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-rw-r--r--math/atest-sincos.c275
1 files changed, 275 insertions, 0 deletions
diff --git a/math/atest-sincos.c b/math/atest-sincos.c
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+/* Copyright (C) 1997 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 Library General Public License as
+ published by the Free Software Foundation; either version 2 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
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public
+ License along with the GNU C Library; see the file COPYING.LIB. If not,
+ write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA. */
+
+#include <stdio.h>
+#include <math.h>
+#include <stdlib/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";
+
+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);
+}
+
+void
+sincosx_mpn (mp1 si, mp1 co, mp1 xx, mp1 ix)
+{
+ int i;
+ mp2 s[4], c[4];
+ mp1 tmp, x;
+ mp_limb_t chk, round;
+
+ 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) \
+ /* d = (n ? -1 : 1) * (s1 + (s2>>sh)) * x / (1>>N); */ \
+ do { \
+ if (s2 != NULL) { \
+ if (sh > 0) { \
+ assert (sh < mpbpl); \
+ mpn_lshift (tmp, s1, SZ, sh); \
+ chk = (n ? mpn_sub_n : mpn_add_n)(tmp,tmp,s2+FRAC/mpbpl,SZ); \
+ } else \
+ chk = (n ? mpn_sub_n : mpn_add_n)(tmp,s1,s2+FRAC/mpbpl,SZ); \
+ /* assert(chk == 0); */ \
+ mpn_mul_n(d,tmp,x,SZ); \
+ } else \
+ mpn_mul_n(d,s1,x,SZ); \
+ /* assert(d[SZ*2-1] == 0); */ \
+ assert(N+sh < mpbpl); \
+ if (N+sh > 0) mpn_rshift(d,d,2*SZ,N+sh); \
+ } while(0)
+#define summ(d,ss,s,n) \
+ /* d = ss +/- (s[0]+2*s[1]+2*s[2]+s[3])/6; */ \
+ do { \
+ chk = mpn_add_n(tmp,s[1]+FRAC/mpbpl,s[2]+FRAC/mpbpl,SZ); \
+ mpn_lshift(tmp,tmp,SZ,1); \
+ chk |= mpn_add_n(tmp,tmp,s[0]+FRAC/mpbpl,SZ); \
+ chk |= mpn_add_n(tmp,tmp,s[3]+FRAC/mpbpl,SZ); \
+ round = mpn_divmod_1(tmp,tmp,SZ,6); \
+ /* chk |= mpn_add_1(tmp,tmp,SZ, (round > 3) ); */ \
+ chk |= (n ? mpn_sub_n : mpn_add_n)(d,ss,tmp,SZ); \
+ /* assert(chk == 0); */ \
+ } 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] & 1 << j) != 0)
+ break;
+
+ return i * 32 + j;
+}
+
+int
+main (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] = 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 > 1 && s2s - s3s < 54
+ || c3s > 1 && 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 ",
+ s2s-s3s < 54 ? s2s - s3s == 53 ? 'e' : 'F' : 'P',
+ 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] = 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] |= (strchr (hexdig, sin1[i]) - hexdig
+ << (FRAC - i * 4 - 4) % mpbpl);
+ c2[(FRAC - i * 4 - 4) / mpbpl] |= (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;
+}
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