#! perl -slw
use strict;
$| = 1;

package FET;
our @EXPORT = 'pCutoff';
use List::Util qw[ sum reduce ];

sub toRatio; sub rpCutoff; sub rdivide; sub fac; sub rtimes; sub cancel; sub merge; sub pCutoff;

sub pCutoff{ toRatio  rpCutoff @_ }

sub rpCutoff {
    my @rs = map{ sum @$_ } @_;
    my @cs = map{ sum @$_ } [ $_[0][0], $_[1][0] ], [ $_[0][1], $_[1][1] ];
    my $n  = sum @rs;
    my @xs = map{ @$_ } @_;
    rdivide facproduct( @rs, @cs ), facproduct( $n, @xs );
}

sub rproduct{ reduce{ rtimes $a, $b } [[],[]], @_ }

sub facproduct{ rproduct map{ fac $_ } @_ }

sub fac{ $_[0] < 2 ? [[],[]] : [[ 2 .. $_[0] ], []]; }

sub toRatio{ [ bigProduct( $_[0][0] ), bigProduct( $_[0][1] ) ] }

sub bigProduct{ reduce{ $a * $b } map{ @$_ } @_ }

sub rdivide{ rtimes $_[0], [ $_[1][1], $_[1][0] ] }

sub rtimes{ [ cancel merge($_[0][0], $_[1][0]), merge($_[0][1], $_[1][1] )] }

sub merge;
sub merge{
    return $_[1] unless defined $_[0] and @{ $_[0] };
    return $_[0] unless defined $_[1] and @{ $_[1] };
    my( $x, @xs ) = @{ $_[0] };
    my( $y, @ys ) = @{ $_[1] };
    $x < $y ? [ $x, @{ merge( \@xs, [ $y, @ys ] ) } ]
            : [ $y, @{ merge( [ $x, @xs ], \@ys ) } ]
}

sub cancel;
sub cancel{
    return @_ unless @{ $_[0] } and @{ $_[1] };
    my( $x, @xs ) = @{ $_[0] };
    my( $y, @ys ) = @{ $_[1] };
    return cancel \@xs, \@ys if $x == $y;
    return do{ my( $xs_, $ys_ ) = 
        cancel \@xs, $_[1]; [$x, @{$xs_}], $ys_ }if $x < $y;
    return do{ my( $xs_,$ys_ ) = 
        cancel $_[0], \@ys; $xs_, [$y, @{$ys_}] };
}

package main;

sub Scientific{ sprintf '%.17f', $_[0][0] / $_[0][1] }

print Scientific FET::pCutoff [ 5, 0], [1, 4];
#print Scientific FET::pCutoff [ 989, 9400 ], [ 43300, 2400];