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37 <p class=
"p1"><b>AbstractFunction
</b></p>
38 <p class=
"p2"><br></p>
39 <p class=
"p3"><b>Inherits from:
</b><a href=
"../Object.html"><span class=
"s1"><b>Object
</b></span></a></p>
40 <p class=
"p2"><br></p>
41 <p class=
"p3">An AbstractFunction is an object which responds to a set of messages that represent
</p>
42 <p class=
"p3">mathematical functions. Subclasses override a smaller set of messages to respond
</p>
43 <p class=
"p3">to the mathematical functions. The intent is to provide a mechanism for functions
</p>
44 <p class=
"p3">that do not calculate values directly but instead compose structures for calculating.
</p>
45 <p class=
"p2"><br></p>
46 <p class=
"p3">Function, Pattern, Stream and UGen are subclasses of AbstractFunction.
</p>
47 <p class=
"p3">For example, if you multiply two UGens together the receiver responds by answering a new
</p>
48 <p class=
"p3">instance of class BinaryOpUGen which has the two operands as inputs.
</p>
49 <p class=
"p2"><br></p>
50 <p class=
"p4"><span class=
"s2">see also:
<a href=
"../../UGens/UGen.html"><span class=
"s3">UGen
</span></a>,
<a href=
"../../Streams-Patterns-Events/Patterns/Pattern.html"><span class=
"s3">Pattern
</span></a>,
<a href=
"Function.html"><span class=
"s3">Function
</span></a></span></p>
51 <p class=
"p2"><br></p>
52 <p class=
"p3"><b>Unary Messages:
</b></p>
53 <p class=
"p2"><br></p>
54 <p class=
"p3">All of the following messages send the message
<b>composeUnaryOp
</b> to the receiver with the
</p>
55 <p class=
"p3">unary message selector as an argument. See:
<a href=
"../UnaryOpFunction.html"><span class=
"s4">UnaryOpFunction
</span></a></p>
56 <p class=
"p2"><br></p>
57 <p class=
"p3"><b>neg, reciprocal, bitNot, abs, asFloat, asInt, ceil, floor, frac, sign, squared, cubed, sqrt
</b></p>
58 <p class=
"p3"><b>exp, midicps, cpsmidi, midiratio, ratiomidi, ampdb, dbamp, octcps, cpsoct, log, log2,
</b></p>
59 <p class=
"p3"><b>log10, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, rand, rand2, linrand, bilinrand,
</b></p>
60 <p class=
"p3"><b>sum3rand, distort, softclip, nyqring, coin, even, odd, isPositive, isNegative,
</b></p>
61 <p class=
"p3"><b>isStrictlyPositive, rho, theta
</b></p>
62 <p class=
"p2"><br></p>
63 <p class=
"p2"><br></p>
64 <p class=
"p2"><br></p>
65 <p class=
"p3"><b>Binary Messages:
</b></p>
66 <p class=
"p5"><br></p>
67 <p class=
"p3">All of the following messages send the message
<b>composeBinaryOp
</b> to the receiver with the
</p>
68 <p class=
"p3">binary message selector and the second operand as arguments. See:
<span class=
"Apple-converted-space"> </span><a href=
"../BinaryOpFunction.html"><span class=
"s4">BinaryOpFunction
</span></a></p>
69 <p class=
"p2"><br></p>
70 <p class=
"p3"><b>+, -, *, /, div, %, **, min, max,
<,
<=,
>,
>=,
&, |, lcm, gcd, round, trunc, atan2,
<span class=
"Apple-converted-space"> </span></b></p>
71 <p class=
"p3"><b>hypot, hypotApx,
>>, +
>>, fill, ring1, ring2, ring3, ring4, difsqr, sumsqr, sqrdif, absdif, amclip,
</b></p>
72 <p class=
"p3"><b>scaleneg, clip2, excess,
<!, rrand, exprand, rotate, dist, bitAnd, bitOr, bitXor, bitHammingDistance, @
</b></p>
73 <p class=
"p2"><br></p>
74 <p class=
"p2"><br></p>
75 <p class=
"p2"><br></p>
76 <p class=
"p3"><b>Messages with more arguments:
</b></p>
77 <p class=
"p2"><br></p>
78 <p class=
"p3">All of the following messages send the message
<b>composeNAryOp
</b> to the receiver with the
</p>
79 <p class=
"p3">binary message selector and the other operands as arguments. See
<a href=
"../NAryOpFunction.html"><span class=
"s4">NAryOpFunction
</span></a></p>
80 <p class=
"p2"><br></p>
81 <p class=
"p3"><b>clip, wrap, fold, blend, linlin, linexp, explin, expexp
</b></p>
82 <p class=
"p2"><br></p>
83 <p class=
"p2"><br></p>
84 <p class=
"p3"><b>applyTo(... args)
</b></p>
85 <p class=
"p2"><br></p>
86 <p class=
"p3">Interface that allows us to combine selectors (
<a href=
"../Symbol.html"><span class=
"s4">Symbol
</span></a>s) and
<a href=
"Function.html"><span class=
"s5">Function
</span></a>s. Sends
<b>valueArray
</b>(args) to
<b>this
</b>.
</p>
87 <p class=
"p2"><br></p>
88 <p class=
"p6">// example:
</p>
89 <p class=
"p7"><br></p>
90 <p class=
"p8">f = [{
<span class=
"s6">|a, b|
</span> a * b *
100.rand }, {
<span class=
"s6">|a, b|
</span> sin(a) * sin(b) },
<span class=
"s7">'*'
</span>,
<span class=
"s7">'/'
</span>];
</p>
91 <p class=
"p8">f.choose.postcs.applyTo(
3,
4);
</p>
92 <p class=
"p7"><br></p>
93 <p class=
"p6">// this is used in
<a href=
"../../Collections/SequenceableCollection.html">SequenceableCollection
</a> reduce:
</p>
94 <p class=
"p8">(
1.
.10).reduce(
<span class=
"s7">'+'
</span>);
</p>
95 <p class=
"p8">(
1.
.10).reduce({
<span class=
"s6">|a, b|
</span> a * b *
1.0.rand });
</p>
96 <p class=
"p2"><br></p>
97 <p class=
"p3"><b>asUGenInput(for)
</b></p>
98 <p class=
"p2"><br></p>
99 <p class=
"p3">returns the result of sending the
<b>value
</b>(for) message to
<b>this
</b>.
</p>
100 <p class=
"p2"><br></p>
101 <p class=
"p6">// example:
</p>
103 <p class=
"p8"><span class=
"s6">var
</span> f, g, product;
</p>
104 <p class=
"p8">f = {
<span class=
"s6">SinOsc
</span>.ar(
400) };
</p>
105 <p class=
"p8">g = {
<span class=
"s6">LFPulse
</span>.kr(
8)
<span class=
"Apple-converted-space"> </span>};
</p>
106 <p class=
"p8">product = f * g *
0.1;
</p>
107 <p class=
"p8">{
<span class=
"s6">Pan2
</span>.ar(product,
<span class=
"s6">SinOsc
</span>.kr(
0.3)) }.play;
<span class=
"Apple-converted-space"> </span></p>
109 <p class=
"p9"><br></p>
110 <p class=
"p10"><b>sampled (function, n, from, to)
</b></p>
111 <p class=
"p11"><b><span class=
"Apple-tab-span"> </span></b></p>
112 <p class=
"p9"><br></p>
113 <p class=
"p12">//sample a function
</p>
114 <p class=
"p13">f = {
<span class=
"s6">|x|
</span> sin(
3*x)*cos(
8*x) }
</p>
115 <p class=
"p13">f.plotGraph2(from:
0,to:
2);
</p>
116 <p class=
"p13">f.sampled(
10,
0,
2).plotGraph2(from:
0,to:
2);
</p>
117 <p class=
"p13">f.sampled(
80,
0,
2).plotGraph2(from:
0,to:
2);
</p>
118 <p class=
"p9"><br></p>
119 <p class=
"p14">//on complicated functions a sampled function is less cpy heavy.
</p>
120 <p class=
"p13">f = {
<span class=
"s6">|x|
</span> 60.collect{
2**((x-rrand(
0.0,
1.0))) }.sum/
60 };
</p>
121 <p class=
"p13">f.plotGraph2(from:
0,to:
1);
</p>
122 <p class=
"p13">g = f.sampled(
200);
</p>
123 <p class=
"p13">g.plotGraph2(from:
0,to:
1);
</p>
124 <p class=
"p13">{
200.collect{ f.(rand(
0.0,
1.0)) } }.bench;
</p>
125 <p class=
"p13">{
200.collect{ g.(rand(
0.0,
1.0)) } }.bench;
</p>
126 <p class=
"p2"><br></p>
127 <p class=
"p3"><b>Function Composition:
</b></p>
128 <p class=
"p2"><br></p>
129 <p class=
"p3">when unary, binary or n-ary operators are appied to an abstract function, it returns an object that represents
</p>
130 <p class=
"p3">this operation, without evaluating the function: UnaryOpFunction, BinaryOpFunction, NAryOpFunction.
</p>
131 <p class=
"p3">Note that different subclasses like Pattern or UGen have their own composition scheme analogous to the one of AbstractFunction itself. More about functions, see
<a href=
"Function.html"><span class=
"s4">Function
</span></a></p>
132 <p class=
"p2"><br></p>
133 <p class=
"p15"><br></p>
134 <p class=
"p6">// examples
</p>
135 <p class=
"p7"><br></p>
136 <p class=
"p8">a = {
1.0.rand } +
8;
</p>
137 <p class=
"p8">a.value;
</p>
138 <p class=
"p7"><br></p>
139 <p class=
"p7"><br></p>
140 <p class=
"p8">y = {
8 } + {
1.0.rand };
</p>
141 <p class=
"p8">y.value;
</p>
142 <p class=
"p7"><br></p>
143 <p class=
"p6">// arguments are passed into both functions
</p>
144 <p class=
"p7"><br></p>
145 <p class=
"p8">y = {
<span class=
"s6">|x=
0|
</span> x } + {
1.0.rand };
</p>
146 <p class=
"p8">y.value(
10);
</p>
147 <p class=
"p7"><br></p>
148 <p class=
"p7"><br></p>
149 <p class=
"p8">y = {
<span class=
"s6">|x=
0|
</span> x *
3 } + { |x=
0| x +
1.0.rand };
</p>
150 <p class=
"p8">y.value(
10);
</p>
151 <p class=
"p7"><br></p>
152 <p class=
"p8">y.postcs;
</p>
153 <p class=
"p7"><br></p>
154 <p class=
"p8">y = {
<span class=
"s6">|x=
0|
</span> x *
3 } + { |x=
0| x +
1.0.rand } * {
<span class=
"s6">|x=
0|
</span> [
50,
100].choose + x } +
1.0;
</p>
155 <p class=
"p8">y.value(
10);
</p>
156 <p class=
"p7"><br></p>
157 <p class=
"p6">// environments can be used as a lookup with valueEnvir:
</p>
158 <p class=
"p7"><br></p>
160 <p class=
"p16">Environment
<span class=
"s2">.use {
</span></p>
161 <p class=
"p8"><span class=
"Apple-tab-span"> </span>~y =
10;
</p>
162 <p class=
"p8"><span class=
"Apple-tab-span"> </span>~x =
2;
</p>
163 <p class=
"p8"><span class=
"Apple-tab-span"> </span>~z = {
<span class=
"s6">|x=
8|
</span> x } + {
<span class=
"s6">|y=
0|
</span> y +
1.0.rand };
</p>
164 <p class=
"p8"><span class=
"Apple-tab-span"> </span>~z.valueEnvir;
</p>
167 <p class=
"p7"><br></p>
168 <p class=
"p6">// n-ary operators:
</p>
169 <p class=
"p7"><br></p>
170 <p class=
"p8">a = blend({
3.0.rand }, {
1000.rand }, {
<span class=
"s6">|frac|
</span> frac });
</p>
171 <p class=
"p8">a.value(
0.5);
</p>
172 <p class=
"p7"><br></p>
173 <p class=
"p6"><span class=
"s2">a.value((
0,
0.06.
.1));
</span>// creates a range of values..
</p>
174 <p class=
"p15"><br></p>
175 <p class=
"p15"><br></p>
176 <p class=
"p15"><br></p>
177 <p class=
"p15"><br></p>
178 <p class=
"p9"><br></p>
179 <p class=
"p9"><br></p>
180 <p class=
"p9"><br></p>
181 <p class=
"p9"><br></p>
182 <p class=
"p9"><br></p>
