234 lines
5.9 KiB
C
234 lines
5.9 KiB
C
/* Copyright (C) 1997-2015 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Geoffrey Keating <Geoff.Keating@anu.edu.au>, 1997.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include <stdio.h>
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#include <math.h>
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#include <gmp.h>
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#include <string.h>
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#include <limits.h>
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#include <assert.h>
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#include <stdlib.h>
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#define PRINT_ERRORS 0
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#define TOL 80
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#define N2 18
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#define FRAC (32*4)
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#define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
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#define SZ (FRAC / mpbpl + 1)
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typedef mp_limb_t mp1[SZ], mp2[SZ * 2];
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#if BITS_PER_MP_LIMB == 64
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# define LIMB64(L, H) 0x ## H ## L
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#elif BITS_PER_MP_LIMB == 32
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# define LIMB64(L, H) 0x ## L, 0x ## H
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#else
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# error
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#endif
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/* Once upon a time these constants were generated to 400 bits.
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We only need FRAC bits (128) at present, but we retain 384 bits
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in the text Just In Case. */
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#define CONSTSZ(INT, F1, F2, F3, F4, F5, F6, F7, F8, F9, Fa, Fb, Fc) \
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LIMB64(F4, F3), LIMB64(F2, F1), INT
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static const mp1 mp_exp1 = {
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CONSTSZ (2, b7e15162, 8aed2a6a, bf715880, 9cf4f3c7, 62e7160f, 38b4da56,
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a784d904, 5190cfef, 324e7738, 926cfbe5, f4bf8d8d, 8c31d763)
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};
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static const mp1 mp_exp_m1 = {
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CONSTSZ (0, 5e2d58d8, b3bcdf1a, badec782, 9054f90d, da9805aa, b56c7733,
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3024b9d0, a507daed, b16400bf, 472b4215, b8245b66, 9d90d27a)
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};
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static const mp1 mp_log2 = {
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CONSTSZ (0, b17217f7, d1cf79ab, c9e3b398, 03f2f6af, 40f34326, 7298b62d,
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8a0d175b, 8baafa2b, e7b87620, 6debac98, 559552fb, 4afa1b10)
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};
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static void
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print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base)
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{
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static const char hexdig[16] = "0123456789abcdef";
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unsigned int i;
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mp1 tx;
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memcpy (tx, x, sizeof (mp1));
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if (base == 16)
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fputs ("0x", stdout);
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assert (x[SZ-1] < base);
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fputc (hexdig[x[SZ - 1]], stdout);
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fputc ('.', stdout);
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for (i = 0; i < dp; i++)
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{
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tx[SZ - 1] = 0;
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mpn_mul_1 (tx, tx, SZ, base);
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assert (tx[SZ - 1] < base);
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fputc (hexdig[tx[SZ - 1]], stdout);
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}
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}
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/* Compute e^x. */
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static void
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exp_mpn (mp1 ex, mp1 x)
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{
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unsigned int n;
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mp1 xp;
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mp2 tmp;
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mp_limb_t chk;
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mp1 tol;
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memset (xp, 0, sizeof (mp1));
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memset (ex, 0, sizeof (mp1));
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xp[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
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memset (tol, 0, sizeof (mp1));
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tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)1 << (FRAC - TOL) % mpbpl;
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n = 0;
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do
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{
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/* Calculate sum(x^n/n!) until the next term is sufficiently small. */
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mpn_mul_n (tmp, xp, x, SZ);
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assert(tmp[SZ * 2 - 1] == 0);
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if (n > 0)
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mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
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chk = mpn_add_n (ex, ex, xp, SZ);
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assert (chk == 0);
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++n;
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assert (n < 80); /* Catch too-high TOL. */
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}
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while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0);
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}
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/* Calculate 2^x. */
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static void
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exp2_mpn (mp1 ex, mp1 x)
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{
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mp2 tmp;
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mpn_mul_n (tmp, x, mp_log2, SZ);
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assert(tmp[SZ * 2 - 1] == 0);
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exp_mpn (ex, tmp + FRAC / mpbpl);
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}
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static int
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mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE)
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{
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int i, j;
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for (i = SIZE - 1; i > 0; --i)
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if (SRC_PTR[i] != 0)
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break;
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for (j = mpbpl - 1; j >= 0; --j)
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if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
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break;
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return i * mpbpl + j;
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}
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static int
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do_test (void)
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{
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mp1 ex, x, xt, e2, e3;
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int i;
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int errors = 0;
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int failures = 0;
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mp1 maxerror;
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int maxerror_s = 0;
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const double sf = pow (2, mpbpl);
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/* assert(mpbpl == mp_bits_per_limb); */
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assert(FRAC / mpbpl * mpbpl == FRAC);
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memset (maxerror, 0, sizeof (mp1));
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memset (xt, 0, sizeof (mp1));
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xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
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for (i = 0; i < (1 << N2); ++i)
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{
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int e2s, e3s, j;
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double de2;
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mpn_mul_1 (x, xt, SZ, i);
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exp2_mpn (ex, x);
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de2 = exp2 (i / (double) (1 << N2));
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for (j = SZ - 1; j >= 0; --j)
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{
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e2[j] = (mp_limb_t) de2;
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de2 = (de2 - e2[j]) * sf;
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}
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if (mpn_cmp (ex, e2, SZ) >= 0)
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mpn_sub_n (e3, ex, e2, SZ);
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else
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mpn_sub_n (e3, e2, ex, SZ);
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e2s = mpn_bitsize (e2, SZ);
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e3s = mpn_bitsize (e3, SZ);
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if (e3s >= 0 && e2s - e3s < 54)
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{
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#if PRINT_ERRORS
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printf ("%06x ", i * (0x100000 / (1 << N2)));
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print_mpn_fp (ex, (FRAC / 4) + 1, 16);
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putchar ('\n');
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fputs (" ",stdout);
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print_mpn_fp (e2, (FRAC / 4) + 1, 16);
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putchar ('\n');
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printf (" %c ",
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e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
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print_mpn_fp (e3, (FRAC / 4) + 1, 16);
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putchar ('\n');
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#endif
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errors += (e2s - e3s == 53);
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failures += (e2s - e3s < 53);
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}
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if (e3s >= maxerror_s
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&& mpn_cmp (e3, maxerror, SZ) > 0)
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{
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memcpy (maxerror, e3, sizeof (mp1));
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maxerror_s = e3s;
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}
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}
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/* Check exp_mpn against precomputed value of exp(1). */
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memset (x, 0, sizeof (mp1));
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x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
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exp_mpn (ex, x);
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if (mpn_cmp (ex, mp_exp1, SZ) >= 0)
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mpn_sub_n (e3, ex, mp_exp1, SZ);
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else
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mpn_sub_n (e3, mp_exp1, ex, SZ);
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printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
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errors * 100.0 / (double) (1 << N2));
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fputs ("maximum error: ", stdout);
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print_mpn_fp (maxerror, (FRAC / 4) + 1, 16);
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putchar ('\n');
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fputs ("error in exp(1): ", stdout);
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print_mpn_fp (e3, (FRAC / 4) + 1, 16);
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putchar ('\n');
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return failures == 0 ? 0 : 1;
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}
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#define TIMEOUT 300
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#define TEST_FUNCTION do_test ()
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#include "../test-skeleton.c"
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