+++ /dev/null
-/* Overridable constants and operations.
- Copyright (C) 2013-2019 Free Software Foundation, Inc.
-
- This program 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 Software Foundation; either version 2.1 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 Lesser General Public License for more details.
-
- You should have received a copy of the GNU Lesser General Public License
- along with this program; if not, see <http://www.gnu.org/licenses/>. */
-
-typedef double mantissa_t;
-typedef double mantissa_store_t;
-
-#define TWOPOW(i) (0x1.0p##i)
-
-#define RADIX TWOPOW (24) /* 2^24 */
-#define CUTTER TWOPOW (76) /* 2^76 */
-#define RADIXI 0x1.0p-24 /* 2^-24 */
-#define TWO52 TWOPOW (52) /* 2^52 */
-
-/* Divide D by RADIX and put the remainder in R. */
-#define DIV_RADIX(d,r) \
- ({ \
- double u = ((d) + CUTTER) - CUTTER; \
- if (u > (d)) \
- u -= RADIX; \
- r = (d) - u; \
- (d) = u * RADIXI; \
- })
-
-/* Put the integer component of a double X in R and retain the fraction in
- X. */
-#define INTEGER_OF(x, r) \
- ({ \
- double u = ((x) + TWO52) - TWO52; \
- if (u > (x)) \
- u -= 1; \
- (r) = u; \
- (x) -= u; \
- })
-
-/* Align IN down to a multiple of F, where F is a power of two. */
-#define ALIGN_DOWN_TO(in, f) \
- ({ \
- double factor = f * TWO52; \
- double u = (in + factor) - factor; \
- if (u > in) \
- u -= f; \
- u; \
- })
+++ /dev/null
-
-/*
- * IBM Accurate Mathematical Library
- * written by International Business Machines Corp.
- * Copyright (C) 2001-2019 Free Software Foundation, Inc.
- *
- * This program 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 Software Foundation; either version 2.1 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 Lesser General Public License for more details.
- *
- * You should have received a copy of the GNU Lesser General Public License
- * along with this program; if not, see <http://www.gnu.org/licenses/>.
- */
-
-/* Define __mul and __sqr and use the rest from generic code. */
-#define NO__MUL
-#define NO__SQR
-
-#include <sysdeps/ieee754/dbl-64/mpa.c>
-
-/* Multiply *X and *Y and store result in *Z. X and Y may overlap but not X
- and Z or Y and Z. For P in [1, 2, 3], the exact result is truncated to P
- digits. In case P > 3 the error is bounded by 1.001 ULP. */
-void
-__mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
-{
- long i, i1, i2, j, k, k2;
- long p2 = p;
- double u, zk, zk2;
-
- /* Is z=0? */
- if (__glibc_unlikely (X[0] * Y[0] == 0))
- {
- Z[0] = 0;
- return;
- }
-
- /* Multiply, add and carry */
- k2 = (p2 < 3) ? p2 + p2 : p2 + 3;
- zk = Z[k2] = 0;
- for (k = k2; k > 1;)
- {
- if (k > p2)
- {
- i1 = k - p2;
- i2 = p2 + 1;
- }
- else
- {
- i1 = 1;
- i2 = k;
- }
-#if 1
- /* Rearrange this inner loop to allow the fmadd instructions to be
- independent and execute in parallel on processors that have
- dual symmetrical FP pipelines. */
- if (i1 < (i2 - 1))
- {
- /* Make sure we have at least 2 iterations. */
- if (((i2 - i1) & 1L) == 1L)
- {
- /* Handle the odd iterations case. */
- zk2 = x->d[i2 - 1] * y->d[i1];
- }
- else
- zk2 = 0.0;
- /* Do two multiply/adds per loop iteration, using independent
- accumulators; zk and zk2. */
- for (i = i1, j = i2 - 1; i < i2 - 1; i += 2, j -= 2)
- {
- zk += x->d[i] * y->d[j];
- zk2 += x->d[i + 1] * y->d[j - 1];
- }
- zk += zk2; /* Final sum. */
- }
- else
- {
- /* Special case when iterations is 1. */
- zk += x->d[i1] * y->d[i1];
- }
-#else
- /* The original code. */
- for (i = i1, j = i2 - 1; i < i2; i++, j--)
- zk += X[i] * Y[j];
-#endif
-
- u = (zk + CUTTER) - CUTTER;
- if (u > zk)
- u -= RADIX;
- Z[k] = zk - u;
- zk = u * RADIXI;
- --k;
- }
- Z[k] = zk;
-
- int e = EX + EY;
- /* Is there a carry beyond the most significant digit? */
- if (Z[1] == 0)
- {
- for (i = 1; i <= p2; i++)
- Z[i] = Z[i + 1];
- e--;
- }
-
- EZ = e;
- Z[0] = X[0] * Y[0];
-}
-
-/* Square *X and store result in *Y. X and Y may not overlap. For P in
- [1, 2, 3], the exact result is truncated to P digits. In case P > 3 the
- error is bounded by 1.001 ULP. This is a faster special case of
- multiplication. */
-void
-__sqr (const mp_no *x, mp_no *y, int p)
-{
- long i, j, k, ip;
- double u, yk;
-
- /* Is z=0? */
- if (__glibc_unlikely (X[0] == 0))
- {
- Y[0] = 0;
- return;
- }
-
- /* We need not iterate through all X's since it's pointless to
- multiply zeroes. */
- for (ip = p; ip > 0; ip--)
- if (X[ip] != 0)
- break;
-
- k = (__glibc_unlikely (p < 3)) ? p + p : p + 3;
-
- while (k > 2 * ip + 1)
- Y[k--] = 0;
-
- yk = 0;
-
- while (k > p)
- {
- double yk2 = 0.0;
- long lim = k / 2;
-
- if (k % 2 == 0)
- {
- yk += X[lim] * X[lim];
- lim--;
- }
-
- /* In __mul, this loop (and the one within the next while loop) run
- between a range to calculate the mantissa as follows:
-
- Z[k] = X[k] * Y[n] + X[k+1] * Y[n-1] ... + X[n-1] * Y[k+1]
- + X[n] * Y[k]
-
- For X == Y, we can get away with summing halfway and doubling the
- result. For cases where the range size is even, the mid-point needs
- to be added separately (above). */
- for (i = k - p, j = p; i <= lim; i++, j--)
- yk2 += X[i] * X[j];
-
- yk += 2.0 * yk2;
-
- u = (yk + CUTTER) - CUTTER;
- if (u > yk)
- u -= RADIX;
- Y[k--] = yk - u;
- yk = u * RADIXI;
- }
-
- while (k > 1)
- {
- double yk2 = 0.0;
- long lim = k / 2;
-
- if (k % 2 == 0)
- {
- yk += X[lim] * X[lim];
- lim--;
- }
-
- /* Likewise for this loop. */
- for (i = 1, j = k - 1; i <= lim; i++, j--)
- yk2 += X[i] * X[j];
-
- yk += 2.0 * yk2;
-
- u = (yk + CUTTER) - CUTTER;
- if (u > yk)
- u -= RADIX;
- Y[k--] = yk - u;
- yk = u * RADIXI;
- }
- Y[k] = yk;
-
- /* Squares are always positive. */
- Y[0] = 1.0;
-
- int e = EX * 2;
- /* Is there a carry beyond the most significant digit? */
- if (__glibc_unlikely (Y[1] == 0))
- {
- for (i = 1; i <= p; i++)
- Y[i] = Y[i + 1];
- e--;
- }
- EY = e;
-}
projects / thirdparty / glibc.git / commitdiff
