/**
 * Mandelbulber v2, a 3D fractal generator  _%}}i*<.        ____                _______
 * Copyright (C) 2018 Mandelbulber Team   _>]|=||i=i<,     / __ \___  ___ ___  / ___/ /
 *                                        \><||i|=>>%)    / /_/ / _ \/ -_) _ \/ /__/ /__
 * This file is part of Mandelbulber.     )<=i=]=|=i<>    \____/ .__/\__/_//_/\___/____/
 * The project is licensed under GPLv3,   -<>>=|><|||`        /_/
 * see also COPYING file in this folder.    ~+{i%+++
 *
 * boxFold4dBulb.
 * This formula contains aux.color and aux.actualScaleA

 * This file has been autogenerated by tools/populateUiInformation.php
 * from the function "BoxFold4dBulbPow2Iteration" in the file fractal_formulas.cpp
 * D O    N O T    E D I T    T H I S    F I L E !
 */

REAL4 BoxFold4dBulbPow2Iteration(REAL4 z, __constant sFractalCl *fractal, sExtendedAuxCl *aux)
{
	REAL colorAdd = 0.0f;
	REAL rrCol = 0.0f;
	REAL4 zCol = z;
	REAL4 oldZ = z;

	// parabolic.w = paraOffset + iter *slope + (iter *iter *scale)
	REAL paraAddP0 = 0.0f;
	if (fractal->Cpara.enabledParabFalse)
	{
		REAL parabScale = 0.0f;
		if (fractal->Cpara.parabScale != 0.0f)
			parabScale = aux->i * aux->i * 0.001f * fractal->Cpara.parabScale;
		paraAddP0 = fractal->Cpara.parabOffset0 + (aux->i * fractal->Cpara.parabSlope) + (parabScale);
		z.w += paraAddP0;
	}

	// sinusoidal *w
	REAL sinAdd = 0.0f;
	if (fractal->transformCommon.functionEnabledDFalse)
	{
		sinAdd = native_sin(native_divide(
							 (aux->i + fractal->transformCommon.offset0), fractal->transformCommon.scaleA1))
						 * fractal->transformCommon.scaleC1;
		z.w += sinAdd;
	}

	if (aux->i >= fractal->transformCommon.startIterationsB
			&& aux->i < fractal->transformCommon.stopIterationsB)
	{
		oldZ = z;
		z.x = fabs(z.x + fractal->transformCommon.offset1111.x)
					- fabs(z.x - fractal->transformCommon.offset1111.x) - z.x;
		z.y = fabs(z.y + fractal->transformCommon.offset1111.y)
					- fabs(z.y - fractal->transformCommon.offset1111.y) - z.y;
		z.z = fabs(z.z + fractal->transformCommon.offset1111.z)
					- fabs(z.z - fractal->transformCommon.offset1111.z) - z.z;
		z.w = fabs(z.w + fractal->transformCommon.offset1111.w)
					- fabs(z.w - fractal->transformCommon.offset1111.w) - z.w;
		zCol = z;
	}

	// sph fold
	if (aux->i >= fractal->transformCommon.startIterationsS
			&& aux->i < fractal->transformCommon.stopIterationsS)
	{
		REAL rr = dot(z, z);

		// r power
		if (fractal->mandelboxVary4D.rPower != 1.0f)
			rr = native_powr(rr, fractal->mandelboxVary4D.rPower);
		rrCol = rr;
		// spherical fold
		z += fractal->transformCommon.offset0000;
		if (rr < fractal->transformCommon.minR2p25)
		{
			z *= fractal->transformCommon.maxMinR2factor;
			aux->DE *= fractal->transformCommon.maxMinR2factor;
		}
		else if (rr < fractal->transformCommon.maxR2d1)
		{
			z *= native_divide(fractal->transformCommon.maxR2d1, rr);
			aux->DE *= native_divide(fractal->transformCommon.maxR2d1, rr);
		}

		z -= fractal->transformCommon.offset0000;
	}

	// scale
	REAL useScale = 1.0f;
	if (aux->i >= fractal->transformCommon.startIterationsC
			&& aux->i < fractal->transformCommon.stopIterationsC)
	{

		useScale = aux->actualScaleA + fractal->transformCommon.scale;

		z *= useScale;
		aux->DE = aux->DE * fabs(useScale);

		if (fractal->transformCommon.functionEnabledSFalse
				&& aux->i >= fractal->transformCommon.startIterationsX
				&& aux->i < fractal->transformCommon.stopIterationsX)
		{
			// update actualScale for next iteration
			REAL vary = fractal->transformCommon.scaleVary0
									* (fabs(aux->actualScaleA) - fractal->transformCommon.scaleB1);
			if (fractal->transformCommon.functionEnabledMFalse)
				aux->actualScaleA = -vary;
			else
				aux->actualScaleA = aux->actualScaleA - vary;
		}
	}

	// 6 plane rotation
	if (fractal->transformCommon.functionEnabledRFalse
			&& aux->i >= fractal->transformCommon.startIterationsR
			&& aux->i < fractal->transformCommon.stopIterationsR)
	{
		REAL4 tp;
		if (fractal->transformCommon.rotation44a.x != 0)
		{
			tp = z;
			REAL alpha = fractal->transformCommon.rotation44a.x * M_PI_180;
			z.x = mad(tp.x, native_cos(alpha), tp.y * native_sin(alpha));
			z.y = mad(tp.x, -native_sin(alpha), tp.y * native_cos(alpha));
		}
		if (fractal->transformCommon.rotation44a.y != 0)
		{
			tp = z;
			REAL beta = fractal->transformCommon.rotation44a.y * M_PI_180;
			z.y = mad(tp.y, native_cos(beta), tp.z * native_sin(beta));
			z.z = mad(tp.y, -native_sin(beta), tp.z * native_cos(beta));
		}
		if (fractal->transformCommon.rotation44a.z != 0)
		{
			tp = z;
			REAL gamma = fractal->transformCommon.rotation44a.z * M_PI_180;
			z.x = mad(tp.x, native_cos(gamma), tp.z * native_sin(gamma));
			z.z = mad(tp.x, -native_sin(gamma), tp.z * native_cos(gamma));
		}
		if (fractal->transformCommon.rotation44b.x != 0)
		{
			tp = z;
			REAL delta = fractal->transformCommon.rotation44b.x * M_PI_180;
			z.x = mad(tp.x, native_cos(delta), tp.w * native_sin(delta));
			z.w = mad(tp.x, -native_sin(delta), tp.w * native_cos(delta));
		}
		if (fractal->transformCommon.rotation44b.y != 0)
		{
			tp = z;
			REAL epsilon = fractal->transformCommon.rotation44b.y * M_PI_180;
			z.y = mad(tp.y, native_cos(epsilon), tp.w * native_sin(epsilon));
			z.w = mad(tp.y, -native_sin(epsilon), tp.w * native_cos(epsilon));
		}
		if (fractal->transformCommon.rotation44b.z != 0)
		{
			tp = z;
			REAL zeta = fractal->transformCommon.rotation44b.z * M_PI_180;
			z.z = mad(tp.z, native_cos(zeta), tp.w * native_sin(zeta));
			z.w = mad(tp.z, -native_sin(zeta), tp.w * native_cos(zeta));
		}
	}
	// offset
	z += fractal->transformCommon.additionConstant0000;

	// bulb pow2
	if (aux->i >= fractal->transformCommon.startIterationsA
			&& aux->i < fractal->transformCommon.stopIterationsA)
	{
		aux->r = length(z);
		aux->DE =
			aux->r * aux->DE * 16.0f * fractal->analyticDE.scale1
				* native_divide(native_sqrt(fractal->foldingIntPow.zFactor * fractal->foldingIntPow.zFactor
																		+ 2.0f + fractal->analyticDE.offset2),
					SQRT_3)
			+ fractal->analyticDE.offset1;

		z = z * 2.0f;
		REAL x2 = z.x * z.x;
		REAL y2 = z.y * z.y;
		REAL z2 = z.z * z.z;
		REAL temp = 1.0f - native_divide(z2, (x2 + y2));
		REAL4 zTemp;
		zTemp.x = (x2 - y2) * temp;
		zTemp.y = 2.0f * z.x * z.y * temp;
		zTemp.z = -2.0f * z.z * native_sqrt(x2 + y2);
		zTemp.w = z.w;
		z = zTemp;
		z.z *= fractal->foldingIntPow.zFactor;
	}

	// color
	if (fractal->foldColor.auxColorEnabledFalse)
	{
		if (fractal->transformCommon.functionEnabledCxFalse)
		{
			if (zCol.x != oldZ.x)
				colorAdd +=
					fractal->mandelbox.color.factor.x * (fabs(zCol.x) - fractal->mandelbox.color.factor4D.x);
			if (zCol.y != oldZ.y)
				colorAdd +=
					fractal->mandelbox.color.factor.y * (fabs(zCol.y) - fractal->mandelbox.color.factor4D.y);
			if (zCol.z != oldZ.z)
				colorAdd +=
					fractal->mandelbox.color.factor.z * (fabs(zCol.z) - fractal->mandelbox.color.factor4D.z);
			if (zCol.w != oldZ.w)
				colorAdd +=
					fractal->mandelbox.color.factor.z * (fabs(zCol.w) - fractal->mandelbox.color.factor4D.w);
			if (rrCol < fractal->transformCommon.maxR2d1)
			{
				if (rrCol < fractal->transformCommon.minR2p25)
					colorAdd +=
						mad(fractal->mandelbox.color.factorSp1, (fractal->transformCommon.minR2p25 - rrCol),
							fractal->mandelbox.color.factorSp2
								* (fractal->transformCommon.maxR2d1 - fractal->transformCommon.minR2p25));
				else
					colorAdd +=
						fractal->mandelbox.color.factorSp2 * (fractal->transformCommon.maxR2d1 - rrCol);
			}
		}
		else
		{
			if (zCol.x != oldZ.x) colorAdd += fractal->mandelbox.color.factor4D.x;
			if (zCol.y != oldZ.y) colorAdd += fractal->mandelbox.color.factor4D.y;
			if (zCol.z != oldZ.z) colorAdd += fractal->mandelbox.color.factor4D.z;
			if (zCol.w != oldZ.w) colorAdd += fractal->mandelbox.color.factor4D.w;
			if (rrCol < fractal->transformCommon.minR2p25)
				colorAdd += fractal->mandelbox.color.factorSp1;
			else if (rrCol < fractal->transformCommon.maxR2d1)
				colorAdd += fractal->mandelbox.color.factorSp2;
		}
		aux->color += colorAdd;
	}
	return z;
}