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/* Copyright (C) 1997-2020 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
<https://www.gnu.org/licenses/>. */
#include <stdio.h>
#include <math.h>
#include <gmp.h>
#include <string.h>
#include <limits.h>
#include <assert.h>
#include <stdlib.h>
#define PRINT_ERRORS 0
#define TOL 80
#define N2 18
#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];
#if BITS_PER_MP_LIMB == 64
# define LIMB64(L, H) 0x ## H ## L
#elif BITS_PER_MP_LIMB == 32
# define LIMB64(L, H) 0x ## L, 0x ## H
#else
# error
#endif
/* Once upon a time these constants were generated to 400 bits.
We only need FRAC bits (128) at present, but we retain 384 bits
in the text Just In Case. */
#define CONSTSZ(INT, F1, F2, F3, F4, F5, F6, F7, F8, F9, Fa, Fb, Fc) \
LIMB64(F4, F3), LIMB64(F2, F1), INT
static const mp1 mp_exp1 = {
CONSTSZ (2, b7e15162, 8aed2a6a, bf715880, 9cf4f3c7, 62e7160f, 38b4da56,
a784d904, 5190cfef, 324e7738, 926cfbe5, f4bf8d8d, 8c31d763)
};
static const mp1 mp_log2 = {
CONSTSZ (0, b17217f7, d1cf79ab, c9e3b398, 03f2f6af, 40f34326, 7298b62d,
8a0d175b, 8baafa2b, e7b87620, 6debac98, 559552fb, 4afa1b10)
};
static void
print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base)
{
static const char hexdig[16] = "0123456789abcdef";
unsigned int i;
mp1 tx;
memcpy (tx, x, sizeof (mp1));
if (base == 16)
fputs ("0x", stdout);
assert (x[SZ-1] < base);
fputc (hexdig[x[SZ - 1]], stdout);
fputc ('.', stdout);
for (i = 0; i < dp; i++)
{
tx[SZ - 1] = 0;
mpn_mul_1 (tx, tx, SZ, base);
assert (tx[SZ - 1] < base);
fputc (hexdig[tx[SZ - 1]], stdout);
}
}
/* Compute e^x. */
static void
exp_mpn (mp1 ex, mp1 x)
{
unsigned int n;
mp1 xp;
mp2 tmp;
mp_limb_t chk __attribute__ ((unused));
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)
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);
}
/* Calculate 2^x. */
static void
exp2_mpn (mp1 ex, mp1 x)
{
mp2 tmp;
mpn_mul_n (tmp, x, mp_log2, SZ);
assert(tmp[SZ * 2 - 1] == 0);
exp_mpn (ex, tmp + FRAC / mpbpl);
}
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;
}
static int
do_test (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);
exp2_mpn (ex, x);
de2 = exp2 (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_fp (ex, (FRAC / 4) + 1, 16);
putchar ('\n');
fputs (" ",stdout);
print_mpn_fp (e2, (FRAC / 4) + 1, 16);
putchar ('\n');
printf (" %c ",
e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
print_mpn_fp (e3, (FRAC / 4) + 1, 16);
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);
if (mpn_cmp (ex, mp_exp1, SZ) >= 0)
mpn_sub_n (e3, ex, mp_exp1, SZ);
else
mpn_sub_n (e3, mp_exp1, 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_fp (maxerror, (FRAC / 4) + 1, 16);
putchar ('\n');
fputs ("error in exp(1): ", stdout);
print_mpn_fp (e3, (FRAC / 4) + 1, 16);
putchar ('\n');
return failures == 0 ? 0 : 1;
}
#define TIMEOUT 300
#define TEST_FUNCTION do_test ()
#include "../test-skeleton.c"
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