| /* Copyright (C) 1997, 1998, 2000, 2006 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 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 <stdio.h> |
| #include <math.h> |
| #include <gmp.h> |
| #include <string.h> |
| #include <limits.h> |
| #include <assert.h> |
| #include <stdlib.h> |
| |
| #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; |
| } |