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/* Copyright (C) 1997-2013 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, see
<http://www.gnu.org/licenses/>. */
#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;
}
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