/**
 * Mandelbulber v2, a 3D fractal generator  _%}}i*<.        ____                _______
 * Copyright (C) 2017 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%+++
 *
 * benesiT1Mod  3D based on benesiT1
 * @reference
 * http://www.fractalforums.com/new-theories-and-research/
 * do-m3d-formula-have-to-be-distance-estimation-formulas/

 * This file has been autogenerated by tools/populateUiInformation.php
 * from the function "TransfBenesiT1ModIteration" in the file fractal_formulas.cpp
 * D O    N O T    E D I T    T H I S    F I L E !
 */

REAL4 TransfBenesiT1ModIteration(REAL4 z, __constant sFractalCl *fractal, sExtendedAuxCl *aux)
{
	REAL tempXZ = mad(z.x, SQRT_2_3, -z.z * SQRT_1_3);
	z = (REAL4){
		(tempXZ - z.y) * SQRT_1_2, (tempXZ + z.y) * SQRT_1_2, z.x * SQRT_1_3 + z.z * SQRT_2_3, z.w};

	REAL4 temp = z;
	REAL tempL = length(temp);
	z = fabs(z) * fractal->transformCommon.scale3D333;
	// if (tempL < 1e-21f) tempL = 1e-21f;
	REAL avgScale = native_divide(length(z), tempL);
	aux->DE = mad(aux->DE, avgScale, 1.0f);

	z = (fabs(z + fractal->transformCommon.additionConstant111)
			 - fabs(z - fractal->transformCommon.additionConstant111) - z);

	if (fractal->transformCommon.rotationEnabled)
	{
		z = Matrix33MulFloat4(fractal->transformCommon.rotationMatrix, z);
	}

	tempXZ = (z.y + z.x) * SQRT_1_2;

	z = (REAL4){z.z * SQRT_1_3 + tempXZ * SQRT_2_3, (z.y - z.x) * SQRT_1_2,
		z.z * SQRT_2_3 - tempXZ * SQRT_1_3, z.w};
	return z;
}