283 lines
8.5 KiB
C
283 lines
8.5 KiB
C
/* Copyright (C) 1997-2014 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Geoffrey Keating <Geoff.Keating@anu.edu.au>, 1997.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include <stdio.h>
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#include <math.h>
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#include <gmp.h>
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#include <string.h>
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#include <limits.h>
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#include <assert.h>
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#define PRINT_ERRORS 0
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#define N 0
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#define N2 20
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#define FRAC (32 * 4)
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#define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
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#define SZ (FRAC / mpbpl + 1)
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typedef mp_limb_t mp1[SZ], mp2[SZ * 2];
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/* These strings have exactly 100 hex digits in them. */
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static const char sin1[101] =
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"d76aa47848677020c6e9e909c50f3c3289e511132f518b4def"
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"b6ca5fd6c649bdfb0bd9ff1edcd4577655b5826a3d3b50c264";
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static const char cos1[101] =
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"8a51407da8345c91c2466d976871bd29a2373a894f96c3b7f2"
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"300240b760e6fa96a94430a52d0e9e43f3450e3b8ff99bc934";
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static const char hexdig[] = "0123456789abcdef";
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static void
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print_mpn_hex (const mp_limb_t *x, unsigned size)
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{
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char value[size + 1];
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unsigned i;
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const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;
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memset (value, '0', size);
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for (i = 0; i < final ; i++)
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value[size-1-i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];
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value[size] = '\0';
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fputs (value, stdout);
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}
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static void
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sincosx_mpn (mp1 si, mp1 co, mp1 xx, mp1 ix)
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{
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int i;
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mp2 s[4], c[4];
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mp1 tmp, x;
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if (ix == NULL)
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{
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memset (si, 0, sizeof (mp1));
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memset (co, 0, sizeof (mp1));
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co[SZ-1] = 1;
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memcpy (x, xx, sizeof (mp1));
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}
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else
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mpn_sub_n (x, xx, ix, SZ);
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for (i = 0; i < 1 << N; i++)
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{
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#define add_shift_mulh(d,x,s1,s2,sh,n) \
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do { \
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if (s2 != NULL) { \
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if (sh > 0) { \
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assert (sh < mpbpl); \
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mpn_lshift (tmp, s1, SZ, sh); \
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if (n) \
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mpn_sub_n (tmp,tmp,s2+FRAC/mpbpl,SZ); \
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else \
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mpn_add_n (tmp,tmp,s2+FRAC/mpbpl,SZ); \
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} else { \
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if (n) \
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mpn_sub_n (tmp,s1,s2+FRAC/mpbpl,SZ); \
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else \
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mpn_add_n (tmp,s1,s2+FRAC/mpbpl,SZ); \
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} \
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mpn_mul_n(d,tmp,x,SZ); \
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} else \
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mpn_mul_n(d,s1,x,SZ); \
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assert(N+sh < mpbpl); \
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if (N+sh > 0) mpn_rshift(d,d,2*SZ,N+sh); \
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} while(0)
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#define summ(d,ss,s,n) \
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do { \
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mpn_add_n(tmp,s[1]+FRAC/mpbpl,s[2]+FRAC/mpbpl,SZ); \
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mpn_lshift(tmp,tmp,SZ,1); \
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mpn_add_n(tmp,tmp,s[0]+FRAC/mpbpl,SZ); \
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mpn_add_n(tmp,tmp,s[3]+FRAC/mpbpl,SZ); \
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mpn_divmod_1(tmp,tmp,SZ,6); \
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if (n) \
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mpn_sub_n (d,ss,tmp,SZ); \
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else \
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mpn_add_n (d,ss,tmp,SZ); \
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} while (0)
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add_shift_mulh (s[0], x, co, NULL, 0, 0); /* s0 = h * c; */
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add_shift_mulh (c[0], x, si, NULL, 0, 0); /* c0 = h * s; */
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add_shift_mulh (s[1], x, co, c[0], 1, 1); /* s1 = h * (c - c0/2); */
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add_shift_mulh (c[1], x, si, s[0], 1, 0); /* c1 = h * (s + s0/2); */
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add_shift_mulh (s[2], x, co, c[1], 1, 1); /* s2 = h * (c - c1/2); */
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add_shift_mulh (c[2], x, si, s[1], 1, 0); /* c2 = h * (s + s1/2); */
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add_shift_mulh (s[3], x, co, c[2], 0, 1); /* s3 = h * (c - c2); */
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add_shift_mulh (c[3], x, si, s[2], 0, 0); /* c3 = h * (s + s2); */
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summ (si, si, s, 0); /* s = s + (s0+2*s1+2*s2+s3)/6; */
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summ (co, co, c, 1); /* c = c - (c0+2*c1+2*c2+c3)/6; */
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}
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#undef add_shift_mulh
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#undef summ
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}
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static int
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mpn_bitsize (const mp_limb_t *SRC_PTR, mp_size_t SIZE)
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{
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int i, j;
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for (i = SIZE - 1; i > 0; i--)
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if (SRC_PTR[i] != 0)
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break;
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for (j = mpbpl - 1; j >= 0; j--)
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if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
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break;
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return i * mpbpl + j;
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}
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static int
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do_test (void)
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{
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mp1 si, co, x, ox, xt, s2, c2, s3, c3;
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int i;
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int sin_errors = 0, cos_errors = 0;
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int sin_failures = 0, cos_failures = 0;
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mp1 sin_maxerror, cos_maxerror;
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int sin_maxerror_s = 0, cos_maxerror_s = 0;
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const double sf = pow (2, mpbpl);
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/* assert(mpbpl == mp_bits_per_limb); */
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assert(FRAC / mpbpl * mpbpl == FRAC);
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memset (sin_maxerror, 0, sizeof (mp1));
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memset (cos_maxerror, 0, sizeof (mp1));
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memset (xt, 0, sizeof (mp1));
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xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
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for (i = 0; i < 1 << N2; i++)
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{
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int s2s, s3s, c2s, c3s, j;
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double ds2,dc2;
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mpn_mul_1 (x, xt, SZ, i);
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sincosx_mpn (si, co, x, i == 0 ? NULL : ox);
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memcpy (ox, x, sizeof (mp1));
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ds2 = sin (i / (double) (1 << N2));
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dc2 = cos (i / (double) (1 << N2));
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for (j = SZ-1; j >= 0; j--)
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{
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s2[j] = (mp_limb_t) ds2;
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ds2 = (ds2 - s2[j]) * sf;
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c2[j] = (mp_limb_t) dc2;
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dc2 = (dc2 - c2[j]) * sf;
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}
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if (mpn_cmp (si, s2, SZ) >= 0)
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mpn_sub_n (s3, si, s2, SZ);
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else
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mpn_sub_n (s3, s2, si, SZ);
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if (mpn_cmp (co, c2, SZ) >= 0)
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mpn_sub_n (c3, co, c2, SZ);
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else
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mpn_sub_n (c3, c2, co, SZ);
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s2s = mpn_bitsize (s2, SZ);
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s3s = mpn_bitsize (s3, SZ);
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c2s = mpn_bitsize (c2, SZ);
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c3s = mpn_bitsize (c3, SZ);
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if ((s3s >= 0 && s2s - s3s < 54)
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|| (c3s >= 0 && c2s - c3s < 54)
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|| 0)
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{
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#if PRINT_ERRORS
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printf ("%06x ", i * (0x100000 / (1 << N2)));
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print_mpn_hex(si, (FRAC / 4) + 1);
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putchar (' ');
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print_mpn_hex (co, (FRAC / 4) + 1);
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putchar ('\n');
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fputs (" ", stdout);
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print_mpn_hex (s2, (FRAC / 4) + 1);
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putchar (' ');
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print_mpn_hex (c2, (FRAC / 4) + 1);
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putchar ('\n');
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printf (" %c%c ",
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s3s >= 0 && s2s-s3s < 54 ? s2s - s3s == 53 ? 'e' : 'F' : 'P',
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c3s >= 0 && c2s-c3s < 54 ? c2s - c3s == 53 ? 'e' : 'F' : 'P');
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print_mpn_hex (s3, (FRAC / 4) + 1);
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putchar (' ');
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print_mpn_hex (c3, (FRAC / 4) + 1);
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putchar ('\n');
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#endif
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sin_errors += s2s - s3s == 53;
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cos_errors += c2s - c3s == 53;
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sin_failures += s2s - s3s < 53;
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cos_failures += c2s - c3s < 53;
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}
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if (s3s >= sin_maxerror_s
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&& mpn_cmp (s3, sin_maxerror, SZ) > 0)
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{
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memcpy (sin_maxerror, s3, sizeof (mp1));
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sin_maxerror_s = s3s;
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}
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if (c3s >= cos_maxerror_s
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&& mpn_cmp (c3, cos_maxerror, SZ) > 0)
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{
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memcpy (cos_maxerror, c3, sizeof (mp1));
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cos_maxerror_s = c3s;
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}
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}
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/* Check Range-Kutta against precomputed values of sin(1) and cos(1). */
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memset (x, 0, sizeof (mp1));
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x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
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sincosx_mpn (si, co, x, ox);
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memset (s2, 0, sizeof (mp1));
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memset (c2, 0, sizeof (mp1));
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for (i = 0; i < 100 && i < FRAC / 4; i++)
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{
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s2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, sin1[i])
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- hexdig)
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<< (FRAC - i * 4 - 4) % mpbpl);
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c2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, cos1[i])
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- hexdig)
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<< (FRAC - i * 4 - 4) % mpbpl);
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}
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if (mpn_cmp (si, s2, SZ) >= 0)
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mpn_sub_n (s3, si, s2, SZ);
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else
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mpn_sub_n (s3, s2, si, SZ);
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if (mpn_cmp (co, c2, SZ) >= 0)
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mpn_sub_n (c3, co, c2, SZ);
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else
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mpn_sub_n (c3, c2, co, SZ);
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printf ("sin:\n");
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printf ("%d failures; %d errors; error rate %0.2f%%\n",
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sin_failures, sin_errors, sin_errors * 100.0 / (double) (1 << N2));
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fputs ("maximum error: ", stdout);
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print_mpn_hex (sin_maxerror, (FRAC / 4) + 1);
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fputs ("\nerror in sin(1): ", stdout);
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print_mpn_hex (s3, (FRAC / 4) + 1);
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fputs ("\n\ncos:\n", stdout);
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printf ("%d failures; %d errors; error rate %0.2f%%\n",
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cos_failures, cos_errors, cos_errors * 100.0 / (double) (1 << N2));
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fputs ("maximum error: ", stdout);
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print_mpn_hex (cos_maxerror, (FRAC / 4) + 1);
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fputs ("\nerror in cos(1): ", stdout);
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print_mpn_hex (c3, (FRAC / 4) + 1);
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putchar ('\n');
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return (sin_failures == 0 && cos_failures == 0) ? 0 : 1;
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}
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#define TEST_FUNCTION do_test ()
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#include "../test-skeleton.c"
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