source: libcfa/src/rational.cfa@ 941e14a

ADT ast-experimental enum forall-pointer-decay pthread-emulation qualifiedEnum
Last change on this file since 941e14a was 5dc4c7e, checked in by Peter A. Buhr <pabuhr@…>, 4 years ago

formatting, use new math trait in rational numbers
  • Property mode set to 100644
File size: 6.8 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 : Tue Jul 20 16:30:06 2021
13// Update Count : 193
14//
15
16#include "rational.hfa"
17#include "fstream.hfa"
18#include "stdlib.hfa"
19
20forall( T | Arithmetic( T ) ) {
21 // helper routines
22
23 // Calculate greatest common denominator of two numbers, the first of which may be negative. Used to reduce
24 // rationals. alternative: https://en.wikipedia.org/wiki/Binary_GCD_algorithm
25 static T gcd( T a, T b ) {
26 for ( ;; ) { // Euclid's algorithm
27 T r = a % b;
28 if ( r == (T){0} ) break;
29 a = b;
30 b = r;
31 } // for
32 return b;
33 } // gcd
34
35 static T simplify( T & n, T & d ) {
36 if ( d == (T){0} ) {
37 abort | "Invalid rational number construction: denominator cannot be equal to 0.";
38 } // exit
39 if ( d < (T){0} ) { d = -d; n = -n; } // move sign to numerator
40 return gcd( abs( n ), d ); // simplify
41 } // Rationalnumber::simplify
42
43 // constructors
44
45 void ?{}( Rational(T) & r, zero_t ) {
46 r{ (T){0}, (T){1} };
47 } // rational
48
49 void ?{}( Rational(T) & r, one_t ) {
50 r{ (T){1}, (T){1} };
51 } // rational
52
53 void ?{}( Rational(T) & r ) {
54 r{ (T){0}, (T){1} };
55 } // rational
56
57 void ?{}( Rational(T) & r, T n ) {
58 r{ n, (T){1} };
59 } // rational
60
61 void ?{}( Rational(T) & r, T n, T d ) {
62 T t = simplify( n, d ); // simplify
63 r.[numerator, denominator] = [n / t, d / t];
64 } // rational
65
66 // getter for numerator/denominator
67
68 T numerator( Rational(T) r ) {
69 return r.numerator;
70 } // numerator
71
72 T denominator( Rational(T) r ) {
73 return r.denominator;
74 } // denominator
75
76 [ T, T ] ?=?( & [ T, T ] dest, Rational(T) src ) {
77 return dest = src.[ numerator, denominator ];
78 } // ?=?
79
80 // setter for numerator/denominator
81
82 T numerator( Rational(T) r, T n ) {
83 T prev = r.numerator;
84 T t = gcd( abs( n ), r.denominator ); // simplify
85 r.[numerator, denominator] = [n / t, r.denominator / t];
86 return prev;
87 } // numerator
88
89 T denominator( Rational(T) r, T d ) {
90 T prev = r.denominator;
91 T t = simplify( r.numerator, d ); // simplify
92 r.[numerator, denominator] = [r.numerator / t, d / t];
93 return prev;
94 } // denominator
95
96 // comparison
97
98 int ?==?( Rational(T) l, Rational(T) r ) {
99 return l.numerator * r.denominator == l.denominator * r.numerator;
100 } // ?==?
101
102 int ?!=?( Rational(T) l, Rational(T) r ) {
103 return ! ( l == r );
104 } // ?!=?
105
106 int ?!=?( Rational(T) l, zero_t ) {
107 return ! ( l == (Rational(T)){ 0 } );
108 } // ?!=?
109
110 int ?<?( Rational(T) l, Rational(T) r ) {
111 return l.numerator * r.denominator < l.denominator * r.numerator;
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 <= r );
120 } // ?>?
121
122 int ?>=?( Rational(T) l, Rational(T) r ) {
123 return ! ( l < r );
124 } // ?>=?
125
126 // arithmetic
127
128 Rational(T) +?( Rational(T) r ) {
129 return (Rational(T)){ r.numerator, r.denominator };
130 } // +?
131
132 Rational(T) -?( Rational(T) r ) {
133 return (Rational(T)){ -r.numerator, r.denominator };
134 } // -?
135
136 Rational(T) ?+?( Rational(T) l, Rational(T) r ) {
137 if ( l.denominator == r.denominator ) { // special case
138 return (Rational(T)){ l.numerator + r.numerator, l.denominator };
139 } else {
140 return (Rational(T)){ l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator };
141 } // if
142 } // ?+?
143
144 Rational(T) ?+=?( Rational(T) & l, Rational(T) r ) {
145 l = l + r;
146 return l;
147 } // ?+?
148
149 Rational(T) ?+=?( Rational(T) & l, one_t ) {
150 l = l + (Rational(T)){ 1 };
151 return l;
152 } // ?+?
153
154 Rational(T) ?-?( Rational(T) l, Rational(T) r ) {
155 if ( l.denominator == r.denominator ) { // special case
156 return (Rational(T)){ l.numerator - r.numerator, l.denominator };
157 } else {
158 return (Rational(T)){ l.numerator * r.denominator - l.denominator * r.numerator, l.denominator * r.denominator };
159 } // if
160 } // ?-?
161
162 Rational(T) ?-=?( Rational(T) & l, Rational(T) r ) {
163 l = l - r;
164 return l;
165 } // ?-?
166
167 Rational(T) ?-=?( Rational(T) & l, one_t ) {
168 l = l - (Rational(T)){ 1 };
169 return l;
170 } // ?-?
171
172 Rational(T) ?*?( Rational(T) l, Rational(T) r ) {
173 return (Rational(T)){ l.numerator * r.numerator, l.denominator * r.denominator };
174 } // ?*?
175
176 Rational(T) ?*=?( Rational(T) & l, Rational(T) r ) {
177 return l = l * r;
178 } // ?*?
179
180 Rational(T) ?/?( Rational(T) l, Rational(T) r ) {
181 if ( r.numerator < (T){0} ) {
182 r.[numerator, denominator] = [-r.numerator, -r.denominator];
183 } // if
184 return (Rational(T)){ l.numerator * r.denominator, l.denominator * r.numerator };
185 } // ?/?
186
187 Rational(T) ?/=?( Rational(T) & l, Rational(T) r ) {
188 return l = l / r;
189 } // ?/?
190
191 // I/O
192
193 forall( istype & | istream( istype ) | { istype & ?|?( istype &, T & ); } )
194 istype & ?|?( istype & is, Rational(T) & r ) {
195 is | r.numerator | r.denominator;
196 T t = simplify( r.numerator, r.denominator );
197 r.numerator /= t;
198 r.denominator /= t;
199 return is;
200 } // ?|?
201
202 forall( ostype & | ostream( ostype ) | { ostype & ?|?( ostype &, T ); } ) {
203 ostype & ?|?( ostype & os, Rational(T) r ) {
204 return os | r.numerator | '/' | r.denominator;
205 } // ?|?
206
207 void ?|?( ostype & os, Rational(T) r ) {
208 (ostype &)(os | r); ends( os );
209 } // ?|?
210 } // distribution
211} // distribution
212
213forall( T | Arithmetic( T ) | { T ?\?( T, unsigned long ); } ) {
214 Rational(T) ?\?( Rational(T) x, long int y ) {
215 if ( y < 0 ) {
216 return (Rational(T)){ x.denominator \ -y, x.numerator \ -y };
217 } else {
218 return (Rational(T)){ x.numerator \ y, x.denominator \ y };
219 } // if
220 } // ?\?
221
222 Rational(T) ?\=?( Rational(T) & x, long int y ) {
223 return x = x \ y;
224 } // ?\?
225} // distribution
226
227// conversion
228
229forall( T | Arithmetic( T ) | { double convert( T ); } )
230double widen( Rational(T) r ) {
231 return convert( r.numerator ) / convert( r.denominator );
232} // widen
233
234forall( T | Arithmetic( T ) | { double convert( T ); T convert( double ); } )
235Rational(T) narrow( double f, T md ) {
236 // http://www.ics.uci.edu/~eppstein/numth/frap.c
237 if ( md <= (T){1} ) { // maximum fractional digits too small?
238 return (Rational(T)){ convert( f ), (T){1}}; // truncate fraction
239 } // if
240
241 // continued fraction coefficients
242 T m00 = {1}, m11 = { 1 }, m01 = { 0 }, m10 = { 0 };
243 T ai, t;
244
245 // find terms until denom gets too big
246 for ( ;; ) {
247 ai = convert( f );
248 if ( ! (m10 * ai + m11 <= md) ) break;
249 t = m00 * ai + m01;
250 m01 = m00;
251 m00 = t;
252 t = m10 * ai + m11;
253 m11 = m10;
254 m10 = t;
255 double temp = convert( ai );
256 if ( f == temp ) break; // prevent division by zero
257 f = 1 / (f - temp);
258 if ( f > (double)0x7FFFFFFF ) break; // representation failure
259 } // for
260 return (Rational(T)){ m00, m10 };
261} // narrow
262
263// Local Variables: //
264// tab-width: 4 //
265// End: //
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