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glibc/math/atest-sincos.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 N 0 | |
#define N2 20 | |
#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]; | |
/* These strings have exactly 100 hex digits in them. */ | |
static const char sin1[101] = | |
"d76aa47848677020c6e9e909c50f3c3289e511132f518b4def" | |
"b6ca5fd6c649bdfb0bd9ff1edcd4577655b5826a3d3b50c264"; | |
static const char cos1[101] = | |
"8a51407da8345c91c2466d976871bd29a2373a894f96c3b7f2" | |
"300240b760e6fa96a94430a52d0e9e43f3450e3b8ff99bc934"; | |
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 | |
sincosx_mpn (mp1 si, mp1 co, mp1 xx, mp1 ix) | |
{ | |
int i; | |
mp2 s[4], c[4]; | |
mp1 tmp, x; | |
if (ix == NULL) | |
{ | |
memset (si, 0, sizeof (mp1)); | |
memset (co, 0, sizeof (mp1)); | |
co[SZ-1] = 1; | |
memcpy (x, xx, sizeof (mp1)); | |
} | |
else | |
mpn_sub_n (x, xx, ix, SZ); | |
for (i = 0; i < 1 << N; i++) | |
{ | |
#define add_shift_mulh(d,x,s1,s2,sh,n) \ | |
do { \ | |
if (s2 != NULL) { \ | |
if (sh > 0) { \ | |
assert (sh < mpbpl); \ | |
mpn_lshift (tmp, s1, SZ, sh); \ | |
if (n) \ | |
mpn_sub_n (tmp,tmp,s2+FRAC/mpbpl,SZ); \ | |
else \ | |
mpn_add_n (tmp,tmp,s2+FRAC/mpbpl,SZ); \ | |
} else { \ | |
if (n) \ | |
mpn_sub_n (tmp,s1,s2+FRAC/mpbpl,SZ); \ | |
else \ | |
mpn_add_n (tmp,s1,s2+FRAC/mpbpl,SZ); \ | |
} \ | |
mpn_mul_n(d,tmp,x,SZ); \ | |
} else \ | |
mpn_mul_n(d,s1,x,SZ); \ | |
assert(N+sh < mpbpl); \ | |
if (N+sh > 0) mpn_rshift(d,d,2*SZ,N+sh); \ | |
} while(0) | |
#define summ(d,ss,s,n) \ | |
do { \ | |
mpn_add_n(tmp,s[1]+FRAC/mpbpl,s[2]+FRAC/mpbpl,SZ); \ | |
mpn_lshift(tmp,tmp,SZ,1); \ | |
mpn_add_n(tmp,tmp,s[0]+FRAC/mpbpl,SZ); \ | |
mpn_add_n(tmp,tmp,s[3]+FRAC/mpbpl,SZ); \ | |
mpn_divmod_1(tmp,tmp,SZ,6); \ | |
if (n) \ | |
mpn_sub_n (d,ss,tmp,SZ); \ | |
else \ | |
mpn_add_n (d,ss,tmp,SZ); \ | |
} while (0) | |
add_shift_mulh (s[0], x, co, NULL, 0, 0); /* s0 = h * c; */ | |
add_shift_mulh (c[0], x, si, NULL, 0, 0); /* c0 = h * s; */ | |
add_shift_mulh (s[1], x, co, c[0], 1, 1); /* s1 = h * (c - c0/2); */ | |
add_shift_mulh (c[1], x, si, s[0], 1, 0); /* c1 = h * (s + s0/2); */ | |
add_shift_mulh (s[2], x, co, c[1], 1, 1); /* s2 = h * (c - c1/2); */ | |
add_shift_mulh (c[2], x, si, s[1], 1, 0); /* c2 = h * (s + s1/2); */ | |
add_shift_mulh (s[3], x, co, c[2], 0, 1); /* s3 = h * (c - c2); */ | |
add_shift_mulh (c[3], x, si, s[2], 0, 0); /* c3 = h * (s + s2); */ | |
summ (si, si, s, 0); /* s = s + (s0+2*s1+2*s2+s3)/6; */ | |
summ (co, co, c, 1); /* c = c - (c0+2*c1+2*c2+c3)/6; */ | |
} | |
#undef add_shift_mulh | |
#undef summ | |
} | |
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 si, co, x, ox, xt, s2, c2, s3, c3; | |
int i; | |
int sin_errors = 0, cos_errors = 0; | |
int sin_failures = 0, cos_failures = 0; | |
mp1 sin_maxerror, cos_maxerror; | |
int sin_maxerror_s = 0, cos_maxerror_s = 0; | |
const double sf = pow (2, mpbpl); | |
/* assert(mpbpl == mp_bits_per_limb); */ | |
assert(FRAC / mpbpl * mpbpl == FRAC); | |
memset (sin_maxerror, 0, sizeof (mp1)); | |
memset (cos_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 s2s, s3s, c2s, c3s, j; | |
double ds2,dc2; | |
mpn_mul_1 (x, xt, SZ, i); | |
sincosx_mpn (si, co, x, i == 0 ? NULL : ox); | |
memcpy (ox, x, sizeof (mp1)); | |
ds2 = sin (i / (double) (1 << N2)); | |
dc2 = cos (i / (double) (1 << N2)); | |
for (j = SZ-1; j >= 0; j--) | |
{ | |
s2[j] = (mp_limb_t) ds2; | |
ds2 = (ds2 - s2[j]) * sf; | |
c2[j] = (mp_limb_t) dc2; | |
dc2 = (dc2 - c2[j]) * sf; | |
} | |
if (mpn_cmp (si, s2, SZ) >= 0) | |
mpn_sub_n (s3, si, s2, SZ); | |
else | |
mpn_sub_n (s3, s2, si, SZ); | |
if (mpn_cmp (co, c2, SZ) >= 0) | |
mpn_sub_n (c3, co, c2, SZ); | |
else | |
mpn_sub_n (c3, c2, co, SZ); | |
s2s = mpn_bitsize (s2, SZ); | |
s3s = mpn_bitsize (s3, SZ); | |
c2s = mpn_bitsize (c2, SZ); | |
c3s = mpn_bitsize (c3, SZ); | |
if ((s3s >= 0 && s2s - s3s < 54) | |
|| (c3s >= 0 && c2s - c3s < 54) | |
|| 0) | |
{ | |
#if PRINT_ERRORS | |
printf ("%06x ", i * (0x100000 / (1 << N2))); | |
print_mpn_hex(si, (FRAC / 4) + 1); | |
putchar (' '); | |
print_mpn_hex (co, (FRAC / 4) + 1); | |
putchar ('\n'); | |
fputs (" ", stdout); | |
print_mpn_hex (s2, (FRAC / 4) + 1); | |
putchar (' '); | |
print_mpn_hex (c2, (FRAC / 4) + 1); | |
putchar ('\n'); | |
printf (" %c%c ", | |
s3s >= 0 && s2s-s3s < 54 ? s2s - s3s == 53 ? 'e' : 'F' : 'P', | |
c3s >= 0 && c2s-c3s < 54 ? c2s - c3s == 53 ? 'e' : 'F' : 'P'); | |
print_mpn_hex (s3, (FRAC / 4) + 1); | |
putchar (' '); | |
print_mpn_hex (c3, (FRAC / 4) + 1); | |
putchar ('\n'); | |
#endif | |
sin_errors += s2s - s3s == 53; | |
cos_errors += c2s - c3s == 53; | |
sin_failures += s2s - s3s < 53; | |
cos_failures += c2s - c3s < 53; | |
} | |
if (s3s >= sin_maxerror_s | |
&& mpn_cmp (s3, sin_maxerror, SZ) > 0) | |
{ | |
memcpy (sin_maxerror, s3, sizeof (mp1)); | |
sin_maxerror_s = s3s; | |
} | |
if (c3s >= cos_maxerror_s | |
&& mpn_cmp (c3, cos_maxerror, SZ) > 0) | |
{ | |
memcpy (cos_maxerror, c3, sizeof (mp1)); | |
cos_maxerror_s = c3s; | |
} | |
} | |
/* Check Range-Kutta against precomputed values of sin(1) and cos(1). */ | |
memset (x, 0, sizeof (mp1)); | |
x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl; | |
sincosx_mpn (si, co, x, ox); | |
memset (s2, 0, sizeof (mp1)); | |
memset (c2, 0, sizeof (mp1)); | |
for (i = 0; i < 100 && i < FRAC / 4; i++) | |
{ | |
s2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, sin1[i]) | |
- hexdig) | |
<< (FRAC - i * 4 - 4) % mpbpl); | |
c2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, cos1[i]) | |
- hexdig) | |
<< (FRAC - i * 4 - 4) % mpbpl); | |
} | |
if (mpn_cmp (si, s2, SZ) >= 0) | |
mpn_sub_n (s3, si, s2, SZ); | |
else | |
mpn_sub_n (s3, s2, si, SZ); | |
if (mpn_cmp (co, c2, SZ) >= 0) | |
mpn_sub_n (c3, co, c2, SZ); | |
else | |
mpn_sub_n (c3, c2, co, SZ); | |
printf ("sin:\n"); | |
printf ("%d failures; %d errors; error rate %0.2f%%\n", | |
sin_failures, sin_errors, sin_errors * 100.0 / (double) (1 << N2)); | |
fputs ("maximum error: ", stdout); | |
print_mpn_hex (sin_maxerror, (FRAC / 4) + 1); | |
fputs ("\nerror in sin(1): ", stdout); | |
print_mpn_hex (s3, (FRAC / 4) + 1); | |
fputs ("\n\ncos:\n", stdout); | |
printf ("%d failures; %d errors; error rate %0.2f%%\n", | |
cos_failures, cos_errors, cos_errors * 100.0 / (double) (1 << N2)); | |
fputs ("maximum error: ", stdout); | |
print_mpn_hex (cos_maxerror, (FRAC / 4) + 1); | |
fputs ("\nerror in cos(1): ", stdout); | |
print_mpn_hex (c3, (FRAC / 4) + 1); | |
putchar ('\n'); | |
return (sin_failures == 0 && cos_failures == 0) ? 0 : 1; | |
} | |
#define TIMEOUT 600 | |
#define TEST_FUNCTION do_test () | |
#include "../test-skeleton.c" |