241 lines
6.0 KiB
C
241 lines
6.0 KiB
C
/* Copyright (C) 1997, 1998, 2000 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, write to the Free
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Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
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02111-1307 USA. */
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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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/* This string has 101 hex digits. */
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static const char exp1[102] = "2" /* point */
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"b7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a7"
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"84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07";
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static const char exp_m1[102] = "0" /* point */
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"5e2d58d8b3bcdf1abadec7829054f90dda9805aab56c773330"
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"24b9d0a507daedb16400bf472b4215b8245b669d90d27a5aea";
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static const char hexdig[] = "0123456789abcdef";
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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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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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static void
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read_mpn_hex(mp_limb_t *x, const char *str)
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{
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int i;
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memset (x, 0, sizeof (mp1));
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for (i = -1; i < 100 && i < FRAC / 4; ++i)
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x[(FRAC - i * 4 - 4) / mpbpl] |= ((strchr (hexdig, str[i + 1]) - hexdig)
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<< (FRAC - i * 4 - 4) % mpbpl);
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}
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static mp_limb_t *get_log2(void) __attribute__((const));
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static mp_limb_t *
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get_log2(void)
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{
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static mp1 log2_m;
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static int log2_m_inited = 0;
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static const char log2[102] = "0" /* point */
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"b17217f7d1cf79abc9e3b39803f2f6af40f343267298b62d8a"
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"0d175b8baafa2be7b876206debac98559552fb4afa1b10ed2e";
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if (!log2_m_inited)
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{
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read_mpn_hex (log2_m, log2);
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log2_m_inited = 1;
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}
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return log2_m;
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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, round;
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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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round = 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, get_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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int
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main (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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read_mpn_hex (e2, exp1);
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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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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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