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# Copyright 2002 by the Massachusetts Institute of Technology.
# All Rights Reserved.
#
# Export of this software from the United States of America may
# require a specific license from the United States Government.
# It is the responsibility of any person or organization contemplating
# export to obtain such a license before exporting.
#
# WITHIN THAT CONSTRAINT, permission to use, copy, modify, and
# distribute this software and its documentation for any purpose and
# without fee is hereby granted, provided that the above copyright
# notice appear in all copies and that both that copyright notice and
# this permission notice appear in supporting documentation, and that
# the name of M.I.T. not be used in advertising or publicity pertaining
# to distribution of the software without specific, written prior
# permission. Furthermore if you modify this software you must label
# your software as modified software and not distribute it in such a
# fashion that it might be confused with the original M.I.T. software.
# M.I.T. makes no representations about the suitability of
# this software for any purpose. It is provided "as is" without express
# or implied warranty.
package Poly;
# Poly: implements some basic operations on polynomials in the field
# of integers (mod 2).
#
# The rep is an array of coefficients, highest order term first.
#
# This is rather slow at the moment.
use overload
'+' => \&add,
'-' => \&add,
'*' => \&mul,
'%' => sub {$_[2] ? mod($_[1], $_[0]) : mod($_[0], $_[1])},
'/' => sub { $_[2] ? scalar(div($_[1], $_[0]))
: scalar(div($_[0], $_[1])) },
'<=>' => sub {$_[2] ? pcmp($_[1], $_[0]) : pcmp($_[0], $_[1])},
'""' => \&str
;
use Carp;
# doesn't do much beyond normalize and bless
sub new {
my $this = shift;
my $class = ref($this) || $this;
my(@x) = @_;
return bless [norm(@x)], $class;
}
# stringified P(x)
sub pretty {
my(@x) = @{+shift};
my $n = @x;
local $_;
return "0" if !@x;
return join " + ", map {$n--; $_ ? ("x^$n") : ()} @x;
}
sub print {
my $self = shift;
print $self->pretty, "\n";
}
# This assumes normalization.
sub order {
my $self = shift;
return $#{$self};
}
sub str {
return overload::StrVal($_[0]);
}
# strip leading zero coefficients
sub norm {
my(@x) = @_;
shift @x while @x && !$x[0];
return @x;
}
# multiply $self by the single term of power $n
sub multerm {
my($self, $n) = @_;
return $self->new(@$self, (0) x $n);
}
# This is really an order comparison; different polys of same order
# compare equal. It also assumes prior normalization.
sub pcmp {
my @x = @{+shift};
my @y = @{+shift};
return @x <=> @y;
}
# convenience constructor; takes list of non-zero terms
sub powers2poly
{
my $self = shift;
my $poly = $self->new;
my $n;
foreach $n (@_) {
$poly += $one->multerm($n);
}
return $poly;
}
sub add {
my $self = shift;
my @x = @$self;
my @y = @{+shift};
my @r;
unshift @r, (pop @x || 0) ^ (pop @y || 0)
while @x || @y;
return $self->new(@r);
}
sub mul {
my($self) = shift;
my @y = @{+shift};
my $r = $self->new;
my $power = 0;
while (@y) {
$r += $self->multerm($power) if pop @y;
$power++;
}
return $r;
}
sub oldmod {
my($self, $div) = @_;
my @num = @$self;
my @div = @$div;
my $r = $self->new(splice @num, 0, @div);
do {
push @$r, shift @num while @num && $r < $div;
$r += $div if $r >= $div;
} while @num;
return $r;
}
sub div {
my($self, $div) = @_;
my $q = $self->new;
my $r = $self->new(@$self);
my $one = $self->new(1);
my ($tp, $power);
croak "divide by zero" if !@$div;
while ($div <= $r) {
$power = 0;
$power++ while ($tp = $div->multerm($power)) < $r;
$q += $one->multerm($power);
$r -= $tp;
}
return wantarray ? ($q, $r) : $q;
}
sub mod {
(&div)[1];
}
# bits and octets both big-endian
sub hex {
my @x = @{+shift};
my $minwidth = shift || 32;
unshift @x, 0 while @x % 8 || @x < $minwidth;
return unpack "H*", pack "B*", join "", @x;
}
# bit-reversal of above
sub revhex {
my @x = @{+shift};
my $minwidth = shift || 32;
unshift @x, 0 while @x % 8 || @x < $minwidth;
return unpack "H*", pack "B*", join "", reverse @x;
}
$one = Poly->new(1);
1;
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