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-rw-r--r--math/atest-exp.c191
1 files changed, 191 insertions, 0 deletions
diff --git a/math/atest-exp.c b/math/atest-exp.c
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+++ b/math/atest-exp.c
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+/* Copyright (C) 1997 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 Library General Public License as
+   published by the Free Software Foundation; either version 2 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
+   Library General Public License for more details.
+
+   You should have received a copy of the GNU Library General Public
+   License along with the GNU C Library; see the file COPYING.LIB.  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 <stdlib/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";
+
+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);
+}
+
+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] = 1 << FRAC % mpbpl;
+   memset (tol,0, sizeof (mp1));
+   tol[(FRAC - TOL) / mpbpl] = 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] & 1 << j) != 0)
+       break;
+
+   return i * 32 + 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] = 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 > 1 && 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] = 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] |= (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;
+}