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5303340c LW |
1 | package bigrat; |
2 | require "bigint.pl"; | |
a6d71656 GS |
3 | # |
4 | # This library is no longer being maintained, and is included for backward | |
5 | # compatibility with Perl 4 programs which may require it. | |
5170d013 S |
6 | # This legacy library is deprecated and will be removed in a future |
7 | # release of perl. | |
a6d71656 GS |
8 | # |
9 | # In particular, this should not be used as an example of modern Perl | |
10 | # programming techniques. | |
11 | # | |
5303340c | 12 | # Arbitrary size rational math package |
5170d013 | 13 | |
bf10efe7 LW |
14 | # by Mark Biggar |
15 | # | |
5303340c LW |
16 | # Input values to these routines consist of strings of the form |
17 | # m|^\s*[+-]?[\d\s]+(/[\d\s]+)?$|. | |
18 | # Examples: | |
19 | # "+0/1" canonical zero value | |
20 | # "3" canonical value "+3/1" | |
21 | # " -123/123 123" canonical value "-1/1001" | |
22 | # "123 456/7890" canonical value "+20576/1315" | |
23 | # Output values always include a sign and no leading zeros or | |
24 | # white space. | |
25 | # This package makes use of the bigint package. | |
26 | # The string 'NaN' is used to represent the result when input arguments | |
27 | # that are not numbers, as well as the result of dividing by zero and | |
28 | # the sqrt of a negative number. | |
29 | # Extreamly naive algorthims are used. | |
30 | # | |
31 | # Routines provided are: | |
32 | # | |
33 | # rneg(RAT) return RAT negation | |
34 | # rabs(RAT) return RAT absolute value | |
35 | # rcmp(RAT,RAT) return CODE compare numbers (undef,<0,=0,>0) | |
36 | # radd(RAT,RAT) return RAT addition | |
37 | # rsub(RAT,RAT) return RAT subtraction | |
38 | # rmul(RAT,RAT) return RAT multiplication | |
39 | # rdiv(RAT,RAT) return RAT division | |
40 | # rmod(RAT) return (RAT,RAT) integer and fractional parts | |
41 | # rnorm(RAT) return RAT normalization | |
42 | # rsqrt(RAT, cycles) return RAT square root | |
43 | \f | |
44 | # Convert a number to the canonical string form m|^[+-]\d+/\d+|. | |
45 | sub main'rnorm { #(string) return rat_num | |
46 | local($_) = @_; | |
47 | s/\s+//g; | |
48 | if (m#^([+-]?\d+)(/(\d*[1-9]0*))?$#) { | |
49 | &norm($1, $3 ? $3 : '+1'); | |
50 | } else { | |
51 | 'NaN'; | |
52 | } | |
53 | } | |
54 | ||
55 | # Normalize by reducing to lowest terms | |
56 | sub norm { #(bint, bint) return rat_num | |
57 | local($num,$dom) = @_; | |
58 | if ($num eq 'NaN') { | |
59 | 'NaN'; | |
60 | } elsif ($dom eq 'NaN') { | |
61 | 'NaN'; | |
62 | } elsif ($dom =~ /^[+-]?0+$/) { | |
63 | 'NaN'; | |
64 | } else { | |
65 | local($gcd) = &'bgcd($num,$dom); | |
748a9306 | 66 | $gcd =~ s/^-/+/; |
5303340c LW |
67 | if ($gcd ne '+1') { |
68 | $num = &'bdiv($num,$gcd); | |
69 | $dom = &'bdiv($dom,$gcd); | |
70 | } else { | |
71 | $num = &'bnorm($num); | |
72 | $dom = &'bnorm($dom); | |
73 | } | |
859172fe | 74 | substr($dom,0,1) = ''; |
5303340c LW |
75 | "$num/$dom"; |
76 | } | |
77 | } | |
78 | ||
79 | # negation | |
80 | sub main'rneg { #(rat_num) return rat_num | |
79072805 | 81 | local($_) = &'rnorm(@_); |
5303340c LW |
82 | tr/-+/+-/ if ($_ ne '+0/1'); |
83 | $_; | |
84 | } | |
85 | ||
86 | # absolute value | |
87 | sub main'rabs { #(rat_num) return $rat_num | |
79072805 | 88 | local($_) = &'rnorm(@_); |
859172fe | 89 | substr($_,0,1) = '+' unless $_ eq 'NaN'; |
5303340c LW |
90 | $_; |
91 | } | |
92 | ||
93 | # multipication | |
94 | sub main'rmul { #(rat_num, rat_num) return rat_num | |
859172fe Z |
95 | local($xn,$xd) = split('/',&'rnorm($_[0])); |
96 | local($yn,$yd) = split('/',&'rnorm($_[1])); | |
5303340c LW |
97 | &norm(&'bmul($xn,$yn),&'bmul($xd,$yd)); |
98 | } | |
99 | ||
100 | # division | |
101 | sub main'rdiv { #(rat_num, rat_num) return rat_num | |
859172fe Z |
102 | local($xn,$xd) = split('/',&'rnorm($_[0])); |
103 | local($yn,$yd) = split('/',&'rnorm($_[1])); | |
5303340c LW |
104 | &norm(&'bmul($xn,$yd),&'bmul($xd,$yn)); |
105 | } | |
106 | \f | |
107 | # addition | |
108 | sub main'radd { #(rat_num, rat_num) return rat_num | |
859172fe Z |
109 | local($xn,$xd) = split('/',&'rnorm($_[0])); |
110 | local($yn,$yd) = split('/',&'rnorm($_[1])); | |
5303340c LW |
111 | &norm(&'badd(&'bmul($xn,$yd),&'bmul($yn,$xd)),&'bmul($xd,$yd)); |
112 | } | |
113 | ||
114 | # subtraction | |
115 | sub main'rsub { #(rat_num, rat_num) return rat_num | |
859172fe Z |
116 | local($xn,$xd) = split('/',&'rnorm($_[0])); |
117 | local($yn,$yd) = split('/',&'rnorm($_[1])); | |
5303340c LW |
118 | &norm(&'bsub(&'bmul($xn,$yd),&'bmul($yn,$xd)),&'bmul($xd,$yd)); |
119 | } | |
120 | ||
121 | # comparison | |
122 | sub main'rcmp { #(rat_num, rat_num) return cond_code | |
859172fe Z |
123 | local($xn,$xd) = split('/',&'rnorm($_[0])); |
124 | local($yn,$yd) = split('/',&'rnorm($_[1])); | |
5303340c LW |
125 | &bigint'cmp(&'bmul($xn,$yd),&'bmul($yn,$xd)); |
126 | } | |
127 | ||
128 | # int and frac parts | |
129 | sub main'rmod { #(rat_num) return (rat_num,rat_num) | |
79072805 | 130 | local($xn,$xd) = split('/',&'rnorm(@_)); |
5303340c LW |
131 | local($i,$f) = &'bdiv($xn,$xd); |
132 | if (wantarray) { | |
133 | ("$i/1", "$f/$xd"); | |
134 | } else { | |
135 | "$i/1"; | |
136 | } | |
137 | } | |
138 | ||
139 | # square root by Newtons method. | |
140 | # cycles specifies the number of iterations default: 5 | |
141 | sub main'rsqrt { #(fnum_str[, cycles]) return fnum_str | |
859172fe | 142 | local($x, $scale) = (&'rnorm($_[0]), $_[1]); |
5303340c LW |
143 | if ($x eq 'NaN') { |
144 | 'NaN'; | |
145 | } elsif ($x =~ /^-/) { | |
146 | 'NaN'; | |
147 | } else { | |
148 | local($gscale, $guess) = (0, '+1/1'); | |
149 | $scale = 5 if (!$scale); | |
150 | while ($gscale++ < $scale) { | |
151 | $guess = &'rmul(&'radd($guess,&'rdiv($x,$guess)),"+1/2"); | |
152 | } | |
153 | "$guess"; # quotes necessary due to perl bug | |
154 | } | |
155 | } | |
156 | ||
157 | 1; |