1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
|
/* Test file for mpfr_div.
Copyright (C) 1999 Free Software Foundation.
This file is part of the MPFR Library.
The MPFR 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 MPFR 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 MPFR 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 <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
#ifdef __mips
#include <sys/fpu.h>
#endif
extern int isnan();
#define check53(n, d, rnd, res) check4(n, d, rnd, 53, res)
void check4(N, D, rnd_mode, p, Q)
double N, D, Q; unsigned char rnd_mode; int p;
{
mpfr_t q, n, d; double Q2;
mpfr_init2(q, p); mpfr_init2(n, p); mpfr_init2(d, p);
mpfr_set_d(n, N, rnd_mode);
mpfr_set_d(d, D, rnd_mode);
mpfr_div(q, n, d, rnd_mode);
#ifdef TEST
mpfr_set_machine_rnd_mode(rnd_mode);
#endif
if (Q==0.0) Q = N/D;
Q2 = mpfr_get_d(q);
if (p==53 && Q!=Q2 && (!isnan(Q) || !isnan(Q2))) {
printf("mpfr_div failed for n=%1.20e, d=%1.20e, rnd_mode=%s\n",
N, D, mpfr_print_rnd_mode(rnd_mode));
printf("expected quotient is %1.20e, got %1.20e (%d ulp)\n", Q, Q2,
ulp(Q2, Q));
exit(1);
}
mpfr_clear(q); mpfr_clear(n); mpfr_clear(d);
}
void check24(float N, float D, unsigned char rnd_mode, float Q)
{
mpfr_t q, n, d; float Q2;
mpfr_init2(q, 24); mpfr_init2(n, 24); mpfr_init2(d, 24);
mpfr_set_d(n, N, rnd_mode);
mpfr_set_d(d, D, rnd_mode);
mpfr_div(q, n, d, rnd_mode);
Q2 = mpfr_get_d(q);
if (Q!=Q2) {
printf("mpfr_div failed for n=%1.10e, d=%1.10e, prec=24, rnd_mode=%s\n",
N, D, mpfr_print_rnd_mode(rnd_mode));
printf("expected quotient is %1.10e, got %1.10e\n", Q, Q2);
exit(1);
}
mpfr_clear(q); mpfr_clear(n); mpfr_clear(d);
}
/* the following examples come from the paper "Number-theoretic Test
Generation for Directed Rounding" from Michael Parks, Table 2 */
void check_float()
{
float b=8388608.0; /* 2^23 */
check24(b*8388610.0, 8388609.0, GMP_RNDN, 8.388609e6);
check24(b*16777215.0, 16777213.0, GMP_RNDN, 8.388609e6);
check24(b*8388612.0, 8388611.0, GMP_RNDN, 8.388609e6);
check24(b*12582914.0, 12582911.0, GMP_RNDN, 8.38861e6);
check24(12582913.0, 12582910.0, GMP_RNDN, 1.000000238);
check24(b*16777215.0, 8388609.0, GMP_RNDN, 1.6777213e7);
check24(b*8388612.0, 8388609.0, GMP_RNDN, 8.388611e6);
check24(b*12582914.0, 8388610.0, GMP_RNDN, 1.2582911e7);
check24(b*12582913.0, 8388610.0, GMP_RNDN, 1.258291e7);
check24(b*8388610.0, 8388609.0, GMP_RNDZ, 8.388608e6);
check24(b*16777215.0, 16777213.0, GMP_RNDZ, 8.388609e6);
check24(b*8388612.0, 8388611.0, GMP_RNDZ, 8.388608e6);
check24(b*12582914.0, 12582911.0, GMP_RNDZ, 8.38861e6);
check24(12582913.0, 12582910.0, GMP_RNDZ, 1.000000238);
check24(b*16777215.0, 8388609.0, GMP_RNDZ, 1.6777213e7);
check24(b*8388612.0, 8388609.0, GMP_RNDZ, 8.38861e6);
check24(b*12582914.0, 8388610.0, GMP_RNDZ, 1.2582911e7);
check24(b*12582913.0, 8388610.0, GMP_RNDZ, 1.258291e7);
check24(b*8388610.0, 8388609.0, GMP_RNDU, 8.388609e6);
check24(b*16777215.0, 16777213.0, GMP_RNDU, 8.38861e6);
check24(b*8388612.0, 8388611.0, GMP_RNDU, 8.388609e6);
check24(b*12582914.0, 12582911.0, GMP_RNDU, 8.388611e6);
check24(12582913.0, 12582910.0, GMP_RNDU, 1.000000357);
check24(b*16777215.0, 8388609.0, GMP_RNDU, 1.6777214e7);
check24(b*8388612.0, 8388609.0, GMP_RNDU, 8.388611e6);
check24(b*12582914.0, 8388610.0, GMP_RNDU, 1.2582912e7);
check24(b*12582913.0, 8388610.0, GMP_RNDU, 1.2582911e7);
check24(b*8388610.0, 8388609.0, GMP_RNDD, 8.388608e6);
check24(b*16777215.0, 16777213.0, GMP_RNDD, 8.388609e6);
check24(b*8388612.0, 8388611.0, GMP_RNDD, 8.388608e6);
check24(b*12582914.0, 12582911.0, GMP_RNDD, 8.38861e6);
check24(12582913.0, 12582910.0, GMP_RNDD, 1.000000238);
check24(b*16777215.0, 8388609.0, GMP_RNDD, 1.6777213e7);
check24(b*8388612.0, 8388609.0, GMP_RNDD, 8.38861e6);
check24(b*12582914.0, 8388610.0, GMP_RNDD, 1.2582911e7);
check24(b*12582913.0, 8388610.0, GMP_RNDD, 1.258291e7);
}
void check_convergence()
{
mpfr_t x, y; int i, j;
mpfr_init2(x, 130);
mpfr_set_str_raw(x, "0.1011111101011010101000001010011111101000011100011101010011111011000011001010000000111100100111110011001010110100100001001000111001E6944");
mpfr_init2(y, 130);
mpfr_set_ui(y, 5, GMP_RNDN);
mpfr_div(x, x, y, GMP_RNDD); /* exact division */
mpfr_set_prec(x, 64);
mpfr_set_prec(y, 64);
mpfr_set_str_raw(x, "0.10010010011011010100101001010111100000101110010010101E55");
mpfr_set_str_raw(y, "0.1E585");
mpfr_div(x, x, y, GMP_RNDN);
mpfr_set_str_raw(y, "0.10010010011011010100101001010111100000101110010010101E-529");
if (mpfr_cmp(x, y)) {
fprintf(stderr, "Error in mpfr_div for prec=64, rnd=GMP_RNDN\n");
printf("got "); mpfr_print_raw(x); putchar('\n');
printf("instead of "); mpfr_print_raw(y); putchar('\n');
exit(1);
}
for (i=32; i<=64; i+=32) {
mpfr_set_prec(x, i);
mpfr_set_prec(y, i);
mpfr_set_d(x, 1.0, GMP_RNDN);
for (j=0;j<4;j++) {
mpfr_set_d(y, 1.0, GMP_RNDN);
mpfr_div(y, x, y, j);
if (mpfr_cmp_ui(y, 1)) {
fprintf(stderr, "mpfr_div failed for x=1.0, y=1.0, prec=%u rnd=%s\n",
i, mpfr_print_rnd_mode(j));
printf("got "); mpfr_print_raw(y); putchar('\n');
exit(1);
}
}
}
mpfr_clear(x); mpfr_clear(y);
}
int main(int argc, char *argv[])
{
int N; long long N2;
double z[1];
#ifdef TEST
int i; double n, d, e;
#ifdef __mips
/* to get denormalized numbers on IRIX64 */
union fpc_csr exp;
exp.fc_word = get_fpc_csr();
exp.fc_struct.flush = 0;
set_fpc_csr(exp.fc_word);
#endif
#endif
N = (argc>1) ? atoi(argv[1]) : 100000;
check_float(); /* checks single precision */
check_convergence();
check53(0.0, 1.0, GMP_RNDZ, 0.0);
check53(-7.4988969224688591e63, 4.8816866450288732e306, GMP_RNDD,
-1.5361282826510687291e-243);
check53(-1.33225773037748601769e+199, 3.63449540676937123913e+79, GMP_RNDZ,
-3.6655920045905428978e119);
check4(4.0, 4.503599627370496e15, GMP_RNDZ, 62, 0.0);
check4(1.0, 2.10263340267725788209e+187, GMP_RNDU, 65, 0.0);
check4(2.44394909079968374564e-150, 2.10263340267725788209e+187, GMP_RNDU,
65, 0.0);
check53(9.89438396044940256501e-134, 5.93472984109987421717e-67, GMP_RNDU,
1.6672003992376663654e-67);
check53(1.0, sqrt(-1.0), GMP_RNDD, sqrt(-1.0));
check53(sqrt(-1.0), 1.0, GMP_RNDD, sqrt(-1.0));
check53(2.0/0.0, 1.0, GMP_RNDD, 1.0/0.0);
check53(1.0, 2.0/0.0, GMP_RNDD, 0.0);
check53(0.0, 0.0, GMP_RNDD, sqrt(-1.0));
check53(1.0/0.0, 1.0/0.0, GMP_RNDD, sqrt(-1.0));
check53(9.89438396044940256501e-134, -5.93472984109987421717e-67, GMP_RNDU,
-1.6672003992376663654e-67);
check53(-4.53063926135729747564e-308, 7.02293374921793516813e-84, GMP_RNDD,
-6.4512060388748850857e-225);
check53(6.25089225176473806123e-01, -2.35527154824420243364e-230, GMP_RNDD,
-2.6540006635008291192e229);
check53(6.52308934689126e15, -1.62063546601505417497e273, GMP_RNDN,
-4.0250194961676020848e-258);
check53(1.04636807108079349236e-189, 3.72295730823253012954e-292, GMP_RNDZ,
2.810583051186143125e102);
#ifdef TEST
srand48(getpid());
for (i=0;i<N;i++) {
do { n = drand(); d = drand(); e = fabs(n)/fabs(d); }
/* smallest normalized is 2^(-1022), largest is 2^(1023)*(2-2^(-52)) */
while (e>=1.7976931348623157081e308 || e<2.225073858507201383e-308);
check4(n, d, rand() % 4, 53, 0.0);
}
#endif
return 0;
}
|
