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Diffstat (limited to 'REORG.TODO/math/atest-exp2.c')
| -rw-r--r-- | REORG.TODO/math/atest-exp2.c | 228 |
1 files changed, 228 insertions, 0 deletions
diff --git a/REORG.TODO/math/atest-exp2.c b/REORG.TODO/math/atest-exp2.c new file mode 100644 index 0000000000..397e7f881d --- /dev/null +++ b/REORG.TODO/math/atest-exp2.c @@ -0,0 +1,228 @@ +/* Copyright (C) 1997-2017 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, see + <http://www.gnu.org/licenses/>. */ + +#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]; + +#if BITS_PER_MP_LIMB == 64 +# define LIMB64(L, H) 0x ## H ## L +#elif BITS_PER_MP_LIMB == 32 +# define LIMB64(L, H) 0x ## L, 0x ## H +#else +# error +#endif + +/* Once upon a time these constants were generated to 400 bits. + We only need FRAC bits (128) at present, but we retain 384 bits + in the text Just In Case. */ +#define CONSTSZ(INT, F1, F2, F3, F4, F5, F6, F7, F8, F9, Fa, Fb, Fc) \ + LIMB64(F4, F3), LIMB64(F2, F1), INT + +static const mp1 mp_exp1 = { + CONSTSZ (2, b7e15162, 8aed2a6a, bf715880, 9cf4f3c7, 62e7160f, 38b4da56, + a784d904, 5190cfef, 324e7738, 926cfbe5, f4bf8d8d, 8c31d763) +}; + +static const mp1 mp_log2 = { + CONSTSZ (0, b17217f7, d1cf79ab, c9e3b398, 03f2f6af, 40f34326, 7298b62d, + 8a0d175b, 8baafa2b, e7b87620, 6debac98, 559552fb, 4afa1b10) +}; + +static void +print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base) +{ + static const char hexdig[16] = "0123456789abcdef"; + 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); + } +} + +/* Compute e^x. */ +static void +exp_mpn (mp1 ex, mp1 x) +{ + unsigned int n; + mp1 xp; + mp2 tmp; + mp_limb_t chk __attribute__ ((unused)); + 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) + 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, mp_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; +} + +static int +do_test (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); + if (mpn_cmp (ex, mp_exp1, SZ) >= 0) + mpn_sub_n (e3, ex, mp_exp1, SZ); + else + mpn_sub_n (e3, mp_exp1, 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; +} + +#define TIMEOUT 300 +#define TEST_FUNCTION do_test () +#include "../test-skeleton.c" |