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/*
SuperCollider real time audio synthesis system
Copyright (c) 2002 James McCartney. All rights reserved.
http://www.audiosynth.com
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include "SC_Complex.h"
#include "SC_Constants.h"
#include "SC_Samp.h"
#include <math.h>
////////////////////////////////////////////////////////////////////////////////
const int32 kPolarLUTSize = 2049;
const int32 kPolarLUTSize2 = kPolarLUTSize >> 1;
const double kSinePhaseScale = (double)kSineSize / twopi;
float gMagLUT[kPolarLUTSize];
float gPhaseLUT[kPolarLUTSize];
void BuildPolarLUT();
void BuildPolarLUT()
{
double rPolarLUTSize2 = 1. / kPolarLUTSize2;
for (int i=0; i < kPolarLUTSize; ++i) {
double slope = (i - kPolarLUTSize2) * rPolarLUTSize2;
double angle = atan(slope);
gPhaseLUT[i] = (float)angle;
gMagLUT[i] = 1.f / (float)cos(angle);
}
}
Polar Complex::ToPolar()
{
return Polar(hypot(imag, real), atan2(imag, real));
}
Complex Polar::ToComplex()
{
return Complex(mag * cos(phase), mag * sin(phase));
}
/*
float fhypotx(float real, float imag);
float fhypotx(float real, float imag)
{
int32 index;
float absreal = fabs(real);
float absimag = fabs(imag);
float slope;
if (absreal > absimag) {
slope = imag/real;
index = kPolarLUTSize2 + kPolarLUTSize2 * slope;
return gMagLUT[index] * absreal;
} else {
slope = real/imag;
index = kPolarLUTSize2 + kPolarLUTSize2 * slope;
return gMagLUT[index] * absimag;
}
}
*/
/**
* Converts cartesian to polar representation, using lookup tables.
* Note: in this implementation the phase values returned lie in the range [-pi/4, 7pi/4]
* rather than the more conventional [0, 2pi] or [-pi, pi].
*/
Polar Complex::ToPolarApx()
{
int32 index;
float absreal = fabs(real);
float absimag = fabs(imag);
float mag, phase, slope;
if (absreal > absimag) {
slope = imag/real;
index = (int32)(kPolarLUTSize2 + kPolarLUTSize2 * slope);
mag = gMagLUT[index] * absreal;
phase = gPhaseLUT[index];
if (real > 0) {
return Polar(mag, phase);
} else {
return Polar(mag, (float)(pi + phase));
}
} else {
slope = real/imag;
index = (int32)(kPolarLUTSize2 + kPolarLUTSize2 * slope);
mag = gMagLUT[index] * absimag;
phase = gPhaseLUT[index];
if (imag > 0) {
return Polar(mag, (float)(pi2 - phase));
} else {
return Polar(mag, (float)(pi32 - phase));
}
}
}
void Complex::ToPolarInPlace()
{
Polar polar = ToPolar();
real = polar.mag;
imag = polar.phase;
}
void Polar::ToComplexInPlace()
{
Complex complx = ToComplex();
mag = complx.real;
phase = complx.imag;
}
Complex Polar::ToComplexApx()
{
uint32 sinindex = (int32)(kSinePhaseScale * phase) & kSineMask;
uint32 cosindex = (sinindex + (kSineSize>>2)) & kSineMask;
return Complex(mag * gSine[cosindex], mag * gSine[sinindex]);
}
void Complex::ToPolarApxInPlace()
{
Polar polar = ToPolarApx();
real = polar.mag;
imag = polar.phase;
}
void Polar::ToComplexApxInPlace()
{
Complex complx = ToComplexApx();
mag = complx.real;
phase = complx.imag;
}
////////////////////////////////////////////////////////////////////////////////
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