math/atest-exp2.c

   1 /* Copyright (C) 1997-2013 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, see
  17    <http://www.gnu.org/licenses/>.  */
  18
  19 #include <stdio.h>
  20 #include <math.h>
  21 #include <gmp.h>
  22 #include <string.h>
  23 #include <limits.h>
  24 #include <assert.h>
  25 #include <stdlib.h>
  26
  27 #define PRINT_ERRORS 0
  28
  29 #define TOL 80
  30 #define N2 18
  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 exp_m1[102] = "0" /* point */
  42 "5e2d58d8b3bcdf1abadec7829054f90dda9805aab56c773330"
  43 "24b9d0a507daedb16400bf472b4215b8245b669d90d27a5aea";
  44
  45 static const char hexdig[] = "0123456789abcdef";
  46
  47 static void
  48 print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base)
  49 {
  50    unsigned int i;
  51    mp1 tx;
  52
  53    memcpy (tx, x, sizeof (mp1));
  54    if (base == 16)
  55      fputs ("0x", stdout);
  56    assert (x[SZ-1] < base);
  57    fputc (hexdig[x[SZ - 1]], stdout);
  58    fputc ('.', stdout);
  59    for (i = 0; i < dp; i++)
  60      {
  61        tx[SZ - 1] = 0;
  62        mpn_mul_1 (tx, tx, SZ, base);
  63        assert (tx[SZ - 1] < base);
  64        fputc (hexdig[tx[SZ - 1]], stdout);
  65      }
  66 }
  67
  68 static void
  69 read_mpn_hex(mp_limb_t *x, const char *str)
  70 {
  71   int i;
  72
  73   memset (x, 0, sizeof (mp1));
  74   for (i = -1; i < 100 && i < FRAC / 4; ++i)
  75     x[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, str[i + 1])
  76                                                    - hexdig)
  77                                       << (FRAC - i * 4 - 4) % mpbpl);
  78 }
  79
  80 static mp_limb_t *get_log2(void) __attribute__((const));
  81 static mp_limb_t *
  82 get_log2(void)
  83 {
  84   static mp1 log2_m;
  85   static int log2_m_inited = 0;
  86   static const char log2[102] = "0" /* point */
  87     "b17217f7d1cf79abc9e3b39803f2f6af40f343267298b62d8a"
  88     "0d175b8baafa2be7b876206debac98559552fb4afa1b10ed2e";
  89
  90   if (!log2_m_inited)
  91     {
  92       read_mpn_hex (log2_m, log2);
  93       log2_m_inited = 1;
  94     }
  95   return log2_m;
  96 }
  97
  98 /* Compute e^x.  */
  99 static void
 100 exp_mpn (mp1 ex, mp1 x)
 101 {
 102    unsigned int n;
 103    mp1 xp;
 104    mp2 tmp;
 105    mp_limb_t chk;
 106    mp1 tol;
 107
 108    memset (xp, 0, sizeof (mp1));
 109    memset (ex, 0, sizeof (mp1));
 110    xp[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
 111    memset (tol, 0, sizeof (mp1));
 112    tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)1 << (FRAC - TOL) % mpbpl;
 113
 114    n = 0;
 115
 116    do
 117      {
 118        /* Calculate sum(x^n/n!) until the next term is sufficiently small.  */
 119
 120        mpn_mul_n (tmp, xp, x, SZ);
 121        assert(tmp[SZ * 2 - 1] == 0);
 122        if (n > 0)
 123          mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
 124        chk = mpn_add_n (ex, ex, xp, SZ);
 125        assert (chk == 0);
 126        ++n;
 127        assert (n < 80); /* Catch too-high TOL.  */
 128      }
 129    while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0);
 130 }
 131
 132 /* Calculate 2^x.  */
 133 static void
 134 exp2_mpn (mp1 ex, mp1 x)
 135 {
 136   mp2 tmp;
 137   mpn_mul_n (tmp, x, get_log2 (), SZ);
 138   assert(tmp[SZ * 2 - 1] == 0);
 139   exp_mpn (ex, tmp + FRAC / mpbpl);
 140 }
 141
 142
 143 static int
 144 mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE)
 145 {
 146   int i, j;
 147   for (i = SIZE - 1; i > 0; --i)
 148     if (SRC_PTR[i] != 0)
 149       break;
 150   for (j = mpbpl - 1; j >= 0; --j)
 151     if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
 152       break;
 153
 154   return i * mpbpl + j;
 155 }
 156
 157 int
 158 main (void)
 159 {
 160   mp1 ex, x, xt, e2, e3;
 161   int i;
 162   int errors = 0;
 163   int failures = 0;
 164   mp1 maxerror;
 165   int maxerror_s = 0;
 166   const double sf = pow (2, mpbpl);
 167
 168   /* assert(mpbpl == mp_bits_per_limb); */
 169   assert(FRAC / mpbpl * mpbpl == FRAC);
 170
 171   memset (maxerror, 0, sizeof (mp1));
 172   memset (xt, 0, sizeof (mp1));
 173   xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
 174
 175   for (i = 0; i < (1 << N2); ++i)
 176     {
 177       int e2s, e3s, j;
 178       double de2;
 179
 180       mpn_mul_1 (x, xt, SZ, i);
 181       exp2_mpn (ex, x);
 182       de2 = exp2 (i / (double) (1 << N2));
 183       for (j = SZ - 1; j >= 0; --j)
 184         {
 185           e2[j] = (mp_limb_t) de2;
 186           de2 = (de2 - e2[j]) * sf;
 187         }
 188       if (mpn_cmp (ex, e2, SZ) >= 0)
 189         mpn_sub_n (e3, ex, e2, SZ);
 190       else
 191         mpn_sub_n (e3, e2, ex, SZ);
 192
 193       e2s = mpn_bitsize (e2, SZ);
 194       e3s = mpn_bitsize (e3, SZ);
 195       if (e3s >= 0 && e2s - e3s < 54)
 196         {
 197 #if PRINT_ERRORS
 198           printf ("%06x ", i * (0x100000 / (1 << N2)));
 199           print_mpn_fp (ex, (FRAC / 4) + 1, 16);
 200           putchar ('\n');
 201           fputs ("       ",stdout);
 202           print_mpn_fp (e2, (FRAC / 4) + 1, 16);
 203           putchar ('\n');
 204           printf (" %c     ",
 205                   e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
 206           print_mpn_fp (e3, (FRAC / 4) + 1, 16);
 207           putchar ('\n');
 208 #endif
 209           errors += (e2s - e3s == 53);
 210           failures += (e2s - e3s < 53);
 211         }
 212       if (e3s >= maxerror_s
 213           && mpn_cmp (e3, maxerror, SZ) > 0)
 214         {
 215           memcpy (maxerror, e3, sizeof (mp1));
 216           maxerror_s = e3s;
 217         }
 218     }
 219
 220   /* Check exp_mpn against precomputed value of exp(1).  */
 221   memset (x, 0, sizeof (mp1));
 222   x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
 223   exp_mpn (ex, x);
 224   read_mpn_hex (e2, exp1);
 225   if (mpn_cmp (ex, e2, SZ) >= 0)
 226     mpn_sub_n (e3, ex, e2, SZ);
 227   else
 228     mpn_sub_n (e3, e2, ex, SZ);
 229
 230   printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
 231           errors * 100.0 / (double) (1 << N2));
 232   fputs ("maximum error:   ", stdout);
 233   print_mpn_fp (maxerror, (FRAC / 4) + 1, 16);
 234   putchar ('\n');
 235   fputs ("error in exp(1): ", stdout);
 236   print_mpn_fp (e3, (FRAC / 4) + 1, 16);
 237   putchar ('\n');
 238
 239   return failures == 0 ? 0 : 1;
 240 }