/* Copyright (C) 1997-2015 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Geoffrey Keating , 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 . */ #include #include #include #include #include #include #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 10 #define TEST_FUNCTION do_test () #include "../test-skeleton.c"