source: src/libcfa/rational.c@ b60f9d9

new-env
Last change on this file since b60f9d9 was 09687aa, checked in by Peter A. Buhr <pabuhr@…>, 8 years ago

complete conversion of iostream/fstream to use references
  • Property mode set to 100644
File size: 7.9 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 Dec 6 23:13:58 2017
13// Update Count : 156
14//
15
16#include "rational"
17#include "fstream"
18#include "stdlib"
19
20// helper routines
21
22// Calculate greatest common denominator of two numbers, the first of which may be negative. Used to reduce rationals.
23// alternative: https://en.wikipedia.org/wiki/Binary_GCD_algorithm
24forall( otype RationalImpl | arithmetic( RationalImpl ) )
25static 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
35forall( otype RationalImpl | arithmetic( RationalImpl ) )
36static RationalImpl simplify( RationalImpl & n, RationalImpl & d ) {
37 if ( d == (RationalImpl){0} ) {
38 serr | "Invalid rational number construction: denominator cannot be equal to 0." | endl;
39 exit( EXIT_FAILURE );
40 } // exit
41 if ( d < (RationalImpl){0} ) { d = -d; n = -n; } // move sign to numerator
42 return gcd( abs( n ), d ); // simplify
43} // Rationalnumber::simplify
44
45
46// constructors
47
48forall( otype RationalImpl | arithmetic( RationalImpl ) )
49void ?{}( Rational(RationalImpl) & r ) {
50 r{ (RationalImpl){0}, (RationalImpl){1} };
51} // rational
52
53forall( otype RationalImpl | arithmetic( RationalImpl ) )
54void ?{}( Rational(RationalImpl) & r, RationalImpl n ) {
55 r{ n, (RationalImpl){1} };
56} // rational
57
58forall( otype RationalImpl | arithmetic( RationalImpl ) )
59void ?{}( Rational(RationalImpl) & r, RationalImpl n, RationalImpl d ) {
60 RationalImpl t = simplify( n, d ); // simplify
61 r.numerator = n / t;
62 r.denominator = d / t;
63} // rational
64
65
66// getter for numerator/denominator
67
68forall( otype RationalImpl | arithmetic( RationalImpl ) )
69RationalImpl numerator( Rational(RationalImpl) r ) {
70 return r.numerator;
71} // numerator
72
73forall( otype RationalImpl | arithmetic( RationalImpl ) )
74RationalImpl denominator( Rational(RationalImpl) r ) {
75 return r.denominator;
76} // denominator
77
78forall( otype RationalImpl | arithmetic( RationalImpl ) )
79[ RationalImpl, RationalImpl ] ?=?( & [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src ) {
80 return dest = src.[ numerator, denominator ];
81}
82
83// setter for numerator/denominator
84
85forall( otype RationalImpl | arithmetic( RationalImpl ) )
86RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n ) {
87 RationalImpl prev = r.numerator;
88 RationalImpl t = gcd( abs( n ), r.denominator ); // simplify
89 r.numerator = n / t;
90 r.denominator = r.denominator / t;
91 return prev;
92} // numerator
93
94forall( otype RationalImpl | arithmetic( RationalImpl ) )
95RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d ) {
96 RationalImpl prev = r.denominator;
97 RationalImpl t = simplify( r.numerator, d ); // simplify
98 r.numerator = r.numerator / t;
99 r.denominator = d / t;
100 return prev;
101} // denominator
102
103
104// comparison
105
106forall( otype RationalImpl | arithmetic( RationalImpl ) )
107int ?==?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
108 return l.numerator * r.denominator == l.denominator * r.numerator;
109} // ?==?
110
111forall( otype RationalImpl | arithmetic( RationalImpl ) )
112int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
113 return ! ( l == r );
114} // ?!=?
115
116forall( otype RationalImpl | arithmetic( RationalImpl ) )
117int ?<?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
118 return l.numerator * r.denominator < l.denominator * r.numerator;
119} // ?<?
120
121forall( otype RationalImpl | arithmetic( RationalImpl ) )
122int ?<=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
123 return l.numerator * r.denominator <= l.denominator * r.numerator;
124} // ?<=?
125
126forall( otype RationalImpl | arithmetic( RationalImpl ) )
127int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
128 return ! ( l <= r );
129} // ?>?
130
131forall( otype RationalImpl | arithmetic( RationalImpl ) )
132int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
133 return ! ( l < r );
134} // ?>=?
135
136
137// arithmetic
138
139forall( otype RationalImpl | arithmetic( RationalImpl ) )
140Rational(RationalImpl) +?( Rational(RationalImpl) r ) {
141 Rational(RationalImpl) t = { r.numerator, r.denominator };
142 return t;
143} // +?
144
145forall( otype RationalImpl | arithmetic( RationalImpl ) )
146Rational(RationalImpl) -?( Rational(RationalImpl) r ) {
147 Rational(RationalImpl) t = { -r.numerator, r.denominator };
148 return t;
149} // -?
150
151forall( otype RationalImpl | arithmetic( RationalImpl ) )
152Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
153 if ( l.denominator == r.denominator ) { // special case
154 Rational(RationalImpl) t = { l.numerator + r.numerator, l.denominator };
155 return t;
156 } else {
157 Rational(RationalImpl) t = { l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator };
158 return t;
159 } // if
160} // ?+?
161
162forall( otype RationalImpl | arithmetic( RationalImpl ) )
163Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
164 if ( l.denominator == r.denominator ) { // special case
165 Rational(RationalImpl) t = { l.numerator - r.numerator, l.denominator };
166 return t;
167 } else {
168 Rational(RationalImpl) t = { l.numerator * r.denominator - l.denominator * r.numerator, l.denominator * r.denominator };
169 return t;
170 } // if
171} // ?-?
172
173forall( otype RationalImpl | arithmetic( RationalImpl ) )
174Rational(RationalImpl) ?*?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
175 Rational(RationalImpl) t = { l.numerator * r.numerator, l.denominator * r.denominator };
176 return t;
177} // ?*?
178
179forall( otype RationalImpl | arithmetic( RationalImpl ) )
180Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
181 if ( r.numerator < (RationalImpl){0} ) {
182 r.numerator = -r.numerator;
183 r.denominator = -r.denominator;
184 } // if
185 Rational(RationalImpl) t = { l.numerator * r.denominator, l.denominator * r.numerator };
186 return t;
187} // ?/?
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
197// http://www.ics.uci.edu/~eppstein/numth/frap.c
198forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); RationalImpl convert( double ); } )
199Rational(RationalImpl) narrow( double f, RationalImpl md ) {
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
227// I/O
228
229forall( otype RationalImpl | arithmetic( RationalImpl ) )
230forall( dtype istype | istream( istype ) | { istype & ?|?( istype &, RationalImpl & ); } )
231istype & ?|?( istype & is, Rational(RationalImpl) & r ) {
232 RationalImpl t;
233 is | r.numerator | r.denominator;
234 t = simplify( r.numerator, r.denominator );
235 r.numerator /= t;
236 r.denominator /= t;
237 return is;
238} // ?|?
239
240forall( otype RationalImpl | arithmetic( RationalImpl ) )
241forall( dtype ostype | ostream( ostype ) | { ostype & ?|?( ostype &, RationalImpl ); } )
242ostype & ?|?( ostype & os, Rational(RationalImpl ) r ) {
243 return os | r.numerator | '/' | r.denominator;
244} // ?|?
245
246// Local Variables: //
247// tab-width: 4 //
248// End: //
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