source: libcfa/src/rational.cfa@ 77bc259

Last change on this file since 77bc259 was 92211d9, checked in by Peter A. Buhr <pabuhr@…>, 2 years ago

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1//
2// Cforall Version 1.0.0 Copyright (C) 2016 University of Waterloo
3//
4// The contents of this file are covered under the licence agreement in the
5// file "LICENCE" distributed with Cforall.
6//
7// rational.c --
8//
9// Author : Peter A. Buhr
10// Created On : Wed Apr 6 17:54:28 2016
11// Last Modified By : Peter A. Buhr
12// Last Modified On : Fri Oct 6 07:52:13 2023
13// Update Count : 198
14//
15
16#include "rational.hfa"
17#include "fstream.hfa"
18#include "stdlib.hfa"
19
20#pragma GCC visibility push(default)
21
22forall( T | arithmetic( T ) ) {
23 // helper routines
24
25 // Calculate greatest common denominator of two numbers, the first of which may be negative. Used to reduce
26 // rationals. alternative: https://en.wikipedia.org/wiki/Binary_GCD_algorithm
27 static T gcd( T a, T b ) {
28 for () { // Euclid's algorithm
29 T r = a % b;
30 if ( r == (T){0} ) break;
31 a = b;
32 b = r;
33 } // for
34 return b;
35 } // gcd
36
37 static T simplify( T & n, T & d ) {
38 if ( d == (T){0} ) {
39 abort | "Invalid rational number construction: denominator cannot be equal to 0.";
40 } // exit
41 if ( d < (T){0} ) { d = -d; n = -n; } // move sign to numerator
42 return gcd( abs( n ), d ); // simplify
43 } // simplify
44
45 // constructors
46
47 void ?{}( rational(T) & r, zero_t ) {
48 r{ (T){0}, (T){1} };
49 } // rational
50
51 void ?{}( rational(T) & r, one_t ) {
52 r{ (T){1}, (T){1} };
53 } // rational
54
55 void ?{}( rational(T) & r ) {
56 r{ (T){0}, (T){1} };
57 } // rational
58
59 void ?{}( rational(T) & r, T n ) {
60 r{ n, (T){1} };
61 } // rational
62
63 void ?{}( rational(T) & r, T n, T d ) {
64 T t = simplify( n, d ); // simplify
65 r.[numerator, denominator] = [n / t, d / t];
66 } // rational
67
68 // getter for numerator/denominator
69
70 T numerator( rational(T) r ) {
71 return r.numerator;
72 } // numerator
73
74 T denominator( rational(T) r ) {
75 return r.denominator;
76 } // denominator
77
78 [ T, T ] ?=?( & [ T, T ] dst, rational(T) src ) {
79 return dst = src.[ numerator, denominator ];
80 } // ?=?
81
82 // setter for numerator/denominator
83
84 T numerator( rational(T) r, T n ) {
85 T prev = r.numerator;
86 T t = gcd( abs( n ), r.denominator ); // simplify
87 r.[numerator, denominator] = [n / t, r.denominator / t];
88 return prev;
89 } // numerator
90
91 T denominator( rational(T) r, T d ) {
92 T prev = r.denominator;
93 T t = simplify( r.numerator, d ); // simplify
94 r.[numerator, denominator] = [r.numerator / t, d / t];
95 return prev;
96 } // denominator
97
98 // comparison
99
100 int ?==?( rational(T) l, rational(T) r ) {
101 return l.numerator * r.denominator == l.denominator * r.numerator;
102 } // ?==?
103
104 int ?!=?( rational(T) l, rational(T) r ) {
105 return ! ( l == r );
106 } // ?!=?
107
108 int ?!=?( rational(T) l, zero_t ) {
109 return ! ( l == (rational(T)){ 0 } );
110 } // ?!=?
111
112 int ?<?( rational(T) l, rational(T) r ) {
113 return l.numerator * r.denominator < l.denominator * r.numerator;
114 } // ?<?
115
116 int ?<=?( rational(T) l, rational(T) r ) {
117 return l.numerator * r.denominator <= l.denominator * r.numerator;
118 } // ?<=?
119
120 int ?>?( rational(T) l, rational(T) r ) {
121 return ! ( l <= r );
122 } // ?>?
123
124 int ?>=?( rational(T) l, rational(T) r ) {
125 return ! ( l < r );
126 } // ?>=?
127
128 // arithmetic
129
130 rational(T) +?( rational(T) r ) {
131 return (rational(T)){ r.numerator, r.denominator };
132 } // +?
133
134 rational(T) -?( rational(T) r ) {
135 return (rational(T)){ -r.numerator, r.denominator };
136 } // -?
137
138 rational(T) ?+?( rational(T) l, rational(T) r ) {
139 if ( l.denominator == r.denominator ) { // special case
140 return (rational(T)){ l.numerator + r.numerator, l.denominator };
141 } else {
142 return (rational(T)){ l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator };
143 } // if
144 } // ?+?
145
146 rational(T) ?+=?( rational(T) & l, rational(T) r ) {
147 l = l + r;
148 return l;
149 } // ?+?
150
151 rational(T) ?+=?( rational(T) & l, one_t ) {
152 l = l + (rational(T)){ 1 };
153 return l;
154 } // ?+?
155
156 rational(T) ?-?( rational(T) l, rational(T) r ) {
157 if ( l.denominator == r.denominator ) { // special case
158 return (rational(T)){ l.numerator - r.numerator, l.denominator };
159 } else {
160 return (rational(T)){ l.numerator * r.denominator - l.denominator * r.numerator, l.denominator * r.denominator };
161 } // if
162 } // ?-?
163
164 rational(T) ?-=?( rational(T) & l, rational(T) r ) {
165 l = l - r;
166 return l;
167 } // ?-?
168
169 rational(T) ?-=?( rational(T) & l, one_t ) {
170 l = l - (rational(T)){ 1 };
171 return l;
172 } // ?-?
173
174 rational(T) ?*?( rational(T) l, rational(T) r ) {
175 return (rational(T)){ l.numerator * r.numerator, l.denominator * r.denominator };
176 } // ?*?
177
178 rational(T) ?*=?( rational(T) & l, rational(T) r ) {
179 return l = l * r;
180 } // ?*?
181
182 rational(T) ?/?( rational(T) l, rational(T) r ) {
183 if ( r.numerator < (T){0} ) {
184 r.[numerator, denominator] = [-r.numerator, -r.denominator];
185 } // if
186 return (rational(T)){ l.numerator * r.denominator, l.denominator * r.numerator };
187 } // ?/?
188
189 rational(T) ?/=?( rational(T) & l, rational(T) r ) {
190 return l = l / r;
191 } // ?/?
192
193 // I/O
194
195 forall( istype & | istream( istype ) | { istype & ?|?( istype &, T & ); } )
196 istype & ?|?( istype & is, rational(T) & r ) {
197 is | r.numerator | r.denominator;
198 T t = simplify( r.numerator, r.denominator );
199 r.numerator /= t;
200 r.denominator /= t;
201 return is;
202 } // ?|?
203
204 forall( ostype & | ostream( ostype ) | { ostype & ?|?( ostype &, T ); } ) {
205 ostype & ?|?( ostype & os, rational(T) r ) {
206 return os | r.numerator | '/' | r.denominator;
207 } // ?|?
208 OSTYPE_VOID_IMPL( rational(T) )
209 } // distribution
210} // distribution
211
212forall( T | arithmetic( T ) | { T ?\?( T, unsigned long ); } ) {
213 rational(T) ?\?( rational(T) x, long int y ) {
214 if ( y < 0 ) {
215 return (rational(T)){ x.denominator \ -y, x.numerator \ -y };
216 } else {
217 return (rational(T)){ x.numerator \ y, x.denominator \ y };
218 } // if
219 } // ?\?
220
221 rational(T) ?\=?( rational(T) & x, long int y ) {
222 return x = x \ y;
223 } // ?\?
224} // distribution
225
226// conversion
227
228forall( T | arithmetic( T ) | { double convert( T ); } )
229double widen( rational(T) r ) {
230 return convert( r.numerator ) / convert( r.denominator );
231} // widen
232
233forall( T | arithmetic( T ) | { double convert( T ); T convert( double ); } )
234rational(T) narrow( double f, T md ) {
235 // http://www.ics.uci.edu/~eppstein/numth/frap.c
236 if ( md <= (T){1} ) { // maximum fractional digits too small?
237 return (rational(T)){ convert( f ), (T){1}}; // truncate fraction
238 } // if
239
240 // continued fraction coefficients
241 T m00 = {1}, m11 = { 1 }, m01 = { 0 }, m10 = { 0 };
242 T ai, t;
243
244 // find terms until denom gets too big
245 for () {
246 ai = convert( f );
247 if ( ! (m10 * ai + m11 <= md) ) break;
248 t = m00 * ai + m01;
249 m01 = m00;
250 m00 = t;
251 t = m10 * ai + m11;
252 m11 = m10;
253 m10 = t;
254 double temp = convert( ai );
255 if ( f == temp ) break; // prevent division by zero
256 f = 1 / (f - temp);
257 if ( f > (double)0x7FFFFFFF ) break; // representation failure
258 } // for
259 return (rational(T)){ m00, m10 };
260} // narrow
261
262// Local Variables: //
263// tab-width: 4 //
264// End: //
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