source: libcfa/src/rational.cfa@ f806b61

ADT arm-eh ast-experimental cleanup-dtors enum forall-pointer-decay jacob/cs343-translation jenkins-sandbox new-ast new-ast-unique-expr pthread-emulation qualifiedEnum
Last change on this file since f806b61 was 0087e0e, checked in by Peter A. Buhr <pabuhr@…>, 7 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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