source: libcfa/src/rational.cfa @ 0087e0e

arm-ehcleanup-dtorsjacob/cs343-translationjenkins-sandboxnew-astnew-ast-unique-expr
Last change on this file since 0087e0e was 0087e0e, checked in by Peter A. Buhr <pabuhr@…>, 3 years ago

add rational exponentiation, code clean up

  • Property mode set to 100644
File size: 7.2 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 Mar 27 08:45:59 2019
13// Update Count     : 180
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.";
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, denominator] = [n / t, d / t];
57        } // rational
58
59
60        // getter for numerator/denominator
61
62        RationalImpl numerator( Rational(RationalImpl) r ) {
63                return r.numerator;
64        } // numerator
65
66        RationalImpl denominator( Rational(RationalImpl) r ) {
67                return r.denominator;
68        } // denominator
69
70        [ RationalImpl, RationalImpl ] ?=?( & [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src ) {
71                return dest = src.[ numerator, denominator ];
72        } // ?=?
73
74        // setter for numerator/denominator
75
76        RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n ) {
77                RationalImpl prev = r.numerator;
78                RationalImpl t = gcd( abs( n ), r.denominator ); // simplify
79                r.[numerator, denominator] = [n / t, r.denominator / t];
80                return prev;
81        } // numerator
82
83        RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d ) {
84                RationalImpl prev = r.denominator;
85                RationalImpl t = simplify( r.numerator, d );    // simplify
86                r.[numerator, denominator] = [r.numerator / t, d / t];
87                return prev;
88        } // denominator
89
90        // comparison
91
92        int ?==?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
93                return l.numerator * r.denominator == l.denominator * r.numerator;
94        } // ?==?
95
96        int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
97                return ! ( l == r );
98        } // ?!=?
99
100        int ?<?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
101                return l.numerator * r.denominator < l.denominator * r.numerator;
102        } // ?<?
103
104        int ?<=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
105                return l.numerator * r.denominator <= l.denominator * r.numerator;
106        } // ?<=?
107
108        int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
109                return ! ( l <= r );
110        } // ?>?
111
112        int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
113                return ! ( l < r );
114        } // ?>=?
115
116        // arithmetic
117
118        Rational(RationalImpl) +?( Rational(RationalImpl) r ) {
119                return (Rational(RationalImpl)){ r.numerator, r.denominator };
120        } // +?
121
122        Rational(RationalImpl) -?( Rational(RationalImpl) r ) {
123                return (Rational(RationalImpl)){ -r.numerator, r.denominator };
124        } // -?
125
126        Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
127                if ( l.denominator == r.denominator ) {                 // special case
128                        return (Rational(RationalImpl)){ l.numerator + r.numerator, l.denominator };
129                } else {
130                        return (Rational(RationalImpl)){ l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator };
131                } // if
132        } // ?+?
133
134        Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
135                if ( l.denominator == r.denominator ) {                 // special case
136                        return (Rational(RationalImpl)){ l.numerator - r.numerator, l.denominator };
137                } else {
138                        return (Rational(RationalImpl)){ l.numerator * r.denominator - l.denominator * r.numerator, l.denominator * r.denominator };
139                } // if
140        } // ?-?
141
142        Rational(RationalImpl) ?*?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
143                return (Rational(RationalImpl)){ l.numerator * r.numerator, l.denominator * r.denominator };
144        } // ?*?
145
146        Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
147                if ( r.numerator < (RationalImpl){0} ) {
148                        r.[numerator, denominator] = [-r.numerator, -r.denominator];
149                } // if
150                return (Rational(RationalImpl)){ l.numerator * r.denominator, l.denominator * r.numerator };
151        } // ?/?
152
153        // I/O
154
155        forall( dtype istype | istream( istype ) | { istype & ?|?( istype &, RationalImpl & ); } )
156        istype & ?|?( istype & is, Rational(RationalImpl) & r ) {
157                is | r.numerator | r.denominator;
158                RationalImpl t = simplify( r.numerator, r.denominator );
159                r.numerator /= t;
160                r.denominator /= t;
161                return is;
162        } // ?|?
163
164        forall( dtype ostype | ostream( ostype ) | { ostype & ?|?( ostype &, RationalImpl ); } ) {
165                ostype & ?|?( ostype & os, Rational(RationalImpl) r ) {
166                        return os | r.numerator | '/' | r.denominator;
167                } // ?|?
168
169                void ?|?( ostype & os, Rational(RationalImpl) r ) {
170                        (ostype &)(os | r); nl( os );
171                } // ?|?
172        } // distribution
173} // distribution
174
175forall( otype RationalImpl | arithmetic( RationalImpl ) | { RationalImpl ?\?( RationalImpl, unsigned long ); } )
176Rational(RationalImpl) ?\?( Rational(RationalImpl) x, long int y ) {
177        if ( y < 0 ) {
178                return (Rational(RationalImpl)){ x.denominator \ -y, x.numerator \ -y };
179        } else {
180                return (Rational(RationalImpl)){ x.numerator \ y, x.denominator \ y };
181        } // if
182}
183
184// conversion
185
186forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); } )
187double widen( Rational(RationalImpl) r ) {
188        return convert( r.numerator ) / convert( r.denominator );
189} // widen
190
191forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); RationalImpl convert( double ); } )
192Rational(RationalImpl) narrow( double f, RationalImpl md ) {
193        // http://www.ics.uci.edu/~eppstein/numth/frap.c
194        if ( md <= (RationalImpl){1} ) {                                        // maximum fractional digits too small?
195                return (Rational(RationalImpl)){ convert( f ), (RationalImpl){1}}; // truncate fraction
196        } // if
197
198        // continued fraction coefficients
199        RationalImpl m00 = {1}, m11 = { 1 }, m01 = { 0 }, m10 = { 0 };
200        RationalImpl ai, t;
201
202        // find terms until denom gets too big
203        for ( ;; ) {
204                ai = convert( f );
205          if ( ! (m10 * ai + m11 <= md) ) break;
206                t = m00 * ai + m01;
207                m01 = m00;
208                m00 = t;
209                t = m10 * ai + m11;
210                m11 = m10;
211                m10 = t;
212                double temp = convert( ai );
213          if ( f == temp ) break;                                                       // prevent division by zero
214                f = 1 / (f - temp);
215          if ( f > (double)0x7FFFFFFF ) break;                          // representation failure
216        } // for
217        return (Rational(RationalImpl)){ m00, m10 };
218} // narrow
219
220// Local Variables: //
221// tab-width: 4 //
222// End: //
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