# This library is no longer being maintained, and is included for backward
# compatibility with Perl 4 programs which may require it.
# In particular, this should not be used as an example of modern Perl
# programming techniques.
# Arbitrary size rational math package
# Input values to these routines consist of strings of the form
# m|^\s*[+-]?[\d\s]+(/[\d\s]+)?$|.
# "+0/1" canonical zero value
# "3" canonical value "+3/1"
# " -123/123 123" canonical value "-1/1001"
# "123 456/7890" canonical value "+20576/1315"
# Output values always include a sign and no leading zeros or
# This package makes use of the bigint package.
# The string 'NaN' is used to represent the result when input arguments
# that are not numbers, as well as the result of dividing by zero and
# the sqrt of a negative number.
# Extreamly naive algorthims are used.
# rneg(RAT) return RAT negation
# rabs(RAT) return RAT absolute value
# rcmp(RAT,RAT) return CODE compare numbers (undef,<0,=0,>0)
# radd(RAT,RAT) return RAT addition
# rsub(RAT,RAT) return RAT subtraction
# rmul(RAT,RAT) return RAT multiplication
# rdiv(RAT,RAT) return RAT division
# rmod(RAT) return (RAT,RAT) integer and fractional parts
# rnorm(RAT) return RAT normalization
# rsqrt(RAT, cycles) return RAT square root
# Convert a number to the canonical string form m|^[+-]\d+/\d+|.
sub main
'rnorm { #(string) return rat_num
if (m#^([+-]?\d+)(/(\d*[1-9]0*))?$#) {
&norm($1, $3 ? $3 : '+1');
# Normalize by reducing to lowest terms
sub norm { #(bint, bint) return rat_num
} elsif ($dom eq 'NaN
') {
} elsif ($dom =~ /^[+-]?0+$/) {
local($gcd) = &'bgcd
($num,$dom);
$num = &'bdiv($num,$gcd);
$dom = &'bdiv
($dom,$gcd);
sub main
'rneg { #(rat_num) return rat_num
tr/-+/+-/ if ($_ ne '+0/1');
sub main
'rabs { #(rat_num) return $rat_num
substr($_,$[,1) = '+' unless $_ eq 'NaN';
sub main
'rmul { #(rat_num, rat_num) return rat_num
local($xn,$xd) = split('/',&'rnorm
($_[$[]));
local($yn,$yd) = split('/',&'rnorm($_[$[+1]));
&norm(&'bmul
($xn,$yn),&'bmul($xd,$yd));
sub main'rdiv
{ #(rat_num, rat_num) return rat_num
local($xn,$xd) = split('/',&'rnorm($_[$[]));
local($yn,$yd) = split('/',&'rnorm
($_[$[+1]));
&norm
(&'bmul($xn,$yd),&'bmul
($xd,$yn));
sub main
'radd { #(rat_num, rat_num) return rat_num
local($xn,$xd) = split('/',&'rnorm
($_[$[]));
local($yn,$yd) = split('/',&'rnorm($_[$[+1]));
&norm(&'badd
(&'bmul($xn,$yd),&'bmul
($yn,$xd)),&'bmul($xd,$yd));
sub main'rsub
{ #(rat_num, rat_num) return rat_num
local($xn,$xd) = split('/',&'rnorm($_[$[]));
local($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,$xd) = split('/',&'rnorm
($_[$[]));
local($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,$xd);
# square root by Newtons method.
# cycles specifies the number of iterations default: 5
sub main'rsqrt
{ #(fnum_str[, cycles]) return fnum_str
local($x, $scale) = (&'rnorm($_[$[]), $_[$[+1]);
local($gscale, $guess) = (0, '+1/1');
while ($gscale++ < $scale) {
$guess = &'rmul
(&'radd($guess,&'rdiv
($x,$guess)),"+1/2");
"$guess"; # quotes necessary due to perl bug