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-rw-r--r--math/atest-exp2.c240
1 files changed, 240 insertions, 0 deletions
diff --git a/math/atest-exp2.c b/math/atest-exp2.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 <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];
+
+/* This string has 101 hex digits. */
+static const char exp1[102] = "2" /* point */
+"b7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a7"
+"84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07";
+static const char exp_m1[102] = "0" /* point */
+"5e2d58d8b3bcdf1abadec7829054f90dda9805aab56c773330"
+"24b9d0a507daedb16400bf472b4215b8245b669d90d27a5aea";
+
+static const char hexdig[] = "0123456789abcdef";
+
+void
+print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base)
+{
+ 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);
+ }
+}
+
+void
+read_mpn_hex(mp_limb_t *x, const char *str)
+{
+ int i;
+
+ memset (x, 0, sizeof (mp1));
+ for (i = -1; i < 100 && i < FRAC / 4; ++i)
+ x[(FRAC - i * 4 - 4) / mpbpl] |= (strchr (hexdig, str[i + 1]) - hexdig
+ << (FRAC - i * 4 - 4) % mpbpl);
+}
+
+static mp_limb_t *get_log2(void) __attribute__((const));
+static mp_limb_t *
+get_log2(void)
+{
+ static mp1 log2_m;
+ static int log2_m_inited = 0;
+ static const char log2[102] = "0" /* point */
+ "b17217f7d1cf79abc9e3b39803f2f6af40f343267298b62d8a"
+ "0d175b8baafa2be7b876206debac98559552fb4afa1b10ed2e";
+
+ if (!log2_m_inited)
+ {
+ read_mpn_hex (log2_m, log2);
+ log2_m_inited = 1;
+ }
+ return log2_m;
+}
+
+/* Compute e^x. */
+void
+exp_mpn (mp1 ex, mp1 x)
+{
+ unsigned int 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);
+}
+
+/* Calculate 2^x. */
+void
+exp2_mpn (mp1 ex, mp1 x)
+{
+ mp2 tmp;
+ mpn_mul_n (tmp, x, get_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] & 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);
+ 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 > 1 && 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] = 1 << FRAC % mpbpl;
+ exp_mpn (ex, x);
+ read_mpn_hex (e2, exp1);
+ 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_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;
+}
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