Created
December 12, 2012 22:29
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modular integers in Perl6
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class Modular does Real { | |
our $.Modulus; | |
has ($.residue, $.modulus); | |
multi method new($residue, :$modulus where * > 1) { self.new: :residue($residue % $modulus), :$modulus } | |
method Bridge { $.residue % $.modulus } | |
multi method gist { "{self.Bridge} 「mod $.modulus」" } | |
method succ { self.Bridge.succ % $.modulus } | |
multi method Inverse { | |
return Mu unless $.residue gcd $.modulus == 1; | |
my ($c, $d, $uc, $vc, $ud, $vd) = ($.residue, $.modulus, 1, 0, 0, 1); | |
my $q; | |
while $c != 0 { | |
($q, $c, $d) = ($d div $c, $d % $c, $c); | |
($uc, $vc, $ud, $vd) = ($ud - $q*$uc, $vd - $q*$vc, $uc, $vc); | |
} | |
return self.new: $ud < 0 ?? $ud + $.modulus !! $ud, :$.modulus; | |
} | |
} | |
sub mod($residue, $modulus = $Modular::Modulus) is export returns Modular { Modular.new: :$residue, :$modulus } | |
multi prefix:<->(Modular $a) is export returns Modular { Modular.new: -$a.Bridge, :modulus($a.modulus) } | |
multi infix:<->(Modular $a, Modular $b where $a.modulus ~~ $b.modulus) is export returns Modular { | |
Modular.new: $a.Bridge - $b.Bridge, :modulus($a.modulus) | |
} | |
proto infix:<+>($, $) is export returns Modular {*} | |
multi infix:<+>(Modular $a, Int $b) { Modular.new: $b + $a.Bridge, :modulus($a.modulus) } | |
multi infix:<+>(Int $a, Modular $b) { Modular.new: $a + $b.Bridge, :modulus($b.modulus) } | |
multi infix:<+>(Modular $a, Modular $b where $a.modulus ~~ $b.modulus) { | |
Modular.new: $a.Bridge + $b.Bridge, :modulus($a.modulus) | |
} | |
proto infix:<*>($, $) is export returns Modular {*} | |
multi infix:<*>(Int $a, Modular $b) { Modular.new: $a * $b.Bridge, :modulus($b.modulus) } | |
multi infix:<*>(Modular $a, Int $b) { Modular.new: $b * $a.Bridge, :modulus($a.modulus) } | |
multi infix:<*>(Modular $a, Modular $b where $a.modulus ~~ $b.modulus) { | |
Modular.new: $a.Bridge * $b.Bridge, :modulus($a.modulus) | |
} | |
proto infix:<div>($, $) is export returns Modular {*} | |
multi infix:<div>($a, Modular $b where $a.modulus ~~ $b.modulus) { $a * $b.Inverse } | |
proto infix:</>($, $) is export returns Modular {*} | |
multi infix:<div>(Modular $a, Modular $b where $a.modulus ~~ $b.modulus) { $a div $b } | |
proto infix:<**>($, $) is export returns Modular {*} | |
multi infix:<**>(Modular $a, Int $e) { | |
Modular.new: $a.Bridge.expmod($e, $a.modulus), :modulus($a.modulus) | |
} | |
# vim: ft=perl6 |
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