source: libcfa/src/rational.cfa @ 58b6d1b

aaron-thesisarm-ehcleanup-dtorsdeferred_resndemanglerjacob/cs343-translationjenkins-sandboxnew-astnew-ast-unique-exprno_listpersistent-indexer
Last change on this file since 58b6d1b was 58b6d1b, checked in by Thierry Delisle <tdelisle@…>, 3 years ago

Fixed tests after headers change

  • 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 : Sat Jun  2 09:24:33 2018
13// Update Count     : 162
14//
15
16#include "rational.hfa"
17#include "fstream.hfa"
18#include "stdlib.hfa"
19
20forall( otype RationalImpl | arithmetic( RationalImpl ) ) {
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 RationalImpl gcd( RationalImpl a, RationalImpl b ) {
26                for ( ;; ) {                                                                    // Euclid's algorithm
27                        RationalImpl r = a % b;
28                  if ( r == (RationalImpl){0} ) break;
29                        a = b;
30                        b = r;
31                } // for
32                return b;
33        } // gcd
34
35        static RationalImpl simplify( RationalImpl & n, RationalImpl & d ) {
36                if ( d == (RationalImpl){0} ) {
37                        serr | "Invalid rational number construction: denominator cannot be equal to 0." | endl;
38                        exit( EXIT_FAILURE );
39                } // exit
40                if ( d < (RationalImpl){0} ) { d = -d; n = -n; } // move sign to numerator
41                return gcd( abs( n ), d );                                              // simplify
42        } // Rationalnumber::simplify
43
44        // constructors
45
46        void ?{}( Rational(RationalImpl) & r ) {
47                r{ (RationalImpl){0}, (RationalImpl){1} };
48        } // rational
49
50        void ?{}( Rational(RationalImpl) & r, RationalImpl n ) {
51                r{ n, (RationalImpl){1} };
52        } // rational
53
54        void ?{}( Rational(RationalImpl) & r, RationalImpl n, RationalImpl d ) {
55                RationalImpl t = simplify( n, d );                              // simplify
56                r.numerator = n / t;
57                r.denominator = d / t;
58        } // rational
59
60
61        // getter for numerator/denominator
62
63        RationalImpl numerator( Rational(RationalImpl) r ) {
64                return r.numerator;
65        } // numerator
66
67        RationalImpl denominator( Rational(RationalImpl) r ) {
68                return r.denominator;
69        } // denominator
70
71        [ RationalImpl, RationalImpl ] ?=?( & [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src ) {
72                return dest = src.[ numerator, denominator ];
73        } // ?=?
74
75        // setter for numerator/denominator
76
77        RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n ) {
78                RationalImpl prev = r.numerator;
79                RationalImpl t = gcd( abs( n ), r.denominator ); // simplify
80                r.numerator = n / t;
81                r.denominator = r.denominator / t;
82                return prev;
83        } // numerator
84
85        RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d ) {
86                RationalImpl prev = r.denominator;
87                RationalImpl t = simplify( r.numerator, d );    // simplify
88                r.numerator = r.numerator / t;
89                r.denominator = d / t;
90                return prev;
91        } // denominator
92
93        // comparison
94
95        int ?==?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
96                return l.numerator * r.denominator == l.denominator * r.numerator;
97        } // ?==?
98
99        int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
100                return ! ( l == r );
101        } // ?!=?
102
103        int ?<?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
104                return l.numerator * r.denominator < l.denominator * r.numerator;
105        } // ?<?
106
107        int ?<=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
108                return l.numerator * r.denominator <= l.denominator * r.numerator;
109        } // ?<=?
110
111        int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
112                return ! ( l <= r );
113        } // ?>?
114
115        int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
116                return ! ( l < r );
117        } // ?>=?
118
119        // arithmetic
120
121        Rational(RationalImpl) +?( Rational(RationalImpl) r ) {
122                Rational(RationalImpl) t = { r.numerator, r.denominator };
123                return t;
124        } // +?
125
126        Rational(RationalImpl) -?( Rational(RationalImpl) r ) {
127                Rational(RationalImpl) t = { -r.numerator, r.denominator };
128                return t;
129        } // -?
130
131        Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
132                if ( l.denominator == r.denominator ) {                 // special case
133                        Rational(RationalImpl) t = { l.numerator + r.numerator, l.denominator };
134                        return t;
135                } else {
136                        Rational(RationalImpl) t = { l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator };
137                        return t;
138                } // if
139        } // ?+?
140
141        Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
142                if ( l.denominator == r.denominator ) {                 // special case
143                        Rational(RationalImpl) t = { l.numerator - r.numerator, l.denominator };
144                        return t;
145                } else {
146                        Rational(RationalImpl) t = { l.numerator * r.denominator - l.denominator * r.numerator, l.denominator * r.denominator };
147                        return t;
148                } // if
149        } // ?-?
150
151        Rational(RationalImpl) ?*?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
152                Rational(RationalImpl) t = { l.numerator * r.numerator, l.denominator * r.denominator };
153                return t;
154        } // ?*?
155
156        Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
157                if ( r.numerator < (RationalImpl){0} ) {
158                        r.numerator = -r.numerator;
159                        r.denominator = -r.denominator;
160                } // if
161                Rational(RationalImpl) t = { l.numerator * r.denominator, l.denominator * r.numerator };
162                return t;
163        } // ?/?
164
165        // I/O
166
167        forall( dtype istype | istream( istype ) | { istype & ?|?( istype &, RationalImpl & ); } )
168        istype & ?|?( istype & is, Rational(RationalImpl) & r ) {
169                RationalImpl t;
170                is | r.numerator | r.denominator;
171                t = simplify( r.numerator, r.denominator );
172                r.numerator /= t;
173                r.denominator /= t;
174                return is;
175        } // ?|?
176
177        forall( dtype ostype | ostream( ostype ) | { ostype & ?|?( ostype &, RationalImpl ); } )
178        ostype & ?|?( ostype & os, Rational(RationalImpl ) r ) {
179                return os | r.numerator | '/' | r.denominator;
180        } // ?|?
181} // distribution
182
183// conversion
184
185forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); } )
186double widen( Rational(RationalImpl) r ) {
187        return convert( r.numerator ) / convert( r.denominator );
188} // widen
189
190forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); RationalImpl convert( double ); } )
191Rational(RationalImpl) narrow( double f, RationalImpl md ) {
192        // http://www.ics.uci.edu/~eppstein/numth/frap.c
193        if ( md <= (RationalImpl){1} ) {                                        // maximum fractional digits too small?
194                return (Rational(RationalImpl)){ convert( f ), (RationalImpl){1}}; // truncate fraction
195        } // if
196
197        // continued fraction coefficients
198        RationalImpl m00 = {1}, m11 = { 1 }, m01 = { 0 }, m10 = { 0 };
199        RationalImpl ai, t;
200
201        // find terms until denom gets too big
202        for ( ;; ) {
203                ai = convert( f );
204          if ( ! (m10 * ai + m11 <= md) ) break;
205                t = m00 * ai + m01;
206                m01 = m00;
207                m00 = t;
208                t = m10 * ai + m11;
209                m11 = m10;
210                m10 = t;
211                double temp = convert( ai );
212          if ( f == temp ) break;                                                       // prevent division by zero
213                f = 1 / (f - temp);
214          if ( f > (double)0x7FFFFFFF ) break;                          // representation failure
215        } // for
216        return (Rational(RationalImpl)){ m00, m10 };
217} // narrow
218
219// Local Variables: //
220// tab-width: 4 //
221// End: //
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