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
|
/* shared routines for mpcheck-xxx
Copyright (C) 2020 INRIA
This file is part of GNU MPC.
GNU MPC 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 3 of the License, or (at your
option) any later version.
GNU MPC 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 this program. If not, see http://www.gnu.org/licenses/ .
*/
#include <sys/types.h>
#include <sys/resource.h>
unsigned long Max_err_re = 0, Max_err_im = 0;
unsigned long Max_err = 0; /* for real-valued functions like abs */
int recheck = 0;
/* y is the reference value computed by MPC */
static unsigned long
ulp_error (mpfr_t x, mpfr_t y)
{
mpfr_t z;
mpfr_prec_t p = mpfr_get_prec (y);
unsigned long n, special = 0;
mpfr_exp_t e;
if (mpfr_cmp (x, y) == 0)
return 0;
assert (!mpfr_nan_p (x));
assert (!mpfr_nan_p (y));
if (mpfr_inf_p (x) || mpfr_inf_p (y))
{
if (mpfr_number_p (x) && mpfr_inf_p (y))
{
/* only MPFR returns Inf: we replace y by the maximal
floating-point number */
if (mpfr_sgn (y) > 0) /* +Inf */
mpfr_nextbelow (y);
else
mpfr_nextabove (y);
special = 1;
}
else
{
/* only glibc returns Inf */
if (mpfr_sgn (x) > 0) /* +Inf */
mpfr_nextbelow (x);
else
mpfr_nextabove (x);
special = 2;
}
}
mpfr_init2 (z, p);
mpfr_sub (z, x, y, MPFR_RNDN);
mpfr_abs (z, z, MPFR_RNDN);
/* divide by ulp(y) = 2^(EXP(y) - p) */
e = mpfr_get_exp (y) - p;
/* take into account subnormals: smallest number is 2^(emin-1) */
if (e < emin - 1)
e = emin - 1;
mpfr_div_2si (z, z, e, MPFR_RNDN);
n = mpfr_get_ui (z, MPFR_RNDZ);
mpfr_clear (z);
if (special == 1) /* restore original y */
{
if (mpfr_sgn (y) > 0)
mpfr_nextabove (y);
else
mpfr_nextbelow (y);
}
if (special == 2) /* restore original x */
{
if (mpfr_sgn (x) > 0)
mpfr_nextabove (x);
else
mpfr_nextbelow (x);
}
if (special == 0)
return n;
else
return (n < ULONG_MAX) ? n + 1 : n;
}
static void
mpcheck_random (mpc_t z)
{
unsigned long erange;
mpc_urandom (z, state);
/* set sign and exponent of the real part */
mpz_set_ui (expz, 2 * (emax - emin + 1));
mpz_urandomm (expz, state, expz);
erange = mpz_get_ui (expz);
/* bit 0 of erange gives the sign */
if (erange & 1)
mpfr_neg (mpc_realref (z), mpc_realref (z), MPFR_RNDN);
mpfr_set_exp (mpc_realref (z), emin + (erange >> 1));
/* make sure the numbers are representable in IEEE format */
mpfr_subnormalize (mpc_realref (z), 0, MPFR_RNDN);
/* set sign and exponent of the imaginary part */
mpz_set_ui (expz, 2 * (emax - emin + 1));
mpz_urandomm (expz, state, expz);
erange = mpz_get_ui (expz);
/* bit 0 of erange gives the sign */
if (erange & 1)
mpfr_neg (mpc_imagref (z), mpc_imagref (z), MPFR_RNDN);
mpfr_set_exp (mpc_imagref (z), emin + (erange >> 1));
/* make sure the numbers are representable in IEEE format */
mpfr_subnormalize (mpc_imagref (z), 0, MPFR_RNDN);
}
/* y is the reference value computed with MPC:
* return 0 if x and y are equal (including both NaN or Inf)
* return 1 if x and y disagree (neither NaN nor Inf)
* return 2 if x is NaN but not y
* return 4 if x and y are infinities of different signs
*/
static int
mpcheck_mpfr_cmp (mpfr_t x, mpfr_t y)
{
if (mpfr_number_p (x) && mpfr_number_p (y))
return mpfr_cmp (x, y);
/* now either x or y is NaN or Inf */
if (mpfr_nan_p (x) || mpfr_nan_p (y))
{
if (mpfr_nan_p (x) && mpfr_nan_p (y))
return 0;
if (mpfr_nan_p (x))
return 2;
fprintf (stderr, "Error, NaN and not NaN\n");
exit (1);
}
/* now either x or y is Inf */
if (mpfr_inf_p (x) && mpfr_inf_p (y))
{
if (mpfr_sgn (x) * mpfr_sgn (y) > 0)
return 0;
return 4;
}
return 1; /* Inf and non-Inf: differ, will be treated by ulp_error */
}
/* y is the reference value computed with MPC */
static int
mpcheck_mpc_cmp (mpc_t x, mpc_t y)
{
return mpcheck_mpfr_cmp (mpc_realref (x), mpc_realref (y)) |
mpcheck_mpfr_cmp (mpc_imagref (x), mpc_imagref (y));
}
static void
report_maximal_errors (void)
{
printf ("Maximal errors: %lu (real), %lu (imag), %lu (abs/arg)\n",
Max_err_re, Max_err_im, Max_err);
}
/* return non-zero if both a and b are NaN, or if both are not NaN
and are equal */
static int
mpfr_agree (mpfr_t a, mpfr_t b, int inex)
{
if (mpfr_nan_p (a) || mpfr_nan_p (b))
return mpfr_nan_p (a) && mpfr_nan_p (b);
else
/* in the case of even rounding, we can't tell for sure */
return mpfr_equal_p (a, b) || inex == 2 || inex == -2;
}
static int
cputime (void)
{
struct rusage rus;
getrusage (0, &rus);
return rus.ru_utime.tv_sec * 1000 + rus.ru_utime.tv_usec / 1000;
}
|
