Elliptic curve arithmetic: Difference between revisions
Rename Perl 6 -> Raku, alphabetize, minor clean-up
Thundergnat (talk | contribs) (Rename Perl 6 -> Raku, alphabetize, minor clean-up) |
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check alignment... ok
</pre>
=={{header|Phix}}==
Line 1,299 ⟶ 1,243:
p*12345 #(10.758570529320806 35.387434774282106)
</lang>
=={{header|Raku}}==
(formerly Perl 6)
<lang perl6>unit module EC;
our ($A, $B) = (0, 7);
role Horizon { method gist { 'EC Point at horizon' } }
class Point {
has ($.x, $.y);
multi method new(
$x, $y where $y**2 ~~ $x**3 + $A*$x + $B
) { self.bless(:$x, :$y) }
multi method new(Horizon $) { self.bless but Horizon }
method gist { "EC Point at x=$.x, y=$.y" }
}
multi prefix:<->(Point $p) { Point.new: x => $p.x, y => -$p.y }
multi prefix:<->(Horizon $) { Horizon }
multi infix:<->(Point $a, Point $b) { $a + -$b }
multi infix:<+>(Horizon $, Point $p) { $p }
multi infix:<+>(Point $p, Horizon) { $p }
multi infix:<*>(Point $u, Int $n) { $n * $u }
multi infix:<*>(Int $n, Horizon) { Horizon }
multi infix:<*>(0, Point) { Horizon }
multi infix:<*>(1, Point $p) { $p }
multi infix:<*>(2, Point $p) {
my $l = (3*$p.x**2 + $A) / (2 *$p.y);
my $y = $l*($p.x - my $x = $l**2 - 2*$p.x) - $p.y;
$p.bless(:$x, :$y);
}
multi infix:<*>(Int $n where $n > 2, Point $p) {
2 * ($n div 2 * $p) + $n % 2 * $p;
}
multi infix:<+>(Point $p, Point $q) {
if $p.x ~~ $q.x {
return $p.y ~~ $q.y ?? 2 * $p !! Horizon;
}
else {
my $slope = ($q.y - $p.y) / ($q.x - $p.x);
my $y = $slope*($p.x - my $x = $slope**2 - $p.x - $q.x) - $p.y;
return $p.new(:$x, :$y);
}
}
say my $p = Point.new: x => $_, y => sqrt(abs($_**3 + $A*$_ + $B)) given 1;
say my $q = Point.new: x => $_, y => sqrt(abs($_**3 + $A*$_ + $B)) given 2;
say my $s = $p + $q;
say "checking alignment: ", abs ($p.x - $q.x)*(-$s.y - $q.y) - ($p.y - $q.y)*($s.x - $q.x);</lang>
{{out}}
<pre>EC Point at x=1, y=2.8284271247461903
EC Point at x=2, y=3.872983346207417
EC Point at x=-1.9089023002066448, y=0.21008487055753378
checking alignment: 0</pre>
=={{header|REXX}}==
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