source: src/libcfa/rational.c@ 6d43cc57

ADT aaron-thesis arm-eh ast-experimental cleanup-dtors deferred_resn demangler enum forall-pointer-decay jacob/cs343-translation jenkins-sandbox new-ast new-ast-unique-expr new-env no_list persistent-indexer pthread-emulation qualifiedEnum with_gc
Last change on this file since 6d43cc57 was 3ce0d440, checked in by Peter A. Buhr <pabuhr@…>, 7 years ago

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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"
17#include "fstream"
18#include "stdlib"
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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