code:mathparser

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 — code:mathparser [2015/11/19 15:03] (current)michfiel created 2015/11/19 15:03 michfiel created 2015/11/19 15:03 michfiel created Line 1: Line 1: + ===== 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, that is: + + 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:round|Rounding functions]]: ceil(), floor(), round(), trunc(), rint(), near() + * 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://en.wikipedia.org/wiki/Sawtooth_wave + * 0.5 - 1/pi * (sin(2*pi*x) + sin(4*pi*x)/2 + sin(6*pi*x)/3  + sin(8*pi*x)/4) + sin(10*x*pi)/5 + * 2/pi * (-sin(2*pi*x) + sin(4*pi*x)/2 - sin(6*pi*x)/3  + sin(8*pi*x)/4) - sin(10*x*pi)/5 + + * Approximated rectangle + * http://en.wikipedia.org/wiki/Square_wave + * 4/pi * (sin(2*pi*x) + sin(6*pi*x)/3 + sin(10*pi*x)/5 + sin(14*pi*x)/7 + sin(18*pi*x)/9 + + * 3-bit sampled sine function: round(sin(x*2*pi) * 4)/4 + + ==== Gaussian tone burst ==== + + Gauss-Funktion für einen Vektor + http://etools.fernuni.ch/matlab/matlab3/de/html/loops_learningObject4.html + + + Mittelwert m und Standardabweichung s + + s=0.5 + m=pi/2 + + 4/(2*sqrt(2*pi)) * exp(-1/2*((x*pi-m)/s)^2) * sin(16*pi*x) + + + + ==== Implementation ==== + + [[http://apptree.net/parser.htm|GCMathParser]] is a Cocoa class © 2006-2008 Graham Cox + + 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 = @"sin(x)"; + for (int sampleIndex = 0; sampleIndex < 64; sampleIndex++) { + double x = sampleIndex / 64.; + [parser setSymbolValue:x forKey:@"x"]; + wave[sampleIndex] = [parser evaluate:expression]; + } + + + Another parser on the web is https://github.com/davedelong/DDMathParser 