/
Rat.pm
140 lines (108 loc) · 3.72 KB
/
Rat.pm
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
class Rat does Real {
has $.numerator;
has $.denominator;
sub gcd(Int $a is copy, Int $b is copy) {
$a = -$a if ($a < 0);
$b = -$b if ($b < 0);
while $a > 0 && $b > 0 {
($a, $b) = ($b, $a) if ($b > $a);
$a %= $b;
}
return $a + $b;
}
multi method new() {
self.bless(*, :numerator(0), :denominator(1));
}
multi method new(Int $numerator is copy, Int $denominator is copy) {
if $denominator < 0 {
$numerator = -$numerator;
$denominator = -$denominator;
}
my $gcd = gcd($numerator, $denominator);
$numerator = $numerator div $gcd;
$denominator = $denominator div $gcd;
self.bless(*, :numerator($numerator), :denominator($denominator));
}
multi method ACCEPTS($other) {
self.Num.ACCEPTS($other);
}
multi method perl() { "$!numerator/$!denominator"; }
method Bridge() {
$!denominator == 0 ?? Inf * $!numerator.sign
!! $!numerator.Bridge / $!denominator.Bridge;
}
our Bool multi method Bool() { $!numerator != 0 ?? Bool::True !! Bool::False }
multi method Num() {
$!denominator == 0 ?? Inf * $!numerator.sign
!! $!numerator.Num / $!denominator.Num;
}
multi method Rat() { self; }
multi method Int() { self.Num.Int; }
multi method Str() { $.Num.Str; }
multi method nude() { $.numerator, $.denominator; }
# Most of the trig functions for Rat are in Any-num.pm, but
# sec is a special case.
our Num multi method sec($base = Radians) {
self.Num.sec($base);
}
multi method succ {
Rat.new($!numerator + $!denominator, $!denominator);
}
multi method pred {
Rat.new($!numerator - $!denominator, $!denominator);
}
}
multi sub infix:<+>(Rat $a, Rat $b) {
my $gcd = Rat::gcd($a.denominator, $b.denominator);
($a.numerator * ($b.denominator div $gcd) + $b.numerator * ($a.denominator div $gcd))
/ (($a.denominator div $gcd) * $b.denominator);
}
multi sub infix:<+>(Rat $a, Int $b) {
($a.numerator + $b * $a.denominator) / $a.denominator;
}
multi sub infix:<+>(Int $a, Rat $b) {
($a * $b.denominator + $b.numerator) / $b.denominator;
}
multi sub infix:<->(Rat $a, Rat $b) {
my $gcd = Rat::gcd($a.denominator, $b.denominator);
($a.numerator * ($b.denominator div $gcd) - $b.numerator * ($a.denominator div $gcd))
/ (($a.denominator div $gcd) * $b.denominator);
}
multi sub infix:<->(Rat $a, Int $b) {
($a.numerator - $b * $a.denominator) / $a.denominator;
}
multi sub infix:<->(Int $a, Rat $b) {
($a * $b.denominator - $b.numerator) / $b.denominator;
}
multi sub prefix:<->(Rat $a) {
Rat.new(-$a.numerator, $a.denominator);
}
multi sub infix:<*>(Rat $a, Rat $b) {
($a.numerator * $b.numerator) / ($a.denominator * $b.denominator);
}
multi sub infix:<*>(Rat $a, Int $b) {
($a.numerator * $b) / $a.denominator;
}
multi sub infix:<*>(Int $a, Rat $b) {
($a * $b.numerator) / $b.denominator;
}
multi sub infix:</>(Rat $a, Rat $b) {
($a.numerator * $b.denominator) / ($a.denominator * $b.numerator);
}
multi sub infix:</>(Rat $a, Int $b) {
$a.numerator / ($a.denominator * $b);
}
multi sub infix:</>(Int $a, Rat $b) {
($b.denominator * $a) / $b.numerator;
}
multi sub infix:</>(Int $a, Int $b) {
Rat.new($a, $b);
}
multi sub infix:<cmp>(Rat $a, Rat $b) { $a.Num <=> $b.Num; }
multi sub infix:<cmp>(Rat $a, $b) { $a.Num <=> $b.Num; }
multi sub infix:<cmp>($a, Rat $b) { $a.Num <=> $b.Num; }
augment class Int {
# CHEAT: Comes from Int.pm, moved here for the moment.
our Rat multi method Rat() { Rat.new(self, 1); }
}
# vim: ft=perl6 sw=4 ts=4 expandtab