math/atest-exp.c

/* Copyright (C) 1997, 1998, 2000, 2006 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Geoffrey Keating <Geoff.Keating@anu.edu.au>, 1997.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, write to the Free
   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
   02111-1307 USA.  */

#include <stdio.h>
#include <math.h>
#include <gmp.h>
#include <string.h>
#include <limits.h>
#include <assert.h>

#define PRINT_ERRORS 0

#define TOL 80
#define N2 17
#define FRAC (32*4)

#define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
#define SZ (FRAC / mpbpl + 1)
typedef mp_limb_t mp1[SZ], mp2[SZ * 2];

/* This string has 101 hex digits.  */
static const char exp1[102] = "2" /* point */
"b7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a7"
"84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07";
static const char hexdig[] = "0123456789abcdef";

static void
print_mpn_hex (const mp_limb_t *x, unsigned size)
{
   char value[size + 1];
   unsigned i;
   const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;

   memset (value, '0', size);

   for (i = 0; i < final ; i++)
     value[size - 1 - i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];

   value[size] = '\0';
   fputs (value, stdout);
}

static void
exp_mpn (mp1 ex, mp1 x)
{
   unsigned n;
   mp1 xp;
   mp2 tmp;
   mp_limb_t chk, round;
   mp1 tol;

   memset (xp, 0, sizeof (mp1));
   memset (ex, 0, sizeof (mp1));
   xp[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
   memset (tol,0, sizeof (mp1));
   tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)1 << (FRAC - TOL) % mpbpl;

   n = 0;

   do
     {
       /* Calculate sum(x^n/n!) until the next term is sufficiently small.  */

       mpn_mul_n (tmp, xp, x, SZ);
       assert (tmp[SZ * 2 - 1] == 0);
       if (n > 0)
	 round = mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
       chk = mpn_add_n (ex, ex, xp, SZ);
       assert (chk == 0);
       n++;
       assert (n < 80); /* Catch too-high TOL.  */
     }
   while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0);
}

static int
mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE)
{
   int i, j;
   for (i = SIZE - 1; i > 0; i--)
     if (SRC_PTR[i] != 0)
       break;
   for (j = mpbpl - 1; j >= 0; j--)
     if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
       break;

   return i * mpbpl + j;
}

int
main (void)
{
   mp1 ex, x, xt, e2, e3;
   int i;
   int errors = 0;
   int failures = 0;
   mp1 maxerror;
   int maxerror_s = 0;
   const double sf = pow (2, mpbpl);

   /* assert (mpbpl == mp_bits_per_limb); */
   assert (FRAC / mpbpl * mpbpl == FRAC);

   memset (maxerror, 0, sizeof (mp1));
   memset (xt, 0, sizeof (mp1));
   xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;

   for (i = 0; i < 1 << N2; i++)
   {
      int e2s, e3s, j;
      double de2;

      mpn_mul_1 (x,xt,SZ,i);
      exp_mpn (ex, x);
      de2 = exp (i / (double) (1 << N2));
      for (j = SZ-1; j >= 0; j--)
	{
	  e2[j] = (mp_limb_t) de2;
	  de2 = (de2 - e2[j]) * sf;
	}
      if (mpn_cmp (ex,e2,SZ) >= 0)
	mpn_sub_n (e3,ex,e2,SZ);
      else
	mpn_sub_n (e3,e2,ex,SZ);

      e2s = mpn_bitsize (e2,SZ);
      e3s = mpn_bitsize (e3,SZ);
      if (e3s >= 0 && e2s - e3s < 54)
	{
#if PRINT_ERRORS
	  printf ("%06x ", i * (0x100000 / (1 << N2)));
	  print_mpn_hex (ex, (FRAC / 4) + 1);
	  fputs ("\n       ",stdout);
	  print_mpn_hex (e2, (FRAC / 4) + 1);
	  printf ("\n %c     ",
		  e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
	  print_mpn_hex (e3, (FRAC / 4) + 1);
	  putchar ('\n');
#endif
	 errors += (e2s - e3s == 53);
	 failures += (e2s - e3s < 53);
	}
      if (e3s >= maxerror_s
	  && mpn_cmp (e3, maxerror, SZ) > 0)
	{
	  memcpy (maxerror, e3, sizeof (mp1));
	  maxerror_s = e3s;
	}
   }

   /* Check exp_mpn against precomputed value of exp(1).  */
   memset (x, '\0', sizeof (mp1));
   x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
   exp_mpn (ex, x);

   memset (e2, '\0', sizeof (mp1));
   for (i = -1; i < 100 && i < FRAC / 4; i++)
     e2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig,
							     exp1[i + 1])
						     - hexdig)
 					<< (FRAC - i * 4 - 4) % mpbpl);

   if (mpn_cmp (ex, e2, SZ) >= 0)
     mpn_sub_n (e3, ex, e2, SZ);
   else
     mpn_sub_n (e3, e2, ex, SZ);

   printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
	   errors * 100.0 / (double) (1 << N2));
   fputs ("maximum error:   ", stdout);
   print_mpn_hex (maxerror, (FRAC / 4) + 1);
   fputs ("\nerror in exp(1): ", stdout);
   print_mpn_hex (e3, (FRAC / 4) + 1);
   putchar ('\n');

   return failures == 0 ? 0 : 1;
}