math/atest-sincos.c

   1 /* Copyright (C) 1997, 1998, 2000, 2006 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, write to the Free
  17    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  18    02111-1307 USA.  */
  19
  20 #include <stdio.h>
  21 #include <math.h>
  22 #include <gmp.h>
  23 #include <string.h>
  24 #include <limits.h>
  25 #include <assert.h>
  26
  27 #define PRINT_ERRORS 0
  28
  29 #define N 0
  30 #define N2 20
  31 #define FRAC (32 * 4)
  32
  33 #define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
  34 #define SZ (FRAC / mpbpl + 1)
  35 typedef mp_limb_t mp1[SZ], mp2[SZ * 2];
  36
  37 /* These strings have exactly 100 hex digits in them.  */
  38 static const char sin1[101] =
  39 "d76aa47848677020c6e9e909c50f3c3289e511132f518b4def"
  40 "b6ca5fd6c649bdfb0bd9ff1edcd4577655b5826a3d3b50c264";
  41 static const char cos1[101] =
  42 "8a51407da8345c91c2466d976871bd29a2373a894f96c3b7f2"
  43 "300240b760e6fa96a94430a52d0e9e43f3450e3b8ff99bc934";
  44 static const char hexdig[] = "0123456789abcdef";
  45
  46 static void
  47 print_mpn_hex (const mp_limb_t *x, unsigned size)
  48 {
  49    char value[size + 1];
  50    unsigned i;
  51    const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;
  52
  53    memset (value, '0', size);
  54
  55    for (i = 0; i < final ; i++)
  56      value[size-1-i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];
  57
  58    value[size] = '\0';
  59    fputs (value, stdout);
  60 }
  61
  62 static void
  63 sincosx_mpn (mp1 si, mp1 co, mp1 xx, mp1 ix)
  64 {
  65    int i;
  66    mp2 s[4], c[4];
  67    mp1 tmp, x;
  68    mp_limb_t chk, round;
  69
  70    if (ix == NULL)
  71      {
  72        memset (si, 0, sizeof (mp1));
  73        memset (co, 0, sizeof (mp1));
  74        co[SZ-1] = 1;
  75        memcpy (x, xx, sizeof (mp1));
  76      }
  77    else
  78       mpn_sub_n (x, xx, ix, SZ);
  79
  80    for (i = 0; i < 1 << N; i++)
  81      {
  82 #define add_shift_mulh(d,x,s1,s2,sh,n) \
  83        /* d = (n ? -1 : 1) * (s1 + (s2>>sh)) * x / (1>>N); */                 \
  84       do {                                                                    \
  85          if (s2 != NULL) {                                                    \
  86             if (sh > 0) {                                                     \
  87                assert (sh < mpbpl);                                           \
  88                mpn_lshift (tmp, s1, SZ, sh);                                  \
  89                chk = (n ? mpn_sub_n : mpn_add_n)(tmp,tmp,s2+FRAC/mpbpl,SZ);   \
  90             } else                                                            \
  91                chk = (n ? mpn_sub_n : mpn_add_n)(tmp,s1,s2+FRAC/mpbpl,SZ);    \
  92             /* assert(chk == 0); */                                           \
  93             mpn_mul_n(d,tmp,x,SZ);                                            \
  94          } else                                                               \
  95             mpn_mul_n(d,s1,x,SZ);                                             \
  96          /* assert(d[SZ*2-1] == 0); */                                        \
  97          assert(N+sh < mpbpl);                                                \
  98          if (N+sh > 0) mpn_rshift(d,d,2*SZ,N+sh);                             \
  99       } while(0)
 100 #define summ(d,ss,s,n) \
 101       /* d = ss +/- (s[0]+2*s[1]+2*s[2]+s[3])/6; */                           \
 102       do {                                                                    \
 103          chk = mpn_add_n(tmp,s[1]+FRAC/mpbpl,s[2]+FRAC/mpbpl,SZ);             \
 104          mpn_lshift(tmp,tmp,SZ,1);                                            \
 105          chk |= mpn_add_n(tmp,tmp,s[0]+FRAC/mpbpl,SZ);                        \
 106          chk |= mpn_add_n(tmp,tmp,s[3]+FRAC/mpbpl,SZ);                        \
 107          round = mpn_divmod_1(tmp,tmp,SZ,6);                                  \
 108          /* chk |= mpn_add_1(tmp,tmp,SZ, (round > 3) ); */                    \
 109          chk |= (n ? mpn_sub_n : mpn_add_n)(d,ss,tmp,SZ);                     \
 110          /* assert(chk == 0); */                                              \
 111       } while (0)
 112
 113       add_shift_mulh (s[0], x, co, NULL, 0, 0); /* s0 = h * c; */
 114       add_shift_mulh (c[0], x, si, NULL, 0, 0); /* c0 = h * s; */
 115       add_shift_mulh (s[1], x, co, c[0], 1, 1); /* s1 = h * (c - c0/2); */
 116       add_shift_mulh (c[1], x, si, s[0], 1, 0); /* c1 = h * (s + s0/2); */
 117       add_shift_mulh (s[2], x, co, c[1], 1, 1); /* s2 = h * (c - c1/2); */
 118       add_shift_mulh (c[2], x, si, s[1], 1, 0); /* c2 = h * (s + s1/2); */
 119       add_shift_mulh (s[3], x, co, c[2], 0, 1); /* s3 = h * (c - c2); */
 120       add_shift_mulh (c[3], x, si, s[2], 0, 0); /* c3 = h * (s + s2); */
 121       summ (si, si, s, 0);        /* s = s + (s0+2*s1+2*s2+s3)/6; */
 122       summ (co, co, c, 1);        /* c = c - (c0+2*c1+2*c2+c3)/6; */
 123    }
 124 #undef add_shift_mulh
 125 #undef summ
 126 }
 127
 128 static int
 129 mpn_bitsize (const mp_limb_t *SRC_PTR, mp_size_t SIZE)
 130 {
 131    int i, j;
 132    for (i = SIZE - 1; i > 0; i--)
 133      if (SRC_PTR[i] != 0)
 134        break;
 135    for (j = mpbpl - 1; j >= 0; j--)
 136      if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
 137        break;
 138
 139    return i * mpbpl + j;
 140 }
 141
 142 int
 143 main (void)
 144 {
 145   mp1 si, co, x, ox, xt, s2, c2, s3, c3;
 146   int i;
 147   int sin_errors = 0, cos_errors = 0;
 148   int sin_failures = 0, cos_failures = 0;
 149   mp1 sin_maxerror, cos_maxerror;
 150   int sin_maxerror_s = 0, cos_maxerror_s = 0;
 151   const double sf = pow (2, mpbpl);
 152
 153   /* assert(mpbpl == mp_bits_per_limb);  */
 154   assert(FRAC / mpbpl * mpbpl == FRAC);
 155
 156   memset (sin_maxerror, 0, sizeof (mp1));
 157   memset (cos_maxerror, 0, sizeof (mp1));
 158   memset (xt, 0, sizeof (mp1));
 159   xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
 160
 161   for (i = 0; i < 1 << N2; i++)
 162     {
 163       int s2s, s3s, c2s, c3s, j;
 164       double ds2,dc2;
 165
 166       mpn_mul_1 (x, xt, SZ, i);
 167       sincosx_mpn (si, co, x, i == 0 ? NULL : ox);
 168       memcpy (ox, x, sizeof (mp1));
 169       ds2 = sin (i / (double) (1 << N2));
 170       dc2 = cos (i / (double) (1 << N2));
 171       for (j = SZ-1; j >= 0; j--)
 172         {
 173           s2[j] = (mp_limb_t) ds2;
 174           ds2 = (ds2 - s2[j]) * sf;
 175           c2[j] = (mp_limb_t) dc2;
 176           dc2 = (dc2 - c2[j]) * sf;
 177         }
 178       if (mpn_cmp (si, s2, SZ) >= 0)
 179         mpn_sub_n (s3, si, s2, SZ);
 180       else
 181         mpn_sub_n (s3, s2, si, SZ);
 182       if (mpn_cmp (co, c2, SZ) >= 0)
 183         mpn_sub_n (c3, co, c2, SZ);
 184       else
 185         mpn_sub_n (c3, c2, co, SZ);
 186
 187       s2s = mpn_bitsize (s2, SZ);
 188       s3s = mpn_bitsize (s3, SZ);
 189       c2s = mpn_bitsize (c2, SZ);
 190       c3s = mpn_bitsize (c3, SZ);
 191       if ((s3s >= 0 && s2s - s3s < 54)
 192           || (c3s >= 0 && c2s - c3s < 54)
 193           || 0)
 194         {
 195 #if PRINT_ERRORS
 196           printf ("%06x ", i * (0x100000 / (1 << N2)));
 197           print_mpn_hex(si, (FRAC / 4) + 1);
 198           putchar (' ');
 199           print_mpn_hex (co, (FRAC / 4) + 1);
 200           putchar ('\n');
 201           fputs ("       ", stdout);
 202           print_mpn_hex (s2, (FRAC / 4) + 1);
 203           putchar (' ');
 204           print_mpn_hex (c2, (FRAC / 4) + 1);
 205           putchar ('\n');
 206           printf (" %c%c    ",
 207                   s3s >= 0 && s2s-s3s < 54 ? s2s - s3s == 53 ? 'e' : 'F' : 'P',
 208                   c3s >= 0 && c2s-c3s < 54 ? c2s - c3s == 53 ? 'e' : 'F' : 'P');
 209           print_mpn_hex (s3, (FRAC / 4) + 1);
 210           putchar (' ');
 211           print_mpn_hex (c3, (FRAC / 4) + 1);
 212           putchar ('\n');
 213 #endif
 214           sin_errors += s2s - s3s == 53;
 215           cos_errors += c2s - c3s == 53;
 216           sin_failures += s2s - s3s < 53;
 217           cos_failures += c2s - c3s < 53;
 218         }
 219       if (s3s >= sin_maxerror_s
 220           && mpn_cmp (s3, sin_maxerror, SZ) > 0)
 221         {
 222           memcpy (sin_maxerror, s3, sizeof (mp1));
 223           sin_maxerror_s = s3s;
 224         }
 225       if (c3s >= cos_maxerror_s
 226           && mpn_cmp (c3, cos_maxerror, SZ) > 0)
 227         {
 228           memcpy (cos_maxerror, c3, sizeof (mp1));
 229           cos_maxerror_s = c3s;
 230         }
 231     }
 232
 233    /* Check Range-Kutta against precomputed values of sin(1) and cos(1).  */
 234    memset (x, 0, sizeof (mp1));
 235    x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
 236    sincosx_mpn (si, co, x, ox);
 237
 238    memset (s2, 0, sizeof (mp1));
 239    memset (c2, 0, sizeof (mp1));
 240    for (i = 0; i < 100 && i < FRAC / 4; i++)
 241      {
 242        s2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, sin1[i])
 243                                                        - hexdig)
 244                                           << (FRAC - i * 4 - 4) % mpbpl);
 245        c2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, cos1[i])
 246                                                        - hexdig)
 247                                           << (FRAC - i * 4 - 4) % mpbpl);
 248      }
 249
 250    if (mpn_cmp (si, s2, SZ) >= 0)
 251      mpn_sub_n (s3, si, s2, SZ);
 252    else
 253      mpn_sub_n (s3, s2, si, SZ);
 254    if (mpn_cmp (co, c2, SZ) >= 0)
 255       mpn_sub_n (c3, co, c2, SZ);
 256    else
 257      mpn_sub_n (c3, c2, co, SZ);
 258
 259    printf ("sin:\n");
 260    printf ("%d failures; %d errors; error rate %0.2f%%\n",
 261            sin_failures, sin_errors, sin_errors * 100.0 / (double) (1 << N2));
 262    fputs ("maximum error:   ", stdout);
 263    print_mpn_hex (sin_maxerror, (FRAC / 4) + 1);
 264    fputs ("\nerror in sin(1): ", stdout);
 265    print_mpn_hex (s3, (FRAC / 4) + 1);
 266
 267    fputs ("\n\ncos:\n", stdout);
 268    printf ("%d failures; %d errors; error rate %0.2f%%\n",
 269            cos_failures, cos_errors, cos_errors * 100.0 / (double) (1 << N2));
 270    fputs ("maximum error:   ", stdout);
 271    print_mpn_hex (cos_maxerror, (FRAC / 4) + 1);
 272    fputs ("\nerror in cos(1): ", stdout);
 273    print_mpn_hex (c3, (FRAC / 4) + 1);
 274    putchar ('\n');
 275
 276    return (sin_failures == 0 && cos_failures == 0) ? 0 : 1;
 277 }