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 -- Rational numbers are numbers written as a ratio, i.e., as a fraction, where the numerator (top number) |
---|
8 | // and the denominator (bottom number) are whole numbers. When creating and computing with rational numbers, results |
---|
9 | // are constantly reduced to keep the numerator and denominator as small as possible. |
---|
10 | // |
---|
11 | // Author : Peter A. Buhr |
---|
12 | // Created On : Wed Apr 6 17:56:25 2016 |
---|
13 | // Last Modified By : Peter A. Buhr |
---|
14 | // Last Modified On : Fri Jul 7 09:34:33 2017 |
---|
15 | // Update Count : 93 |
---|
16 | // |
---|
17 | |
---|
18 | #pragma once |
---|
19 | |
---|
20 | #include "iostream" |
---|
21 | |
---|
22 | trait scalar( otype T ) { |
---|
23 | }; |
---|
24 | |
---|
25 | trait arithmetic( otype T | scalar( T ) ) { |
---|
26 | int !?( T ); |
---|
27 | int ?==?( T, T ); |
---|
28 | int ?!=?( T, T ); |
---|
29 | int ?<?( T, T ); |
---|
30 | int ?<=?( T, T ); |
---|
31 | int ?>?( T, T ); |
---|
32 | int ?>=?( T, T ); |
---|
33 | void ?{}( T *, zero_t ); |
---|
34 | void ?{}( T *, one_t ); |
---|
35 | T +?( T ); |
---|
36 | T -?( T ); |
---|
37 | T ?+?( T, T ); |
---|
38 | T ?-?( T, T ); |
---|
39 | T ?*?( T, T ); |
---|
40 | T ?/?( T, T ); |
---|
41 | T ?%?( T, T ); |
---|
42 | T ?/=?( T *, T ); |
---|
43 | T abs( T ); |
---|
44 | }; |
---|
45 | |
---|
46 | // implementation |
---|
47 | |
---|
48 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
49 | struct Rational { |
---|
50 | RationalImpl numerator, denominator; // invariant: denominator > 0 |
---|
51 | }; // Rational |
---|
52 | |
---|
53 | // constructors |
---|
54 | |
---|
55 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
56 | void ?{}( Rational(RationalImpl) * r ); |
---|
57 | |
---|
58 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
59 | void ?{}( Rational(RationalImpl) * r, RationalImpl n ); |
---|
60 | |
---|
61 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
62 | void ?{}( Rational(RationalImpl) * r, RationalImpl n, RationalImpl d ); |
---|
63 | |
---|
64 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
65 | void ?{}( Rational(RationalImpl) * r, zero_t ); |
---|
66 | |
---|
67 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
68 | void ?{}( Rational(RationalImpl) * r, one_t ); |
---|
69 | |
---|
70 | // numerator/denominator getter |
---|
71 | |
---|
72 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
73 | RationalImpl numerator( Rational(RationalImpl) r ); |
---|
74 | |
---|
75 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
76 | RationalImpl denominator( Rational(RationalImpl) r ); |
---|
77 | |
---|
78 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
79 | [ RationalImpl, RationalImpl ] ?=?( * [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src ); |
---|
80 | |
---|
81 | // numerator/denominator setter |
---|
82 | |
---|
83 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
84 | RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n ); |
---|
85 | |
---|
86 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
87 | RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d ); |
---|
88 | |
---|
89 | // comparison |
---|
90 | |
---|
91 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
92 | int ?==?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
---|
93 | |
---|
94 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
95 | int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
---|
96 | |
---|
97 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
98 | int ?<?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
---|
99 | |
---|
100 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
101 | int ?<=?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
---|
102 | |
---|
103 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
104 | int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
---|
105 | |
---|
106 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
107 | int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
---|
108 | |
---|
109 | // arithmetic |
---|
110 | |
---|
111 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
112 | Rational(RationalImpl) +?( Rational(RationalImpl) r ); |
---|
113 | |
---|
114 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
115 | Rational(RationalImpl) -?( Rational(RationalImpl) r ); |
---|
116 | |
---|
117 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
118 | Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
---|
119 | |
---|
120 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
121 | Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
---|
122 | |
---|
123 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
124 | Rational(RationalImpl) ?*?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
---|
125 | |
---|
126 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
127 | Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
---|
128 | |
---|
129 | // conversion |
---|
130 | forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); } ) |
---|
131 | double widen( Rational(RationalImpl) r ); |
---|
132 | forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); RationalImpl convert( double );} ) |
---|
133 | Rational(RationalImpl) narrow( double f, RationalImpl md ); |
---|
134 | |
---|
135 | // I/O |
---|
136 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
137 | forall( dtype istype | istream( istype ) | { istype * ?|?( istype *, RationalImpl * ); } ) |
---|
138 | istype * ?|?( istype *, Rational(RationalImpl) * ); |
---|
139 | |
---|
140 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
---|
141 | forall( dtype ostype | ostream( ostype ) | { ostype * ?|?( ostype *, RationalImpl ); } ) |
---|
142 | ostype * ?|?( ostype *, Rational(RationalImpl ) ); |
---|
143 | |
---|
144 | // Local Variables: // |
---|
145 | // mode: c // |
---|
146 | // tab-width: 4 // |
---|
147 | // End: // |
---|