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glibc/math/atest-exp.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> | |
#define PRINT_ERRORS 0 | |
#define TOL 80 | |
#define N2 17 | |
#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 hexdig[] = "0123456789abcdef"; | |
static void | |
print_mpn_hex (const mp_limb_t *x, unsigned size) | |
{ | |
char value[size + 1]; | |
unsigned i; | |
const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size; | |
memset (value, '0', size); | |
for (i = 0; i < final ; i++) | |
value[size - 1 - i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf]; | |
value[size] = '\0'; | |
fputs (value, stdout); | |
} | |
static void | |
exp_mpn (mp1 ex, mp1 x) | |
{ | |
unsigned 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); | |
} | |
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); | |
exp_mpn (ex, x); | |
de2 = exp (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_hex (ex, (FRAC / 4) + 1); | |
fputs ("\n ",stdout); | |
print_mpn_hex (e2, (FRAC / 4) + 1); | |
printf ("\n %c ", | |
e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P'); | |
print_mpn_hex (e3, (FRAC / 4) + 1); | |
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); | |
memset (e2, '\0', sizeof (mp1)); | |
for (i = -1; i < 100 && i < FRAC / 4; i++) | |
e2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, | |
exp1[i + 1]) | |
- hexdig) | |
<< (FRAC - i * 4 - 4) % mpbpl); | |
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_hex (maxerror, (FRAC / 4) + 1); | |
fputs ("\nerror in exp(1): ", stdout); | |
print_mpn_hex (e3, (FRAC / 4) + 1); | |
putchar ('\n'); | |
return failures == 0 ? 0 : 1; | |
} | |
#define TIMEOUT 200 | |
#define TEST_FUNCTION do_test () | |
#include "../test-skeleton.c" |