code:mathparser
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— | code:mathparser [2015/11/19 15:03] (current) – created michfiel | ||
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+ | ===== Math expression parser ===== | ||
+ | |||
+ | ==== Motivation ==== | ||
+ | |||
+ | In order to fill a wavetable with waves, a tool is needed to make this task as simple and effective as possible. | ||
+ | So the idea to do it with the help of some math was born. An expression parser takes a formula as input and after evaluation all wavetable data gets visualized and can be dumped to the blofeld. | ||
+ | |||
+ | ==== How it works ==== | ||
+ | |||
+ | Two variables are set automatically, | ||
+ | |||
+ | x moves from 0.0 to 1.0 for all 128 samples in a wave.a | ||
+ | y moves from 0.0 to 1.0 for each table entry in the range [0..64] | ||
+ | |||
+ | ==== Overview of implemented operators ==== | ||
+ | |||
+ | * Basic operators: +, -, * (multiply) and / (divide) | ||
+ | * % Mod operator | ||
+ | * Exponentiation operator: ^ | ||
+ | * Negation: unary - | ||
+ | * Assignment: = | ||
+ | * Log functions: log(), log2(), ln(), exp() | ||
+ | * Transcendental functions: sin(), cos(), tan(), asin(), acos(), atan(), sinh(), cosh(), tanh(), asinh(), acosh(), atanh() | ||
+ | * Square root function: sqrt() | ||
+ | * [[hgk: | ||
+ | * Angular conversion functions: dtor(), rtod() | ||
+ | * Absolute value function: abs() | ||
+ | * Constants: pi | ||
+ | |||
+ | ==== Example expressions ==== | ||
+ | |||
+ | * Sawtooth: 2*x-1 | ||
+ | * Rectangle: 2*round(x)-1 | ||
+ | |||
+ | * Approximated sawtooth | ||
+ | * http:// | ||
+ | * 0.5 - 1/pi * (sin(2*pi*x) + sin(4*pi*x)/ | ||
+ | * 2/pi * (-sin(2*pi*x) + sin(4*pi*x)/ | ||
+ | |||
+ | * Approximated rectangle | ||
+ | * http:// | ||
+ | * 4/pi * (sin(2*pi*x) + sin(6*pi*x)/ | ||
+ | |||
+ | * 3-bit sampled sine function: round(sin(x*2*pi) * 4)/4 | ||
+ | |||
+ | ==== Gaussian tone burst ==== | ||
+ | |||
+ | Gauss-Funktion für einen Vektor | ||
+ | http:// | ||
+ | |||
+ | < | ||
+ | Mittelwert m und Standardabweichung s | ||
+ | |||
+ | s=0.5 | ||
+ | m=pi/2 | ||
+ | |||
+ | 4/ | ||
+ | |||
+ | </ | ||
+ | |||
+ | ==== Implementation ==== | ||
+ | |||
+ | [[http:// | ||
+ | |||
+ | It uses ZExpParser MacZoop expression parser | ||
+ | |||
+ | The Xcode project compiles fine, just set SDKROOT = macosx and replace cString with UTF8String (in general is a much better choice when converting arbitrary NSStrings into 8-bit representations) | ||
+ | |||
+ | < | ||
+ | GCMathParser* parser = [GCMathParser parser]; | ||
+ | NSString* expression = @" | ||
+ | for (int sampleIndex = 0; sampleIndex < 64; sampleIndex++) { | ||
+ | double x = sampleIndex / 64.; | ||
+ | [parser setSymbolValue: | ||
+ | wave[sampleIndex] = [parser evaluate: | ||
+ | } | ||
+ | </ | ||
+ | |||
+ | Another parser on the web is https:// | ||
code/mathparser.txt · Last modified: 2015/11/19 15:03 by michfiel