/* Copyright (C) 1997, 1998 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Geoffrey Keating <Geoff.Keating@anu.edu.au>, 1997. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Library General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. The GNU C Library 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 Library General Public License for more details. You should have received a copy of the GNU Library General Public License along with the GNU C Library; see the file COPYING.LIB. If not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ #include <stdio.h> #include <math.h> #include <stdlib/gmp.h> #include <string.h> #include <limits.h> #include <assert.h> #define PRINT_ERRORS 0 #define TOL 80 #define N2 17 #define FRAC (32*4) #define mpbpl (CHAR_BIT * sizeof (mp_limb_t)) #define SZ (FRAC / mpbpl + 1) typedef mp_limb_t mp1[SZ], mp2[SZ * 2]; /* This string has 101 hex digits. */ static const char exp1[102] = "2" /* point */ "b7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a7" "84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07"; static const char hexdig[] = "0123456789abcdef"; void print_mpn_hex (const mp_limb_t *x, unsigned size) { char value[size + 1]; unsigned i; const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size; memset (value, '0', size); for (i = 0; i < final ; i++) value[size - 1 - i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf]; value[size] = '\0'; fputs (value, stdout); } void exp_mpn (mp1 ex, mp1 x) { unsigned n; mp1 xp; mp2 tmp; mp_limb_t chk, round; mp1 tol; memset (xp, 0, sizeof (mp1)); memset (ex, 0, sizeof (mp1)); xp[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl; memset (tol,0, sizeof (mp1)); tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)1 << (FRAC - TOL) % mpbpl; n = 0; do { /* Calculate sum(x^n/n!) until the next term is sufficiently small. */ mpn_mul_n (tmp, xp, x, SZ); assert (tmp[SZ * 2 - 1] == 0); if (n > 0) round = mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n); chk = mpn_add_n (ex, ex, xp, SZ); assert (chk == 0); n++; assert (n < 80); /* Catch too-high TOL. */ } while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0); } static int mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE) { int i, j; for (i = SIZE - 1; i > 0; i--) if (SRC_PTR[i] != 0) break; for (j = mpbpl - 1; j >= 0; j--) if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0) break; return i * mpbpl + j; } int main (void) { mp1 ex, x, xt, e2, e3; int i; int errors = 0; int failures = 0; mp1 maxerror; int maxerror_s = 0; const double sf = pow (2, mpbpl); /* assert (mpbpl == mp_bits_per_limb); */ assert (FRAC / mpbpl * mpbpl == FRAC); memset (maxerror, 0, sizeof (mp1)); memset (xt, 0, sizeof (mp1)); xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl; for (i = 0; i < 1 << N2; i++) { int e2s, e3s, j; double de2; mpn_mul_1 (x,xt,SZ,i); exp_mpn (ex, x); de2 = exp (i / (double) (1 << N2)); for (j = SZ-1; j >= 0; j--) { e2[j] = (mp_limb_t) de2; de2 = (de2 - e2[j]) * sf; } if (mpn_cmp (ex,e2,SZ) >= 0) mpn_sub_n (e3,ex,e2,SZ); else mpn_sub_n (e3,e2,ex,SZ); e2s = mpn_bitsize (e2,SZ); e3s = mpn_bitsize (e3,SZ); if (e3s >= 0 && e2s - e3s < 54) { #if PRINT_ERRORS printf ("%06x ", i * (0x100000 / (1 << N2))); print_mpn_hex (ex, (FRAC / 4) + 1); fputs ("\n ",stdout); print_mpn_hex (e2, (FRAC / 4) + 1); printf ("\n %c ", e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P'); print_mpn_hex (e3, (FRAC / 4) + 1); putchar ('\n'); #endif errors += (e2s - e3s == 53); failures += (e2s - e3s < 53); } if (e3s >= maxerror_s && mpn_cmp (e3, maxerror, SZ) > 0) { memcpy (maxerror, e3, sizeof (mp1)); maxerror_s = e3s; } } /* Check exp_mpn against precomputed value of exp(1). */ memset (x, '\0', sizeof (mp1)); x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl; exp_mpn (ex, x); memset (e2, '\0', sizeof (mp1)); for (i = -1; i < 100 && i < FRAC / 4; i++) e2[(FRAC - i * 4 - 4) / mpbpl] |= ((strchr (hexdig, exp1[i + 1]) - hexdig) << (FRAC - i * 4 - 4) % mpbpl); if (mpn_cmp (ex, e2, SZ) >= 0) mpn_sub_n (e3, ex, e2, SZ); else mpn_sub_n (e3, e2, ex, SZ); printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors, errors * 100.0 / (double) (1 << N2)); fputs ("maximum error: ", stdout); print_mpn_hex (maxerror, (FRAC / 4) + 1); fputs ("\nerror in exp(1): ", stdout); print_mpn_hex (e3, (FRAC / 4) + 1); putchar ('\n'); return failures == 0 ? 0 : 1; }