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
|
# -*- mode: perl; -*-
use strict;
use warnings;
use Test::More tests => 12 + 42;
use Math::BigFloat;
note("batan() as a class method");
cmp_ok(Math::BigFloat -> batan("-inf"), "==",
"-1.570796326794896619231321691639751442098",
'Math::BigFloat -> batan("-inf")');
cmp_ok(Math::BigFloat -> batan("-2"), "==",
"-1.107148717794090503017065460178537040070",
'Math::BigFloat -> batan("-2")');
cmp_ok(Math::BigFloat -> batan(0), "==", "0",
'Math::BigFloat -> batan(0)');
cmp_ok(Math::BigFloat -> batan("2"), "==",
"1.107148717794090503017065460178537040070",
'Math::BigFloat -> batan("2")');
cmp_ok(Math::BigFloat -> batan("inf"), "==",
"1.570796326794896619231321691639751442098",
'Math::BigFloat -> batan("inf")');
is(Math::BigFloat -> batan("NaN"), "NaN",
'Math::BigFloat -> batan("NaN")');
note("batan() as an instance method");
cmp_ok(Math::BigFloat -> new("-inf") -> batan(), "==",
"-1.570796326794896619231321691639751442098",
'Math::BigFloat -> new("-inf")');
cmp_ok(Math::BigFloat -> new("-2") -> batan(), "==",
"-1.107148717794090503017065460178537040070",
'Math::BigFloat -> new("-2")');
cmp_ok(Math::BigFloat -> new(0) -> batan(), "==", "0",
'Math::BigFloat -> new(0)');
cmp_ok(Math::BigFloat -> new("2") -> batan(), "==",
"1.107148717794090503017065460178537040070",
'Math::BigFloat -> new("2")');
cmp_ok(Math::BigFloat -> new("inf") -> batan(), "==",
"1.570796326794896619231321691639751442098",
'Math::BigFloat -> new("inf")');
is(Math::BigFloat -> new("NaN") -> batan(), "NaN",
'Math::BigFloat -> new("NaN")');
################################################################################
use Math::Complex ();
my $inf = $Math::Complex::Inf;
my $nan = $inf - $inf;
my $class = 'Math::BigFloat';
# atan X
sub atan { atan2($_[0], 1) }
# isnan X
sub isnan { $_[0] != $_[0] }
# linspace MIN, MAX, N
#
# Returns N linearly spaced elements from MIN to MAX.
sub linspace {
my ($xmin, $xmax, $n) = @_;
if ($n == 0) {
return ();
} elsif ($n == 1) {
return ($xmin);
} else {
my $c = ($xmax - $xmin) / ($n - 1);
return map { $xmin + $c * $_ } 0 .. ($n - 1);
}
}
# logspace MIN, MAX, N
#
# Returns N logarithmically spaced elements from MIN to MAX.
sub logspace {
my ($xmin, $xmax, $n) = @_;
if ($n == 0) {
return ();
} elsif ($n == 1) {
return ($xmin);
} else {
my @lin = linspace(log($xmin), log($xmax), $n);
my @log = map { exp } @lin;
$log[ 0 ] = $xmin;
$log[ $#log ] = $xmax;
return @log;
}
}
my @x;
@x = logspace(0.01, 12, 20);
@x = map { sprintf "%.3g", $_ } @x;
@x = (reverse(map( { -$_ } @x)), 0, @x, $nan);
my $accu = 16;
my $tol = 1e-13;
my $max_relerr = 0;
for (my $i = 0; $i <= $#x ; ++$i) {
my $x = $x[$i];
my $pl = atan($x);
my $bf = $class -> new("$x") -> batan($accu);
my $desc = qq|$class->new("$x")->batan($accu) vs. CORE::atan2("$x", 1)|;
if (isnan($x)) {
is($bf, "NaN", $desc);
} elsif ($x == 0) {
cmp_ok($bf, '==', $pl, $desc);
} else {
my $relerr = abs(($bf - $pl) / $pl); # relative error
#printf("# %23.15e %23.15e %23.15e %23.15e\n", $x, $pl, $bf, $relerr);
cmp_ok($relerr, '<', $tol, "relative error of $desc");
$max_relerr = $relerr if $relerr > $max_relerr;
}
}
diag("Maximum relative error = ", $max_relerr -> numify(), "\n");
|
