/coreutils-*.tar.xz
/coreutils-*.tar.xz.sig
/gnulib-tests
-/lib/.cvsignore
+/lib/.dirstamp
/lib/.gitignore
/lib/alloca.h
/lib/arg-nonnull.h
/lib/ref-del.sed
/lib/selinux
/lib/signal.h
+/lib/spawn.h
/lib/stamp-h1
/lib/stdalign.h
/lib/stdio.h
/po/remove-potcdate.sin
/po/stamp-po
/src/cu-progs.mk
+/src/make-prime-list
+/src/primes.h
/src/version.c
/src/version.h
/stamp-h1
/tests/*/*.log
/tests/*/*.trs
/tests/.built-programs
+/tests/factor/[0-9]*.sh
/tests/t?
/tests/test-suite.log
ID
env: Richard Mlynarik, David MacKenzie
expand: David MacKenzie
expr: Mike Parker, James Youngman, Paul Eggert
-factor: Paul Rubin
+factor: Paul Rubin, Torbjörn Granlund, Niels Möller
false: Jim Meyering
fmt: Ross Paterson
fold: David MacKenzie
for t in $(all_tests); do echo $$t; done; \
cd $(top_srcdir); \
$(SHELL) build-aux/vc-list-files tests \
- | grep -v '^tests/init\.sh$$' \
+ | grep -Ev '^tests/(factor/run|init)\.sh$$' \
| $(EGREP) "$$test_extensions_rx\$$"; \
} | sort | uniq -u | grep . && exit 1; :
# List syntax-check exemptions.
exclude_file_name_regexp--sc_space_tab = \
^(tests/pr/|tests/misc/nl\.sh$$|gl/.*\.diff$$)
-exclude_file_name_regexp--sc_bindtextdomain = ^(gl/.*|lib/euidaccess-stat)\.c$$
+exclude_file_name_regexp--sc_bindtextdomain = \
+ ^(gl/.*|lib/euidaccess-stat|src/make-prime-list)\.c$$
exclude_file_name_regexp--sc_trailing_blank = ^tests/pr/
exclude_file_name_regexp--sc_system_h_headers = \
- ^src/((system|copy)\.h|libstdbuf\.c)$$
+ ^src/((system|copy)\.h|libstdbuf\.c|make-prime-list\.c)$$
_src = (false|lbracket|ls-(dir|ls|vdir)|tac-pipe|uname-(arch|uname))
exclude_file_name_regexp--sc_require_config_h_first = \
exclude_file_name_regexp--sc_prohibit_always-defined_macros = \
^src/(seq|remove)\.c$$
exclude_file_name_regexp--sc_prohibit_empty_lines_at_EOF = ^tests/pr/
-exclude_file_name_regexp--sc_program_name = ^(gl/.*|lib/euidaccess-stat)\.c$$
+exclude_file_name_regexp--sc_program_name = \
+ ^(gl/.*|lib/euidaccess-stat|src/make-prime-list)\.c$$
exclude_file_name_regexp--sc_file_system = \
NEWS|^(init\.cfg|src/df\.c|tests/df/df-P\.sh)$$
exclude_file_name_regexp--sc_prohibit_always_true_header_tests = \
(^.*/git-hooks/commit-msg|^tests/init\.sh|Makefile\.am|\.mk|.*\.texi)$$
exclude_file_name_regexp--sc_prohibit_atoi_atof = ^lib/euidaccess-stat\.c$$
+# longlong.h is maintained elsewhere.
+_ll = ^src/longlong\.h$$
+exclude_file_name_regexp--sc_useless_cpp_parens = $(_ll)
+exclude_file_name_regexp--sc_long_lines = $(_ll)
+exclude_file_name_regexp--sc_space_before_open_paren = $(_ll)
+
tbi_1 = ^tests/pr/|(^gl/lib/reg.*\.c\.diff|\.mk|^man/help2man)$$
tbi_2 = ^scripts/git-hooks/(pre-commit|pre-applypatch|applypatch-msg)$$
-tbi_3 = (GNU)?[Mm]akefile(\.am)?$$
+tbi_3 = (GNU)?[Mm]akefile(\.am)?$$|$(_ll)
exclude_file_name_regexp--sc_prohibit_tab_based_indentation = \
$(tbi_1)|$(tbi_2)|$(tbi_3)
exclude_file_name_regexp--sc_preprocessor_indentation = \
- ^(gl/lib/rand-isaac\.[ch]|gl/tests/test-rand-isaac\.c)$$
+ ^(gl/lib/rand-isaac\.[ch]|gl/tests/test-rand-isaac\.c)$$|$(__ll)
exclude_file_name_regexp--sc_prohibit_stat_st_blocks = \
^(src/system\.h|tests/du/2g\.sh)$$
exclude_file_name_regexp--sc_prohibit_operator_at_end_of_line = \
^src/(ptx|test|head)\.c$$
+exclude_file_name_regexp--sc_error_message_uppercase = ^src/factor\.c$$
+exclude_file_name_regexp--sc_prohibit_atoi_atof = ^src/make-prime-list\.c$$
+
# Augment AM_CFLAGS to include our per-directory options:
AM_CFLAGS += $($(@D)_CFLAGS)
users
vdir
wc
-wheel-size.h
-wheel.h
who
whoami
yes
+++ /dev/null
-/* Factoring of uintmax_t numbers.
-
- Contributed to the GNU project by Torbjörn Granlund and Niels Möller
- Contains code from GNU MP.
-
-Copyright 1995, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2005, 2009, 2012
-Free Software Foundation, Inc.
-
-This program is free software; you can redistribute it and/or modify it under
-the terms of the GNU General Public License as published by the Free Software
-Foundation; either version 3 of the License, or (at your option) any later
-version.
-
-This program is distributed in the hope that it will be useful, but WITHOUT ANY
-WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
-PARTICULAR PURPOSE. See the GNU General Public License for more details.
-
-You should have received a copy of the GNU General Public License along with
-this program. If not, see http://www.gnu.org/licenses/. */
-
-/* Efficiently factor numbers that fit in one or two words (word = uintmax_t),
- or, with GMP, numbers of any size.
-
- Code organisation:
-
- There are several variants of many functions, for handling one word, two
- words, and GMP's mpz_t type. If the one-word variant is called foo, the
- two-word variant will be foo2, and the one for mpz_t will be mp_foo. In
- some cases, the plain function variants will handle both one-word and
- two-word numbers, evidenced by function arguments.
-
- The factoring code for two words will fall into the code for one word when
- progress allows that.
-
- Using GMP is optional. Define HAVE_GMP to make this code include GMP
- factoring code. The GMP factoring code is based on GMP's demos/factorize.c
- (last synched 2012-09-07). The GMP-based factoring code will stay in GMP
- factoring code even if numbers get small enough for using the two-word
- code.
-
- Algorithm:
-
- (1) Perform trial division using a small primes table, but without hardware
- division since the primes table store inverses modulo the word base.
- (The GMP variant of this code doesn't make use of the precomputed
- inverses, but instead relies on GMP for fast divisibility testing.)
- (2) Check the nature of any non-factored part using Miller-Rabin for
- detecting composites, and Lucas for detecting primes.
- (3) Factor any remaining composite part using the Pollard-Brent rho
- algorithm or the SQUFOF algorithm, checking status of found factors
- again using Miller-Rabin and Lucas.
-
- We prefer using Hensel norm in the divisions, not the more familiar
- Euclidian norm, since the former leads to much faster code. In the
- Pollard-Brent rho code and the the prime testing code, we use Montgomery's
- trick of multiplying all n-residues by the word base, allowing cheap Hensel
- reductions mod n.
-
- Improvements:
-
- * Use modular inverses also for exact division in the Lucas code, and
- elsewhere. A problem is to locate the inverses not from an index, but
- from a prime. We might instead compute the inverse on-the-fly.
-
- * Tune trial division table size (not forgetting that this is a standalone
- program where the table will be read from disk for each invocation).
-
- * Implement less naive powm, using k-ary exponentiation for k = 3 or
- perhaps k = 4.
-
- * Try to speed trial division code for single uintmax_t numbers, i.e., the
- code using DIVBLOCK. It currently runs at 2 cycles per prime (Intel SBR,
- IBR), 3 cycles per prime (AMD Stars) and 5 cycles per prime (AMD BD) when
- using gcc 4.6 and 4.7. Some software pipelining should help; 1, 2, and 4
- respectively cycles ought to be possible.
-
- * The redcify function could be vastly improved by using (plain Euclidian)
- pre-inversion (such as GMP's invert_limb) and udiv_qrnnd_preinv (from
- GMP's gmp-impl.h). The redcify2 function could be vastly improved using
- similar methoods. These functions currently dominate run time when using
- the -w option.
-*/
-
-#include <config.h>
-
-#include <stdlib.h>
-#include <stdio.h>
-#include <inttypes.h>
-#include <errno.h>
-#include <assert.h>
-#include <ctype.h>
-#include <string.h> /* for memmove */
-#include <unistd.h> /* for getopt */
-#include <stdbool.h>
-
-#include "system.h"
-
-#if HAVE_GMP
-# include <gmp.h>
-#endif
-
-#ifndef STAT_SQUFOF
-# define STAT_SQUFOF 0
-#endif
-
-#ifndef USE_LONGLONG_H
-# define USE_LONGLONG_H 1
-#endif
-
-#if USE_LONGLONG_H
-
-/* Make definitions for longlong.h to make it do what it can do for us */
-# define W_TYPE_SIZE 64 /* bitcount for uintmax_t */
-# define UWtype uintmax_t
-# define UHWtype unsigned long int
-# undef UDWtype
-# if HAVE_ATTRIBUTE_MODE
-typedef unsigned int UQItype __attribute__ ((mode (QI)));
-typedef int SItype __attribute__ ((mode (SI)));
-typedef unsigned int USItype __attribute__ ((mode (SI)));
-typedef int DItype __attribute__ ((mode (DI)));
-typedef unsigned int UDItype __attribute__ ((mode (DI)));
-# else
-typedef unsigned char UQItype;
-typedef long SItype;
-typedef unsigned long int USItype;
-# if HAVE_LONG_LONG
-typedef long long int DItype;
-typedef unsigned long long int UDItype;
-# else /* Assume `long' gives us a wide enough type. Needed for hppa2.0w. */
-typedef long int DItype;
-typedef unsigned long int UDItype;
-# endif
-# endif
-# define LONGLONG_STANDALONE /* Don't require GMP's longlong.h mdep files */
-# define ASSERT(x) /* FIXME make longlong.h really standalone */
-# define __GMP_DECLSPEC /* FIXME make longlong.h really standalone */
-# define __clz_tab factor_clz_tab /* Rename to avoid glibc collision */
-# ifndef __GMP_GNUC_PREREQ
-# define __GMP_GNUC_PREREQ(a,b) 1
-# endif
-# if _ARCH_PPC
-# define HAVE_HOST_CPU_FAMILY_powerpc 1
-# endif
-# include "longlong.h"
-# ifdef COUNT_LEADING_ZEROS_NEED_CLZ_TAB
-const unsigned char factor_clz_tab[129] =
-{
- 1,2,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
- 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
- 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
- 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
- 9
-};
-# endif
-
-#else /* not USE_LONGLONG_H */
-
-# define W_TYPE_SIZE (8 * sizeof (uintmax_t))
-# define __ll_B ((uintmax_t) 1 << (W_TYPE_SIZE / 2))
-# define __ll_lowpart(t) ((uintmax_t) (t) & (__ll_B - 1))
-# define __ll_highpart(t) ((uintmax_t) (t) >> (W_TYPE_SIZE / 2))
-
-#endif
-
-enum alg_type { ALG_POLLARD_RHO = 1, ALG_SQUFOF = 2 };
-
-static enum alg_type alg;
-
-/* 2*3*5*7*11...*101 is 128 bits, and has 26 prime factors */
-#define MAX_NFACTS 26
-
-struct factors
-{
- uintmax_t plarge[2]; /* Can have a single large factor */
- uintmax_t p[MAX_NFACTS];
- unsigned char e[MAX_NFACTS];
- unsigned char nfactors;
-};
-
-#if HAVE_GMP
-struct mp_factors
-{
- mpz_t *p;
- unsigned long int *e;
- unsigned long int nfactors;
-};
-#endif
-
-static void factor (uintmax_t, uintmax_t, struct factors *);
-
-#ifndef umul_ppmm
-# define umul_ppmm(w1, w0, u, v) \
- do { \
- uintmax_t __x0, __x1, __x2, __x3; \
- unsigned long int __ul, __vl, __uh, __vh; \
- uintmax_t __u = (u), __v = (v); \
- \
- __ul = __ll_lowpart (__u); \
- __uh = __ll_highpart (__u); \
- __vl = __ll_lowpart (__v); \
- __vh = __ll_highpart (__v); \
- \
- __x0 = (uintmax_t) __ul * __vl; \
- __x1 = (uintmax_t) __ul * __vh; \
- __x2 = (uintmax_t) __uh * __vl; \
- __x3 = (uintmax_t) __uh * __vh; \
- \
- __x1 += __ll_highpart (__x0);/* this can't give carry */ \
- __x1 += __x2; /* but this indeed can */ \
- if (__x1 < __x2) /* did we get it? */ \
- __x3 += __ll_B; /* yes, add it in the proper pos. */ \
- \
- (w1) = __x3 + __ll_highpart (__x1); \
- (w0) = (__x1 << W_TYPE_SIZE / 2) + __ll_lowpart (__x0); \
- } while (0)
-#endif
-
-#if !defined(udiv_qrnnd) || defined(UDIV_NEEDS_NORMALIZATION)
-/* Define our own, not needing normalization. This function is
- currently not performance critical, so keep it simple. Similar to
- the mod macro below. */
-# undef udiv_qrnnd
-# define udiv_qrnnd(q, r, n1, n0, d) \
- do { \
- uintmax_t __d1, __d0, __q, __r1, __r0; \
- \
- assert ((n1) < (d)); \
- __d1 = (d); __d0 = 0; \
- __r1 = (n1); __r0 = (n0); \
- __q = 0; \
- for (unsigned int __i = W_TYPE_SIZE; __i > 0; __i--) \
- { \
- rsh2 (__d1, __d0, __d1, __d0, 1); \
- __q <<= 1; \
- if (ge2 (__r1, __r0, __d1, __d0)) \
- { \
- __q++; \
- sub_ddmmss (__r1, __r0, __r1, __r0, __d1, __d0); \
- } \
- } \
- (r) = __r0; \
- (q) = __q; \
- } while (0)
-#endif
-
-#if !defined (add_ssaaaa)
-# define add_ssaaaa(sh, sl, ah, al, bh, bl) \
- do { \
- uintmax_t _add_x; \
- _add_x = (al) + (bl); \
- (sh) = (ah) + (bh) + (_add_x < (al)); \
- (sl) = _add_x; \
- } while (0)
-#endif
-
-#define rsh2(rh, rl, ah, al, cnt) \
- do { \
- (rl) = ((ah) << (W_TYPE_SIZE - (cnt))) | ((al) >> (cnt)); \
- (rh) = (ah) >> (cnt); \
- } while (0)
-
-#define lsh2(rh, rl, ah, al, cnt) \
- do { \
- (rh) = ((ah) << cnt) | ((al) >> (W_TYPE_SIZE - (cnt))); \
- (rl) = (al) << (cnt); \
- } while (0)
-
-#define ge2(ah, al, bh, bl) \
- ((ah) > (bh) || ((ah) == (bh) && (al) >= (bl)))
-
-#define gt2(ah, al, bh, bl) \
- ((ah) > (bh) || ((ah) == (bh) && (al) > (bl)))
-
-#ifndef sub_ddmmss
-# define sub_ddmmss(rh, rl, ah, al, bh, bl) \
- do { \
- uintmax_t _cy; \
- _cy = (al) < (bl); \
- (rl) = (al) - (bl); \
- (rh) = (ah) - (bh) - _cy; \
- } while (0)
-#endif
-
-#ifndef count_leading_zeros
-# define count_leading_zeros(count, x) do { \
- uintmax_t __clz_x = (x); \
- unsigned int __clz_c; \
- for (__clz_c = 0; \
- (__clz_x & ((uintmax_t) 0xff << (W_TYPE_SIZE - 8))) == 0; \
- __clz_c += 8) \
- __clz_x <<= 8; \
- for (; (intmax_t)__clz_x >= 0; __clz_c++) \
- __clz_x <<= 1; \
- (count) = __clz_c; \
- } while (0)
-#endif
-
-#ifndef count_trailing_zeros
-# define count_trailing_zeros(count, x) do { \
- uintmax_t __ctz_x = (x); \
- unsigned int __ctz_c = 0; \
- while ((__ctz_x & 1) == 0) \
- { \
- __ctz_x >>= 1; \
- __ctz_c++; \
- } \
- (count) = __ctz_c; \
- } while (0)
-#endif
-
-/* Requires that a < n and b <= n */
-#define submod(r,a,b,n) \
- do { \
- uintmax_t _t = - (uintmax_t) (a < b); \
- (r) = ((n) & _t) + (a) - (b); \
- } while (0)
-
-#define addmod(r,a,b,n) \
- submod((r), (a), ((n) - (b)), (n))
-
-/* Modular two-word addition and subtraction. For performance reasons, the
- most significant bit of n1 must be clear. The destination variables must be
- distinct from the mod operand. */
-#define addmod2(r1, r0, a1, a0, b1, b0, n1, n0) \
- do { \
- add_ssaaaa ((r1), (r0), (a1), (a0), (b1), (b0)); \
- if (ge2 ((r1), (r0), (n1), (n0))) \
- sub_ddmmss ((r1), (r0), (r1), (r0), (n1), (n0)); \
- } while (0)
-#define submod2(r1, r0, a1, a0, b1, b0, n1, n0) \
- do { \
- sub_ddmmss ((r1), (r0), (a1), (a0), (b1), (b0)); \
- if ((intmax_t) (r1) < 0) \
- add_ssaaaa ((r1), (r0), (r1), (r0), (n1), (n0)); \
- } while (0)
-
-#define HIGHBIT_TO_MASK(x) \
- (((intmax_t)-1 >> 1) < 0 \
- ? (uintmax_t)((intmax_t)(x) >> (W_TYPE_SIZE - 1)) \
- : ((x) & ((uintmax_t) 1 << (W_TYPE_SIZE - 1)) \
- ? UINTMAX_MAX : (uintmax_t) 0))
-
-/* Compute r = a mod d, where r = <*t1,retval>, a = <a1,a0>, d = <d1,d0>.
- Requires that d1 != 0. */
-static uintmax_t
-mod2 (uintmax_t *r1, uintmax_t a1, uintmax_t a0, uintmax_t d1, uintmax_t d0)
-{
- int cntd, cnta;
-
- assert (d1 != 0);
-
- if (a1 == 0)
- {
- *r1 = 0;
- return a0;
- }
-
- count_leading_zeros (cntd, d1);
- count_leading_zeros (cnta, a1);
- int cnt = cntd - cnta;
- lsh2 (d1, d0, d1, d0, cnt);
- for (int i = 0; i < cnt; i++)
- {
- if (ge2 (a1, a0, d1, d0))
- sub_ddmmss (a1, a0, a1, a0, d1, d0);
- rsh2 (d1, d0, d1, d0, 1);
- }
-
- *r1 = a1;
- return a0;
-}
-
-static uintmax_t _GL_ATTRIBUTE_CONST
-gcd_odd (uintmax_t a, uintmax_t b)
-{
- if ( (b & 1) == 0)
- {
- uintmax_t t = b;
- b = a;
- a = t;
- }
- if (a == 0)
- return b;
-
- /* Take out least significant one bit, to make room for sign */
- b >>= 1;
-
- for (;;)
- {
- uintmax_t t;
- uintmax_t bgta;
-
- while ((a & 1) == 0)
- a >>= 1;
- a >>= 1;
-
- t = a - b;
- if (t == 0)
- return (a << 1) + 1;
-
- bgta = HIGHBIT_TO_MASK (t);
-
- /* b <-- min (a, b) */
- b += (bgta & t);
-
- /* a <-- |a - b| */
- a = (t ^ bgta) - bgta;
- }
-}
-
-static uintmax_t
-gcd2_odd (uintmax_t *r1, uintmax_t a1, uintmax_t a0, uintmax_t b1, uintmax_t b0)
-{
- while ((a0 & 1) == 0)
- rsh2 (a1, a0, a1, a0, 1);
- while ((b0 & 1) == 0)
- rsh2 (b1, b0, b1, b0, 1);
-
- for (;;)
- {
- if ((b1 | a1) == 0)
- {
- *r1 = 0;
- return gcd_odd (b0, a0);
- }
-
- if (gt2 (a1, a0, b1, b0))
- {
- sub_ddmmss (a1, a0, a1, a0, b1, b0);
- do
- rsh2 (a1, a0, a1, a0, 1);
- while ((a0 & 1) == 0);
- }
- else if (gt2 (b1, b0, a1, a0))
- {
- sub_ddmmss (b1, b0, b1, b0, a1, a0);
- do
- rsh2 (b1, b0, b1, b0, 1);
- while ((b0 & 1) == 0);
- }
- else
- break;
- }
-
- *r1 = a1;
- return a0;
-}
-
-static void
-factor_insert_multiplicity (struct factors *factors,
- uintmax_t prime, unsigned int m)
-{
- unsigned int nfactors = factors->nfactors;
- uintmax_t *p = factors->p;
- unsigned char *e = factors->e;
-
- /* Locate position for insert new or increment e. */
- int i;
- for (i = nfactors - 1; i >= 0; i--)
- {
- if (p[i] <= prime)
- break;
- }
-
- if (i < 0 || p[i] != prime)
- {
- for (int j = nfactors - 1; j > i; j--)
- {
- p[j + 1] = p[j];
- e[j + 1] = e[j];
- }
- p[i + 1] = prime;
- e[i + 1] = m;
- factors->nfactors = nfactors + 1;
- }
- else
- {
- e[i] += m;
- }
-}
-
-#define factor_insert(f, p) factor_insert_multiplicity(f, p, 1)
-
-static void
-factor_insert_large (struct factors *factors,
- uintmax_t p1, uintmax_t p0)
-{
- if (p1 > 0)
- {
- assert (factors->plarge[1] == 0);
- factors->plarge[0] = p0;
- factors->plarge[1] = p1;
- }
- else
- factor_insert (factors, p0);
-}
-
-#if HAVE_GMP
-static void mp_factor (mpz_t, struct mp_factors *);
-
-static void
-mp_factor_init (struct mp_factors *factors)
-{
- factors->p = malloc (1);
- factors->e = malloc (1);
- factors->nfactors = 0;
-}
-
-static void
-mp_factor_clear (struct mp_factors *factors)
-{
- for (unsigned int i = 0; i < factors->nfactors; i++)
- mpz_clear (factors->p[i]);
-
- free (factors->p);
- free (factors->e);
-}
-
-static void
-mp_factor_insert (struct mp_factors *factors, mpz_t prime)
-{
- unsigned long int nfactors = factors->nfactors;
- mpz_t *p = factors->p;
- unsigned long int *e = factors->e;
- long i;
-
- /* Locate position for insert new or increment e. */
- for (i = nfactors - 1; i >= 0; i--)
- {
- if (mpz_cmp (p[i], prime) <= 0)
- break;
- }
-
- if (i < 0 || mpz_cmp (p[i], prime) != 0)
- {
- p = realloc (p, (nfactors + 1) * sizeof p[0]);
- e = realloc (e, (nfactors + 1) * sizeof e[0]);
-
- mpz_init (p[nfactors]);
- for (long j = nfactors - 1; j > i; j--)
- {
- mpz_set (p[j + 1], p[j]);
- e[j + 1] = e[j];
- }
- mpz_set (p[i + 1], prime);
- e[i + 1] = 1;
-
- factors->p = p;
- factors->e = e;
- factors->nfactors = nfactors + 1;
- }
- else
- {
- e[i] += 1;
- }
-}
-
-static void
-mp_factor_insert_ui (struct mp_factors *factors, unsigned long int prime)
-{
- mpz_t pz;
-
- mpz_init_set_ui (pz, prime);
- mp_factor_insert (factors, pz);
- mpz_clear (pz);
-}
-#endif /* HAVE_GMP */
-
-
-#define P(a,b,c,d) a,
-static const unsigned char primes_diff[] = {
-#include "primes.h"
-0,0,0,0,0,0,0 /* 7 sentinels for 8-way loop */
-};
-#undef P
-
-#define PRIMES_PTAB_ENTRIES (sizeof(primes_diff) / sizeof(primes_diff[0]) - 8 + 1)
-
-#define P(a,b,c,d) b,
-static const unsigned char primes_diff8[] = {
-#include "primes.h"
-0,0,0,0,0,0,0 /* 7 sentinels for 8-way loop */
-};
-#undef P
-
-struct primes_dtab
-{
- uintmax_t binv, lim;
-};
-
-#define P(a,b,c,d) {c,d},
-static const struct primes_dtab primes_dtab[] = {
-#include "primes.h"
-{1,0},{1,0},{1,0},{1,0},{1,0},{1,0},{1,0} /* 7 sentinels for 8-way loop */
-};
-#undef P
-
-/* This flag is honoured just in the GMP code. */
-static int flag_verbose = 0;
-
-/* Prove primality or run probabilistic tests. */
-static int flag_prove_primality = 1;
-
-/* Number of Miller-Rabin tests to run when not proving primality. */
-#define MR_REPS 25
-
-#define LIKELY(cond) __builtin_expect ((cond) != 0, 1)
-#define UNLIKELY(cond) __builtin_expect ((cond) != 0, 0)
-
-static void
-factor_insert_refind (struct factors *factors, uintmax_t p, unsigned int i,
- unsigned int off)
-{
- for (unsigned int j = 0; j < off; j++)
- p += primes_diff[i + j];
- factor_insert (factors, p);
-}
-
-/* Trial division with odd primes uses the following trick.
-
- Let p be an odd prime, and B = 2^{W_TYPE_SIZE}. For simplicity,
- consider the case t < B (this is the second loop below).
-
- From our tables we get
-
- binv = p^{-1} (mod B)
- lim = floor ( (B-1) / p ).
-
- First assume that t is a multiple of p, t = q * p. Then 0 <= q <=
- lim (and all quotients in this range occur for some t).
-
- Then t = q * p is true also (mod B), and p is invertible we get
-
- q = t * binv (mod B).
-
- Next, assume that t is *not* divisible by p. Since multiplication
- by binv (mod B) is a one-to-one mapping,
-
- t * binv (mod B) > lim,
-
- because all the smaller values are already taken.
-
- This can be summed up by saying that the function
-
- q(t) = binv * t (mod B)
-
- is a permutation of the range 0 <= t < B, with the curious property
- that it maps the multiples of p onto the range 0 <= q <= lim, in
- order, and the non-multiples of p onto the range lim < q < B.
- */
-
-static uintmax_t
-factor_using_division (uintmax_t *t1p, uintmax_t t1, uintmax_t t0,
- struct factors *factors)
-{
- if (t0 % 2 == 0)
- {
- unsigned int cnt;
-
- if (t0 == 0)
- {
- count_trailing_zeros (cnt, t1);
- t0 = t1 >> cnt;
- t1 = 0;
- cnt += W_TYPE_SIZE;
- }
- else
- {
- count_trailing_zeros (cnt, t0);
- rsh2 (t1, t0, t1, t0, cnt);
- }
-
- factor_insert_multiplicity (factors, 2, cnt);
- }
-
- uintmax_t p = 3;
- unsigned int i;
- for (i = 0; t1 > 0 && i < PRIMES_PTAB_ENTRIES; i++)
- {
- for (;;)
- {
- uintmax_t q1, q0, hi, lo;
-
- q0 = t0 * primes_dtab[i].binv;
- umul_ppmm (hi, lo, q0, p);
- if (hi > t1)
- break;
- hi = t1 - hi;
- q1 = hi * primes_dtab[i].binv;
- if (LIKELY (q1 > primes_dtab[i].lim))
- break;
- t1 = q1; t0 = q0;
- factor_insert (factors, p);
- }
- p += primes_diff[i + 1];
- }
- if (t1p)
- *t1p = t1;
-
-#define DIVBLOCK(I) \
- do { \
- for (;;) \
- { \
- q = t0 * pd[I].binv; \
- if (LIKELY (q > pd[I].lim)) \
- break; \
- t0 = q; \
- factor_insert_refind (factors, p, i + 1, I); \
- } \
- } while (0)
-
- for (; i < PRIMES_PTAB_ENTRIES; i += 8)
- {
- uintmax_t q;
- const struct primes_dtab *pd = &primes_dtab[i];
- DIVBLOCK (0);
- DIVBLOCK (1);
- DIVBLOCK (2);
- DIVBLOCK (3);
- DIVBLOCK (4);
- DIVBLOCK (5);
- DIVBLOCK (6);
- DIVBLOCK (7);
-
- p += primes_diff8[i];
- if (p * p > t0)
- break;
- }
-
- return t0;
-}
-
-#if HAVE_GMP
-static void
-mp_factor_using_division (mpz_t t, struct mp_factors *factors)
-{
- mpz_t q;
- unsigned long int p;
-
- if (flag_verbose > 0)
- {
- printf ("[trial division] ");
- }
-
- mpz_init (q);
-
- p = mpz_scan1 (t, 0);
- mpz_div_2exp (t, t, p);
- while (p)
- {
- mp_factor_insert_ui (factors, 2);
- --p;
- }
-
- p = 3;
- for (unsigned int i = 1; i <= PRIMES_PTAB_ENTRIES;)
- {
- if (! mpz_divisible_ui_p (t, p))
- {
- p += primes_diff[i++];
- if (mpz_cmp_ui (t, p * p) < 0)
- break;
- }
- else
- {
- mpz_tdiv_q_ui (t, t, p);
- mp_factor_insert_ui (factors, p);
- }
- }
-
- mpz_clear (q);
-}
-#endif
-
-/* Entry i contains (2i+1)^(-1) mod 2^8. */
-static const unsigned char binvert_table[128] =
-{
- 0x01, 0xAB, 0xCD, 0xB7, 0x39, 0xA3, 0xC5, 0xEF,
- 0xF1, 0x1B, 0x3D, 0xA7, 0x29, 0x13, 0x35, 0xDF,
- 0xE1, 0x8B, 0xAD, 0x97, 0x19, 0x83, 0xA5, 0xCF,
- 0xD1, 0xFB, 0x1D, 0x87, 0x09, 0xF3, 0x15, 0xBF,
- 0xC1, 0x6B, 0x8D, 0x77, 0xF9, 0x63, 0x85, 0xAF,
- 0xB1, 0xDB, 0xFD, 0x67, 0xE9, 0xD3, 0xF5, 0x9F,
- 0xA1, 0x4B, 0x6D, 0x57, 0xD9, 0x43, 0x65, 0x8F,
- 0x91, 0xBB, 0xDD, 0x47, 0xC9, 0xB3, 0xD5, 0x7F,
- 0x81, 0x2B, 0x4D, 0x37, 0xB9, 0x23, 0x45, 0x6F,
- 0x71, 0x9B, 0xBD, 0x27, 0xA9, 0x93, 0xB5, 0x5F,
- 0x61, 0x0B, 0x2D, 0x17, 0x99, 0x03, 0x25, 0x4F,
- 0x51, 0x7B, 0x9D, 0x07, 0x89, 0x73, 0x95, 0x3F,
- 0x41, 0xEB, 0x0D, 0xF7, 0x79, 0xE3, 0x05, 0x2F,
- 0x31, 0x5B, 0x7D, 0xE7, 0x69, 0x53, 0x75, 0x1F,
- 0x21, 0xCB, 0xED, 0xD7, 0x59, 0xC3, 0xE5, 0x0F,
- 0x11, 0x3B, 0x5D, 0xC7, 0x49, 0x33, 0x55, 0xFF
-};
-
-/* Compute n^(-1) mod B, using a Newton iteration. */
-#define binv(inv,n) \
- do { \
- uintmax_t __n = (n); \
- uintmax_t __inv; \
- \
- __inv = binvert_table[(__n / 2) & 0x7F]; /* 8 */ \
- if (W_TYPE_SIZE > 8) __inv = 2 * __inv - __inv * __inv * __n; \
- if (W_TYPE_SIZE > 16) __inv = 2 * __inv - __inv * __inv * __n; \
- if (W_TYPE_SIZE > 32) __inv = 2 * __inv - __inv * __inv * __n; \
- \
- if (W_TYPE_SIZE > 64) \
- { \
- int __invbits = 64; \
- do { \
- __inv = 2 * __inv - __inv * __inv * __n; \
- __invbits *= 2; \
- } while (__invbits < W_TYPE_SIZE); \
- } \
- \
- (inv) = __inv; \
- } while (0)
-
-/* q = u / d, assuming d|u. */
-#define divexact_21(q1, q0, u1, u0, d) \
- do { \
- uintmax_t _di, _q0; \
- binv (_di, (d)); \
- _q0 = (u0) * _di; \
- if ((u1) >= (d)) \
- { \
- uintmax_t _p1, _p0; \
- umul_ppmm (_p1, _p0, _q0, d); \
- (q1) = ((u1) - _p1) * _di; \
- (q0) = _q0; \
- } \
- else \
- { \
- (q0) = _q0; \
- (q1) = 0; \
- } \
- } while(0)
-
-/* x B (mod n). */
-#define redcify(r_prim, r, n) \
- do { \
- uintmax_t _redcify_q; \
- udiv_qrnnd (_redcify_q, r_prim, r, 0, n); \
- } while (0)
-
-/* x B^2 (mod n). Requires x > 0, n1 < B/2 */
-#define redcify2(r1, r0, x, n1, n0) \
- do { \
- uintmax_t _r1, _r0, _i; \
- if ((x) < (n1)) \
- { \
- _r1 = (x); _r0 = 0; \
- _i = W_TYPE_SIZE; \
- } \
- else \
- { \
- _r1 = 0; _r0 = (x); \
- _i = 2*W_TYPE_SIZE; \
- } \
- while (_i-- > 0) \
- { \
- lsh2 (_r1, _r0, _r1, _r0, 1); \
- if (ge2 (_r1, _r0, (n1), (n0))) \
- sub_ddmmss (_r1, _r0, _r1, _r0, (n1), (n0)); \
- } \
- (r1) = _r1; \
- (r0) = _r0; \
- } while (0)
-
-/* Modular two-word multiplication, r = a * b mod m, with mi = m^(-1) mod B.
- Both a and b must be in redc form, the result will be in redc form too. */
-static inline uintmax_t
-mulredc (uintmax_t a, uintmax_t b, uintmax_t m, uintmax_t mi)
-{
- uintmax_t rh, rl, q, th, tl, xh;
-
- umul_ppmm (rh, rl, a, b);
- q = rl * mi;
- umul_ppmm (th, tl, q, m);
- xh = rh - th;
- if (rh < th)
- xh += m;
-
- return xh;
-}
-
-/* Modular two-word multiplication, r = a * b mod m, with mi = m^(-1) mod B.
- Both a and b must be in redc form, the result will be in redc form too.
- For performance reasons, the most significant bit of m must be clear. */
-static uintmax_t
-mulredc2 (uintmax_t *r1p,
- uintmax_t a1, uintmax_t a0, uintmax_t b1, uintmax_t b0,
- uintmax_t m1, uintmax_t m0, uintmax_t mi)
-{
- uintmax_t r1, r0, q, p1, p0, t1, t0, s1, s0;
- mi = -mi;
- assert ( (a1 >> (W_TYPE_SIZE - 1)) == 0);
- assert ( (b1 >> (W_TYPE_SIZE - 1)) == 0);
- assert ( (m1 >> (W_TYPE_SIZE - 1)) == 0);
-
- /* First compute a0 * <b1, b0> B^{-1}
- +-----+
- |a0 b0|
- +--+--+--+
- |a0 b1|
- +--+--+--+
- |q0 m0|
- +--+--+--+
- |q0 m1|
- -+--+--+--+
- |r1|r0| 0|
- +--+--+--+
- */
- umul_ppmm (t1, t0, a0, b0);
- umul_ppmm (r1, r0, a0, b1);
- q = mi * t0;
- umul_ppmm (p1, p0, q, m0);
- umul_ppmm (s1, s0, q, m1);
- r0 += (t0 != 0); /* Carry */
- add_ssaaaa (r1, r0, r1, r0, 0, p1);
- add_ssaaaa (r1, r0, r1, r0, 0, t1);
- add_ssaaaa (r1, r0, r1, r0, s1, s0);
-
- /* Next, (a1 * <b1, b0> + <r1, r0> B^{-1}
- +-----+
- |a1 b0|
- +--+--+
- |r1|r0|
- +--+--+--+
- |a1 b1|
- +--+--+--+
- |q1 m0|
- +--+--+--+
- |q1 m1|
- -+--+--+--+
- |r1|r0| 0|
- +--+--+--+
- */
- umul_ppmm (t1, t0, a1, b0);
- umul_ppmm (s1, s0, a1, b1);
- add_ssaaaa (t1, t0, t1, t0, 0, r0);
- q = mi * t0;
- add_ssaaaa (r1, r0, s1, s0, 0, r1);
- umul_ppmm (p1, p0, q, m0);
- umul_ppmm (s1, s0, q, m1);
- r0 += (t0 != 0); /* Carry */
- add_ssaaaa (r1, r0, r1, r0, 0, p1);
- add_ssaaaa (r1, r0, r1, r0, 0, t1);
- add_ssaaaa (r1, r0, r1, r0, s1, s0);
-
- if (ge2 (r1, r0, m1, m0))
- sub_ddmmss (r1, r0, r1, r0, m1, m0);
-
- *r1p = r1;
- return r0;
-}
-
-static uintmax_t _GL_ATTRIBUTE_CONST
-powm (uintmax_t b, uintmax_t e, uintmax_t n, uintmax_t ni, uintmax_t one)
-{
- uintmax_t y = one;
-
- if (e & 1)
- y = b;
-
- while (e != 0)
- {
- b = mulredc (b, b, n, ni);
- e >>= 1;
-
- if (e & 1)
- y = mulredc (y, b, n, ni);
- }
-
- return y;
-}
-
-static uintmax_t
-powm2 (uintmax_t *r1m,
- const uintmax_t *bp, const uintmax_t *ep, const uintmax_t *np,
- uintmax_t ni, const uintmax_t *one)
-{
- uintmax_t r1, r0, b1, b0, n1, n0;
- unsigned int i;
- uintmax_t e;
-
- b0 = bp[0];
- b1 = bp[1];
- n0 = np[0];
- n1 = np[1];
-
- r0 = one[0];
- r1 = one[1];
-
- for (e = ep[0], i = W_TYPE_SIZE; i > 0; i--, e >>= 1)
- {
- if (e & 1)
- {
- r0 = mulredc2 (r1m, r1, r0, b1, b0, n1, n0, ni);
- r1 = *r1m;
- }
- b0 = mulredc2 (r1m, b1, b0, b1, b0, n1, n0, ni);
- b1 = *r1m;
- }
- for (e = ep[1]; e > 0; e >>= 1)
- {
- if (e & 1)
- {
- r0 = mulredc2 (r1m, r1, r0, b1, b0, n1, n0, ni);
- r1 = *r1m;
- }
- b0 = mulredc2 (r1m, b1, b0, b1, b0, n1, n0, ni);
- b1 = *r1m;
- }
- *r1m = r1;
- return r0;
-}
-
-static bool _GL_ATTRIBUTE_CONST
-millerrabin (uintmax_t n, uintmax_t ni, uintmax_t b, uintmax_t q,
- unsigned int k, uintmax_t one)
-{
- uintmax_t y = powm (b, q, n, ni, one);
-
- uintmax_t nm1 = n - one; /* -1, but in redc representation. */
-
- if (y == one || y == nm1)
- return true;
-
- for (unsigned int i = 1; i < k; i++)
- {
- y = mulredc (y, y, n, ni);
-
- if (y == nm1)
- return true;
- if (y == one)
- return false;
- }
- return false;
-}
-
-static bool
-millerrabin2 (const uintmax_t *np, uintmax_t ni, const uintmax_t *bp,
- const uintmax_t *qp, unsigned int k, const uintmax_t *one)
-{
- uintmax_t y1, y0, nm1_1, nm1_0, r1m;
-
- y0 = powm2 (&r1m, bp, qp, np, ni, one);
- y1 = r1m;
-
- if (y0 == one[0] && y1 == one[1])
- return true;
-
- sub_ddmmss (nm1_1, nm1_0, np[1], np[0], one[1], one[0]);
-
- if (y0 == nm1_0 && y1 == nm1_1)
- return true;
-
- for (unsigned int i = 1; i < k; i++)
- {
- y0 = mulredc2 (&r1m, y1, y0, y1, y0, np[1], np[0], ni);
- y1 = r1m;
-
- if (y0 == nm1_0 && y1 == nm1_1)
- return true;
- if (y0 == one[0] && y1 == one[1])
- return false;
- }
- return false;
-}
-
-#if HAVE_GMP
-static bool
-mp_millerrabin (mpz_srcptr n, mpz_srcptr nm1, mpz_ptr x, mpz_ptr y,
- mpz_srcptr q, unsigned long int k)
-{
- mpz_powm (y, x, q, n);
-
- if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, nm1) == 0)
- return true;
-
- for (unsigned long int i = 1; i < k; i++)
- {
- mpz_powm_ui (y, y, 2, n);
- if (mpz_cmp (y, nm1) == 0)
- return true;
- if (mpz_cmp_ui (y, 1) == 0)
- return false;
- }
- return false;
-}
-#endif
-
-/* Lucas' prime test. The number of iterations vary greatly, up to a few dozen
- have been observed. The average seem to be about 2. */
-static bool
-prime_p (uintmax_t n)
-{
- int k;
- bool is_prime;
- uintmax_t a_prim, one, ni;
- struct factors factors;
-
- if (n <= 1)
- return false;
-
- /* We have already casted out small primes. */
- if (n < (uintmax_t) FIRST_OMITTED_PRIME * FIRST_OMITTED_PRIME)
- return true;
-
- /* Precomputation for Miller-Rabin. */
- uintmax_t q = n - 1;
- for (k = 0; (q & 1) == 0; k++)
- q >>= 1;
-
- uintmax_t a = 2;
- binv (ni, n); /* ni <- 1/n mod B */
- redcify (one, 1, n);
- addmod (a_prim, one, one, n); /* i.e., redcify a = 2 */
-
- /* Perform a Miller-Rabin test, finds most composites quickly. */
- if (!millerrabin (n, ni, a_prim, q, k, one))
- return false;
-
- if (flag_prove_primality)
- {
- /* Factor n-1 for Lucas. */
- factor (0, n - 1, &factors);
- }
-
- /* Loop until Lucas proves our number prime, or Miller-Rabin proves our
- number composite. */
- for (unsigned int r = 0; r < PRIMES_PTAB_ENTRIES; r++)
- {
- if (flag_prove_primality)
- {
- is_prime = true;
- for (unsigned int i = 0; i < factors.nfactors && is_prime; i++)
- {
- is_prime = powm (a_prim, (n - 1) / factors.p[i], n, ni, one) != one;
- }
- }
- else
- {
- /* After enough Miller-Rabin runs, be content. */
- is_prime = (r == MR_REPS - 1);
- }
-
- if (is_prime)
- return true;
-
- a += primes_diff[r]; /* Establish new base. */
-
- /* The following is equivalent to redcify (a_prim, a, n). It runs faster
- on most processors, since it avoids udiv_qrnnd. If we go down the
- udiv_qrnnd_preinv path, this code should be replaced. */
- {
- uintmax_t dummy, s1, s0;
- umul_ppmm (s1, s0, one, a);
- if (LIKELY (s1 == 0))
- a_prim = s0 % n;
- else
- udiv_qrnnd (dummy, a_prim, s1, s0, n);
- }
-
- if (!millerrabin (n, ni, a_prim, q, k, one))
- return false;
- }
-
- fprintf (stderr, "Lucas prime test failure. This should not happen\n");
- abort ();
-}
-
-static bool
-prime2_p (uintmax_t n1, uintmax_t n0)
-{
- uintmax_t q[2], nm1[2];
- uintmax_t a_prim[2];
- uintmax_t one[2];
- uintmax_t na[2];
- uintmax_t ni;
- unsigned int k;
- struct factors factors;
-
- if (n1 == 0)
- return prime_p (n0);
-
- nm1[1] = n1 - (n0 == 0);
- nm1[0] = n0 - 1;
- if (nm1[0] == 0)
- {
- count_trailing_zeros (k, nm1[1]);
-
- q[0] = nm1[1] >> k;
- q[1] = 0;
- k += W_TYPE_SIZE;
- }
- else
- {
- count_trailing_zeros (k, nm1[0]);
- rsh2 (q[1], q[0], nm1[1], nm1[0], k);
- }
-
- uintmax_t a = 2;
- binv (ni, n0);
- redcify2 (one[1], one[0], 1, n1, n0);
- addmod2 (a_prim[1], a_prim[0], one[1], one[0], one[1], one[0], n1, n0);
-
- /* FIXME: Use scalars or pointers in arguments? Some consistency needed. */
- na[0] = n0;
- na[1] = n1;
-
- if (!millerrabin2 (na, ni, a_prim, q, k, one))
- return false;
-
- if (flag_prove_primality)
- {
- /* Factor n-1 for Lucas. */
- factor (nm1[1], nm1[0], &factors);
- }
-
- /* Loop until Lucas proves our number prime, or Miller-Rabin proves our
- number composite. */
- for (unsigned int r = 0; r < PRIMES_PTAB_ENTRIES; r++)
- {
- bool is_prime;
- uintmax_t e[2], y[2];
-
- if (flag_prove_primality)
- {
- is_prime = true;
- if (factors.plarge[1])
- {
- uintmax_t pi;
- binv (pi, factors.plarge[0]);
- e[0] = pi * nm1[0];
- e[1] = 0;
- y[0] = powm2 (&y[1], a_prim, e, na, ni, one);
- is_prime = (y[0] != one[0] || y[1] != one[1]);
- }
- for (unsigned int i = 0; i < factors.nfactors && is_prime; i++)
- {
- /* FIXME: We always have the factor 2. Do we really need to handle it
- here? We have done the same powering as part of millerrabin. */
- if (factors.p[i] == 2)
- rsh2 (e[1], e[0], nm1[1], nm1[0], 1);
- else
- divexact_21 (e[1], e[0], nm1[1], nm1[0], factors.p[i]);
- y[0] = powm2 (&y[1], a_prim, e, na, ni, one);
- is_prime = (y[0] != one[0] || y[1] != one[1]);
- }
- }
- else
- {
- /* After enough Miller-Rabin runs, be content. */
- is_prime = (r == MR_REPS - 1);
- }
-
- if (is_prime)
- return true;
-
- a += primes_diff[r]; /* Establish new base. */
- redcify2 (a_prim[1], a_prim[0], a, n1, n0);
-
- if (!millerrabin2 (na, ni, a_prim, q, k, one))
- return false;
- }
-
- fprintf (stderr, "Lucas prime test failure. This should not happen\n");
- abort ();
-}
-
-#if HAVE_GMP
-static bool
-mp_prime_p (mpz_t n)
-{
- bool is_prime;
- mpz_t q, a, nm1, tmp;
- struct mp_factors factors;
-
- if (mpz_cmp_ui (n, 1) <= 0)
- return false;
-
- /* We have already casted out small primes. */
- if (mpz_cmp_ui (n, (long) FIRST_OMITTED_PRIME * FIRST_OMITTED_PRIME) < 0)
- return true;
-
- mpz_inits (q, a, nm1, tmp, NULL);
-
- /* Precomputation for Miller-Rabin. */
- mpz_sub_ui (nm1, n, 1);
-
- /* Find q and k, where q is odd and n = 1 + 2**k * q. */
- unsigned long int k = mpz_scan1 (nm1, 0);
- mpz_tdiv_q_2exp (q, nm1, k);
-
- mpz_set_ui (a, 2);
-
- /* Perform a Miller-Rabin test, finds most composites quickly. */
- if (!mp_millerrabin (n, nm1, a, tmp, q, k))
- {
- is_prime = false;
- goto ret2;
- }
-
- if (flag_prove_primality)
- {
- /* Factor n-1 for Lucas. */
- mpz_set (tmp, nm1);
- mp_factor (tmp, &factors);
- }
-
- /* Loop until Lucas proves our number prime, or Miller-Rabin proves our
- number composite. */
- for (unsigned int r = 0; r < PRIMES_PTAB_ENTRIES; r++)
- {
- if (flag_prove_primality)
- {
- is_prime = true;
- for (unsigned long int i = 0; i < factors.nfactors && is_prime; i++)
- {
- mpz_divexact (tmp, nm1, factors.p[i]);
- mpz_powm (tmp, a, tmp, n);
- is_prime = mpz_cmp_ui (tmp, 1) != 0;
- }
- }
- else
- {
- /* After enough Miller-Rabin runs, be content. */
- is_prime = (r == MR_REPS - 1);
- }
-
- if (is_prime)
- goto ret1;
-
- mpz_add_ui (a, a, primes_diff[r]); /* Establish new base. */
-
- if (!mp_millerrabin (n, nm1, a, tmp, q, k))
- {
- is_prime = false;
- goto ret1;
- }
- }
-
- fprintf (stderr, "Lucas prime test failure. This should not happen\n");
- abort ();
-
- ret1:
- if (flag_prove_primality)
- mp_factor_clear (&factors);
- ret2:
- mpz_clears (q, a, nm1, tmp, NULL);
-
- return is_prime;
-}
-#endif
-
-static void
-factor_using_pollard_rho (uintmax_t n, unsigned long int a,
- struct factors *factors)
-{
- uintmax_t x, z, y, P, t, ni, g;
-
- unsigned long int k = 1;
- unsigned long int l = 1;
-
- redcify (P, 1, n);
- addmod (x, P, P, n); /* i.e., redcify(2) */
- y = z = x;
-
- while (n != 1)
- {
- assert (a < n);
-
- binv (ni, n); /* FIXME: when could we use old 'ni' value? */
-
- for (;;)
- {
- do
- {
- x = mulredc (x, x, n, ni);
- addmod (x, x, a, n);
-
- submod (t, z, x, n);
- P = mulredc (P, t, n, ni);
-
- if (k % 32 == 1)
- {
- if (gcd_odd (P, n) != 1)
- goto factor_found;
- y = x;
- }
- }
- while (--k != 0);
-
- z = x;
- k = l;
- l = 2 * l;
- for (unsigned long int i = 0; i < k; i++)
- {
- x = mulredc (x, x, n, ni);
- addmod (x, x, a, n);
- }
- y = x;
- }
-
- factor_found:
- do
- {
- y = mulredc (y, y, n, ni);
- addmod (y, y, a, n);
-
- submod (t, z, y, n);
- g = gcd_odd (t, n);
- }
- while (g == 1);
-
- n = n / g;
-
- if (!prime_p (g))
- factor_using_pollard_rho (g, a + 1, factors);
- else
- factor_insert (factors, g);
-
- if (prime_p (n))
- {
- factor_insert (factors, n);
- break;
- }
-
- x = x % n;
- z = z % n;
- y = y % n;
- }
-}
-
-static void
-factor_using_pollard_rho2 (uintmax_t n1, uintmax_t n0, unsigned long int a,
- struct factors *factors)
-{
- uintmax_t x1, x0, z1, z0, y1, y0, P1, P0, t1, t0, ni, g1, g0, r1m;
-
- unsigned long int k = 1;
- unsigned long int l = 1;
-
- redcify2 (P1, P0, 1, n1, n0);
- addmod2 (x1, x0, P1, P0, P1, P0, n1, n0); /* i.e., redcify(2) */
- y1 = z1 = x1;
- y0 = z0 = x0;
-
- while (n1 != 0 || n0 != 1)
- {
- binv (ni, n0);
-
- for (;;)
- {
- do
- {
- x0 = mulredc2 (&r1m, x1, x0, x1, x0, n1, n0, ni);
- x1 = r1m;
- addmod2 (x1, x0, x1, x0, 0, a, n1, n0);
-
- submod2 (t1, t0, z1, z0, x1, x0, n1, n0);
- P0 = mulredc2 (&r1m, P1, P0, t1, t0, n1, n0, ni);
- P1 = r1m;
-
- if (k % 32 == 1)
- {
- g0 = gcd2_odd (&g1, P1, P0, n1, n0);
- if (g1 != 0 || g0 != 1)
- goto factor_found;
- y1 = x1; y0 = x0;
- }
- }
- while (--k != 0);
-
- z1 = x1; z0 = x0;
- k = l;
- l = 2 * l;
- for (unsigned long int i = 0; i < k; i++)
- {
- x0 = mulredc2 (&r1m, x1, x0, x1, x0, n1, n0, ni);
- x1 = r1m;
- addmod2 (x1, x0, x1, x0, 0, a, n1, n0);
- }
- y1 = x1; y0 = x0;
- }
-
- factor_found:
- do
- {
- y0 = mulredc2 (&r1m, y1, y0, y1, y0, n1, n0, ni);
- y1 = r1m;
- addmod2 (y1, y0, y1, y0, 0, a, n1, n0);
-
- submod2 (t1, t0, z1, z0, y1, y0, n1, n0);
- g0 = gcd2_odd (&g1, t1, t0, n1, n0);
- }
- while (g1 == 0 && g0 == 1);
-
- if (g1 == 0)
- {
- /* The found factor is one word. */
- divexact_21 (n1, n0, n1, n0, g0); /* n = n / g */
-
- if (!prime_p (g0))
- factor_using_pollard_rho (g0, a + 1, factors);
- else
- factor_insert (factors, g0);
- }
- else
- {
- /* The found factor is two words. This is highly unlikely, thus hard
- to trigger. Please be careful before you change this code! */
- uintmax_t ginv;
-
- binv (ginv, g0); /* Compute n = n / g. Since the result will */
- n0 = ginv * n0; /* fit one word, we can compute the quotient */
- n1 = 0; /* modulo B, ignoring the high divisor word. */
-
- if (!prime2_p (g1, g0))
- factor_using_pollard_rho2 (g1, g0, a + 1, factors);
- else
- factor_insert_large (factors, g1, g0);
- }
-
- if (n1 == 0)
- {
- if (prime_p (n0))
- {
- factor_insert (factors, n0);
- break;
- }
-
- factor_using_pollard_rho (n0, a, factors);
- return;
- }
-
- if (prime2_p (n1, n0))
- {
- factor_insert_large (factors, n1, n0);
- break;
- }
-
- x0 = mod2 (&x1, x1, x0, n1, n0);
- z0 = mod2 (&z1, z1, z0, n1, n0);
- y0 = mod2 (&y1, y1, y0, n1, n0);
- }
-}
-
-#if HAVE_GMP
-static void
-mp_factor_using_pollard_rho (mpz_t n, unsigned long int a,
- struct mp_factors *factors)
-{
- mpz_t x, z, y, P;
- mpz_t t, t2;
- unsigned long long int k, l;
-
- if (flag_verbose > 0)
- {
- printf ("[pollard-rho (%lu)] ", a);
- }
-
- mpz_inits (t, t2, NULL);
- mpz_init_set_si (y, 2);
- mpz_init_set_si (x, 2);
- mpz_init_set_si (z, 2);
- mpz_init_set_ui (P, 1);
- k = 1;
- l = 1;
-
- while (mpz_cmp_ui (n, 1) != 0)
- {
- for (;;)
- {
- do
- {
- mpz_mul (t, x, x);
- mpz_mod (x, t, n);
- mpz_add_ui (x, x, a);
-
- mpz_sub (t, z, x);
- mpz_mul (t2, P, t);
- mpz_mod (P, t2, n);
-
- if (k % 32 == 1)
- {
- mpz_gcd (t, P, n);
- if (mpz_cmp_ui (t, 1) != 0)
- goto factor_found;
- mpz_set (y, x);
- }
- }
- while (--k != 0);
-
- mpz_set (z, x);
- k = l;
- l = 2 * l;
- for (unsigned long long int i = 0; i < k; i++)
- {
- mpz_mul (t, x, x);
- mpz_mod (x, t, n);
- mpz_add_ui (x, x, a);
- }
- mpz_set (y, x);
- }
-
- factor_found:
- do
- {
- mpz_mul (t, y, y);
- mpz_mod (y, t, n);
- mpz_add_ui (y, y, a);
-
- mpz_sub (t, z, y);
- mpz_gcd (t, t, n);
- }
- while (mpz_cmp_ui (t, 1) == 0);
-
- mpz_divexact (n, n, t); /* divide by t, before t is overwritten */
-
- if (!mp_prime_p (t))
- {
- if (flag_verbose > 0)
- {
- printf ("[composite factor--restarting pollard-rho] ");
- }
- mp_factor_using_pollard_rho (t, a + 1, factors);
- }
- else
- {
- mp_factor_insert (factors, t);
- }
-
- if (mp_prime_p (n))
- {
- mp_factor_insert (factors, n);
- break;
- }
-
- mpz_mod (x, x, n);
- mpz_mod (z, z, n);
- mpz_mod (y, y, n);
- }
-
- mpz_clears (P, t2, t, z, x, y, NULL);
-}
-#endif
-
-/* FIXME: Maybe better to use an iteration converging to 1/sqrt(n)? If
- algorithm is replaced, consider also returning the remainder. */
-static uintmax_t _GL_ATTRIBUTE_CONST
-isqrt (uintmax_t n)
-{
- uintmax_t x;
- unsigned c;
- if (n == 0)
- return 0;
-
- count_leading_zeros (c, n);
-
- /* Make x > sqrt(n). This will be invariant through the loop. */
- x = (uintmax_t) 1 << ((W_TYPE_SIZE + 1 - c) / 2);
-
- for (;;)
- {
- uintmax_t y = (x + n/x) / 2;
- if (y >= x)
- return x;
-
- x = y;
- }
-}
-
-static uintmax_t _GL_ATTRIBUTE_CONST
-isqrt2 (uintmax_t nh, uintmax_t nl)
-{
- unsigned int shift;
- uintmax_t x;
-
- /* Ensures the remainder fits in an uintmax_t. */
- assert (nh < ((uintmax_t) 1 << (W_TYPE_SIZE - 2)));
-
- if (nh == 0)
- return isqrt (nl);
-
- count_leading_zeros (shift, nh);
- shift &= ~1;
-
- /* Make x > sqrt(n) */
- x = isqrt ( (nh << shift) + (nl >> (W_TYPE_SIZE - shift))) + 1;
- x <<= (W_TYPE_SIZE - shift) / 2;
-
- /* Do we need more than one iteration? */
- for (;;)
- {
- uintmax_t q, r, y;
- udiv_qrnnd (q, r, nh, nl, x);
- y = (x + q) / 2;
-
- if (y >= x)
- {
- uintmax_t hi, lo;
- umul_ppmm (hi, lo, x + 1, x + 1);
- assert (gt2 (hi, lo, nh, nl));
-
- umul_ppmm (hi, lo, x, x);
- assert (ge2 (nh, nl, hi, lo));
- sub_ddmmss (hi, lo, nh, nl, hi, lo);
- assert (hi == 0);
-
- return x;
- }
-
- x = y;
- }
-}
-
-/* MAGIC[N] has a bit i set iff i is a quadratic residue mod N. */
-#define MAGIC64 ((uint64_t) 0x0202021202030213ULL)
-#define MAGIC63 ((uint64_t) 0x0402483012450293ULL)
-#define MAGIC65 ((uint64_t) 0x218a019866014613ULL)
-#define MAGIC11 0x23b
-
-/* Returns the square root if the input is a square, otherwise 0. */
-static uintmax_t _GL_ATTRIBUTE_CONST
-is_square (uintmax_t x)
-{
- /* Uses the tests suggested by Cohen. Excludes 99% of the non-squares before
- computing the square root. */
- if (((MAGIC64 >> (x & 63)) & 1)
- && ((MAGIC63 >> (x % 63)) & 1)
- /* Both 0 and 64 are squares mod (65) */
- && ((MAGIC65 >> ((x % 65) & 63)) & 1)
- && ((MAGIC11 >> (x % 11) & 1)))
- {
- uintmax_t r = isqrt (x);
- if (r*r == x)
- return r;
- }
- return 0;
-}
-
-/* invtab[i] = floor(0x10000 / (0x100 + i) */
-static const unsigned short invtab[0x81] =
- {
- 0x200,
- 0x1fc, 0x1f8, 0x1f4, 0x1f0, 0x1ec, 0x1e9, 0x1e5, 0x1e1,
- 0x1de, 0x1da, 0x1d7, 0x1d4, 0x1d0, 0x1cd, 0x1ca, 0x1c7,
- 0x1c3, 0x1c0, 0x1bd, 0x1ba, 0x1b7, 0x1b4, 0x1b2, 0x1af,
- 0x1ac, 0x1a9, 0x1a6, 0x1a4, 0x1a1, 0x19e, 0x19c, 0x199,
- 0x197, 0x194, 0x192, 0x18f, 0x18d, 0x18a, 0x188, 0x186,
- 0x183, 0x181, 0x17f, 0x17d, 0x17a, 0x178, 0x176, 0x174,
- 0x172, 0x170, 0x16e, 0x16c, 0x16a, 0x168, 0x166, 0x164,
- 0x162, 0x160, 0x15e, 0x15c, 0x15a, 0x158, 0x157, 0x155,
- 0x153, 0x151, 0x150, 0x14e, 0x14c, 0x14a, 0x149, 0x147,
- 0x146, 0x144, 0x142, 0x141, 0x13f, 0x13e, 0x13c, 0x13b,
- 0x139, 0x138, 0x136, 0x135, 0x133, 0x132, 0x130, 0x12f,
- 0x12e, 0x12c, 0x12b, 0x129, 0x128, 0x127, 0x125, 0x124,
- 0x123, 0x121, 0x120, 0x11f, 0x11e, 0x11c, 0x11b, 0x11a,
- 0x119, 0x118, 0x116, 0x115, 0x114, 0x113, 0x112, 0x111,
- 0x10f, 0x10e, 0x10d, 0x10c, 0x10b, 0x10a, 0x109, 0x108,
- 0x107, 0x106, 0x105, 0x104, 0x103, 0x102, 0x101, 0x100,
- };
-
-/* Compute q = [u/d], r = u mod d. Avoids slow hardware division for the case
- that q < 0x40; here it instead uses a table of (Euclidian) inverses. */
-#define div_smallq(q, r, u, d) \
- do { \
- if ((u) / 0x40 < (d)) \
- { \
- int _cnt; \
- uintmax_t _dinv, _mask, _q, _r; \
- count_leading_zeros (_cnt, (d)); \
- _r = (u); \
- if (UNLIKELY (_cnt > (W_TYPE_SIZE - 8))) \
- { \
- _dinv = invtab[((d) << (_cnt + 8 - W_TYPE_SIZE)) - 0x80]; \
- _q = _dinv * _r >> (8 + W_TYPE_SIZE - _cnt); \
- } \
- else \
- { \
- _dinv = invtab[((d) >> (W_TYPE_SIZE - 8 - _cnt)) - 0x7f]; \
- _q = _dinv * (_r >> (W_TYPE_SIZE - 3 - _cnt)) >> 11; \
- } \
- _r -= _q*(d); \
- \
- _mask = -(uintmax_t) (_r >= (d)); \
- (r) = _r - (_mask & (d)); \
- (q) = _q - _mask; \
- assert ( (q) * (d) + (r) == u); \
- } \
- else \
- { \
- uintmax_t _q = (u) / (d); \
- (r) = (u) - _q * (d); \
- (q) = _q; \
- } \
- } while (0)
-
-/* Notes: Example N = 22117019. After first phase we find Q1 = 6314, Q
- = 3025, P = 1737, representing F_{18} = (-6314, 2* 1737, 3025),
- with 3025 = 55^2.
-
- Constructing the square root, we get Q1 = 55, Q = 8653, P = 4652,
- representing G_0 = (-55, 2*4652, 8653).
-
- In the notation of the paper:
-
- S_{-1} = 55, S_0 = 8653, R_0 = 4652
-
- Put
-
- t_0 = floor([q_0 + R_0] / S0) = 1
- R_1 = t_0 * S_0 - R_0 = 4001
- S_1 = S_{-1} +t_0 (R_0 - R_1) = 706
-*/
-
-/* Multipliers, in order of efficiency:
- 0.7268 3*5*7*11 = 1155 = 3 (mod 4)
- 0.7317 3*5*7 = 105 = 1
- 0.7820 3*5*11 = 165 = 1
- 0.7872 3*5 = 15 = 3
- 0.8101 3*7*11 = 231 = 3
- 0.8155 3*7 = 21 = 1
- 0.8284 5*7*11 = 385 = 1
- 0.8339 5*7 = 35 = 3
- 0.8716 3*11 = 33 = 1
- 0.8774 3 = 3 = 3
- 0.8913 5*11 = 55 = 3
- 0.8972 5 = 5 = 1
- 0.9233 7*11 = 77 = 1
- 0.9295 7 = 7 = 3
- 0.9934 11 = 11 = 3
-*/
-#define QUEUE_SIZE 50
-
-#if STAT_SQUFOF
-# define Q_FREQ_SIZE 50
-/* Element 0 keeps the total */
-static unsigned int q_freq[Q_FREQ_SIZE + 1];
-# define MIN(a,b) ((a) < (b) ? (a) : (b))
-#endif
-
-/* Return true on success. Expected to fail only for numbers
- >= 2^{2*W_TYPE_SIZE - 2}, or close to that limit. */
-static bool
-factor_using_squfof (uintmax_t n1, uintmax_t n0, struct factors *factors)
-{
- /* Uses algorithm and notation from
-
- SQUARE FORM FACTORIZATION
- JASON E. GOWER AND SAMUEL S. WAGSTAFF, JR.
-
- http://homes.cerias.purdue.edu/~ssw/squfof.pdf
- */
-
- static const unsigned int multipliers_1[] =
- { /* = 1 (mod 4) */
- 105, 165, 21, 385, 33, 5, 77, 1, 0
- };
- static const unsigned int multipliers_3[] =
- { /* = 3 (mod 4) */
- 1155, 15, 231, 35, 3, 55, 7, 11, 0
- };
-
- const unsigned int *m;
-
- struct { uintmax_t Q; uintmax_t P; } queue[QUEUE_SIZE];
-
- if (n1 >= ((uintmax_t) 1 << (W_TYPE_SIZE - 2)))
- return false;
-
- uintmax_t sqrt_n = isqrt2 (n1, n0);
-
- if (n0 == sqrt_n * sqrt_n)
- {
- uintmax_t p1, p0;
-
- umul_ppmm (p1, p0, sqrt_n, sqrt_n);
- assert (p0 == n0);
-
- if (n1 == p1)
- {
- if (prime_p (sqrt_n))
- factor_insert_multiplicity (factors, sqrt_n, 2);
- else
- {
- struct factors f;
-
- f.nfactors = 0;
- if (!factor_using_squfof (0, sqrt_n, &f))
- {
- /* Try pollard rho instead */
- factor_using_pollard_rho (sqrt_n, 1, &f);
- }
- /* Duplicate the new factors */
- for (unsigned int i = 0; i < f.nfactors; i++)
- factor_insert_multiplicity (factors, f.p[i], 2*f.e[i]);
- }
- return true;
- }
- }
-
- /* Select multipliers so we always get n * mu = 3 (mod 4) */
- for (m = (n0 % 4 == 1) ? multipliers_3 : multipliers_1;
- *m; m++)
- {
- uintmax_t S, Dh, Dl, Q1, Q, P, L, L1, B;
- unsigned int i;
- unsigned int mu = *m;
- unsigned int qpos = 0;
-
- assert (mu * n0 % 4 == 3);
-
- /* In the notation of the paper, with mu * n == 3 (mod 4), we
- get \Delta = 4 mu * n, and the paper's \mu is 2 mu. As far as
- I understand it, the necessary bound is 4 \mu^3 < n, or 32
- mu^3 < n.
-
- However, this seems insufficient: With n = 37243139 and mu =
- 105, we get a trivial factor, from the square 38809 = 197^2,
- without any corresponding Q earlier in the iteration.
-
- Requiring 64 mu^3 < n seems sufficient. */
- if (n1 == 0)
- {
- if ((uintmax_t) mu*mu*mu >= n0 / 64)
- continue;
- }
- else
- {
- if (n1 > ((uintmax_t) 1 << (W_TYPE_SIZE - 2)) / mu)
- continue;
- }
- umul_ppmm (Dh, Dl, n0, mu);
- Dh += n1 * mu;
-
- assert (Dl % 4 != 1);
- assert (Dh < (uintmax_t) 1 << (W_TYPE_SIZE - 2));
-
- S = isqrt2 (Dh, Dl);
-
- Q1 = 1;
- P = S;
-
- /* Square root remainder fits in one word, so ignore high part. */
- Q = Dl - P*P;
- /* FIXME: When can this differ from floor(sqrt(2 sqrt(D)))? */
- L = isqrt (2*S);
- B = 2*L;
- L1 = mu * 2 * L;
-
- /* The form is (+/- Q1, 2P, -/+ Q), of discriminant 4 (P^2 + Q Q1) =
- 4 D. */
-
- for (i = 0; i <= B; i++)
- {
- uintmax_t q, P1, t, rem;
-
- div_smallq (q, rem, S+P, Q);
- P1 = S - rem; /* P1 = q*Q - P */
-
-#if STAT_SQUFOF
- assert (q > 0);
- q_freq[0]++;
- q_freq[MIN(q, Q_FREQ_SIZE)]++;
-#endif
-
- if (Q <= L1)
- {
- uintmax_t g = Q;
-
- if ( (Q & 1) == 0)
- g /= 2;
-
- g /= gcd_odd (g, mu);
-
- if (g <= L)
- {
- if (qpos >= QUEUE_SIZE)
- {
- fprintf (stderr, "squfof queue overflow.\n");
- exit (EXIT_FAILURE);
- }
- queue[qpos].Q = g;
- queue[qpos].P = P % g;
- qpos++;
- }
- }
-
- /* I think the difference can be either sign, but mod
- 2^W_TYPE_SIZE arithmetic should be fine. */
- t = Q1 + q * (P - P1);
- Q1 = Q;
- Q = t;
- P = P1;
-
- if ( (i & 1) == 0)
- {
- uintmax_t r = is_square (Q);
- if (r)
- {
- unsigned int j;
-
- for (j = 0; j < qpos; j++)
- {
- if (queue[j].Q == r)
- {
- if (r == 1)
- /* Traversed entire cycle. */
- goto next_multiplier;
-
- /* Need the absolute value for divisibility test. */
- if (P >= queue[j].P)
- t = P - queue[j].P;
- else
- t = queue[j].P - P;
- if (t % r == 0)
- {
- /* Delete entries up to and including entry
- j, which matched. */
- memmove (queue, queue + j + 1,
- (qpos - j - 1) * sizeof (queue[0]));
- qpos -= (j + 1);
- }
- goto next_i;
- }
- }
-
- /* We have found a square form, which should give a
- factor. */
- Q1 = r;
- assert (S >= P); /* What signs are possible? */
- P += r * ((S - P) / r);
-
- /* Note: Paper says (N - P*P) / Q1, that seems incorrect
- for the case D = 2N. */
- /* Compute Q = (D - P*P) / Q1, but we need double
- precision. */
- uintmax_t hi, lo;
- umul_ppmm (hi, lo, P, P);
- sub_ddmmss (hi, lo, Dh, Dl, hi, lo);
- udiv_qrnnd (Q, rem, hi, lo, Q1);
- assert (rem == 0);
-
- for (;;)
- {
- /* Note: There appears to by a typo in the paper,
- Step 4a in the algorithm description says q <--
- floor([S+P]/\hat Q), but looking at the equations
- in Sec. 3.1, it should be q <-- floor([S+P] / Q).
- (In this code, \hat Q is Q1). */
- div_smallq (q, rem, S+P, Q);
- P1 = S - rem; /* P1 = q*Q - P */
-
-#if STAT_SQUFOF
- q_freq[0]++;
- q_freq[MIN (q, Q_FREQ_SIZE)]++;
-#endif
- if (P == P1)
- break;
- t = Q1 + q * (P - P1);
- Q1 = Q;
- Q = t;
- P = P1;
- }
-
- if ( (Q & 1) == 0)
- Q /= 2;
- Q /= gcd_odd (Q, mu);
-
- assert (Q > 1 && (n1 || Q < n0));
-
- if (prime_p (Q))
- factor_insert (factors, Q);
- else if (!factor_using_squfof (0, Q, factors))
- factor_using_pollard_rho (Q, 2, factors);
-
- divexact_21 (n1, n0, n1, n0, Q);
-
- if (prime2_p (n1, n0))
- factor_insert_large (factors, n1, n0);
- else
- {
- if (!factor_using_squfof (n1, n0, factors))
- {
- if (n1 == 0)
- factor_using_pollard_rho (n0, 1, factors);
- else
- factor_using_pollard_rho2 (n1, n0, 1, factors);
- }
- }
-
- return true;
- }
- }
- next_i:
- ;
- }
- next_multiplier:
- ;
- }
- return false;
-}
-
-static void
-factor (uintmax_t t1, uintmax_t t0, struct factors *factors)
-{
- factors->nfactors = 0;
- factors->plarge[1] = 0;
-
- if (t1 == 0 && t0 < 2)
- return;
-
- t0 = factor_using_division (&t1, t1, t0, factors);
-
- if (t1 == 0 && t0 < 2)
- return;
-
- if (prime2_p (t1, t0))
- factor_insert_large (factors, t1, t0);
- else
- {
- if (alg == ALG_SQUFOF)
- if (factor_using_squfof (t1, t0, factors))
- return;
-
- if (t1 == 0)
- factor_using_pollard_rho (t0, 1, factors);
- else
- factor_using_pollard_rho2 (t1, t0, 1, factors);
- }
-}
-
-#if HAVE_GMP
-static void
-mp_factor (mpz_t t, struct mp_factors *factors)
-{
- mp_factor_init (factors);
-
- if (mpz_sgn (t) != 0)
- {
- mp_factor_using_division (t, factors);
-
- if (mpz_cmp_ui (t, 1) != 0)
- {
- if (flag_verbose > 0)
- {
- printf ("[is number prime?] ");
- }
- if (mp_prime_p (t))
- mp_factor_insert (factors, t);
- else
- mp_factor_using_pollard_rho (t, 1, factors);
- }
- }
-}
-#endif
-
-static int
-strto2uintmax (uintmax_t *hip, uintmax_t *lop, const char *s)
-{
- int errcode;
- unsigned int lo_carry;
- uintmax_t hi, lo;
-
- errcode = -1;
-
- hi = lo = 0;
- for (;;)
- {
- unsigned int c = *s++;
- if (c == 0)
- break;
-
- if (UNLIKELY (c < '0' || c > '9'))
- {
- errcode = -1;
- break;
- }
- c -= '0';
-
- errcode = 0; /* we've seen at least one valid digit */
-
- if (UNLIKELY (hi > ~(uintmax_t)0 / 10))
- {
- errcode = -1; /* overflow */
- break;
- }
- hi = 10 * hi;
-
- lo_carry = (lo >> (W_TYPE_SIZE - 3)) + (lo >> (W_TYPE_SIZE - 1));
- lo_carry += 10 * lo < 2 * lo;
-
- lo = 10 * lo;
- lo += c;
-
- lo_carry += lo < c;
- hi += lo_carry;
- if (UNLIKELY (hi < lo_carry))
- {
- errcode = -1; /* overflow */
- break;
- }
- }
-
- *hip = hi;
- *lop = lo;
-
- return errcode;
-}
-
-static void
-print_uintmaxes (uintmax_t t1, uintmax_t t0)
-{
- uintmax_t q, r;
-
- if (t1 == 0)
- printf ("%ju", t0);
- else
- {
- /* Use very plain code here since it seems hard to write fast code
- without assuming a specific word size. */
- q = t1 / 1000000000;
- r = t1 % 1000000000;
- udiv_qrnnd (t0, r, r, t0, 1000000000);
- print_uintmaxes (q, t0);
- printf ("%09u", (int) r);
- }
-}
-
-static void
-factor_one (const char *input)
-{
- uintmax_t t1, t0;
- int errcode;
-
- /* Try converting the number to one or two words. If it fails, use GMP or
- print an error message. The 2nd condition checks that the most
- significant bit of the two-word number is clear, in a typesize neutral
- way. */
- errcode = strto2uintmax (&t1, &t0, input);
- if (errcode == 0 && ((t1 << 1) >> 1) == t1)
- {
- struct factors factors;
-
- print_uintmaxes (t1, t0);
- printf (":");
-
- factor (t1, t0, &factors);
-
- for (unsigned int j = 0; j < factors.nfactors; j++)
- for (unsigned int k = 0; k < factors.e[j]; k++)
- printf (" %ju", factors.p[j]);
-
- if (factors.plarge[1])
- {
- printf (" ");
- print_uintmaxes (factors.plarge[1], factors.plarge[0]);
- }
- puts ("");
- }
- else
- {
-#if HAVE_GMP
- mpz_t t;
- struct mp_factors factors;
-
- mpz_init_set_str (t, input, 10);
-
- gmp_printf ("%Zd:", t);
- mp_factor (t, &factors);
-
- for (unsigned int j = 0; j < factors.nfactors; j++)
- for (unsigned int k = 0; k < factors.e[j]; k++)
- gmp_printf (" %Zd", factors.p[j]);
-
- mp_factor_clear (&factors);
- mpz_clear (t);
- puts ("");
-#else
- fprintf (stderr, "error: number %s not parsable or too large\n", input);
- exit (EXIT_FAILURE);
-#endif
- }
-}
-
-struct inbuf
-{
- char *buf;
- size_t alloc;
-};
-
-/* Read white-space delimited items. Return 1 on success, 0 on EOF.
- Exit on I/O errors. */
-int
-read_item (struct inbuf *bufstruct)
-{
- int c;
- size_t i;
- char *buf = bufstruct->buf;
-
- do
- c = getchar_unlocked ();
- while (isspace (c));
-
- for (i = 0; !isspace(c); i++)
- {
- if (c < 0)
- {
- if (ferror (stdin))
- {
- fprintf (stderr, "read error on stdin: %s\n", strerror(errno));
- exit (EXIT_FAILURE);
- }
- if (i == 0)
- return 0;
- else
- break;
- }
-
- if (UNLIKELY (bufstruct->alloc <= i + 1)) /* +1 byte for terminating NUL */
- {
- bufstruct->alloc = bufstruct->alloc * 5 / 4 + 1;
- bufstruct->buf = realloc (bufstruct->buf, bufstruct->alloc);
- buf = bufstruct->buf;
- }
-
- buf[i] = c;
- c = getchar_unlocked ();
- }
-
- buf[i] = '\0';
- return 1;
-}
-
-int
-main (int argc, char *argv[])
-{
- int c;
-
- alg = ALG_POLLARD_RHO; /* Default to Pollard rho */
-
- while ( (c = getopt(argc, argv, "svw")) != -1)
- switch (c)
- {
- case 's':
- alg = ALG_SQUFOF;
- break;
- case 'v':
- flag_verbose = 1;
- break;
- case 'w':
- flag_prove_primality = 0;
- break;
- case '?':
- printf ("Usage: %s [-s] number ...\n", argv[0]);
- return EXIT_FAILURE;
- }
-#if STAT_SQUFOF
- if (alg == ALG_SQUFOF)
- memset (q_freq, 0, sizeof (q_freq));
-#endif
-
- if (optind < argc)
- for (int i = optind; i < argc; i++)
- factor_one (argv[i]);
- else
- {
- struct inbuf bufstruct;
- bufstruct.alloc = 50; /* enough unless HAVE_GMP */
- bufstruct.buf = malloc (bufstruct.alloc);
- while (read_item (&bufstruct))
- factor_one (bufstruct.buf);
- }
-
-#if STAT_SQUFOF
- if (alg == ALG_SQUFOF && q_freq[0] > 0)
- {
- double acc_f;
- printf ("q freq. cum. freq.(total: %d)\n", q_freq[0]);
- for (unsigned int i = 1, acc_f = 0.0; i <= Q_FREQ_SIZE; i++)
- {
- double f = (double) q_freq[i] / q_freq[0];
- acc_f += f;
- printf ("%s%d %.2f%% %.2f%%\n", i == Q_FREQ_SIZE ? ">=" : "", i,
- 100.0 * f, 100.0 * acc_f);
- }
- }
-#endif
-
- exit (EXIT_SUCCESS);
-}
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>. */
-/*
Written by Paul Rubin <phr@ocf.berkeley.edu>.
+/*
Originally written by Paul Rubin <phr@ocf.berkeley.edu>.
Adapted for GNU, fixed to factor UINT_MAX by Jim Meyering.
Arbitrary-precision code adapted by James Youngman from Torbjörn
Granlund's factorize.c, from GNU MP version 4.2.2.
+ In 2012, the core was rewritten by Torbjörn Granlund and Niels Möller.
+ Contains code from GNU MP. */
+
+/* Efficiently factor numbers that fit in one or two words (word = uintmax_t),
+ or, with GMP, numbers of any size.
+
+ Code organisation:
+
+ There are several variants of many functions, for handling one word, two
+ words, and GMP's mpz_t type. If the one-word variant is called foo, the
+ two-word variant will be foo2, and the one for mpz_t will be mp_foo. In
+ some cases, the plain function variants will handle both one-word and
+ two-word numbers, evidenced by function arguments.
+
+ The factoring code for two words will fall into the code for one word when
+ progress allows that.
+
+ Using GMP is optional. Define HAVE_GMP to make this code include GMP
+ factoring code. The GMP factoring code is based on GMP's demos/factorize.c
+ (last synched 2012-09-07). The GMP-based factoring code will stay in GMP
+ factoring code even if numbers get small enough for using the two-word
+ code.
+
+ Algorithm:
+
+ (1) Perform trial division using a small primes table, but without hardware
+ division since the primes table store inverses modulo the word base.
+ (The GMP variant of this code doesn't make use of the precomputed
+ inverses, but instead relies on GMP for fast divisibility testing.)
+ (2) Check the nature of any non-factored part using Miller-Rabin for
+ detecting composites, and Lucas for detecting primes.
+ (3) Factor any remaining composite part using the Pollard-Brent rho
+ algorithm or the SQUFOF algorithm, checking status of found factors
+ again using Miller-Rabin and Lucas.
+
+ We prefer using Hensel norm in the divisions, not the more familiar
+ Euclidian norm, since the former leads to much faster code. In the
+ Pollard-Brent rho code and the prime testing code, we use Montgomery's
+ trick of multiplying all n-residues by the word base, allowing cheap Hensel
+ reductions mod n.
+
+ Improvements:
+
+ * Use modular inverses also for exact division in the Lucas code, and
+ elsewhere. A problem is to locate the inverses not from an index, but
+ from a prime. We might instead compute the inverse on-the-fly.
+
+ * Tune trial division table size (not forgetting that this is a standalone
+ program where the table will be read from disk for each invocation).
+
+ * Implement less naive powm, using k-ary exponentiation for k = 3 or
+ perhaps k = 4.
+
+ * Try to speed trial division code for single uintmax_t numbers, i.e., the
+ code using DIVBLOCK. It currently runs at 2 cycles per prime (Intel SBR,
+ IBR), 3 cycles per prime (AMD Stars) and 5 cycles per prime (AMD BD) when
+ using gcc 4.6 and 4.7. Some software pipelining should help; 1, 2, and 4
+ respectively cycles ought to be possible.
+
+ * The redcify function could be vastly improved by using (plain Euclidian)
+ pre-inversion (such as GMP's invert_limb) and udiv_qrnnd_preinv (from
+ GMP's gmp-impl.h). The redcify2 function could be vastly improved using
+ similar methoods. These functions currently dominate run time when using
+ the -w option.
*/
#include <config.h>
#include <getopt.h>
-#include <stdarg.h>
#include <stdio.h>
-#include <sys/types.h>
#if HAVE_GMP
# include <gmp.h>
#endif
/* The official name of this program (e.g., no 'g' prefix). */
#define PROGRAM_NAME "factor"
-#define AUTHORS proper_name ("Paul Rubin")
+#define AUTHORS \
+ proper_name ("Paul Rubin"), \
+ proper_name_utf8 ("Torbjorn Granlund", "Torbj\303\266rn Granlund"), \
+ proper_name_utf8 ("Niels Moller", "Niels M\303\266ller")
/* Token delimiters when reading from a file. */
#define DELIM "\n\t "
-static bool verbose = false;
+#ifndef STAT_SQUFOF
+# define STAT_SQUFOF 0
+#endif
+
+#ifndef USE_LONGLONG_H
+# define USE_LONGLONG_H 1
+#endif
+
+#if USE_LONGLONG_H
+
+/* Make definitions for longlong.h to make it do what it can do for us */
+# define W_TYPE_SIZE 64 /* bitcount for uintmax_t */
+# define UWtype uintmax_t
+# define UHWtype unsigned long int
+# undef UDWtype
+# if HAVE_ATTRIBUTE_MODE
+typedef unsigned int UQItype __attribute__ ((mode (QI)));
+typedef int SItype __attribute__ ((mode (SI)));
+typedef unsigned int USItype __attribute__ ((mode (SI)));
+typedef int DItype __attribute__ ((mode (DI)));
+typedef unsigned int UDItype __attribute__ ((mode (DI)));
+# else
+typedef unsigned char UQItype;
+typedef long SItype;
+typedef unsigned long int USItype;
+# if HAVE_LONG_LONG
+typedef long long int DItype;
+typedef unsigned long long int UDItype;
+# else /* Assume `long' gives us a wide enough type. Needed for hppa2.0w. */
+typedef long int DItype;
+typedef unsigned long int UDItype;
+# endif
+# endif
+# define LONGLONG_STANDALONE /* Don't require GMP's longlong.h mdep files */
+# define ASSERT(x) /* FIXME make longlong.h really standalone */
+# define __clz_tab factor_clz_tab /* Rename to avoid glibc collision */
+# ifndef __GMP_GNUC_PREREQ
+# define __GMP_GNUC_PREREQ(a,b) 1
+# endif
+# if _ARCH_PPC
+# define HAVE_HOST_CPU_FAMILY_powerpc 1
+# endif
+# include "longlong.h"
+# ifdef COUNT_LEADING_ZEROS_NEED_CLZ_TAB
+const unsigned char factor_clz_tab[129] =
+{
+ 1,2,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
+ 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
+ 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
+ 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
+ 9
+};
+# endif
+
+#else /* not USE_LONGLONG_H */
+
+# define W_TYPE_SIZE (8 * sizeof (uintmax_t))
+# define __ll_B ((uintmax_t) 1 << (W_TYPE_SIZE / 2))
+# define __ll_lowpart(t) ((uintmax_t) (t) & (__ll_B - 1))
+# define __ll_highpart(t) ((uintmax_t) (t) >> (W_TYPE_SIZE / 2))
+
+#endif
+
+enum alg_type { ALG_POLLARD_RHO = 1, ALG_SQUFOF = 2 };
+
+static enum alg_type alg;
+
+/* 2*3*5*7*11...*101 is 128 bits, and has 26 prime factors */
+#define MAX_NFACTS 26
+
+enum
+{
+ VERBOSE_OPTION = CHAR_MAX + 1
+};
+
+static struct option const long_options[] =
+{
+ {"verbose", no_argument, NULL, VERBOSE_OPTION},
+ {GETOPT_HELP_OPTION_DECL},
+ {GETOPT_VERSION_OPTION_DECL},
+ {NULL, 0, NULL, 0}
+};
+
+struct factors
+{
+ uintmax_t plarge[2]; /* Can have a single large factor */
+ uintmax_t p[MAX_NFACTS];
+ unsigned char e[MAX_NFACTS];
+ unsigned char nfactors;
+};
#if HAVE_GMP
-static mpz_t *factor = NULL;
-static size_t nfactors_found = 0;
-static size_t nfactors_allocated = 0;
+struct mp_factors
+{
+ mpz_t *p;
+ unsigned long int *e;
+ unsigned long int nfactors;
+};
+#endif
+
+static void factor (uintmax_t, uintmax_t, struct factors *);
+
+#ifndef umul_ppmm
+# define umul_ppmm(w1, w0, u, v) \
+ do { \
+ uintmax_t __x0, __x1, __x2, __x3; \
+ unsigned long int __ul, __vl, __uh, __vh; \
+ uintmax_t __u = (u), __v = (v); \
+ \
+ __ul = __ll_lowpart (__u); \
+ __uh = __ll_highpart (__u); \
+ __vl = __ll_lowpart (__v); \
+ __vh = __ll_highpart (__v); \
+ \
+ __x0 = (uintmax_t) __ul * __vl; \
+ __x1 = (uintmax_t) __ul * __vh; \
+ __x2 = (uintmax_t) __uh * __vl; \
+ __x3 = (uintmax_t) __uh * __vh; \
+ \
+ __x1 += __ll_highpart (__x0);/* this can't give carry */ \
+ __x1 += __x2; /* but this indeed can */ \
+ if (__x1 < __x2) /* did we get it? */ \
+ __x3 += __ll_B; /* yes, add it in the proper pos. */ \
+ \
+ (w1) = __x3 + __ll_highpart (__x1); \
+ (w0) = (__x1 << W_TYPE_SIZE / 2) + __ll_lowpart (__x0); \
+ } while (0)
+#endif
+
+#if !defined udiv_qrnnd || defined UDIV_NEEDS_NORMALIZATION
+/* Define our own, not needing normalization. This function is
+ currently not performance critical, so keep it simple. Similar to
+ the mod macro below. */
+# undef udiv_qrnnd
+# define udiv_qrnnd(q, r, n1, n0, d) \
+ do { \
+ uintmax_t __d1, __d0, __q, __r1, __r0; \
+ \
+ assert ((n1) < (d)); \
+ __d1 = (d); __d0 = 0; \
+ __r1 = (n1); __r0 = (n0); \
+ __q = 0; \
+ for (unsigned int __i = W_TYPE_SIZE; __i > 0; __i--) \
+ { \
+ rsh2 (__d1, __d0, __d1, __d0, 1); \
+ __q <<= 1; \
+ if (ge2 (__r1, __r0, __d1, __d0)) \
+ { \
+ __q++; \
+ sub_ddmmss (__r1, __r0, __r1, __r0, __d1, __d0); \
+ } \
+ } \
+ (r) = __r0; \
+ (q) = __q; \
+ } while (0)
+#endif
+
+#if !defined add_ssaaaa
+# define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+ do { \
+ uintmax_t _add_x; \
+ _add_x = (al) + (bl); \
+ (sh) = (ah) + (bh) + (_add_x < (al)); \
+ (sl) = _add_x; \
+ } while (0)
+#endif
+
+#define rsh2(rh, rl, ah, al, cnt) \
+ do { \
+ (rl) = ((ah) << (W_TYPE_SIZE - (cnt))) | ((al) >> (cnt)); \
+ (rh) = (ah) >> (cnt); \
+ } while (0)
+
+#define lsh2(rh, rl, ah, al, cnt) \
+ do { \
+ (rh) = ((ah) << cnt) | ((al) >> (W_TYPE_SIZE - (cnt))); \
+ (rl) = (al) << (cnt); \
+ } while (0)
+
+#define ge2(ah, al, bh, bl) \
+ ((ah) > (bh) || ((ah) == (bh) && (al) >= (bl)))
+
+#define gt2(ah, al, bh, bl) \
+ ((ah) > (bh) || ((ah) == (bh) && (al) > (bl)))
+
+#ifndef sub_ddmmss
+# define sub_ddmmss(rh, rl, ah, al, bh, bl) \
+ do { \
+ uintmax_t _cy; \
+ _cy = (al) < (bl); \
+ (rl) = (al) - (bl); \
+ (rh) = (ah) - (bh) - _cy; \
+ } while (0)
+#endif
+
+#ifndef count_leading_zeros
+# define count_leading_zeros(count, x) do { \
+ uintmax_t __clz_x = (x); \
+ unsigned int __clz_c; \
+ for (__clz_c = 0; \
+ (__clz_x & ((uintmax_t) 0xff << (W_TYPE_SIZE - 8))) == 0; \
+ __clz_c += 8) \
+ __clz_x <<= 8; \
+ for (; (intmax_t)__clz_x >= 0; __clz_c++) \
+ __clz_x <<= 1; \
+ (count) = __clz_c; \
+ } while (0)
+#endif
+
+#ifndef count_trailing_zeros
+# define count_trailing_zeros(count, x) do { \
+ uintmax_t __ctz_x = (x); \
+ unsigned int __ctz_c = 0; \
+ while ((__ctz_x & 1) == 0) \
+ { \
+ __ctz_x >>= 1; \
+ __ctz_c++; \
+ } \
+ (count) = __ctz_c; \
+ } while (0)
+#endif
+
+/* Requires that a < n and b <= n */
+#define submod(r,a,b,n) \
+ do { \
+ uintmax_t _t = - (uintmax_t) (a < b); \
+ (r) = ((n) & _t) + (a) - (b); \
+ } while (0)
+
+#define addmod(r,a,b,n) \
+ submod ((r), (a), ((n) - (b)), (n))
+
+/* Modular two-word addition and subtraction. For performance reasons, the
+ most significant bit of n1 must be clear. The destination variables must be
+ distinct from the mod operand. */
+#define addmod2(r1, r0, a1, a0, b1, b0, n1, n0) \
+ do { \
+ add_ssaaaa ((r1), (r0), (a1), (a0), (b1), (b0)); \
+ if (ge2 ((r1), (r0), (n1), (n0))) \
+ sub_ddmmss ((r1), (r0), (r1), (r0), (n1), (n0)); \
+ } while (0)
+#define submod2(r1, r0, a1, a0, b1, b0, n1, n0) \
+ do { \
+ sub_ddmmss ((r1), (r0), (a1), (a0), (b1), (b0)); \
+ if ((intmax_t) (r1) < 0) \
+ add_ssaaaa ((r1), (r0), (r1), (r0), (n1), (n0)); \
+ } while (0)
+
+#define HIGHBIT_TO_MASK(x) \
+ (((intmax_t)-1 >> 1) < 0 \
+ ? (uintmax_t)((intmax_t)(x) >> (W_TYPE_SIZE - 1)) \
+ : ((x) & ((uintmax_t) 1 << (W_TYPE_SIZE - 1)) \
+ ? UINTMAX_MAX : (uintmax_t) 0))
+
+/* Compute r = a mod d, where r = <*t1,retval>, a = <a1,a0>, d = <d1,d0>.
+ Requires that d1 != 0. */
+static uintmax_t
+mod2 (uintmax_t *r1, uintmax_t a1, uintmax_t a0, uintmax_t d1, uintmax_t d0)
+{
+ int cntd, cnta;
+
+ assert (d1 != 0);
+
+ if (a1 == 0)
+ {
+ *r1 = 0;
+ return a0;
+ }
+
+ count_leading_zeros (cntd, d1);
+ count_leading_zeros (cnta, a1);
+ int cnt = cntd - cnta;
+ lsh2 (d1, d0, d1, d0, cnt);
+ for (int i = 0; i < cnt; i++)
+ {
+ if (ge2 (a1, a0, d1, d0))
+ sub_ddmmss (a1, a0, a1, a0, d1, d0);
+ rsh2 (d1, d0, d1, d0, 1);
+ }
+
+ *r1 = a1;
+ return a0;
+}
+
+static uintmax_t _GL_ATTRIBUTE_CONST
+gcd_odd (uintmax_t a, uintmax_t b)
+{
+ if ( (b & 1) == 0)
+ {
+ uintmax_t t = b;
+ b = a;
+ a = t;
+ }
+ if (a == 0)
+ return b;
+
+ /* Take out least significant one bit, to make room for sign */
+ b >>= 1;
+
+ for (;;)
+ {
+ uintmax_t t;
+ uintmax_t bgta;
+
+ while ((a & 1) == 0)
+ a >>= 1;
+ a >>= 1;
+
+ t = a - b;
+ if (t == 0)
+ return (a << 1) + 1;
+
+ bgta = HIGHBIT_TO_MASK (t);
+
+ /* b <-- min (a, b) */
+ b += (bgta & t);
+
+ /* a <-- |a - b| */
+ a = (t ^ bgta) - bgta;
+ }
+}
+
+static uintmax_t
+gcd2_odd (uintmax_t *r1, uintmax_t a1, uintmax_t a0, uintmax_t b1, uintmax_t b0)
+{
+ while ((a0 & 1) == 0)
+ rsh2 (a1, a0, a1, a0, 1);
+ while ((b0 & 1) == 0)
+ rsh2 (b1, b0, b1, b0, 1);
+
+ for (;;)
+ {
+ if ((b1 | a1) == 0)
+ {
+ *r1 = 0;
+ return gcd_odd (b0, a0);
+ }
+
+ if (gt2 (a1, a0, b1, b0))
+ {
+ sub_ddmmss (a1, a0, a1, a0, b1, b0);
+ do
+ rsh2 (a1, a0, a1, a0, 1);
+ while ((a0 & 1) == 0);
+ }
+ else if (gt2 (b1, b0, a1, a0))
+ {
+ sub_ddmmss (b1, b0, b1, b0, a1, a0);
+ do
+ rsh2 (b1, b0, b1, b0, 1);
+ while ((b0 & 1) == 0);
+ }
+ else
+ break;
+ }
+
+ *r1 = a1;
+ return a0;
+}
+
+static void
+factor_insert_multiplicity (struct factors *factors,
+ uintmax_t prime, unsigned int m)
+{
+ unsigned int nfactors = factors->nfactors;
+ uintmax_t *p = factors->p;
+ unsigned char *e = factors->e;
+
+ /* Locate position for insert new or increment e. */
+ int i;
+ for (i = nfactors - 1; i >= 0; i--)
+ {
+ if (p[i] <= prime)
+ break;
+ }
+
+ if (i < 0 || p[i] != prime)
+ {
+ for (int j = nfactors - 1; j > i; j--)
+ {
+ p[j + 1] = p[j];
+ e[j + 1] = e[j];
+ }
+ p[i + 1] = prime;
+ e[i + 1] = m;
+ factors->nfactors = nfactors + 1;
+ }
+ else
+ {
+ e[i] += m;
+ }
+}
+
+#define factor_insert(f, p) factor_insert_multiplicity (f, p, 1)
+
+static void
+factor_insert_large (struct factors *factors,
+ uintmax_t p1, uintmax_t p0)
+{
+ if (p1 > 0)
+ {
+ assert (factors->plarge[1] == 0);
+ factors->plarge[0] = p0;
+ factors->plarge[1] = p1;
+ }
+ else
+ factor_insert (factors, p0);
+}
+
+#if HAVE_GMP
+static void mp_factor (mpz_t, struct mp_factors *);
+
+static void
+mp_factor_init (struct mp_factors *factors)
+{
+ factors->p = xmalloc (1);
+ factors->e = xmalloc (1);
+ factors->nfactors = 0;
+}
+
+static void
+mp_factor_clear (struct mp_factors *factors)
+{
+ for (unsigned int i = 0; i < factors->nfactors; i++)
+ mpz_clear (factors->p[i]);
+
+ free (factors->p);
+ free (factors->e);
+}
+
+static void
+mp_factor_insert (struct mp_factors *factors, mpz_t prime)
+{
+ unsigned long int nfactors = factors->nfactors;
+ mpz_t *p = factors->p;
+ unsigned long int *e = factors->e;
+ long i;
+
+ /* Locate position for insert new or increment e. */
+ for (i = nfactors - 1; i >= 0; i--)
+ {
+ if (mpz_cmp (p[i], prime) <= 0)
+ break;
+ }
+
+ if (i < 0 || mpz_cmp (p[i], prime) != 0)
+ {
+ p = xrealloc (p, (nfactors + 1) * sizeof p[0]);
+ e = xrealloc (e, (nfactors + 1) * sizeof e[0]);
+
+ mpz_init (p[nfactors]);
+ for (long j = nfactors - 1; j > i; j--)
+ {
+ mpz_set (p[j + 1], p[j]);
+ e[j + 1] = e[j];
+ }
+ mpz_set (p[i + 1], prime);
+ e[i + 1] = 1;
+
+ factors->p = p;
+ factors->e = e;
+ factors->nfactors = nfactors + 1;
+ }
+ else
+ {
+ e[i] += 1;
+ }
+}
+
+static void
+mp_factor_insert_ui (struct mp_factors *factors, unsigned long int prime)
+{
+ mpz_t pz;
+
+ mpz_init_set_ui (pz, prime);
+ mp_factor_insert (factors, pz);
+ mpz_clear (pz);
+}
+#endif /* HAVE_GMP */
+
+
+#define P(a,b,c,d) a,
+static const unsigned char primes_diff[] = {
+#include "primes.h"
+0,0,0,0,0,0,0 /* 7 sentinels for 8-way loop */
+};
+#undef P
+
+#define PRIMES_PTAB_ENTRIES \
+ (sizeof (primes_diff) / sizeof (primes_diff[0]) - 8 + 1)
+
+#define P(a,b,c,d) b,
+static const unsigned char primes_diff8[] = {
+#include "primes.h"
+0,0,0,0,0,0,0 /* 7 sentinels for 8-way loop */
+};
+#undef P
+
+struct primes_dtab
+{
+ uintmax_t binv, lim;
+};
+
+#define P(a,b,c,d) {c,d},
+static const struct primes_dtab primes_dtab[] = {
+#include "primes.h"
+{1,0},{1,0},{1,0},{1,0},{1,0},{1,0},{1,0} /* 7 sentinels for 8-way loop */
+};
+#undef P
+
+/* This flag is honored only in the GMP code. */
+static int verbose = 0;
+
+/* Prove primality or run probabilistic tests. */
+static bool flag_prove_primality = true;
+
+/* Number of Miller-Rabin tests to run when not proving primality. */
+#define MR_REPS 25
+
+#ifdef __GNUC__
+# define LIKELY(cond) __builtin_expect ((cond), 1)
+# define UNLIKELY(cond) __builtin_expect ((cond), 0)
+#else
+# define LIKELY(cond) (cond)
+# define UNLIKELY(cond) (cond)
+#endif
static void
debug (char const *fmt, ...)
}
static void
-emit_factor (mpz_t n)
+factor_insert_refind (struct factors *factors, uintmax_t p, unsigned int i,
+ unsigned int off)
{
- if (nfactors_found == nfactors_allocated)
- factor = X2NREALLOC (factor, &nfactors_allocated);
- mpz_init (factor[nfactors_found]);
- mpz_set (factor[nfactors_found], n);
- ++nfactors_found;
+ for (unsigned int j = 0; j < off; j++)
+ p += primes_diff[i + j];
+ factor_insert (factors, p);
}
+/* Trial division with odd primes uses the following trick.
+
+ Let p be an odd prime, and B = 2^{W_TYPE_SIZE}. For simplicity,
+ consider the case t < B (this is the second loop below).
+
+ From our tables we get
+
+ binv = p^{-1} (mod B)
+ lim = floor ( (B-1) / p ).
+
+ First assume that t is a multiple of p, t = q * p. Then 0 <= q <= lim
+ (and all quotients in this range occur for some t).
+
+ Then t = q * p is true also (mod B), and p is invertible we get
+
+ q = t * binv (mod B).
+
+ Next, assume that t is *not* divisible by p. Since multiplication
+ by binv (mod B) is a one-to-one mapping,
+
+ t * binv (mod B) > lim,
+
+ because all the smaller values are already taken.
+
+ This can be summed up by saying that the function
+
+ q(t) = binv * t (mod B)
+
+ is a permutation of the range 0 <= t < B, with the curious property
+ that it maps the multiples of p onto the range 0 <= q <= lim, in
+ order, and the non-multiples of p onto the range lim < q < B.
+ */
+
+static uintmax_t
+factor_using_division (uintmax_t *t1p, uintmax_t t1, uintmax_t t0,
+ struct factors *factors)
+{
+ if (t0 % 2 == 0)
+ {
+ unsigned int cnt;
+
+ if (t0 == 0)
+ {
+ count_trailing_zeros (cnt, t1);
+ t0 = t1 >> cnt;
+ t1 = 0;
+ cnt += W_TYPE_SIZE;
+ }
+ else
+ {
+ count_trailing_zeros (cnt, t0);
+ rsh2 (t1, t0, t1, t0, cnt);
+ }
+
+ factor_insert_multiplicity (factors, 2, cnt);
+ }
+
+ uintmax_t p = 3;
+ unsigned int i;
+ for (i = 0; t1 > 0 && i < PRIMES_PTAB_ENTRIES; i++)
+ {
+ for (;;)
+ {
+ uintmax_t q1, q0, hi, lo;
+
+ q0 = t0 * primes_dtab[i].binv;
+ umul_ppmm (hi, lo, q0, p);
+ if (hi > t1)
+ break;
+ hi = t1 - hi;
+ q1 = hi * primes_dtab[i].binv;
+ if (LIKELY (q1 > primes_dtab[i].lim))
+ break;
+ t1 = q1; t0 = q0;
+ factor_insert (factors, p);
+ }
+ p += primes_diff[i + 1];
+ }
+ if (t1p)
+ *t1p = t1;
+
+#define DIVBLOCK(I) \
+ do { \
+ for (;;) \
+ { \
+ q = t0 * pd[I].binv; \
+ if (LIKELY (q > pd[I].lim)) \
+ break; \
+ t0 = q; \
+ factor_insert_refind (factors, p, i + 1, I); \
+ } \
+ } while (0)
+
+ for (; i < PRIMES_PTAB_ENTRIES; i += 8)
+ {
+ uintmax_t q;
+ const struct primes_dtab *pd = &primes_dtab[i];
+ DIVBLOCK (0);
+ DIVBLOCK (1);
+ DIVBLOCK (2);
+ DIVBLOCK (3);
+ DIVBLOCK (4);
+ DIVBLOCK (5);
+ DIVBLOCK (6);
+ DIVBLOCK (7);
+
+ p += primes_diff8[i];
+ if (p * p > t0)
+ break;
+ }
+
+ return t0;
+}
+
+#if HAVE_GMP
static void
-emit_ul_factor (unsigned long int i)
+mp_factor_using_division (mpz_t t, struct mp_factors *factors)
{
- mpz_t t;
- mpz_init (t);
- mpz_set_ui (t, i);
- emit_factor (t);
- mpz_clear (t);
+ mpz_t q;
+ unsigned long int p;
+
+ debug ("[trial division] ");
+
+ mpz_init (q);
+
+ p = mpz_scan1 (t, 0);
+ mpz_div_2exp (t, t, p);
+ while (p)
+ {
+ mp_factor_insert_ui (factors, 2);
+ --p;
+ }
+
+ p = 3;
+ for (unsigned int i = 1; i <= PRIMES_PTAB_ENTRIES;)
+ {
+ if (! mpz_divisible_ui_p (t, p))
+ {
+ p += primes_diff[i++];
+ if (mpz_cmp_ui (t, p * p) < 0)
+ break;
+ }
+ else
+ {
+ mpz_tdiv_q_ui (t, t, p);
+ mp_factor_insert_ui (factors, p);
+ }
+ }
+
+ mpz_clear (q);
+}
+#endif
+
+/* Entry i contains (2i+1)^(-1) mod 2^8. */
+static const unsigned char binvert_table[128] =
+{
+ 0x01, 0xAB, 0xCD, 0xB7, 0x39, 0xA3, 0xC5, 0xEF,
+ 0xF1, 0x1B, 0x3D, 0xA7, 0x29, 0x13, 0x35, 0xDF,
+ 0xE1, 0x8B, 0xAD, 0x97, 0x19, 0x83, 0xA5, 0xCF,
+ 0xD1, 0xFB, 0x1D, 0x87, 0x09, 0xF3, 0x15, 0xBF,
+ 0xC1, 0x6B, 0x8D, 0x77, 0xF9, 0x63, 0x85, 0xAF,
+ 0xB1, 0xDB, 0xFD, 0x67, 0xE9, 0xD3, 0xF5, 0x9F,
+ 0xA1, 0x4B, 0x6D, 0x57, 0xD9, 0x43, 0x65, 0x8F,
+ 0x91, 0xBB, 0xDD, 0x47, 0xC9, 0xB3, 0xD5, 0x7F,
+ 0x81, 0x2B, 0x4D, 0x37, 0xB9, 0x23, 0x45, 0x6F,
+ 0x71, 0x9B, 0xBD, 0x27, 0xA9, 0x93, 0xB5, 0x5F,
+ 0x61, 0x0B, 0x2D, 0x17, 0x99, 0x03, 0x25, 0x4F,
+ 0x51, 0x7B, 0x9D, 0x07, 0x89, 0x73, 0x95, 0x3F,
+ 0x41, 0xEB, 0x0D, 0xF7, 0x79, 0xE3, 0x05, 0x2F,
+ 0x31, 0x5B, 0x7D, 0xE7, 0x69, 0x53, 0x75, 0x1F,
+ 0x21, 0xCB, 0xED, 0xD7, 0x59, 0xC3, 0xE5, 0x0F,
+ 0x11, 0x3B, 0x5D, 0xC7, 0x49, 0x33, 0x55, 0xFF
+};
+
+/* Compute n^(-1) mod B, using a Newton iteration. */
+#define binv(inv,n) \
+ do { \
+ uintmax_t __n = (n); \
+ uintmax_t __inv; \
+ \
+ __inv = binvert_table[(__n / 2) & 0x7F]; /* 8 */ \
+ if (W_TYPE_SIZE > 8) __inv = 2 * __inv - __inv * __inv * __n; \
+ if (W_TYPE_SIZE > 16) __inv = 2 * __inv - __inv * __inv * __n; \
+ if (W_TYPE_SIZE > 32) __inv = 2 * __inv - __inv * __inv * __n; \
+ \
+ if (W_TYPE_SIZE > 64) \
+ { \
+ int __invbits = 64; \
+ do { \
+ __inv = 2 * __inv - __inv * __inv * __n; \
+ __invbits *= 2; \
+ } while (__invbits < W_TYPE_SIZE); \
+ } \
+ \
+ (inv) = __inv; \
+ } while (0)
+
+/* q = u / d, assuming d|u. */
+#define divexact_21(q1, q0, u1, u0, d) \
+ do { \
+ uintmax_t _di, _q0; \
+ binv (_di, (d)); \
+ _q0 = (u0) * _di; \
+ if ((u1) >= (d)) \
+ { \
+ uintmax_t _p1, _p0; \
+ umul_ppmm (_p1, _p0, _q0, d); \
+ (q1) = ((u1) - _p1) * _di; \
+ (q0) = _q0; \
+ } \
+ else \
+ { \
+ (q0) = _q0; \
+ (q1) = 0; \
+ } \
+ } while (0)
+
+/* x B (mod n). */
+#define redcify(r_prim, r, n) \
+ do { \
+ uintmax_t _redcify_q ATTRIBUTE_UNUSED; \
+ udiv_qrnnd (_redcify_q, r_prim, r, 0, n); \
+ } while (0)
+
+/* x B^2 (mod n). Requires x > 0, n1 < B/2 */
+#define redcify2(r1, r0, x, n1, n0) \
+ do { \
+ uintmax_t _r1, _r0, _i; \
+ if ((x) < (n1)) \
+ { \
+ _r1 = (x); _r0 = 0; \
+ _i = W_TYPE_SIZE; \
+ } \
+ else \
+ { \
+ _r1 = 0; _r0 = (x); \
+ _i = 2*W_TYPE_SIZE; \
+ } \
+ while (_i-- > 0) \
+ { \
+ lsh2 (_r1, _r0, _r1, _r0, 1); \
+ if (ge2 (_r1, _r0, (n1), (n0))) \
+ sub_ddmmss (_r1, _r0, _r1, _r0, (n1), (n0)); \
+ } \
+ (r1) = _r1; \
+ (r0) = _r0; \
+ } while (0)
+
+/* Modular two-word multiplication, r = a * b mod m, with mi = m^(-1) mod B.
+ Both a and b must be in redc form, the result will be in redc form too. */
+static inline uintmax_t
+mulredc (uintmax_t a, uintmax_t b, uintmax_t m, uintmax_t mi)
+{
+ uintmax_t rh, rl, q, th, tl, xh;
+
+ umul_ppmm (rh, rl, a, b);
+ q = rl * mi;
+ umul_ppmm (th, tl, q, m);
+ xh = rh - th;
+ if (rh < th)
+ xh += m;
+
+ return xh;
+}
+
+/* Modular two-word multiplication, r = a * b mod m, with mi = m^(-1) mod B.
+ Both a and b must be in redc form, the result will be in redc form too.
+ For performance reasons, the most significant bit of m must be clear. */
+static uintmax_t
+mulredc2 (uintmax_t *r1p,
+ uintmax_t a1, uintmax_t a0, uintmax_t b1, uintmax_t b0,
+ uintmax_t m1, uintmax_t m0, uintmax_t mi)
+{
+ uintmax_t r1, r0, q, p1, p0, t1, t0, s1, s0;
+ mi = -mi;
+ assert ( (a1 >> (W_TYPE_SIZE - 1)) == 0);
+ assert ( (b1 >> (W_TYPE_SIZE - 1)) == 0);
+ assert ( (m1 >> (W_TYPE_SIZE - 1)) == 0);
+
+ /* First compute a0 * <b1, b0> B^{-1}
+ +-----+
+ |a0 b0|
+ +--+--+--+
+ |a0 b1|
+ +--+--+--+
+ |q0 m0|
+ +--+--+--+
+ |q0 m1|
+ -+--+--+--+
+ |r1|r0| 0|
+ +--+--+--+
+ */
+ umul_ppmm (t1, t0, a0, b0);
+ umul_ppmm (r1, r0, a0, b1);
+ q = mi * t0;
+ umul_ppmm (p1, p0, q, m0);
+ umul_ppmm (s1, s0, q, m1);
+ r0 += (t0 != 0); /* Carry */
+ add_ssaaaa (r1, r0, r1, r0, 0, p1);
+ add_ssaaaa (r1, r0, r1, r0, 0, t1);
+ add_ssaaaa (r1, r0, r1, r0, s1, s0);
+
+ /* Next, (a1 * <b1, b0> + <r1, r0> B^{-1}
+ +-----+
+ |a1 b0|
+ +--+--+
+ |r1|r0|
+ +--+--+--+
+ |a1 b1|
+ +--+--+--+
+ |q1 m0|
+ +--+--+--+
+ |q1 m1|
+ -+--+--+--+
+ |r1|r0| 0|
+ +--+--+--+
+ */
+ umul_ppmm (t1, t0, a1, b0);
+ umul_ppmm (s1, s0, a1, b1);
+ add_ssaaaa (t1, t0, t1, t0, 0, r0);
+ q = mi * t0;
+ add_ssaaaa (r1, r0, s1, s0, 0, r1);
+ umul_ppmm (p1, p0, q, m0);
+ umul_ppmm (s1, s0, q, m1);
+ r0 += (t0 != 0); /* Carry */
+ add_ssaaaa (r1, r0, r1, r0, 0, p1);
+ add_ssaaaa (r1, r0, r1, r0, 0, t1);
+ add_ssaaaa (r1, r0, r1, r0, s1, s0);
+
+ if (ge2 (r1, r0, m1, m0))
+ sub_ddmmss (r1, r0, r1, r0, m1, m0);
+
+ *r1p = r1;
+ return r0;
+}
+
+static uintmax_t _GL_ATTRIBUTE_CONST
+powm (uintmax_t b, uintmax_t e, uintmax_t n, uintmax_t ni, uintmax_t one)
+{
+ uintmax_t y = one;
+
+ if (e & 1)
+ y = b;
+
+ while (e != 0)
+ {
+ b = mulredc (b, b, n, ni);
+ e >>= 1;
+
+ if (e & 1)
+ y = mulredc (y, b, n, ni);
+ }
+
+ return y;
+}
+
+static uintmax_t
+powm2 (uintmax_t *r1m,
+ const uintmax_t *bp, const uintmax_t *ep, const uintmax_t *np,
+ uintmax_t ni, const uintmax_t *one)
+{
+ uintmax_t r1, r0, b1, b0, n1, n0;
+ unsigned int i;
+ uintmax_t e;
+
+ b0 = bp[0];
+ b1 = bp[1];
+ n0 = np[0];
+ n1 = np[1];
+
+ r0 = one[0];
+ r1 = one[1];
+
+ for (e = ep[0], i = W_TYPE_SIZE; i > 0; i--, e >>= 1)
+ {
+ if (e & 1)
+ {
+ r0 = mulredc2 (r1m, r1, r0, b1, b0, n1, n0, ni);
+ r1 = *r1m;
+ }
+ b0 = mulredc2 (r1m, b1, b0, b1, b0, n1, n0, ni);
+ b1 = *r1m;
+ }
+ for (e = ep[1]; e > 0; e >>= 1)
+ {
+ if (e & 1)
+ {
+ r0 = mulredc2 (r1m, r1, r0, b1, b0, n1, n0, ni);
+ r1 = *r1m;
+ }
+ b0 = mulredc2 (r1m, b1, b0, b1, b0, n1, n0, ni);
+ b1 = *r1m;
+ }
+ *r1m = r1;
+ return r0;
+}
+
+static bool _GL_ATTRIBUTE_CONST
+millerrabin (uintmax_t n, uintmax_t ni, uintmax_t b, uintmax_t q,
+ unsigned int k, uintmax_t one)
+{
+ uintmax_t y = powm (b, q, n, ni, one);
+
+ uintmax_t nm1 = n - one; /* -1, but in redc representation. */
+
+ if (y == one || y == nm1)
+ return true;
+
+ for (unsigned int i = 1; i < k; i++)
+ {
+ y = mulredc (y, y, n, ni);
+
+ if (y == nm1)
+ return true;
+ if (y == one)
+ return false;
+ }
+ return false;
+}
+
+static bool
+millerrabin2 (const uintmax_t *np, uintmax_t ni, const uintmax_t *bp,
+ const uintmax_t *qp, unsigned int k, const uintmax_t *one)
+{
+ uintmax_t y1, y0, nm1_1, nm1_0, r1m;
+
+ y0 = powm2 (&r1m, bp, qp, np, ni, one);
+ y1 = r1m;
+
+ if (y0 == one[0] && y1 == one[1])
+ return true;
+
+ sub_ddmmss (nm1_1, nm1_0, np[1], np[0], one[1], one[0]);
+
+ if (y0 == nm1_0 && y1 == nm1_1)
+ return true;
+
+ for (unsigned int i = 1; i < k; i++)
+ {
+ y0 = mulredc2 (&r1m, y1, y0, y1, y0, np[1], np[0], ni);
+ y1 = r1m;
+
+ if (y0 == nm1_0 && y1 == nm1_1)
+ return true;
+ if (y0 == one[0] && y1 == one[1])
+ return false;
+ }
+ return false;
+}
+
+#if HAVE_GMP
+static bool
+mp_millerrabin (mpz_srcptr n, mpz_srcptr nm1, mpz_ptr x, mpz_ptr y,
+ mpz_srcptr q, unsigned long int k)
+{
+ mpz_powm (y, x, q, n);
+
+ if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, nm1) == 0)
+ return true;
+
+ for (unsigned long int i = 1; i < k; i++)
+ {
+ mpz_powm_ui (y, y, 2, n);
+ if (mpz_cmp (y, nm1) == 0)
+ return true;
+ if (mpz_cmp_ui (y, 1) == 0)
+ return false;
+ }
+ return false;
+}
+#endif
+
+/* Lucas' prime test. The number of iterations vary greatly, up to a few dozen
+ have been observed. The average seem to be about 2. */
+static bool
+prime_p (uintmax_t n)
+{
+ int k;
+ bool is_prime;
+ uintmax_t a_prim, one, ni;
+ struct factors factors;
+
+ if (n <= 1)
+ return false;
+
+ /* We have already casted out small primes. */
+ if (n < (uintmax_t) FIRST_OMITTED_PRIME * FIRST_OMITTED_PRIME)
+ return true;
+
+ /* Precomputation for Miller-Rabin. */
+ uintmax_t q = n - 1;
+ for (k = 0; (q & 1) == 0; k++)
+ q >>= 1;
+
+ uintmax_t a = 2;
+ binv (ni, n); /* ni <- 1/n mod B */
+ redcify (one, 1, n);
+ addmod (a_prim, one, one, n); /* i.e., redcify a = 2 */
+
+ /* Perform a Miller-Rabin test, finds most composites quickly. */
+ if (!millerrabin (n, ni, a_prim, q, k, one))
+ return false;
+
+ if (flag_prove_primality)
+ {
+ /* Factor n-1 for Lucas. */
+ factor (0, n - 1, &factors);
+ }
+
+ /* Loop until Lucas proves our number prime, or Miller-Rabin proves our
+ number composite. */
+ for (unsigned int r = 0; r < PRIMES_PTAB_ENTRIES; r++)
+ {
+ if (flag_prove_primality)
+ {
+ is_prime = true;
+ for (unsigned int i = 0; i < factors.nfactors && is_prime; i++)
+ {
+ is_prime
+ = powm (a_prim, (n - 1) / factors.p[i], n, ni, one) != one;
+ }
+ }
+ else
+ {
+ /* After enough Miller-Rabin runs, be content. */
+ is_prime = (r == MR_REPS - 1);
+ }
+
+ if (is_prime)
+ return true;
+
+ a += primes_diff[r]; /* Establish new base. */
+
+ /* The following is equivalent to redcify (a_prim, a, n). It runs faster
+ on most processors, since it avoids udiv_qrnnd. If we go down the
+ udiv_qrnnd_preinv path, this code should be replaced. */
+ {
+ uintmax_t s1, s0;
+ umul_ppmm (s1, s0, one, a);
+ if (LIKELY (s1 == 0))
+ a_prim = s0 % n;
+ else
+ {
+ uintmax_t dummy ATTRIBUTE_UNUSED;
+ udiv_qrnnd (dummy, a_prim, s1, s0, n);
+ }
+ }
+
+ if (!millerrabin (n, ni, a_prim, q, k, one))
+ return false;
+ }
+
+ error (0, 0, _("Lucas prime test failure. This should not happen"));
+ abort ();
+}
+
+static bool
+prime2_p (uintmax_t n1, uintmax_t n0)
+{
+ uintmax_t q[2], nm1[2];
+ uintmax_t a_prim[2];
+ uintmax_t one[2];
+ uintmax_t na[2];
+ uintmax_t ni;
+ unsigned int k;
+ struct factors factors;
+
+ if (n1 == 0)
+ return prime_p (n0);
+
+ nm1[1] = n1 - (n0 == 0);
+ nm1[0] = n0 - 1;
+ if (nm1[0] == 0)
+ {
+ count_trailing_zeros (k, nm1[1]);
+
+ q[0] = nm1[1] >> k;
+ q[1] = 0;
+ k += W_TYPE_SIZE;
+ }
+ else
+ {
+ count_trailing_zeros (k, nm1[0]);
+ rsh2 (q[1], q[0], nm1[1], nm1[0], k);
+ }
+
+ uintmax_t a = 2;
+ binv (ni, n0);
+ redcify2 (one[1], one[0], 1, n1, n0);
+ addmod2 (a_prim[1], a_prim[0], one[1], one[0], one[1], one[0], n1, n0);
+
+ /* FIXME: Use scalars or pointers in arguments? Some consistency needed. */
+ na[0] = n0;
+ na[1] = n1;
+
+ if (!millerrabin2 (na, ni, a_prim, q, k, one))
+ return false;
+
+ if (flag_prove_primality)
+ {
+ /* Factor n-1 for Lucas. */
+ factor (nm1[1], nm1[0], &factors);
+ }
+
+ /* Loop until Lucas proves our number prime, or Miller-Rabin proves our
+ number composite. */
+ for (unsigned int r = 0; r < PRIMES_PTAB_ENTRIES; r++)
+ {
+ bool is_prime;
+ uintmax_t e[2], y[2];
+
+ if (flag_prove_primality)
+ {
+ is_prime = true;
+ if (factors.plarge[1])
+ {
+ uintmax_t pi;
+ binv (pi, factors.plarge[0]);
+ e[0] = pi * nm1[0];
+ e[1] = 0;
+ y[0] = powm2 (&y[1], a_prim, e, na, ni, one);
+ is_prime = (y[0] != one[0] || y[1] != one[1]);
+ }
+ for (unsigned int i = 0; i < factors.nfactors && is_prime; i++)
+ {
+ /* FIXME: We always have the factor 2. Do we really need to
+ handle it here? We have done the same powering as part
+ of millerrabin. */
+ if (factors.p[i] == 2)
+ rsh2 (e[1], e[0], nm1[1], nm1[0], 1);
+ else
+ divexact_21 (e[1], e[0], nm1[1], nm1[0], factors.p[i]);
+ y[0] = powm2 (&y[1], a_prim, e, na, ni, one);
+ is_prime = (y[0] != one[0] || y[1] != one[1]);
+ }
+ }
+ else
+ {
+ /* After enough Miller-Rabin runs, be content. */
+ is_prime = (r == MR_REPS - 1);
+ }
+
+ if (is_prime)
+ return true;
+
+ a += primes_diff[r]; /* Establish new base. */
+ redcify2 (a_prim[1], a_prim[0], a, n1, n0);
+
+ if (!millerrabin2 (na, ni, a_prim, q, k, one))
+ return false;
+ }
+
+ error (0, 0, _("Lucas prime test failure. This should not happen"));
+ abort ();
+}
+
+#if HAVE_GMP
+static bool
+mp_prime_p (mpz_t n)
+{
+ bool is_prime;
+ mpz_t q, a, nm1, tmp;
+ struct mp_factors factors;
+
+ if (mpz_cmp_ui (n, 1) <= 0)
+ return false;
+
+ /* We have already casted out small primes. */
+ if (mpz_cmp_ui (n, (long) FIRST_OMITTED_PRIME * FIRST_OMITTED_PRIME) < 0)
+ return true;
+
+ mpz_inits (q, a, nm1, tmp, NULL);
+
+ /* Precomputation for Miller-Rabin. */
+ mpz_sub_ui (nm1, n, 1);
+
+ /* Find q and k, where q is odd and n = 1 + 2**k * q. */
+ unsigned long int k = mpz_scan1 (nm1, 0);
+ mpz_tdiv_q_2exp (q, nm1, k);
+
+ mpz_set_ui (a, 2);
+
+ /* Perform a Miller-Rabin test, finds most composites quickly. */
+ if (!mp_millerrabin (n, nm1, a, tmp, q, k))
+ {
+ is_prime = false;
+ goto ret2;
+ }
+
+ if (flag_prove_primality)
+ {
+ /* Factor n-1 for Lucas. */
+ mpz_set (tmp, nm1);
+ mp_factor (tmp, &factors);
+ }
+
+ /* Loop until Lucas proves our number prime, or Miller-Rabin proves our
+ number composite. */
+ for (unsigned int r = 0; r < PRIMES_PTAB_ENTRIES; r++)
+ {
+ if (flag_prove_primality)
+ {
+ is_prime = true;
+ for (unsigned long int i = 0; i < factors.nfactors && is_prime; i++)
+ {
+ mpz_divexact (tmp, nm1, factors.p[i]);
+ mpz_powm (tmp, a, tmp, n);
+ is_prime = mpz_cmp_ui (tmp, 1) != 0;
+ }
+ }
+ else
+ {
+ /* After enough Miller-Rabin runs, be content. */
+ is_prime = (r == MR_REPS - 1);
+ }
+
+ if (is_prime)
+ goto ret1;
+
+ mpz_add_ui (a, a, primes_diff[r]); /* Establish new base. */
+
+ if (!mp_millerrabin (n, nm1, a, tmp, q, k))
+ {
+ is_prime = false;
+ goto ret1;
+ }
+ }
+
+ error (0, 0, _("Lucas prime test failure. This should not happen"));
+ abort ();
+
+ ret1:
+ if (flag_prove_primality)
+ mp_factor_clear (&factors);
+ ret2:
+ mpz_clears (q, a, nm1, tmp, NULL);
+
+ return is_prime;
}
+#endif
+
+static void
+factor_using_pollard_rho (uintmax_t n, unsigned long int a,
+ struct factors *factors)
+{
+ uintmax_t x, z, y, P, t, ni, g;
+
+ unsigned long int k = 1;
+ unsigned long int l = 1;
+
+ redcify (P, 1, n);
+ addmod (x, P, P, n); /* i.e., redcify(2) */
+ y = z = x;
+
+ while (n != 1)
+ {
+ assert (a < n);
+
+ binv (ni, n); /* FIXME: when could we use old 'ni' value? */
+
+ for (;;)
+ {
+ do
+ {
+ x = mulredc (x, x, n, ni);
+ addmod (x, x, a, n);
+
+ submod (t, z, x, n);
+ P = mulredc (P, t, n, ni);
+
+ if (k % 32 == 1)
+ {
+ if (gcd_odd (P, n) != 1)
+ goto factor_found;
+ y = x;
+ }
+ }
+ while (--k != 0);
+
+ z = x;
+ k = l;
+ l = 2 * l;
+ for (unsigned long int i = 0; i < k; i++)
+ {
+ x = mulredc (x, x, n, ni);
+ addmod (x, x, a, n);
+ }
+ y = x;
+ }
+
+ factor_found:
+ do
+ {
+ y = mulredc (y, y, n, ni);
+ addmod (y, y, a, n);
+
+ submod (t, z, y, n);
+ g = gcd_odd (t, n);
+ }
+ while (g == 1);
+
+ n = n / g;
+
+ if (!prime_p (g))
+ factor_using_pollard_rho (g, a + 1, factors);
+ else
+ factor_insert (factors, g);
+
+ if (prime_p (n))
+ {
+ factor_insert (factors, n);
+ break;
+ }
+
+ x = x % n;
+ z = z % n;
+ y = y % n;
+ }
+}
+
+static void
+factor_using_pollard_rho2 (uintmax_t n1, uintmax_t n0, unsigned long int a,
+ struct factors *factors)
+{
+ uintmax_t x1, x0, z1, z0, y1, y0, P1, P0, t1, t0, ni, g1, g0, r1m;
+
+ unsigned long int k = 1;
+ unsigned long int l = 1;
+
+ redcify2 (P1, P0, 1, n1, n0);
+ addmod2 (x1, x0, P1, P0, P1, P0, n1, n0); /* i.e., redcify(2) */
+ y1 = z1 = x1;
+ y0 = z0 = x0;
+
+ while (n1 != 0 || n0 != 1)
+ {
+ binv (ni, n0);
+
+ for (;;)
+ {
+ do
+ {
+ x0 = mulredc2 (&r1m, x1, x0, x1, x0, n1, n0, ni);
+ x1 = r1m;
+ addmod2 (x1, x0, x1, x0, 0, a, n1, n0);
+
+ submod2 (t1, t0, z1, z0, x1, x0, n1, n0);
+ P0 = mulredc2 (&r1m, P1, P0, t1, t0, n1, n0, ni);
+ P1 = r1m;
+
+ if (k % 32 == 1)
+ {
+ g0 = gcd2_odd (&g1, P1, P0, n1, n0);
+ if (g1 != 0 || g0 != 1)
+ goto factor_found;
+ y1 = x1; y0 = x0;
+ }
+ }
+ while (--k != 0);
+
+ z1 = x1; z0 = x0;
+ k = l;
+ l = 2 * l;
+ for (unsigned long int i = 0; i < k; i++)
+ {
+ x0 = mulredc2 (&r1m, x1, x0, x1, x0, n1, n0, ni);
+ x1 = r1m;
+ addmod2 (x1, x0, x1, x0, 0, a, n1, n0);
+ }
+ y1 = x1; y0 = x0;
+ }
-static void
-factor_using_division (mpz_t t, unsigned int limit)
-{
- mpz_t q, r;
- unsigned long int f;
- int ai;
- static unsigned int const add[] = {4, 2, 4, 2, 4, 6, 2, 6};
- unsigned int const *addv = add;
- unsigned int failures;
+ factor_found:
+ do
+ {
+ y0 = mulredc2 (&r1m, y1, y0, y1, y0, n1, n0, ni);
+ y1 = r1m;
+ addmod2 (y1, y0, y1, y0, 0, a, n1, n0);
- debug ("[trial division (%u)] ", limit);
+ submod2 (t1, t0, z1, z0, y1, y0, n1, n0);
+ g0 = gcd2_odd (&g1, t1, t0, n1, n0);
+ }
+ while (g1 == 0 && g0 == 1);
- mpz_init (q);
- mpz_init (r);
+ if (g1 == 0)
+ {
+ /* The found factor is one word. */
+ divexact_21 (n1, n0, n1, n0, g0); /* n = n / g */
- f = mpz_scan1 (t, 0);
- mpz_div_2exp (t, t, f);
- while (f)
- {
- emit_ul_factor (2);
- --f;
- }
+ if (!prime_p (g0))
+ factor_using_pollard_rho (g0, a + 1, factors);
+ else
+ factor_insert (factors, g0);
+ }
+ else
+ {
+ /* The found factor is two words. This is highly unlikely, thus hard
+ to trigger. Please be careful before you change this code! */
+ uintmax_t ginv;
- while (true)
- {
- mpz_tdiv_qr_ui (q, r, t, 3);
- if (mpz_cmp_ui (r, 0) != 0)
- break;
- mpz_set (t, q);
- emit_ul_factor (3);
- }
+ binv (ginv, g0); /* Compute n = n / g. Since the result will */
+ n0 = ginv * n0; /* fit one word, we can compute the quotient */
+ n1 = 0; /* modulo B, ignoring the high divisor word. */
- while (true)
- {
- mpz_tdiv_qr_ui (q, r, t, 5);
- if (mpz_cmp_ui (r, 0) != 0)
- break;
- mpz_set (t, q);
- emit_ul_factor (5);
- }
+ if (!prime2_p (g1, g0))
+ factor_using_pollard_rho2 (g1, g0, a + 1, factors);
+ else
+ factor_insert_large (factors, g1, g0);
+ }
- failures = 0;
- f = 7;
- ai = 0;
- while (mpz_cmp_ui (t, 1) != 0)
- {
- mpz_tdiv_qr_ui (q, r, t, f);
- if (mpz_cmp_ui (r, 0) != 0)
+ if (n1 == 0)
{
- f += addv[ai];
- if (mpz_cmp_ui (q, f) < 0)
- break;
- ai = (ai + 1) & 7;
- failures++;
- if (failures > limit)
- break;
+ if (prime_p (n0))
+ {
+ factor_insert (factors, n0);
+ break;
+ }
+
+ factor_using_pollard_rho (n0, a, factors);
+ return;
}
- else
+
+ if (prime2_p (n1, n0))
{
- mpz_swap (t, q);
- emit_ul_factor (f);
- failures = 0;
+ factor_insert_large (factors, n1, n0);
+ break;
}
- }
- mpz_clear (q);
- mpz_clear (r);
+ x0 = mod2 (&x1, x1, x0, n1, n0);
+ z0 = mod2 (&z1, z1, z0, n1, n0);
+ y0 = mod2 (&y1, y1, y0, n1, n0);
+ }
}
-/* The number of Miller-Rabin tests we require. */
-enum { MR_REPS = 25 };
-
+#if HAVE_GMP
static void
-factor_using_pollard_rho (mpz_t n, int a_int)
+mp_factor_using_pollard_rho (mpz_t n, unsigned long int a,
+ struct mp_factors *factors)
{
- mpz_t x, x1, y, P;
- mpz_t a;
- mpz_t g;
- mpz_t t1, t2;
- int k, l, c;
-
- debug ("[pollard-rho (%d)] ", a_int);
+ mpz_t x, z, y, P;
+ mpz_t t, t2;
- mpz_init (g);
- mpz_init (t1);
- mpz_init (t2);
+ debug ("[pollard-rho (%lu)] ", a);
- mpz_init_set_si (a, a_int);
+ mpz_inits (t, t2, NULL);
mpz_init_set_si (y, 2);
mpz_init_set_si (x, 2);
- mpz_init_set_si (x1, 2);
- k = 1;
- l = 1;
+ mpz_init_set_si (z, 2);
mpz_init_set_ui (P, 1);
- c = 0;
+
+ unsigned long long int k = 1;
+ unsigned long long int l = 1;
while (mpz_cmp_ui (n, 1) != 0)
{
-S2:
- mpz_mul (x, x, x); mpz_add (x, x, a); mpz_mod (x, x, n);
-
- mpz_sub (t1, x1, x); mpz_mul (t2, P, t1); mpz_mod (P, t2, n);
- c++;
- if (c == 20)
+ for (;;)
{
- c = 0;
- mpz_gcd (g, P, n);
- if (mpz_cmp_ui (g, 1) != 0)
- goto S4;
+ do
+ {
+ mpz_mul (t, x, x);
+ mpz_mod (x, t, n);
+ mpz_add_ui (x, x, a);
+
+ mpz_sub (t, z, x);
+ mpz_mul (t2, P, t);
+ mpz_mod (P, t2, n);
+
+ if (k % 32 == 1)
+ {
+ mpz_gcd (t, P, n);
+ if (mpz_cmp_ui (t, 1) != 0)
+ goto factor_found;
+ mpz_set (y, x);
+ }
+ }
+ while (--k != 0);
+
+ mpz_set (z, x);
+ k = l;
+ l = 2 * l;
+ for (unsigned long long int i = 0; i < k; i++)
+ {
+ mpz_mul (t, x, x);
+ mpz_mod (x, t, n);
+ mpz_add_ui (x, x, a);
+ }
mpz_set (y, x);
}
- k--;
- if (k > 0)
- goto S2;
-
- mpz_gcd (g, P, n);
- if (mpz_cmp_ui (g, 1) != 0)
- goto S4;
-
- mpz_set (x1, x);
- k = l;
- l = 2 * l;
- unsigned int i;
- for (i = 0; i < k; i++)
- {
- mpz_mul (x, x, x); mpz_add (x, x, a); mpz_mod (x, x, n);
- }
- mpz_set (y, x);
- c = 0;
- goto S2;
-S4:
+ factor_found:
do
{
- mpz_mul (y, y, y); mpz_add (y, y, a); mpz_mod (y, y, n);
- mpz_sub (t1, x1, y); mpz_gcd (g, t1, n);
+ mpz_mul (t, y, y);
+ mpz_mod (y, t, n);
+ mpz_add_ui (y, y, a);
+
+ mpz_sub (t, z, y);
+ mpz_gcd (t, t, n);
}
- while (mpz_cmp_ui (g, 1) == 0);
+ while (mpz_cmp_ui (t, 1) == 0);
- mpz_div (n, n, g); /* divide by g, before g is overwritten */
+ mpz_divexact (n, n, t); /* divide by t, before t is overwritten */
- if (!mpz_probab_prime_p (g, MR_REPS))
+ if (!mp_prime_p (t))
{
- do
- {
- mp_limb_t a_limb;
- mpn_random (&a_limb, (mp_size_t) 1);
- a_int = (int) a_limb;
- }
- while (a_int == -2 || a_int == 0);
-
debug ("[composite factor--restarting pollard-rho] ");
- factor_using_pollard_rho (g, a_int);
+ mp_factor_using_pollard_rho (t, a + 1, factors);
}
else
{
- emit_factor (g);
+ mp_factor_insert (factors, t);
}
- mpz_mod (x, x, n);
- mpz_mod (x1, x1, n);
- mpz_mod (y, y, n);
- if (mpz_probab_prime_p (n, MR_REPS))
+
+ if (mp_prime_p (n))
{
- emit_factor (n);
+ mp_factor_insert (factors, n);
break;
}
+
+ mpz_mod (x, x, n);
+ mpz_mod (z, z, n);
+ mpz_mod (y, y, n);
}
- mpz_clear (g);
- mpz_clear (P);
- mpz_clear (t2);
- mpz_clear (t1);
- mpz_clear (a);
- mpz_clear (x1);
- mpz_clear (x);
- mpz_clear (y);
+ mpz_clears (P, t2, t, z, x, y, NULL);
}
+#endif
-#else
-
-static void
-debug (char const *fmt ATTRIBUTE_UNUSED, ...)
+/* FIXME: Maybe better to use an iteration converging to 1/sqrt(n)? If
+ algorithm is replaced, consider also returning the remainder. */
+static uintmax_t _GL_ATTRIBUTE_CONST
+isqrt (uintmax_t n)
{
+ uintmax_t x;
+ unsigned c;
+ if (n == 0)
+ return 0;
+
+ count_leading_zeros (c, n);
+
+ /* Make x > sqrt(n). This will be invariant through the loop. */
+ x = (uintmax_t) 1 << ((W_TYPE_SIZE + 1 - c) / 2);
+
+ for (;;)
+ {
+ uintmax_t y = (x + n/x) / 2;
+ if (y >= x)
+ return x;
+
+ x = y;
+ }
}
-#endif
+static uintmax_t _GL_ATTRIBUTE_CONST
+isqrt2 (uintmax_t nh, uintmax_t nl)
+{
+ unsigned int shift;
+ uintmax_t x;
+
+ /* Ensures the remainder fits in an uintmax_t. */
+ assert (nh < ((uintmax_t) 1 << (W_TYPE_SIZE - 2)));
+
+ if (nh == 0)
+ return isqrt (nl);
+
+ count_leading_zeros (shift, nh);
+ shift &= ~1;
+
+ /* Make x > sqrt(n) */
+ x = isqrt ( (nh << shift) + (nl >> (W_TYPE_SIZE - shift))) + 1;
+ x <<= (W_TYPE_SIZE - shift) / 2;
-/* The maximum number of factors, including -1, for negative numbers. */
-#define MAX_N_FACTORS (sizeof (uintmax_t) * CHAR_BIT)
+ /* Do we need more than one iteration? */
+ for (;;)
+ {
+ uintmax_t r ATTRIBUTE_UNUSED;
+ uintmax_t q, y;
+ udiv_qrnnd (q, r, nh, nl, x);
+ y = (x + q) / 2;
+
+ if (y >= x)
+ {
+ uintmax_t hi, lo;
+ umul_ppmm (hi, lo, x + 1, x + 1);
+ assert (gt2 (hi, lo, nh, nl));
+
+ umul_ppmm (hi, lo, x, x);
+ assert (ge2 (nh, nl, hi, lo));
+ sub_ddmmss (hi, lo, nh, nl, hi, lo);
+ assert (hi == 0);
+
+ return x;
+ }
+
+ x = y;
+ }
+}
+
+/* MAGIC[N] has a bit i set iff i is a quadratic residue mod N. */
+#define MAGIC64 ((uint64_t) 0x0202021202030213ULL)
+#define MAGIC63 ((uint64_t) 0x0402483012450293ULL)
+#define MAGIC65 ((uint64_t) 0x218a019866014613ULL)
+#define MAGIC11 0x23b
-/* The trial divisor increment wheel. Use it to skip over divisors that
- are composites of 2, 3, 5, 7, or 11. The part from WHEEL_START up to
- WHEEL_END is reused periodically, while the "lead in" is used to test
- for those primes and to jump onto the wheel. For more information, see
- http://www.utm.edu/research/primes/glossary/WheelFactorization.html */
+/* Returns the square root if the input is a square, otherwise 0. */
+static uintmax_t _GL_ATTRIBUTE_CONST
+is_square (uintmax_t x)
+{
+ /* Uses the tests suggested by Cohen. Excludes 99% of the non-squares before
+ computing the square root. */
+ if (((MAGIC64 >> (x & 63)) & 1)
+ && ((MAGIC63 >> (x % 63)) & 1)
+ /* Both 0 and 64 are squares mod (65) */
+ && ((MAGIC65 >> ((x % 65) & 63)) & 1)
+ && ((MAGIC11 >> (x % 11) & 1)))
+ {
+ uintmax_t r = isqrt (x);
+ if (r*r == x)
+ return r;
+ }
+ return 0;
+}
-#include "wheel-size.h" /* For the definition of WHEEL_SIZE. */
-static const unsigned char wheel_tab[] =
+/* invtab[i] = floor(0x10000 / (0x100 + i) */
+static const unsigned short invtab[0x81] =
{
-#include "wheel.h"
+ 0x200,
+ 0x1fc, 0x1f8, 0x1f4, 0x1f0, 0x1ec, 0x1e9, 0x1e5, 0x1e1,
+ 0x1de, 0x1da, 0x1d7, 0x1d4, 0x1d0, 0x1cd, 0x1ca, 0x1c7,
+ 0x1c3, 0x1c0, 0x1bd, 0x1ba, 0x1b7, 0x1b4, 0x1b2, 0x1af,
+ 0x1ac, 0x1a9, 0x1a6, 0x1a4, 0x1a1, 0x19e, 0x19c, 0x199,
+ 0x197, 0x194, 0x192, 0x18f, 0x18d, 0x18a, 0x188, 0x186,
+ 0x183, 0x181, 0x17f, 0x17d, 0x17a, 0x178, 0x176, 0x174,
+ 0x172, 0x170, 0x16e, 0x16c, 0x16a, 0x168, 0x166, 0x164,
+ 0x162, 0x160, 0x15e, 0x15c, 0x15a, 0x158, 0x157, 0x155,
+ 0x153, 0x151, 0x150, 0x14e, 0x14c, 0x14a, 0x149, 0x147,
+ 0x146, 0x144, 0x142, 0x141, 0x13f, 0x13e, 0x13c, 0x13b,
+ 0x139, 0x138, 0x136, 0x135, 0x133, 0x132, 0x130, 0x12f,
+ 0x12e, 0x12c, 0x12b, 0x129, 0x128, 0x127, 0x125, 0x124,
+ 0x123, 0x121, 0x120, 0x11f, 0x11e, 0x11c, 0x11b, 0x11a,
+ 0x119, 0x118, 0x116, 0x115, 0x114, 0x113, 0x112, 0x111,
+ 0x10f, 0x10e, 0x10d, 0x10c, 0x10b, 0x10a, 0x109, 0x108,
+ 0x107, 0x106, 0x105, 0x104, 0x103, 0x102, 0x101, 0x100,
};
-#define WHEEL_START (wheel_tab + WHEEL_SIZE)
-#define WHEEL_END (wheel_tab + ARRAY_CARDINALITY (wheel_tab))
+/* Compute q = [u/d], r = u mod d. Avoids slow hardware division for the case
+ that q < 0x40; here it instead uses a table of (Euclidian) inverses. */
+#define div_smallq(q, r, u, d) \
+ do { \
+ if ((u) / 0x40 < (d)) \
+ { \
+ int _cnt; \
+ uintmax_t _dinv, _mask, _q, _r; \
+ count_leading_zeros (_cnt, (d)); \
+ _r = (u); \
+ if (UNLIKELY (_cnt > (W_TYPE_SIZE - 8))) \
+ { \
+ _dinv = invtab[((d) << (_cnt + 8 - W_TYPE_SIZE)) - 0x80]; \
+ _q = _dinv * _r >> (8 + W_TYPE_SIZE - _cnt); \
+ } \
+ else \
+ { \
+ _dinv = invtab[((d) >> (W_TYPE_SIZE - 8 - _cnt)) - 0x7f]; \
+ _q = _dinv * (_r >> (W_TYPE_SIZE - 3 - _cnt)) >> 11; \
+ } \
+ _r -= _q*(d); \
+ \
+ _mask = -(uintmax_t) (_r >= (d)); \
+ (r) = _r - (_mask & (d)); \
+ (q) = _q - _mask; \
+ assert ( (q) * (d) + (r) == u); \
+ } \
+ else \
+ { \
+ uintmax_t _q = (u) / (d); \
+ (r) = (u) - _q * (d); \
+ (q) = _q; \
+ } \
+ } while (0)
+
+/* Notes: Example N = 22117019. After first phase we find Q1 = 6314, Q
+ = 3025, P = 1737, representing F_{18} = (-6314, 2* 1737, 3025),
+ with 3025 = 55^2.
+
+ Constructing the square root, we get Q1 = 55, Q = 8653, P = 4652,
+ representing G_0 = (-55, 2*4652, 8653).
+
+ In the notation of the paper:
+
+ S_{-1} = 55, S_0 = 8653, R_0 = 4652
+
+ Put
+
+ t_0 = floor([q_0 + R_0] / S0) = 1
+ R_1 = t_0 * S_0 - R_0 = 4001
+ S_1 = S_{-1} +t_0 (R_0 - R_1) = 706
+*/
+
+/* Multipliers, in order of efficiency:
+ 0.7268 3*5*7*11 = 1155 = 3 (mod 4)
+ 0.7317 3*5*7 = 105 = 1
+ 0.7820 3*5*11 = 165 = 1
+ 0.7872 3*5 = 15 = 3
+ 0.8101 3*7*11 = 231 = 3
+ 0.8155 3*7 = 21 = 1
+ 0.8284 5*7*11 = 385 = 1
+ 0.8339 5*7 = 35 = 3
+ 0.8716 3*11 = 33 = 1
+ 0.8774 3 = 3 = 3
+ 0.8913 5*11 = 55 = 3
+ 0.8972 5 = 5 = 1
+ 0.9233 7*11 = 77 = 1
+ 0.9295 7 = 7 = 3
+ 0.9934 11 = 11 = 3
+*/
+#define QUEUE_SIZE 50
-/* FIXME: comment */
+#if STAT_SQUFOF
+# define Q_FREQ_SIZE 50
+/* Element 0 keeps the total */
+static unsigned int q_freq[Q_FREQ_SIZE + 1];
+# define MIN(a,b) ((a) < (b) ? (a) : (b))
+#endif
-static size_t
-factor_wheel (uintmax_t n0, size_t max_n_factors, uintmax_t *factors)
+/* Return true on success. Expected to fail only for numbers
+ >= 2^{2*W_TYPE_SIZE - 2}, or close to that limit. */
+static bool
+factor_using_squfof (uintmax_t n1, uintmax_t n0, struct factors *factors)
{
- uintmax_t n = n0, d, q;
- size_t n_factors = 0;
- unsigned char const *w = wheel_tab;
+ /* Uses algorithm and notation from
- if (n <= 1)
- return n_factors;
+ SQUARE FORM FACTORIZATION
+ JASON E. GOWER AND SAMUEL S. WAGSTAFF, JR.
+
+ http://homes.cerias.purdue.edu/~ssw/squfof.pdf
+ */
+
+ static const unsigned int multipliers_1[] =
+ { /* = 1 (mod 4) */
+ 105, 165, 21, 385, 33, 5, 77, 1, 0
+ };
+ static const unsigned int multipliers_3[] =
+ { /* = 3 (mod 4) */
+ 1155, 15, 231, 35, 3, 55, 7, 11, 0
+ };
+
+ const unsigned int *m;
+
+ struct { uintmax_t Q; uintmax_t P; } queue[QUEUE_SIZE];
- /* The exit condition in the following loop is correct because
- any time it is tested one of these 3 conditions holds:
- (1) d divides n
- (2) n is prime
- (3) n is composite but has no factors less than d.
- If (1) or (2) obviously the right thing happens.
- If (3), then since n is composite it is >= d^2. */
+ if (n1 >= ((uintmax_t) 1 << (W_TYPE_SIZE - 2)))
+ return false;
- d = 2;
- do
+ uintmax_t sqrt_n = isqrt2 (n1, n0);
+
+ if (n0 == sqrt_n * sqrt_n)
{
- q = n / d;
- while (n == q * d)
+ uintmax_t p1, p0;
+
+ umul_ppmm (p1, p0, sqrt_n, sqrt_n);
+ assert (p0 == n0);
+
+ if (n1 == p1)
{
- assert (n_factors < max_n_factors);
- factors[n_factors++] = d;
- n = q;
- q = n / d;
+ if (prime_p (sqrt_n))
+ factor_insert_multiplicity (factors, sqrt_n, 2);
+ else
+ {
+ struct factors f;
+
+ f.nfactors = 0;
+ if (!factor_using_squfof (0, sqrt_n, &f))
+ {
+ /* Try pollard rho instead */
+ factor_using_pollard_rho (sqrt_n, 1, &f);
+ }
+ /* Duplicate the new factors */
+ for (unsigned int i = 0; i < f.nfactors; i++)
+ factor_insert_multiplicity (factors, f.p[i], 2*f.e[i]);
+ }
+ return true;
}
- d += *(w++);
- if (w == WHEEL_END)
- w = WHEEL_START;
}
- while (d <= q);
- if (n != 1 || n0 == 1)
+ /* Select multipliers so we always get n * mu = 3 (mod 4) */
+ for (m = (n0 % 4 == 1) ? multipliers_3 : multipliers_1;
+ *m; m++)
{
- assert (n_factors < max_n_factors);
- factors[n_factors++] = n;
- }
+ uintmax_t S, Dh, Dl, Q1, Q, P, L, L1, B;
+ unsigned int i;
+ unsigned int mu = *m;
+ unsigned int qpos = 0;
+
+ assert (mu * n0 % 4 == 3);
+
+ /* In the notation of the paper, with mu * n == 3 (mod 4), we
+ get \Delta = 4 mu * n, and the paper's \mu is 2 mu. As far as
+ I understand it, the necessary bound is 4 \mu^3 < n, or 32
+ mu^3 < n.
+
+ However, this seems insufficient: With n = 37243139 and mu =
+ 105, we get a trivial factor, from the square 38809 = 197^2,
+ without any corresponding Q earlier in the iteration.
+
+ Requiring 64 mu^3 < n seems sufficient. */
+ if (n1 == 0)
+ {
+ if ((uintmax_t) mu*mu*mu >= n0 / 64)
+ continue;
+ }
+ else
+ {
+ if (n1 > ((uintmax_t) 1 << (W_TYPE_SIZE - 2)) / mu)
+ continue;
+ }
+ umul_ppmm (Dh, Dl, n0, mu);
+ Dh += n1 * mu;
+
+ assert (Dl % 4 != 1);
+ assert (Dh < (uintmax_t) 1 << (W_TYPE_SIZE - 2));
+
+ S = isqrt2 (Dh, Dl);
+
+ Q1 = 1;
+ P = S;
+
+ /* Square root remainder fits in one word, so ignore high part. */
+ Q = Dl - P*P;
+ /* FIXME: When can this differ from floor(sqrt(2 sqrt(D)))? */
+ L = isqrt (2*S);
+ B = 2*L;
+ L1 = mu * 2 * L;
+
+ /* The form is (+/- Q1, 2P, -/+ Q), of discriminant 4 (P^2 + Q Q1) =
+ 4 D. */
+
+ for (i = 0; i <= B; i++)
+ {
+ uintmax_t q, P1, t, rem;
+
+ div_smallq (q, rem, S+P, Q);
+ P1 = S - rem; /* P1 = q*Q - P */
+
+#if STAT_SQUFOF
+ assert (q > 0);
+ q_freq[0]++;
+ q_freq[MIN (q, Q_FREQ_SIZE)]++;
+#endif
+
+ if (Q <= L1)
+ {
+ uintmax_t g = Q;
+
+ if ( (Q & 1) == 0)
+ g /= 2;
+
+ g /= gcd_odd (g, mu);
- return n_factors;
+ if (g <= L)
+ {
+ if (qpos >= QUEUE_SIZE)
+ error (EXIT_FAILURE, 0, _("squfof queue overflow"));
+ queue[qpos].Q = g;
+ queue[qpos].P = P % g;
+ qpos++;
+ }
+ }
+
+ /* I think the difference can be either sign, but mod
+ 2^W_TYPE_SIZE arithmetic should be fine. */
+ t = Q1 + q * (P - P1);
+ Q1 = Q;
+ Q = t;
+ P = P1;
+
+ if ( (i & 1) == 0)
+ {
+ uintmax_t r = is_square (Q);
+ if (r)
+ {
+ for (unsigned int j = 0; j < qpos; j++)
+ {
+ if (queue[j].Q == r)
+ {
+ if (r == 1)
+ /* Traversed entire cycle. */
+ goto next_multiplier;
+
+ /* Need the absolute value for divisibility test. */
+ if (P >= queue[j].P)
+ t = P - queue[j].P;
+ else
+ t = queue[j].P - P;
+ if (t % r == 0)
+ {
+ /* Delete entries up to and including entry
+ j, which matched. */
+ memmove (queue, queue + j + 1,
+ (qpos - j - 1) * sizeof (queue[0]));
+ qpos -= (j + 1);
+ }
+ goto next_i;
+ }
+ }
+
+ /* We have found a square form, which should give a
+ factor. */
+ Q1 = r;
+ assert (S >= P); /* What signs are possible? */
+ P += r * ((S - P) / r);
+
+ /* Note: Paper says (N - P*P) / Q1, that seems incorrect
+ for the case D = 2N. */
+ /* Compute Q = (D - P*P) / Q1, but we need double
+ precision. */
+ uintmax_t hi, lo;
+ umul_ppmm (hi, lo, P, P);
+ sub_ddmmss (hi, lo, Dh, Dl, hi, lo);
+ udiv_qrnnd (Q, rem, hi, lo, Q1);
+ assert (rem == 0);
+
+ for (;;)
+ {
+ /* Note: There appears to by a typo in the paper,
+ Step 4a in the algorithm description says q <--
+ floor([S+P]/\hat Q), but looking at the equations
+ in Sec. 3.1, it should be q <-- floor([S+P] / Q).
+ (In this code, \hat Q is Q1). */
+ div_smallq (q, rem, S+P, Q);
+ P1 = S - rem; /* P1 = q*Q - P */
+
+#if STAT_SQUFOF
+ q_freq[0]++;
+ q_freq[MIN (q, Q_FREQ_SIZE)]++;
+#endif
+ if (P == P1)
+ break;
+ t = Q1 + q * (P - P1);
+ Q1 = Q;
+ Q = t;
+ P = P1;
+ }
+
+ if ( (Q & 1) == 0)
+ Q /= 2;
+ Q /= gcd_odd (Q, mu);
+
+ assert (Q > 1 && (n1 || Q < n0));
+
+ if (prime_p (Q))
+ factor_insert (factors, Q);
+ else if (!factor_using_squfof (0, Q, factors))
+ factor_using_pollard_rho (Q, 2, factors);
+
+ divexact_21 (n1, n0, n1, n0, Q);
+
+ if (prime2_p (n1, n0))
+ factor_insert_large (factors, n1, n0);
+ else
+ {
+ if (!factor_using_squfof (n1, n0, factors))
+ {
+ if (n1 == 0)
+ factor_using_pollard_rho (n0, 1, factors);
+ else
+ factor_using_pollard_rho2 (n1, n0, 1, factors);
+ }
+ }
+
+ return true;
+ }
+ }
+ next_i:;
+ }
+ next_multiplier:;
+ }
+ return false;
}
-/* Single-precision factoring */
static void
-print_factors_single (uintmax_t n)
+factor (uintmax_t t1, uintmax_t t0, struct factors *factors)
{
- uintmax_t factors[MAX_N_FACTORS];
- size_t n_factors = factor_wheel (n, MAX_N_FACTORS, factors);
- size_t i;
- char buf[INT_BUFSIZE_BOUND (uintmax_t)];
+ factors->nfactors = 0;
+ factors->plarge[1] = 0;
- printf ("%s:", umaxtostr (n, buf));
- for (i = 0; i < n_factors; i++)
- printf (" %s", umaxtostr (factors[i], buf));
- putchar ('\n');
-}
+ if (t1 == 0 && t0 < 2)
+ return;
-#if HAVE_GMP
-static int
-mpcompare (const void *av, const void *bv)
-{
- mpz_t *const *a = av;
- mpz_t *const *b = bv;
- return mpz_cmp (**a, **b);
+ t0 = factor_using_division (&t1, t1, t0, factors);
+
+ if (t1 == 0 && t0 < 2)
+ return;
+
+ if (prime2_p (t1, t0))
+ factor_insert_large (factors, t1, t0);
+ else
+ {
+ if (alg == ALG_SQUFOF)
+ if (factor_using_squfof (t1, t0, factors))
+ return;
+
+ if (t1 == 0)
+ factor_using_pollard_rho (t0, 1, factors);
+ else
+ factor_using_pollard_rho2 (t1, t0, 1, factors);
+ }
}
+#if HAVE_GMP
static void
-sort_and_print_factors (void)
+mp_factor (mpz_t t, struct mp_factors *factors)
{
- mpz_t **faclist;
- size_t i;
+ mp_factor_init (factors);
- faclist = xcalloc (nfactors_found, sizeof *faclist);
- for (i = 0; i < nfactors_found; ++i)
+ if (mpz_sgn (t) != 0)
{
- faclist[i] = &factor[i];
+ mp_factor_using_division (t, factors);
+
+ if (mpz_cmp_ui (t, 1) != 0)
+ {
+ debug ("[is number prime?] ");
+ if (mp_prime_p (t))
+ mp_factor_insert (factors, t);
+ else
+ mp_factor_using_pollard_rho (t, 1, factors);
+ }
}
- qsort (faclist, nfactors_found, sizeof *faclist, mpcompare);
+}
+#endif
+
+static strtol_error
+strto2uintmax (uintmax_t *hip, uintmax_t *lop, const char *s)
+{
+ unsigned int lo_carry;
+ uintmax_t hi, lo;
- for (i = 0; i < nfactors_found; ++i)
+ strtol_error err;
+
+ hi = lo = 0;
+ for (;;)
{
- fputc (' ', stdout);
- mpz_out_str (stdout, 10, *faclist[i]);
+ unsigned int c = *s++;
+ if (c == 0)
+ break;
+
+ if (UNLIKELY (!ISDIGIT (c)))
+ {
+ err = LONGINT_INVALID;
+ break;
+ }
+ c -= '0';
+
+ err = LONGINT_OK; /* we've seen at least one valid digit */
+
+ if (UNLIKELY (hi > ~(uintmax_t)0 / 10))
+ {
+ err = LONGINT_OVERFLOW;
+ break;
+ }
+ hi = 10 * hi;
+
+ lo_carry = (lo >> (W_TYPE_SIZE - 3)) + (lo >> (W_TYPE_SIZE - 1));
+ lo_carry += 10 * lo < 2 * lo;
+
+ lo = 10 * lo;
+ lo += c;
+
+ lo_carry += lo < c;
+ hi += lo_carry;
+ if (UNLIKELY (hi < lo_carry))
+ {
+ err = LONGINT_OVERFLOW;
+ break;
+ }
}
- putchar ('\n');
- free (faclist);
+
+ *hip = hi;
+ *lop = lo;
+
+ return err;
}
static void
-free_factors (void)
+print_uintmaxes (uintmax_t t1, uintmax_t t0)
{
- size_t i;
+ uintmax_t q, r;
- for (i = 0; i < nfactors_found; ++i)
+ if (t1 == 0)
+ printf ("%ju", t0);
+ else
{
- mpz_clear (factor[i]);
+ /* Use very plain code here since it seems hard to write fast code
+ without assuming a specific word size. */
+ q = t1 / 1000000000;
+ r = t1 % 1000000000;
+ udiv_qrnnd (t0, r, r, t0, 1000000000);
+ print_uintmaxes (q, t0);
+ printf ("%09u", (int) r);
}
- /* Don't actually free factor[] because in the case where we are
- reading numbers from stdin, we may be about to use it again. */
- nfactors_found = 0;
}
-/* Arbitrary-precision factoring */
+/* Single-precision factoring */
static void
-print_factors_multi (mpz_t t)
+print_factors_single (uintmax_t t1, uintmax_t t0)
{
- mpz_out_str (stdout, 10, t);
+ struct factors factors;
+
+ print_uintmaxes (t1, t0);
putchar (':');
- if (mpz_sgn (t) != 0)
- {
- /* Set the trial division limit according to the size of t. */
- size_t n_bits = mpz_sizeinbase (t, 2);
- unsigned int division_limit = MIN (n_bits, 1000);
- division_limit *= division_limit;
+ factor (t1, t0, &factors);
- factor_using_division (t, division_limit);
+ for (unsigned int j = 0; j < factors.nfactors; j++)
+ for (unsigned int k = 0; k < factors.e[j]; k++)
+ printf (" %ju", factors.p[j]);
- if (mpz_cmp_ui (t, 1) != 0)
- {
- debug ("[is number prime?] ");
- if (mpz_probab_prime_p (t, MR_REPS))
- emit_factor (t);
- else
- factor_using_pollard_rho (t, 1);
- }
+ if (factors.plarge[1])
+ {
+ putchar (' ');
+ print_uintmaxes (factors.plarge[1], factors.plarge[0]);
}
-
- mpz_clear (t);
- sort_and_print_factors ();
- free_factors ();
+ putchar ('\n');
}
-#endif
-
/* Emit the factors of the indicated number. If we have the option of using
either algorithm, we select on the basis of the length of the number.
has enough digits, because the algorithm is better. The turnover point
depends on the value. */
static bool
-print_factors (char const *s)
+print_factors (const char *input)
{
- uintmax_t n;
- strtol_error err = xstrtoumax (s, NULL, 10, &n, "");
+ uintmax_t t1, t0;
-#if HAVE_GMP
- enum { GMP_TURNOVER_POINT = 100000 };
+ /* Try converting the number to one or two words. If it fails, use GMP or
+ print an error message. The 2nd condition checks that the most
+ significant bit of the two-word number is clear, in a typesize neutral
+ way. */
+ strtol_error err = strto2uintmax (&t1, &t0, input);
- if (err == LONGINT_OVERFLOW
- || (err == LONGINT_OK && GMP_TURNOVER_POINT <= n))
+ switch (err)
{
- mpz_t t;
- mpz_init (t);
- if (gmp_sscanf (s, "%Zd", t) == 1)
+ case LONGINT_OK:
+ if (((t1 << 1) >> 1) == t1)
{
- debug ("[%s]", _("using arbitrary-precision arithmetic"));
- print_factors_multi (t);
+ debug ("[%s]", _("using single-precision arithmetic"));
+ print_factors_single (t1, t0);
return true;
}
- err = LONGINT_INVALID;
- }
-#endif
-
- switch (err)
- {
- case LONGINT_OK:
- debug ("[%s]", _("using single-precision arithmetic"));
- print_factors_single (n);
- return true;
-
- case LONGINT_OVERFLOW:
- error (0, 0, _("%s is too large"), quote (s));
- return false;
+ break;
default:
- error (0, 0, _("%s is not a valid positive integer"), quote (s));
+ error (0, 0, _("%s is not a valid positive integer"), quote (input));
return false;
}
-}
-enum
-{
- VERBOSE_OPTION = CHAR_MAX + 1
-};
+#if HAVE_GMP
+ debug ("[%s]", _("using arbitrary-precision arithmetic"));
+ mpz_t t;
+ struct mp_factors factors;
-static struct option const long_options[] =
-{
- {"verbose", no_argument, NULL, VERBOSE_OPTION},
- {GETOPT_HELP_OPTION_DECL},
- {GETOPT_VERSION_OPTION_DECL},
- {NULL, 0, NULL, 0}
-};
+ mpz_init_set_str (t, input, 10);
+
+ gmp_printf ("%Zd:", t);
+ mp_factor (t, &factors);
+
+ for (unsigned int j = 0; j < factors.nfactors; j++)
+ for (unsigned int k = 0; k < factors.e[j]; k++)
+ gmp_printf (" %Zd", factors.p[j]);
+
+ mp_factor_clear (&factors);
+ mpz_clear (t);
+ putchar ('\n');
+ return true;
+#else
+ error (0, 0, _("%s is too large"), quote (input));
+ return false;
+#endif
+}
void
usage (int status)
int
main (int argc, char **argv)
{
- bool ok;
- int c;
-
initialize_main (&argc, &argv);
set_program_name (argv[0]);
setlocale (LC_ALL, "");
atexit (close_stdout);
+ alg = ALG_POLLARD_RHO; /* Default to Pollard rho */
+
+ int c;
while ((c = getopt_long (argc, argv, "", long_options, NULL)) != -1)
{
switch (c)
{
case VERBOSE_OPTION:
- verbose = true;
+ verbose = 1;
+ break;
+
+ case 's':
+ alg = ALG_SQUFOF;
+ break;
+
+ case 'w':
+ flag_prove_primality = false;
break;
case_GETOPT_HELP_CHAR;
}
}
+#if STAT_SQUFOF
+ if (alg == ALG_SQUFOF)
+ memset (q_freq, 0, sizeof (q_freq));
+#endif
+
+ bool ok;
if (argc <= optind)
ok = do_stdin ();
else
{
- int i;
ok = true;
- for (i = optind; i < argc; i++)
+ for (int i = optind; i < argc; i++)
if (! print_factors (argv[i]))
ok = false;
}
-#if HAVE_GMP
- free (factor);
+
+#if STAT_SQUFOF
+ if (alg == ALG_SQUFOF && q_freq[0] > 0)
+ {
+ double acc_f;
+ printf ("q freq. cum. freq.(total: %d)\n", q_freq[0]);
+ for (unsigned int i = 1, acc_f = 0.0; i <= Q_FREQ_SIZE; i++)
+ {
+ double f = (double) q_freq[i] / q_freq[0];
+ acc_f += f;
+ printf ("%s%d %.2f%% %.2f%%\n", i == Q_FREQ_SIZE ? ">=" : "", i,
+ 100.0 * f, 100.0 * acc_f);
+ }
+ }
#endif
+
exit (ok ? EXIT_SUCCESS : EXIT_FAILURE);
}
pkglibexec_PROGRAMS = @pkglibexec_PROGRAMS@
# Needed by the testsuite.
-noinst_PROGRAMS = src/setuidgid src/getlimits
+noinst_PROGRAMS = \
+ src/getlimits \
+ src/make-prime-list \
+ src/setuidgid
noinst_HEADERS = \
src/chown-core.h \
src/fs-is-local.h \
src/group-list.h \
src/ioblksize.h \
+ src/longlong.h \
src/ls.h \
src/operand2sig.h \
src/prog-fprintf.h \
src/remove.h \
src/system.h \
- src/wheel-size.h \
- src/wheel.h \
src/uname.h
EXTRA_DIST += \
src/dcgen \
src/dircolors.hin \
src/tac-pipe.c \
- src/wheel-gen.pl \
src/extract-magic \
src/c99-to-c89.diff
src_ln_LDADD = $(LDADD)
src_logname_LDADD = $(LDADD)
src_ls_LDADD = $(LDADD)
+
+# This must *not* depend on anything in lib/, since it is used to generate
+# src/primes.h. If it depended on libcoreutils.a, that would pull all lib/*.c
+# into BUILT_SOURCES.
+src_make_prime_list_LDADD =
+
src_md5sum_LDADD = $(LDADD)
src_mkdir_LDADD = $(LDADD)
src_mkfifo_LDADD = $(LDADD)
$(AM_V_at)chmod a-w $@-t
$(AM_V_at)mv $@-t $@
-wheel_size = 5
-
-BUILT_SOURCES += src/wheel-size.h
-src/wheel-size.h: Makefile.am
- $(AM_V_GEN)rm -f $@ $@-t
- $(AM_V_at)echo '#define WHEEL_SIZE $(wheel_size)' > $@-t
- $(AM_V_at)chmod a-w $@-t
- $(AM_V_at)mv $@-t $@
-
-BUILT_SOURCES += src/wheel.h
-src/wheel.h: src/wheel-gen.pl Makefile.am
+BUILT_SOURCES += src/primes.h
+CLEANFILES += src/primes.h
+src/primes.h: src/make-prime-list
$(AM_V_GEN)rm -f $@ $@-t
- $(AM_V_at)$(srcdir)/src/wheel-gen.pl $(wheel_size) > $@-t
+ $(AM_V_at)src/make-prime-list 5000 > $@-t
$(AM_V_at)chmod a-w $@-t
$(AM_V_at)mv $@-t $@
/* longlong.h -- definitions for mixed size 32/64 bit arithmetic.
Copyright 1991, 1992, 1993, 1994, 1996, 1997, 1999, 2000, 2001, 2002, 2003,
-2004, 2005, 2007, 2008, 2009, 2011 Free Software Foundation, Inc.
+2004, 2005, 2007, 2008, 2009, 2011, 2012 Free Software Foundation, Inc.
This file is free software; you can redistribute it and/or modify it under the
terms of the GNU Lesser General Public License as published by the Free
__GMP_DECLSPEC UWtype __MPN(udiv_w_sdiv) (UWtype *, UWtype, UWtype, UWtype);
#endif
+#ifndef __GMP_DECLSPEC
+#define __GMP_DECLSPEC /* empty */
+#endif
+
/* If udiv_qrnnd was not defined for this processor, use __udiv_qrnnd_c. */
#if !defined (udiv_qrnnd)
#define UDIV_NEEDS_NORMALIZATION 1
+++ /dev/null
-#!/usr/bin/perl -w
-# Generate the spokes of a wheel, for wheel factorization.
-
-# Copyright (C) 2001-2012 Free Software Foundation, Inc.
-
-# This program is free software: you can redistribute it and/or modify
-# it under the terms of the GNU General Public License as published by
-# the Free Software Foundation, either version 3 of the License, or
-# (at your option) any later version.
-
-# This program is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-# GNU General Public License for more details.
-
-# You should have received a copy of the GNU General Public License
-# along with this program. If not, see <http://www.gnu.org/licenses/>.
-
-eval 'exec /usr/bin/perl -S $0 ${1+"$@"}'
- if 0;
-
-use strict;
-(my $ME = $0) =~ s|.*/||;
-
-# A global destructor to close standard output with error checking.
-sub END
-{
- defined fileno STDOUT
- or return;
- close STDOUT
- and return;
- warn "$ME: closing standard output: $!\n";
- $? ||= 1;
-}
-
-sub is_prime ($)
-{
- my ($n) = @_;
- use integer;
-
- $n == 2
- and return 1;
-
- my $d = 2;
- my $w = 1;
- while (1)
- {
- my $q = $n / $d;
- $n == $q * $d
- and return 0;
- $d += $w;
- $q < $d
- and last;
- $w = 2;
- }
- return 1;
-}
-
-{
- @ARGV == 1
- or die "$ME: missing argument\n";
-
- my $wheel_size = $ARGV[0];
-
- my @primes = (2);
- my $product = $primes[0];
- my $n_primes = 1;
- for (my $i = 3; ; $i += 2)
- {
- if (is_prime $i)
- {
- push @primes, $i;
- $product *= $i;
- ++$n_primes == $wheel_size
- and last;
- }
- }
-
- my $ws_m1 = $wheel_size - 1;
- print <<EOF;
-/* The first $ws_m1 elements correspond to the incremental offsets of the
- first $wheel_size primes (@primes). The $wheel_size(th) element is the
- difference between that last prime and the next largest integer
- that is not a multiple of those primes. The remaining numbers
- define the wheel. For more information, see
- http://www.utm.edu/research/primes/glossary/WheelFactorization.html. */
-EOF
-
- my @increments;
- my $prev = 2;
- for (my $i = 3; ; $i += 2)
- {
- my $rel_prime = 1;
- foreach my $divisor (@primes)
- {
- $i != $divisor && $i % $divisor == 0
- and $rel_prime = 0;
- }
-
- if ($rel_prime)
- {
- #warn $i, ' ', $i - $prev, "\n";
- push @increments, $i - $prev;
- $prev = $i;
-
- $product + 1 < $i
- and last;
- }
- }
-
- print join (",\n", @increments), "\n";
-
- exit 0;
-}
--- /dev/null
+#!/bin/sh
+# Test the factor rewrite.
+# Expect to be invoked via a file whose basename matches
+# /^(\d+)\-(\d+)\-([\da-f]{40})\.sh$/
+# The test is to run this command
+# seq $1 $2 | factor | shasum -c --status <(echo $3 -)
+# I.e., to ensure that the factorizations of integers $1..$2
+# match what we expect.
+
+# Copyright (C) 2012 Free Software Foundation, Inc.
+
+. "${srcdir=.}/tests/init.sh"; path_prepend_ ./src
+
+# Don't run these tests by default.
+very_expensive_
+
+print_ver_ factor seq
+
+# Remove the ".sh" suffix:
+t=${ME_%.sh}
+
+# Make IFS include "-", so that a simple "set" will separate the args:
+IFS=-$IFS
+set $t
+echo "$3 -" > exp
+
+f=1
+seq $1 $2 | factor | shasum -c --status exp && f=0
+
+Exit $f
## along with this program. If not, see <http://www.gnu.org/licenses/>.
# Indirections required so that we'll still be able to know the
-# complete list of our tests even if the user override TESTS from the
-# command line (which he's allowed to do by the test harness API).
-TESTS = $(all_tests)
+# complete list of our tests even if the user overrides TESTS
+# from the command line (as permitted by the test harness API).
+TESTS = $(all_tests) $(factor_tests)
root_tests = $(all_root_tests)
EXTRA_DIST += $(all_tests)
VERBOSE = yes
EXTRA_DIST += \
+ init.cfg \
tests/Coreutils.pm \
tests/CuSkip.pm \
tests/CuTmpdir.pm \
tests/d_type-check \
tests/envvar-check \
+ tests/factor/run.sh \
tests/filefrag-extent-compare \
tests/fiemap-capable \
- init.cfg \
tests/init.sh \
tests/lang-default \
tests/no-perl \
tests/touch/trailing-slash.sh \
$(all_root_tests)
+# prefix of 2^64
+p = 184467440737
+# prefix of 2^96
+q = 79228162514264337593543
+
+# Each of these numbers has a Pollard rho factor larger than 2^64,
+# and thus exercises some hard-to-reach code in factor.c.
+t1 = 170141183460469225450570946617781744489
+t2 = 170141183460469229545748130981302223887
+# Factors of the above:
+# t1: 9223372036854775421 18446744073709551709
+# t2: 9223372036854775643 18446744073709551709
+
+# Each tests is a triple: lo, hi, sha1 of result.
+# The test script, run.sh, runs seq lo hi|factor|sha1sum
+# and verifies that the actual and expected checksums are the same.
+tf = tests/factor
+factor_tests = \
+ $(tf)/0-10000000-a451244522b1b662c86cb3cbb55aee3e085a61a0.sh \
+ $(tf)/10000000-20000000-c792a2e02f1c8536b5121f624b04039d20187016.sh \
+ $(tf)/20000000-30000000-8115e8dff97d1674134ec054598d939a2a5f6113.sh \
+ $(tf)/30000000-40000000-fe7b832c8e0ed55035152c0f9ebd59de73224a60.sh \
+ $(tf)/40000000-50000000-b8786d66c432e48bc5b342ee3c6752b7f096f206.sh \
+ $(tf)/50000000-60000000-a74fe518c5f79873c2b9016745b88b42c8fd3ede.sh \
+ $(tf)/60000000-70000000-689bc70d681791e5d1b8ac1316a05d0c4473d6db.sh \
+ $(tf)/70000000-80000000-d370808f2ab8c865f64c2ff909c5722db5b7d58d.sh \
+ $(tf)/80000000-90000000-7978aa66bf2bdb446398336ea6f02605e9a77581.sh \
+ $(tf)/$(t1)-$(t1)-4622287c5f040cdb7b3bbe4d19d29a71ab277827.sh \
+ $(tf)/$(t2)-$(t2)-dea308253708b57afad357e8c0d2a111460ef50e.sh \
+ $(tf)/$(p)08551616-$(p)08651615-66c57cd58f4fb572df7f088d17e4f4c1d4f01bb1.sh \
+ $(tf)/$(p)08651616-$(p)08751615-729228e693b1a568ecc85b199927424c7d16d410.sh \
+ $(tf)/$(p)08751616-$(p)08851615-5a0c985017c2d285e4698f836f5a059e0b684563.sh \
+ $(tf)/$(p)08851616-$(p)08951615-0482295c514e371c98ce9fd335deed0c9c44a4f4.sh \
+ $(tf)/$(p)08951616-$(p)09051615-9c0e1105ac7c45e27e7bbeb5e213f530d2ad1a71.sh \
+ $(tf)/$(p)09051616-$(p)09151615-604366d2b1d75371d0679e6a68962d66336cd383.sh \
+ $(tf)/$(p)09151616-$(p)09251615-9192d2bdee930135b28d7160e6d395a7027871da.sh \
+ $(tf)/$(p)09251616-$(p)09351615-bcf56ae55d20d700690cff4d3327b78f83fc01bf.sh \
+ $(tf)/$(p)09351616-$(p)09451615-16b106398749e5f24d278ba7c58229ae43f650ac.sh \
+ $(tf)/$(p)09451616-$(p)09551615-ad2c6ed63525f8e7c83c4c416e7715fa1bebc54c.sh \
+ $(tf)/$(p)09551616-$(p)09651615-2b6f9c11742d9de045515a6627c27a042c49f8ba.sh \
+ $(tf)/$(p)09651616-$(p)09751615-54851acd51c4819beb666e26bc0100dc9adbc310.sh \
+ $(tf)/$(p)09751616-$(p)09851615-6939c2a7afd2d81f45f818a159b7c5226f83a50b.sh \
+ $(tf)/$(p)09851616-$(p)09951615-0f2c8bc011d2a45e2afa01459391e68873363c6c.sh \
+ $(tf)/$(p)09951616-$(p)10051615-630dc2ad72f4c222bad1405e6c5bea590f92a98c.sh \
+ $(tf)/$(q)940336-$(q)942335-63cbd6313d78247b04d63bbbac50cb8f8d33ff71.sh \
+ $(tf)/$(q)942336-$(q)944335-0d03d63653767173182491b86fa18f8f680bb036.sh \
+ $(tf)/$(q)944336-$(q)946335-ca43bd38cd9f97cc5bb63613cb19643578640f0b.sh \
+ $(tf)/$(q)946336-$(q)948335-86d59545a0c13567fa96811821ea5cde950611b1.sh \
+ $(tf)/$(q)948336-$(q)950335-c3740e702fa9c97e6cf00150860e0b936a141a6b.sh \
+ $(tf)/$(q)950336-$(q)952335-551c3c4c4640d86fda311b5c3006dac45505c0ce.sh \
+ $(tf)/$(q)952336-$(q)954335-b1b0b00463c2f853d70ef9c4f7a96de5cb614156.sh \
+ $(tf)/$(q)954336-$(q)956335-8938a484a9ef6bb16478091d294fcde9f8ecea69.sh \
+ $(tf)/$(q)956336-$(q)958335-d1ae6bc712d994f35edf55c785d71ddf31f16535.sh \
+ $(tf)/$(q)958336-$(q)960335-2374919a89196e1fce93adfe779cb4664556d4b6.sh \
+ $(tf)/$(q)960336-$(q)962335-569e4363e8d9e8830a187d9ab27365eef08abde1.sh
+
+$(factor_tests): tests/factor/run.sh
+ $(AM_V_GEN)$(MKDIR_P) $(tf)
+ $(AM_V_at)ln -f $(srcdir)/tests/factor/run.sh $@
+
+CLEANFILES += $(factor_tests)
+
pr_data = \
tests/pr/0F \
tests/pr/0FF \
projects / thirdparty / coreutils.git / commitdiff
