1 /* Copyright (C) 1997 Free Software Foundation, Inc.
2 This file is part of the GNU C Library.
3 Contributed by Geoffrey Keating <Geoff.Keating@anu.edu.au>, 1997.
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Library General Public License as
7 published by the Free Software Foundation; either version 2 of the
8 License, or (at your option) any later version.
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Library General Public License for more details.
15 You should have received a copy of the GNU Library General Public
16 License along with the GNU C Library; see the file COPYING.LIB. If not,
17 write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
18 Boston, MA 02111-1307, USA. */
22 #include <stdlib/gmp.h>
27 #define PRINT_ERRORS 0
33 #define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
34 #define SZ (FRAC / mpbpl + 1)
35 typedef mp_limb_t mp1[SZ], mp2[SZ * 2];
37 /* This string has 101 hex digits. */
38 static const char exp1[102] = "2" /* point */
39 "b7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a7"
40 "84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07";
41 static const char hexdig[] = "0123456789abcdef";
44 print_mpn_hex (const mp_limb_t *x, unsigned size)
48 const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;
50 memset (value, '0', size);
52 for (i = 0; i < final ; i++)
53 value[size - 1 - i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];
56 fputs (value, stdout);
60 exp_mpn (mp1 ex, mp1 x)
68 memset (xp, 0, sizeof (mp1));
69 memset (ex, 0, sizeof (mp1));
70 xp[FRAC / mpbpl] = 1 << FRAC % mpbpl;
71 memset (tol,0, sizeof (mp1));
72 tol[(FRAC - TOL) / mpbpl] = 1 << (FRAC - TOL) % mpbpl;
78 /* Calculate sum(x^n/n!) until the next term is sufficiently small. */
80 mpn_mul_n (tmp, xp, x, SZ);
81 assert (tmp[SZ * 2 - 1] == 0);
83 round = mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
84 chk = mpn_add_n (ex, ex, xp, SZ);
87 assert (n < 80); /* Catch too-high TOL. */
89 while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0);
93 mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE)
96 for (i = SIZE - 1; i > 0; i--)
99 for (j = mpbpl - 1; j > 0; j--)
100 if ((SRC_PTR[i] & 1 << j) != 0)
109 mp1 ex, x, xt, e2, e3;
115 const double sf = pow (2, mpbpl);
117 /* assert (mpbpl == mp_bits_per_limb); */
118 assert (FRAC / mpbpl * mpbpl == FRAC);
120 memset (maxerror, 0, sizeof (mp1));
121 memset (xt, 0, sizeof (mp1));
122 xt[(FRAC - N2) / mpbpl] = 1 << (FRAC - N2) % mpbpl;
124 for (i = 0; i < 1 << N2; i++)
129 mpn_mul_1 (x,xt,SZ,i);
131 de2 = exp (i / (double) (1 << N2));
132 for (j = SZ-1; j >= 0; j--)
134 e2[j] = (mp_limb_t) de2;
135 de2 = (de2 - e2[j]) * sf;
137 if (mpn_cmp (ex,e2,SZ) >= 0)
138 mpn_sub_n (e3,ex,e2,SZ);
140 mpn_sub_n (e3,e2,ex,SZ);
142 e2s = mpn_bitsize (e2,SZ);
143 e3s = mpn_bitsize (e3,SZ);
144 if (e3s > 1 && e2s - e3s < 54)
147 printf ("%06x ", i * (0x100000 / (1 << N2)));
148 print_mpn_hex (ex, (FRAC / 4) + 1);
149 fputs ("\n ",stdout);
150 print_mpn_hex (e2, (FRAC / 4) + 1);
152 e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
153 print_mpn_hex (e3, (FRAC / 4) + 1);
156 errors += (e2s - e3s == 53);
157 failures += (e2s - e3s < 53);
159 if (e3s >= maxerror_s
160 && mpn_cmp (e3, maxerror, SZ) > 0)
162 memcpy (maxerror, e3, sizeof (mp1));
167 /* Check exp_mpn against precomputed value of exp(1). */
168 memset (x, '\0', sizeof (mp1));
169 x[FRAC / mpbpl] = 1 << FRAC % mpbpl;
172 memset (e2, '\0', sizeof (mp1));
173 for (i = -1; i < 100 && i < FRAC / 4; i++)
174 e2[(FRAC - i * 4 - 4) / mpbpl] |= (strchr (hexdig, exp1[i + 1]) - hexdig
175 << (FRAC - i * 4 - 4) % mpbpl);
177 if (mpn_cmp (ex, e2, SZ) >= 0)
178 mpn_sub_n (e3, ex, e2, SZ);
180 mpn_sub_n (e3, e2, ex, SZ);
182 printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
183 errors * 100.0 / (double) (1 << N2));
184 fputs ("maximum error: ", stdout);
185 print_mpn_hex (maxerror, (FRAC / 4) + 1);
186 fputs ("\nerror in exp(1): ", stdout);
187 print_mpn_hex (e3, (FRAC / 4) + 1);
190 return failures == 0 ? 0 : 1;