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