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glibc/math/atest-exp2.c
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/* Copyright (C) 1997-2016 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" |