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Diffstat (limited to 'math/atest-exp2.c')
| -rw-r--r-- | math/atest-exp2.c | 240 |
1 files changed, 240 insertions, 0 deletions
diff --git a/math/atest-exp2.c b/math/atest-exp2.c new file mode 100644 index 0000000000..95e72aa507 --- /dev/null +++ b/math/atest-exp2.c @@ -0,0 +1,240 @@ +/* Copyright (C) 1997 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 <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"; + +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); + } +} + +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] |= (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. */ +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] = 1 << FRAC % mpbpl; + memset (tol, 0, sizeof (mp1)); + tol[(FRAC - TOL) / mpbpl] = 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. */ +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] & 1 << j) != 0) + break; + + return i * 32 + 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] = 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 > 1 && 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] = 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; +} |