math/atest-sincos.c

   1 /* Copyright (C) 1997-2013 Free Software Foundation, Inc.
   2    This file is part of the GNU C Library.
   3    Contributed by Geoffrey Keating <Geoff.Keating@anu.edu.au>, 1997.
   4
   5    The GNU C Library is free software; you can redistribute it and/or
   6    modify it under the terms of the GNU Lesser General Public
   7    License as published by the Free Software Foundation; either
   8    version 2.1 of the License, or (at your option) any later version.
   9
  10    The GNU C Library is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13    Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public
  16    License along with the GNU C Library; if not, see
  17    <http://www.gnu.org/licenses/>.  */
  18
  19 #include <stdio.h>
  20 #include <math.h>
  21 #include <gmp.h>
  22 #include <string.h>
  23 #include <limits.h>
  24 #include <assert.h>
  25
  26 #define PRINT_ERRORS 0
  27
  28 #define N 0
  29 #define N2 20
  30 #define FRAC (32 * 4)
  31
  32 #define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
  33 #define SZ (FRAC / mpbpl + 1)
  34 typedef mp_limb_t mp1[SZ], mp2[SZ * 2];
  35
  36 /* These strings have exactly 100 hex digits in them.  */
  37 static const char sin1[101] =
  38 "d76aa47848677020c6e9e909c50f3c3289e511132f518b4def"
  39 "b6ca5fd6c649bdfb0bd9ff1edcd4577655b5826a3d3b50c264";
  40 static const char cos1[101] =
  41 "8a51407da8345c91c2466d976871bd29a2373a894f96c3b7f2"
  42 "300240b760e6fa96a94430a52d0e9e43f3450e3b8ff99bc934";
  43 static const char hexdig[] = "0123456789abcdef";
  44
  45 static void
  46 print_mpn_hex (const mp_limb_t *x, unsigned size)
  47 {
  48    char value[size + 1];
  49    unsigned i;
  50    const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;
  51
  52    memset (value, '0', size);
  53
  54    for (i = 0; i < final ; i++)
  55      value[size-1-i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];
  56
  57    value[size] = '\0';
  58    fputs (value, stdout);
  59 }
  60
  61 static void
  62 sincosx_mpn (mp1 si, mp1 co, mp1 xx, mp1 ix)
  63 {
  64    int i;
  65    mp2 s[4], c[4];
  66    mp1 tmp, x;
  67
  68    if (ix == NULL)
  69      {
  70        memset (si, 0, sizeof (mp1));
  71        memset (co, 0, sizeof (mp1));
  72        co[SZ-1] = 1;
  73        memcpy (x, xx, sizeof (mp1));
  74      }
  75    else
  76       mpn_sub_n (x, xx, ix, SZ);
  77
  78    for (i = 0; i < 1 << N; i++)
  79      {
  80 #define add_shift_mulh(d,x,s1,s2,sh,n) \
  81       do {                                                                    \
  82          if (s2 != NULL) {                                                    \
  83             if (sh > 0) {                                                     \
  84                assert (sh < mpbpl);                                           \
  85                mpn_lshift (tmp, s1, SZ, sh);                                  \
  86                if (n)                                                         \
  87                  mpn_sub_n (tmp,tmp,s2+FRAC/mpbpl,SZ);                        \
  88                else                                                           \
  89                  mpn_add_n (tmp,tmp,s2+FRAC/mpbpl,SZ);                        \
  90             } else {                                                          \
  91                if (n)                                                         \
  92                  mpn_sub_n (tmp,s1,s2+FRAC/mpbpl,SZ);                         \
  93                else                                                           \
  94                  mpn_add_n (tmp,s1,s2+FRAC/mpbpl,SZ);                         \
  95             }                                                                 \
  96             mpn_mul_n(d,tmp,x,SZ);                                            \
  97          } else                                                               \
  98             mpn_mul_n(d,s1,x,SZ);                                             \
  99          assert(N+sh < mpbpl);                                                \
 100          if (N+sh > 0) mpn_rshift(d,d,2*SZ,N+sh);                             \
 101       } while(0)
 102 #define summ(d,ss,s,n) \
 103       do {                                                                    \
 104          mpn_add_n(tmp,s[1]+FRAC/mpbpl,s[2]+FRAC/mpbpl,SZ);                   \
 105          mpn_lshift(tmp,tmp,SZ,1);                                            \
 106          mpn_add_n(tmp,tmp,s[0]+FRAC/mpbpl,SZ);                               \
 107          mpn_add_n(tmp,tmp,s[3]+FRAC/mpbpl,SZ);                               \
 108          mpn_divmod_1(tmp,tmp,SZ,6);                                          \
 109          if (n)                                                               \
 110            mpn_sub_n (d,ss,tmp,SZ);                                           \
 111          else                                                                 \
 112            mpn_add_n (d,ss,tmp,SZ);                                           \
 113       } while (0)
 114
 115       add_shift_mulh (s[0], x, co, NULL, 0, 0); /* s0 = h * c; */
 116       add_shift_mulh (c[0], x, si, NULL, 0, 0); /* c0 = h * s; */
 117       add_shift_mulh (s[1], x, co, c[0], 1, 1); /* s1 = h * (c - c0/2); */
 118       add_shift_mulh (c[1], x, si, s[0], 1, 0); /* c1 = h * (s + s0/2); */
 119       add_shift_mulh (s[2], x, co, c[1], 1, 1); /* s2 = h * (c - c1/2); */
 120       add_shift_mulh (c[2], x, si, s[1], 1, 0); /* c2 = h * (s + s1/2); */
 121       add_shift_mulh (s[3], x, co, c[2], 0, 1); /* s3 = h * (c - c2); */
 122       add_shift_mulh (c[3], x, si, s[2], 0, 0); /* c3 = h * (s + s2); */
 123       summ (si, si, s, 0);        /* s = s + (s0+2*s1+2*s2+s3)/6; */
 124       summ (co, co, c, 1);        /* c = c - (c0+2*c1+2*c2+c3)/6; */
 125    }
 126 #undef add_shift_mulh
 127 #undef summ
 128 }
 129
 130 static int
 131 mpn_bitsize (const mp_limb_t *SRC_PTR, mp_size_t SIZE)
 132 {
 133    int i, j;
 134    for (i = SIZE - 1; i > 0; i--)
 135      if (SRC_PTR[i] != 0)
 136        break;
 137    for (j = mpbpl - 1; j >= 0; j--)
 138      if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
 139        break;
 140
 141    return i * mpbpl + j;
 142 }
 143
 144 int
 145 main (void)
 146 {
 147   mp1 si, co, x, ox, xt, s2, c2, s3, c3;
 148   int i;
 149   int sin_errors = 0, cos_errors = 0;
 150   int sin_failures = 0, cos_failures = 0;
 151   mp1 sin_maxerror, cos_maxerror;
 152   int sin_maxerror_s = 0, cos_maxerror_s = 0;
 153   const double sf = pow (2, mpbpl);
 154
 155   /* assert(mpbpl == mp_bits_per_limb);  */
 156   assert(FRAC / mpbpl * mpbpl == FRAC);
 157
 158   memset (sin_maxerror, 0, sizeof (mp1));
 159   memset (cos_maxerror, 0, sizeof (mp1));
 160   memset (xt, 0, sizeof (mp1));
 161   xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
 162
 163   for (i = 0; i < 1 << N2; i++)
 164     {
 165       int s2s, s3s, c2s, c3s, j;
 166       double ds2,dc2;
 167
 168       mpn_mul_1 (x, xt, SZ, i);
 169       sincosx_mpn (si, co, x, i == 0 ? NULL : ox);
 170       memcpy (ox, x, sizeof (mp1));
 171       ds2 = sin (i / (double) (1 << N2));
 172       dc2 = cos (i / (double) (1 << N2));
 173       for (j = SZ-1; j >= 0; j--)
 174         {
 175           s2[j] = (mp_limb_t) ds2;
 176           ds2 = (ds2 - s2[j]) * sf;
 177           c2[j] = (mp_limb_t) dc2;
 178           dc2 = (dc2 - c2[j]) * sf;
 179         }
 180       if (mpn_cmp (si, s2, SZ) >= 0)
 181         mpn_sub_n (s3, si, s2, SZ);
 182       else
 183         mpn_sub_n (s3, s2, si, SZ);
 184       if (mpn_cmp (co, c2, SZ) >= 0)
 185         mpn_sub_n (c3, co, c2, SZ);
 186       else
 187         mpn_sub_n (c3, c2, co, SZ);
 188
 189       s2s = mpn_bitsize (s2, SZ);
 190       s3s = mpn_bitsize (s3, SZ);
 191       c2s = mpn_bitsize (c2, SZ);
 192       c3s = mpn_bitsize (c3, SZ);
 193       if ((s3s >= 0 && s2s - s3s < 54)
 194           || (c3s >= 0 && c2s - c3s < 54)
 195           || 0)
 196         {
 197 #if PRINT_ERRORS
 198           printf ("%06x ", i * (0x100000 / (1 << N2)));
 199           print_mpn_hex(si, (FRAC / 4) + 1);
 200           putchar (' ');
 201           print_mpn_hex (co, (FRAC / 4) + 1);
 202           putchar ('\n');
 203           fputs ("       ", stdout);
 204           print_mpn_hex (s2, (FRAC / 4) + 1);
 205           putchar (' ');
 206           print_mpn_hex (c2, (FRAC / 4) + 1);
 207           putchar ('\n');
 208           printf (" %c%c    ",
 209                   s3s >= 0 && s2s-s3s < 54 ? s2s - s3s == 53 ? 'e' : 'F' : 'P',
 210                   c3s >= 0 && c2s-c3s < 54 ? c2s - c3s == 53 ? 'e' : 'F' : 'P');
 211           print_mpn_hex (s3, (FRAC / 4) + 1);
 212           putchar (' ');
 213           print_mpn_hex (c3, (FRAC / 4) + 1);
 214           putchar ('\n');
 215 #endif
 216           sin_errors += s2s - s3s == 53;
 217           cos_errors += c2s - c3s == 53;
 218           sin_failures += s2s - s3s < 53;
 219           cos_failures += c2s - c3s < 53;
 220         }
 221       if (s3s >= sin_maxerror_s
 222           && mpn_cmp (s3, sin_maxerror, SZ) > 0)
 223         {
 224           memcpy (sin_maxerror, s3, sizeof (mp1));
 225           sin_maxerror_s = s3s;
 226         }
 227       if (c3s >= cos_maxerror_s
 228           && mpn_cmp (c3, cos_maxerror, SZ) > 0)
 229         {
 230           memcpy (cos_maxerror, c3, sizeof (mp1));
 231           cos_maxerror_s = c3s;
 232         }
 233     }
 234
 235    /* Check Range-Kutta against precomputed values of sin(1) and cos(1).  */
 236    memset (x, 0, sizeof (mp1));
 237    x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
 238    sincosx_mpn (si, co, x, ox);
 239
 240    memset (s2, 0, sizeof (mp1));
 241    memset (c2, 0, sizeof (mp1));
 242    for (i = 0; i < 100 && i < FRAC / 4; i++)
 243      {
 244        s2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, sin1[i])
 245                                                        - hexdig)
 246                                           << (FRAC - i * 4 - 4) % mpbpl);
 247        c2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, cos1[i])
 248                                                        - hexdig)
 249                                           << (FRAC - i * 4 - 4) % mpbpl);
 250      }
 251
 252    if (mpn_cmp (si, s2, SZ) >= 0)
 253      mpn_sub_n (s3, si, s2, SZ);
 254    else
 255      mpn_sub_n (s3, s2, si, SZ);
 256    if (mpn_cmp (co, c2, SZ) >= 0)
 257       mpn_sub_n (c3, co, c2, SZ);
 258    else
 259      mpn_sub_n (c3, c2, co, SZ);
 260
 261    printf ("sin:\n");
 262    printf ("%d failures; %d errors; error rate %0.2f%%\n",
 263            sin_failures, sin_errors, sin_errors * 100.0 / (double) (1 << N2));
 264    fputs ("maximum error:   ", stdout);
 265    print_mpn_hex (sin_maxerror, (FRAC / 4) + 1);
 266    fputs ("\nerror in sin(1): ", stdout);
 267    print_mpn_hex (s3, (FRAC / 4) + 1);
 268
 269    fputs ("\n\ncos:\n", stdout);
 270    printf ("%d failures; %d errors; error rate %0.2f%%\n",
 271            cos_failures, cos_errors, cos_errors * 100.0 / (double) (1 << N2));
 272    fputs ("maximum error:   ", stdout);
 273    print_mpn_hex (cos_maxerror, (FRAC / 4) + 1);
 274    fputs ("\nerror in cos(1): ", stdout);
 275    print_mpn_hex (c3, (FRAC / 4) + 1);
 276    putchar ('\n');
 277
 278    return (sin_failures == 0 && cos_failures == 0) ? 0 : 1;
 279 }