source: libcfa/src/rational.cfa@ 88b49bb

ADT ast-experimental
Last change on this file since 88b49bb was f6a4917, checked in by Peter A. Buhr <pabuhr@…>, 3 years ago

change C loop control to CFA loop control
  • Property mode set to 100644
File size: 6.9 KB
RevLine 
[a493682]1//
[53ba273]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.
[a493682]6//
7// rational.c --
8//
[53ba273]9// Author : Peter A. Buhr
10// Created On : Wed Apr 6 17:54:28 2016
11// Last Modified By : Peter A. Buhr
[f6a4917]12// Last Modified On : Thu Aug 25 18:09:58 2022
13// Update Count : 194
[a493682]14//
[53ba273]15
[58b6d1b]16#include "rational.hfa"
17#include "fstream.hfa"
18#include "stdlib.hfa"
[53ba273]19
[0aa4beb]20#pragma GCC visibility push(default)
21
[5dc4c7e]22forall( T | Arithmetic( T ) ) {
[3ce0d440]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
[5dc4c7e]27 static T gcd( T a, T b ) {
[f6a4917]28 for () { // Euclid's algorithm
[5dc4c7e]29 T r = a % b;
30 if ( r == (T){0} ) break;
[3ce0d440]31 a = b;
32 b = r;
33 } // for
34 return b;
35 } // gcd
36
[5dc4c7e]37 static T simplify( T & n, T & d ) {
38 if ( d == (T){0} ) {
[ff2a33e]39 abort | "Invalid rational number construction: denominator cannot be equal to 0.";
[3ce0d440]40 } // exit
[5dc4c7e]41 if ( d < (T){0} ) { d = -d; n = -n; } // move sign to numerator
[3ce0d440]42 return gcd( abs( n ), d ); // simplify
43 } // Rationalnumber::simplify
44
45 // constructors
46
[5dc4c7e]47 void ?{}( Rational(T) & r, zero_t ) {
48 r{ (T){0}, (T){1} };
[3ce0d440]49 } // rational
50
[5dc4c7e]51 void ?{}( Rational(T) & r, one_t ) {
52 r{ (T){1}, (T){1} };
[3ce0d440]53 } // rational
54
[5dc4c7e]55 void ?{}( Rational(T) & r ) {
56 r{ (T){0}, (T){1} };
[3ce0d440]57 } // rational
58
[5dc4c7e]59 void ?{}( Rational(T) & r, T n ) {
60 r{ n, (T){1} };
[f00b2c2c]61 } // rational
62
[5dc4c7e]63 void ?{}( Rational(T) & r, T n, T d ) {
64 T t = simplify( n, d ); // simplify
65 r.[numerator, denominator] = [n / t, d / t];
[f00b2c2c]66 } // rational
[3ce0d440]67
68 // getter for numerator/denominator
69
[5dc4c7e]70 T numerator( Rational(T) r ) {
[3ce0d440]71 return r.numerator;
72 } // numerator
73
[5dc4c7e]74 T denominator( Rational(T) r ) {
[3ce0d440]75 return r.denominator;
76 } // denominator
77
[5dc4c7e]78 [ T, T ] ?=?( & [ T, T ] dest, Rational(T) src ) {
[3ce0d440]79 return dest = src.[ numerator, denominator ];
80 } // ?=?
81
82 // setter for numerator/denominator
83
[5dc4c7e]84 T numerator( Rational(T) r, T n ) {
85 T prev = r.numerator;
86 T t = gcd( abs( n ), r.denominator ); // simplify
[0087e0e]87 r.[numerator, denominator] = [n / t, r.denominator / t];
[3ce0d440]88 return prev;
89 } // numerator
90
[5dc4c7e]91 T denominator( Rational(T) r, T d ) {
92 T prev = r.denominator;
93 T t = simplify( r.numerator, d ); // simplify
[0087e0e]94 r.[numerator, denominator] = [r.numerator / t, d / t];
[3ce0d440]95 return prev;
96 } // denominator
97
98 // comparison
99
[5dc4c7e]100 int ?==?( Rational(T) l, Rational(T) r ) {
[3ce0d440]101 return l.numerator * r.denominator == l.denominator * r.numerator;
102 } // ?==?
103
[5dc4c7e]104 int ?!=?( Rational(T) l, Rational(T) r ) {
[3ce0d440]105 return ! ( l == r );
106 } // ?!=?
107
[5dc4c7e]108 int ?!=?( Rational(T) l, zero_t ) {
109 return ! ( l == (Rational(T)){ 0 } );
110 } // ?!=?
111
112 int ?<?( Rational(T) l, Rational(T) r ) {
[3ce0d440]113 return l.numerator * r.denominator < l.denominator * r.numerator;
114 } // ?<?
115
[5dc4c7e]116 int ?<=?( Rational(T) l, Rational(T) r ) {
[3ce0d440]117 return l.numerator * r.denominator <= l.denominator * r.numerator;
118 } // ?<=?
119
[5dc4c7e]120 int ?>?( Rational(T) l, Rational(T) r ) {
[3ce0d440]121 return ! ( l <= r );
122 } // ?>?
123
[5dc4c7e]124 int ?>=?( Rational(T) l, Rational(T) r ) {
[3ce0d440]125 return ! ( l < r );
126 } // ?>=?
127
128 // arithmetic
129
[5dc4c7e]130 Rational(T) +?( Rational(T) r ) {
131 return (Rational(T)){ r.numerator, r.denominator };
[3ce0d440]132 } // +?
[53ba273]133
[5dc4c7e]134 Rational(T) -?( Rational(T) r ) {
135 return (Rational(T)){ -r.numerator, r.denominator };
[3ce0d440]136 } // -?
137
[5dc4c7e]138 Rational(T) ?+?( Rational(T) l, Rational(T) r ) {
[3ce0d440]139 if ( l.denominator == r.denominator ) { // special case
[5dc4c7e]140 return (Rational(T)){ l.numerator + r.numerator, l.denominator };
[3ce0d440]141 } else {
[5dc4c7e]142 return (Rational(T)){ l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator };
[3ce0d440]143 } // if
144 } // ?+?
145
[5dc4c7e]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 ) {
[3ce0d440]157 if ( l.denominator == r.denominator ) { // special case
[5dc4c7e]158 return (Rational(T)){ l.numerator - r.numerator, l.denominator };
[3ce0d440]159 } else {
[5dc4c7e]160 return (Rational(T)){ l.numerator * r.denominator - l.denominator * r.numerator, l.denominator * r.denominator };
[3ce0d440]161 } // if
162 } // ?-?
163
[5dc4c7e]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;
[3ce0d440]180 } // ?*?
181
[5dc4c7e]182 Rational(T) ?/?( Rational(T) l, Rational(T) r ) {
183 if ( r.numerator < (T){0} ) {
[0087e0e]184 r.[numerator, denominator] = [-r.numerator, -r.denominator];
[3ce0d440]185 } // if
[5dc4c7e]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;
[3ce0d440]191 } // ?/?
192
193 // I/O
194
[5dc4c7e]195 forall( istype & | istream( istype ) | { istype & ?|?( istype &, T & ); } )
196 istype & ?|?( istype & is, Rational(T) & r ) {
[3ce0d440]197 is | r.numerator | r.denominator;
[5dc4c7e]198 T t = simplify( r.numerator, r.denominator );
[3ce0d440]199 r.numerator /= t;
200 r.denominator /= t;
201 return is;
202 } // ?|?
203
[5dc4c7e]204 forall( ostype & | ostream( ostype ) | { ostype & ?|?( ostype &, T ); } ) {
205 ostype & ?|?( ostype & os, Rational(T) r ) {
[200fcb3]206 return os | r.numerator | '/' | r.denominator;
207 } // ?|?
208
[5dc4c7e]209 void ?|?( ostype & os, Rational(T) r ) {
[65240bb]210 (ostype &)(os | r); ends( os );
[200fcb3]211 } // ?|?
212 } // distribution
[3ce0d440]213} // distribution
[630a82a]214
[5dc4c7e]215forall( T | Arithmetic( T ) | { T ?\?( T, unsigned long ); } ) {
216 Rational(T) ?\?( Rational(T) x, long int y ) {
217 if ( y < 0 ) {
218 return (Rational(T)){ x.denominator \ -y, x.numerator \ -y };
219 } else {
220 return (Rational(T)){ x.numerator \ y, x.denominator \ y };
221 } // if
222 } // ?\?
223
224 Rational(T) ?\=?( Rational(T) & x, long int y ) {
225 return x = x \ y;
226 } // ?\?
227} // distribution
[0087e0e]228
[630a82a]229// conversion
230
[5dc4c7e]231forall( T | Arithmetic( T ) | { double convert( T ); } )
232double widen( Rational(T) r ) {
[6c6455f]233 return convert( r.numerator ) / convert( r.denominator );
234} // widen
235
[5dc4c7e]236forall( T | Arithmetic( T ) | { double convert( T ); T convert( double ); } )
237Rational(T) narrow( double f, T md ) {
[3ce0d440]238 // http://www.ics.uci.edu/~eppstein/numth/frap.c
[5dc4c7e]239 if ( md <= (T){1} ) { // maximum fractional digits too small?
240 return (Rational(T)){ convert( f ), (T){1}}; // truncate fraction
[6c6455f]241 } // if
242
243 // continued fraction coefficients
[5dc4c7e]244 T m00 = {1}, m11 = { 1 }, m01 = { 0 }, m10 = { 0 };
245 T ai, t;
[6c6455f]246
247 // find terms until denom gets too big
[f6a4917]248 for () {
[6c6455f]249 ai = convert( f );
250 if ( ! (m10 * ai + m11 <= md) ) break;
251 t = m00 * ai + m01;
252 m01 = m00;
253 m00 = t;
254 t = m10 * ai + m11;
255 m11 = m10;
256 m10 = t;
257 double temp = convert( ai );
258 if ( f == temp ) break; // prevent division by zero
259 f = 1 / (f - temp);
260 if ( f > (double)0x7FFFFFFF ) break; // representation failure
261 } // for
[5dc4c7e]262 return (Rational(T)){ m00, m10 };
[6c6455f]263} // narrow
[53ba273]264
265// Local Variables: //
266// tab-width: 4 //
267// End: //
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