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
|
Complex : Number {
var <>real, <>imag;
*new { arg real, imag;
^super.newCopyArgs(real, imag);
}
+ { arg aNumber, adverb;
if ( aNumber.isNumber, {
^Complex.new(real + aNumber.real, imag + aNumber.imag)
},{
^aNumber.performBinaryOpOnComplex('+', this, adverb)
});
}
- { arg aNumber, adverb;
if ( aNumber.isNumber, {
^Complex.new(real - aNumber.real, imag - aNumber.imag)
},{
^aNumber.performBinaryOpOnComplex('-', this, adverb)
});
}
* { arg aNumber, adverb;
if ( aNumber.isNumber, {
^Complex.new(
// these are implemented as additional message sends so that UGens can
// optimize the 6 operations down to 2 UGen instances.
(real * aNumber.real) - (imag * aNumber.imag),
(real * aNumber.imag) + (imag * aNumber.real)
)
},{
^aNumber.performBinaryOpOnComplex('*', this, adverb)
});
}
/ { arg aNumber, adverb;
var denom, yr, yi;
if ( aNumber.isNumber, {
yr = aNumber.real;
yi = aNumber.imag;
denom = 1.0 / (yr * yr + (yi * yi));
^Complex.new(
((real * yr) + (imag * yi)) * denom,
((imag * yr) - (real * yi)) * denom)
},{
^aNumber.performBinaryOpOnComplex('/', this, adverb)
});
}
< { arg aNumber, adverb;
if ( aNumber.isNumber, {
^real < aNumber.real
},{
^aNumber.performBinaryOpOnComplex('<', this, adverb)
});
}
== { arg aNumber, adverb;
if ( aNumber.isNumber, {
^real == aNumber.real and: { imag == aNumber.imag }
},{
^aNumber.performBinaryOpOnComplex('==', this, adverb)
});
}
hash {
^real.hash << 1 bitXor: imag.hash
}
// double dispatch
performBinaryOpOnSimpleNumber { arg aSelector, aNumber, adverb;
^aNumber.asComplex.perform(aSelector, this, adverb)
}
performBinaryOpOnSignal { arg aSelector, aSignal, adverb;
^aSignal.asComplex.perform(aSelector, this)
}
performBinaryOpOnComplex { arg aSelector, aNumber, adverb;
BinaryOpFailureError(this, aSelector, [aNumber, adverb]).throw;
}
performBinaryOpOnUGen { arg aSelector, aUGen, adverb;
^aUGen.asComplex.perform(aSelector, this, adverb)
}
neg { ^Complex.new(real.neg, imag.neg) }
conjugate { ^Complex.new(real, imag.neg) }
squared { ^this * this }
cubed { ^this * this * this }
exp { ^exp(real) * Complex.new(cos(imag), sin(imag)) }
pow { arg aNumber; // return(this ** aNumber)
// Notation below:
// t=this, p=power, i=sqrt(-1)
// Derivation:
// t ** p = exp(p*log(t)) = ... = r*exp(i*a)
var p_real, p_imag, t_mag, t_phase, t_maglog;
var mag, phase;
aNumber = aNumber.asComplex;
p_real = aNumber.real;
p_imag = aNumber.imag;
if(p_real == 0.0 and: { p_imag == 0 }) { ^Complex(1.0, 0.0) };
if(p_imag == 0.0 and: { imag == 0.0 } and: { real > 0.0 }) {
^Complex(real ** p_real, 0.0)
};
t_mag = this.magnitude;
if(t_mag == 0.0) { ^Complex(0.0, 0.0) };
t_maglog = 0.5 * log(t_mag);
t_phase = this.phase;
mag = exp((p_real * t_maglog) - (p_imag * t_phase));
phase = (p_imag * t_maglog) + (p_real * t_phase);
^Complex(mag * cos(phase), mag * sin(phase))
}
magnitude { ^hypot(real, imag) }
abs { ^hypot(real, imag) }
rho { ^hypot(real, imag) }
magnitudeApx { ^hypotApx(real, imag) }
angle { ^atan2(imag, real) }
phase { ^atan2(imag, real) }
theta { ^atan2(imag, real) }
coerce { arg aNumber; ^aNumber.asComplex }
round { arg aNumber = 1.0;
^Complex(real.round(aNumber), imag.round(aNumber))
}
asInteger { ^real.asInteger }
asFloat { ^real.asFloat }
asComplex { ^this }
asPolar { ^Polar.new(this.rho, this.theta) }
asPoint { ^Point.new(this.real, this.imag) }
printOn { arg stream;
stream << "Complex( " << real << ", " << imag << " )";
}
}
|
