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: #include <stdlib.h>
   27: 
   28: #define PRINT_ERRORS 0
   29: 
   30: #define TOL 80
   31: #define N2 18
   32: #define FRAC (32*4)
   33: 
   34: #define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
   35: #define SZ (FRAC / mpbpl + 1)
   36: typedef mp_limb_t mp1[SZ], mp2[SZ * 2];
   37: 
   38: /* This string has 101 hex digits.  */
   39: static const char exp1[102] = "2" /* point */
   40: "b7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a7"
   41: "84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07";
   42: static const char exp_m1[102] = "0" /* point */
   43: "5e2d58d8b3bcdf1abadec7829054f90dda9805aab56c773330"
   44: "24b9d0a507daedb16400bf472b4215b8245b669d90d27a5aea";
   45: 
   46: static const char hexdig[] = "0123456789abcdef";
   47: 
   48: static void
   49: print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base)
   50: {
   51:    unsigned int i;
   52:    mp1 tx;
   53: 
   54:    memcpy (tx, x, sizeof (mp1));
   55:    if (base == 16)
   56:      fputs ("0x", stdout);
   57:    assert (x[SZ-1] < base);
   58:    fputc (hexdig[x[SZ - 1]], stdout);
   59:    fputc ('.', stdout);
   60:    for (i = 0; i < dp; i++)
   61:      {
   62:        tx[SZ - 1] = 0;
   63:        mpn_mul_1 (tx, tx, SZ, base);
   64:        assert (tx[SZ - 1] < base);
   65:        fputc (hexdig[tx[SZ - 1]], stdout);
   66:      }
   67: }
   68: 
   69: static void
   70: read_mpn_hex(mp_limb_t *x, const char *str)
   71: {
   72:   int i;
   73: 
   74:   memset (x, 0, sizeof (mp1));
   75:   for (i = -1; i < 100 && i < FRAC / 4; ++i)
   76:     x[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, str[i + 1])
   77:                                                    - hexdig)
   78:                                       << (FRAC - i * 4 - 4) % mpbpl);
   79: }
   80: 
   81: static mp_limb_t *get_log2(void) __attribute__((const));
   82: static mp_limb_t *
   83: get_log2(void)
   84: {
   85:   static mp1 log2_m;
   86:   static int log2_m_inited = 0;
   87:   static const char log2[102] = "0" /* point */
   88:     "b17217f7d1cf79abc9e3b39803f2f6af40f343267298b62d8a"
   89:     "0d175b8baafa2be7b876206debac98559552fb4afa1b10ed2e";
   90: 
   91:   if (!log2_m_inited)
   92:     {
   93:       read_mpn_hex (log2_m, log2);
   94:       log2_m_inited = 1;
   95:     }
   96:   return log2_m;
   97: }
   98: 
   99: /* Compute e^x.  */
  100: static void
  101: exp_mpn (mp1 ex, mp1 x)
  102: {
  103:    unsigned int n;
  104:    mp1 xp;
  105:    mp2 tmp;
  106:    mp_limb_t chk, round;
  107:    mp1 tol;
  108: 
  109:    memset (xp, 0, sizeof (mp1));
  110:    memset (ex, 0, sizeof (mp1));
  111:    xp[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
  112:    memset (tol, 0, sizeof (mp1));
  113:    tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)1 << (FRAC - TOL) % mpbpl;
  114: 
  115:    n = 0;
  116: 
  117:    do
  118:      {
  119:        /* Calculate sum(x^n/n!) until the next term is sufficiently small.  */
  120: 
  121:        mpn_mul_n (tmp, xp, x, SZ);
  122:        assert(tmp[SZ * 2 - 1] == 0);
  123:        if (n > 0)
  124:          round = mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
  125:        chk = mpn_add_n (ex, ex, xp, SZ);
  126:        assert (chk == 0);
  127:        ++n;
  128:        assert (n < 80); /* Catch too-high TOL.  */
  129:      }
  130:    while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0);
  131: }
  132: 
  133: /* Calculate 2^x.  */
  134: static void
  135: exp2_mpn (mp1 ex, mp1 x)
  136: {
  137:   mp2 tmp;
  138:   mpn_mul_n (tmp, x, get_log2 (), SZ);
  139:   assert(tmp[SZ * 2 - 1] == 0);
  140:   exp_mpn (ex, tmp + FRAC / mpbpl);
  141: }
  142: 
  143: 
  144: static int
  145: mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE)
  146: {
  147:   int i, j;
  148:   for (i = SIZE - 1; i > 0; --i)
  149:     if (SRC_PTR[i] != 0)
  150:       break;
  151:   for (j = mpbpl - 1; j >= 0; --j)
  152:     if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
  153:       break;
  154: 
  155:   return i * mpbpl + j;
  156: }
  157: 
  158: int
  159: main (void)
  160: {
  161:   mp1 ex, x, xt, e2, e3;
  162:   int i;
  163:   int errors = 0;
  164:   int failures = 0;
  165:   mp1 maxerror;
  166:   int maxerror_s = 0;
  167:   const double sf = pow (2, mpbpl);
  168: 
  169:   /* assert(mpbpl == mp_bits_per_limb); */
  170:   assert(FRAC / mpbpl * mpbpl == FRAC);
  171: 
  172:   memset (maxerror, 0, sizeof (mp1));
  173:   memset (xt, 0, sizeof (mp1));
  174:   xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
  175: 
  176:   for (i = 0; i < (1 << N2); ++i)
  177:     {
  178:       int e2s, e3s, j;
  179:       double de2;
  180: 
  181:       mpn_mul_1 (x, xt, SZ, i);
  182:       exp2_mpn (ex, x);
  183:       de2 = exp2 (i / (double) (1 << N2));
  184:       for (j = SZ - 1; j >= 0; --j)
  185:         {
  186:           e2[j] = (mp_limb_t) de2;
  187:           de2 = (de2 - e2[j]) * sf;
  188:         }
  189:       if (mpn_cmp (ex, e2, SZ) >= 0)
  190:         mpn_sub_n (e3, ex, e2, SZ);
  191:       else
  192:         mpn_sub_n (e3, e2, ex, SZ);
  193: 
  194:       e2s = mpn_bitsize (e2, SZ);
  195:       e3s = mpn_bitsize (e3, SZ);
  196:       if (e3s >= 0 && e2s - e3s < 54)
  197:         {
  198: #if PRINT_ERRORS
  199:           printf ("%06x ", i * (0x100000 / (1 << N2)));
  200:           print_mpn_fp (ex, (FRAC / 4) + 1, 16);
  201:           putchar ('\n');
  202:           fputs ("       ",stdout);
  203:           print_mpn_fp (e2, (FRAC / 4) + 1, 16);
  204:           putchar ('\n');
  205:           printf (" %c     ",
  206:                   e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
  207:           print_mpn_fp (e3, (FRAC / 4) + 1, 16);
  208:           putchar ('\n');
  209: #endif
  210:           errors += (e2s - e3s == 53);
  211:           failures += (e2s - e3s < 53);
  212:         }
  213:       if (e3s >= maxerror_s
  214:           && mpn_cmp (e3, maxerror, SZ) > 0)
  215:         {
  216:           memcpy (maxerror, e3, sizeof (mp1));
  217:           maxerror_s = e3s;
  218:         }
  219:     }
  220: 
  221:   /* Check exp_mpn against precomputed value of exp(1).  */
  222:   memset (x, 0, sizeof (mp1));
  223:   x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
  224:   exp_mpn (ex, x);
  225:   read_mpn_hex (e2, exp1);
  226:   if (mpn_cmp (ex, e2, SZ) >= 0)
  227:     mpn_sub_n (e3, ex, e2, SZ);
  228:   else
  229:     mpn_sub_n (e3, e2, ex, SZ);
  230: 
  231:   printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
  232:           errors * 100.0 / (double) (1 << N2));
  233:   fputs ("maximum error:   ", stdout);
  234:   print_mpn_fp (maxerror, (FRAC / 4) + 1, 16);
  235:   putchar ('\n');
  236:   fputs ("error in exp(1): ", stdout);
  237:   print_mpn_fp (e3, (FRAC / 4) + 1, 16);
  238:   putchar ('\n');
  239: 
  240:   return failures == 0 ? 0 : 1;
  241: }