| 1 | package bigrat;
|
|---|
| 2 | require "bigint.pl";
|
|---|
| 3 | #
|
|---|
| 4 | # This library is no longer being maintained, and is included for backward
|
|---|
| 5 | # compatibility with Perl 4 programs which may require it.
|
|---|
| 6 | #
|
|---|
| 7 | # In particular, this should not be used as an example of modern Perl
|
|---|
| 8 | # programming techniques.
|
|---|
| 9 | #
|
|---|
| 10 | # Arbitrary size rational math package
|
|---|
| 11 | #
|
|---|
| 12 | # by Mark Biggar
|
|---|
| 13 | #
|
|---|
| 14 | # Input values to these routines consist of strings of the form
|
|---|
| 15 | # m|^\s*[+-]?[\d\s]+(/[\d\s]+)?$|.
|
|---|
| 16 | # Examples:
|
|---|
| 17 | # "+0/1" canonical zero value
|
|---|
| 18 | # "3" canonical value "+3/1"
|
|---|
| 19 | # " -123/123 123" canonical value "-1/1001"
|
|---|
| 20 | # "123 456/7890" canonical value "+20576/1315"
|
|---|
| 21 | # Output values always include a sign and no leading zeros or
|
|---|
| 22 | # white space.
|
|---|
| 23 | # This package makes use of the bigint package.
|
|---|
| 24 | # The string 'NaN' is used to represent the result when input arguments
|
|---|
| 25 | # that are not numbers, as well as the result of dividing by zero and
|
|---|
| 26 | # the sqrt of a negative number.
|
|---|
| 27 | # Extreamly naive algorthims are used.
|
|---|
| 28 | #
|
|---|
| 29 | # Routines provided are:
|
|---|
| 30 | #
|
|---|
| 31 | # rneg(RAT) return RAT negation
|
|---|
| 32 | # rabs(RAT) return RAT absolute value
|
|---|
| 33 | # rcmp(RAT,RAT) return CODE compare numbers (undef,<0,=0,>0)
|
|---|
| 34 | # radd(RAT,RAT) return RAT addition
|
|---|
| 35 | # rsub(RAT,RAT) return RAT subtraction
|
|---|
| 36 | # rmul(RAT,RAT) return RAT multiplication
|
|---|
| 37 | # rdiv(RAT,RAT) return RAT division
|
|---|
| 38 | # rmod(RAT) return (RAT,RAT) integer and fractional parts
|
|---|
| 39 | # rnorm(RAT) return RAT normalization
|
|---|
| 40 | # rsqrt(RAT, cycles) return RAT square root
|
|---|
| 41 | |
|---|
| 42 |
|
|---|
| 43 | # Convert a number to the canonical string form m|^[+-]\d+/\d+|.
|
|---|
| 44 | sub main'rnorm { #(string) return rat_num
|
|---|
| 45 | local($_) = @_;
|
|---|
| 46 | s/\s+//g;
|
|---|
| 47 | if (m#^([+-]?\d+)(/(\d*[1-9]0*))?$#) {
|
|---|
| 48 | &norm($1, $3 ? $3 : '+1');
|
|---|
| 49 | } else {
|
|---|
| 50 | 'NaN';
|
|---|
| 51 | }
|
|---|
| 52 | }
|
|---|
| 53 |
|
|---|
| 54 | # Normalize by reducing to lowest terms
|
|---|
| 55 | sub norm { #(bint, bint) return rat_num
|
|---|
| 56 | local($num,$dom) = @_;
|
|---|
| 57 | if ($num eq 'NaN') {
|
|---|
| 58 | 'NaN';
|
|---|
| 59 | } elsif ($dom eq 'NaN') {
|
|---|
| 60 | 'NaN';
|
|---|
| 61 | } elsif ($dom =~ /^[+-]?0+$/) {
|
|---|
| 62 | 'NaN';
|
|---|
| 63 | } else {
|
|---|
| 64 | local($gcd) = &'bgcd($num,$dom);
|
|---|
| 65 | $gcd =~ s/^-/+/;
|
|---|
| 66 | if ($gcd ne '+1') {
|
|---|
| 67 | $num = &'bdiv($num,$gcd);
|
|---|
| 68 | $dom = &'bdiv($dom,$gcd);
|
|---|
| 69 | } else {
|
|---|
| 70 | $num = &'bnorm($num);
|
|---|
| 71 | $dom = &'bnorm($dom);
|
|---|
| 72 | }
|
|---|
| 73 | substr($dom,$[,1) = '';
|
|---|
| 74 | "$num/$dom";
|
|---|
| 75 | }
|
|---|
| 76 | }
|
|---|
| 77 |
|
|---|
| 78 | # negation
|
|---|
| 79 | sub main'rneg { #(rat_num) return rat_num
|
|---|
| 80 | local($_) = &'rnorm(@_);
|
|---|
| 81 | tr/-+/+-/ if ($_ ne '+0/1');
|
|---|
| 82 | $_;
|
|---|
| 83 | }
|
|---|
| 84 |
|
|---|
| 85 | # absolute value
|
|---|
| 86 | sub main'rabs { #(rat_num) return $rat_num
|
|---|
| 87 | local($_) = &'rnorm(@_);
|
|---|
| 88 | substr($_,$[,1) = '+' unless $_ eq 'NaN';
|
|---|
| 89 | $_;
|
|---|
|
|---|
