math/atest-sincos.c

   1 /* Copyright (C) 1997-2023 Free Software Foundation, Inc.
   2    This file is part of the GNU C Library.
   3
   4    The GNU C Library is free software; you can redistribute it and/or
   5    modify it under the terms of the GNU Lesser General Public
   6    License as published by the Free Software Foundation; either
   7    version 2.1 of the License, or (at your option) any later version.
   8
   9    The GNU C Library is distributed in the hope that it will be useful,
  10    but WITHOUT ANY WARRANTY; without even the implied warranty of
  11    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  12    Lesser General Public License for more details.
  13
  14    You should have received a copy of the GNU Lesser General Public
  15    License along with the GNU C Library; if not, see
  16    <https://www.gnu.org/licenses/>.  */
  17
  18 #include <stdio.h>
  19 #include <math.h>
  20 #include <gmp.h>
  21 #include <string.h>
  22 #include <limits.h>
  23 #include <assert.h>
  24
  25 #define PRINT_ERRORS 0
  26
  27 #define N 0
  28 #define N2 20
  29 #define FRAC (32 * 4)
  30
  31 #define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
  32 #define SZ (FRAC / mpbpl + 1)
  33 typedef mp_limb_t mp1[SZ], mp2[SZ * 2];
  34
  35 /* These strings have exactly 100 hex digits in them.  */
  36 static const char sin1[101] =
  37 "d76aa47848677020c6e9e909c50f3c3289e511132f518b4def"
  38 "b6ca5fd6c649bdfb0bd9ff1edcd4577655b5826a3d3b50c264";
  39 static const char cos1[101] =
  40 "8a51407da8345c91c2466d976871bd29a2373a894f96c3b7f2"
  41 "300240b760e6fa96a94430a52d0e9e43f3450e3b8ff99bc934";
  42 static const char hexdig[] = "0123456789abcdef";
  43
  44 static void
  45 print_mpn_hex (const mp_limb_t *x, unsigned size)
  46 {
  47    char value[size + 1];
  48    unsigned i;
  49    const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;
  50
  51    memset (value, '0', size);
  52
  53    for (i = 0; i < final ; i++)
  54      value[size-1-i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];
  55
  56    value[size] = '\0';
  57    fputs (value, stdout);
  58 }
  59
  60 static void
  61 sincosx_mpn (mp1 si, mp1 co, mp1 xx, mp1 ix)
  62 {
  63    int i;
  64    mp2 s[4], c[4];
  65    mp1 tmp, x;
  66
  67    if (ix == NULL)
  68      {
  69        memset (si, 0, sizeof (mp1));
  70        memset (co, 0, sizeof (mp1));
  71        co[SZ-1] = 1;
  72        memcpy (x, xx, sizeof (mp1));
  73      }
  74    else
  75       mpn_sub_n (x, xx, ix, SZ);
  76
  77    for (i = 0; i < 1 << N; i++)
  78      {
  79 #define add_shift_mulh(d,x,s1,s2,sh,n) \
  80       do {                                                                    \
  81          if (s2 != NULL) {                                                    \
  82             if (sh > 0) {                                                     \
  83                assert (sh < mpbpl);                                           \
  84                mpn_lshift (tmp, s1, SZ, sh);                                  \
  85                if (n)                                                         \
  86                  mpn_sub_n (tmp,tmp,s2+FRAC/mpbpl,SZ);                        \
  87                else                                                           \
  88                  mpn_add_n (tmp,tmp,s2+FRAC/mpbpl,SZ);                        \
  89             } else {                                                          \
  90                if (n)                                                         \
  91                  mpn_sub_n (tmp,s1,s2+FRAC/mpbpl,SZ);                         \
  92                else                                                           \
  93                  mpn_add_n (tmp,s1,s2+FRAC/mpbpl,SZ);                         \
  94             }                                                                 \
  95             mpn_mul_n(d,tmp,x,SZ);                                            \
  96          } else                                                               \
  97             mpn_mul_n(d,s1,x,SZ);                                             \
  98          assert(N+sh < mpbpl);                                                \
  99          if (N+sh > 0) mpn_rshift(d,d,2*SZ,N+sh);                             \
 100       } while(0)
 101 #define summ(d,ss,s,n) \
 102       do {                                                                    \
 103          mpn_add_n(tmp,s[1]+FRAC/mpbpl,s[2]+FRAC/mpbpl,SZ);                   \
 104          mpn_lshift(tmp,tmp,SZ,1);                                            \
 105          mpn_add_n(tmp,tmp,s[0]+FRAC/mpbpl,SZ);                               \
 106          mpn_add_n(tmp,tmp,s[3]+FRAC/mpbpl,SZ);                               \
 107          mpn_divmod_1(tmp,tmp,SZ,6);                                          \
 108          if (n)                                                               \
 109            mpn_sub_n (d,ss,tmp,SZ);                                           \
 110          else                                                                 \
 111            mpn_add_n (d,ss,tmp,SZ);                                           \
 112       } while (0)
 113
 114       add_shift_mulh (s[0], x, co, NULL, 0, 0); /* s0 = h * c; */
 115       add_shift_mulh (c[0], x, si, NULL, 0, 0); /* c0 = h * s; */
 116       add_shift_mulh (s[1], x, co, c[0], 1, 1); /* s1 = h * (c - c0/2); */
 117       add_shift_mulh (c[1], x, si, s[0], 1, 0); /* c1 = h * (s + s0/2); */
 118       add_shift_mulh (s[2], x, co, c[1], 1, 1); /* s2 = h * (c - c1/2); */
 119       add_shift_mulh (c[2], x, si, s[1], 1, 0); /* c2 = h * (s + s1/2); */
 120       add_shift_mulh (s[3], x, co, c[2], 0, 1); /* s3 = h * (c - c2); */
 121       add_shift_mulh (c[3], x, si, s[2], 0, 0); /* c3 = h * (s + s2); */
 122       summ (si, si, s, 0);        /* s = s + (s0+2*s1+2*s2+s3)/6; */
 123       summ (co, co, c, 1);        /* c = c - (c0+2*c1+2*c2+c3)/6; */
 124    }
 125 #undef add_shift_mulh
 126 #undef summ
 127 }
 128
 129 static int
 130 mpn_bitsize (const mp_limb_t *SRC_PTR, mp_size_t SIZE)
 131 {
 132    int i, j;
 133    for (i = SIZE - 1; i > 0; i--)
 134      if (SRC_PTR[i] != 0)
 135        break;
 136    for (j = mpbpl - 1; j >= 0; j--)
 137      if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
 138        break;
 139
 140    return i * mpbpl + j;
 141 }
 142
 143 static int
 144 do_test (void)
 145 {
 146   mp1 si, co, x, ox, xt, s2, c2, s3, c3;
 147   int i;
 148   int sin_errors = 0, cos_errors = 0;
 149   int sin_failures = 0, cos_failures = 0;
 150   mp1 sin_maxerror, cos_maxerror;
 151   int sin_maxerror_s = 0, cos_maxerror_s = 0;
 152   const double sf = pow (2, mpbpl);
 153
 154   /* assert(mpbpl == mp_bits_per_limb);  */
 155   assert(FRAC / mpbpl * mpbpl == FRAC);
 156
 157   memset (sin_maxerror, 0, sizeof (mp1));
 158   memset (cos_maxerror, 0, sizeof (mp1));
 159   memset (xt, 0, sizeof (mp1));
 160   xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
 161
 162   for (i = 0; i < 1 << N2; i++)
 163     {
 164       int s2s, s3s, c2s, c3s, j;
 165       double ds2,dc2;
 166
 167       mpn_mul_1 (x, xt, SZ, i);
 168       sincosx_mpn (si, co, x, i == 0 ? NULL : ox);
 169       memcpy (ox, x, sizeof (mp1));
 170       ds2 = sin (i / (double) (1 << N2));
 171       dc2 = cos (i / (double) (1 << N2));
 172       for (j = SZ-1; j >= 0; j--)
 173         {
 174           s2[j] = (mp_limb_t) ds2;
 175           ds2 = (ds2 - s2[j]) * sf;
 176           c2[j] = (mp_limb_t) dc2;
 177           dc2 = (dc2 - c2[j]) * sf;
 178         }
 179       if (mpn_cmp (si, s2, SZ) >= 0)
 180         mpn_sub_n (s3, si, s2, SZ);
 181       else
 182         mpn_sub_n (s3, s2, si, SZ);
 183       if (mpn_cmp (co, c2, SZ) >= 0)
 184         mpn_sub_n (c3, co, c2, SZ);
 185       else
 186         mpn_sub_n (c3, c2, co, SZ);
 187
 188       s2s = mpn_bitsize (s2, SZ);
 189       s3s = mpn_bitsize (s3, SZ);
 190       c2s = mpn_bitsize (c2, SZ);
 191       c3s = mpn_bitsize (c3, SZ);
 192       if ((s3s >= 0 && s2s - s3s < 54)
 193           || (c3s >= 0 && c2s - c3s < 54)
 194           || 0)
 195         {
 196 #if PRINT_ERRORS
 197           printf ("%06x ", i * (0x100000 / (1 << N2)));
 198           print_mpn_hex(si, (FRAC / 4) + 1);
 199           putchar (' ');
 200           print_mpn_hex (co, (FRAC / 4) + 1);
 201           putchar ('\n');
 202           fputs ("       ", stdout);
 203           print_mpn_hex (s2, (FRAC / 4) + 1);
 204           putchar (' ');
 205           print_mpn_hex (c2, (FRAC / 4) + 1);
 206           putchar ('\n');
 207           printf (" %c%c    ",
 208                   s3s >= 0 && s2s-s3s < 54 ? s2s - s3s == 53 ? 'e' : 'F' : 'P',
 209                   c3s >= 0 && c2s-c3s < 54 ? c2s - c3s == 53 ? 'e' : 'F' : 'P');
 210           print_mpn_hex (s3, (FRAC / 4) + 1);
 211           putchar (' ');
 212           print_mpn_hex (c3, (FRAC / 4) + 1);
 213           putchar ('\n');
 214 #endif
 215           sin_errors += s2s - s3s == 53;
 216           cos_errors += c2s - c3s == 53;
 217           sin_failures += s2s - s3s < 53;
 218           cos_failures += c2s - c3s < 53;
 219         }
 220       if (s3s >= sin_maxerror_s
 221           && mpn_cmp (s3, sin_maxerror, SZ) > 0)
 222         {
 223           memcpy (sin_maxerror, s3, sizeof (mp1));
 224           sin_maxerror_s = s3s;
 225         }
 226       if (c3s >= cos_maxerror_s
 227           && mpn_cmp (c3, cos_maxerror, SZ) > 0)
 228         {
 229           memcpy (cos_maxerror, c3, sizeof (mp1));
 230           cos_maxerror_s = c3s;
 231         }
 232     }
 233
 234    /* Check Range-Kutta against precomputed values of sin(1) and cos(1).  */
 235    memset (x, 0, sizeof (mp1));
 236    x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
 237    sincosx_mpn (si, co, x, ox);
 238
 239    memset (s2, 0, sizeof (mp1));
 240    memset (c2, 0, sizeof (mp1));
 241    for (i = 0; i < 100 && i < FRAC / 4; i++)
 242      {
 243        s2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, sin1[i])
 244                                                        - hexdig)
 245                                           << (FRAC - i * 4 - 4) % mpbpl);
 246        c2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, cos1[i])
 247                                                        - hexdig)
 248                                           << (FRAC - i * 4 - 4) % mpbpl);
 249      }
 250
 251    if (mpn_cmp (si, s2, SZ) >= 0)
 252      mpn_sub_n (s3, si, s2, SZ);
 253    else
 254      mpn_sub_n (s3, s2, si, SZ);
 255    if (mpn_cmp (co, c2, SZ) >= 0)
 256       mpn_sub_n (c3, co, c2, SZ);
 257    else
 258      mpn_sub_n (c3, c2, co, SZ);
 259
 260    printf ("sin:\n");
 261    printf ("%d failures; %d errors; error rate %0.2f%%\n",
 262            sin_failures, sin_errors, sin_errors * 100.0 / (double) (1 << N2));
 263    fputs ("maximum error:   ", stdout);
 264    print_mpn_hex (sin_maxerror, (FRAC / 4) + 1);
 265    fputs ("\nerror in sin(1): ", stdout);
 266    print_mpn_hex (s3, (FRAC / 4) + 1);
 267
 268    fputs ("\n\ncos:\n", stdout);
 269    printf ("%d failures; %d errors; error rate %0.2f%%\n",
 270            cos_failures, cos_errors, cos_errors * 100.0 / (double) (1 << N2));
 271    fputs ("maximum error:   ", stdout);
 272    print_mpn_hex (cos_maxerror, (FRAC / 4) + 1);
 273    fputs ("\nerror in cos(1): ", stdout);
 274    print_mpn_hex (c3, (FRAC / 4) + 1);
 275    putchar ('\n');
 276
 277    return (sin_failures == 0 && cos_failures == 0) ? 0 : 1;
 278 }
 279
 280 #define TIMEOUT 600
 281 #define TEST_FUNCTION do_test ()
 282 #include "../test-skeleton.c"