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
|
# Test file for Rmpfr_asinpi(), Rmpfr_acospi(), Rmpfr_atanpi(), Rmpfr_atan2pi(),
# and also for Rmpfr_asinu(), Rmpfr_acosu(), Rmpfr_atanu() anf Rmpfr_atan2u().
use strict;
use warnings;
use Config;
use Test::More;
use Math::MPFR qw(:mpfr);
my $inex;
my $has_420 = 0;
$has_420++ if MPFR_VERSION() >= 262656; # mpfr-4.2.0 or later
my $rop = Math::MPFR->new();
my $rop2 = Math::MPFR->new();
my $ropu = Math::MPFR->new();
my $roppi = Math::MPFR->new();
my $pi = Math::MPFR->new('3.1415926535897931');
my $op = Math::MPFR->new('0.5');
my $op2 = Math::MPFR->new('0.7');
my $pinf = Math::MPFR->new();
my $ui = 128;
Rmpfr_set_inf($pinf, 1);
my $ninf = $pinf * -1;
if($has_420) {
#### acos ####
Rmpfr_acos ($rop, $op, MPFR_RNDN);
Rmpfr_acospi($roppi, $op, MPFR_RNDN);
Rmpfr_acosu ($ropu, $op, 128, MPFR_RNDN);
# $ropu = $rop * 128 / (2 * $pi)
my $rop_check = ($rop * 128) / (2 * $pi);
cmp_ok(abs($ropu - $rop_check), '<', 1e-14, "Rmpfr_acosu in range ($ropu | $rop_check");
$inex = Rmpfr_acosu($rop2, Math::MPFR->new(0.5), 360, MPFR_RNDN);
cmp_ok( $rop2, '==', 60, "inverse cosine of 0.5 is 60 degrees");
cmp_ok($inex, '==', 0, 'result was exact');
# $roppi = $rop / $pi
$rop_check = $rop / $pi;
cmp_ok(abs($roppi - $rop_check), '<', 1e-16, "Rmpfr_acospi in range ($roppi | $rop_check");
$inex = Rmpfr_acospi($rop2, Math::MPFR->new(-1), MPFR_RNDN);
cmp_ok($rop2, '==', 1, 'acospi(-1) is 1');
cmp_ok($inex, '==', 0, 'result was exact');
$inex = Rmpfr_acospi($rop2, Math::MPFR->new(0), MPFR_RNDN);
cmp_ok($rop2, '==', 0.5, 'acospi(0) is 0.5');
cmp_ok($inex, '==', 0, 'result was exact');
### asin ###
Rmpfr_asin ($rop, $op, MPFR_RNDN);
Rmpfr_asinpi($roppi, $op, MPFR_RNDN);
Rmpfr_asinu ($ropu, $op, 128, MPFR_RNDN);
$inex = Rmpfr_asinu($rop2, Math::MPFR->new(0.5), 360, MPFR_RNDN);
cmp_ok( $rop2, '==', 30, "inverse sine of 0.5 is 30 degrees");
cmp_ok($inex, '==', 0, 'result was exact');
# $ropu = $rop * 128 / (2 * $pi)
$rop_check = ($rop * 128) / (2 * $pi);
cmp_ok(abs($ropu - $rop_check), '<', 1e-14, "Rmpfr_asinu in range ($ropu | $rop_check");
# $roppi = $rop / $pi
$rop_check = $rop / $pi;
cmp_ok(abs($roppi - $rop_check), '<', 1e-16, "Rmpfr_asinpi in range ($roppi | $rop_check");
$inex = Rmpfr_asinpi($rop2, Math::MPFR->new(0), MPFR_RNDN);
cmp_ok($rop2, '==', 0, 'asinpi(0) is 0');
cmp_ok($inex, '==', 0, 'result was exact');
$inex = Rmpfr_asinpi($rop2, Math::MPFR->new(1), MPFR_RNDN);
cmp_ok($rop2, '==', 0.5, 'asinpi(1) is 0.5');
cmp_ok($inex, '==', 0, 'result was exact');
$inex = Rmpfr_asinpi($rop2, Math::MPFR->new(-1), MPFR_RNDN);
cmp_ok($rop2, '==', -0.5, 'asinpi(-1) is -0.5');
cmp_ok($inex, '==', 0, 'result was exact');
### atan ###
Rmpfr_atan ($rop, $op, MPFR_RNDN);
Rmpfr_atanpi($roppi, $op, MPFR_RNDN);
Rmpfr_atanu ($ropu, $op, 128, MPFR_RNDN);
# $ropu = $rop * 128 / (2 * $pi)
$rop_check = ($rop * 128) / (2 * $pi);
cmp_ok(abs($ropu - $rop_check), '==', 0, "Rmpfr_atanu in range ($ropu | $rop_check"); # 1e-14
$inex = Rmpfr_atanu($rop2, Math::MPFR->new(1), 360, MPFR_RNDN);
cmp_ok( $rop2, '==', 45, "inverse tan of 1 is 45 degrees");
cmp_ok($inex, '==', 0, 'result was exact');
# $roppi = $rop / $pi
$rop_check = $rop / $pi;
cmp_ok(abs($roppi - $rop_check), '==', 0, "Rmpfr_atanpi in range ($roppi | $rop_check"); # 1e-16
$inex = Rmpfr_atanpi($rop2, Math::MPFR->new(0), MPFR_RNDN);
cmp_ok("$rop2", 'eq', '0', 'atanpi(0) is 0');
cmp_ok($inex, '==', 0, 'result was exact');
$inex = Rmpfr_atanpi($rop2, $pinf, MPFR_RNDN);
cmp_ok($rop2, '==', 0.5, 'atanpi(Inf) is 0.5');
cmp_ok($inex, '==', 0, 'result was exact');
$inex = Rmpfr_atanpi($rop2, $ninf, MPFR_RNDN);
cmp_ok($rop2, '==', -0.5, 'atanpi(-Inf) is -0.5');
cmp_ok($inex, '==', 0, 'result was exact');
$inex = Rmpfr_atanpi($rop2, Math::MPFR->new(1), MPFR_RNDN);
cmp_ok($rop2, '==', 0.25, 'atanpi(1) is 0.25');
cmp_ok($inex, '==', 0, 'result was exact');
$inex = Rmpfr_atanpi($rop2, Math::MPFR->new(-1), MPFR_RNDN);
cmp_ok($rop2, '==', -0.25, 'atanpi(-1) is -0.25');
cmp_ok($inex, '==', 0, 'result was exact');
#### atan2 ####
Rmpfr_atan2 ($rop, $op, $op2, MPFR_RNDN);
Rmpfr_atan2pi($roppi, $op, $op2, MPFR_RNDN);
Rmpfr_atan2u ($ropu, $op, $op2, 128, MPFR_RNDN);
# $ropu = ($rop * 128) / (2 * $pi)
$rop_check = ($rop * 128) / (2 * $pi);
cmp_ok(abs($ropu - $rop_check), '==', 0, "Rmpfr_atan2u in range ($ropu | $rop_check"); # 1e-14
Rmpfr_atan2u ($rop_check, $op, $op2, 2, MPFR_RNDN);
cmp_ok(abs($roppi - $rop_check), '==', 0, "Rmpfr_atan2pi in range ($roppi | $rop_check"); # 1e-16
}
else {
for (qw(Rmpfr_acosu Rmpfr_acospi Rmpfr_asinu Rmpfr_asinpi Rmpfr_atanu Rmpfr_atanpi Rmpfr_atan2u Rmpfr_atan2pi)) {
if($_ =~ /u/) { version_check($_, 'u') }
else { version_check($_, 'pi') }
}
}
done_testing();
sub version_check{
my $f = shift;
my $which = shift;
my $op = Math::MPFR->new('0.5');
my $s;
if($which eq 'pi') {
if($f =~ /2/) { $s = "$f(\$op, \$op, \$op, MPFR_RNDN)" } # atan2
else { $s = "$f(\$op, \$op, MPFR_RNDN)" }
eval( $s );
}
else {
if($f =~ /2/) { $s = "$f(\$op, \$op, \$op, 7, MPFR_RNDN)" } # atan2
else { $s = "$f(\$op, \$op, 7, MPFR_RNDN)" }
eval( $s );
}
like($@, qr/^$f function not implemented until/, "$f not implemented");
}
|
