/*
	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
*/


#ifndef _SC_Complex_
#define _SC_Complex_

#include <cmath>

#include "SC_Types.h"
#include "SC_Constants.h"
#include "float.h"

#ifdef _MSC_VER
// hypotf is c99, but not c++
#define hypotf _hypotf
#endif

////////////////////////////////////////////////////////////////////////////////

namespace detail {

const int kSineSize = 8192;
const int kSineMask = kSineSize - 1;
const double kSinePhaseScale = kSineSize / twopi;
const int32 kPolarLUTSize = 2049;
const int32 kPolarLUTSize2 = kPolarLUTSize >> 1;


/* each object file that is including this header will have separate lookup tables */
namespace {

float gMagLUT[kPolarLUTSize];
float gPhaseLUT[kPolarLUTSize];
float gSine[kSineSize+1];

static bool initTables(void)
{
	double sineIndexToPhase = twopi / kSineSize;
	for (int i=0; i <= kSineSize; ++i) {
		double phase = i * sineIndexToPhase;
		float32 d = sin(phase);
		gSine[i] = d;
	}

	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] = (float)(1.f / cos(angle));
	}

	return true;
}

bool dummy = initTables();

}

struct Polar;


struct Complex
{
	Complex() {}
	Complex(float r, float i) : real(r), imag(i) {}
	void Set(float r, float i) { real = r; imag = i; }

	Complex& operator=(Complex b) { real = b.real; imag = b.imag; return *this; }
	Complex& operator=(float b) { real = b; imag = 0.; return *this; }

	Polar ToPolar();

	/**
	* 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 ToPolarApx();

	void ToPolarInPlace();

	void ToPolarApxInPlace();

	float real, imag;
};

struct Polar
{
	Polar() {}
	Polar(float m, float p) : mag(m), phase(p) {}
	void Set(float m, float p) { mag = m; phase = p; }

	Complex ToComplex()
    {
        return Complex(mag * std::cos(phase), mag * std::sin(phase));
    }

	Complex ToComplexApx()
	{
		uint32 sinindex = (int32)(kSinePhaseScale * phase) & kSineMask;
		uint32 cosindex = (sinindex + (kSineSize>>2)) & kSineMask;
		return Complex(mag * gSine[cosindex], mag * gSine[sinindex]);
	}

	void ToComplexInPlace()
	{
		Complex complx = ToComplex();
		mag = complx.real;
		phase = complx.imag;
	}

	void ToComplexApxInPlace()
	{
		Complex complx = ToComplexApx();
		mag = complx.real;
		phase = complx.imag;
	}

	float mag, phase;
};

inline Polar Complex::ToPolar()
{
	return Polar(hypotf(imag, real), std::atan2(imag, real));
}

inline 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 if (absimag > 0) {
		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));
		}
	} else return Polar(0, 0);
}

inline void Complex::ToPolarInPlace()
{
	Polar polar = ToPolar();
	real = polar.mag;
	imag = polar.phase;
}

inline void Complex::ToPolarApxInPlace()
{
	Polar polar = ToPolarApx();
	real = polar.mag;
	imag = polar.phase;
}

}

using detail::Polar;
using detail::Complex;

struct ComplexFT
{
	float dc, nyq;
	Complex complex[1];
};

struct PolarFT
{
	float dc, nyq;
	Polar polar[1];
};

void ToComplex(Polar in, Complex& out);

inline Complex operator+(Complex a, Complex b) { return Complex(a.real + b.real, a.imag + b.imag); }
inline Complex operator+(Complex a, float b) { return Complex(a.real + b, a.imag); }
inline Complex operator+(float a, Complex b) { return Complex(a + b.real, b.imag); }

inline Complex& operator+=(Complex& a, const Complex& b) { a.real += b.real, a.imag += b.imag; return a; }
inline Complex& operator+=(Complex& a, float b) { a.real += b; return a; }

inline Complex operator-(Complex a, Complex b) { return Complex(a.real - b.real, a.imag - b.imag); }
inline Complex operator-(Complex a, float b) { return Complex(a.real - b, a.imag); }
inline Complex operator-(float a, Complex b) { return Complex(a - b.real, b.imag); }

inline Complex operator-=(Complex a, Complex b) { a.real -= b.real, a.imag -= b.imag; return a; }
inline Complex operator-=(Complex a, float b) { a.real -= b; return a; }

inline Complex operator*(Complex a, Complex b)
{
	return Complex(a.real * b.real - a.imag * b.imag, a.real * b.imag + a.imag * b.real);
}

inline Complex operator*(Complex a, float b)
{
	return Complex(a.real * b, a.imag * b);
}

inline Complex operator*(float a, Complex b)
{
	return Complex(b.real * a, b.imag * a);
}

inline Complex operator*=(Complex a, Complex b)
{
	a.Set(
		a.real * b.real - a.imag * b.imag,
		a.real * b.imag + a.imag * b.real
	);
	return a;
}

inline Complex operator*=(Complex a, float b)
{
	a.real *= b;
	a.imag *= b;
	return a;
}


inline Polar operator*(Polar a, float b)
{
	return Polar(a.mag * b, a.phase);
}

inline Polar operator*(float a, Polar b)
{
	return Polar(a * b.mag, b.phase);
}

inline Polar operator*=(Polar a, float b)
{
	a.mag *= b;
	return a;
}

#endif
