source: libcfa/src/rational.cfa@ d60a4c2

Last change on this file since d60a4c2 was eae8b37, checked in by JiadaL <j82liang@…>, 10 months ago

Move enum.hfa/enum.cfa to prelude
  • Property mode set to 100644
File size: 6.9 KB
Line 
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 : Wed Nov 27 18:06:43 2024
13// Update Count : 208
14//
15
16#include "rational.hfa"
17#include "fstream.hfa"
18#include "stdlib.hfa"
19
20#pragma GCC visibility push(default)
21
22// Arithmetic, Relational
23forall( T | Simple(T) ) {
24 // helper routines
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
46forall( T | arithmetic( T ) ) {
47 // constructors
48
49 void ?{}( rational(T) & r, zero_t ) {
50 r{ (T){0}, (T){1} };
51 } // rational
52
53 void ?{}( rational(T) & r, one_t ) {
54 r{ (T){1}, (T){1} };
55 } // rational
56
57 void ?{}( rational(T) & r ) {
58 r{ (T){0}, (T){1} };
59 } // rational
60
61 void ?{}( rational(T) & r, T n ) {
62 r{ n, (T){1} };
63 } // rational
64
65 void ?{}( rational(T) & r, T n, T d ) {
66 T t = simplify( n, d ); // simplify
67 r.[numerator, denominator] = [n / t, d / t];
68 } // rational
69
70 // getter for numerator/denominator
71
72 T numerator( rational(T) r ) {
73 return r.numerator;
74 } // numerator
75
76 T denominator( rational(T) r ) {
77 return r.denominator;
78 } // denominator
79
80 [ T, T ] ?=?( & [ T, T ] dst, rational(T) src ) {
81 return dst = src.[ numerator, denominator ];
82 } // ?=?
83
84 // setter for numerator/denominator
85
86 T numerator( rational(T) r, T n ) {
87 T prev = r.numerator;
88 T t = gcd( abs( n ), r.denominator ); // simplify
89 r.[numerator, denominator] = [n / t, r.denominator / t];
90 return prev;
91 } // numerator
92
93 T denominator( rational(T) r, T d ) {
94 T prev = r.denominator;
95 T t = simplify( r.numerator, d ); // simplify
96 r.[numerator, denominator] = [r.numerator / t, d / t];
97 return prev;
98 } // denominator
99
100 // comparison
101
102 int ?==?( rational(T) l, rational(T) r ) {
103 return l.numerator * r.denominator == l.denominator * r.numerator;
104 } // ?==?
105
106 int ?!=?( rational(T) l, rational(T) r ) {
107 return ! ( l == r );
108 } // ?!=?
109
110 int ?!=?( rational(T) l, zero_t ) {
111 return ! ( l == (rational(T)){ 0 } );
112 } // ?!=?
113
114 int ?<?( rational(T) l, rational(T) r ) {
115 return l.numerator * r.denominator < l.denominator * r.numerator;
116 } // ?<?
117
118 int ?<=?( rational(T) l, rational(T) r ) {
119 return l.numerator * r.denominator <= l.denominator * r.numerator;
120 } // ?<=?
121
122 int ?>?( rational(T) l, rational(T) r ) {
123 return ! ( l <= r );
124 } // ?>?
125
126 int ?>=?( rational(T) l, rational(T) r ) {
127 return ! ( l < r );
128 } // ?>=?
129
130 // arithmetic
131
132 rational(T) +?( rational(T) r ) {
133 return (rational(T)){ r.numerator, r.denominator };
134 } // +?
135
136 rational(T) -?( rational(T) r ) {
137 return (rational(T)){ -r.numerator, r.denominator };
138 } // -?
139
140 rational(T) ?+?( rational(T) l, rational(T) r ) {
141 if ( l.denominator == r.denominator ) { // special case
142 return (rational(T)){ l.numerator + r.numerator, l.denominator };
143 } else {
144 return (rational(T)){ l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator };
145 } // if
146 } // ?+?
147
148 rational(T) ?+=?( rational(T) & l, rational(T) r ) {
149 l = l + r;
150 return l;
151 } // ?+?
152
153 rational(T) ?+=?( rational(T) & l, one_t ) {
154 l = l + (rational(T)){ 1 };
155 return l;
156 } // ?+?
157
158 rational(T) ?-?( rational(T) l, rational(T) r ) {
159 if ( l.denominator == r.denominator ) { // special case
160 return (rational(T)){ l.numerator - r.numerator, l.denominator };
161 } else {
162 return (rational(T)){ l.numerator * r.denominator - l.denominator * r.numerator, l.denominator * r.denominator };
163 } // if
164 } // ?-?
165
166 rational(T) ?-=?( rational(T) & l, rational(T) r ) {
167 l = l - r;
168 return l;
169 } // ?-?
170
171 rational(T) ?-=?( rational(T) & l, one_t ) {
172 l = l - (rational(T)){ 1 };
173 return l;
174 } // ?-?
175
176 rational(T) ?*?( rational(T) l, rational(T) r ) {
177 return (rational(T)){ l.numerator * r.numerator, l.denominator * r.denominator };
178 } // ?*?
179
180 rational(T) ?*=?( rational(T) & l, rational(T) r ) {
181 return l = l * r;
182 } // ?*?
183
184 rational(T) ?/?( rational(T) l, rational(T) r ) {
185 if ( r.numerator < (T){0} ) {
186 r.[numerator, denominator] = [-r.numerator, -r.denominator];
187 } // if
188 return (rational(T)){ l.numerator * r.denominator, l.denominator * r.numerator };
189 } // ?/?
190
191 rational(T) ?/=?( rational(T) & l, rational(T) r ) {
192 return l = l / r;
193 } // ?/?
194} // distribution
195
196// I/O
197
198forall( T ) {
199 forall( istype & | istream( istype ) | { istype & ?|?( istype &, T & ); } | Simple(T) )
200 istype & ?|?( istype & is, rational(T) & r ) {
201 is | r.numerator | r.denominator;
202 T t = simplify( r.numerator, r.denominator );
203 r.numerator /= t;
204 r.denominator /= t;
205 return is;
206 } // ?|?
207
208 forall( ostype & | ostream( ostype ) | { ostype & ?|?( ostype &, T ); } ) {
209 ostype & ?|?( ostype & os, rational(T) r ) {
210 return os | r.numerator | '/' | r.denominator;
211 } // ?|?
212 OSTYPE_VOID_IMPL( os, rational(T) )
213 } // distribution
214} // distribution
215
216// Exponentiation
217
218forall( T | arithmetic( T ) | { T ?\?( T, unsigned long ); } ) {
219 rational(T) ?\?( rational(T) x, long int y ) {
220 if ( y < 0 ) {
221 return (rational(T)){ x.denominator \ -y, x.numerator \ -y };
222 } else {
223 return (rational(T)){ x.numerator \ y, x.denominator \ y };
224 } // if
225 } // ?\?
226
227 rational(T) ?\=?( rational(T) & x, long int y ) {
228 return x = x \ y;
229 } // ?\?
230} // distribution
231
232// Conversion
233
234forall( T | arithmetic( T ) | { double convert( T ); } )
235double widen( rational(T) r ) {
236 return convert( r.numerator ) / convert( r.denominator );
237} // widen
238
239forall( T | arithmetic( T ) | { double convert( T ); T convert( double ); } )
240rational(T) narrow( double f, T md ) {
241 // http://www.ics.uci.edu/~eppstein/numth/frap.c
242 if ( md <= (T){1} ) { // maximum fractional digits too small?
243 return (rational(T)){ convert( f ), (T){1}}; // truncate fraction
244 } // if
245
246 // continued fraction coefficients
247 T m00 = {1}, m11 = { 1 }, m01 = { 0 }, m10 = { 0 };
248 T ai, t;
249
250 // find terms until denom gets too big
251 for () {
252 ai = convert( f );
253 if ( ! (m10 * ai + m11 <= md) ) break;
254 t = m00 * ai + m01;
255 m01 = m00;
256 m00 = t;
257 t = m10 * ai + m11;
258 m11 = m10;
259 m10 = t;
260 double temp = convert( ai );
261 if ( f == temp ) break; // prevent division by zero
262 f = 1 / (f - temp);
263 if ( f > (double)0x7FFFFFFF ) break; // representation failure
264 } // for
265 return (rational(T)){ m00, m10 };
266} // narrow
267
268// Local Variables: //
269// tab-width: 4 //
270// End: //
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