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