#lang scribble/manual @(require (for-label racket)) @title{AbstractFunction} An object which responds to a set of messages that represent mathematical functions@section{categories} Core>Kernel @section{related} Classes/UGen,Classes/Pattern,Classes/Function,Overviews/Operators @section{description} An AbstractFunction is an object which responds to a set of messages that represent mathematical functions. Subclasses override a smaller set of messages to respond to the mathematical functions. The intent is to provide a mechanism for functions that do not calculate values directly but instead compose structures for calculating (lazy evaluation). Function, Pattern, Stream and UGen are subclasses of AbstractFunction. For example, if you multiply two UGens together the receiver responds by returning a new instance of class BinaryOpUGen which has the two operands as inputs. @racketblock[ { var a, b; a = LFSaw.ar(220); b = LFPulse.ar(1442); [a, b, a * b] }.plot; :: For an overview of common operators, see link::Overviews/Operators::, for specific examples, see also e.g. link::Classes/Function::, link::Classes/UGen::, link::Classes/Pattern::. To see which classes implement a specific method, see that method in the generated link::Overviews/Methods:: overview. ] @section{instanceMethods} @section{subsection} Unary Messages The following messages return an object which represents a delayed unary operation, i.e. an operation on one object. For example, the reciprocal of a function will result in a new function that, when called, returns the reciprocal of the evaluation of the operand. All of the following messages send the message composeUnaryOp to the receiver with the unary message selector as an argument. See link::Classes/UnaryOpFunction::. @section{method} neg @racketblock[ a = { 10.rand.postln }; b = a.neg; b.value; // Patterns, Streams, UGens, and Proxies are AbstractFunctions, too: a = Pgeom(1, 2, 5).neg; a.asStream.nextN(8); { a = LFNoise1.ar(1500); [a, a.neg] }.plot; :: ] @section{method} reciprocal @racketblock[ a = { 10.rand.postln }; b = a.reciprocal; b.value; a = Pgeom(1, 2, 5).reciprocal; a.asStream.nextN(8); { a = LFNoise1.ar(1500) + 2; [a, a.reciprocal] }.plot; :: ] @section{method} bitNot Bitwise integer negation. @section{method} abs Absolute value @racketblock[ a = { 10.rand - 10.rand }; b = a.abs; b.value; a = Pseries(3, -1.8, inf).abs; a.asStream.nextN(8); { a = LFNoise1.ar(1500); [a, a.abs] }.plot; :: ] @section{method} asFloat @racketblock[ a = { "123.471".scramble }; b = a.asFloat; b.value; :: ] @section{method} asInt @racketblock[ a = { "123471".scramble }; b = a.asInt; b.value; :: ] @section{method} ceil, floor, frac @racketblock[ a = { 10.0.rand2.postln }; b = a.ceil; b.value; a = { 10.0.rand2.postln }; b = a.floor; b.value; a = Pgeom(1, 1.2, inf).ceil; a.asStream.nextN(8); a = Pgeom(1, 1.2, inf).floor; a.asStream.nextN(8); { a = SinOsc.ar(150) * 1.5; [a, a.ceil, a.floor, a.frac] }.plot.superpose_(true); :: ] @section{method} sign Returns a function that returns -1 if receiver returns a negative number, 1 if positive, and 0 if zero. @racketblock[ a = { 10.0.rand2.postln }; b = a.sign; b.value; { a = LFNoise1.ar(1500) * 1.5; [a, a.sign] }.plot; :: ] @section{method} squared @racketblock[ a = { |x| x + 1 }; b = a.squared; [a.value(1), b.value(1)]; a = Pseries(0, 1, inf).squared; a.asStream.nextN(8); { a = LFNoise1.ar(1500); [a, a.squared] }.plot; :: ] @section{method} cubed @racketblock[ a = { |x| x + 1 }; b = a.cubed; [a.value(1), b.value(1)]; a = Pseries(0, 1, inf).cubed; a.asStream.nextN(8); { a = LFNoise1.ar(1500); [a, a.cubed] }.plot; :: ] @section{method} sqrt @racketblock[ a = { |x| x + 1 }; b = a.sqrt; [a.value(1), b.value(1)]; a = Pseries(0, 1, inf).sqrt; a.asStream.nextN(8); { a = LFNoise1.ar(1500); [a, a.sqrt] }.plot; :: ] @section{method} exp Returns e to the power of this. @racketblock[ a = { |x| x + 1 }; b = a.exp; [a.value(1), b.value(1)]; a = Pseries(0, 0.25, inf).exp; a.asStream.nextN(8); { a = LFNoise1.ar(1500); [a, a.exp] }.plot; :: ] @section{method} midicps Converts midinote into cycles per seconds (Hz). @racketblock[ a = { |x, root = 60| x + root }; b = a.midicps; [a.value(9), b.value(9)]; a = Pseries(60, 1, inf).midicps; a.asStream.nextN(12); { a = LFNoise1.ar(1) * 5 + 60; Pulse.ar(a.round.midicps) * 0.1 }.play; :: ] @section{method} cpsmidi Converts cycles per seconds (Hz) into midinote. @racketblock[ a = { |x| #[440, 720, 801, 1020.2].at(x) }; b = a.cpsmidi; [a.value(3), b.value(3)]; a = Pseries(220, 220, inf).cpsmidi; a.asStream.nextN(12); // overtone series as midinotes // follow but round to next midinote { a = Pitch.kr(SoundIn.ar).at(1); Pulse.ar(a.cpsmidi.round.midicps) * 0.1 }.play; :: ] @section{method} midiratio @section{method} ratiomidi @section{method} ampdb @section{method} dbamp @section{method} octcps @section{method} cpsoct @section{method} log @section{method} log2 @section{method} log10 @section{method} sin @section{method} cos @section{method} tan @section{method} asin @section{method} acos @section{method} atan @section{method} sinh @section{method} cosh @section{method} tanh @section{method} rand @section{method} rand2 @section{method} linrand @section{method} bilinrand @section{method} sum3rand @section{method} distort @section{method} softclip @section{method} coin @section{method} even @section{method} odd @section{method} isPositive @section{method} isNegative @section{method} isStrictlyPositive @section{method} rho @section{method} theta @section{subsection} Binary Messages The following messages return an object which represents a delayed binary operation, i.e. an operation between two objects. For example, adding two functions will result in a new function that, when called, adds the results of the evaluation of the two operands. All of the following messages send the message composeBinaryOp to the receiver with the binary message selector and the second operand as arguments. See: link::Classes/BinaryOpFunction::. Examples: @racketblock[ ( // Add two functions: var x = { |x| x + 1000 } + { |x| x * 100 }; // Evaluate the result, passing in one argument: x.value(2); // posts 1202 ) // either operand can be another object: ( // Add two functions: var x = 1871 + { |x| x * 12 }; x.value(12); ) :: ] @racketblock[ ( // Add two UGens { SinOsc.ar(440, 0, 0.2) + PinkNoise.ar(0.1); }.play ) :: // Add two Patterns ] @racketblock[ (Pseq([1, 2, 3, 4]) + Prand([0, 0.1, -0.1], inf)).asStream.nextN(5); :: // Add two NodeProxies ] @racketblock[ Ndef(\x, { SinOsc.ar(440, 0, 0.2) }); Ndef(\y, { PinkNoise.ar(0.1) }); Ndef(\z, Ndef(\x) + Ndef(\y)).play; :: ] @section{method} + @racketblock[ ({ |x| x.squared } + 3).value(2); :: ] @section{method} - @racketblock[ ({ |x| x.squared } - 3).value(2); :: ] @section{method} * @racketblock[ ({ |x| x.squared } * { |x| x.squared }).value(2); :: ] @section{method} / @racketblock[ ({ |x| x.squared } / 4).value(2); :: ] @section{method} div @racketblock[ ({ |x| x.squared } div: 3).value(2); :: ] @section{method} % @racketblock[ ({ |x| x.squared } % 3).value(2); :: ] @section{method} ** @racketblock[ ({ |x| x.squared } ** 3).value(2); :: ] @section{method} min @racketblock[ ({ |x| x.squared } min: 0).value(2); :: ] @section{method} max @racketblock[ ({ |x| x.squared } max: 0).value(2); :: ] @section{method} < @racketblock[ ({ |x| x.squared } < 3).value(2); :: ] @section{method} <= @racketblock[ ({ |x| x.squared } <= 3).value(2); :: ] @section{method} > @racketblock[ ({ |x| x.squared } > 3).value(2); :: ] @section{method} >= @racketblock[ ({ |x| x.squared } >= 3).value(2); :: ] @section{method} & @racketblock[ a = { |min, max| ({ rrand(min, max) } ! 4).postln }; (a & a).value(0, 8); :: ] @section{method} | @racketblock[ a = { |min, max| ({ rrand(min, max) } ! 4).postln }; (a | a).value(0, 8); :: ] @section{method} lcm @racketblock[ a = { |min, max| rrand(min, max).postln }; (a lcm: a).value(0, 8); :: ] @section{method} gcd @racketblock[ a = { |min, max| rrand(min, max).postln }; (a gcd: a).value(0, 8); :: ] @section{method} round @racketblock[ a = { |max| max.rand.postln }; (a round: 0.5).value(1.0); :: ] @section{method} trunc @racketblock[ a = { |max| max.rand.postln }; (a trunc: 2).value(10); :: ] @section{method} atan2 @racketblock[ a = { 1.0.rand2 }; a.atan2.dup(10); :: ] @section{method} hypot @racketblock[ a = { 1.0.rand2 }; a.hypot.dup(10); :: ] @section{method} hypotApx @racketblock[ a = { 1.0.rand2 }; a.hypotApx.dup(10); :: ] @section{method} >> @racketblock[ a = { [2r10010, 2r101011, 2r11100].choose.postln }; b = a >> 2; b.value.asBinaryDigits.join; :: ] @section{method} +>> @racketblock[ a = { [2r10010, 2r101011, 2r11100].choose.postln }; b = a +>> 2; b.value.asBinaryDigits.join; :: ] @section{method} ring1 (a * b) + a @racketblock[ ({ [5, 6, 2].choose.postln } ring1: { [2, -1, 3].choose.postln }).value // UGens are also abstract functions ( { a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1)); ring1(a, b) * 0.1 }.play; ) :: ] @section{method} ring2 ((a*b) + a + b) @racketblock[ ({ [5, 6, 2].choose.postln } ring2: { [2, -1, 3].choose.postln }).value ( { a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1)); ring2(a, b) * 0.1 }.play; ) :: ] @section{method} ring3 (a * a * b) @racketblock[ ({ [5, 6, 2].choose.postln } ring3: { [2, -1, 3].choose.postln }).value ( { a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1)); ring3(a, b) * 0.1 }.play; ) :: ] @section{method} ring4 ((a*a *b) - (a*b*b)) @racketblock[ ({ [5, 6, 2].choose.postln } ring4: { [2, -1, 3].choose.postln }).value ( { a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1)); ring4(a, b) * 0.1 }.play; ) :: ] @section{method} difsqr (a*a) - (b*b) @racketblock[ ({ [5, 6, 2].choose.postln } difsqr: { [2, -1, 3].choose.postln }).value ( { a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1)); difsqr(a, b) * 0.1 }.play; ) :: ] @section{method} sumsqr (a*a) + (b*b) @racketblock[ ({ [5, 6, 2].choose.postln } sumsqr: { [2, -1, 3].choose.postln }).value ( { a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1)); sumsqr(a, b) * 0.1 }.play; ) :: ] @section{method} sqrdif (a - b) ** 2 @racketblock[ ({ [5, 6, 2].choose.postln } sqrdif: { [2, -1, 3].choose.postln }).value ( { a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1)); ring4(a, b) * 0.1 }.play; ) :: ] @section{method} sqrsum (a + b) ** 2 @racketblock[ ({ [5, 6, 2].choose.postln } sqrsum: { [2, -1, 3].choose.postln }).value ( { a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1)); sqrsum(a, b) * 0.1 }.play; ) :: ] @section{method} absdif (a - b).abs @racketblock[ ({ [5, 6, 2].choose.postln } absdif: { [2, -1, 3].choose.postln }).value ( { a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1)); absdif(a, b) * 0.1 }.play; ) :: ] @section{method} moddif absolute difference in modulo arithmetics. @section{method} amclip 0 when b <= 0, a*b when b > 0 @section{method} scaleneg a * b when a < 0, otherwise a. @section{method} clip2 clips receiver to +/- aNumber @section{method} excess Returns the difference of the receiver and its clipped form. @section{method} { |x, y| rrand(4, 8) }; a.value; // compose a function from a that selects only odd values b = { |x| x.select(_.odd) } <> a; b.value; :: ] @section{examples} @racketblock[ // examples a = { 1.0.rand } + 8; a.value; y = { 8 } + { 1.0.rand }; y.value; :: ] @racketblock[ // arguments are passed into both functions y = { |x=0| x } + { 1.0.rand }; y.value(10); y = { |x=0| x * 3 } + { |x=0| x + 1.0.rand }; y.value(10); y.postcs; y = { |x=0| x * 3 } + { |x=0| x + 1.0.rand } * { |x=0| [50, 100].choose + x } + 1.0; y.value(10); :: ] @racketblock[ // environments can be used as a lookup with valueEnvir: ( Environment.use { ~y = 10; ~x = 2; ~z = { |x=8| x } + { |y=0| y + 1.0.rand }; ~z.valueEnvir; } ) :: ] @racketblock[ // n-ary operators: a = blend({ 3.0.rand }, { 1000.rand }, { |frac| frac }); a.value(0.5); a.value((0, 0.06..1)); // creates a range of values.. :: ]