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: }