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#
# Perl5 Package for complex numbers
#
# 1994 by David Nadler
# Coding know-how provided by Tom Christiansen, Tim Bunce, and Larry Wall
# sqrt() added by Tom Christiansen; beware should have two roots,
# but only returns one. (use wantarray?)
#
#
# The functions "Re", "Im", and "arg" are provided.
# "~" is used as the conjugation operator and "abs" is overloaded.
#
# Transcendental functions overloaded: so far only sin, cos, and exp.
#
package Math::Complex;
require Exporter;
@ISA = ('Exporter');
# just to make use happy
%OVERLOAD= (
'+' => sub { my($x1,$y1,$x2,$y2) = (@{$_[0]},@{$_[1]});
bless [ $x1+$x2, $y1+$y2];
},
'-' => sub { my($x1,$y1,$x2,$y2) = (@{$_[0]},@{$_[1]});
bless [ $x1-$x2, $y1-$y2];
},
'*' => sub { my($x1,$y1,$x2,$y2) = (@{$_[0]},@{$_[1]});
bless [ $x1*$x2-$y1*$y2,$x1*$y2+$x2*$y1];
},
'/' => sub { my($x1,$y1,$x2,$y2) = (@{$_[0]},@{$_[1]});
my $q = $x2*$x2+$y2*$y2;
bless [($x1*$x2+$y1*$y2)/$q, ($y1*$x2-$y2*$x1)/$q];
},
'neg' => sub { my($x,$y) = @{$_[0]}; bless [ -$x, -$y];
},
'~' => sub { my($x,$y) = @{$_[0]}; bless [ $x, -$y];
},
'abs' => sub { my($x,$y) = @{$_[0]}; sqrt $x*$x+$y*$y;
},
'cos' => sub { my($x,$y) = @{$_[0]};
my ($ab,$c,$s) = (exp $y, cos $x, sin $x);
my $abr = 1/(2*$ab); $ab /= 2;
bless [ ($abr+$ab)*$c, ($abr-$ab)*$s];
},
'sin' => sub { my($x,$y) = @{$_[0]};
my ($ab,$c,$s) = (exp $y, cos $x, sin $x);
my $abr = 1/(2*$ab); $ab /= 2;
bless [ (-$abr-$ab)*$s, ($abr-$ab)*$c];
},
'exp' => sub { my($x,$y) = @{$_[0]};
my ($ab,$c,$s) = (exp $x, cos $y, sin $y);
bless [ $ab*$c, $ab*$s ];
},
'sqrt' => sub {
my($zr,$zi) = @{$_[0]};
my ($x, $y, $r, $w);
my $c = new Math::Complex (0,0);
if (($zr == 0) && ($zi == 0)) {
# nothing, $c already set
}
else {
$x = abs($zr);
$y = abs($zi);
if ($x >= $y) {
$r = $y/$x;
$w = sqrt($x) * sqrt(0.5*(1.0+sqrt(1.0+$r*$r)));
}
else {
$r = $x/$y;
$w = sqrt($y) * sqrt($y) * sqrt(0.5*($r+sqrt(1.0+$r*$r)));
}
if ( $zr >= 0) {
@$c = ($w, $zi/(2 * $w) );
}
else {
$c->[1] = ($zi >= 0) ? $w : -$w;
$c->[0] = $zi/(2.0* $c->[1]);
}
}
return $c;
},
qw("" stringify)
);
sub new {
shift;
my @C = @_;
bless \@C;
}
sub Re {
my($x,$y) = @{$_[0]};
$x;
}
sub Im {
my($x,$y) = @{$_[0]};
$y;
}
sub arg {
my($x,$y) = @{$_[0]};
atan2($y,$x);
}
sub stringify {
my($x,$y) = @{$_[0]};
my($re,$im);
$re = $x if ($x);
if ($y == 1) {$im = 'i';}
elsif ($y == -1){$im = '-i';}
elsif ($y) {$im = "${y}i"; }
local $_ = $re.'+'.$im;
s/\+-/-/;
s/^\+//;
s/[\+-]$//;
$_ = 0 if ($_ eq '');
return $_;
}
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