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--- hgk:hacks:mathparser [2015/11/17 12:09] – created michfiel
+++ hgk:hacks:mathparser [2015/11/19 15:03] (current) – removed michfiel
@@ 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
-<code>
-Mittelwert m und Standardabweichung s
-s=0.5
-m=pi/2
-/(2*sqrt(2*pi)) * exp(-1/2*((x*pi-m)/s)^2) * sin(16*pi*x)
-</code>
-==== 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)
-<code>
-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];
-}
-</code>
-Another parser on the web is https://github.com/davedelong/DDMathParser