM|_MCW_RC|_MCW_PC;
- unsigned int dummy;
-
- __control87_2(0, 0, &cw, NULL);
- __control87_2(flags, mask, &dummy, NULL);
-#else
- cw = _mpd_get_control87();
- _mpd_set_control87(cw|0xF3F);
-#endif
- return cw;
-}
-
-static void
-mpd_restore_fenv(unsigned int cw)
-{
-#ifdef _MSC_VER
- unsigned int mask = _MCW_EM|_MCW_RC|_MCW_PC;
- unsigned int dummy;
-
- __control87_2(cw, mask, &dummy, NULL);
-#else
- _mpd_set_control87((unsigned short)cw);
-#endif
-}
-#endif /* PPRO */
-
-/*
- * Multiply u and v, using the fast number theoretic transform. Returns
- * a pointer to the result or NULL in case of failure (malloc error).
- */
-static mpd_uint_t *
-_mpd_fntmul(const mpd_uint_t *u, const mpd_uint_t *v,
- mpd_size_t ulen, mpd_size_t vlen,
- mpd_size_t *rsize)
-{
- mpd_uint_t *c1 = NULL, *c2 = NULL, *c3 = NULL, *vtmp = NULL;
- mpd_size_t n;
-
-#ifdef PPRO
- unsigned int cw;
- cw = mpd_set_fenv();
-#endif
-
- *rsize = add_size_t(ulen, vlen);
- if ((n = _mpd_get_transform_len(*rsize)) == MPD_SIZE_MAX) {
- goto malloc_error;
- }
-
- if ((c1 = mpd_calloc(n, sizeof *c1)) == NULL) {
- goto malloc_error;
- }
- if ((c2 = mpd_calloc(n, sizeof *c2)) == NULL) {
- goto malloc_error;
- }
- if ((c3 = mpd_calloc(n, sizeof *c3)) == NULL) {
- goto malloc_error;
- }
-
- memcpy(c1, u, ulen * (sizeof *c1));
- memcpy(c2, u, ulen * (sizeof *c2));
- memcpy(c3, u, ulen * (sizeof *c3));
-
- if (u == v) {
- if (!fnt_autoconvolute(c1, n, P1) ||
- !fnt_autoconvolute(c2, n, P2) ||
- !fnt_autoconvolute(c3, n, P3)) {
- goto malloc_error;
- }
- }
- else {
- if ((vtmp = mpd_calloc(n, sizeof *vtmp)) == NULL) {
- goto malloc_error;
- }
-
- memcpy(vtmp, v, vlen * (sizeof *vtmp));
- if (!fnt_convolute(c1, vtmp, n, P1)) {
- mpd_free(vtmp);
- goto malloc_error;
- }
-
- memcpy(vtmp, v, vlen * (sizeof *vtmp));
- mpd_uint_zero(vtmp+vlen, n-vlen);
- if (!fnt_convolute(c2, vtmp, n, P2)) {
- mpd_free(vtmp);
- goto malloc_error;
- }
-
- memcpy(vtmp, v, vlen * (sizeof *vtmp));
- mpd_uint_zero(vtmp+vlen, n-vlen);
- if (!fnt_convolute(c3, vtmp, n, P3)) {
- mpd_free(vtmp);
- goto malloc_error;
- }
-
- mpd_free(vtmp);
- }
-
- crt3(c1, c2, c3, *rsize);
-
-out:
-#ifdef PPRO
- mpd_restore_fenv(cw);
-#endif
- if (c2) mpd_free(c2);
- if (c3) mpd_free(c3);
- return c1;
-
-malloc_error:
- if (c1) mpd_free(c1);
- c1 = NULL;
- goto out;
-}
-
-
-/*
- * Karatsuba multiplication with FNT/basemul as the base case.
- */
-static int
-_karatsuba_rec_fnt(mpd_uint_t *c, const mpd_uint_t *a, const mpd_uint_t *b,
- mpd_uint_t *w, mpd_size_t la, mpd_size_t lb)
-{
- mpd_size_t m, lt;
-
- assert(la >= lb && lb > 0);
- assert(la <= 3*(MPD_MAXTRANSFORM_2N/2) || w != NULL);
-
- if (la <= 3*(MPD_MAXTRANSFORM_2N/2)) {
-
- if (lb <= 192) {
- _mpd_basemul(c, b, a, lb, la);
- }
- else {
- mpd_uint_t *result;
- mpd_size_t dummy;
-
- if ((result = _mpd_fntmul(a, b, la, lb, &dummy)) == NULL) {
- return 0;
- }
- memcpy(c, result, (la+lb) * (sizeof *result));
- mpd_free(result);
- }
- return 1;
- }
-
- m = (la+1)/2; /* ceil(la/2) */
-
- /* lb <= m < la */
- if (lb <= m) {
-
- /* lb can now be larger than la-m */
- if (lb > la-m) {
- lt = lb + lb + 1; /* space needed for result array */
- mpd_uint_zero(w, lt); /* clear result array */
- if (!_karatsuba_rec_fnt(w, b, a+m, w+lt, lb, la-m)) { /* b*ah */
- return 0; /* GCOV_UNLIKELY */
- }
- }
- else {
- lt = (la-m) + (la-m) + 1; /* space needed for result array */
- mpd_uint_zero(w, lt); /* clear result array */
- if (!_karatsuba_rec_fnt(w, a+m, b, w+lt, la-m, lb)) { /* ah*b */
- return 0; /* GCOV_UNLIKELY */
- }
- }
- _mpd_baseaddto(c+m, w, (la-m)+lb); /* add ah*b*B**m */
-
- lt = m + m + 1; /* space needed for the result array */
- mpd_uint_zero(w, lt); /* clear result array */
- if (!_karatsuba_rec_fnt(w, a, b, w+lt, m, lb)) { /* al*b */
- return 0; /* GCOV_UNLIKELY */
- }
- _mpd_baseaddto(c, w, m+lb); /* add al*b */
-
- return 1;
- }
-
- /* la >= lb > m */
- memcpy(w, a, m * sizeof *w);
- w[m] = 0;
- _mpd_baseaddto(w, a+m, la-m);
-
- memcpy(w+(m+1), b, m * sizeof *w);
- w[m+1+m] = 0;
- _mpd_baseaddto(w+(m+1), b+m, lb-m);
-
- if (!_karatsuba_rec_fnt(c+m, w, w+(m+1), w+2*(m+1), m+1, m+1)) {
- return 0; /* GCOV_UNLIKELY */
- }
-
- lt = (la-m) + (la-m) + 1;
- mpd_uint_zero(w, lt);
-
- if (!_karatsuba_rec_fnt(w, a+m, b+m, w+lt, la-m, lb-m)) {
- return 0; /* GCOV_UNLIKELY */
- }
-
- _mpd_baseaddto(c+2*m, w, (la-m) + (lb-m));
- _mpd_basesubfrom(c+m, w, (la-m) + (lb-m));
-
- lt = m + m + 1;
- mpd_uint_zero(w, lt);
-
- if (!_karatsuba_rec_fnt(w, a, b, w+lt, m, m)) {
- return 0; /* GCOV_UNLIKELY */
- }
- _mpd_baseaddto(c, w, m+m);
- _mpd_basesubfrom(c+m, w, m+m);
-
- return 1;
-}
-
-/*
- * Multiply u and v, using Karatsuba multiplication with the FNT as the
- * base case. Returns a pointer to the result or NULL in case of failure
- * (malloc error). Conditions: ulen >= vlen, ulen >= 4.
- */
-static mpd_uint_t *
-_mpd_kmul_fnt(const mpd_uint_t *u, const mpd_uint_t *v,
- mpd_size_t ulen, mpd_size_t vlen,
- mpd_size_t *rsize)
-{
- mpd_uint_t *result = NULL, *w = NULL;
- mpd_size_t m;
-
- assert(ulen >= 4);
- assert(ulen >= vlen);
-
- *rsize = _kmul_resultsize(ulen, vlen);
- if ((result = mpd_calloc(*rsize, sizeof *result)) == NULL) {
- return NULL;
- }
-
- m = _kmul_worksize(ulen, 3*(MPD_MAXTRANSFORM_2N/2));
- if (m && ((w = mpd_calloc(m, sizeof *w)) == NULL)) {
- mpd_free(result); /* GCOV_UNLIKELY */
- return NULL; /* GCOV_UNLIKELY */
- }
-
- if (!_karatsuba_rec_fnt(result, u, v, w, ulen, vlen)) {
- mpd_free(result);
- result = NULL;
- }
-
-
- if (w) mpd_free(w);
- return result;
-}
-
-
-/* Deal with the special cases of multiplying infinities. */
-static void
-_mpd_qmul_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status)
-{
- if (mpd_isinfinite(a)) {
- if (mpd_iszero(b)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- }
- else {
- mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF);
- }
- return;
- }
- assert(mpd_isinfinite(b));
- if (mpd_iszero(a)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- }
- else {
- mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF);
- }
-}
-
-/*
- * Internal function: Multiply a and b. _mpd_qmul deals with specials but
- * does NOT finalize the result. This is for use in mpd_fma().
- */
-static inline void
-_mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- const mpd_t *big = a, *small = b;
- mpd_uint_t *rdata = NULL;
- mpd_uint_t rbuf[MPD_MINALLOC_MAX];
- mpd_size_t rsize, i;
-
-
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_qcheck_nans(result, a, b, ctx, status)) {
- return;
- }
- _mpd_qmul_inf(result, a, b, status);
- return;
- }
-
- if (small->len > big->len) {
- _mpd_ptrswap(&big, &small);
- }
-
- rsize = big->len + small->len;
-
- if (big->len == 1) {
- _mpd_singlemul(result->data, big->data[0], small->data[0]);
- goto finish;
- }
- if (rsize <= (mpd_size_t)MPD_MINALLOC_MAX) {
- if (big->len == 2) {
- _mpd_mul_2_le2(rbuf, big->data, small->data, small->len);
- }
- else {
- mpd_uint_zero(rbuf, rsize);
- if (small->len == 1) {
- _mpd_shortmul(rbuf, big->data, big->len, small->data[0]);
- }
- else {
- _mpd_basemul(rbuf, small->data, big->data, small->len, big->len);
- }
- }
- if (!mpd_qresize(result, rsize, status)) {
- return;
- }
- for(i = 0; i < rsize; i++) {
- result->data[i] = rbuf[i];
- }
- goto finish;
- }
-
-
- if (small->len <= 256) {
- rdata = mpd_calloc(rsize, sizeof *rdata);
- if (rdata != NULL) {
- if (small->len == 1) {
- _mpd_shortmul(rdata, big->data, big->len, small->data[0]);
- }
- else {
- _mpd_basemul(rdata, small->data, big->data, small->len, big->len);
- }
- }
- }
- else if (rsize <= 1024) {
- rdata = _mpd_kmul(big->data, small->data, big->len, small->len, &rsize);
- }
- else if (rsize <= 3*MPD_MAXTRANSFORM_2N) {
- rdata = _mpd_fntmul(big->data, small->data, big->len, small->len, &rsize);
- }
- else {
- rdata = _mpd_kmul_fnt(big->data, small->data, big->len, small->len, &rsize);
- }
-
- if (rdata == NULL) {
- mpd_seterror(result, MPD_Malloc_error, status);
- return;
- }
-
- if (mpd_isdynamic_data(result)) {
- mpd_free(result->data);
- }
- result->data = rdata;
- result->alloc = rsize;
- mpd_set_dynamic_data(result);
-
-
-finish:
- mpd_set_flags(result, mpd_sign(a)^mpd_sign(b));
- result->exp = big->exp + small->exp;
- result->len = _mpd_real_size(result->data, rsize);
- /* resize to smaller cannot fail */
- mpd_qresize(result, result->len, status);
- mpd_setdigits(result);
-}
-
-/* Multiply a and b. */
-void
-mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- _mpd_qmul(result, a, b, ctx, status);
- mpd_qfinalize(result, ctx, status);
-}
-
-/* Multiply a and b. Set NaN/Invalid_operation if the result is inexact. */
-static void
-_mpd_qmul_exact(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- uint32_t workstatus = 0;
-
- mpd_qmul(result, a, b, ctx, &workstatus);
- *status |= workstatus;
- if (workstatus & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- }
-}
-
-/* Multiply decimal and mpd_ssize_t. */
-void
-mpd_qmul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qsset_ssize(&bb, b, &maxcontext, status);
- mpd_qmul(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-
-/* Multiply decimal and mpd_uint_t. */
-void
-mpd_qmul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qsset_uint(&bb, b, &maxcontext, status);
- mpd_qmul(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-
-void
-mpd_qmul_i32(mpd_t *result, const mpd_t *a, int32_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qmul_ssize(result, a, b, ctx, status);
-}
-
-void
-mpd_qmul_u32(mpd_t *result, const mpd_t *a, uint32_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qmul_uint(result, a, b, ctx, status);
-}
-
-#ifdef CONFIG_64
-void
-mpd_qmul_i64(mpd_t *result, const mpd_t *a, int64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qmul_ssize(result, a, b, ctx, status);
-}
-
-void
-mpd_qmul_u64(mpd_t *result, const mpd_t *a, uint64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_qmul_uint(result, a, b, ctx, status);
-}
-#elif !defined(LEGACY_COMPILER)
-/* Multiply decimal and int64_t. */
-void
-mpd_qmul_i64(mpd_t *result, const mpd_t *a, int64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qset_i64(&bb, b, &maxcontext, status);
- mpd_qmul(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-
-/* Multiply decimal and uint64_t. */
-void
-mpd_qmul_u64(mpd_t *result, const mpd_t *a, uint64_t b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(bb,0,0,0,0);
-
- mpd_maxcontext(&maxcontext);
- mpd_qset_u64(&bb, b, &maxcontext, status);
- mpd_qmul(result, a, &bb, ctx, status);
- mpd_del(&bb);
-}
-#endif
-
-/* Like the minus operator. */
-void
-mpd_qminus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- if (mpd_isspecial(a)) {
- if (mpd_qcheck_nan(result, a, ctx, status)) {
- return;
- }
- }
-
- if (mpd_iszero(a) && ctx->round != MPD_ROUND_FLOOR) {
- mpd_qcopy_abs(result, a, status);
- }
- else {
- mpd_qcopy_negate(result, a, status);
- }
-
- mpd_qfinalize(result, ctx, status);
-}
-
-/* Like the plus operator. */
-void
-mpd_qplus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- if (mpd_isspecial(a)) {
- if (mpd_qcheck_nan(result, a, ctx, status)) {
- return;
- }
- }
-
- if (mpd_iszero(a) && ctx->round != MPD_ROUND_FLOOR) {
- mpd_qcopy_abs(result, a, status);
- }
- else {
- mpd_qcopy(result, a, status);
- }
-
- mpd_qfinalize(result, ctx, status);
-}
-
-/* The largest representable number that is smaller than the operand. */
-void
-mpd_qnext_minus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_context_t workctx;
- MPD_NEW_CONST(tiny,MPD_POS,mpd_etiny(ctx)-1,1,1,1,1);
-
- if (mpd_isspecial(a)) {
- if (mpd_qcheck_nan(result, a, ctx, status)) {
- return;
- }
-
- assert(mpd_isinfinite(a));
- if (mpd_isnegative(a)) {
- mpd_qcopy(result, a, status);
- return;
- }
- else {
- mpd_clear_flags(result);
- mpd_qmaxcoeff(result, ctx, status);
- if (mpd_isnan(result)) {
- return;
- }
- result->exp = mpd_etop(ctx);
- return;
- }
- }
-
- mpd_workcontext(&workctx, ctx);
- workctx.round = MPD_ROUND_FLOOR;
-
- if (!mpd_qcopy(result, a, status)) {
- return;
- }
-
- mpd_qfinalize(result, &workctx, &workctx.status);
- if (workctx.status&(MPD_Inexact|MPD_Errors)) {
- *status |= (workctx.status&MPD_Errors);
- return;
- }
-
- workctx.status = 0;
- mpd_qsub(result, a, &tiny, &workctx, &workctx.status);
- *status |= (workctx.status&MPD_Errors);
-}
-
-/* The smallest representable number that is larger than the operand. */
-void
-mpd_qnext_plus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_context_t workctx;
- MPD_NEW_CONST(tiny,MPD_POS,mpd_etiny(ctx)-1,1,1,1,1);
-
- if (mpd_isspecial(a)) {
- if (mpd_qcheck_nan(result, a, ctx, status)) {
- return;
- }
-
- assert(mpd_isinfinite(a));
- if (mpd_ispositive(a)) {
- mpd_qcopy(result, a, status);
- }
- else {
- mpd_clear_flags(result);
- mpd_qmaxcoeff(result, ctx, status);
- if (mpd_isnan(result)) {
- return;
- }
- mpd_set_flags(result, MPD_NEG);
- result->exp = mpd_etop(ctx);
- }
- return;
- }
-
- mpd_workcontext(&workctx, ctx);
- workctx.round = MPD_ROUND_CEILING;
-
- if (!mpd_qcopy(result, a, status)) {
- return;
- }
-
- mpd_qfinalize(result, &workctx, &workctx.status);
- if (workctx.status & (MPD_Inexact|MPD_Errors)) {
- *status |= (workctx.status&MPD_Errors);
- return;
- }
-
- workctx.status = 0;
- mpd_qadd(result, a, &tiny, &workctx, &workctx.status);
- *status |= (workctx.status&MPD_Errors);
-}
-
-/*
- * The number closest to the first operand that is in the direction towards
- * the second operand.
- */
-void
-mpd_qnext_toward(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- int c;
-
- if (mpd_qcheck_nans(result, a, b, ctx, status)) {
- return;
- }
-
- c = _mpd_cmp(a, b);
- if (c == 0) {
- mpd_qcopy_sign(result, a, b, status);
- return;
- }
-
- if (c < 0) {
- mpd_qnext_plus(result, a, ctx, status);
- }
- else {
- mpd_qnext_minus(result, a, ctx, status);
- }
-
- if (mpd_isinfinite(result)) {
- *status |= (MPD_Overflow|MPD_Rounded|MPD_Inexact);
- }
- else if (mpd_adjexp(result) < ctx->emin) {
- *status |= (MPD_Underflow|MPD_Subnormal|MPD_Rounded|MPD_Inexact);
- if (mpd_iszero(result)) {
- *status |= MPD_Clamped;
- }
- }
-}
-
-/*
- * Internal function: Integer power with mpd_uint_t exponent. The function
- * can fail with MPD_Malloc_error.
- *
- * The error is equal to the error incurred in k-1 multiplications. Assuming
- * the upper bound for the relative error in each operation:
- *
- * abs(err) = 5 * 10**-prec
- * result = x**k * (1 + err)**(k-1)
- */
-static inline void
-_mpd_qpow_uint(mpd_t *result, const mpd_t *base, mpd_uint_t exp,
- uint8_t resultsign, const mpd_context_t *ctx, uint32_t *status)
-{
- uint32_t workstatus = 0;
- mpd_uint_t n;
-
- if (exp == 0) {
- _settriple(result, resultsign, 1, 0); /* GCOV_NOT_REACHED */
- return; /* GCOV_NOT_REACHED */
- }
-
- if (!mpd_qcopy(result, base, status)) {
- return;
- }
-
- n = mpd_bits[mpd_bsr(exp)];
- while (n >>= 1) {
- mpd_qmul(result, result, result, ctx, &workstatus);
- if (exp & n) {
- mpd_qmul(result, result, base, ctx, &workstatus);
- }
- if (mpd_isspecial(result) ||
- (mpd_iszerocoeff(result) && (workstatus & MPD_Clamped))) {
- break;
- }
- }
-
- *status |= workstatus;
- mpd_set_sign(result, resultsign);
-}
-
-/*
- * Internal function: Integer power with mpd_t exponent, tbase and texp
- * are modified!! Function can fail with MPD_Malloc_error.
- *
- * The error is equal to the error incurred in k multiplications. Assuming
- * the upper bound for the relative error in each operation:
- *
- * abs(err) = 5 * 10**-prec
- * result = x**k * (1 + err)**k
- */
-static inline void
-_mpd_qpow_mpd(mpd_t *result, mpd_t *tbase, mpd_t *texp, uint8_t resultsign,
- const mpd_context_t *ctx, uint32_t *status)
-{
- uint32_t workstatus = 0;
- mpd_context_t maxctx;
- MPD_NEW_CONST(two,0,0,1,1,1,2);
-
-
- mpd_maxcontext(&maxctx);
-
- /* resize to smaller cannot fail */
- mpd_qcopy(result, &one, status);
-
- while (!mpd_iszero(texp)) {
- if (mpd_isodd(texp)) {
- mpd_qmul(result, result, tbase, ctx, &workstatus);
- *status |= workstatus;
- if (mpd_isspecial(result) ||
- (mpd_iszerocoeff(result) && (workstatus & MPD_Clamped))) {
- break;
- }
- }
- mpd_qmul(tbase, tbase, tbase, ctx, &workstatus);
- mpd_qdivint(texp, texp, &two, &maxctx, &workstatus);
- if (mpd_isnan(tbase) || mpd_isnan(texp)) {
- mpd_seterror(result, workstatus&MPD_Errors, status);
- return;
- }
- }
- mpd_set_sign(result, resultsign);
-}
-
-/*
- * The power function for integer exponents. Relative error _before_ the
- * final rounding to prec:
- * abs(result - base**exp) < 0.1 * 10**-prec * abs(base**exp)
- */
-static void
-_mpd_qpow_int(mpd_t *result, const mpd_t *base, const mpd_t *exp,
- uint8_t resultsign,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t workctx;
- MPD_NEW_STATIC(tbase,0,0,0,0);
- MPD_NEW_STATIC(texp,0,0,0,0);
- mpd_uint_t n;
-
-
- mpd_workcontext(&workctx, ctx);
- workctx.prec += (exp->digits + exp->exp + 2);
- workctx.round = MPD_ROUND_HALF_EVEN;
- workctx.clamp = 0;
- if (mpd_isnegative(exp)) {
- uint32_t workstatus = 0;
- workctx.prec += 1;
- mpd_qdiv(&tbase, &one, base, &workctx, &workstatus);
- *status |= workstatus;
- if (workstatus&MPD_Errors) {
- mpd_setspecial(result, MPD_POS, MPD_NAN);
- goto finish;
- }
- }
- else {
- if (!mpd_qcopy(&tbase, base, status)) {
- mpd_setspecial(result, MPD_POS, MPD_NAN);
- goto finish;
- }
- }
-
- n = mpd_qabs_uint(exp, &workctx.status);
- if (workctx.status&MPD_Invalid_operation) {
- if (!mpd_qcopy(&texp, exp, status)) {
- mpd_setspecial(result, MPD_POS, MPD_NAN); /* GCOV_UNLIKELY */
- goto finish; /* GCOV_UNLIKELY */
- }
- _mpd_qpow_mpd(result, &tbase, &texp, resultsign, &workctx, status);
- }
- else {
- _mpd_qpow_uint(result, &tbase, n, resultsign, &workctx, status);
- }
-
- if (mpd_isinfinite(result)) {
- /* for ROUND_DOWN, ROUND_FLOOR, etc. */
- _settriple(result, resultsign, 1, MPD_EXP_INF);
- }
-
-finish:
- mpd_del(&tbase);
- mpd_del(&texp);
- mpd_qfinalize(result, ctx, status);
-}
-
-/*
- * If the exponent is infinite and base equals one, the result is one
- * with a coefficient of length prec. Otherwise, result is undefined.
- * Return the value of the comparison against one.
- */
-static int
-_qcheck_pow_one_inf(mpd_t *result, const mpd_t *base, uint8_t resultsign,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_ssize_t shift;
- int cmp;
-
- if ((cmp = _mpd_cmp(base, &one)) == 0) {
- shift = ctx->prec-1;
- mpd_qshiftl(result, &one, shift, status);
- result->exp = -shift;
- mpd_set_flags(result, resultsign);
- *status |= (MPD_Inexact|MPD_Rounded);
- }
-
- return cmp;
-}
-
-/*
- * If abs(base) equals one, calculate the correct power of one result.
- * Otherwise, result is undefined. Return the value of the comparison
- * against 1.
- *
- * This is an internal function that does not check for specials.
- */
-static int
-_qcheck_pow_one(mpd_t *result, const mpd_t *base, const mpd_t *exp,
- uint8_t resultsign,
- const mpd_context_t *ctx, uint32_t *status)
-{
- uint32_t workstatus = 0;
- mpd_ssize_t shift;
- int cmp;
-
- if ((cmp = _mpd_cmp_abs(base, &one)) == 0) {
- if (_mpd_isint(exp)) {
- if (mpd_isnegative(exp)) {
- _settriple(result, resultsign, 1, 0);
- return 0;
- }
- /* 1.000**3 = 1.000000000 */
- mpd_qmul_ssize(result, exp, -base->exp, ctx, &workstatus);
- if (workstatus&MPD_Errors) {
- *status |= (workstatus&MPD_Errors);
- return 0;
- }
- /* digits-1 after exponentiation */
- shift = mpd_qget_ssize(result, &workstatus);
- /* shift is MPD_SSIZE_MAX if result is too large */
- if (shift > ctx->prec-1) {
- shift = ctx->prec-1;
- *status |= MPD_Rounded;
- }
- }
- else if (mpd_ispositive(base)) {
- shift = ctx->prec-1;
- *status |= (MPD_Inexact|MPD_Rounded);
- }
- else {
- return -2; /* GCOV_NOT_REACHED */
- }
- if (!mpd_qshiftl(result, &one, shift, status)) {
- return 0;
- }
- result->exp = -shift;
- mpd_set_flags(result, resultsign);
- }
-
- return cmp;
-}
-
-/*
- * Detect certain over/underflow of x**y.
- * ACL2 proof: pow-bounds.lisp.
- *
- * Symbols:
- *
- * e: EXP_INF or EXP_CLAMP
- * x: base
- * y: exponent
- *
- * omega(e) = log10(abs(e))
- * zeta(x) = log10(abs(log10(x)))
- * theta(y) = log10(abs(y))
- *
- * Upper and lower bounds:
- *
- * ub_omega(e) = ceil(log10(abs(e)))
- * lb_theta(y) = floor(log10(abs(y)))
- *
- * | floor(log10(floor(abs(log10(x))))) if x < 1/10 or x >= 10
- * lb_zeta(x) = | floor(log10(abs(x-1)/10)) if 1/10 <= x < 1
- * | floor(log10(abs((x-1)/100))) if 1 < x < 10
- *
- * ub_omega(e) and lb_theta(y) are obviously upper and lower bounds
- * for omega(e) and theta(y).
- *
- * lb_zeta is a lower bound for zeta(x):
- *
- * x < 1/10 or x >= 10:
- *
- * abs(log10(x)) >= 1, so the outer log10 is well defined. Since log10
- * is strictly increasing, the end result is a lower bound.
- *
- * 1/10 <= x < 1:
- *
- * We use: log10(x) <= (x-1)/log(10)
- * abs(log10(x)) >= abs(x-1)/log(10)
- * abs(log10(x)) >= abs(x-1)/10
- *
- * 1 < x < 10:
- *
- * We use: (x-1)/(x*log(10)) < log10(x)
- * abs((x-1)/100) < abs(log10(x))
- *
- * XXX: abs((x-1)/10) would work, need ACL2 proof.
- *
- *
- * Let (0 < x < 1 and y < 0) or (x > 1 and y > 0). (H1)
- * Let ub_omega(exp_inf) < lb_zeta(x) + lb_theta(y) (H2)
- *
- * Then:
- * log10(abs(exp_inf)) < log10(abs(log10(x))) + log10(abs(y)). (1)
- * exp_inf < log10(x) * y (2)
- * 10**exp_inf < x**y (3)
- *
- * Let (0 < x < 1 and y > 0) or (x > 1 and y < 0). (H3)
- * Let ub_omega(exp_clamp) < lb_zeta(x) + lb_theta(y) (H4)
- *
- * Then:
- * log10(abs(exp_clamp)) < log10(abs(log10(x))) + log10(abs(y)). (4)
- * log10(x) * y < exp_clamp (5)
- * x**y < 10**exp_clamp (6)
- *
- */
-static mpd_ssize_t
-_lower_bound_zeta(const mpd_t *x, uint32_t *status)
-{
- mpd_context_t maxctx;
- MPD_NEW_STATIC(scratch,0,0,0,0);
- mpd_ssize_t t, u;
-
- t = mpd_adjexp(x);
- if (t > 0) {
- /* x >= 10 -> floor(log10(floor(abs(log10(x))))) */
- return mpd_exp_digits(t) - 1;
- }
- else if (t < -1) {
- /* x < 1/10 -> floor(log10(floor(abs(log10(x))))) */
- return mpd_exp_digits(t+1) - 1;
- }
- else {
- mpd_maxcontext(&maxctx);
- mpd_qsub(&scratch, x, &one, &maxctx, status);
- if (mpd_isspecial(&scratch)) {
- mpd_del(&scratch);
- return MPD_SSIZE_MAX;
- }
- u = mpd_adjexp(&scratch);
- mpd_del(&scratch);
-
- /* t == -1, 1/10 <= x < 1 -> floor(log10(abs(x-1)/10))
- * t == 0, 1 < x < 10 -> floor(log10(abs(x-1)/100)) */
- return (t == 0) ? u-2 : u-1;
- }
-}
-
-/*
- * Detect cases of certain overflow/underflow in the power function.
- * Assumptions: x != 1, y != 0. The proof above is for positive x.
- * If x is negative and y is an odd integer, x**y == -(abs(x)**y),
- * so the analysis does not change.
- */
-static int
-_qcheck_pow_bounds(mpd_t *result, const mpd_t *x, const mpd_t *y,
- uint8_t resultsign,
- const mpd_context_t *ctx, uint32_t *status)
-{
- MPD_NEW_SHARED(abs_x, x);
- mpd_ssize_t ub_omega, lb_zeta, lb_theta;
- uint8_t sign;
-
- mpd_set_positive(&abs_x);
-
- lb_theta = mpd_adjexp(y);
- lb_zeta = _lower_bound_zeta(&abs_x, status);
- if (lb_zeta == MPD_SSIZE_MAX) {
- mpd_seterror(result, MPD_Malloc_error, status);
- return 1;
- }
-
- sign = (mpd_adjexp(&abs_x) < 0) ^ mpd_sign(y);
- if (sign == 0) {
- /* (0 < |x| < 1 and y < 0) or (|x| > 1 and y > 0) */
- ub_omega = mpd_exp_digits(ctx->emax);
- if (ub_omega < lb_zeta + lb_theta) {
- _settriple(result, resultsign, 1, MPD_EXP_INF);
- mpd_qfinalize(result, ctx, status);
- return 1;
- }
- }
- else {
- /* (0 < |x| < 1 and y > 0) or (|x| > 1 and y < 0). */
- ub_omega = mpd_exp_digits(mpd_etiny(ctx));
- if (ub_omega < lb_zeta + lb_theta) {
- _settriple(result, resultsign, 1, mpd_etiny(ctx)-1);
- mpd_qfinalize(result, ctx, status);
- return 1;
- }
- }
-
- return 0;
-}
-
-/*
- * TODO: Implement algorithm for computing exact powers from decimal.py.
- * In order to prevent infinite loops, this has to be called before
- * using Ziv's strategy for correct rounding.
- */
-/*
-static int
-_mpd_qpow_exact(mpd_t *result, const mpd_t *base, const mpd_t *exp,
- const mpd_context_t *ctx, uint32_t *status)
-{
- return 0;
-}
-*/
-
-/*
- * The power function for real exponents.
- * Relative error: abs(result - e**y) < e**y * 1/5 * 10**(-prec - 1)
- */
-static void
-_mpd_qpow_real(mpd_t *result, const mpd_t *base, const mpd_t *exp,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t workctx;
- MPD_NEW_STATIC(texp,0,0,0,0);
-
- if (!mpd_qcopy(&texp, exp, status)) {
- mpd_seterror(result, MPD_Malloc_error, status);
- return;
- }
-
- mpd_maxcontext(&workctx);
- workctx.prec = (base->digits > ctx->prec) ? base->digits : ctx->prec;
- workctx.prec += (4 + MPD_EXPDIGITS);
- workctx.round = MPD_ROUND_HALF_EVEN;
- workctx.allcr = ctx->allcr;
-
- /*
- * extra := MPD_EXPDIGITS = MPD_EXP_MAX_T
- * wp := prec + 4 + extra
- * abs(err) < 5 * 10**-wp
- * y := log(base) * exp
- * Calculate:
- * 1) e**(y * (1 + err)**2) * (1 + err)
- * = e**y * e**(y * (2*err + err**2)) * (1 + err)
- * ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
- * Relative error of the underlined term:
- * 2) abs(e**(y * (2*err + err**2)) - 1)
- * Case abs(y) >= 10**extra:
- * 3) adjexp(y)+1 > log10(abs(y)) >= extra
- * This triggers the Overflow/Underflow shortcut in _mpd_qexp(),
- * so no further analysis is necessary.
- * Case abs(y) < 10**extra:
- * 4) abs(y * (2*err + err**2)) < 1/5 * 10**(-prec - 2)
- * Use (see _mpd_qexp):
- * 5) abs(x) <= 9/10 * 10**-p ==> abs(e**x - 1) < 10**-p
- * With 2), 4) and 5):
- * 6) abs(e**(y * (2*err + err**2)) - 1) < 10**(-prec - 2)
- * The complete relative error of 1) is:
- * 7) abs(result - e**y) < e**y * 1/5 * 10**(-prec - 1)
- */
- mpd_qln(result, base, &workctx, &workctx.status);
- mpd_qmul(result, result, &texp, &workctx, &workctx.status);
- mpd_qexp(result, result, &workctx, status);
-
- mpd_del(&texp);
- *status |= (workctx.status&MPD_Errors);
- *status |= (MPD_Inexact|MPD_Rounded);
-}
-
-/* The power function: base**exp */
-void
-mpd_qpow(mpd_t *result, const mpd_t *base, const mpd_t *exp,
- const mpd_context_t *ctx, uint32_t *status)
-{
- uint8_t resultsign = 0;
- int intexp = 0;
- int cmp;
-
- if (mpd_isspecial(base) || mpd_isspecial(exp)) {
- if (mpd_qcheck_nans(result, base, exp, ctx, status)) {
- return;
- }
- }
- if (mpd_isinteger(exp)) {
- intexp = 1;
- resultsign = mpd_isnegative(base) && mpd_isodd(exp);
- }
-
- if (mpd_iszero(base)) {
- if (mpd_iszero(exp)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- }
- else if (mpd_isnegative(exp)) {
- mpd_setspecial(result, resultsign, MPD_INF);
- }
- else {
- _settriple(result, resultsign, 0, 0);
- }
- return;
- }
- if (mpd_isnegative(base)) {
- if (!intexp || mpd_isinfinite(exp)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- }
- if (mpd_isinfinite(exp)) {
- /* power of one */
- cmp = _qcheck_pow_one_inf(result, base, resultsign, ctx, status);
- if (cmp == 0) {
- return;
- }
- else {
- cmp *= mpd_arith_sign(exp);
- if (cmp < 0) {
- _settriple(result, resultsign, 0, 0);
- }
- else {
- mpd_setspecial(result, resultsign, MPD_INF);
- }
- }
- return;
- }
- if (mpd_isinfinite(base)) {
- if (mpd_iszero(exp)) {
- _settriple(result, resultsign, 1, 0);
- }
- else if (mpd_isnegative(exp)) {
- _settriple(result, resultsign, 0, 0);
- }
- else {
- mpd_setspecial(result, resultsign, MPD_INF);
- }
- return;
- }
- if (mpd_iszero(exp)) {
- _settriple(result, resultsign, 1, 0);
- return;
- }
- if (_qcheck_pow_one(result, base, exp, resultsign, ctx, status) == 0) {
- return;
- }
- if (_qcheck_pow_bounds(result, base, exp, resultsign, ctx, status)) {
- return;
- }
-
- if (intexp) {
- _mpd_qpow_int(result, base, exp, resultsign, ctx, status);
- }
- else {
- _mpd_qpow_real(result, base, exp, ctx, status);
- if (!mpd_isspecial(result) && _mpd_cmp(result, &one) == 0) {
- mpd_ssize_t shift = ctx->prec-1;
- mpd_qshiftl(result, &one, shift, status);
- result->exp = -shift;
- }
- if (mpd_isinfinite(result)) {
- /* for ROUND_DOWN, ROUND_FLOOR, etc. */
- _settriple(result, MPD_POS, 1, MPD_EXP_INF);
- }
- mpd_qfinalize(result, ctx, status);
- }
-}
-
-/*
- * Internal function: Integer powmod with mpd_uint_t exponent, base is modified!
- * Function can fail with MPD_Malloc_error.
- */
-static inline void
-_mpd_qpowmod_uint(mpd_t *result, mpd_t *base, mpd_uint_t exp,
- const mpd_t *mod, uint32_t *status)
-{
- mpd_context_t maxcontext;
-
- mpd_maxcontext(&maxcontext);
-
- /* resize to smaller cannot fail */
- mpd_qcopy(result, &one, status);
-
- while (exp > 0) {
- if (exp & 1) {
- _mpd_qmul_exact(result, result, base, &maxcontext, status);
- mpd_qrem(result, result, mod, &maxcontext, status);
- }
- _mpd_qmul_exact(base, base, base, &maxcontext, status);
- mpd_qrem(base, base, mod, &maxcontext, status);
- exp >>= 1;
- }
-}
-
-/* The powmod function: (base**exp) % mod */
-void
-mpd_qpowmod(mpd_t *result, const mpd_t *base, const mpd_t *exp,
- const mpd_t *mod,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(tbase,0,0,0,0);
- MPD_NEW_STATIC(texp,0,0,0,0);
- MPD_NEW_STATIC(tmod,0,0,0,0);
- MPD_NEW_STATIC(tmp,0,0,0,0);
- MPD_NEW_CONST(two,0,0,1,1,1,2);
- mpd_ssize_t tbase_exp, texp_exp;
- mpd_ssize_t i;
- mpd_t t;
- mpd_uint_t r;
- uint8_t sign;
-
-
- if (mpd_isspecial(base) || mpd_isspecial(exp) || mpd_isspecial(mod)) {
- if (mpd_qcheck_3nans(result, base, exp, mod, ctx, status)) {
- return;
- }
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
-
- if (!_mpd_isint(base) || !_mpd_isint(exp) || !_mpd_isint(mod)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- if (mpd_iszerocoeff(mod)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- if (mod->digits+mod->exp > ctx->prec) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- sign = (mpd_isnegative(base)) && (mpd_isodd(exp));
- if (mpd_iszerocoeff(exp)) {
- if (mpd_iszerocoeff(base)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- r = (_mpd_cmp_abs(mod, &one)==0) ? 0 : 1;
- _settriple(result, sign, r, 0);
- return;
- }
- if (mpd_isnegative(exp)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- if (mpd_iszerocoeff(base)) {
- _settriple(result, sign, 0, 0);
- return;
- }
-
- mpd_maxcontext(&maxcontext);
-
- mpd_qrescale(&tmod, mod, 0, &maxcontext, &maxcontext.status);
- if (maxcontext.status&MPD_Errors) {
- mpd_seterror(result, maxcontext.status&MPD_Errors, status);
- goto out;
- }
- maxcontext.status = 0;
- mpd_set_positive(&tmod);
-
- mpd_qround_to_int(&tbase, base, &maxcontext, status);
- mpd_set_positive(&tbase);
- tbase_exp = tbase.exp;
- tbase.exp = 0;
-
- mpd_qround_to_int(&texp, exp, &maxcontext, status);
- texp_exp = texp.exp;
- texp.exp = 0;
-
- /* base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo */
- mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status);
- mpd_qshiftl(result, &one, tbase_exp, status);
- mpd_qrem(result, result, &tmod, &maxcontext, status);
- _mpd_qmul_exact(&tbase, &tbase, result, &maxcontext, status);
- mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status);
- if (mpd_isspecial(&tbase) ||
- mpd_isspecial(&texp) ||
- mpd_isspecial(&tmod)) {
- goto mpd_errors;
- }
-
- for (i = 0; i < texp_exp; i++) {
- _mpd_qpowmod_uint(&tmp, &tbase, 10, &tmod, status);
- t = tmp;
- tmp = tbase;
- tbase = t;
- }
- if (mpd_isspecial(&tbase)) {
- goto mpd_errors; /* GCOV_UNLIKELY */
- }
-
- /* resize to smaller cannot fail */
- mpd_qcopy(result, &one, status);
- while (mpd_isfinite(&texp) && !mpd_iszero(&texp)) {
- if (mpd_isodd(&texp)) {
- _mpd_qmul_exact(result, result, &tbase, &maxcontext, status);
- mpd_qrem(result, result, &tmod, &maxcontext, status);
- }
- _mpd_qmul_exact(&tbase, &tbase, &tbase, &maxcontext, status);
- mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status);
- mpd_qdivint(&texp, &texp, &two, &maxcontext, status);
- }
- if (mpd_isspecial(&texp) || mpd_isspecial(&tbase) ||
- mpd_isspecial(&tmod) || mpd_isspecial(result)) {
- /* MPD_Malloc_error */
- goto mpd_errors;
- }
- else {
- mpd_set_sign(result, sign);
- }
-
-out:
- mpd_del(&tbase);
- mpd_del(&texp);
- mpd_del(&tmod);
- mpd_del(&tmp);
- return;
-
-mpd_errors:
- mpd_setspecial(result, MPD_POS, MPD_NAN);
- goto out;
-}
-
-void
-mpd_qquantize(mpd_t *result, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- uint32_t workstatus = 0;
- mpd_ssize_t b_exp = b->exp;
- mpd_ssize_t expdiff, shift;
- mpd_uint_t rnd;
-
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_qcheck_nans(result, a, b, ctx, status)) {
- return;
- }
- if (mpd_isinfinite(a) && mpd_isinfinite(b)) {
- mpd_qcopy(result, a, status);
- return;
- }
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- if (b->exp > ctx->emax || b->exp < mpd_etiny(ctx)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- if (mpd_iszero(a)) {
- _settriple(result, mpd_sign(a), 0, b->exp);
- mpd_qfinalize(result, ctx, status);
- return;
- }
-
-
- expdiff = a->exp - b->exp;
- if (a->digits + expdiff > ctx->prec) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- if (expdiff >= 0) {
- shift = expdiff;
- if (!mpd_qshiftl(result, a, shift, status)) {
- return;
- }
- result->exp = b_exp;
- }
- else {
- /* At this point expdiff < 0 and a->digits+expdiff <= prec,
- * so the shift before an increment will fit in prec. */
- shift = -expdiff;
- rnd = mpd_qshiftr(result, a, shift, status);
- if (rnd == MPD_UINT_MAX) {
- return;
- }
- result->exp = b_exp;
- if (!_mpd_apply_round_fit(result, rnd, ctx, status)) {
- return;
- }
- workstatus |= MPD_Rounded;
- if (rnd) {
- workstatus |= MPD_Inexact;
- }
- }
-
- if (mpd_adjexp(result) > ctx->emax ||
- mpd_adjexp(result) < mpd_etiny(ctx)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- *status |= workstatus;
- mpd_qfinalize(result, ctx, status);
-}
-
-void
-mpd_qreduce(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_ssize_t shift, maxexp, maxshift;
- uint8_t sign_a = mpd_sign(a);
-
- if (mpd_isspecial(a)) {
- if (mpd_qcheck_nan(result, a, ctx, status)) {
- return;
- }
- mpd_qcopy(result, a, status);
- return;
- }
-
- if (!mpd_qcopy(result, a, status)) {
- return;
- }
- mpd_qfinalize(result, ctx, status);
- if (mpd_isspecial(result)) {
- return;
- }
- if (mpd_iszero(result)) {
- _settriple(result, sign_a, 0, 0);
- return;
- }
-
- shift = mpd_trail_zeros(result);
- maxexp = (ctx->clamp) ? mpd_etop(ctx) : ctx->emax;
- /* After the finalizing above result->exp <= maxexp. */
- maxshift = maxexp - result->exp;
- shift = (shift > maxshift) ? maxshift : shift;
-
- mpd_qshiftr_inplace(result, shift);
- result->exp += shift;
-}
-
-void
-mpd_qrem(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx,
- uint32_t *status)
-{
- MPD_NEW_STATIC(q,0,0,0,0);
-
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_qcheck_nans(r, a, b, ctx, status)) {
- return;
- }
- if (mpd_isinfinite(a)) {
- mpd_seterror(r, MPD_Invalid_operation, status);
- return;
- }
- if (mpd_isinfinite(b)) {
- mpd_qcopy(r, a, status);
- mpd_qfinalize(r, ctx, status);
- return;
- }
- /* debug */
- abort(); /* GCOV_NOT_REACHED */
- }
- if (mpd_iszerocoeff(b)) {
- if (mpd_iszerocoeff(a)) {
- mpd_seterror(r, MPD_Division_undefined, status);
- }
- else {
- mpd_seterror(r, MPD_Invalid_operation, status);
- }
- return;
- }
-
- _mpd_qdivmod(&q, r, a, b, ctx, status);
- mpd_del(&q);
- mpd_qfinalize(r, ctx, status);
-}
-
-void
-mpd_qrem_near(mpd_t *r, const mpd_t *a, const mpd_t *b,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_context_t workctx;
- MPD_NEW_STATIC(btmp,0,0,0,0);
- MPD_NEW_STATIC(q,0,0,0,0);
- mpd_ssize_t expdiff, qdigits;
- int cmp, isodd, allnine;
-
- assert(r != NULL); /* annotation for scan-build */
-
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- if (mpd_qcheck_nans(r, a, b, ctx, status)) {
- return;
- }
- if (mpd_isinfinite(a)) {
- mpd_seterror(r, MPD_Invalid_operation, status);
- return;
- }
- if (mpd_isinfinite(b)) {
- mpd_qcopy(r, a, status);
- mpd_qfinalize(r, ctx, status);
- return;
- }
- /* debug */
- abort(); /* GCOV_NOT_REACHED */
- }
- if (mpd_iszerocoeff(b)) {
- if (mpd_iszerocoeff(a)) {
- mpd_seterror(r, MPD_Division_undefined, status);
- }
- else {
- mpd_seterror(r, MPD_Invalid_operation, status);
- }
- return;
- }
-
- if (r == b) {
- if (!mpd_qcopy(&btmp, b, status)) {
- mpd_seterror(r, MPD_Malloc_error, status);
- return;
- }
- b = &btmp;
- }
-
- _mpd_qdivmod(&q, r, a, b, ctx, status);
- if (mpd_isnan(&q) || mpd_isnan(r)) {
- goto finish;
- }
- if (mpd_iszerocoeff(r)) {
- goto finish;
- }
-
- expdiff = mpd_adjexp(b) - mpd_adjexp(r);
- if (-1 <= expdiff && expdiff <= 1) {
-
- allnine = mpd_coeff_isallnine(&q);
- qdigits = q.digits;
- isodd = mpd_isodd(&q);
-
- mpd_maxcontext(&workctx);
- if (mpd_sign(a) == mpd_sign(b)) {
- /* sign(r) == sign(b) */
- _mpd_qsub(&q, r, b, &workctx, &workctx.status);
- }
- else {
- /* sign(r) != sign(b) */
- _mpd_qadd(&q, r, b, &workctx, &workctx.status);
- }
-
- if (workctx.status&MPD_Errors) {
- mpd_seterror(r, workctx.status&MPD_Errors, status);
- goto finish;
- }
-
- cmp = _mpd_cmp_abs(&q, r);
- if (cmp < 0 || (cmp == 0 && isodd)) {
- /* abs(r) > abs(b)/2 or abs(r) == abs(b)/2 and isodd(quotient) */
- if (allnine && qdigits == ctx->prec) {
- /* abs(quotient) + 1 == 10**prec */
- mpd_seterror(r, MPD_Division_impossible, status);
- goto finish;
- }
- mpd_qcopy(r, &q, status);
- }
- }
-
-
-finish:
- mpd_del(&btmp);
- mpd_del(&q);
- mpd_qfinalize(r, ctx, status);
-}
-
-static void
-_mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_ssize_t expdiff, shift;
- mpd_uint_t rnd;
-
- if (mpd_isspecial(a)) {
- mpd_qcopy(result, a, status);
- return;
- }
-
- if (mpd_iszero(a)) {
- _settriple(result, mpd_sign(a), 0, exp);
- return;
- }
-
- expdiff = a->exp - exp;
- if (expdiff >= 0) {
- shift = expdiff;
- if (a->digits + shift > MPD_MAX_PREC+1) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- if (!mpd_qshiftl(result, a, shift, status)) {
- return;
- }
- result->exp = exp;
- }
- else {
- shift = -expdiff;
- rnd = mpd_qshiftr(result, a, shift, status);
- if (rnd == MPD_UINT_MAX) {
- return;
- }
- result->exp = exp;
- _mpd_apply_round_excess(result, rnd, ctx, status);
- *status |= MPD_Rounded;
- if (rnd) {
- *status |= MPD_Inexact;
- }
- }
-
- if (mpd_issubnormal(result, ctx)) {
- *status |= MPD_Subnormal;
- }
-}
-
-/*
- * Rescale a number so that it has exponent 'exp'. Does not regard context
- * precision, emax, emin, but uses the rounding mode. Special numbers are
- * quietly copied. Restrictions:
- *
- * MPD_MIN_ETINY <= exp <= MPD_MAX_EMAX+1
- * result->digits <= MPD_MAX_PREC+1
- */
-void
-mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp,
- const mpd_context_t *ctx, uint32_t *status)
-{
- if (exp > MPD_MAX_EMAX+1 || exp < MPD_MIN_ETINY) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- _mpd_qrescale(result, a, exp, ctx, status);
-}
-
-/*
- * Same as mpd_qrescale, but with relaxed restrictions. The result of this
- * function should only be used for formatting a number and never as input
- * for other operations.
- *
- * MPD_MIN_ETINY-MPD_MAX_PREC <= exp <= MPD_MAX_EMAX+1
- * result->digits <= MPD_MAX_PREC+1
- */
-void
-mpd_qrescale_fmt(mpd_t *result, const mpd_t *a, mpd_ssize_t exp,
- const mpd_context_t *ctx, uint32_t *status)
-{
- if (exp > MPD_MAX_EMAX+1 || exp < MPD_MIN_ETINY-MPD_MAX_PREC) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- _mpd_qrescale(result, a, exp, ctx, status);
-}
-
-/* Round to an integer according to 'action' and ctx->round. */
-enum {TO_INT_EXACT, TO_INT_SILENT, TO_INT_TRUNC};
-static void
-_mpd_qround_to_integral(int action, mpd_t *result, const mpd_t *a,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_uint_t rnd;
-
- if (mpd_isspecial(a)) {
- if (mpd_qcheck_nan(result, a, ctx, status)) {
- return;
- }
- mpd_qcopy(result, a, status);
- return;
- }
- if (a->exp >= 0) {
- mpd_qcopy(result, a, status);
- return;
- }
- if (mpd_iszerocoeff(a)) {
- _settriple(result, mpd_sign(a), 0, 0);
- return;
- }
-
- rnd = mpd_qshiftr(result, a, -a->exp, status);
- if (rnd == MPD_UINT_MAX) {
- return;
- }
- result->exp = 0;
-
- if (action == TO_INT_EXACT || action == TO_INT_SILENT) {
- _mpd_apply_round_excess(result, rnd, ctx, status);
- if (action == TO_INT_EXACT) {
- *status |= MPD_Rounded;
- if (rnd) {
- *status |= MPD_Inexact;
- }
- }
- }
-}
-
-void
-mpd_qround_to_intx(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- (void)_mpd_qround_to_integral(TO_INT_EXACT, result, a, ctx, status);
-}
-
-void
-mpd_qround_to_int(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a, ctx, status);
-}
-
-void
-mpd_qtrunc(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- if (mpd_isspecial(a)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- (void)_mpd_qround_to_integral(TO_INT_TRUNC, result, a, ctx, status);
-}
-
-void
-mpd_qfloor(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_context_t workctx = *ctx;
-
- if (mpd_isspecial(a)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- workctx.round = MPD_ROUND_FLOOR;
- (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a,
- &workctx, status);
-}
-
-void
-mpd_qceil(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_context_t workctx = *ctx;
-
- if (mpd_isspecial(a)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- workctx.round = MPD_ROUND_CEILING;
- (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a,
- &workctx, status);
-}
-
-int
-mpd_same_quantum(const mpd_t *a, const mpd_t *b)
-{
- if (mpd_isspecial(a) || mpd_isspecial(b)) {
- return ((mpd_isnan(a) && mpd_isnan(b)) ||
- (mpd_isinfinite(a) && mpd_isinfinite(b)));
- }
-
- return a->exp == b->exp;
-}
-
-/* Schedule the increase in precision for the Newton iteration. */
-static inline int
-recpr_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2],
- mpd_ssize_t maxprec, mpd_ssize_t initprec)
-{
- mpd_ssize_t k;
- int i;
-
- assert(maxprec > 0 && initprec > 0);
- if (maxprec <= initprec) return -1;
-
- i = 0; k = maxprec;
- do {
- k = (k+1) / 2;
- klist[i++] = k;
- } while (k > initprec);
-
- return i-1;
-}
-
-/*
- * Initial approximation for the reciprocal:
- * k_0 := MPD_RDIGITS-2
- * z_0 := 10**(-k_0) * floor(10**(2*k_0 + 2) / floor(v * 10**(k_0 + 2)))
- * Absolute error:
- * |1/v - z_0| < 10**(-k_0)
- * ACL2 proof: maxerror-inverse-approx
- */
-static void
-_mpd_qreciprocal_approx(mpd_t *z, const mpd_t *v, uint32_t *status)
-{
- mpd_uint_t p10data[2] = {0, mpd_pow10[MPD_RDIGITS-2]};
- mpd_uint_t dummy, word;
- int n;
-
- assert(v->exp == -v->digits);
-
- _mpd_get_msdigits(&dummy, &word, v, MPD_RDIGITS);
- n = mpd_word_digits(word);
- word *= mpd_pow10[MPD_RDIGITS-n];
-
- mpd_qresize(z, 2, status);
- (void)_mpd_shortdiv(z->data, p10data, 2, word);
-
- mpd_clear_flags(z);
- z->exp = -(MPD_RDIGITS-2);
- z->len = (z->data[1] == 0) ? 1 : 2;
- mpd_setdigits(z);
-}
-
-/*
- * Reciprocal, calculated with Newton's Method. Assumption: result != a.
- * NOTE: The comments in the function show that certain operations are
- * exact. The proof for the maximum error is too long to fit in here.
- * ACL2 proof: maxerror-inverse-complete
- */
-static void
-_mpd_qreciprocal(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_context_t varcontext, maxcontext;
- mpd_t *z = result; /* current approximation */
- mpd_t *v; /* a, normalized to a number between 0.1 and 1 */
- MPD_NEW_SHARED(vtmp, a); /* v shares data with a */
- MPD_NEW_STATIC(s,0,0,0,0); /* temporary variable */
- MPD_NEW_STATIC(t,0,0,0,0); /* temporary variable */
- MPD_NEW_CONST(two,0,0,1,1,1,2); /* const 2 */
- mpd_ssize_t klist[MPD_MAX_PREC_LOG2];
- mpd_ssize_t adj, maxprec, initprec;
- uint8_t sign = mpd_sign(a);
- int i;
-
- assert(result != a);
-
- v = &vtmp;
- mpd_clear_flags(v);
- adj = v->digits + v->exp;
- v->exp = -v->digits;
-
- /* Initial approximation */
- _mpd_qreciprocal_approx(z, v, status);
-
- mpd_maxcontext(&varcontext);
- mpd_maxcontext(&maxcontext);
- varcontext.round = maxcontext.round = MPD_ROUND_TRUNC;
- varcontext.emax = maxcontext.emax = MPD_MAX_EMAX + 100;
- varcontext.emin = maxcontext.emin = MPD_MIN_EMIN - 100;
- maxcontext.prec = MPD_MAX_PREC + 100;
-
- maxprec = ctx->prec;
- maxprec += 2;
- initprec = MPD_RDIGITS-3;
-
- i = recpr_schedule_prec(klist, maxprec, initprec);
- for (; i >= 0; i--) {
- /* Loop invariant: z->digits <= klist[i]+7 */
- /* Let s := z**2, exact result */
- _mpd_qmul_exact(&s, z, z, &maxcontext, status);
- varcontext.prec = 2*klist[i] + 5;
- if (v->digits > varcontext.prec) {
- /* Let t := v, truncated to n >= 2*k+5 fraction digits */
- mpd_qshiftr(&t, v, v->digits-varcontext.prec, status);
- t.exp = -varcontext.prec;
- /* Let t := trunc(v)*s, truncated to n >= 2*k+1 fraction digits */
- mpd_qmul(&t, &t, &s, &varcontext, status);
- }
- else { /* v->digits <= 2*k+5 */
- /* Let t := v*s, truncated to n >= 2*k+1 fraction digits */
- mpd_qmul(&t, v, &s, &varcontext, status);
- }
- /* Let s := 2*z, exact result */
- _mpd_qmul_exact(&s, z, &two, &maxcontext, status);
- /* s.digits < t.digits <= 2*k+5, |adjexp(s)-adjexp(t)| <= 1,
- * so the subtraction generates at most 2*k+6 <= klist[i+1]+7
- * digits. The loop invariant is preserved. */
- _mpd_qsub_exact(z, &s, &t, &maxcontext, status);
- }
-
- if (!mpd_isspecial(z)) {
- z->exp -= adj;
- mpd_set_flags(z, sign);
- }
-
- mpd_del(&s);
- mpd_del(&t);
- mpd_qfinalize(z, ctx, status);
-}
-
-/*
- * Internal function for large numbers:
- *
- * q, r = divmod(coeff(a), coeff(b))
- *
- * Strategy: Multiply the dividend by the reciprocal of the divisor. The
- * inexact result is fixed by a small loop, using at most one iteration.
- *
- * ACL2 proofs:
- * ------------
- * 1) q is a natural number. (ndivmod-quotient-natp)
- * 2) r is a natural number. (ndivmod-remainder-natp)
- * 3) a = q * b + r (ndivmod-q*b+r==a)
- * 4) r < b (ndivmod-remainder-<-b)
- */
-static void
-_mpd_base_ndivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b,
- uint32_t *status)
-{
- mpd_context_t workctx;
- mpd_t *qq = q, *rr = r;
- mpd_t aa, bb;
- int k;
-
- _mpd_copy_shared(&aa, a);
- _mpd_copy_shared(&bb, b);
-
- mpd_set_positive(&aa);
- mpd_set_positive(&bb);
- aa.exp = 0;
- bb.exp = 0;
-
- if (q == a || q == b) {
- if ((qq = mpd_qnew()) == NULL) {
- *status |= MPD_Malloc_error;
- goto nanresult;
- }
- }
- if (r == a || r == b) {
- if ((rr = mpd_qnew()) == NULL) {
- *status |= MPD_Malloc_error;
- goto nanresult;
- }
- }
-
- mpd_maxcontext(&workctx);
-
- /* Let prec := adigits - bdigits + 4 */
- workctx.prec = a->digits - b->digits + 1 + 3;
- if (a->digits > MPD_MAX_PREC || workctx.prec > MPD_MAX_PREC) {
- *status |= MPD_Division_impossible;
- goto nanresult;
- }
-
- /* Let x := _mpd_qreciprocal(b, prec)
- * Then x is bounded by:
- * 1) 1/b - 10**(-prec - bdigits) < x < 1/b + 10**(-prec - bdigits)
- * 2) 1/b - 10**(-adigits - 4) < x < 1/b + 10**(-adigits - 4)
- */
- _mpd_qreciprocal(rr, &bb, &workctx, &workctx.status);
-
- /* Get an estimate for the quotient. Let q := a * x
- * Then q is bounded by:
- * 3) a/b - 10**-4 < q < a/b + 10**-4
- */
- _mpd_qmul(qq, &aa, rr, &workctx, &workctx.status);
- /* Truncate q to an integer:
- * 4) a/b - 2 < trunc(q) < a/b + 1
- */
- mpd_qtrunc(qq, qq, &workctx, &workctx.status);
-
- workctx.prec = aa.digits + 3;
- workctx.emax = MPD_MAX_EMAX + 3;
- workctx.emin = MPD_MIN_EMIN - 3;
- /* Multiply the estimate for q by b:
- * 5) a - 2 * b < trunc(q) * b < a + b
- */
- _mpd_qmul(rr, &bb, qq, &workctx, &workctx.status);
- /* Get the estimate for r such that a = q * b + r. */
- _mpd_qsub_exact(rr, &aa, rr, &workctx, &workctx.status);
-
- /* Fix the result. At this point -b < r < 2*b, so the correction loop
- takes at most one iteration. */
- for (k = 0;; k++) {
- if (mpd_isspecial(qq) || mpd_isspecial(rr)) {
- *status |= (workctx.status&MPD_Errors);
- goto nanresult;
- }
- if (k > 2) { /* Allow two iterations despite the proof. */
- mpd_err_warn("libmpdec: internal error in " /* GCOV_NOT_REACHED */
- "_mpd_base_ndivmod: please report"); /* GCOV_NOT_REACHED */
- *status |= MPD_Invalid_operation; /* GCOV_NOT_REACHED */
- goto nanresult; /* GCOV_NOT_REACHED */
- }
- /* r < 0 */
- else if (_mpd_cmp(&zero, rr) == 1) {
- _mpd_qadd_exact(rr, rr, &bb, &workctx, &workctx.status);
- _mpd_qadd_exact(qq, qq, &minus_one, &workctx, &workctx.status);
- }
- /* 0 <= r < b */
- else if (_mpd_cmp(rr, &bb) == -1) {
- break;
- }
- /* r >= b */
- else {
- _mpd_qsub_exact(rr, rr, &bb, &workctx, &workctx.status);
- _mpd_qadd_exact(qq, qq, &one, &workctx, &workctx.status);
- }
- }
-
- if (qq != q) {
- if (!mpd_qcopy(q, qq, status)) {
- goto nanresult; /* GCOV_UNLIKELY */
- }
- mpd_del(qq);
- }
- if (rr != r) {
- if (!mpd_qcopy(r, rr, status)) {
- goto nanresult; /* GCOV_UNLIKELY */
- }
- mpd_del(rr);
- }
-
- *status |= (workctx.status&MPD_Errors);
- return;
-
-
-nanresult:
- if (qq && qq != q) mpd_del(qq);
- if (rr && rr != r) mpd_del(rr);
- mpd_setspecial(q, MPD_POS, MPD_NAN);
- mpd_setspecial(r, MPD_POS, MPD_NAN);
-}
-
-/* LIBMPDEC_ONLY */
-/*
- * Schedule the optimal precision increase for the Newton iteration.
- * v := input operand
- * z_0 := initial approximation
- * initprec := natural number such that abs(sqrt(v) - z_0) < 10**-initprec
- * maxprec := target precision
- *
- * For convenience the output klist contains the elements in reverse order:
- * klist := [k_n-1, ..., k_0], where
- * 1) k_0 <= initprec and
- * 2) abs(sqrt(v) - result) < 10**(-2*k_n-1 + 2) <= 10**-maxprec.
- */
-static inline int
-invroot_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2],
- mpd_ssize_t maxprec, mpd_ssize_t initprec)
-{
- mpd_ssize_t k;
- int i;
-
- assert(maxprec >= 3 && initprec >= 3);
- if (maxprec <= initprec) return -1;
-
- i = 0; k = maxprec;
- do {
- k = (k+3) / 2;
- klist[i++] = k;
- } while (k > initprec);
-
- return i-1;
-}
-
-/*
- * Initial approximation for the inverse square root function.
- * Input:
- * v := rational number, with 1 <= v < 100
- * vhat := floor(v * 10**6)
- * Output:
- * z := approximation to 1/sqrt(v), such that abs(z - 1/sqrt(v)) < 10**-3.
- */
-static inline void
-_invroot_init_approx(mpd_t *z, mpd_uint_t vhat)
-{
- mpd_uint_t lo = 1000;
- mpd_uint_t hi = 10000;
- mpd_uint_t a, sq;
-
- assert(lo*lo <= vhat && vhat < (hi+1)*(hi+1));
-
- for(;;) {
- a = (lo + hi) / 2;
- sq = a * a;
- if (vhat >= sq) {
- if (vhat < sq + 2*a + 1) {
- break;
- }
- lo = a + 1;
- }
- else {
- hi = a - 1;
- }
- }
-
- /*
- * After the binary search we have:
- * 1) a**2 <= floor(v * 10**6) < (a + 1)**2
- * This implies:
- * 2) a**2 <= v * 10**6 < (a + 1)**2
- * 3) a <= sqrt(v) * 10**3 < a + 1
- * Since 10**3 <= a:
- * 4) 0 <= 10**prec/a - 1/sqrt(v) < 10**-prec
- * We have:
- * 5) 10**3/a - 10**-3 < floor(10**9/a) * 10**-6 <= 10**3/a
- * Merging 4) and 5):
- * 6) abs(floor(10**9/a) * 10**-6 - 1/sqrt(v)) < 10**-3
- */
- mpd_minalloc(z);
- mpd_clear_flags(z);
- z->data[0] = 1000000000UL / a;
- z->len = 1;
- z->exp = -6;
- mpd_setdigits(z);
-}
-
-/*
- * Set 'result' to 1/sqrt(a).
- * Relative error: abs(result - 1/sqrt(a)) < 10**-prec * 1/sqrt(a)
- */
-static void
-_mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- uint32_t workstatus = 0;
- mpd_context_t varcontext, maxcontext;
- mpd_t *z = result; /* current approximation */
- mpd_t *v; /* a, normalized to a number between 1 and 100 */
- MPD_NEW_SHARED(vtmp, a); /* by default v will share data with a */
- MPD_NEW_STATIC(s,0,0,0,0); /* temporary variable */
- MPD_NEW_STATIC(t,0,0,0,0); /* temporary variable */
- MPD_NEW_CONST(one_half,0,-1,1,1,1,5);
- MPD_NEW_CONST(three,0,0,1,1,1,3);
- mpd_ssize_t klist[MPD_MAX_PREC_LOG2];
- mpd_ssize_t ideal_exp, shift;
- mpd_ssize_t adj, tz;
- mpd_ssize_t maxprec, fracdigits;
- mpd_uint_t vhat, dummy;
- int i, n;
-
-
- ideal_exp = -(a->exp - (a->exp & 1)) / 2;
-
- v = &vtmp;
- if (result == a) {
- if ((v = mpd_qncopy(a)) == NULL) {
- mpd_seterror(result, MPD_Malloc_error, status);
- return;
- }
- }
-
- /* normalize a to 1 <= v < 100 */
- if ((v->digits+v->exp) & 1) {
- fracdigits = v->digits - 1;
- v->exp = -fracdigits;
- n = (v->digits > 7) ? 7 : (int)v->digits;
- /* Let vhat := floor(v * 10**(2*initprec)) */
- _mpd_get_msdigits(&dummy, &vhat, v, n);
- if (n < 7) {
- vhat *= mpd_pow10[7-n];
- }
- }
- else {
- fracdigits = v->digits - 2;
- v->exp = -fracdigits;
- n = (v->digits > 8) ? 8 : (int)v->digits;
- /* Let vhat := floor(v * 10**(2*initprec)) */
- _mpd_get_msdigits(&dummy, &vhat, v, n);
- if (n < 8) {
- vhat *= mpd_pow10[8-n];
- }
- }
- adj = (a->exp-v->exp) / 2;
-
- /* initial approximation */
- _invroot_init_approx(z, vhat);
-
- mpd_maxcontext(&maxcontext);
- mpd_maxcontext(&varcontext);
- varcontext.round = MPD_ROUND_TRUNC;
- maxprec = ctx->prec + 1;
-
- /* initprec == 3 */
- i = invroot_schedule_prec(klist, maxprec, 3);
- for (; i >= 0; i--) {
- varcontext.prec = 2*klist[i]+2;
- mpd_qmul(&s, z, z, &maxcontext, &workstatus);
- if (v->digits > varcontext.prec) {
- shift = v->digits - varcontext.prec;
- mpd_qshiftr(&t, v, shift, &workstatus);
- t.exp += shift;
- mpd_qmul(&t, &t, &s, &varcontext, &workstatus);
- }
- else {
- mpd_qmul(&t, v, &s, &varcontext, &workstatus);
- }
- mpd_qsub(&t, &three, &t, &maxcontext, &workstatus);
- mpd_qmul(z, z, &t, &varcontext, &workstatus);
- mpd_qmul(z, z, &one_half, &maxcontext, &workstatus);
- }
-
- z->exp -= adj;
-
- tz = mpd_trail_zeros(result);
- shift = ideal_exp - result->exp;
- shift = (tz > shift) ? shift : tz;
- if (shift > 0) {
- mpd_qshiftr_inplace(result, shift);
- result->exp += shift;
- }
-
-
- mpd_del(&s);
- mpd_del(&t);
- if (v != &vtmp) mpd_del(v);
- *status |= (workstatus&MPD_Errors);
- *status |= (MPD_Rounded|MPD_Inexact);
-}
-
-void
-mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_context_t workctx;
-
- if (mpd_isspecial(a)) {
- if (mpd_qcheck_nan(result, a, ctx, status)) {
- return;
- }
- if (mpd_isnegative(a)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- /* positive infinity */
- _settriple(result, MPD_POS, 0, mpd_etiny(ctx));
- *status |= MPD_Clamped;
- return;
- }
- if (mpd_iszero(a)) {
- mpd_setspecial(result, mpd_sign(a), MPD_INF);
- *status |= MPD_Division_by_zero;
- return;
- }
- if (mpd_isnegative(a)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- workctx = *ctx;
- workctx.prec += 2;
- workctx.round = MPD_ROUND_HALF_EVEN;
- _mpd_qinvroot(result, a, &workctx, status);
- mpd_qfinalize(result, ctx, status);
-}
-/* END LIBMPDEC_ONLY */
-
-/* Algorithm from decimal.py */
-static void
-_mpd_qsqrt(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- mpd_context_t maxcontext;
- MPD_NEW_STATIC(c,0,0,0,0);
- MPD_NEW_STATIC(q,0,0,0,0);
- MPD_NEW_STATIC(r,0,0,0,0);
- MPD_NEW_CONST(two,0,0,1,1,1,2);
- mpd_ssize_t prec, ideal_exp;
- mpd_ssize_t l, shift;
- int exact = 0;
-
-
- ideal_exp = (a->exp - (a->exp & 1)) / 2;
-
- if (mpd_isspecial(a)) {
- if (mpd_qcheck_nan(result, a, ctx, status)) {
- return;
- }
- if (mpd_isnegative(a)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
- mpd_setspecial(result, MPD_POS, MPD_INF);
- return;
- }
- if (mpd_iszero(a)) {
- _settriple(result, mpd_sign(a), 0, ideal_exp);
- mpd_qfinalize(result, ctx, status);
- return;
- }
- if (mpd_isnegative(a)) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- mpd_maxcontext(&maxcontext);
- prec = ctx->prec + 1;
-
- if (!mpd_qcopy(&c, a, status)) {
- goto malloc_error;
- }
- c.exp = 0;
-
- if (a->exp & 1) {
- if (!mpd_qshiftl(&c, &c, 1, status)) {
- goto malloc_error;
- }
- l = (a->digits >> 1) + 1;
- }
- else {
- l = (a->digits + 1) >> 1;
- }
-
- shift = prec - l;
- if (shift >= 0) {
- if (!mpd_qshiftl(&c, &c, 2*shift, status)) {
- goto malloc_error;
- }
- exact = 1;
- }
- else {
- exact = !mpd_qshiftr_inplace(&c, -2*shift);
- }
-
- ideal_exp -= shift;
-
- /* find result = floor(sqrt(c)) using Newton's method */
- if (!mpd_qshiftl(result, &one, prec, status)) {
- goto malloc_error;
- }
-
- while (1) {
- _mpd_qdivmod(&q, &r, &c, result, &maxcontext, &maxcontext.status);
- if (mpd_isspecial(result) || mpd_isspecial(&q)) {
- mpd_seterror(result, maxcontext.status&MPD_Errors, status);
- goto out;
- }
- if (_mpd_cmp(result, &q) <= 0) {
- break;
- }
- _mpd_qadd_exact(result, result, &q, &maxcontext, &maxcontext.status);
- if (mpd_isspecial(result)) {
- mpd_seterror(result, maxcontext.status&MPD_Errors, status);
- goto out;
- }
- _mpd_qdivmod(result, &r, result, &two, &maxcontext, &maxcontext.status);
- }
-
- if (exact) {
- _mpd_qmul_exact(&r, result, result, &maxcontext, &maxcontext.status);
- if (mpd_isspecial(&r)) {
- mpd_seterror(result, maxcontext.status&MPD_Errors, status);
- goto out;
- }
- exact = (_mpd_cmp(&r, &c) == 0);
- }
-
- if (exact) {
- if (shift >= 0) {
- mpd_qshiftr_inplace(result, shift);
- }
- else {
- if (!mpd_qshiftl(result, result, -shift, status)) {
- goto malloc_error;
- }
- }
- ideal_exp += shift;
- }
- else {
- int lsd = (int)mpd_lsd(result->data[0]);
- if (lsd == 0 || lsd == 5) {
- result->data[0] += 1;
- }
- }
-
- result->exp = ideal_exp;
-
-
-out:
- mpd_del(&c);
- mpd_del(&q);
- mpd_del(&r);
- maxcontext = *ctx;
- maxcontext.round = MPD_ROUND_HALF_EVEN;
- mpd_qfinalize(result, &maxcontext, status);
- return;
-
-malloc_error:
- mpd_seterror(result, MPD_Malloc_error, status);
- goto out;
-}
-
-void
-mpd_qsqrt(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
- uint32_t *status)
-{
- MPD_NEW_STATIC(aa,0,0,0,0);
- uint32_t xstatus = 0;
-
- if (result == a) {
- if (!mpd_qcopy(&aa, a, status)) {
- mpd_seterror(result, MPD_Malloc_error, status);
- goto out;
- }
- a = &aa;
- }
-
- _mpd_qsqrt(result, a, ctx, &xstatus);
-
- if (xstatus & (MPD_Malloc_error|MPD_Division_impossible)) {
- /* The above conditions can occur at very high context precisions
- * if intermediate values get too large. Retry the operation with
- * a lower context precision in case the result is exact.
- *
- * If the result is exact, an upper bound for the number of digits
- * is the number of digits in the input.
- *
- * NOTE: sqrt(40e9) = 2.0e+5 /\ digits(40e9) = digits(2.0e+5) = 2
- */
- uint32_t ystatus = 0;
- mpd_context_t workctx = *ctx;
-
- workctx.prec = a->digits;
- if (workctx.prec >= ctx->prec) {
- *status |= (xstatus|MPD_Errors);
- goto out; /* No point in repeating this, keep the original error. */
- }
-
- _mpd_qsqrt(result, a, &workctx, &ystatus);
- if (ystatus != 0) {
- ystatus = *status | ((xstatus|ystatus)&MPD_Errors);
- mpd_seterror(result, ystatus, status);
- }
- }
- else {
- *status |= xstatus;
- }
-
-out:
- mpd_del(&aa);
-}
-
-
-/******************************************************************************/
-/* Base conversions */
-/******************************************************************************/
-
-/* Space needed to represent an integer mpd_t in base 'base'. */
-size_t
-mpd_sizeinbase(const mpd_t *a, uint32_t base)
-{
- double x;
- size_t digits;
- double upper_bound;
-
- assert(mpd_isinteger(a));
- assert(base >= 2);
-
- if (mpd_iszero(a)) {
- return 1;
- }
-
- digits = a->digits+a->exp;
-
-#ifdef CONFIG_64
- /* ceil(2711437152599294 / log10(2)) + 4 == 2**53 */
- if (digits > 2711437152599294ULL) {
- return SIZE_MAX;
- }
-
- upper_bound = (double)((1ULL<<53)-1);
-#else
- upper_bound = (double)(SIZE_MAX-1);
-#endif
-
- x = (double)digits / log10(base);
- return (x > upper_bound) ? SIZE_MAX : (size_t)x + 1;
-}
-
-/* Space needed to import a base 'base' integer of length 'srclen'. */
-static mpd_ssize_t
-_mpd_importsize(size_t srclen, uint32_t base)
-{
- double x;
- double upper_bound;
-
- assert(srclen > 0);
- assert(base >= 2);
-
-#if SIZE_MAX == UINT64_MAX
- if (srclen > (1ULL<<53)) {
- return MPD_SSIZE_MAX;
- }
-
- assert((1ULL<<53) <= MPD_MAXIMPORT);
- upper_bound = (double)((1ULL<<53)-1);
-#else
- upper_bound = MPD_MAXIMPORT-1;
-#endif
-
- x = (double)srclen * (log10(base)/MPD_RDIGITS);
- return (x > upper_bound) ? MPD_SSIZE_MAX : (mpd_ssize_t)x + 1;
-}
-
-static uint8_t
-mpd_resize_u16(uint16_t **w, size_t nmemb)
-{
- uint8_t err = 0;
- *w = mpd_realloc(*w, nmemb, sizeof **w, &err);
- return !err;
-}
-
-static uint8_t
-mpd_resize_u32(uint32_t **w, size_t nmemb)
-{
- uint8_t err = 0;
- *w = mpd_realloc(*w, nmemb, sizeof **w, &err);
- return !err;
-}
-
-static size_t
-_baseconv_to_u16(uint16_t **w, size_t wlen, mpd_uint_t wbase,
- mpd_uint_t *u, mpd_ssize_t ulen)
-{
- size_t n = 0;
-
- assert(wlen > 0 && ulen > 0);
- assert(wbase <= (1U<<16));
-
- do {
- if (n >= wlen) {
- if (!mpd_resize_u16(w, n+1)) {
- return SIZE_MAX;
- }
- wlen = n+1;
- }
- (*w)[n++] = (uint16_t)_mpd_shortdiv(u, u, ulen, wbase);
- /* ulen is at least 1. u[ulen-1] can only be zero if ulen == 1. */
- ulen = _mpd_real_size(u, ulen);
-
- } while (u[ulen-1] != 0);
-
- return n;
-}
-
-static size_t
-_coeff_from_u16(mpd_t *w, mpd_ssize_t wlen,
- const mpd_uint_t *u, size_t ulen, uint32_t ubase,
- uint32_t *status)
-{
- mpd_ssize_t n = 0;
- mpd_uint_t carry;
-
- assert(wlen > 0 && ulen > 0);
- assert(ubase <= (1U<<16));
-
- w->data[n++] = u[--ulen];
- while (--ulen != SIZE_MAX) {
- carry = _mpd_shortmul_c(w->data, w->data, n, ubase);
- if (carry) {
- if (n >= wlen) {
- if (!mpd_qresize(w, n+1, status)) {
- return SIZE_MAX;
- }
- wlen = n+1;
- }
- w->data[n++] = carry;
- }
- carry = _mpd_shortadd(w->data, n, u[ulen]);
- if (carry) {
- if (n >= wlen) {
- if (!mpd_qresize(w, n+1, status)) {
- return SIZE_MAX;
- }
- wlen = n+1;
- }
- w->data[n++] = carry;
- }
- }
-
- return n;
-}
-
-/* target base wbase < source base ubase */
-static size_t
-_baseconv_to_smaller(uint32_t **w, size_t wlen, uint32_t wbase,
- mpd_uint_t *u, mpd_ssize_t ulen, mpd_uint_t ubase)
-{
- size_t n = 0;
-
- assert(wlen > 0 && ulen > 0);
- assert(wbase < ubase);
-
- do {
- if (n >= wlen) {
- if (!mpd_resize_u32(w, n+1)) {
- return SIZE_MAX;
- }
- wlen = n+1;
- }
- (*w)[n++] = (uint32_t)_mpd_shortdiv_b(u, u, ulen, wbase, ubase);
- /* ulen is at least 1. u[ulen-1] can only be zero if ulen == 1. */
- ulen = _mpd_real_size(u, ulen);
-
- } while (u[ulen-1] != 0);
-
- return n;
-}
-
-#ifdef CONFIG_32
-/* target base 'wbase' == source base 'ubase' */
-static size_t
-_copy_equal_base(uint32_t **w, size_t wlen,
- const uint32_t *u, size_t ulen)
-{
- if (wlen < ulen) {
- if (!mpd_resize_u32(w, ulen)) {
- return SIZE_MAX;
- }
- }
-
- memcpy(*w, u, ulen * (sizeof **w));
- return ulen;
-}
-
-/* target base 'wbase' > source base 'ubase' */
-static size_t
-_baseconv_to_larger(uint32_t **w, size_t wlen, mpd_uint_t wbase,
- const mpd_uint_t *u, size_t ulen, mpd_uint_t ubase)
-{
- size_t n = 0;
- mpd_uint_t carry;
-
- assert(wlen > 0 && ulen > 0);
- assert(ubase < wbase);
-
- (*w)[n++] = u[--ulen];
- while (--ulen != SIZE_MAX) {
- carry = _mpd_shortmul_b(*w, *w, n, ubase, wbase);
- if (carry) {
- if (n >= wlen) {
- if (!mpd_resize_u32(w, n+1)) {
- return SIZE_MAX;
- }
- wlen = n+1;
- }
- (*w)[n++] = carry;
- }
- carry = _mpd_shortadd_b(*w, n, u[ulen], wbase);
- if (carry) {
- if (n >= wlen) {
- if (!mpd_resize_u32(w, n+1)) {
- return SIZE_MAX;
- }
- wlen = n+1;
- }
- (*w)[n++] = carry;
- }
- }
-
- return n;
-}
-
-/* target base wbase < source base ubase */
-static size_t
-_coeff_from_larger_base(mpd_t *w, size_t wlen, mpd_uint_t wbase,
- mpd_uint_t *u, mpd_ssize_t ulen, mpd_uint_t ubase,
- uint32_t *status)
-{
- size_t n = 0;
-
- assert(wlen > 0 && ulen > 0);
- assert(wbase < ubase);
-
- do {
- if (n >= wlen) {
- if (!mpd_qresize(w, n+1, status)) {
- return SIZE_MAX;
- }
- wlen = n+1;
- }
- w->data[n++] = (uint32_t)_mpd_shortdiv_b(u, u, ulen, wbase, ubase);
- /* ulen is at least 1. u[ulen-1] can only be zero if ulen == 1. */
- ulen = _mpd_real_size(u, ulen);
-
- } while (u[ulen-1] != 0);
-
- return n;
-}
-#endif
-
-/* target base 'wbase' > source base 'ubase' */
-static size_t
-_coeff_from_smaller_base(mpd_t *w, mpd_ssize_t wlen, mpd_uint_t wbase,
- const uint32_t *u, size_t ulen, mpd_uint_t ubase,
- uint32_t *status)
-{
- mpd_ssize_t n = 0;
- mpd_uint_t carry;
-
- assert(wlen > 0 && ulen > 0);
- assert(wbase > ubase);
-
- w->data[n++] = u[--ulen];
- while (--ulen != SIZE_MAX) {
- carry = _mpd_shortmul_b(w->data, w->data, n, ubase, wbase);
- if (carry) {
- if (n >= wlen) {
- if (!mpd_qresize(w, n+1, status)) {
- return SIZE_MAX;
- }
- wlen = n+1;
- }
- w->data[n++] = carry;
- }
- carry = _mpd_shortadd_b(w->data, n, u[ulen], wbase);
- if (carry) {
- if (n >= wlen) {
- if (!mpd_qresize(w, n+1, status)) {
- return SIZE_MAX;
- }
- wlen = n+1;
- }
- w->data[n++] = carry;
- }
- }
-
- return n;
-}
-
-/*
- * Convert an integer mpd_t to a multiprecision integer with base <= 2**16.
- * The least significant word of the result is (*rdata)[0].
- *
- * If rdata is NULL, space is allocated by the function and rlen is irrelevant.
- * In case of an error any allocated storage is freed and rdata is set back to
- * NULL.
- *
- * If rdata is non-NULL, it MUST be allocated by one of libmpdec's allocation
- * functions and rlen MUST be correct. If necessary, the function will resize
- * rdata. In case of an error the caller must free rdata.
- *
- * Return value: In case of success, the exact length of rdata, SIZE_MAX
- * otherwise.
- */
-size_t
-mpd_qexport_u16(uint16_t **rdata, size_t rlen, uint32_t rbase,
- const mpd_t *src, uint32_t *status)
-{
- MPD_NEW_STATIC(tsrc,0,0,0,0);
- int alloc = 0; /* rdata == NULL */
- size_t n;
-
- assert(rbase <= (1U<<16));
-
- if (mpd_isspecial(src) || !_mpd_isint(src)) {
- *status |= MPD_Invalid_operation;
- return SIZE_MAX;
- }
-
- if (*rdata == NULL) {
- rlen = mpd_sizeinbase(src, rbase);
- if (rlen == SIZE_MAX) {
- *status |= MPD_Invalid_operation;
- return SIZE_MAX;
- }
- *rdata = mpd_alloc(rlen, sizeof **rdata);
- if (*rdata == NULL) {
- goto malloc_error;
- }
- alloc = 1;
- }
-
- if (mpd_iszero(src)) {
- **rdata = 0;
- return 1;
- }
-
- if (src->exp >= 0) {
- if (!mpd_qshiftl(&tsrc, src, src->exp, status)) {
- goto malloc_error;
- }
- }
- else {
- if (mpd_qshiftr(&tsrc, src, -src->exp, status) == MPD_UINT_MAX) {
- goto malloc_error;
- }
- }
-
- n = _baseconv_to_u16(rdata, rlen, rbase, tsrc.data, tsrc.len);
- if (n == SIZE_MAX) {
- goto malloc_error;
- }
-
-
-out:
- mpd_del(&tsrc);
- return n;
-
-malloc_error:
- if (alloc) {
- mpd_free(*rdata);
- *rdata = NULL;
- }
- n = SIZE_MAX;
- *status |= MPD_Malloc_error;
- goto out;
-}
-
-/*
- * Convert an integer mpd_t to a multiprecision integer with base<=UINT32_MAX.
- * The least significant word of the result is (*rdata)[0].
- *
- * If rdata is NULL, space is allocated by the function and rlen is irrelevant.
- * In case of an error any allocated storage is freed and rdata is set back to
- * NULL.
- *
- * If rdata is non-NULL, it MUST be allocated by one of libmpdec's allocation
- * functions and rlen MUST be correct. If necessary, the function will resize
- * rdata. In case of an error the caller must free rdata.
- *
- * Return value: In case of success, the exact length of rdata, SIZE_MAX
- * otherwise.
- */
-size_t
-mpd_qexport_u32(uint32_t **rdata, size_t rlen, uint32_t rbase,
- const mpd_t *src, uint32_t *status)
-{
- MPD_NEW_STATIC(tsrc,0,0,0,0);
- int alloc = 0; /* rdata == NULL */
- size_t n;
-
- if (mpd_isspecial(src) || !_mpd_isint(src)) {
- *status |= MPD_Invalid_operation;
- return SIZE_MAX;
- }
-
- if (*rdata == NULL) {
- rlen = mpd_sizeinbase(src, rbase);
- if (rlen == SIZE_MAX) {
- *status |= MPD_Invalid_operation;
- return SIZE_MAX;
- }
- *rdata = mpd_alloc(rlen, sizeof **rdata);
- if (*rdata == NULL) {
- goto malloc_error;
- }
- alloc = 1;
- }
-
- if (mpd_iszero(src)) {
- **rdata = 0;
- return 1;
- }
-
- if (src->exp >= 0) {
- if (!mpd_qshiftl(&tsrc, src, src->exp, status)) {
- goto malloc_error;
- }
- }
- else {
- if (mpd_qshiftr(&tsrc, src, -src->exp, status) == MPD_UINT_MAX) {
- goto malloc_error;
- }
- }
-
-#ifdef CONFIG_64
- n = _baseconv_to_smaller(rdata, rlen, rbase,
- tsrc.data, tsrc.len, MPD_RADIX);
-#else
- if (rbase == MPD_RADIX) {
- n = _copy_equal_base(rdata, rlen, tsrc.data, tsrc.len);
- }
- else if (rbase < MPD_RADIX) {
- n = _baseconv_to_smaller(rdata, rlen, rbase,
- tsrc.data, tsrc.len, MPD_RADIX);
- }
- else {
- n = _baseconv_to_larger(rdata, rlen, rbase,
- tsrc.data, tsrc.len, MPD_RADIX);
- }
-#endif
-
- if (n == SIZE_MAX) {
- goto malloc_error;
- }
-
-
-out:
- mpd_del(&tsrc);
- return n;
-
-malloc_error:
- if (alloc) {
- mpd_free(*rdata);
- *rdata = NULL;
- }
- n = SIZE_MAX;
- *status |= MPD_Malloc_error;
- goto out;
-}
-
-
-/*
- * Converts a multiprecision integer with base <= UINT16_MAX+1 to an mpd_t.
- * The least significant word of the source is srcdata[0].
- */
-void
-mpd_qimport_u16(mpd_t *result,
- const uint16_t *srcdata, size_t srclen,
- uint8_t srcsign, uint32_t srcbase,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_uint_t *usrc; /* uint16_t src copied to an mpd_uint_t array */
- mpd_ssize_t rlen; /* length of the result */
- size_t n;
-
- assert(srclen > 0);
- assert(srcbase <= (1U<<16));
-
- rlen = _mpd_importsize(srclen, srcbase);
- if (rlen == MPD_SSIZE_MAX) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- usrc = mpd_alloc((mpd_size_t)srclen, sizeof *usrc);
- if (usrc == NULL) {
- mpd_seterror(result, MPD_Malloc_error, status);
- return;
- }
- for (n = 0; n < srclen; n++) {
- usrc[n] = srcdata[n];
- }
-
- if (!mpd_qresize(result, rlen, status)) {
- goto finish;
- }
-
- n = _coeff_from_u16(result, rlen, usrc, srclen, srcbase, status);
- if (n == SIZE_MAX) {
- goto finish;
- }
-
- mpd_set_flags(result, srcsign);
- result->exp = 0;
- result->len = n;
- mpd_setdigits(result);
-
- mpd_qresize(result, result->len, status);
- mpd_qfinalize(result, ctx, status);
-
-
-finish:
- mpd_free(usrc);
-}
-
-/*
- * Converts a multiprecision integer with base <= UINT32_MAX to an mpd_t.
- * The least significant word of the source is srcdata[0].
- */
-void
-mpd_qimport_u32(mpd_t *result,
- const uint32_t *srcdata, size_t srclen,
- uint8_t srcsign, uint32_t srcbase,
- const mpd_context_t *ctx, uint32_t *status)
-{
- mpd_ssize_t rlen; /* length of the result */
- size_t n;
-
- assert(srclen > 0);
-
- rlen = _mpd_importsize(srclen, srcbase);
- if (rlen == MPD_SSIZE_MAX) {
- mpd_seterror(result, MPD_Invalid_operation, status);
- return;
- }
-
- if (!mpd_qresize(result, rlen, status)) {
- return;
- }
-
-#ifdef CONFIG_64
- n = _coeff_from_smaller_base(result, rlen, MPD_RADIX,
- srcdata, srclen, srcbase,
- status);
-#else
- if (srcbase == MPD_RADIX) {
- if (!mpd_qresize(result, srclen, status)) {
- return;
- }
- memcpy(result->data, srcdata, srclen * (sizeof *srcdata));
- n = srclen;
- }
- else if (srcbase < MPD_RADIX) {
- n = _coeff_from_smaller_base(result, rlen, MPD_RADIX,
- srcdata, srclen, srcbase,
- status);
- }
- else {
- mpd_uint_t *usrc = mpd_alloc((mpd_size_t)srclen, sizeof *usrc);
- if (usrc == NULL) {
- mpd_seterror(result, MPD_Malloc_error, status);
- return;
- }
- for (n = 0; n < srclen; n++) {
- usrc[n] = srcdata[n];
- }
-
- n = _coeff_from_larger_base(result, rlen, MPD_RADIX,
- usrc, (mpd_ssize_t)srclen, srcbase,
- status);
- mpd_free(usrc);
- }
-#endif
-
- if (n == SIZE_MAX) {
- return;
- }
-
- mpd_set_flags(result, srcsign);
- result->exp = 0;
- result->len = n;
- mpd_setdigits(result);
-
- mpd_qresize(result, result->len, status);
- mpd_qfinalize(result, ctx, status);
-}
-
-
-/******************************************************************************/
-/* From triple */
-/******************************************************************************/
-
-#if defined(CONFIG_64) && defined(__SIZEOF_INT128__)
-static mpd_ssize_t
-_set_coeff(uint64_t data[3], uint64_t hi, uint64_t lo)
-{
- __uint128_t d = ((__uint128_t)hi << 64) + lo;
- __uint128_t q, r;
-
- q = d / MPD_RADIX;
- r = d % MPD_RADIX;
- data[0] = (uint64_t)r;
- d = q;
-
- q = d / MPD_RADIX;
- r = d % MPD_RADIX;
- data[1] = (uint64_t)r;
- d = q;
-
- q = d / MPD_RADIX;
- r = d % MPD_RADIX;
- data[2] = (uint64_t)r;
-
- if (q != 0) {
- abort(); /* GCOV_NOT_REACHED */
- }
-
- return data[2] != 0 ? 3 : (data[1] != 0 ? 2 : 1);
-}
-#else
-static size_t
-_uint_from_u16(mpd_uint_t *w, mpd_ssize_t wlen, const uint16_t *u, size_t ulen)
-{
- const mpd_uint_t ubase = 1U<<16;
- mpd_ssize_t n = 0;
- mpd_uint_t carry;
-
- assert(wlen > 0 && ulen > 0);
-
- w[n++] = u[--ulen];
- while (--ulen != SIZE_MAX) {
- carry = _mpd_shortmul_c(w, w, n, ubase);
- if (carry) {
- if (n >= wlen) {
- abort(); /* GCOV_NOT_REACHED */
- }
- w[n++] = carry;
- }
- carry = _mpd_shortadd(w, n, u[ulen]);
- if (carry) {
- if (n >= wlen) {
- abort(); /* GCOV_NOT_REACHED */
- }
- w[n++] = carry;
- }
- }
-
- return n;
-}
-
-static mpd_ssize_t
-_set_coeff(mpd_uint_t *data, mpd_ssize_t len, uint64_t hi, uint64_t lo)
-{
- uint16_t u16[8] = {0};
-
- u16[7] = (uint16_t)((hi & 0xFFFF000000000000ULL) >> 48);
- u16[6] = (uint16_t)((hi & 0x0000FFFF00000000ULL) >> 32);
- u16[5] = (uint16_t)((hi & 0x00000000FFFF0000ULL) >> 16);
- u16[4] = (uint16_t) (hi & 0x000000000000FFFFULL);
-
- u16[3] = (uint16_t)((lo & 0xFFFF000000000000ULL) >> 48);
- u16[2] = (uint16_t)((lo & 0x0000FFFF00000000ULL) >> 32);
- u16[1] = (uint16_t)((lo & 0x00000000FFFF0000ULL) >> 16);
- u16[0] = (uint16_t) (lo & 0x000000000000FFFFULL);
-
- return (mpd_ssize_t)_uint_from_u16(data, len, u16, 8);
-}
-#endif
-
-static int
-_set_uint128_coeff_exp(mpd_t *result, uint64_t hi, uint64_t lo, mpd_ssize_t exp)
-{
- mpd_uint_t data[5] = {0};
- uint32_t status = 0;
- mpd_ssize_t len;
-
-#if defined(CONFIG_64) && defined(__SIZEOF_INT128__)
- len = _set_coeff(data, hi, lo);
-#else
- len = _set_coeff(data, 5, hi, lo);
-#endif
-
- if (!mpd_qresize(result, len, &status)) {
- return -1;
- }
-
- for (mpd_ssize_t i = 0; i < len; i++) {
- result->data[i] = data[i];
- }
-
- result->exp = exp;
- result->len = len;
- mpd_setdigits(result);
-
- return 0;
-}
-
-int
-mpd_from_uint128_triple(mpd_t *result, const mpd_uint128_triple_t *triple, uint32_t *status)
-{
- static const mpd_context_t maxcontext = {
- .prec=MPD_MAX_PREC,
- .emax=MPD_MAX_EMAX,
- .emin=MPD_MIN_EMIN,
- .round=MPD_ROUND_HALF_EVEN,
- .traps=MPD_Traps,
- .status=0,
- .newtrap=0,
- .clamp=0,
- .allcr=1,
- };
- const enum mpd_triple_class tag = triple->tag;
- const uint8_t sign = triple->sign;
- const uint64_t hi = triple->hi;
- const uint64_t lo = triple->lo;
- mpd_ssize_t exp;
-
-#ifdef CONFIG_32
- if (triple->exp < MPD_SSIZE_MIN || triple->exp > MPD_SSIZE_MAX) {
- goto conversion_error;
- }
-#endif
- exp = (mpd_ssize_t)triple->exp;
-
- switch (tag) {
- case MPD_TRIPLE_QNAN: case MPD_TRIPLE_SNAN: {
- if (sign > 1 || exp != 0) {
- goto conversion_error;
- }
-
- const uint8_t flags = tag == MPD_TRIPLE_QNAN ? MPD_NAN : MPD_SNAN;
- mpd_setspecial(result, sign, flags);
-
- if (hi == 0 && lo == 0) { /* no payload */
- return 0;
- }
-
- if (_set_uint128_coeff_exp(result, hi, lo, exp) < 0) {
- goto malloc_error;
- }
-
- return 0;
- }
-
- case MPD_TRIPLE_INF: {
- if (sign > 1 || hi != 0 || lo != 0 || exp != 0) {
- goto conversion_error;
- }
-
- mpd_setspecial(result, sign, MPD_INF);
-
- return 0;
- }
-
- case MPD_TRIPLE_NORMAL: {
- if (sign > 1) {
- goto conversion_error;
- }
-
- const uint8_t flags = sign ? MPD_NEG : MPD_POS;
- mpd_set_flags(result, flags);
-
- if (exp > MPD_EXP_INF) {
- exp = MPD_EXP_INF;
- }
- if (exp == MPD_SSIZE_MIN) {
- exp = MPD_SSIZE_MIN+1;
- }
-
- if (_set_uint128_coeff_exp(result, hi, lo, exp) < 0) {
- goto malloc_error;
- }
-
- uint32_t workstatus = 0;
- mpd_qfinalize(result, &maxcontext, &workstatus);
- if (workstatus & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) {
- goto conversion_error;
- }
-
- return 0;
- }
-
- default:
- goto conversion_error;
- }
-
-conversion_error:
- mpd_seterror(result, MPD_Conversion_syntax, status);
- return -1;
-
-malloc_error:
- mpd_seterror(result, MPD_Malloc_error, status);
- return -1;
-}
-
-
-/******************************************************************************/
-/* As triple */
-/******************************************************************************/
-
-#if defined(CONFIG_64) && defined(__SIZEOF_INT128__)
-static void
-_get_coeff(uint64_t *hi, uint64_t *lo, const mpd_t *a)
-{
- __uint128_t u128 = 0;
-
- switch (a->len) {
- case 3:
- u128 = a->data[2]; /* fall through */
- case 2:
- u128 = u128 * MPD_RADIX + a->data[1]; /* fall through */
- case 1:
- u128 = u128 * MPD_RADIX + a->data[0];
- break;
- default:
- abort(); /* GCOV_NOT_REACHED */
- }
-
- *hi = u128 >> 64;
- *lo = (uint64_t)u128;
-}
-#else
-static size_t
-_uint_to_u16(uint16_t w[8], mpd_uint_t *u, mpd_ssize_t ulen)
-{
- const mpd_uint_t wbase = 1U<<16;
- size_t n = 0;
-
- assert(ulen > 0);
-
- do {
- if (n >= 8) {
- abort(); /* GCOV_NOT_REACHED */
- }
- w[n++] = (uint16_t)_mpd_shortdiv(u, u, ulen, wbase);
- /* ulen is at least 1. u[ulen-1] can only be zero if ulen == 1. */
- ulen = _mpd_real_size(u, ulen);
-
- } while (u[ulen-1] != 0);
-
- return n;
-}
-
-static void
-_get_coeff(uint64_t *hi, uint64_t *lo, const mpd_t *a)
-{
- uint16_t u16[8] = {0};
- mpd_uint_t data[5] = {0};
-
- switch (a->len) {
- case 5:
- data[4] = a->data[4]; /* fall through */
- case 4:
- data[3] = a->data[3]; /* fall through */
- case 3:
- data[2] = a->data[2]; /* fall through */
- case 2:
- data[1] = a->data[1]; /* fall through */
- case 1:
- data[0] = a->data[0];
- break;
- default:
- abort(); /* GCOV_NOT_REACHED */
- }
-
- _uint_to_u16(u16, data, a->len);
-
- *hi = (uint64_t)u16[7] << 48;
- *hi |= (uint64_t)u16[6] << 32;
- *hi |= (uint64_t)u16[5] << 16;
- *hi |= (uint64_t)u16[4];
-
- *lo = (uint64_t)u16[3] << 48;
- *lo |= (uint64_t)u16[2] << 32;
- *lo |= (uint64_t)u16[1] << 16;
- *lo |= (uint64_t)u16[0];
-}
-#endif
-
-static enum mpd_triple_class
-_coeff_as_uint128(uint64_t *hi, uint64_t *lo, const mpd_t *a)
-{
-#ifdef CONFIG_64
- static mpd_uint_t uint128_max_data[3] = { 3374607431768211455ULL, 4028236692093846346ULL, 3ULL };
- static const mpd_t uint128_max = { MPD_STATIC|MPD_CONST_DATA, 0, 39, 3, 3, uint128_max_data };
-#else
- static mpd_uint_t uint128_max_data[5] = { 768211455U, 374607431U, 938463463U, 282366920U, 340U };
- static const mpd_t uint128_max = { MPD_STATIC|MPD_CONST_DATA, 0, 39, 5, 5, uint128_max_data };
-#endif
- enum mpd_triple_class ret = MPD_TRIPLE_NORMAL;
- uint32_t status = 0;
- mpd_t coeff;
-
- *hi = *lo = 0ULL;
-
- if (mpd_isspecial(a)) {
- if (mpd_isinfinite(a)) {
- return MPD_TRIPLE_INF;
- }
-
- ret = mpd_isqnan(a) ? MPD_TRIPLE_QNAN : MPD_TRIPLE_SNAN;
- if (a->len == 0) { /* no payload */
- return ret;
- }
- }
- else if (mpd_iszero(a)) {
- return ret;
- }
-
- _mpd_copy_shared(&coeff, a);
- mpd_set_flags(&coeff, 0);
- coeff.exp = 0;
-
- if (mpd_qcmp(&coeff, &uint128_max, &status) > 0) {
- return MPD_TRIPLE_ERROR;
- }
-
- _get_coeff(hi, lo, &coeff);
- return ret;
-}
-
-mpd_uint128_triple_t
-mpd_as_uint128_triple(const mpd_t *a)
-{
- mpd_uint128_triple_t triple = { MPD_TRIPLE_ERROR, 0, 0, 0, 0 };
-
- triple.tag = _coeff_as_uint128(&triple.hi, &triple.lo, a);
- if (triple.tag == MPD_TRIPLE_ERROR) {
- return triple;
- }
-
- triple.sign = !!mpd_isnegative(a);
- if (triple.tag == MPD_TRIPLE_NORMAL) {
- triple.exp = a->exp;
- }
-
- return triple;
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_MPDECIMAL_H_
-#define LIBMPDEC_MPDECIMAL_H_
-
-
-#ifndef _MSC_VER
- #include "pyconfig.h"
-#endif
-
-#ifdef __cplusplus
- #include <cinttypes>
- #include <climits>
- #include <cstdint>
- #include <cstdio>
- #include <cstdlib>
- #define MPD_UINT8_C(x) (static_cast<uint8_t>(x))
-extern "C" {
-#else
- #include <inttypes.h>
- #include <limits.h>
- #include <stdint.h>
- #include <stdio.h>
- #include <stdlib.h>
- #define MPD_UINT8_C(x) ((uint8_t)x)
-#endif
-
-
-#if (defined(__linux__) || defined(__FreeBSD__) || defined(__APPLE__)) && \
- defined(__GNUC__) && __GNUC__ >= 4 && !defined(__INTEL_COMPILER)
- #define MPD_PRAGMA(x) _Pragma(x)
- #define MPD_HIDE_SYMBOLS_START "GCC visibility push(hidden)"
- #define MPD_HIDE_SYMBOLS_END "GCC visibility pop"
-#else
- #define MPD_PRAGMA(x)
- #define MPD_HIDE_SYMBOLS_START
- #define MPD_HIDE_SYMBOLS_END
-#endif
-
-#if defined(_MSC_VER)
- #define EXTINLINE extern inline
-#else
- #define EXTINLINE
-#endif
-
-
-/* This header file is internal for the purpose of building _decimal.so.
- * All symbols should have local scope in the DSO. */
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
-
-
-/******************************************************************************/
-/* Version */
-/******************************************************************************/
-
-#define MPD_MAJOR_VERSION 2
-#define MPD_MINOR_VERSION 5
-#define MPD_MICRO_VERSION 1
-
-#define MPD_VERSION "2.5.1"
-
-#define MPD_VERSION_HEX ((MPD_MAJOR_VERSION << 24) | \
- (MPD_MINOR_VERSION << 16) | \
- (MPD_MICRO_VERSION << 8))
-
-const char *mpd_version(void);
-
-
-/******************************************************************************/
-/* Configuration */
-/******************************************************************************/
-
-#if defined(UNIVERSAL)
- #if defined(CONFIG_64) || defined(CONFIG_32)
- #error "cannot use CONFIG_64 or CONFIG_32 with UNIVERSAL."
- #endif
- #if defined(__ppc__)
- #define CONFIG_32
- #define ANSI
- #elif defined(__ppc64__)
- #define CONFIG_64
- #define ANSI
- #elif defined(__i386__)
- #define CONFIG_32
- #define ANSI
- #elif defined(__x86_64__)
- #define CONFIG_64
- #define ASM
- #elif defined(__arm64__)
- #define CONFIG_64
- #define ANSI
- #else
- #error "unknown architecture for universal build."
- #endif
-#endif
-
-
-/* BEGIN CONFIG_64 */
-#if defined(CONFIG_64)
-/* types for modular and base arithmetic */
-#define MPD_UINT_MAX UINT64_MAX
-#define MPD_BITS_PER_UINT 64
-typedef uint64_t mpd_uint_t; /* unsigned mod type */
-
-#define MPD_SIZE_MAX SIZE_MAX
-typedef size_t mpd_size_t; /* unsigned size type */
-
-/* type for exp, digits, len, prec */
-#define MPD_SSIZE_MAX INT64_MAX
-#define MPD_SSIZE_MIN INT64_MIN
-typedef int64_t mpd_ssize_t;
-#define _mpd_strtossize strtoll
-
-/* decimal arithmetic */
-#define MPD_RADIX 10000000000000000000ULL /* 10**19 */
-#define MPD_RDIGITS 19
-#define MPD_MAX_POW10 19
-#define MPD_EXPDIGITS 19 /* MPD_EXPDIGITS <= MPD_RDIGITS+1 */
-
-#define MPD_MAXTRANSFORM_2N 4294967296ULL /* 2**32 */
-#define MPD_MAX_PREC 999999999999999999LL
-#define MPD_MAX_PREC_LOG2 64
-#define MPD_ELIMIT 1000000000000000000LL
-#define MPD_MAX_EMAX 999999999999999999LL /* ELIMIT-1 */
-#define MPD_MIN_EMIN (-999999999999999999LL) /* -EMAX */
-#define MPD_MIN_ETINY (MPD_MIN_EMIN-(MPD_MAX_PREC-1))
-#define MPD_EXP_INF 2000000000000000001LL
-#define MPD_EXP_CLAMP (-4000000000000000001LL)
-#define MPD_MAXIMPORT 105263157894736842L /* ceil((2*MPD_MAX_PREC)/MPD_RDIGITS) */
-#define MPD_IEEE_CONTEXT_MAX_BITS 512 /* 16*(log2(MPD_MAX_EMAX / 3)-3) */
-
-/* conversion specifiers */
-#define PRI_mpd_uint_t PRIu64
-#define PRI_mpd_ssize_t PRIi64
-/* END CONFIG_64 */
-
-
-/* BEGIN CONFIG_32 */
-#elif defined(CONFIG_32)
-/* types for modular and base arithmetic */
-#define MPD_UINT_MAX UINT32_MAX
-#define MPD_BITS_PER_UINT 32
-typedef uint32_t mpd_uint_t; /* unsigned mod type */
-
-#ifndef LEGACY_COMPILER
-#define MPD_UUINT_MAX UINT64_MAX
-typedef uint64_t mpd_uuint_t; /* double width unsigned mod type */
-#endif
-
-#define MPD_SIZE_MAX SIZE_MAX
-typedef size_t mpd_size_t; /* unsigned size type */
-
-/* type for dec->len, dec->exp, ctx->prec */
-#define MPD_SSIZE_MAX INT32_MAX
-#define MPD_SSIZE_MIN INT32_MIN
-typedef int32_t mpd_ssize_t;
-#define _mpd_strtossize strtol
-
-/* decimal arithmetic */
-#define MPD_RADIX 1000000000UL /* 10**9 */
-#define MPD_RDIGITS 9
-#define MPD_MAX_POW10 9
-#define MPD_EXPDIGITS 10 /* MPD_EXPDIGITS <= MPD_RDIGITS+1 */
-
-#define MPD_MAXTRANSFORM_2N 33554432UL /* 2**25 */
-#define MPD_MAX_PREC 425000000L
-#define MPD_MAX_PREC_LOG2 32
-#define MPD_ELIMIT 425000001L
-#define MPD_MAX_EMAX 425000000L /* ELIMIT-1 */
-#define MPD_MIN_EMIN (-425000000L) /* -EMAX */
-#define MPD_MIN_ETINY (MPD_MIN_EMIN-(MPD_MAX_PREC-1))
-#define MPD_EXP_INF 1000000001L /* allows for emax=999999999 in the tests */
-#define MPD_EXP_CLAMP (-2000000001L) /* allows for emin=-999999999 in the tests */
-#define MPD_MAXIMPORT 94444445L /* ceil((2*MPD_MAX_PREC)/MPD_RDIGITS) */
-#define MPD_IEEE_CONTEXT_MAX_BITS 256 /* 16*(log2(MPD_MAX_EMAX / 3)-3) */
-
-/* conversion specifiers */
-#define PRI_mpd_uint_t PRIu32
-#define PRI_mpd_ssize_t PRIi32
-/* END CONFIG_32 */
-
-#else
- #error "define CONFIG_64 or CONFIG_32"
-#endif
-/* END CONFIG */
-
-
-#if MPD_SIZE_MAX != MPD_UINT_MAX
- #error "unsupported platform: need mpd_size_t == mpd_uint_t"
-#endif
-
-
-/******************************************************************************/
-/* Context */
-/******************************************************************************/
-
-enum {
- MPD_ROUND_UP, /* round away from 0 */
- MPD_ROUND_DOWN, /* round toward 0 (truncate) */
- MPD_ROUND_CEILING, /* round toward +infinity */
- MPD_ROUND_FLOOR, /* round toward -infinity */
- MPD_ROUND_HALF_UP, /* 0.5 is rounded up */
- MPD_ROUND_HALF_DOWN, /* 0.5 is rounded down */
- MPD_ROUND_HALF_EVEN, /* 0.5 is rounded to even */
- MPD_ROUND_05UP, /* round zero or five away from 0 */
- MPD_ROUND_TRUNC, /* truncate, but set infinity */
- MPD_ROUND_GUARD
-};
-
-enum { MPD_CLAMP_DEFAULT, MPD_CLAMP_IEEE_754, MPD_CLAMP_GUARD };
-
-extern const char * const mpd_round_string[MPD_ROUND_GUARD];
-extern const char * const mpd_clamp_string[MPD_CLAMP_GUARD];
-
-
-typedef struct mpd_context_t {
- mpd_ssize_t prec; /* precision */
- mpd_ssize_t emax; /* max positive exp */
- mpd_ssize_t emin; /* min negative exp */
- uint32_t traps; /* status events that should be trapped */
- uint32_t status; /* status flags */
- uint32_t newtrap; /* set by mpd_addstatus_raise() */
- int round; /* rounding mode */
- int clamp; /* clamp mode */
- int allcr; /* all functions correctly rounded */
-} mpd_context_t;
-
-
-/* Status flags */
-#define MPD_Clamped 0x00000001U
-#define MPD_Conversion_syntax 0x00000002U
-#define MPD_Division_by_zero 0x00000004U
-#define MPD_Division_impossible 0x00000008U
-#define MPD_Division_undefined 0x00000010U
-#define MPD_Fpu_error 0x00000020U
-#define MPD_Inexact 0x00000040U
-#define MPD_Invalid_context 0x00000080U
-#define MPD_Invalid_operation 0x00000100U
-#define MPD_Malloc_error 0x00000200U
-#define MPD_Not_implemented 0x00000400U
-#define MPD_Overflow 0x00000800U
-#define MPD_Rounded 0x00001000U
-#define MPD_Subnormal 0x00002000U
-#define MPD_Underflow 0x00004000U
-#define MPD_Max_status (0x00008000U-1U)
-
-/* Conditions that result in an IEEE 754 exception */
-#define MPD_IEEE_Invalid_operation (MPD_Conversion_syntax | \
- MPD_Division_impossible | \
- MPD_Division_undefined | \
- MPD_Fpu_error | \
- MPD_Invalid_context | \
- MPD_Invalid_operation | \
- MPD_Malloc_error) \
-
-/* Errors that require the result of an operation to be set to NaN */
-#define MPD_Errors (MPD_IEEE_Invalid_operation | \
- MPD_Division_by_zero)
-
-/* Default traps */
-#define MPD_Traps (MPD_IEEE_Invalid_operation | \
- MPD_Division_by_zero | \
- MPD_Overflow | \
- MPD_Underflow)
-
-/* Official name */
-#define MPD_Insufficient_storage MPD_Malloc_error
-
-/* IEEE 754 interchange format contexts */
-#define MPD_DECIMAL32 32
-#define MPD_DECIMAL64 64
-#define MPD_DECIMAL128 128
-
-
-#define MPD_MINALLOC_MIN 2
-#define MPD_MINALLOC_MAX 64
-extern mpd_ssize_t MPD_MINALLOC;
-extern void (* mpd_traphandler)(mpd_context_t *);
-void mpd_dflt_traphandler(mpd_context_t *);
-
-void mpd_setminalloc(mpd_ssize_t n);
-void mpd_init(mpd_context_t *ctx, mpd_ssize_t prec);
-
-void mpd_maxcontext(mpd_context_t *ctx);
-void mpd_defaultcontext(mpd_context_t *ctx);
-void mpd_basiccontext(mpd_context_t *ctx);
-int mpd_ieee_context(mpd_context_t *ctx, int bits);
-
-mpd_ssize_t mpd_getprec(const mpd_context_t *ctx);
-mpd_ssize_t mpd_getemax(const mpd_context_t *ctx);
-mpd_ssize_t mpd_getemin(const mpd_context_t *ctx);
-int mpd_getround(const mpd_context_t *ctx);
-uint32_t mpd_gettraps(const mpd_context_t *ctx);
-uint32_t mpd_getstatus(const mpd_context_t *ctx);
-int mpd_getclamp(const mpd_context_t *ctx);
-int mpd_getcr(const mpd_context_t *ctx);
-
-int mpd_qsetprec(mpd_context_t *ctx, mpd_ssize_t prec);
-int mpd_qsetemax(mpd_context_t *ctx, mpd_ssize_t emax);
-int mpd_qsetemin(mpd_context_t *ctx, mpd_ssize_t emin);
-int mpd_qsetround(mpd_context_t *ctx, int newround);
-int mpd_qsettraps(mpd_context_t *ctx, uint32_t flags);
-int mpd_qsetstatus(mpd_context_t *ctx, uint32_t flags);
-int mpd_qsetclamp(mpd_context_t *ctx, int c);
-int mpd_qsetcr(mpd_context_t *ctx, int c);
-void mpd_addstatus_raise(mpd_context_t *ctx, uint32_t flags);
-
-
-/******************************************************************************/
-/* Decimal Arithmetic */
-/******************************************************************************/
-
-/* mpd_t flags */
-#define MPD_POS MPD_UINT8_C(0)
-#define MPD_NEG MPD_UINT8_C(1)
-#define MPD_INF MPD_UINT8_C(2)
-#define MPD_NAN MPD_UINT8_C(4)
-#define MPD_SNAN MPD_UINT8_C(8)
-#define MPD_SPECIAL (MPD_INF|MPD_NAN|MPD_SNAN)
-#define MPD_STATIC MPD_UINT8_C(16)
-#define MPD_STATIC_DATA MPD_UINT8_C(32)
-#define MPD_SHARED_DATA MPD_UINT8_C(64)
-#define MPD_CONST_DATA MPD_UINT8_C(128)
-#define MPD_DATAFLAGS (MPD_STATIC_DATA|MPD_SHARED_DATA|MPD_CONST_DATA)
-
-/* mpd_t */
-typedef struct mpd_t {
- uint8_t flags;
- mpd_ssize_t exp;
- mpd_ssize_t digits;
- mpd_ssize_t len;
- mpd_ssize_t alloc;
- mpd_uint_t *data;
-} mpd_t;
-
-
-/******************************************************************************/
-/* Triple */
-/******************************************************************************/
-
-/* status cases for getting a triple */
-enum mpd_triple_class {
- MPD_TRIPLE_NORMAL,
- MPD_TRIPLE_INF,
- MPD_TRIPLE_QNAN,
- MPD_TRIPLE_SNAN,
- MPD_TRIPLE_ERROR,
-};
-
-typedef struct {
- enum mpd_triple_class tag;
- uint8_t sign;
- uint64_t hi;
- uint64_t lo;
- int64_t exp;
-} mpd_uint128_triple_t;
-
-int mpd_from_uint128_triple(mpd_t *result, const mpd_uint128_triple_t *triple, uint32_t *status);
-mpd_uint128_triple_t mpd_as_uint128_triple(const mpd_t *a);
-
-
-/******************************************************************************/
-/* Quiet, thread-safe functions */
-/******************************************************************************/
-
-/* format specification */
-typedef struct mpd_spec_t {
- mpd_ssize_t min_width; /* minimum field width */
- mpd_ssize_t prec; /* fraction digits or significant digits */
- char type; /* conversion specifier */
- char align; /* alignment */
- char sign; /* sign printing/alignment */
- char fill[5]; /* fill character */
- const char *dot; /* decimal point */
- const char *sep; /* thousands separator */
- const char *grouping; /* grouping of digits */
-} mpd_spec_t;
-
-/* output to a string */
-char *mpd_to_sci(const mpd_t *dec, int fmt);
-char *mpd_to_eng(const mpd_t *dec, int fmt);
-mpd_ssize_t mpd_to_sci_size(char **res, const mpd_t *dec, int fmt);
-mpd_ssize_t mpd_to_eng_size(char **res, const mpd_t *dec, int fmt);
-int mpd_validate_lconv(mpd_spec_t *spec);
-int mpd_parse_fmt_str(mpd_spec_t *spec, const char *fmt, int caps);
-char *mpd_qformat_spec(const mpd_t *dec, const mpd_spec_t *spec, const mpd_context_t *ctx, uint32_t *status);
-char *mpd_qformat(const mpd_t *dec, const char *fmt, const mpd_context_t *ctx, uint32_t *status);
-
-#define MPD_NUM_FLAGS 15
-#define MPD_MAX_FLAG_STRING 208
-#define MPD_MAX_FLAG_LIST (MPD_MAX_FLAG_STRING+18)
-#define MPD_MAX_SIGNAL_LIST 121
-int mpd_snprint_flags(char *dest, int nmemb, uint32_t flags);
-int mpd_lsnprint_flags(char *dest, int nmemb, uint32_t flags, const char *flag_string[]);
-int mpd_lsnprint_signals(char *dest, int nmemb, uint32_t flags, const char *signal_string[]);
-
-/* output to a file */
-void mpd_fprint(FILE *file, const mpd_t *dec);
-void mpd_print(const mpd_t *dec);
-
-/* assignment from a string */
-void mpd_qset_string(mpd_t *dec, const char *s, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qset_string_exact(mpd_t *dec, const char *s, uint32_t *status);
-
-/* set to NaN with error flags */
-void mpd_seterror(mpd_t *result, uint32_t flags, uint32_t *status);
-/* set a special with sign and type */
-void mpd_setspecial(mpd_t *result, uint8_t sign, uint8_t type);
-/* set coefficient to zero or all nines */
-void mpd_zerocoeff(mpd_t *result);
-void mpd_qmaxcoeff(mpd_t *result, const mpd_context_t *ctx, uint32_t *status);
-
-/* quietly assign a C integer type to an mpd_t */
-void mpd_qset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, uint32_t *status);
-#ifndef LEGACY_COMPILER
-void mpd_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qset_i64_exact(mpd_t *result, int64_t a, uint32_t *status);
-void mpd_qset_u64_exact(mpd_t *result, uint64_t a, uint32_t *status);
-#endif
-
-/* quietly assign a C integer type to an mpd_t with a static coefficient */
-void mpd_qsset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qsset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qsset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qsset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, uint32_t *status);
-
-/* quietly get a C integer type from an mpd_t */
-mpd_ssize_t mpd_qget_ssize(const mpd_t *dec, uint32_t *status);
-mpd_uint_t mpd_qget_uint(const mpd_t *dec, uint32_t *status);
-mpd_uint_t mpd_qabs_uint(const mpd_t *dec, uint32_t *status);
-
-int32_t mpd_qget_i32(const mpd_t *dec, uint32_t *status);
-uint32_t mpd_qget_u32(const mpd_t *dec, uint32_t *status);
-#ifndef LEGACY_COMPILER
-int64_t mpd_qget_i64(const mpd_t *dec, uint32_t *status);
-uint64_t mpd_qget_u64(const mpd_t *dec, uint32_t *status);
-#endif
-
-/* quiet functions */
-int mpd_qcheck_nan(mpd_t *nanresult, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-int mpd_qcheck_nans(mpd_t *nanresult, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qfinalize(mpd_t *result, const mpd_context_t *ctx, uint32_t *status);
-
-const char *mpd_class(const mpd_t *a, const mpd_context_t *ctx);
-
-int mpd_qcopy(mpd_t *result, const mpd_t *a, uint32_t *status);
-int mpd_qcopy_cxx(mpd_t *result, const mpd_t *a);
-mpd_t *mpd_qncopy(const mpd_t *a);
-int mpd_qcopy_abs(mpd_t *result, const mpd_t *a, uint32_t *status);
-int mpd_qcopy_negate(mpd_t *result, const mpd_t *a, uint32_t *status);
-int mpd_qcopy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status);
-
-void mpd_qand(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qinvert(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qlogb(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qor(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qscaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qxor(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-int mpd_same_quantum(const mpd_t *a, const mpd_t *b);
-
-void mpd_qrotate(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-int mpd_qshiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status);
-mpd_uint_t mpd_qshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status);
-mpd_uint_t mpd_qshiftr_inplace(mpd_t *result, mpd_ssize_t n);
-void mpd_qshift(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qshiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, const mpd_context_t *ctx, uint32_t *status);
-
-int mpd_qcmp(const mpd_t *a, const mpd_t *b, uint32_t *status);
-int mpd_qcompare(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-int mpd_qcompare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-int mpd_cmp_total(const mpd_t *a, const mpd_t *b);
-int mpd_cmp_total_mag(const mpd_t *a, const mpd_t *b);
-int mpd_compare_total(mpd_t *result, const mpd_t *a, const mpd_t *b);
-int mpd_compare_total_mag(mpd_t *result, const mpd_t *a, const mpd_t *b);
-
-void mpd_qround_to_intx(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qround_to_int(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qtrunc(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qfloor(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qceil(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-
-void mpd_qabs(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qmax(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qmax_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qmin(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qmin_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qminus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qplus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qnext_minus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qnext_plus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qnext_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qquantize(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qrescale_fmt(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qreduce(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qadd_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qadd_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qadd_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qadd_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qsub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qsub_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qsub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qsub_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qmul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qmul_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qmul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qmul_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qfma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qdiv(mpd_t *q, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qdiv_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qdiv_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qdiv_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qdiv_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qdivint(mpd_t *q, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qrem(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qrem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qpow(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qpowmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_t *mod, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qln10(mpd_t *result, mpd_ssize_t prec, uint32_t *status);
-void mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qlog10(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qsqrt(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
-
-#ifndef LEGACY_COMPILER
-void mpd_qadd_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qadd_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qsub_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qsub_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qmul_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qmul_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qdiv_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qdiv_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status);
-#endif
-
-
-size_t mpd_sizeinbase(const mpd_t *a, uint32_t base);
-void mpd_qimport_u16(mpd_t *result, const uint16_t *srcdata, size_t srclen,
- uint8_t srcsign, uint32_t srcbase,
- const mpd_context_t *ctx, uint32_t *status);
-void mpd_qimport_u32(mpd_t *result, const uint32_t *srcdata, size_t srclen,
- uint8_t srcsign, uint32_t srcbase,
- const mpd_context_t *ctx, uint32_t *status);
-size_t mpd_qexport_u16(uint16_t **rdata, size_t rlen, uint32_t base,
- const mpd_t *src, uint32_t *status);
-size_t mpd_qexport_u32(uint32_t **rdata, size_t rlen, uint32_t base,
- const mpd_t *src, uint32_t *status);
-
-
-/******************************************************************************/
-/* Signalling functions */
-/******************************************************************************/
-
-char *mpd_format(const mpd_t *dec, const char *fmt, mpd_context_t *ctx);
-void mpd_import_u16(mpd_t *result, const uint16_t *srcdata, size_t srclen, uint8_t srcsign, uint32_t base, mpd_context_t *ctx);
-void mpd_import_u32(mpd_t *result, const uint32_t *srcdata, size_t srclen, uint8_t srcsign, uint32_t base, mpd_context_t *ctx);
-size_t mpd_export_u16(uint16_t **rdata, size_t rlen, uint32_t base, const mpd_t *src, mpd_context_t *ctx);
-size_t mpd_export_u32(uint32_t **rdata, size_t rlen, uint32_t base, const mpd_t *src, mpd_context_t *ctx);
-void mpd_finalize(mpd_t *result, mpd_context_t *ctx);
-int mpd_check_nan(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-int mpd_check_nans(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_set_string(mpd_t *result, const char *s, mpd_context_t *ctx);
-void mpd_maxcoeff(mpd_t *result, mpd_context_t *ctx);
-void mpd_sset_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx);
-void mpd_sset_i32(mpd_t *result, int32_t a, mpd_context_t *ctx);
-void mpd_sset_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx);
-void mpd_sset_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx);
-void mpd_set_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx);
-void mpd_set_i32(mpd_t *result, int32_t a, mpd_context_t *ctx);
-void mpd_set_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx);
-void mpd_set_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx);
-#ifndef LEGACY_COMPILER
-void mpd_set_i64(mpd_t *result, int64_t a, mpd_context_t *ctx);
-void mpd_set_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx);
-#endif
-mpd_ssize_t mpd_get_ssize(const mpd_t *a, mpd_context_t *ctx);
-mpd_uint_t mpd_get_uint(const mpd_t *a, mpd_context_t *ctx);
-mpd_uint_t mpd_abs_uint(const mpd_t *a, mpd_context_t *ctx);
-int32_t mpd_get_i32(const mpd_t *a, mpd_context_t *ctx);
-uint32_t mpd_get_u32(const mpd_t *a, mpd_context_t *ctx);
-#ifndef LEGACY_COMPILER
-int64_t mpd_get_i64(const mpd_t *a, mpd_context_t *ctx);
-uint64_t mpd_get_u64(const mpd_t *a, mpd_context_t *ctx);
-#endif
-void mpd_and(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_copy(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_canonical(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_copy_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_copy_negate(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_copy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_invert(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_logb(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_or(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_rotate(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_scaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_shiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx);
-mpd_uint_t mpd_shiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx);
-void mpd_shiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx);
-void mpd_shift(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_xor(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-int mpd_cmp(const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-int mpd_compare(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-int mpd_compare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_add(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_add_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx);
-void mpd_add_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx);
-void mpd_add_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx);
-void mpd_add_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx);
-void mpd_sub(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_sub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx);
-void mpd_sub_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx);
-void mpd_sub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx);
-void mpd_sub_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx);
-void mpd_div(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_div_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx);
-void mpd_div_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx);
-void mpd_div_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx);
-void mpd_div_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx);
-void mpd_divmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_divint(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_exp(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_fma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, mpd_context_t *ctx);
-void mpd_ln(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_log10(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_max(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_max_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_min(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_min_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_mul(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_mul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx);
-void mpd_mul_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx);
-void mpd_mul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx);
-void mpd_mul_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx);
-void mpd_next_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_next_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_next_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_pow(mpd_t *result, const mpd_t *base, const mpd_t *exp, mpd_context_t *ctx);
-void mpd_powmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_t *mod, mpd_context_t *ctx);
-void mpd_quantize(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_rescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, mpd_context_t *ctx);
-void mpd_reduce(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_rem(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_rem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
-void mpd_round_to_intx(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_round_to_int(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_trunc(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_floor(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_ceil(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_sqrt(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-void mpd_invroot(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
-
-#ifndef LEGACY_COMPILER
-void mpd_add_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx);
-void mpd_add_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx);
-void mpd_sub_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx);
-void mpd_sub_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx);
-void mpd_div_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx);
-void mpd_div_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx);
-void mpd_mul_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx);
-void mpd_mul_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx);
-#endif
-
-
-/******************************************************************************/
-/* Configuration specific */
-/******************************************************************************/
-
-#ifdef CONFIG_64
-void mpd_qsset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_qsset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, uint32_t *status);
-void mpd_sset_i64(mpd_t *result, int64_t a, mpd_context_t *ctx);
-void mpd_sset_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx);
-#endif
-
-
-/******************************************************************************/
-/* Get attributes of a decimal */
-/******************************************************************************/
-
-EXTINLINE mpd_ssize_t mpd_adjexp(const mpd_t *dec);
-EXTINLINE mpd_ssize_t mpd_etiny(const mpd_context_t *ctx);
-EXTINLINE mpd_ssize_t mpd_etop(const mpd_context_t *ctx);
-EXTINLINE mpd_uint_t mpd_msword(const mpd_t *dec);
-EXTINLINE int mpd_word_digits(mpd_uint_t word);
-/* most significant digit of a word */
-EXTINLINE mpd_uint_t mpd_msd(mpd_uint_t word);
-/* least significant digit of a word */
-EXTINLINE mpd_uint_t mpd_lsd(mpd_uint_t word);
-/* coefficient size needed to store 'digits' */
-EXTINLINE mpd_ssize_t mpd_digits_to_size(mpd_ssize_t digits);
-/* number of digits in the exponent, undefined for MPD_SSIZE_MIN */
-EXTINLINE int mpd_exp_digits(mpd_ssize_t exp);
-EXTINLINE int mpd_iscanonical(const mpd_t *dec);
-EXTINLINE int mpd_isfinite(const mpd_t *dec);
-EXTINLINE int mpd_isinfinite(const mpd_t *dec);
-EXTINLINE int mpd_isinteger(const mpd_t *dec);
-EXTINLINE int mpd_isnan(const mpd_t *dec);
-EXTINLINE int mpd_isnegative(const mpd_t *dec);
-EXTINLINE int mpd_ispositive(const mpd_t *dec);
-EXTINLINE int mpd_isqnan(const mpd_t *dec);
-EXTINLINE int mpd_issigned(const mpd_t *dec);
-EXTINLINE int mpd_issnan(const mpd_t *dec);
-EXTINLINE int mpd_isspecial(const mpd_t *dec);
-EXTINLINE int mpd_iszero(const mpd_t *dec);
-/* undefined for special numbers */
-EXTINLINE int mpd_iszerocoeff(const mpd_t *dec);
-EXTINLINE int mpd_isnormal(const mpd_t *dec, const mpd_context_t *ctx);
-EXTINLINE int mpd_issubnormal(const mpd_t *dec, const mpd_context_t *ctx);
-/* odd word */
-EXTINLINE int mpd_isoddword(mpd_uint_t word);
-/* odd coefficient */
-EXTINLINE int mpd_isoddcoeff(const mpd_t *dec);
-/* odd decimal, only defined for integers */
-int mpd_isodd(const mpd_t *dec);
-/* even decimal, only defined for integers */
-int mpd_iseven(const mpd_t *dec);
-/* 0 if dec is positive, 1 if dec is negative */
-EXTINLINE uint8_t mpd_sign(const mpd_t *dec);
-/* 1 if dec is positive, -1 if dec is negative */
-EXTINLINE int mpd_arith_sign(const mpd_t *dec);
-EXTINLINE long mpd_radix(void);
-EXTINLINE int mpd_isdynamic(const mpd_t *dec);
-EXTINLINE int mpd_isstatic(const mpd_t *dec);
-EXTINLINE int mpd_isdynamic_data(const mpd_t *dec);
-EXTINLINE int mpd_isstatic_data(const mpd_t *dec);
-EXTINLINE int mpd_isshared_data(const mpd_t *dec);
-EXTINLINE int mpd_isconst_data(const mpd_t *dec);
-EXTINLINE mpd_ssize_t mpd_trail_zeros(const mpd_t *dec);
-
-
-/******************************************************************************/
-/* Set attributes of a decimal */
-/******************************************************************************/
-
-/* set number of decimal digits in the coefficient */
-EXTINLINE void mpd_setdigits(mpd_t *result);
-EXTINLINE void mpd_set_sign(mpd_t *result, uint8_t sign);
-/* copy sign from another decimal */
-EXTINLINE void mpd_signcpy(mpd_t *result, const mpd_t *a);
-EXTINLINE void mpd_set_infinity(mpd_t *result);
-EXTINLINE void mpd_set_qnan(mpd_t *result);
-EXTINLINE void mpd_set_snan(mpd_t *result);
-EXTINLINE void mpd_set_negative(mpd_t *result);
-EXTINLINE void mpd_set_positive(mpd_t *result);
-EXTINLINE void mpd_set_dynamic(mpd_t *result);
-EXTINLINE void mpd_set_static(mpd_t *result);
-EXTINLINE void mpd_set_dynamic_data(mpd_t *result);
-EXTINLINE void mpd_set_static_data(mpd_t *result);
-EXTINLINE void mpd_set_shared_data(mpd_t *result);
-EXTINLINE void mpd_set_const_data(mpd_t *result);
-EXTINLINE void mpd_clear_flags(mpd_t *result);
-EXTINLINE void mpd_set_flags(mpd_t *result, uint8_t flags);
-EXTINLINE void mpd_copy_flags(mpd_t *result, const mpd_t *a);
-
-
-/******************************************************************************/
-/* Error Macros */
-/******************************************************************************/
-
-#define mpd_err_fatal(...) \
- do {fprintf(stderr, "%s:%d: error: ", __FILE__, __LINE__); \
- fprintf(stderr, __VA_ARGS__); fputc('\n', stderr); \
- abort(); \
- } while (0)
-#define mpd_err_warn(...) \
- do {fprintf(stderr, "%s:%d: warning: ", __FILE__, __LINE__); \
- fprintf(stderr, __VA_ARGS__); fputc('\n', stderr); \
- } while (0)
-
-
-/******************************************************************************/
-/* Memory handling */
-/******************************************************************************/
-
-extern void *(* mpd_mallocfunc)(size_t size);
-extern void *(* mpd_callocfunc)(size_t nmemb, size_t size);
-extern void *(* mpd_reallocfunc)(void *ptr, size_t size);
-extern void (* mpd_free)(void *ptr);
-
-void *mpd_callocfunc_em(size_t nmemb, size_t size);
-
-void *mpd_alloc(mpd_size_t nmemb, mpd_size_t size);
-void *mpd_calloc(mpd_size_t nmemb, mpd_size_t size);
-void *mpd_realloc(void *ptr, mpd_size_t nmemb, mpd_size_t size, uint8_t *err);
-void *mpd_sh_alloc(mpd_size_t struct_size, mpd_size_t nmemb, mpd_size_t size);
-
-mpd_t *mpd_qnew(void);
-mpd_t *mpd_new(mpd_context_t *ctx);
-mpd_t *mpd_qnew_size(mpd_ssize_t nwords);
-EXTINLINE void mpd_del(mpd_t *dec);
-
-EXTINLINE void mpd_uint_zero(mpd_uint_t *dest, mpd_size_t len);
-EXTINLINE int mpd_qresize(mpd_t *result, mpd_ssize_t nwords, uint32_t *status);
-EXTINLINE int mpd_qresize_zero(mpd_t *result, mpd_ssize_t nwords, uint32_t *status);
-EXTINLINE void mpd_minalloc(mpd_t *result);
-
-int mpd_resize(mpd_t *result, mpd_ssize_t nwords, mpd_context_t *ctx);
-int mpd_resize_zero(mpd_t *result, mpd_ssize_t nwords, mpd_context_t *ctx);
-
-
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
-
-
-#ifdef __cplusplus
-} /* END extern "C" */
-#endif
-
-
-#endif /* LIBMPDEC_MPDECIMAL_H_ */
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <stddef.h>
-#include <stdint.h>
-
-
-/* Signaling wrappers for the quiet functions in mpdecimal.c. */
-
-
-char *
-mpd_format(const mpd_t *dec, const char *fmt, mpd_context_t *ctx)
-{
- char *ret;
- uint32_t status = 0;
- ret = mpd_qformat(dec, fmt, ctx, &status);
- mpd_addstatus_raise(ctx, status);
- return ret;
-}
-
-void
-mpd_import_u16(mpd_t *result, const uint16_t *srcdata, size_t srclen,
- uint8_t srcsign, uint32_t base, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qimport_u16(result, srcdata, srclen, srcsign, base, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_import_u32(mpd_t *result, const uint32_t *srcdata, size_t srclen,
- uint8_t srcsign, uint32_t base, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qimport_u32(result, srcdata, srclen, srcsign, base, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-size_t
-mpd_export_u16(uint16_t **rdata, size_t rlen, uint32_t base, const mpd_t *src,
- mpd_context_t *ctx)
-{
- size_t n;
- uint32_t status = 0;
- n = mpd_qexport_u16(rdata, rlen, base, src, &status);
- mpd_addstatus_raise(ctx, status);
- return n;
-}
-
-size_t
-mpd_export_u32(uint32_t **rdata, size_t rlen, uint32_t base, const mpd_t *src,
- mpd_context_t *ctx)
-{
- size_t n;
- uint32_t status = 0;
- n = mpd_qexport_u32(rdata, rlen, base, src, &status);
- mpd_addstatus_raise(ctx, status);
- return n;
-}
-
-void
-mpd_finalize(mpd_t *result, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qfinalize(result, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-int
-mpd_check_nan(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- if (mpd_qcheck_nan(result, a, ctx, &status)) {
- mpd_addstatus_raise(ctx, status);
- return 1;
- }
- return 0;
-}
-
-int
-mpd_check_nans(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- if (mpd_qcheck_nans(result, a, b, ctx, &status)) {
- mpd_addstatus_raise(ctx, status);
- return 1;
- }
- return 0;
-}
-
-void
-mpd_set_string(mpd_t *result, const char *s, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qset_string(result, s, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_maxcoeff(mpd_t *result, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qmaxcoeff(result, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-/* set static mpd from signed integer */
-void
-mpd_sset_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qsset_ssize(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_sset_i32(mpd_t *result, int32_t a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qsset_i32(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-#ifdef CONFIG_64
-void
-mpd_sset_i64(mpd_t *result, int64_t a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qsset_i64(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-#endif
-
-/* set static mpd from unsigned integer */
-void
-mpd_sset_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qsset_uint(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_sset_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qsset_u32(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-#ifdef CONFIG_64
-void
-mpd_sset_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qsset_u64(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-#endif
-
-/* set mpd from signed integer */
-void
-mpd_set_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qset_ssize(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_set_i32(mpd_t *result, int32_t a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qset_i32(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-#ifndef LEGACY_COMPILER
-void
-mpd_set_i64(mpd_t *result, int64_t a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qset_i64(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-#endif
-
-/* set mpd from unsigned integer */
-void
-mpd_set_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qset_uint(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_set_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qset_u32(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-#ifndef LEGACY_COMPILER
-void
-mpd_set_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qset_u64(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-#endif
-
-/* convert mpd to signed integer */
-mpd_ssize_t
-mpd_get_ssize(const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_ssize_t ret;
-
- ret = mpd_qget_ssize(a, &status);
- mpd_addstatus_raise(ctx, status);
- return ret;
-}
-
-int32_t
-mpd_get_i32(const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- int32_t ret;
-
- ret = mpd_qget_i32(a, &status);
- mpd_addstatus_raise(ctx, status);
- return ret;
-}
-
-#ifndef LEGACY_COMPILER
-int64_t
-mpd_get_i64(const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- int64_t ret;
-
- ret = mpd_qget_i64(a, &status);
- mpd_addstatus_raise(ctx, status);
- return ret;
-}
-#endif
-
-mpd_uint_t
-mpd_get_uint(const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_uint_t ret;
-
- ret = mpd_qget_uint(a, &status);
- mpd_addstatus_raise(ctx, status);
- return ret;
-}
-
-mpd_uint_t
-mpd_abs_uint(const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_uint_t ret;
-
- ret = mpd_qabs_uint(a, &status);
- mpd_addstatus_raise(ctx, status);
- return ret;
-}
-
-uint32_t
-mpd_get_u32(const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- uint32_t ret;
-
- ret = mpd_qget_u32(a, &status);
- mpd_addstatus_raise(ctx, status);
- return ret;
-}
-
-#ifndef LEGACY_COMPILER
-uint64_t
-mpd_get_u64(const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- uint64_t ret;
-
- ret = mpd_qget_u64(a, &status);
- mpd_addstatus_raise(ctx, status);
- return ret;
-}
-#endif
-
-void
-mpd_and(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qand(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_copy(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- if (!mpd_qcopy(result, a, &status)) {
- mpd_addstatus_raise(ctx, status);
- }
-}
-
-void
-mpd_canonical(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- mpd_copy(result, a, ctx);
-}
-
-void
-mpd_copy_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- if (!mpd_qcopy_abs(result, a, &status)) {
- mpd_addstatus_raise(ctx, status);
- }
-}
-
-void
-mpd_copy_negate(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- if (!mpd_qcopy_negate(result, a, &status)) {
- mpd_addstatus_raise(ctx, status);
- }
-}
-
-void
-mpd_copy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- if (!mpd_qcopy_sign(result, a, b, &status)) {
- mpd_addstatus_raise(ctx, status);
- }
-}
-
-void
-mpd_invert(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qinvert(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_logb(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qlogb(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_or(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qor(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_rotate(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qrotate(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_scaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qscaleb(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_shiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qshiftl(result, a, n, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-mpd_uint_t
-mpd_shiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_uint_t rnd;
-
- rnd = mpd_qshiftr(result, a, n, &status);
- mpd_addstatus_raise(ctx, status);
- return rnd;
-}
-
-void
-mpd_shiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qshiftn(result, a, n, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_shift(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qshift(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_xor(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qxor(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qabs(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-int
-mpd_cmp(const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- int c;
- c = mpd_qcmp(a, b, &status);
- mpd_addstatus_raise(ctx, status);
- return c;
-}
-
-int
-mpd_compare(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- int c;
- c = mpd_qcompare(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
- return c;
-}
-
-int
-mpd_compare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- int c;
- c = mpd_qcompare_signal(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
- return c;
-}
-
-void
-mpd_add(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qadd(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_sub(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qsub(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_add_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qadd_ssize(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_add_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qadd_i32(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-#ifndef LEGACY_COMPILER
-void
-mpd_add_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qadd_i64(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-#endif
-
-void
-mpd_add_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qadd_uint(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_add_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qadd_u32(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-#ifndef LEGACY_COMPILER
-void
-mpd_add_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qadd_u64(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-#endif
-
-void
-mpd_sub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qsub_ssize(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_sub_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qsub_i32(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-#ifndef LEGACY_COMPILER
-void
-mpd_sub_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qsub_i64(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-#endif
-
-void
-mpd_sub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qsub_uint(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_sub_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qsub_u32(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-#ifndef LEGACY_COMPILER
-void
-mpd_sub_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qsub_u64(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-#endif
-
-void
-mpd_div(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qdiv(q, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_div_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qdiv_ssize(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_div_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qdiv_i32(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-#ifndef LEGACY_COMPILER
-void
-mpd_div_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qdiv_i64(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-#endif
-
-void
-mpd_div_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qdiv_uint(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_div_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qdiv_u32(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-#ifndef LEGACY_COMPILER
-void
-mpd_div_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qdiv_u64(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-#endif
-
-void
-mpd_divmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qdivmod(q, r, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_divint(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qdivint(q, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_exp(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qexp(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_fma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c,
- mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qfma(result, a, b, c, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_ln(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qln(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_log10(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qlog10(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_max(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qmax(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_max_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qmax_mag(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_min(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qmin(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_min_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qmin_mag(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qminus(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_mul(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qmul(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_mul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qmul_ssize(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_mul_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qmul_i32(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-#ifndef LEGACY_COMPILER
-void
-mpd_mul_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qmul_i64(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-#endif
-
-void
-mpd_mul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qmul_uint(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_mul_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qmul_u32(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-#ifndef LEGACY_COMPILER
-void
-mpd_mul_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qmul_u64(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-#endif
-
-void
-mpd_next_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qnext_minus(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_next_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qnext_plus(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_next_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qnext_toward(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qplus(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_pow(mpd_t *result, const mpd_t *base, const mpd_t *exp, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qpow(result, base, exp, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_powmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_t *mod,
- mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qpowmod(result, base, exp, mod, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_quantize(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qquantize(result, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_rescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qrescale(result, a, exp, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_reduce(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qreduce(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_rem(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qrem(r, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_rem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qrem_near(r, a, b, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_round_to_intx(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qround_to_intx(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_round_to_int(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qround_to_int(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_trunc(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qtrunc(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_floor(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qfloor(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_ceil(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qceil(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_sqrt(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qsqrt(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
-
-void
-mpd_invroot(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
-{
- uint32_t status = 0;
- mpd_qinvroot(result, a, ctx, &status);
- mpd_addstatus_raise(ctx, status);
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <assert.h>
-#include <stdlib.h>
-
-#include "bits.h"
-#include "numbertheory.h"
-#include "umodarith.h"
-
-
-/* Bignum: Initialize the Number Theoretic Transform. */
-
-
-/*
- * Return the nth root of unity in F(p). This corresponds to e**((2*pi*i)/n)
- * in the Fourier transform. We have w**n == 1 (mod p).
- * n := transform length.
- * sign := -1 for forward transform, 1 for backward transform.
- * modnum := one of {P1, P2, P3}.
- */
-mpd_uint_t
-_mpd_getkernel(mpd_uint_t n, int sign, int modnum)
-{
- mpd_uint_t umod, p, r, xi;
-#ifdef PPRO
- double dmod;
- uint32_t dinvmod[3];
-#endif
-
- SETMODULUS(modnum);
- r = mpd_roots[modnum]; /* primitive root of F(p) */
- p = umod;
- xi = (p-1) / n;
-
- if (sign == -1)
- return POWMOD(r, (p-1-xi));
- else
- return POWMOD(r, xi);
-}
-
-/*
- * Initialize and return transform parameters.
- * n := transform length.
- * sign := -1 for forward transform, 1 for backward transform.
- * modnum := one of {P1, P2, P3}.
- */
-struct fnt_params *
-_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum)
-{
- struct fnt_params *tparams;
- mpd_uint_t umod;
-#ifdef PPRO
- double dmod;
- uint32_t dinvmod[3];
-#endif
- mpd_uint_t kernel, w;
- mpd_uint_t i;
- mpd_size_t nhalf;
-
- assert(ispower2(n));
- assert(sign == -1 || sign == 1);
- assert(P1 <= modnum && modnum <= P3);
-
- nhalf = n/2;
- tparams = mpd_sh_alloc(sizeof *tparams, nhalf, sizeof (mpd_uint_t));
- if (tparams == NULL) {
- return NULL;
- }
-
- SETMODULUS(modnum);
- kernel = _mpd_getkernel(n, sign, modnum);
-
- tparams->modnum = modnum;
- tparams->modulus = umod;
- tparams->kernel = kernel;
-
- /* wtable[] := w**0, w**1, ..., w**(nhalf-1) */
- w = 1;
- for (i = 0; i < nhalf; i++) {
- tparams->wtable[i] = w;
- w = MULMOD(w, kernel);
- }
-
- return tparams;
-}
-
-/* Initialize wtable of size three. */
-void
-_mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum)
-{
- mpd_uint_t umod;
-#ifdef PPRO
- double dmod;
- uint32_t dinvmod[3];
-#endif
- mpd_uint_t kernel;
-
- SETMODULUS(modnum);
- kernel = _mpd_getkernel(3, sign, modnum);
-
- w3table[0] = 1;
- w3table[1] = kernel;
- w3table[2] = POWMOD(kernel, 2);
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_NUMBERTHEORY_H_
-#define LIBMPDEC_NUMBERTHEORY_H_
-
-
-#include "mpdecimal.h"
-#include "constants.h"
-
-
-/* Internal header file: all symbols have local scope in the DSO */
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
-
-
-/* transform parameters */
-struct fnt_params {
- int modnum;
- mpd_uint_t modulus;
- mpd_uint_t kernel;
- mpd_uint_t wtable[];
-};
-
-
-mpd_uint_t _mpd_getkernel(mpd_uint_t n, int sign, int modnum);
-struct fnt_params *_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum);
-void _mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum);
-
-
-#ifdef PPRO
-static inline void
-ppro_setmodulus(int modnum, mpd_uint_t *umod, double *dmod, uint32_t dinvmod[3])
-{
- *dmod = *umod = mpd_moduli[modnum];
- dinvmod[0] = mpd_invmoduli[modnum][0];
- dinvmod[1] = mpd_invmoduli[modnum][1];
- dinvmod[2] = mpd_invmoduli[modnum][2];
-}
-#else
-static inline void
-std_setmodulus(int modnum, mpd_uint_t *umod)
-{
- *umod = mpd_moduli[modnum];
-}
-#endif
-
-
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
-
-
-#endif /* LIBMPDEC_NUMBERTHEORY_H_ */
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <assert.h>
-#include <stdio.h>
-
-#include "bits.h"
-#include "constants.h"
-#include "difradix2.h"
-#include "numbertheory.h"
-#include "sixstep.h"
-#include "transpose.h"
-#include "umodarith.h"
-
-
-/* Bignum: Cache efficient Matrix Fourier Transform for arrays of the
- form 2**n (See literature/six-step.txt). */
-
-
-/* forward transform with sign = -1 */
-int
-six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
-{
- struct fnt_params *tparams;
- mpd_size_t log2n, C, R;
- mpd_uint_t kernel;
- mpd_uint_t umod;
-#ifdef PPRO
- double dmod;
- uint32_t dinvmod[3];
-#endif
- mpd_uint_t *x, w0, w1, wstep;
- mpd_size_t i, k;
-
-
- assert(ispower2(n));
- assert(n >= 16);
- assert(n <= MPD_MAXTRANSFORM_2N);
-
- log2n = mpd_bsr(n);
- C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */
- R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */
-
-
- /* Transpose the matrix. */
- if (!transpose_pow2(a, R, C)) {
- return 0;
- }
-
- /* Length R transform on the rows. */
- if ((tparams = _mpd_init_fnt_params(R, -1, modnum)) == NULL) {
- return 0;
- }
- for (x = a; x < a+n; x += R) {
- fnt_dif2(x, R, tparams);
- }
-
- /* Transpose the matrix. */
- if (!transpose_pow2(a, C, R)) {
- mpd_free(tparams);
- return 0;
- }
-
- /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
- SETMODULUS(modnum);
- kernel = _mpd_getkernel(n, -1, modnum);
- for (i = 1; i < R; i++) {
- w0 = 1; /* r**(i*0): initial value for k=0 */
- w1 = POWMOD(kernel, i); /* r**(i*1): initial value for k=1 */
- wstep = MULMOD(w1, w1); /* r**(2*i) */
- for (k = 0; k < C; k += 2) {
- mpd_uint_t x0 = a[i*C+k];
- mpd_uint_t x1 = a[i*C+k+1];
- MULMOD2(&x0, w0, &x1, w1);
- MULMOD2C(&w0, &w1, wstep); /* r**(i*(k+2)) = r**(i*k) * r**(2*i) */
- a[i*C+k] = x0;
- a[i*C+k+1] = x1;
- }
- }
-
- /* Length C transform on the rows. */
- if (C != R) {
- mpd_free(tparams);
- if ((tparams = _mpd_init_fnt_params(C, -1, modnum)) == NULL) {
- return 0;
- }
- }
- for (x = a; x < a+n; x += C) {
- fnt_dif2(x, C, tparams);
- }
- mpd_free(tparams);
-
-#if 0
- /* An unordered transform is sufficient for convolution. */
- /* Transpose the matrix. */
- if (!transpose_pow2(a, R, C)) {
- return 0;
- }
-#endif
-
- return 1;
-}
-
-
-/* reverse transform, sign = 1 */
-int
-inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
-{
- struct fnt_params *tparams;
- mpd_size_t log2n, C, R;
- mpd_uint_t kernel;
- mpd_uint_t umod;
-#ifdef PPRO
- double dmod;
- uint32_t dinvmod[3];
-#endif
- mpd_uint_t *x, w0, w1, wstep;
- mpd_size_t i, k;
-
-
- assert(ispower2(n));
- assert(n >= 16);
- assert(n <= MPD_MAXTRANSFORM_2N);
-
- log2n = mpd_bsr(n);
- C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */
- R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */
-
-
-#if 0
- /* An unordered transform is sufficient for convolution. */
- /* Transpose the matrix, producing an R*C matrix. */
- if (!transpose_pow2(a, C, R)) {
- return 0;
- }
-#endif
-
- /* Length C transform on the rows. */
- if ((tparams = _mpd_init_fnt_params(C, 1, modnum)) == NULL) {
- return 0;
- }
- for (x = a; x < a+n; x += C) {
- fnt_dif2(x, C, tparams);
- }
-
- /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
- SETMODULUS(modnum);
- kernel = _mpd_getkernel(n, 1, modnum);
- for (i = 1; i < R; i++) {
- w0 = 1;
- w1 = POWMOD(kernel, i);
- wstep = MULMOD(w1, w1);
- for (k = 0; k < C; k += 2) {
- mpd_uint_t x0 = a[i*C+k];
- mpd_uint_t x1 = a[i*C+k+1];
- MULMOD2(&x0, w0, &x1, w1);
- MULMOD2C(&w0, &w1, wstep);
- a[i*C+k] = x0;
- a[i*C+k+1] = x1;
- }
- }
-
- /* Transpose the matrix. */
- if (!transpose_pow2(a, R, C)) {
- mpd_free(tparams);
- return 0;
- }
-
- /* Length R transform on the rows. */
- if (R != C) {
- mpd_free(tparams);
- if ((tparams = _mpd_init_fnt_params(R, 1, modnum)) == NULL) {
- return 0;
- }
- }
- for (x = a; x < a+n; x += R) {
- fnt_dif2(x, R, tparams);
- }
- mpd_free(tparams);
-
- /* Transpose the matrix. */
- if (!transpose_pow2(a, C, R)) {
- return 0;
- }
-
- return 1;
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_SIXSTEP_H_
-#define LIBMPDEC_SIXSTEP_H_
-
-
-#include "mpdecimal.h"
-
-
-/* Internal header file: all symbols have local scope in the DSO */
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
-
-
-int six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum);
-int inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum);
-
-
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
-
-
-#endif /* LIBMPDEC_SIXSTEP_H_ */
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#include "mpdecimal.h"
-
-#include <assert.h>
-#include <limits.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-
-#include "bits.h"
-#include "constants.h"
-#include "transpose.h"
-#include "typearith.h"
-
-
-#define BUFSIZE 4096
-#define SIDE 128
-
-
-/* Bignum: The transpose functions are used for very large transforms
- in sixstep.c and fourstep.c. */
-
-
-/* Definition of the matrix transpose */
-void
-std_trans(mpd_uint_t dest[], mpd_uint_t src[], mpd_size_t rows, mpd_size_t cols)
-{
- mpd_size_t idest, isrc;
- mpd_size_t r, c;
-
- for (r = 0; r < rows; r++) {
- isrc = r * cols;
- idest = r;
- for (c = 0; c < cols; c++) {
- dest[idest] = src[isrc];
- isrc += 1;
- idest += rows;
- }
- }
-}
-
-/*
- * Swap half-rows of 2^n * (2*2^n) matrix.
- * FORWARD_CYCLE: even/odd permutation of the halfrows.
- * BACKWARD_CYCLE: reverse the even/odd permutation.
- */
-static int
-swap_halfrows_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols, int dir)
-{
- mpd_uint_t buf1[BUFSIZE];
- mpd_uint_t buf2[BUFSIZE];
- mpd_uint_t *readbuf, *writebuf, *hp;
- mpd_size_t *done, dbits;
- mpd_size_t b = BUFSIZE, stride;
- mpd_size_t hn, hmax; /* halfrow number */
- mpd_size_t m, r=0;
- mpd_size_t offset;
- mpd_size_t next;
-
-
- assert(cols == mul_size_t(2, rows));
-
- if (dir == FORWARD_CYCLE) {
- r = rows;
- }
- else if (dir == BACKWARD_CYCLE) {
- r = 2;
- }
- else {
- abort(); /* GCOV_NOT_REACHED */
- }
-
- m = cols - 1;
- hmax = rows; /* cycles start at odd halfrows */
- dbits = 8 * sizeof *done;
- if ((done = mpd_calloc(hmax/(sizeof *done) + 1, sizeof *done)) == NULL) {
- return 0;
- }
-
- for (hn = 1; hn <= hmax; hn += 2) {
-
- if (done[hn/dbits] & mpd_bits[hn%dbits]) {
- continue;
- }
-
- readbuf = buf1; writebuf = buf2;
-
- for (offset = 0; offset < cols/2; offset += b) {
-
- stride = (offset + b < cols/2) ? b : cols/2-offset;
-
- hp = matrix + hn*cols/2;
- memcpy(readbuf, hp+offset, stride*(sizeof *readbuf));
- pointerswap(&readbuf, &writebuf);
-
- next = mulmod_size_t(hn, r, m);
- hp = matrix + next*cols/2;
-
- while (next != hn) {
-
- memcpy(readbuf, hp+offset, stride*(sizeof *readbuf));
- memcpy(hp+offset, writebuf, stride*(sizeof *writebuf));
- pointerswap(&readbuf, &writebuf);
-
- done[next/dbits] |= mpd_bits[next%dbits];
-
- next = mulmod_size_t(next, r, m);
- hp = matrix + next*cols/2;
-
- }
-
- memcpy(hp+offset, writebuf, stride*(sizeof *writebuf));
-
- done[hn/dbits] |= mpd_bits[hn%dbits];
- }
- }
-
- mpd_free(done);
- return 1;
-}
-
-/* In-place transpose of a square matrix */
-static inline void
-squaretrans(mpd_uint_t *buf, mpd_size_t cols)
-{
- mpd_uint_t tmp;
- mpd_size_t idest, isrc;
- mpd_size_t r, c;
-
- for (r = 0; r < cols; r++) {
- c = r+1;
- isrc = r*cols + c;
- idest = c*cols + r;
- for (c = r+1; c < cols; c++) {
- tmp = buf[isrc];
- buf[isrc] = buf[idest];
- buf[idest] = tmp;
- isrc += 1;
- idest += cols;
- }
- }
-}
-
-/*
- * Transpose 2^n * 2^n matrix. For cache efficiency, the matrix is split into
- * square blocks with side length 'SIDE'. First, the blocks are transposed,
- * then a square transposition is done on each individual block.
- */
-static void
-squaretrans_pow2(mpd_uint_t *matrix, mpd_size_t size)
-{
- mpd_uint_t buf1[SIDE*SIDE];
- mpd_uint_t buf2[SIDE*SIDE];
- mpd_uint_t *to, *from;
- mpd_size_t b = size;
- mpd_size_t r, c;
- mpd_size_t i;
-
- while (b > SIDE) b >>= 1;
-
- for (r = 0; r < size; r += b) {
-
- for (c = r; c < size; c += b) {
-
- from = matrix + r*size + c;
- to = buf1;
- for (i = 0; i < b; i++) {
- memcpy(to, from, b*(sizeof *to));
- from += size;
- to += b;
- }
- squaretrans(buf1, b);
-
- if (r == c) {
- to = matrix + r*size + c;
- from = buf1;
- for (i = 0; i < b; i++) {
- memcpy(to, from, b*(sizeof *to));
- from += b;
- to += size;
- }
- continue;
- }
- else {
- from = matrix + c*size + r;
- to = buf2;
- for (i = 0; i < b; i++) {
- memcpy(to, from, b*(sizeof *to));
- from += size;
- to += b;
- }
- squaretrans(buf2, b);
-
- to = matrix + c*size + r;
- from = buf1;
- for (i = 0; i < b; i++) {
- memcpy(to, from, b*(sizeof *to));
- from += b;
- to += size;
- }
-
- to = matrix + r*size + c;
- from = buf2;
- for (i = 0; i < b; i++) {
- memcpy(to, from, b*(sizeof *to));
- from += b;
- to += size;
- }
- }
- }
- }
-
-}
-
-/*
- * In-place transposition of a 2^n x 2^n or a 2^n x (2*2^n)
- * or a (2*2^n) x 2^n matrix.
- */
-int
-transpose_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols)
-{
- mpd_size_t size = mul_size_t(rows, cols);
-
- assert(ispower2(rows));
- assert(ispower2(cols));
-
- if (cols == rows) {
- squaretrans_pow2(matrix, rows);
- }
- else if (cols == mul_size_t(2, rows)) {
- if (!swap_halfrows_pow2(matrix, rows, cols, FORWARD_CYCLE)) {
- return 0;
- }
- squaretrans_pow2(matrix, rows);
- squaretrans_pow2(matrix+(size/2), rows);
- }
- else if (rows == mul_size_t(2, cols)) {
- squaretrans_pow2(matrix, cols);
- squaretrans_pow2(matrix+(size/2), cols);
- if (!swap_halfrows_pow2(matrix, cols, rows, BACKWARD_CYCLE)) {
- return 0;
- }
- }
- else {
- abort(); /* GCOV_NOT_REACHED */
- }
-
- return 1;
-}
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_TRANSPOSE_H_
-#define LIBMPDEC_TRANSPOSE_H_
-
-
-#include "mpdecimal.h"
-
-
-/* Internal header file: all symbols have local scope in the DSO */
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
-
-
-enum {FORWARD_CYCLE, BACKWARD_CYCLE};
-
-
-void std_trans(mpd_uint_t dest[], mpd_uint_t src[], mpd_size_t rows, mpd_size_t cols);
-int transpose_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols);
-void transpose_3xpow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols);
-
-
-static inline void pointerswap(mpd_uint_t **a, mpd_uint_t **b)
-{
- mpd_uint_t *tmp;
-
- tmp = *b;
- *b = *a;
- *a = tmp;
-}
-
-
-MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
-
-
-#endif /* LIBMPDEC_TRANSPOSE_H_ */
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_TYPEARITH_H_
-#define LIBMPDEC_TYPEARITH_H_
-
-
-#include "mpdecimal.h"
-
-#include <assert.h>
-
-
-/*****************************************************************************/
-/* Low level native arithmetic on basic types */
-/*****************************************************************************/
-
-
-/** ------------------------------------------------------------
- ** Double width multiplication and division
- ** ------------------------------------------------------------
- */
-
-#if defined(CONFIG_64)
-#if defined(ANSI)
-#if defined(HAVE_UINT128_T)
-static inline void
-_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
-{
- __uint128_t hl;
-
- hl = (__uint128_t)a * b;
-
- *hi = hl >> 64;
- *lo = (mpd_uint_t)hl;
-}
-
-static inline void
-_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
- mpd_uint_t d)
-{
- __uint128_t hl;
-
- hl = ((__uint128_t)hi<<64) + lo;
- *q = (mpd_uint_t)(hl / d); /* quotient is known to fit */
- *r = (mpd_uint_t)(hl - (__uint128_t)(*q) * d);
-}
-#else
-static inline void
-_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
-{
- uint32_t w[4], carry;
- uint32_t ah, al, bh, bl;
- uint64_t hl;
-
- ah = (uint32_t)(a>>32); al = (uint32_t)a;
- bh = (uint32_t)(b>>32); bl = (uint32_t)b;
-
- hl = (uint64_t)al * bl;
- w[0] = (uint32_t)hl;
- carry = (uint32_t)(hl>>32);
-
- hl = (uint64_t)ah * bl + carry;
- w[1] = (uint32_t)hl;
- w[2] = (uint32_t)(hl>>32);
-
- hl = (uint64_t)al * bh + w[1];
- w[1] = (uint32_t)hl;
- carry = (uint32_t)(hl>>32);
-
- hl = ((uint64_t)ah * bh + w[2]) + carry;
- w[2] = (uint32_t)hl;
- w[3] = (uint32_t)(hl>>32);
-
- *hi = ((uint64_t)w[3]<<32) + w[2];
- *lo = ((uint64_t)w[1]<<32) + w[0];
-}
-
-/*
- * By Henry S. Warren: http://www.hackersdelight.org/HDcode/divlu.c.txt
- * http://www.hackersdelight.org/permissions.htm:
- * "You are free to use, copy, and distribute any of the code on this web
- * site, whether modified by you or not. You need not give attribution."
- *
- * Slightly modified, comments are mine.
- */
-static inline int
-nlz(uint64_t x)
-{
- int n;
-
- if (x == 0) return(64);
-
- n = 0;
- if (x <= 0x00000000FFFFFFFF) {n = n +32; x = x <<32;}
- if (x <= 0x0000FFFFFFFFFFFF) {n = n +16; x = x <<16;}
- if (x <= 0x00FFFFFFFFFFFFFF) {n = n + 8; x = x << 8;}
- if (x <= 0x0FFFFFFFFFFFFFFF) {n = n + 4; x = x << 4;}
- if (x <= 0x3FFFFFFFFFFFFFFF) {n = n + 2; x = x << 2;}
- if (x <= 0x7FFFFFFFFFFFFFFF) {n = n + 1;}
-
- return n;
-}
-
-static inline void
-_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t u1, mpd_uint_t u0,
- mpd_uint_t v)
-{
- const mpd_uint_t b = 4294967296;
- mpd_uint_t un1, un0,
- vn1, vn0,
- q1, q0,
- un32, un21, un10,
- rhat, t;
- int s;
-
- assert(u1 < v);
-
- s = nlz(v);
- v = v << s;
- vn1 = v >> 32;
- vn0 = v & 0xFFFFFFFF;
-
- t = (s == 0) ? 0 : u0 >> (64 - s);
- un32 = (u1 << s) | t;
- un10 = u0 << s;
-
- un1 = un10 >> 32;
- un0 = un10 & 0xFFFFFFFF;
-
- q1 = un32 / vn1;
- rhat = un32 - q1*vn1;
-again1:
- if (q1 >= b || q1*vn0 > b*rhat + un1) {
- q1 = q1 - 1;
- rhat = rhat + vn1;
- if (rhat < b) goto again1;
- }
-
- /*
- * Before again1 we had:
- * (1) q1*vn1 + rhat = un32
- * (2) q1*vn1*b + rhat*b + un1 = un32*b + un1
- *
- * The statements inside the if-clause do not change the value
- * of the left-hand side of (2), and the loop is only exited
- * if q1*vn0 <= rhat*b + un1, so:
- *
- * (3) q1*vn1*b + q1*vn0 <= un32*b + un1
- * (4) q1*v <= un32*b + un1
- * (5) 0 <= un32*b + un1 - q1*v
- *
- * By (5) we are certain that the possible add-back step from
- * Knuth's algorithm D is never required.
- *
- * Since the final quotient is less than 2**64, the following
- * must be true:
- *
- * (6) un32*b + un1 - q1*v <= UINT64_MAX
- *
- * This means that in the following line, the high words
- * of un32*b and q1*v can be discarded without any effect
- * on the result.
- */
- un21 = un32*b + un1 - q1*v;
-
- q0 = un21 / vn1;
- rhat = un21 - q0*vn1;
-again2:
- if (q0 >= b || q0*vn0 > b*rhat + un0) {
- q0 = q0 - 1;
- rhat = rhat + vn1;
- if (rhat < b) goto again2;
- }
-
- *q = q1*b + q0;
- *r = (un21*b + un0 - q0*v) >> s;
-}
-#endif
-
-/* END ANSI */
-#elif defined(ASM)
-static inline void
-_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
-{
- mpd_uint_t h, l;
-
- __asm__ ( "mulq %3\n\t"
- : "=d" (h), "=a" (l)
- : "%a" (a), "rm" (b)
- : "cc"
- );
-
- *hi = h;
- *lo = l;
-}
-
-static inline void
-_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
- mpd_uint_t d)
-{
- mpd_uint_t qq, rr;
-
- __asm__ ( "divq %4\n\t"
- : "=a" (qq), "=d" (rr)
- : "a" (lo), "d" (hi), "rm" (d)
- : "cc"
- );
-
- *q = qq;
- *r = rr;
-}
-/* END GCC ASM */
-#elif defined(MASM)
-#include <intrin.h>
-#pragma intrinsic(_umul128)
-
-static inline void
-_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
-{
- *lo = _umul128(a, b, hi);
-}
-
-void _mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
- mpd_uint_t d);
-
-/* END MASM (_MSC_VER) */
-#else
- #error "need platform specific 128 bit multiplication and division"
-#endif
-
-#define DIVMOD(q, r, v, d) *q = v / d; *r = v - *q * d
-static inline void
-_mpd_divmod_pow10(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t exp)
-{
- assert(exp <= 19);
-
- if (exp <= 9) {
- if (exp <= 4) {
- switch (exp) {
- case 0: *q = v; *r = 0; break;
- case 1: DIVMOD(q, r, v, 10UL); break;
- case 2: DIVMOD(q, r, v, 100UL); break;
- case 3: DIVMOD(q, r, v, 1000UL); break;
- case 4: DIVMOD(q, r, v, 10000UL); break;
- }
- }
- else {
- switch (exp) {
- case 5: DIVMOD(q, r, v, 100000UL); break;
- case 6: DIVMOD(q, r, v, 1000000UL); break;
- case 7: DIVMOD(q, r, v, 10000000UL); break;
- case 8: DIVMOD(q, r, v, 100000000UL); break;
- case 9: DIVMOD(q, r, v, 1000000000UL); break;
- }
- }
- }
- else {
- if (exp <= 14) {
- switch (exp) {
- case 10: DIVMOD(q, r, v, 10000000000ULL); break;
- case 11: DIVMOD(q, r, v, 100000000000ULL); break;
- case 12: DIVMOD(q, r, v, 1000000000000ULL); break;
- case 13: DIVMOD(q, r, v, 10000000000000ULL); break;
- case 14: DIVMOD(q, r, v, 100000000000000ULL); break;
- }
- }
- else {
- switch (exp) {
- case 15: DIVMOD(q, r, v, 1000000000000000ULL); break;
- case 16: DIVMOD(q, r, v, 10000000000000000ULL); break;
- case 17: DIVMOD(q, r, v, 100000000000000000ULL); break;
- case 18: DIVMOD(q, r, v, 1000000000000000000ULL); break;
- case 19: DIVMOD(q, r, v, 10000000000000000000ULL); break; /* GCOV_NOT_REACHED */
- }
- }
- }
-}
-
-/* END CONFIG_64 */
-#elif defined(CONFIG_32)
-#if defined(ANSI)
-#if !defined(LEGACY_COMPILER)
-static inline void
-_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
-{
- mpd_uuint_t hl;
-
- hl = (mpd_uuint_t)a * b;
-
- *hi = hl >> 32;
- *lo = (mpd_uint_t)hl;
-}
-
-static inline void
-_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
- mpd_uint_t d)
-{
- mpd_uuint_t hl;
-
- hl = ((mpd_uuint_t)hi<<32) + lo;
- *q = (mpd_uint_t)(hl / d); /* quotient is known to fit */
- *r = (mpd_uint_t)(hl - (mpd_uuint_t)(*q) * d);
-}
-/* END ANSI + uint64_t */
-#else
-static inline void
-_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
-{
- uint16_t w[4], carry;
- uint16_t ah, al, bh, bl;
- uint32_t hl;
-
- ah = (uint16_t)(a>>16); al = (uint16_t)a;
- bh = (uint16_t)(b>>16); bl = (uint16_t)b;
-
- hl = (uint32_t)al * bl;
- w[0] = (uint16_t)hl;
- carry = (uint16_t)(hl>>16);
-
- hl = (uint32_t)ah * bl + carry;
- w[1] = (uint16_t)hl;
- w[2] = (uint16_t)(hl>>16);
-
- hl = (uint32_t)al * bh + w[1];
- w[1] = (uint16_t)hl;
- carry = (uint16_t)(hl>>16);
-
- hl = ((uint32_t)ah * bh + w[2]) + carry;
- w[2] = (uint16_t)hl;
- w[3] = (uint16_t)(hl>>16);
-
- *hi = ((uint32_t)w[3]<<16) + w[2];
- *lo = ((uint32_t)w[1]<<16) + w[0];
-}
-
-/*
- * By Henry S. Warren: http://www.hackersdelight.org/HDcode/divlu.c.txt
- * http://www.hackersdelight.org/permissions.htm:
- * "You are free to use, copy, and distribute any of the code on this web
- * site, whether modified by you or not. You need not give attribution."
- *
- * Slightly modified, comments are mine.
- */
-static inline int
-nlz(uint32_t x)
-{
- int n;
-
- if (x == 0) return(32);
-
- n = 0;
- if (x <= 0x0000FFFF) {n = n +16; x = x <<16;}
- if (x <= 0x00FFFFFF) {n = n + 8; x = x << 8;}
- if (x <= 0x0FFFFFFF) {n = n + 4; x = x << 4;}
- if (x <= 0x3FFFFFFF) {n = n + 2; x = x << 2;}
- if (x <= 0x7FFFFFFF) {n = n + 1;}
-
- return n;
-}
-
-static inline void
-_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t u1, mpd_uint_t u0,
- mpd_uint_t v)
-{
- const mpd_uint_t b = 65536;
- mpd_uint_t un1, un0,
- vn1, vn0,
- q1, q0,
- un32, un21, un10,
- rhat, t;
- int s;
-
- assert(u1 < v);
-
- s = nlz(v);
- v = v << s;
- vn1 = v >> 16;
- vn0 = v & 0xFFFF;
-
- t = (s == 0) ? 0 : u0 >> (32 - s);
- un32 = (u1 << s) | t;
- un10 = u0 << s;
-
- un1 = un10 >> 16;
- un0 = un10 & 0xFFFF;
-
- q1 = un32 / vn1;
- rhat = un32 - q1*vn1;
-again1:
- if (q1 >= b || q1*vn0 > b*rhat + un1) {
- q1 = q1 - 1;
- rhat = rhat + vn1;
- if (rhat < b) goto again1;
- }
-
- /*
- * Before again1 we had:
- * (1) q1*vn1 + rhat = un32
- * (2) q1*vn1*b + rhat*b + un1 = un32*b + un1
- *
- * The statements inside the if-clause do not change the value
- * of the left-hand side of (2), and the loop is only exited
- * if q1*vn0 <= rhat*b + un1, so:
- *
- * (3) q1*vn1*b + q1*vn0 <= un32*b + un1
- * (4) q1*v <= un32*b + un1
- * (5) 0 <= un32*b + un1 - q1*v
- *
- * By (5) we are certain that the possible add-back step from
- * Knuth's algorithm D is never required.
- *
- * Since the final quotient is less than 2**32, the following
- * must be true:
- *
- * (6) un32*b + un1 - q1*v <= UINT32_MAX
- *
- * This means that in the following line, the high words
- * of un32*b and q1*v can be discarded without any effect
- * on the result.
- */
- un21 = un32*b + un1 - q1*v;
-
- q0 = un21 / vn1;
- rhat = un21 - q0*vn1;
-again2:
- if (q0 >= b || q0*vn0 > b*rhat + un0) {
- q0 = q0 - 1;
- rhat = rhat + vn1;
- if (rhat < b) goto again2;
- }
-
- *q = q1*b + q0;
- *r = (un21*b + un0 - q0*v) >> s;
-}
-#endif /* END ANSI + LEGACY_COMPILER */
-
-/* END ANSI */
-#elif defined(ASM)
-static inline void
-_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
-{
- mpd_uint_t h, l;
-
- __asm__ ( "mull %3\n\t"
- : "=d" (h), "=a" (l)
- : "%a" (a), "rm" (b)
- : "cc"
- );
-
- *hi = h;
- *lo = l;
-}
-
-static inline void
-_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
- mpd_uint_t d)
-{
- mpd_uint_t qq, rr;
-
- __asm__ ( "divl %4\n\t"
- : "=a" (qq), "=d" (rr)
- : "a" (lo), "d" (hi), "rm" (d)
- : "cc"
- );
-
- *q = qq;
- *r = rr;
-}
-/* END GCC ASM */
-#elif defined(MASM)
-static inline void __cdecl
-_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
-{
- mpd_uint_t h, l;
-
- __asm {
- mov eax, a
- mul b
- mov h, edx
- mov l, eax
- }
-
- *hi = h;
- *lo = l;
-}
-
-static inline void __cdecl
-_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
- mpd_uint_t d)
-{
- mpd_uint_t qq, rr;
-
- __asm {
- mov eax, lo
- mov edx, hi
- div d
- mov qq, eax
- mov rr, edx
- }
-
- *q = qq;
- *r = rr;
-}
-/* END MASM (_MSC_VER) */
-#else
- #error "need platform specific 64 bit multiplication and division"
-#endif
-
-#define DIVMOD(q, r, v, d) *q = v / d; *r = v - *q * d
-static inline void
-_mpd_divmod_pow10(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t exp)
-{
- assert(exp <= 9);
-
- if (exp <= 4) {
- switch (exp) {
- case 0: *q = v; *r = 0; break;
- case 1: DIVMOD(q, r, v, 10UL); break;
- case 2: DIVMOD(q, r, v, 100UL); break;
- case 3: DIVMOD(q, r, v, 1000UL); break;
- case 4: DIVMOD(q, r, v, 10000UL); break;
- }
- }
- else {
- switch (exp) {
- case 5: DIVMOD(q, r, v, 100000UL); break;
- case 6: DIVMOD(q, r, v, 1000000UL); break;
- case 7: DIVMOD(q, r, v, 10000000UL); break;
- case 8: DIVMOD(q, r, v, 100000000UL); break;
- case 9: DIVMOD(q, r, v, 1000000000UL); break; /* GCOV_NOT_REACHED */
- }
- }
-}
-/* END CONFIG_32 */
-
-/* NO CONFIG */
-#else
- #error "define CONFIG_64 or CONFIG_32"
-#endif /* CONFIG */
-
-
-static inline void
-_mpd_div_word(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t d)
-{
- *q = v / d;
- *r = v - *q * d;
-}
-
-static inline void
-_mpd_idiv_word(mpd_ssize_t *q, mpd_ssize_t *r, mpd_ssize_t v, mpd_ssize_t d)
-{
- *q = v / d;
- *r = v - *q * d;
-}
-
-
-/** ------------------------------------------------------------
- ** Arithmetic with overflow checking
- ** ------------------------------------------------------------
- */
-
-/* The following macros do call exit() in case of an overflow.
- If the library is used correctly (i.e. with valid context
- parameters), such overflows cannot occur. The macros are used
- as sanity checks in a couple of strategic places and should
- be viewed as a handwritten version of gcc's -ftrapv option. */
-
-static inline mpd_size_t
-add_size_t(mpd_size_t a, mpd_size_t b)
-{
- if (a > MPD_SIZE_MAX - b) {
- mpd_err_fatal("add_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */
- }
- return a + b;
-}
-
-static inline mpd_size_t
-sub_size_t(mpd_size_t a, mpd_size_t b)
-{
- if (b > a) {
- mpd_err_fatal("sub_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */
- }
- return a - b;
-}
-
-#if MPD_SIZE_MAX != MPD_UINT_MAX
- #error "adapt mul_size_t() and mulmod_size_t()"
-#endif
-
-static inline mpd_size_t
-mul_size_t(mpd_size_t a, mpd_size_t b)
-{
- mpd_uint_t hi, lo;
-
- _mpd_mul_words(&hi, &lo, (mpd_uint_t)a, (mpd_uint_t)b);
- if (hi) {
- mpd_err_fatal("mul_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */
- }
- return lo;
-}
-
-static inline mpd_size_t
-add_size_t_overflow(mpd_size_t a, mpd_size_t b, mpd_size_t *overflow)
-{
- mpd_size_t ret;
-
- *overflow = 0;
- ret = a + b;
- if (ret < a) *overflow = 1;
- return ret;
-}
-
-static inline mpd_size_t
-mul_size_t_overflow(mpd_size_t a, mpd_size_t b, mpd_size_t *overflow)
-{
- mpd_uint_t hi, lo;
-
- _mpd_mul_words(&hi, &lo, (mpd_uint_t)a, (mpd_uint_t)b);
- *overflow = (mpd_size_t)hi;
- return lo;
-}
-
-static inline mpd_ssize_t
-mod_mpd_ssize_t(mpd_ssize_t a, mpd_ssize_t m)
-{
- mpd_ssize_t r = a % m;
- return (r < 0) ? r + m : r;
-}
-
-static inline mpd_size_t
-mulmod_size_t(mpd_size_t a, mpd_size_t b, mpd_size_t m)
-{
- mpd_uint_t hi, lo;
- mpd_uint_t q, r;
-
- _mpd_mul_words(&hi, &lo, (mpd_uint_t)a, (mpd_uint_t)b);
- _mpd_div_words(&q, &r, hi, lo, (mpd_uint_t)m);
-
- return r;
-}
-
-
-#endif /* LIBMPDEC_TYPEARITH_H_ */
+++ /dev/null
-/*
- * Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-
-#ifndef LIBMPDEC_UMODARITH_H_
-#define LIBMPDEC_UMODARITH_H_
-
-
-#include "mpdecimal.h"
-
-#include "constants.h"
-#include "typearith.h"
-
-
-/* Bignum: Low level routines for unsigned modular arithmetic. These are
- used in the fast convolution functions for very large coefficients. */
-
-
-/**************************************************************************/
-/* ANSI modular arithmetic */
-/**************************************************************************/
-
-
-/*
- * Restrictions: a < m and b < m
- * ACL2 proof: umodarith.lisp: addmod-correct
- */
-static inline mpd_uint_t
-addmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
-{
- mpd_uint_t s;
-
- s = a + b;
- s = (s < a) ? s - m : s;
- s = (s >= m) ? s - m : s;
-
- return s;
-}
-
-/*
- * Restrictions: a < m and b < m
- * ACL2 proof: umodarith.lisp: submod-2-correct
- */
-static inline mpd_uint_t
-submod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
-{
- mpd_uint_t d;
-
- d = a - b;
- d = (a < b) ? d + m : d;
-
- return d;
-}
-
-/*
- * Restrictions: a < 2m and b < 2m
- * ACL2 proof: umodarith.lisp: section ext-submod
- */
-static inline mpd_uint_t
-ext_submod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
-{
- mpd_uint_t d;
-
- a = (a >= m) ? a - m : a;
- b = (b >= m) ? b - m : b;
-
- d = a - b;
- d = (a < b) ? d + m : d;
-
- return d;
-}
-
-/*
- * Reduce double word modulo m.
- * Restrictions: m != 0
- * ACL2 proof: umodarith.lisp: section dw-reduce
- */
-static inline mpd_uint_t
-dw_reduce(mpd_uint_t hi, mpd_uint_t lo, mpd_uint_t m)
-{
- mpd_uint_t r1, r2, w;
-
- _mpd_div_word(&w, &r1, hi, m);
- _mpd_div_words(&w, &r2, r1, lo, m);
-
- return r2;
-}
-
-/*
- * Subtract double word from a.
- * Restrictions: a < m
- * ACL2 proof: umodarith.lisp: section dw-submod
- */
-static inline mpd_uint_t
-dw_submod(mpd_uint_t a, mpd_uint_t hi, mpd_uint_t lo, mpd_uint_t m)
-{
- mpd_uint_t d, r;
-
- r = dw_reduce(hi, lo, m);
- d = a - r;
- d = (a < r) ? d + m : d;
-
- return d;
-}
-
-#ifdef CONFIG_64
-
-/**************************************************************************/
-/* 64-bit modular arithmetic */
-/**************************************************************************/
-
-/*
- * A proof of the algorithm is in literature/mulmod-64.txt. An ACL2
- * proof is in umodarith.lisp: section "Fast modular reduction".
- *
- * Algorithm: calculate (a * b) % p:
- *
- * a) hi, lo <- a * b # Calculate a * b.
- *
- * b) hi, lo <- R(hi, lo) # Reduce modulo p.
- *
- * c) Repeat step b) until 0 <= hi * 2**64 + lo < 2*p.
- *
- * d) If the result is less than p, return lo. Otherwise return lo - p.
- */
-
-static inline mpd_uint_t
-x64_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
-{
- mpd_uint_t hi, lo, x, y;
-
-
- _mpd_mul_words(&hi, &lo, a, b);
-
- if (m & (1ULL<<32)) { /* P1 */
-
- /* first reduction */
- x = y = hi;
- hi >>= 32;
-
- x = lo - x;
- if (x > lo) hi--;
-
- y <<= 32;
- lo = y + x;
- if (lo < y) hi++;
-
- /* second reduction */
- x = y = hi;
- hi >>= 32;
-
- x = lo - x;
- if (x > lo) hi--;
-
- y <<= 32;
- lo = y + x;
- if (lo < y) hi++;
-
- return (hi || lo >= m ? lo - m : lo);
- }
- else if (m & (1ULL<<34)) { /* P2 */
-
- /* first reduction */
- x = y = hi;
- hi >>= 30;
-
- x = lo - x;
- if (x > lo) hi--;
-
- y <<= 34;
- lo = y + x;
- if (lo < y) hi++;
-
- /* second reduction */
- x = y = hi;
- hi >>= 30;
-
- x = lo - x;
- if (x > lo) hi--;
-
- y <<= 34;
- lo = y + x;
- if (lo < y) hi++;
-
- /* third reduction */
- x = y = hi;
- hi >>= 30;
-
- x = lo - x;
- if (x > lo) hi--;
-
- y <<= 34;
- lo = y + x;
- if (lo < y) hi++;
-
- return (hi || lo >= m ? lo - m : lo);
- }
- else { /* P3 */
-
- /* first reduction */
- x = y = hi;
- hi >>= 24;
-
- x = lo - x;
- if (x > lo) hi--;
-
- y <<= 40;
- lo = y + x;
- if (lo < y) hi++;
-
- /* second reduction */
- x = y = hi;
- hi >>= 24;
-
- x = lo - x;
- if (x > lo) hi--;
-
- y <<= 40;
- lo = y + x;
- if (lo < y) hi++;
-
- /* third reduction */
- x = y = hi;
- hi >>= 24;
-
- x = lo - x;
- if (x > lo) hi--;
-
- y <<= 40;
- lo = y + x;
- if (lo < y) hi++;
-
- return (hi || lo >= m ? lo - m : lo);
- }
-}
-
-static inline void
-x64_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m)
-{
- *a = x64_mulmod(*a, w, m);
- *b = x64_mulmod(*b, w, m);
-}
-
-static inline void
-x64_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
- mpd_uint_t m)
-{
- *a0 = x64_mulmod(*a0, b0, m);
- *a1 = x64_mulmod(*a1, b1, m);
-}
-
-static inline mpd_uint_t
-x64_powmod(mpd_uint_t base, mpd_uint_t exp, mpd_uint_t umod)
-{
- mpd_uint_t r = 1;
-
- while (exp > 0) {
- if (exp & 1)
- r = x64_mulmod(r, base, umod);
- base = x64_mulmod(base, base, umod);
- exp >>= 1;
- }
-
- return r;
-}
-
-/* END CONFIG_64 */
-#else /* CONFIG_32 */
-
-
-/**************************************************************************/
-/* 32-bit modular arithmetic */
-/**************************************************************************/
-
-#if defined(ANSI)
-#if !defined(LEGACY_COMPILER)
-/* HAVE_UINT64_T */
-static inline mpd_uint_t
-std_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
-{
- return ((mpd_uuint_t) a * b) % m;
-}
-
-static inline void
-std_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m)
-{
- *a = ((mpd_uuint_t) *a * w) % m;
- *b = ((mpd_uuint_t) *b * w) % m;
-}
-
-static inline void
-std_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
- mpd_uint_t m)
-{
- *a0 = ((mpd_uuint_t) *a0 * b0) % m;
- *a1 = ((mpd_uuint_t) *a1 * b1) % m;
-}
-/* END HAVE_UINT64_T */
-#else
-/* LEGACY_COMPILER */
-static inline mpd_uint_t
-std_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
-{
- mpd_uint_t hi, lo, q, r;
- _mpd_mul_words(&hi, &lo, a, b);
- _mpd_div_words(&q, &r, hi, lo, m);
- return r;
-}
-
-static inline void
-std_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m)
-{
- *a = std_mulmod(*a, w, m);
- *b = std_mulmod(*b, w, m);
-}
-
-static inline void
-std_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
- mpd_uint_t m)
-{
- *a0 = std_mulmod(*a0, b0, m);
- *a1 = std_mulmod(*a1, b1, m);
-}
-/* END LEGACY_COMPILER */
-#endif
-
-static inline mpd_uint_t
-std_powmod(mpd_uint_t base, mpd_uint_t exp, mpd_uint_t umod)
-{
- mpd_uint_t r = 1;
-
- while (exp > 0) {
- if (exp & 1)
- r = std_mulmod(r, base, umod);
- base = std_mulmod(base, base, umod);
- exp >>= 1;
- }
-
- return r;
-}
-#endif /* ANSI CONFIG_32 */
-
-
-/**************************************************************************/
-/* Pentium Pro modular arithmetic */
-/**************************************************************************/
-
-/*
- * A proof of the algorithm is in literature/mulmod-ppro.txt. The FPU
- * control word must be set to 64-bit precision and truncation mode
- * prior to using these functions.
- *
- * Algorithm: calculate (a * b) % p:
- *
- * p := prime < 2**31
- * pinv := (long double)1.0 / p (precalculated)
- *
- * a) n = a * b # Calculate exact product.
- * b) qest = n * pinv # Calculate estimate for q = n / p.
- * c) q = (qest+2**63)-2**63 # Truncate qest to the exact quotient.
- * d) r = n - q * p # Calculate remainder.
- *
- * Remarks:
- *
- * - p = dmod and pinv = dinvmod.
- * - dinvmod points to an array of three uint32_t, which is interpreted
- * as an 80 bit long double by fldt.
- * - Intel compilers prior to version 11 do not seem to handle the
- * __GNUC__ inline assembly correctly.
- * - random tests are provided in tests/extended/ppro_mulmod.c
- */
-
-#if defined(PPRO)
-#if defined(ASM)
-
-/* Return (a * b) % dmod */
-static inline mpd_uint_t
-ppro_mulmod(mpd_uint_t a, mpd_uint_t b, double *dmod, uint32_t *dinvmod)
-{
- mpd_uint_t retval;
-
- __asm__ (
- "fildl %2\n\t"
- "fildl %1\n\t"
- "fmulp %%st, %%st(1)\n\t"
- "fldt (%4)\n\t"
- "fmul %%st(1), %%st\n\t"
- "flds %5\n\t"
- "fadd %%st, %%st(1)\n\t"
- "fsubrp %%st, %%st(1)\n\t"
- "fldl (%3)\n\t"
- "fmulp %%st, %%st(1)\n\t"
- "fsubrp %%st, %%st(1)\n\t"
- "fistpl %0\n\t"
- : "=m" (retval)
- : "m" (a), "m" (b), "r" (dmod), "r" (dinvmod), "m" (MPD_TWO63)
- : "st", "memory"
- );
-
- return retval;
-}
-
-/*
- * Two modular multiplications in parallel:
- * *a0 = (*a0 * w) % dmod
- * *a1 = (*a1 * w) % dmod
- */
-static inline void
-ppro_mulmod2c(mpd_uint_t *a0, mpd_uint_t *a1, mpd_uint_t w,
- double *dmod, uint32_t *dinvmod)
-{
- __asm__ (
- "fildl %2\n\t"
- "fildl (%1)\n\t"
- "fmul %%st(1), %%st\n\t"
- "fxch %%st(1)\n\t"
- "fildl (%0)\n\t"
- "fmulp %%st, %%st(1) \n\t"
- "fldt (%4)\n\t"
- "flds %5\n\t"
- "fld %%st(2)\n\t"
- "fmul %%st(2)\n\t"
- "fadd %%st(1)\n\t"
- "fsub %%st(1)\n\t"
- "fmull (%3)\n\t"
- "fsubrp %%st, %%st(3)\n\t"
- "fxch %%st(2)\n\t"
- "fistpl (%0)\n\t"
- "fmul %%st(2)\n\t"
- "fadd %%st(1)\n\t"
- "fsubp %%st, %%st(1)\n\t"
- "fmull (%3)\n\t"
- "fsubrp %%st, %%st(1)\n\t"
- "fistpl (%1)\n\t"
- : : "r" (a0), "r" (a1), "m" (w),
- "r" (dmod), "r" (dinvmod),
- "m" (MPD_TWO63)
- : "st", "memory"
- );
-}
-
-/*
- * Two modular multiplications in parallel:
- * *a0 = (*a0 * b0) % dmod
- * *a1 = (*a1 * b1) % dmod
- */
-static inline void
-ppro_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
- double *dmod, uint32_t *dinvmod)
-{
- __asm__ (
- "fildl %3\n\t"
- "fildl (%2)\n\t"
- "fmulp %%st, %%st(1)\n\t"
- "fildl %1\n\t"
- "fildl (%0)\n\t"
- "fmulp %%st, %%st(1)\n\t"
- "fldt (%5)\n\t"
- "fld %%st(2)\n\t"
- "fmul %%st(1), %%st\n\t"
- "fxch %%st(1)\n\t"
- "fmul %%st(2), %%st\n\t"
- "flds %6\n\t"
- "fldl (%4)\n\t"
- "fxch %%st(3)\n\t"
- "fadd %%st(1), %%st\n\t"
- "fxch %%st(2)\n\t"
- "fadd %%st(1), %%st\n\t"
- "fxch %%st(2)\n\t"
- "fsub %%st(1), %%st\n\t"
- "fxch %%st(2)\n\t"
- "fsubp %%st, %%st(1)\n\t"
- "fxch %%st(1)\n\t"
- "fmul %%st(2), %%st\n\t"
- "fxch %%st(1)\n\t"
- "fmulp %%st, %%st(2)\n\t"
- "fsubrp %%st, %%st(3)\n\t"
- "fsubrp %%st, %%st(1)\n\t"
- "fxch %%st(1)\n\t"
- "fistpl (%2)\n\t"
- "fistpl (%0)\n\t"
- : : "r" (a0), "m" (b0), "r" (a1), "m" (b1),
- "r" (dmod), "r" (dinvmod),
- "m" (MPD_TWO63)
- : "st", "memory"
- );
-}
-/* END PPRO GCC ASM */
-#elif defined(MASM)
-
-/* Return (a * b) % dmod */
-static inline mpd_uint_t __cdecl
-ppro_mulmod(mpd_uint_t a, mpd_uint_t b, double *dmod, uint32_t *dinvmod)
-{
- mpd_uint_t retval;
-
- __asm {
- mov eax, dinvmod
- mov edx, dmod
- fild b
- fild a
- fmulp st(1), st
- fld TBYTE PTR [eax]
- fmul st, st(1)
- fld MPD_TWO63
- fadd st(1), st
- fsubp st(1), st
- fld QWORD PTR [edx]
- fmulp st(1), st
- fsubp st(1), st
- fistp retval
- }
-
- return retval;
-}
-
-/*
- * Two modular multiplications in parallel:
- * *a0 = (*a0 * w) % dmod
- * *a1 = (*a1 * w) % dmod
- */
-static inline mpd_uint_t __cdecl
-ppro_mulmod2c(mpd_uint_t *a0, mpd_uint_t *a1, mpd_uint_t w,
- double *dmod, uint32_t *dinvmod)
-{
- __asm {
- mov ecx, dmod
- mov edx, a1
- mov ebx, dinvmod
- mov eax, a0
- fild w
- fild DWORD PTR [edx]
- fmul st, st(1)
- fxch st(1)
- fild DWORD PTR [eax]
- fmulp st(1), st
- fld TBYTE PTR [ebx]
- fld MPD_TWO63
- fld st(2)
- fmul st, st(2)
- fadd st, st(1)
- fsub st, st(1)
- fmul QWORD PTR [ecx]
- fsubp st(3), st
- fxch st(2)
- fistp DWORD PTR [eax]
- fmul st, st(2)
- fadd st, st(1)
- fsubrp st(1), st
- fmul QWORD PTR [ecx]
- fsubp st(1), st
- fistp DWORD PTR [edx]
- }
-}
-
-/*
- * Two modular multiplications in parallel:
- * *a0 = (*a0 * b0) % dmod
- * *a1 = (*a1 * b1) % dmod
- */
-static inline void __cdecl
-ppro_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
- double *dmod, uint32_t *dinvmod)
-{
- __asm {
- mov ecx, dmod
- mov edx, a1
- mov ebx, dinvmod
- mov eax, a0
- fild b1
- fild DWORD PTR [edx]
- fmulp st(1), st
- fild b0
- fild DWORD PTR [eax]
- fmulp st(1), st
- fld TBYTE PTR [ebx]
- fld st(2)
- fmul st, st(1)
- fxch st(1)
- fmul st, st(2)
- fld DWORD PTR MPD_TWO63
- fld QWORD PTR [ecx]
- fxch st(3)
- fadd st, st(1)
- fxch st(2)
- fadd st, st(1)
- fxch st(2)
- fsub st, st(1)
- fxch st(2)
- fsubrp st(1), st
- fxch st(1)
- fmul st, st(2)
- fxch st(1)
- fmulp st(2), st
- fsubp st(3), st
- fsubp st(1), st
- fxch st(1)
- fistp DWORD PTR [edx]
- fistp DWORD PTR [eax]
- }
-}
-#endif /* PPRO MASM (_MSC_VER) */
-
-
-/* Return (base ** exp) % dmod */
-static inline mpd_uint_t
-ppro_powmod(mpd_uint_t base, mpd_uint_t exp, double *dmod, uint32_t *dinvmod)
-{
- mpd_uint_t r = 1;
-
- while (exp > 0) {
- if (exp & 1)
- r = ppro_mulmod(r, base, dmod, dinvmod);
- base = ppro_mulmod(base, base, dmod, dinvmod);
- exp >>= 1;
- }
-
- return r;
-}
-#endif /* PPRO */
-#endif /* CONFIG_32 */
-
-
-#endif /* LIBMPDEC_UMODARITH_H_ */
+++ /dev/null
-;
-; Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
-;
-; Redistribution and use in source and binary forms, with or without
-; modification, are permitted provided that the following conditions
-; are met:
-;
-; 1. Redistributions of source code must retain the above copyright
-; notice, this list of conditions and the following disclaimer.
-;
-; 2. Redistributions in binary form must reproduce the above copyright
-; notice, this list of conditions and the following disclaimer in the
-; documentation and/or other materials provided with the distribution.
-;
-; THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
-; ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
-; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
-; ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
-; FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
-; DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
-; OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
-; HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
-; LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
-; OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
-; SUCH DAMAGE.
-;
-
-
-PUBLIC _mpd_div_words
-_TEXT SEGMENT
-q$ = 8
-r$ = 16
-hi$ = 24
-lo$ = 32
-d$ = 40
-_mpd_div_words PROC
- mov r10, rdx
- mov rdx, r8
- mov rax, r9
- div QWORD PTR d$[rsp]
- mov QWORD PTR [r10], rdx
- mov QWORD PTR [rcx], rax
- ret 0
-_mpd_div_words ENDP
-_TEXT ENDS
-END
# values to 'exclude' if we create new files within tracked
# directories that aren't sourced from third-party packages.
PACKAGE_TO_FILES = {
- "mpdecimal": PackageFiles(
- include=["Modules/_decimal/libmpdec/**"]
- ),
"expat": PackageFiles(
include=["Modules/expat/**"],
exclude=[
('*', './Include/internal'),
('*', './Include/internal/mimalloc'),
- ('Modules/_decimal/**/*.c', 'Modules/_decimal/libmpdec'),
-
('Modules/_elementtree.c', 'Modules/expat'),
('Modules/pyexpat.c', 'Modules/expat'),
# ('Modules/_dbmmodule.c', 'USE_BERKDB', '1'),
# See: setup.py
- ('Modules/_decimal/**/*.c', 'CONFIG_64', '1'),
- ('Modules/_decimal/**/*.c', 'ASM', '1'),
('Modules/expat/xmlparse.c', 'HAVE_EXPAT_CONFIG_H', '1'),
('Modules/expat/xmlparse.c', 'XML_POOR_ENTROPY', '1'),
('Modules/_dbmmodule.c', 'HAVE_GDBM_DASH_NDBM_H', '1'),
TCLTK_CFLAGS
LIBSQLITE3_LIBS
LIBSQLITE3_CFLAGS
-LIBMPDEC_INTERNAL
LIBMPDEC_LIBS
LIBMPDEC_CFLAGS
MODULE__CTYPES_MALLOC_CLOSURE
with_tzpath
with_libs
with_system_expat
-with_system_libmpdec
with_decimal_contextvar
enable_loadable_sqlite_extensions
with_dbmliborder
--with-libs='lib1 ...' link against additional libs (default is no)
--with-system-expat build pyexpat module using an installed expat
library, see Doc/library/pyexpat.rst (default is no)
- --with-system-libmpdec build _decimal module using an installed mpdecimal
- library, see Doc/library/decimal.rst (default is
- yes)
--with-decimal-contextvar
build _decimal module using a coroutine-local rather
than a thread-local context (default is yes)
fi
-# Check for use of the system libmpdec library
-{ printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for --with-system-libmpdec" >&5
-printf %s "checking for --with-system-libmpdec... " >&6; }
-
-
-# Check whether --with-system_libmpdec was given.
-if test ${with_system_libmpdec+y}
-then :
- withval=$with_system_libmpdec; if test "x$with_system_libmpdec" = xno
-then :
- LIBMPDEC_CFLAGS="-I\$(srcdir)/Modules/_decimal/libmpdec"
- LIBMPDEC_LIBS="-lm \$(LIBMPDEC_A)"
- LIBMPDEC_INTERNAL="\$(LIBMPDEC_HEADERS) \$(LIBMPDEC_A)"
- have_mpdec=yes
- with_system_libmpdec=no
-fi
-else case e in #(
- e) with_system_libmpdec="yes" ;;
-esac
-fi
-
-{ printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $with_system_libmpdec" >&5
-printf "%s\n" "$with_system_libmpdec" >&6; }
-
-if test "x$with_system_libmpdec" = xyes
-then :
pkg_failed=no
{ printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for libmpdec >= 2.5.0" >&5
# Put the nasty error message in config.log where it belongs
echo "$LIBMPDEC_PKG_ERRORS" >&5
- LIBMPDEC_CFLAGS=${LIBMPDEC_CFLAGS-""}
+
+ save_CFLAGS=$CFLAGS
+save_CPPFLAGS=$CPPFLAGS
+save_LDFLAGS=$LDFLAGS
+save_LIBS=$LIBS
+
+
+ CPPFLAGS="$CPPFLAGS $LIBMPDEC_CFLAGS"
+ LIBS="$LIBS $LIBMPDEC_LIBS"
+
+ cat confdefs.h - <<_ACEOF >conftest.$ac_ext
+/* end confdefs.h. */
+
+
+ #include <mpdecimal.h>
+ #if MPD_VERSION_HEX < 0x02050000
+ # error "mpdecimal 2.5.0 or higher required"
+ #endif
+
+int
+main (void)
+{
+const char *x = mpd_version();
+ ;
+ return 0;
+}
+_ACEOF
+if ac_fn_c_try_link "$LINENO"
+then :
+ have_mpdec=yes
+else case e in #(
+ e) have_mpdec=no ;;
+esac
+fi
+rm -f core conftest.err conftest.$ac_objext conftest.beam \
+ conftest$ac_exeext conftest.$ac_ext
+
+ if test "x$have_mpdec" = xyes
+then :
+
+ LIBMPDEC_CFLAGS=${LIBMPDEC_CFLAGS-""}
LIBMPDEC_LIBS=${LIBMPDEC_LIBS-"-lmpdec -lm"}
- LIBMPDEC_INTERNAL=
+
+fi
+
+CFLAGS=$save_CFLAGS
+CPPFLAGS=$save_CPPFLAGS
+LDFLAGS=$save_LDFLAGS
+LIBS=$save_LIBS
+
+
+
elif test $pkg_failed = untried; then
{ printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: no" >&5
printf "%s\n" "no" >&6; }
- LIBMPDEC_CFLAGS=${LIBMPDEC_CFLAGS-""}
- LIBMPDEC_LIBS=${LIBMPDEC_LIBS-"-lmpdec -lm"}
- LIBMPDEC_INTERNAL=
-else
- LIBMPDEC_CFLAGS=$pkg_cv_LIBMPDEC_CFLAGS
- LIBMPDEC_LIBS=$pkg_cv_LIBMPDEC_LIBS
- { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: yes" >&5
-printf "%s\n" "yes" >&6; }
-fi
-fi
-
-if test "x$with_system_libmpdec" = xyes
-then :
save_CFLAGS=$CFLAGS
save_CPPFLAGS=$CPPFLAGS
save_LDFLAGS=$LDFLAGS
rm -f core conftest.err conftest.$ac_objext conftest.beam \
conftest$ac_exeext conftest.$ac_ext
+ if test "x$have_mpdec" = xyes
+then :
+
+ LIBMPDEC_CFLAGS=${LIBMPDEC_CFLAGS-""}
+ LIBMPDEC_LIBS=${LIBMPDEC_LIBS-"-lmpdec -lm"}
+
+fi
+
CFLAGS=$save_CFLAGS
CPPFLAGS=$save_CPPFLAGS
LDFLAGS=$save_LDFLAGS
LIBS=$save_LIBS
+
+else
+ LIBMPDEC_CFLAGS=$pkg_cv_LIBMPDEC_CFLAGS
+ LIBMPDEC_LIBS=$pkg_cv_LIBMPDEC_LIBS
+ { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: yes" >&5
+printf "%s\n" "yes" >&6; }
+ have_mpdec=yes
fi
# Disable forced inlining in debug builds, see GH-94847
{ printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $with_decimal_contextvar" >&5
printf "%s\n" "$with_decimal_contextvar" >&6; }
-if test "x$with_system_libmpdec" = xno
-then :
- # Check for libmpdec machine flavor
- { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for decimal libmpdec machine" >&5
-printf %s "checking for decimal libmpdec machine... " >&6; }
- case $ac_sys_system in #(
- Darwin*) :
- libmpdec_system=Darwin ;; #(
- SunOS*) :
- libmpdec_system=sunos ;; #(
- *) :
- libmpdec_system=other
- ;;
-esac
-
- libmpdec_machine=unknown
- if test "$libmpdec_system" = Darwin; then
- # universal here means: build libmpdec with the same arch options
- # the python interpreter was built with
- libmpdec_machine=universal
- elif test $ac_cv_sizeof_size_t -eq 8; then
- if test "$ac_cv_gcc_asm_for_x64" = yes; then
- libmpdec_machine=x64
- elif test "$ac_cv_type___uint128_t" = yes; then
- libmpdec_machine=uint128
- else
- libmpdec_machine=ansi64
- fi
- elif test $ac_cv_sizeof_size_t -eq 4; then
- if test "$ac_cv_gcc_asm_for_x87" = yes -a "$libmpdec_system" != sunos; then
- case $ac_cv_cc_name in #(
- *gcc*) :
- libmpdec_machine=ppro ;; #(
- *clang*) :
- libmpdec_machine=ppro ;; #(
- *) :
- libmpdec_machine=ansi32
- ;;
-esac
- else
- libmpdec_machine=ansi32
- fi
- fi
- { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $libmpdec_machine" >&5
-printf "%s\n" "$libmpdec_machine" >&6; }
-
- case $libmpdec_machine in #(
- x64) :
- as_fn_append LIBMPDEC_CFLAGS " -DCONFIG_64=1 -DASM=1" ;; #(
- uint128) :
- as_fn_append LIBMPDEC_CFLAGS " -DCONFIG_64=1 -DANSI=1 -DHAVE_UINT128_T=1" ;; #(
- ansi64) :
- as_fn_append LIBMPDEC_CFLAGS " -DCONFIG_64=1 -DANSI=1" ;; #(
- ppro) :
- as_fn_append LIBMPDEC_CFLAGS " -DCONFIG_32=1 -DANSI=1 -DASM=1 -Wno-unknown-pragmas" ;; #(
- ansi32) :
- as_fn_append LIBMPDEC_CFLAGS " -DCONFIG_32=1 -DANSI=1" ;; #(
- ansi-legacy) :
- as_fn_append LIBMPDEC_CFLAGS " -DCONFIG_32=1 -DANSI=1 -DLEGACY_COMPILER=1" ;; #(
- universal) :
- as_fn_append LIBMPDEC_CFLAGS " -DUNIVERSAL=1" ;; #(
- *) :
- as_fn_error $? "_decimal: unsupported architecture" "$LINENO" 5
- ;;
-esac
-fi
-
-if test "$have_ipa_pure_const_bug" = yes; then
- # Some versions of gcc miscompile inline asm:
- # https://gcc.gnu.org/bugzilla/show_bug.cgi?id=46491
- # https://gcc.gnu.org/ml/gcc/2010-11/msg00366.html
- as_fn_append LIBMPDEC_CFLAGS " -fno-ipa-pure-const"
-fi
-
-if test "$have_glibc_memmove_bug" = yes; then
- # _FORTIFY_SOURCE wrappers for memmove and bcopy are incorrect:
- # https://sourceware.org/ml/libc-alpha/2010-12/msg00009.html
- as_fn_append LIBMPDEC_CFLAGS " -U_FORTIFY_SOURCE"
-fi
-
-
-
-
-
Modules \
Modules/_ctypes \
Modules/_decimal \
- Modules/_decimal/libmpdec \
Modules/_hacl \
Modules/_io \
Modules/_multiprocessing \
printf "%s\n" "$py_cv_module__decimal" >&6; }
-if test "x$with_system_libmpdec" = xno
-then :
- { printf "%s\n" "$as_me:${as_lineno-$LINENO}: WARNING: the bundled copy of libmpdec is scheduled for removal in Python 3.16; consider using a system installed mpdecimal library." >&5
-printf "%s\n" "$as_me: WARNING: the bundled copy of libmpdec is scheduled for removal in Python 3.16; consider using a system installed mpdecimal library." >&2;}
-fi
-if test "$with_system_libmpdec" = "yes" && test "$have_mpdec" = "no"
+if test "$have_mpdec" = "no"
then :
{ printf "%s\n" "$as_me:${as_lineno-$LINENO}: WARNING: no system libmpdec found; falling back to pure-Python version for the decimal module" >&5
printf "%s\n" "$as_me: WARNING: no system libmpdec found; falling back to pure-Python version for the decimal module" >&2;}
[Defined if _Complex C type can be used with libffi.])
fi
-# Check for use of the system libmpdec library
-AC_MSG_CHECKING([for --with-system-libmpdec])
-AC_DEFUN([USE_BUNDLED_LIBMPDEC],
- [LIBMPDEC_CFLAGS="-I\$(srcdir)/Modules/_decimal/libmpdec"
- LIBMPDEC_LIBS="-lm \$(LIBMPDEC_A)"
- LIBMPDEC_INTERNAL="\$(LIBMPDEC_HEADERS) \$(LIBMPDEC_A)"
- have_mpdec=yes
- with_system_libmpdec=no])
-AC_ARG_WITH(
- [system_libmpdec],
- [AS_HELP_STRING(
- [--with-system-libmpdec],
- [build _decimal module using an installed mpdecimal library, see Doc/library/decimal.rst (default is yes)]
- )],
- [AS_IF([test "x$with_system_libmpdec" = xno],
- [USE_BUNDLED_LIBMPDEC()])],
- [with_system_libmpdec="yes"])
-AC_MSG_RESULT([$with_system_libmpdec])
-
-AS_VAR_IF(
- [with_system_libmpdec], [yes],
- [PKG_CHECK_MODULES(
- [LIBMPDEC], [libmpdec >= 2.5.0], [],
- [LIBMPDEC_CFLAGS=${LIBMPDEC_CFLAGS-""}
- LIBMPDEC_LIBS=${LIBMPDEC_LIBS-"-lmpdec -lm"}
- LIBMPDEC_INTERNAL=])])
-
-AS_VAR_IF([with_system_libmpdec], [yes],
- [WITH_SAVE_ENV([
+dnl Check for libmpdec >= 2.5.0
+PKG_CHECK_MODULES([LIBMPDEC], [libmpdec >= 2.5.0], [have_mpdec=yes], [
+ WITH_SAVE_ENV([
CPPFLAGS="$CPPFLAGS $LIBMPDEC_CFLAGS"
LIBS="$LIBS $LIBMPDEC_LIBS"
], [const char *x = mpd_version();])],
[have_mpdec=yes],
[have_mpdec=no])
- ])])
+
+ AS_VAR_IF([have_mpdec], [yes], [
+ LIBMPDEC_CFLAGS=${LIBMPDEC_CFLAGS-""}
+ LIBMPDEC_LIBS=${LIBMPDEC_LIBS-"-lmpdec -lm"}
+ ])
+ ])
+])
# Disable forced inlining in debug builds, see GH-94847
AS_VAR_IF(
AC_MSG_RESULT([$with_decimal_contextvar])
-AS_VAR_IF(
- [with_system_libmpdec], [no],
- [# Check for libmpdec machine flavor
- AC_MSG_CHECKING([for decimal libmpdec machine])
- AS_CASE([$ac_sys_system],
- [Darwin*], [libmpdec_system=Darwin],
- [SunOS*], [libmpdec_system=sunos],
- [libmpdec_system=other]
- )
-
- libmpdec_machine=unknown
- if test "$libmpdec_system" = Darwin; then
- # universal here means: build libmpdec with the same arch options
- # the python interpreter was built with
- libmpdec_machine=universal
- elif test $ac_cv_sizeof_size_t -eq 8; then
- if test "$ac_cv_gcc_asm_for_x64" = yes; then
- libmpdec_machine=x64
- elif test "$ac_cv_type___uint128_t" = yes; then
- libmpdec_machine=uint128
- else
- libmpdec_machine=ansi64
- fi
- elif test $ac_cv_sizeof_size_t -eq 4; then
- if test "$ac_cv_gcc_asm_for_x87" = yes -a "$libmpdec_system" != sunos; then
- AS_CASE([$ac_cv_cc_name],
- [*gcc*], [libmpdec_machine=ppro],
- [*clang*], [libmpdec_machine=ppro],
- [libmpdec_machine=ansi32]
- )
- else
- libmpdec_machine=ansi32
- fi
- fi
- AC_MSG_RESULT([$libmpdec_machine])
-
- AS_CASE([$libmpdec_machine],
- [x64], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DCONFIG_64=1 -DASM=1"])],
- [uint128], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DCONFIG_64=1 -DANSI=1 -DHAVE_UINT128_T=1"])],
- [ansi64], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DCONFIG_64=1 -DANSI=1"])],
- [ppro], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DCONFIG_32=1 -DANSI=1 -DASM=1 -Wno-unknown-pragmas"])],
- [ansi32], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DCONFIG_32=1 -DANSI=1"])],
- [ansi-legacy], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DCONFIG_32=1 -DANSI=1 -DLEGACY_COMPILER=1"])],
- [universal], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DUNIVERSAL=1"])],
- [AC_MSG_ERROR([_decimal: unsupported architecture])]
- )])
-
-if test "$have_ipa_pure_const_bug" = yes; then
- # Some versions of gcc miscompile inline asm:
- # https://gcc.gnu.org/bugzilla/show_bug.cgi?id=46491
- # https://gcc.gnu.org/ml/gcc/2010-11/msg00366.html
- AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -fno-ipa-pure-const"])
-fi
-
-if test "$have_glibc_memmove_bug" = yes; then
- # _FORTIFY_SOURCE wrappers for memmove and bcopy are incorrect:
- # https://sourceware.org/ml/libc-alpha/2010-12/msg00009.html
- AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -U_FORTIFY_SOURCE"])
-fi
-
-AC_SUBST([LIBMPDEC_CFLAGS])
-AC_SUBST([LIBMPDEC_INTERNAL])
-
-
dnl detect sqlite3 from Emscripten emport
PY_CHECK_EMSCRIPTEN_PORT([LIBSQLITE3], [-sUSE_SQLITE3])
Modules \
Modules/_ctypes \
Modules/_decimal \
- Modules/_decimal/libmpdec \
Modules/_hacl \
Modules/_io \
Modules/_multiprocessing \
[], [test "$have_mpdec" = "yes"],
[$LIBMPDEC_CFLAGS], [$LIBMPDEC_LIBS])
-AS_VAR_IF([with_system_libmpdec], [no],
- [AC_MSG_WARN([m4_normalize([
- the bundled copy of libmpdec is scheduled for removal in Python 3.16;
- consider using a system installed mpdecimal library.])])])
-AS_IF([test "$with_system_libmpdec" = "yes" && test "$have_mpdec" = "no"],
+AS_IF([test "$have_mpdec" = "no"],
[AC_MSG_WARN([m4_normalize([
no system libmpdec found; falling back to pure-Python version
for the decimal module])])])
projects / thirdparty / Python / cpython.git / commitdiff
