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 TOL 80
   30: #define N2 17
   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: /* This string has 101 hex digits.  */
   38: static const char exp1[102] = "2" /* point */
   39: "b7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a7"
   40: "84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07";
   41: static const char hexdig[] = "0123456789abcdef";
   42: 
   43: static void
   44: print_mpn_hex (const mp_limb_t *x, unsigned size)
   45: {
   46:    char value[size + 1];
   47:    unsigned i;
   48:    const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;
   49: 
   50:    memset (value, '0', size);
   51: 
   52:    for (i = 0; i < final ; i++)
   53:      value[size - 1 - i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];
   54: 
   55:    value[size] = '\0';
   56:    fputs (value, stdout);
   57: }
   58: 
   59: static void
   60: exp_mpn (mp1 ex, mp1 x)
   61: {
   62:    unsigned n;
   63:    mp1 xp;
   64:    mp2 tmp;
   65:    mp_limb_t chk, round;
   66:    mp1 tol;
   67: 
   68:    memset (xp, 0, sizeof (mp1));
   69:    memset (ex, 0, sizeof (mp1));
   70:    xp[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
   71:    memset (tol,0, sizeof (mp1));
   72:    tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)1 << (FRAC - TOL) % mpbpl;
   73: 
   74:    n = 0;
   75: 
   76:    do
   77:      {
   78:        /* Calculate sum(x^n/n!) until the next term is sufficiently small.  */
   79: 
   80:        mpn_mul_n (tmp, xp, x, SZ);
   81:        assert (tmp[SZ * 2 - 1] == 0);
   82:        if (n > 0)
   83:          round = mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
   84:        chk = mpn_add_n (ex, ex, xp, SZ);
   85:        assert (chk == 0);
   86:        n++;
   87:        assert (n < 80); /* Catch too-high TOL.  */
   88:      }
   89:    while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0);
   90: }
   91: 
   92: static int
   93: mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE)
   94: {
   95:    int i, j;
   96:    for (i = SIZE - 1; i > 0; i--)
   97:      if (SRC_PTR[i] != 0)
   98:        break;
   99:    for (j = mpbpl - 1; j >= 0; j--)
  100:      if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
  101:        break;
  102: 
  103:    return i * mpbpl + j;
  104: }
  105: 
  106: int
  107: main (void)
  108: {
  109:    mp1 ex, x, xt, e2, e3;
  110:    int i;
  111:    int errors = 0;
  112:    int failures = 0;
  113:    mp1 maxerror;
  114:    int maxerror_s = 0;
  115:    const double sf = pow (2, mpbpl);
  116: 
  117:    /* assert (mpbpl == mp_bits_per_limb); */
  118:    assert (FRAC / mpbpl * mpbpl == FRAC);
  119: 
  120:    memset (maxerror, 0, sizeof (mp1));
  121:    memset (xt, 0, sizeof (mp1));
  122:    xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
  123: 
  124:    for (i = 0; i < 1 << N2; i++)
  125:    {
  126:       int e2s, e3s, j;
  127:       double de2;
  128: 
  129:       mpn_mul_1 (x,xt,SZ,i);
  130:       exp_mpn (ex, x);
  131:       de2 = exp (i / (double) (1 << N2));
  132:       for (j = SZ-1; j >= 0; j--)
  133:         {
  134:           e2[j] = (mp_limb_t) de2;
  135:           de2 = (de2 - e2[j]) * sf;
  136:         }
  137:       if (mpn_cmp (ex,e2,SZ) >= 0)
  138:         mpn_sub_n (e3,ex,e2,SZ);
  139:       else
  140:         mpn_sub_n (e3,e2,ex,SZ);
  141: 
  142:       e2s = mpn_bitsize (e2,SZ);
  143:       e3s = mpn_bitsize (e3,SZ);
  144:       if (e3s >= 0 && e2s - e3s < 54)
  145:         {
  146: #if PRINT_ERRORS
  147:           printf ("%06x ", i * (0x100000 / (1 << N2)));
  148:           print_mpn_hex (ex, (FRAC / 4) + 1);
  149:           fputs ("\n       ",stdout);
  150:           print_mpn_hex (e2, (FRAC / 4) + 1);
  151:           printf ("\n %c     ",
  152:                   e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
  153:           print_mpn_hex (e3, (FRAC / 4) + 1);
  154:           putchar ('\n');
  155: #endif
  156:          errors += (e2s - e3s == 53);
  157:          failures += (e2s - e3s < 53);
  158:         }
  159:       if (e3s >= maxerror_s
  160:           && mpn_cmp (e3, maxerror, SZ) > 0)
  161:         {
  162:           memcpy (maxerror, e3, sizeof (mp1));
  163:           maxerror_s = e3s;
  164:         }
  165:    }
  166: 
  167:    /* Check exp_mpn against precomputed value of exp(1).  */
  168:    memset (x, '\0', sizeof (mp1));
  169:    x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
  170:    exp_mpn (ex, x);
  171: 
  172:    memset (e2, '\0', sizeof (mp1));
  173:    for (i = -1; i < 100 && i < FRAC / 4; i++)
  174:      e2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig,
  175:                                                              exp1[i + 1])
  176:                                                      - hexdig)
  177:                                         << (FRAC - i * 4 - 4) % mpbpl);
  178: 
  179:    if (mpn_cmp (ex, e2, SZ) >= 0)
  180:      mpn_sub_n (e3, ex, e2, SZ);
  181:    else
  182:      mpn_sub_n (e3, e2, ex, SZ);
  183: 
  184:    printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
  185:            errors * 100.0 / (double) (1 << N2));
  186:    fputs ("maximum error:   ", stdout);
  187:    print_mpn_hex (maxerror, (FRAC / 4) + 1);
  188:    fputs ("\nerror in exp(1): ", stdout);
  189:    print_mpn_hex (e3, (FRAC / 4) + 1);
  190:    putchar ('\n');
  191: 
  192:    return failures == 0 ? 0 : 1;
  193: }