[14489] | 1 | package bigrat;
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| 2 | require "bigint.pl";
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| 3 | #
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| 4 | # This library is no longer being maintained, and is included for backward
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| 5 | # compatibility with Perl 4 programs which may require it.
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| 6 | #
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| 7 | # In particular, this should not be used as an example of modern Perl
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| 8 | # programming techniques.
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| 9 | #
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| 10 | # Arbitrary size rational math package
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| 11 | #
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| 12 | # by Mark Biggar
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| 13 | #
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| 14 | # Input values to these routines consist of strings of the form
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| 15 | # m|^\s*[+-]?[\d\s]+(/[\d\s]+)?$|.
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| 16 | # Examples:
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| 17 | # "+0/1" canonical zero value
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| 18 | # "3" canonical value "+3/1"
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| 19 | # " -123/123 123" canonical value "-1/1001"
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| 20 | # "123 456/7890" canonical value "+20576/1315"
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| 21 | # Output values always include a sign and no leading zeros or
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| 22 | # white space.
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| 23 | # This package makes use of the bigint package.
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| 24 | # The string 'NaN' is used to represent the result when input arguments
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| 25 | # that are not numbers, as well as the result of dividing by zero and
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| 26 | # the sqrt of a negative number.
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| 27 | # Extreamly naive algorthims are used.
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| 28 | #
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| 29 | # Routines provided are:
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| 30 | #
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| 31 | # rneg(RAT) return RAT negation
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| 32 | # rabs(RAT) return RAT absolute value
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| 33 | # rcmp(RAT,RAT) return CODE compare numbers (undef,<0,=0,>0)
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| 34 | # radd(RAT,RAT) return RAT addition
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| 35 | # rsub(RAT,RAT) return RAT subtraction
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| 36 | # rmul(RAT,RAT) return RAT multiplication
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| 37 | # rdiv(RAT,RAT) return RAT division
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| 38 | # rmod(RAT) return (RAT,RAT) integer and fractional parts
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| 39 | # rnorm(RAT) return RAT normalization
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| 40 | # rsqrt(RAT, cycles) return RAT square root
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| 41 | |
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| 42 |
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| 43 | # Convert a number to the canonical string form m|^[+-]\d+/\d+|.
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| 44 | sub main'rnorm { #(string) return rat_num
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| 45 | local($_) = @_;
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| 46 | s/\s+//g;
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| 47 | if (m#^([+-]?\d+)(/(\d*[1-9]0*))?$#) {
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| 48 | &norm($1, $3 ? $3 : '+1');
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| 49 | } else {
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| 50 | 'NaN';
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| 51 | }
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| 52 | }
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| 53 |
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| 54 | # Normalize by reducing to lowest terms
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| 55 | sub norm { #(bint, bint) return rat_num
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| 56 | local($num,$dom) = @_;
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| 57 | if ($num eq 'NaN') {
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| 58 | 'NaN';
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| 59 | } elsif ($dom eq 'NaN') {
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| 60 | 'NaN';
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| 61 | } elsif ($dom =~ /^[+-]?0+$/) {
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| 62 | 'NaN';
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| 63 | } else {
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| 64 | local($gcd) = &'bgcd($num,$dom);
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| 65 | $gcd =~ s/^-/+/;
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| 66 | if ($gcd ne '+1') {
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| 67 | $num = &'bdiv($num,$gcd);
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| 68 | $dom = &'bdiv($dom,$gcd);
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| 69 | } else {
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| 70 | $num = &'bnorm($num);
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| 71 | $dom = &'bnorm($dom);
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| 72 | }
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| 73 | substr($dom,$[,1) = '';
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| 74 | "$num/$dom";
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| 75 | }
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| 76 | }
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| 77 |
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| 78 | # negation
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| 79 | sub main'rneg { #(rat_num) return rat_num
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| 80 | local($_) = &'rnorm(@_);
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| 81 | tr/-+/+-/ if ($_ ne '+0/1');
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| 82 | $_;
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| 83 | }
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| 84 |
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| 85 | # absolute value
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| 86 | sub main'rabs { #(rat_num) return $rat_num
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| 87 | local($_) = &'rnorm(@_);
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| 88 | substr($_,$[,1) = '+' unless $_ eq 'NaN';
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| 89 | $_;
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| 90 | }
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| 91 |
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| 92 | # multipication
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| 93 | sub main'rmul { #(rat_num, rat_num) return rat_num
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| 94 | local($xn,$xd) = split('/',&'rnorm($_[$[]));
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| 95 | local($yn,$yd) = split('/',&'rnorm($_[$[+1]));
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| 96 | &norm(&'bmul($xn,$yn),&'bmul($xd,$yd));
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| 97 | }
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| 98 |
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| 99 | # division
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| 100 | sub main'rdiv { #(rat_num, rat_num) return rat_num
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| 101 | local($xn,$xd) = split('/',&'rnorm($_[$[]));
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| 102 | local($yn,$yd) = split('/',&'rnorm($_[$[+1]));
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| 103 | &norm(&'bmul($xn,$yd),&'bmul($xd,$yn));
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| 104 | }
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| 105 | |
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| 106 |
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| 107 | # addition
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| 108 | sub main'radd { #(rat_num, rat_num) return rat_num
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| 109 | local($xn,$xd) = split('/',&'rnorm($_[$[]));
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| 110 | local($yn,$yd) = split('/',&'rnorm($_[$[+1]));
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| 111 | &norm(&'badd(&'bmul($xn,$yd),&'bmul($yn,$xd)),&'bmul($xd,$yd));
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| 112 | }
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| 113 |
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| 114 | # subtraction
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| 115 | sub main'rsub { #(rat_num, rat_num) return rat_num
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| 116 | local($xn,$xd) = split('/',&'rnorm($_[$[]));
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| 117 | local($yn,$yd) = split('/',&'rnorm($_[$[+1]));
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| 118 | &norm(&'bsub(&'bmul($xn,$yd),&'bmul($yn,$xd)),&'bmul($xd,$yd));
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| 119 | }
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| 120 |
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| 121 | # comparison
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| 122 | sub main'rcmp { #(rat_num, rat_num) return cond_code
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| 123 | local($xn,$xd) = split('/',&'rnorm($_[$[]));
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| 124 | local($yn,$yd) = split('/',&'rnorm($_[$[+1]));
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| 125 | &bigint'cmp(&'bmul($xn,$yd),&'bmul($yn,$xd));
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| 126 | }
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| 127 |
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| 128 | # int and frac parts
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| 129 | sub main'rmod { #(rat_num) return (rat_num,rat_num)
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| 130 | local($xn,$xd) = split('/',&'rnorm(@_));
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| 131 | local($i,$f) = &'bdiv($xn,$xd);
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| 132 | if (wantarray) {
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| 133 | ("$i/1", "$f/$xd");
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| 134 | } else {
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| 135 | "$i/1";
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| 136 | }
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| 137 | }
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| 138 |
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| 139 | # square root by Newtons method.
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| 140 | # cycles specifies the number of iterations default: 5
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| 141 | sub main'rsqrt { #(fnum_str[, cycles]) return fnum_str
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| 142 | local($x, $scale) = (&'rnorm($_[$[]), $_[$[+1]);
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| 143 | if ($x eq 'NaN') {
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| 144 | 'NaN';
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| 145 | } elsif ($x =~ /^-/) {
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| 146 | 'NaN';
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| 147 | } else {
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| 148 | local($gscale, $guess) = (0, '+1/1');
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| 149 | $scale = 5 if (!$scale);
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| 150 | while ($gscale++ < $scale) {
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| 151 | $guess = &'rmul(&'radd($guess,&'rdiv($x,$guess)),"+1/2");
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| 152 | }
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| 153 | "$guess"; # quotes necessary due to perl bug
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| 154 | }
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| 155 | }
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| 156 |
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| 157 | 1;
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