package bigrat;
require "bigint.pl";
sub main'rnorm { #(string) return rat_num
local($_) = @_;
s/\s+//g;
if (m#^([+-]?\d+)(/(\d*[1-9]0*))?$#) {
&norm($1, $3 ? $3 : '+1');
} else {
'NaN';
}
}
# Normalize by reducing to lowest terms
sub norm { #(bint, bint) return rat_num
local($num,$dom) = @_;
if ($num eq 'NaN') {
'NaN';
} elsif ($dom eq 'NaN') {
'NaN';
} elsif ($dom =~ /^[+-]?0+$/) {
'NaN';
} else {
local($gcd) = &'bgcd($num,$dom);
$gcd =~ s/^-/+/;
if ($gcd ne '+1') {
$num = &'bdiv($num,$gcd);
$dom = &'bdiv($dom,$gcd);
} else {
$num = &'bnorm($num);
$dom = &'bnorm($dom);
}
substr($dom,0,1) = '';
"$num/$dom";
}
}
sub main'rneg { #(rat_num) return rat_num
local($_) = &'rnorm(@_);
tr/-+/+-/ if ($_ ne '+0/1');
$_;
}
sub main'rabs { #(rat_num) return $rat_num
local($_) = &'rnorm(@_);
substr($_,0,1) = '+' unless $_ eq 'NaN';
$_;
}
sub main'rmul { #(rat_num, rat_num) return rat_num
local($xn,$xd) = split('/',&'rnorm($_[0]));
local($yn,$yd) = split('/',&'rnorm($_[1]));
&norm(&'bmul($xn,$yn),&'bmul($xd,$yd));
}
# division
sub main'rdiv { local($xn,$xd) = split('/',&'rnorm($_[0]));
local($yn,$yd) = split('/',&'rnorm($_[1]));
&norm(&'bmul($xn,$yd),&'bmul($xd,$yn));
}
sub main'radd { #(rat_num, rat_num) return rat_num
local($xn,$xd) = split('/',&'rnorm($_[0]));
local($yn,$yd) = split('/',&'rnorm($_[1]));
&norm(&'badd(&'bmul($xn,$yd),&'bmul($yn,$xd)),&'bmul($xd,$yd));
}
# subtraction
sub main'rsub { local($xn,$xd) = split('/',&'rnorm($_[0]));
local($yn,$yd) = split('/',&'rnorm($_[1]));
&norm(&'bsub(&'bmul($xn,$yd),&'bmul($yn,$xd)),&'bmul($xd,$yd));
}
sub main'rcmp { #(rat_num, rat_num) return cond_code
local($xn,$xd) = split('/',&'rnorm($_[0]));
local($yn,$yd) = split('/',&'rnorm($_[1]));
&bigint'cmp(&'bmul($xn,$yd),&'bmul($yn,$xd));
}
sub main'rmod { #(rat_num) return (rat_num,rat_num)
local($xn,$xd) = split('/',&'rnorm(@_));
local($i,$f) = &'bdiv($xn,$xd);
if (wantarray) {
("$i/1", "$f/$xd");
} else {
"$i/1";
}
}
# square root by Newtons method.
# cycles specifies the number of iterations default: 5
sub main'rsqrt { local($x, $scale) = (&'rnorm($_[0]), $_[1]);
if ($x eq 'NaN') {
'NaN';
} elsif ($x =~ /^-/) {
'NaN';
} else {
local($gscale, $guess) = (0, '+1/1');
$scale = 5 if (!$scale);
while ($gscale++ < $scale) {
$guess = &'rmul(&'radd($guess,&'rdiv($x,$guess)),"+1/2");
}
"$guess"; }
}
1;