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
|
# -*- mode: perl; -*-
use strict;
use warnings;
use Test::More tests => 106;
use Math::BigRat;
subtest "Called as class method without argument.", sub {
# With no argument, the default div_scale of 40 is used.
my $x = Math::BigRat -> bpi();
isa_ok($x, 'Math::BigRat');
# Compute reference value with Math::BigFloat and compare.
my $mbf_ref = Math::BigFloat -> bpi(50);
my $rel_err = $x -> as_float(50) -> bsub($mbf_ref) -> bdiv($mbf_ref);
$rel_err -> babs() -> bround(5);
my $rel_tol = Math::BigFloat -> new("1e-40");
my $rel_err_num = $rel_err -> numify();
my $rel_tol_num = $rel_tol -> numify();
ok(abs($rel_err) < $rel_tol);
note(sprintf(<<"EOF", $rel_err_num, $rel_tol_num));
relative error: %+.5e
relative tolerance: %+.5e
EOF
};
subtest "Called as class method with scalar argument.", sub {
my $x = Math::BigRat -> bpi(16);
isa_ok($x, 'Math::BigRat');
# Compute reference value with Math::BigFloat and compare.
my $mbf_ref = Math::BigFloat -> bpi(26);
my $rel_err = $x -> as_float(26) -> bsub($mbf_ref) -> bdiv($mbf_ref);
$rel_err -> babs() -> bround(5);
my $rel_tol = Math::BigFloat -> new("1e-16");
my $rel_err_num = $rel_err -> numify();
my $rel_tol_num = $rel_tol -> numify();
ok(abs($rel_err) < $rel_tol);
note(sprintf(<<"EOF", $rel_err_num, $rel_tol_num));
relative error: %+.5e
relative tolerance: %+.5e
EOF
};
subtest "Called as class method with instance argument.", sub {
my $n = Math::BigRat -> new("16");
my $x = Math::BigRat -> bpi($n);
isa_ok($x, 'Math::BigRat');
# Compute reference value with Math::BigFloat and compare.
my $mbf_ref = Math::BigFloat -> bpi(26);
my $rel_err = $x -> as_float(26) -> bsub($mbf_ref) -> bdiv($mbf_ref);
my $rel_tol = Math::BigFloat -> new("1e-16");
$rel_err -> babs() -> bround(5);
my $rel_err_num = $rel_err -> numify();
my $rel_tol_num = $rel_tol -> numify();
ok(abs($rel_err) < $rel_tol);
note(sprintf(<<"EOF", $rel_err_num, $rel_tol_num));
relative error: %+.5e
relative tolerance: %+.5e
EOF
};
subtest "Called as instance method without argument.", sub {
# With no argument, the default div_scale of 40 is used.
my $x = Math::BigRat -> bnan();
$x -> bpi();
isa_ok($x, 'Math::BigRat');
# Compute reference value with Math::BigFloat and compare.
my $mbf_ref = Math::BigFloat -> bpi(50);
my $rel_err = $x -> as_float(50) -> bsub($mbf_ref) -> bdiv($mbf_ref);
$rel_err -> babs() -> bround(5);
my $rel_tol = Math::BigFloat -> new("1e-40");
my $rel_err_num = $rel_err -> numify();
my $rel_tol_num = $rel_tol -> numify();
ok(abs($rel_err) < $rel_tol);
note(sprintf(<<"EOF", $rel_err_num, $rel_tol_num));
relative error: %+.5e
relative tolerance: %+.5e
EOF
};
subtest "Called as instance method with scalar argument.", sub {
my $x = Math::BigRat -> bnan();
$x -> bpi(16);
isa_ok($x, 'Math::BigRat');
# Compute reference value with Math::BigFloat and compare.
my $mbf_ref = Math::BigFloat -> bpi(26);
my $rel_err = $x -> as_float(26) -> bsub($mbf_ref) -> bdiv($mbf_ref);
$rel_err -> babs() -> bround(5);
my $rel_tol = Math::BigFloat -> new("1e-16");
my $rel_err_num = $rel_err -> numify();
my $rel_tol_num = $rel_tol -> numify();
ok(abs($rel_err) < $rel_tol);
note(sprintf(<<"EOF", $rel_err_num, $rel_tol_num));
relative error: %+.5e
relative tolerance: %+.5e
EOF
};
subtest "Called as instance method with instance argument.", sub {
my $n = Math::BigRat -> new("16");
my $x = Math::BigRat -> bnan();
$x -> bpi($n);
isa_ok($x, 'Math::BigRat');
# Compute reference value with Math::BigFloat and compare.
my $mbf_ref = Math::BigFloat -> bpi(26);
my $rel_err = $x -> as_float(26) -> bsub($mbf_ref) -> bdiv($mbf_ref);
$rel_err -> babs() -> bround(5);
my $rel_tol = Math::BigFloat -> new("1e-16");
my $rel_err_num = $rel_err -> numify();
my $rel_tol_num = $rel_tol -> numify();
ok(abs($rel_err) < $rel_tol);
note(sprintf(<<"EOF", $rel_err_num, $rel_tol_num));
relative error: %+.5e
relative tolerance: %+.5e
EOF
};
for my $n (1 .. 100) {
note "\nMath::BigRat -> bpi($n);\n\n";
# Compute rational approximation of PI.
my $mbr = Math::BigRat -> bpi($n);
# Convert rational approximation to a floating point number using some
# extra digits.
my $mbf = $mbr -> as_float($n + 10);
# Compute reference value, again using some extra digits.
my $mbf_ref = Math::BigFloat -> bpi($n + 10);
# Compute the absolute error.
my $abs_err = $mbf - $mbf_ref;
# Compute the relative error.
my $rel_err = $abs_err / $mbf_ref;
my $rel_tol = Math::BigFloat -> new("0.1") -> bpow($n);
my $rel_err_num = $rel_err -> numify();
my $rel_tol_num = $rel_tol -> numify();
ok(abs($rel_err) < $rel_tol);
note(sprintf(<<"EOF", $rel_err_num, $rel_tol_num));
relative error: %+.5e
relative tolerance: %+.5e
EOF
};
|
