#+TITLE: PhaseWarp* OverviewPhaseWarp can be thought of as a special kind of filter fornormalized phasor signals. When used with a phasor and atable-lookup oscillator this produces what is known as[[https://en.wikipedia.org/wiki/Phase_distortion_synthesis][phase distortion synthesis]], famously used on Casiosynthesizers like the VZ-1.* AlgorithmThe algorithm for PhaseWarp works by adjusting the midpointposition where the phasor reaches 0.5. The adjustment amountis usually a normalized bipolar signal in the range -1 to 1.When the position value is positive, it warps the midpointtowards the upper bounds, causing a greater slope in theupper half, while decreasing the slope in the lower half.A negative position does opposite, creating a higher slopein the lower half, and a lower slope in the upper half. (The whole thing makes a lot more sense when you graph it.Someday, I'll do that here. For now, you'll just have totake my word for it.)* Tangled Files=phasewarp.c= and =phasewarp.h=. #+NAME: phasewarp.c#+BEGIN_SRC c :tangle phasewarp.c#include "phasewarp.h"<<funcs>>#+END_SRC #+NAME: phasewarp.h#+BEGIN_SRC c :tangle phasewarp.h#ifndef SK_PHASEWARP_H#define SK_PHASEWARP_H #ifndef SKFLT#define SKFLT float#endif <<funcdefs>>#endif#+END_SRC* ComputeThis algorithm is so simple, it can be done in a statelessfunction called =sk_phasewarp_tick=. Its arguments arethe input phasor signal and the warp factor. #+NAME: funcdefs#+BEGIN_SRC cSKFLT sk_phasewarp_tick(SKFLT in, SKFLT warp);#+END_SRC #+NAME: funcs#+BEGIN_SRC cSKFLT sk_phasewarp_tick(SKFLT in, SKFLT warp){    SKFLT out;    SKFLT wmp;     out = 0;     <<calculate_warped_midpoint>>    <<determine_side_and_warp>>    return out;}#+END_SRC Calculate warped midpoint. Call it =wmp=. #+NAME: calculate_warped_midpoint#+BEGIN_SRC cwmp = (warp + 1.0) * 0.5;#+END_SRC Determine side and compute. If the phasor position isless than the warped midpoint, than computewith lefthand slope. Otherwise, compute righthand slope. #+NAME: determine_side_and_warp#+BEGIN_SRC cif (in < wmp) {    <<compute_with_lefthand_slope>>} else {    <<compute_with_righthand_slope>>}#+END_SRC Compute With Lefthand Slope. This slope is equal to=0.5/wmp=. This value scales the phasor input =slope * in=. #+NAME: compute_with_lefthand_slope#+BEGIN_SRC cif (wmp != 0) out = ((SKFLT)0.5 / wmp) * in;#+END_SRC Compute Righthand Slope. The righthand slope is computed as=0.5/(1 - wmp)=. The output is computed as=slope * (in - wmp) + 0.5=. #+NAME: compute_with_righthand_slope#+BEGIN_SRC cif (wmp != 1.0) {    out = ((SKFLT)0.5 / (SKFLT)(1.0 - wmp)) * (in - wmp) + 0.5;}#+END_SRC