192 lines
5.0 KiB
C
192 lines
5.0 KiB
C
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/* Copyright (C) 1997 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 Library General Public License as
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published by the Free Software Foundation; either version 2 of the
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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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Library General Public License for more details.
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You should have received a copy of the GNU Library General Public
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License along with the GNU C Library; see the file COPYING.LIB. If not,
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write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
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Boston, MA 02111-1307, USA. */
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#include <stdio.h>
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#include <math.h>
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#include <stdlib/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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#define PRINT_ERRORS 0
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#define TOL 80
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#define N2 17
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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 hexdig[] = "0123456789abcdef";
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void
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print_mpn_hex (const mp_limb_t *x, unsigned size)
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{
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char value[size + 1];
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unsigned i;
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const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;
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memset (value, '0', size);
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for (i = 0; i < final ; i++)
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value[size - 1 - i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];
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value[size] = '\0';
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fputs (value, stdout);
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}
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void
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exp_mpn (mp1 ex, mp1 x)
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{
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unsigned 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] = 1 << FRAC % mpbpl;
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memset (tol,0, sizeof (mp1));
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tol[(FRAC - TOL) / mpbpl] = 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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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] & 1 << j) != 0)
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break;
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return i * 32 + 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] = 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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exp_mpn (ex, x);
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de2 = exp (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 > 1 && 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_hex (ex, (FRAC / 4) + 1);
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fputs ("\n ",stdout);
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print_mpn_hex (e2, (FRAC / 4) + 1);
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printf ("\n %c ",
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e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
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print_mpn_hex (e3, (FRAC / 4) + 1);
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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] = 1 << FRAC % mpbpl;
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exp_mpn (ex, x);
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memset (e2, '\0', sizeof (mp1));
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for (i = -1; i < 100 && i < FRAC / 4; i++)
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e2[(FRAC - i * 4 - 4) / mpbpl] |= (strchr (hexdig, exp1[i + 1]) - hexdig
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<< (FRAC - i * 4 - 4) % mpbpl);
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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_hex (maxerror, (FRAC / 4) + 1);
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fputs ("\nerror in exp(1): ", stdout);
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print_mpn_hex (e3, (FRAC / 4) + 1);
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putchar ('\n');
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return failures == 0 ? 0 : 1;
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}
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