source: libcfa/src/rational.cfa@ 0cc3c47

ADT arm-eh ast-experimental enum forall-pointer-decay jacob/cs343-translation jenkins-sandbox new-ast new-ast-unique-expr pthread-emulation qualifiedEnum
Last change on this file since 0cc3c47 was f00b2c2c, checked in by Peter A. Buhr <pabuhr@…>, 6 years ago

defined rational constructor from 0 [fixes #117]
  • Property mode set to 100644
File size: 7.4 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 Feb 8 17:56:36 2020
13// Update Count : 187
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 abort | "Invalid rational number construction: denominator cannot be equal to 0.";
38 } // exit
39 if ( d < (RationalImpl){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(RationalImpl) & r ) {
46 r{ (RationalImpl){0}, (RationalImpl){1} };
47 } // rational
48
49 void ?{}( Rational(RationalImpl) & r, RationalImpl n ) {
50 r{ n, (RationalImpl){1} };
51 } // rational
52
53 void ?{}( Rational(RationalImpl) & r, RationalImpl n, RationalImpl d ) {
54 RationalImpl t = simplify( n, d ); // simplify
55 r.[numerator, denominator] = [n / t, d / t];
56 } // rational
57
58 void ?{}( Rational(RationalImpl) & r, zero_t ) {
59 r{ (RationalImpl){0}, (RationalImpl){1} };
60 } // rational
61
62 void ?{}( Rational(RationalImpl) & r, one_t ) {
63 r{ (RationalImpl){1}, (RationalImpl){1} };
64 } // rational
65
66 // getter for numerator/denominator
67
68 RationalImpl numerator( Rational(RationalImpl) r ) {
69 return r.numerator;
70 } // numerator
71
72 RationalImpl denominator( Rational(RationalImpl) r ) {
73 return r.denominator;
74 } // denominator
75
76 [ RationalImpl, RationalImpl ] ?=?( & [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src ) {
77 return dest = src.[ numerator, denominator ];
78 } // ?=?
79
80 // setter for numerator/denominator
81
82 RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n ) {
83 RationalImpl prev = r.numerator;
84 RationalImpl t = gcd( abs( n ), r.denominator ); // simplify
85 r.[numerator, denominator] = [n / t, r.denominator / t];
86 return prev;
87 } // numerator
88
89 RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d ) {
90 RationalImpl prev = r.denominator;
91 RationalImpl 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(RationalImpl) l, Rational(RationalImpl) r ) {
99 return l.numerator * r.denominator == l.denominator * r.numerator;
100 } // ?==?
101
102 int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
103 return ! ( l == r );
104 } // ?!=?
105
106 int ?<?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
107 return l.numerator * r.denominator < l.denominator * r.numerator;
108 } // ?<?
109
110 int ?<=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
111 return l.numerator * r.denominator <= l.denominator * r.numerator;
112 } // ?<=?
113
114 int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
115 return ! ( l <= r );
116 } // ?>?
117
118 int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
119 return ! ( l < r );
120 } // ?>=?
121
122 // arithmetic
123
124 Rational(RationalImpl) +?( Rational(RationalImpl) r ) {
125 return (Rational(RationalImpl)){ r.numerator, r.denominator };
126 } // +?
127
128 Rational(RationalImpl) -?( Rational(RationalImpl) r ) {
129 return (Rational(RationalImpl)){ -r.numerator, r.denominator };
130 } // -?
131
132 Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
133 if ( l.denominator == r.denominator ) { // special case
134 return (Rational(RationalImpl)){ l.numerator + r.numerator, l.denominator };
135 } else {
136 return (Rational(RationalImpl)){ l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator };
137 } // if
138 } // ?+?
139
140 Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
141 if ( l.denominator == r.denominator ) { // special case
142 return (Rational(RationalImpl)){ l.numerator - r.numerator, l.denominator };
143 } else {
144 return (Rational(RationalImpl)){ l.numerator * r.denominator - l.denominator * r.numerator, l.denominator * r.denominator };
145 } // if
146 } // ?-?
147
148 Rational(RationalImpl) ?*?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
149 return (Rational(RationalImpl)){ l.numerator * r.numerator, l.denominator * r.denominator };
150 } // ?*?
151
152 Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
153 if ( r.numerator < (RationalImpl){0} ) {
154 r.[numerator, denominator] = [-r.numerator, -r.denominator];
155 } // if
156 return (Rational(RationalImpl)){ l.numerator * r.denominator, l.denominator * r.numerator };
157 } // ?/?
158
159 // I/O
160
161 forall( dtype istype | istream( istype ) | { istype & ?|?( istype &, RationalImpl & ); } )
162 istype & ?|?( istype & is, Rational(RationalImpl) & r ) {
163 is | r.numerator | r.denominator;
164 RationalImpl t = simplify( r.numerator, r.denominator );
165 r.numerator /= t;
166 r.denominator /= t;
167 return is;
168 } // ?|?
169
170 forall( dtype ostype | ostream( ostype ) | { ostype & ?|?( ostype &, RationalImpl ); } ) {
171 ostype & ?|?( ostype & os, Rational(RationalImpl) r ) {
172 return os | r.numerator | '/' | r.denominator;
173 } // ?|?
174
175 void ?|?( ostype & os, Rational(RationalImpl) r ) {
176 (ostype &)(os | r); ends( os );
177 } // ?|?
178 } // distribution
179} // distribution
180
181forall( otype RationalImpl | arithmetic( RationalImpl ) | { RationalImpl ?\?( RationalImpl, unsigned long ); } )
182Rational(RationalImpl) ?\?( Rational(RationalImpl) x, long int y ) {
183 if ( y < 0 ) {
184 return (Rational(RationalImpl)){ x.denominator \ -y, x.numerator \ -y };
185 } else {
186 return (Rational(RationalImpl)){ x.numerator \ y, x.denominator \ y };
187 } // if
188}
189
190// conversion
191
192forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); } )
193double widen( Rational(RationalImpl) r ) {
194 return convert( r.numerator ) / convert( r.denominator );
195} // widen
196
197forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); RationalImpl convert( double ); } )
198Rational(RationalImpl) narrow( double f, RationalImpl md ) {
199 // http://www.ics.uci.edu/~eppstein/numth/frap.c
200 if ( md <= (RationalImpl){1} ) { // maximum fractional digits too small?
201 return (Rational(RationalImpl)){ convert( f ), (RationalImpl){1}}; // truncate fraction
202 } // if
203
204 // continued fraction coefficients
205 RationalImpl m00 = {1}, m11 = { 1 }, m01 = { 0 }, m10 = { 0 };
206 RationalImpl ai, t;
207
208 // find terms until denom gets too big
209 for ( ;; ) {
210 ai = convert( f );
211 if ( ! (m10 * ai + m11 <= md) ) break;
212 t = m00 * ai + m01;
213 m01 = m00;
214 m00 = t;
215 t = m10 * ai + m11;
216 m11 = m10;
217 m10 = t;
218 double temp = convert( ai );
219 if ( f == temp ) break; // prevent division by zero
220 f = 1 / (f - temp);
221 if ( f > (double)0x7FFFFFFF ) break; // representation failure
222 } // for
223 return (Rational(RationalImpl)){ m00, m10 };
224} // narrow
225
226// Local Variables: //
227// tab-width: 4 //
228// End: //
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