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 #if BITS_PER_MP_LIMB == 64
  38 # define LIMB64(L, H) 0x ## H ## L
  39 #elif BITS_PER_MP_LIMB == 32
  40 # define LIMB64(L, H) 0x ## L, 0x ## H
  41 #else
  42 # error
  43 #endif
  44
  45 /* Once upon a time these constants were generated to 400 bits.
  46    We only need FRAC bits (128) at present, but we retain 384 bits
  47    in the text Just In Case.  */
  48 #define CONSTSZ(INT, F1, F2, F3, F4, F5, F6, F7, F8, F9, Fa, Fb, Fc) \
  49         LIMB64(F4, F3), LIMB64(F2, F1), INT
  50
  51 static const mp1 mp_exp1 = {
  52   CONSTSZ (2, b7e15162, 8aed2a6a, bf715880, 9cf4f3c7, 62e7160f, 38b4da56,
  53            a784d904, 5190cfef, 324e7738, 926cfbe5, f4bf8d8d, 8c31d763)
  54 };
  55
  56 static const mp1 mp_exp_m1 = {
  57   CONSTSZ (0, 5e2d58d8, b3bcdf1a, badec782, 9054f90d, da9805aa, b56c7733,
  58            3024b9d0, a507daed, b16400bf, 472b4215, b8245b66, 9d90d27a)
  59 };
  60
  61 static const mp1 mp_log2 = {
  62   CONSTSZ (0, b17217f7, d1cf79ab, c9e3b398, 03f2f6af, 40f34326, 7298b62d,
  63            8a0d175b, 8baafa2b, e7b87620, 6debac98, 559552fb, 4afa1b10)
  64 };
  65
  66 static void
  67 print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base)
  68 {
  69    static const char hexdig[16] = "0123456789abcdef";
  70    unsigned int i;
  71    mp1 tx;
  72
  73    memcpy (tx, x, sizeof (mp1));
  74    if (base == 16)
  75      fputs ("0x", stdout);
  76    assert (x[SZ-1] < base);
  77    fputc (hexdig[x[SZ - 1]], stdout);
  78    fputc ('.', stdout);
  79    for (i = 0; i < dp; i++)
  80      {
  81        tx[SZ - 1] = 0;
  82        mpn_mul_1 (tx, tx, SZ, base);
  83        assert (tx[SZ - 1] < base);
  84        fputc (hexdig[tx[SZ - 1]], stdout);
  85      }
  86 }
  87
  88 /* Compute e^x.  */
  89 static void
  90 exp_mpn (mp1 ex, mp1 x)
  91 {
  92    unsigned int n;
  93    mp1 xp;
  94    mp2 tmp;
  95    mp_limb_t chk;
  96    mp1 tol;
  97
  98    memset (xp, 0, sizeof (mp1));
  99    memset (ex, 0, sizeof (mp1));
 100    xp[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
 101    memset (tol, 0, sizeof (mp1));
 102    tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)1 << (FRAC - TOL) % mpbpl;
 103
 104    n = 0;
 105
 106    do
 107      {
 108        /* Calculate sum(x^n/n!) until the next term is sufficiently small.  */
 109
 110        mpn_mul_n (tmp, xp, x, SZ);
 111        assert(tmp[SZ * 2 - 1] == 0);
 112        if (n > 0)
 113          mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
 114        chk = mpn_add_n (ex, ex, xp, SZ);
 115        assert (chk == 0);
 116        ++n;
 117        assert (n < 80); /* Catch too-high TOL.  */
 118      }
 119    while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0);
 120 }
 121
 122 /* Calculate 2^x.  */
 123 static void
 124 exp2_mpn (mp1 ex, mp1 x)
 125 {
 126   mp2 tmp;
 127   mpn_mul_n (tmp, x, mp_log2, SZ);
 128   assert(tmp[SZ * 2 - 1] == 0);
 129   exp_mpn (ex, tmp + FRAC / mpbpl);
 130 }
 131
 132
 133 static int
 134 mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE)
 135 {
 136   int i, j;
 137   for (i = SIZE - 1; i > 0; --i)
 138     if (SRC_PTR[i] != 0)
 139       break;
 140   for (j = mpbpl - 1; j >= 0; --j)
 141     if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
 142       break;
 143
 144   return i * mpbpl + j;
 145 }
 146
 147 int
 148 main (void)
 149 {
 150   mp1 ex, x, xt, e2, e3;
 151   int i;
 152   int errors = 0;
 153   int failures = 0;
 154   mp1 maxerror;
 155   int maxerror_s = 0;
 156   const double sf = pow (2, mpbpl);
 157
 158   /* assert(mpbpl == mp_bits_per_limb); */
 159   assert(FRAC / mpbpl * mpbpl == FRAC);
 160
 161   memset (maxerror, 0, sizeof (mp1));
 162   memset (xt, 0, sizeof (mp1));
 163   xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
 164
 165   for (i = 0; i < (1 << N2); ++i)
 166     {
 167       int e2s, e3s, j;
 168       double de2;
 169
 170       mpn_mul_1 (x, xt, SZ, i);
 171       exp2_mpn (ex, x);
 172       de2 = exp2 (i / (double) (1 << N2));
 173       for (j = SZ - 1; j >= 0; --j)
 174         {
 175           e2[j] = (mp_limb_t) de2;
 176           de2 = (de2 - e2[j]) * sf;
 177         }
 178       if (mpn_cmp (ex, e2, SZ) >= 0)
 179         mpn_sub_n (e3, ex, e2, SZ);
 180       else
 181         mpn_sub_n (e3, e2, ex, SZ);
 182
 183       e2s = mpn_bitsize (e2, SZ);
 184       e3s = mpn_bitsize (e3, SZ);
 185       if (e3s >= 0 && e2s - e3s < 54)
 186         {
 187 #if PRINT_ERRORS
 188           printf ("%06x ", i * (0x100000 / (1 << N2)));
 189           print_mpn_fp (ex, (FRAC / 4) + 1, 16);
 190           putchar ('\n');
 191           fputs ("       ",stdout);
 192           print_mpn_fp (e2, (FRAC / 4) + 1, 16);
 193           putchar ('\n');
 194           printf (" %c     ",
 195                   e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
 196           print_mpn_fp (e3, (FRAC / 4) + 1, 16);
 197           putchar ('\n');
 198 #endif
 199           errors += (e2s - e3s == 53);
 200           failures += (e2s - e3s < 53);
 201         }
 202       if (e3s >= maxerror_s
 203           && mpn_cmp (e3, maxerror, SZ) > 0)
 204         {
 205           memcpy (maxerror, e3, sizeof (mp1));
 206           maxerror_s = e3s;
 207         }
 208     }
 209
 210   /* Check exp_mpn against precomputed value of exp(1).  */
 211   memset (x, 0, sizeof (mp1));
 212   x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
 213   exp_mpn (ex, x);
 214   if (mpn_cmp (ex, mp_exp1, SZ) >= 0)
 215     mpn_sub_n (e3, ex, mp_exp1, SZ);
 216   else
 217     mpn_sub_n (e3, mp_exp1, ex, SZ);
 218
 219   printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
 220           errors * 100.0 / (double) (1 << N2));
 221   fputs ("maximum error:   ", stdout);
 222   print_mpn_fp (maxerror, (FRAC / 4) + 1, 16);
 223   putchar ('\n');
 224   fputs ("error in exp(1): ", stdout);
 225   print_mpn_fp (e3, (FRAC / 4) + 1, 16);
 226   putchar ('\n');
 227
 228   return failures == 0 ? 0 : 1;
 229 }