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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