/* Copyright (C) 1997, 1998, 2000, 2006 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Geoffrey Keating , 1997. The GNU C Library 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. 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 Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU C Library; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. */ #include #include #include #include #include #include #include #define PRINT_ERRORS 0 #define TOL 80 #define N2 18 #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 exp_m1[102] = "0" /* point */ "5e2d58d8b3bcdf1abadec7829054f90dda9805aab56c773330" "24b9d0a507daedb16400bf472b4215b8245b669d90d27a5aea"; static const char hexdig[] = "0123456789abcdef"; static void print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base) { unsigned int i; mp1 tx; memcpy (tx, x, sizeof (mp1)); if (base == 16) fputs ("0x", stdout); assert (x[SZ-1] < base); fputc (hexdig[x[SZ - 1]], stdout); fputc ('.', stdout); for (i = 0; i < dp; i++) { tx[SZ - 1] = 0; mpn_mul_1 (tx, tx, SZ, base); assert (tx[SZ - 1] < base); fputc (hexdig[tx[SZ - 1]], stdout); } } static void read_mpn_hex(mp_limb_t *x, const char *str) { int i; memset (x, 0, sizeof (mp1)); for (i = -1; i < 100 && i < FRAC / 4; ++i) x[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, str[i + 1]) - hexdig) << (FRAC - i * 4 - 4) % mpbpl); } static mp_limb_t *get_log2(void) __attribute__((const)); static mp_limb_t * get_log2(void) { static mp1 log2_m; static int log2_m_inited = 0; static const char log2[102] = "0" /* point */ "b17217f7d1cf79abc9e3b39803f2f6af40f343267298b62d8a" "0d175b8baafa2be7b876206debac98559552fb4afa1b10ed2e"; if (!log2_m_inited) { read_mpn_hex (log2_m, log2); log2_m_inited = 1; } return log2_m; } /* Compute e^x. */ static void exp_mpn (mp1 ex, mp1 x) { unsigned int 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); } /* Calculate 2^x. */ static void exp2_mpn (mp1 ex, mp1 x) { mp2 tmp; mpn_mul_n (tmp, x, get_log2 (), SZ); assert(tmp[SZ * 2 - 1] == 0); exp_mpn (ex, tmp + FRAC / mpbpl); } 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); exp2_mpn (ex, x); de2 = exp2 (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_fp (ex, (FRAC / 4) + 1, 16); putchar ('\n'); fputs (" ",stdout); print_mpn_fp (e2, (FRAC / 4) + 1, 16); putchar ('\n'); printf (" %c ", e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P'); print_mpn_fp (e3, (FRAC / 4) + 1, 16); 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); read_mpn_hex (e2, exp1); 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_fp (maxerror, (FRAC / 4) + 1, 16); putchar ('\n'); fputs ("error in exp(1): ", stdout); print_mpn_fp (e3, (FRAC / 4) + 1, 16); putchar ('\n'); return failures == 0 ? 0 : 1; }