1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
|
//=============================================================================
// MuseScore
// Music Composition & Notation
//
// Copyright (C) 2009 Werner Schweer
//
// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License version 2
// as published by the Free Software Foundation and appearing in
// the file LICENCE.GPL
//=============================================================================
#include "fraction.h"
#include "mscore.h"
namespace Ms {
//---------------------------------------------------------
// gcd
// greatest common divisor
//---------------------------------------------------------
static int gcd(int a, int b)
{
if (b == 0)
return a < 0 ? -a : a;
return gcd(b, a % b);
}
//---------------------------------------------------------
// lcm
// least common multiple
//---------------------------------------------------------
static unsigned lcm(int a, int b)
{
return a * b / gcd(a, b);
}
//---------------------------------------------------------
// Fraction
//---------------------------------------------------------
Fraction::Fraction(int z, int n)
: _numerator(z), _denominator(n)
{
}
//---------------------------------------------------------
// reduce
//---------------------------------------------------------
void Fraction::reduce()
{
int tmp = gcd(_numerator, _denominator);
_numerator /= tmp;
_denominator /= tmp;
}
//---------------------------------------------------------
// reduced
//---------------------------------------------------------
Fraction Fraction::reduced() const
{
int tmp = gcd(_numerator, _denominator);
return Fraction(_numerator / tmp, _denominator / tmp);
}
//---------------------------------------------------------
// absValue
//---------------------------------------------------------
Fraction Fraction::absValue() const
{
return Fraction(qAbs(_numerator), qAbs(_denominator));
}
// --- comparison --- //
bool Fraction::operator<(const Fraction& val) const
{
const int v = lcm(_denominator, val._denominator);
return _numerator * (v / _denominator) < val._numerator * (v / val._denominator);
}
bool Fraction::operator<=(const Fraction& val) const
{
const int v = lcm(_denominator, val._denominator);
return _numerator * (v / _denominator) <= val._numerator * (v / val._denominator);
}
bool Fraction::operator>=(const Fraction& val) const
{
const int v = lcm(_denominator, val._denominator);
return _numerator * (v / _denominator) >= val._numerator * (v / val._denominator);
}
bool Fraction::operator>(const Fraction& val) const
{
const int v = lcm(_denominator, val._denominator);
return (_numerator * (v / _denominator)) > (val._numerator * (v / val._denominator));
}
bool Fraction::operator==(const Fraction& val) const
{
const int v = lcm(_denominator, val._denominator);
return (_numerator * (v / _denominator)) == (val._numerator * (v / val._denominator));
// return (_numerator == val._numerator) && (_denominator == val._denominator);
}
bool Fraction::operator!=(const Fraction& val) const
{
const int v = lcm(_denominator, val._denominator);
return (_numerator * (v / _denominator)) != (val._numerator * (v / val._denominator));
// return (_numerator != val._numerator) || (_denominator != val._denominator);
}
//---------------------------------------------------------
// operator+=
//---------------------------------------------------------
Fraction& Fraction::operator+=(const Fraction& val)
{
const int tmp = lcm(_denominator, val._denominator);
_numerator = _numerator * (tmp / _denominator) + val._numerator * (tmp / val._denominator);
_denominator = tmp;
return *this;
}
//---------------------------------------------------------
// operator-=
//---------------------------------------------------------
Fraction& Fraction::operator-=(const Fraction& val)
{
const unsigned tmp = lcm(_denominator, val._denominator);
_numerator = _numerator * (tmp / _denominator) - val._numerator * (tmp / val._denominator);
_denominator = tmp;
return *this;
}
//---------------------------------------------------------
// operator*=
//---------------------------------------------------------
Fraction& Fraction::operator*=(const Fraction& val)
{
_numerator *= val._numerator;
_denominator *= val._denominator;
return *this;
}
Fraction& Fraction::operator*=(int val)
{
_numerator *= val;
return *this;
}
//---------------------------------------------------------
// operator/=
//---------------------------------------------------------
Fraction& Fraction::operator/=(const Fraction& val)
{
_numerator *= val._denominator;
_denominator *= val._numerator;
return *this;
}
Fraction& Fraction::operator/=(int val)
{
_denominator *= val;
return *this;
}
//---------------------------------------------------------
// fromTicks
//---------------------------------------------------------
Fraction Fraction::fromTicks(int ticks)
{
return Fraction(ticks, MScore::division * 4).reduced();
}
//---------------------------------------------------------
// ticks
//---------------------------------------------------------
int Fraction::ticks() const
{
// MScore::division - ticks per quarter note
// MScore::division * 4 - ticks per whole note
// result: rounded (MScore::division * 4 * _numerator * 1.0 / _denominator) value
return (_numerator * MScore::division * 4 + (_denominator/2)) / _denominator;
}
} // namespace Ms
|
