| /* 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" |