/*
 * Copyright 2011-2018 Branimir Karadzic. All rights reserved.
 * License: https://github.com/bkaradzic/bx#license-bsd-2-clause
 */

#include "bx_p.h"
#include <bx/math.h>
#include <bx/uint32_t.h>

namespace bx
{
	const float kPi = 3.1415926535897932384626433832795f;
	const float kPi2 = 6.2831853071795864769252867665590f;
	const float kInvPi = 1.0f/kPi;
	const float kPiHalf = 1.5707963267948966192313216916398f;
	const float kPiQuarter = 0.7853981633974483096156608458199f;
	const float kSqrt2 = 1.4142135623730950488016887242097f;
	const float kLogNat10 = 2.3025850929940456840179914546844f;
	const float kInvLogNat2 = 1.4426950408889634073599246810019f;
	const float kLogNat2Hi = 0.6931471805599453094172321214582f;
	const float kLogNat2Lo = 1.90821492927058770002e-10f;
	const float kE = 2.7182818284590452353602874713527f;
	const float kNearZero = 1.0f/float(1 << 28);
	const float kFloatMin = 1.175494e-38f;
	const float kFloatMax = 3.402823e+38f;
	const float kInfinity = bitsToFloat(UINT32_C(0x7f800000) );

	namespace
	{
		static const float kSinC2 = -0.16666667163372039794921875f;
		static const float kSinC4 = 8.333347737789154052734375e-3f;
		static const float kSinC6 = -1.9842604524455964565277099609375e-4f;
		static const float kSinC8 = 2.760012648650445044040679931640625e-6f;
		static const float kSinC10 = -2.50293279435709337121807038784027099609375e-8f;

		static const float kCosC2 = -0.5f;
		static const float kCosC4 = 4.166664183139801025390625e-2f;
		static const float kCosC6 = -1.388833043165504932403564453125e-3f;
		static const float kCosC8 = 2.47562347794882953166961669921875e-5f;
		static const float kCosC10 = -2.59630184018533327616751194000244140625e-7f;

	} // namespace

	BX_CONST_FUNC float cos(float _a)
	{
		const float scaled = _a * 2.0f*kInvPi;
		const float real = floor(scaled);
		const float xx = _a - real * kPiHalf;
		const int32_t bits = int32_t(real) & 3;

		float c0, c2, c4, c6, c8, c10;

		if (bits == 0
		|| bits == 2)
		{
			c0 = 1.0f;
			c2 = kCosC2;
			c4 = kCosC4;
			c6 = kCosC6;
			c8 = kCosC8;
			c10 = kCosC10;
		}
		else
		{
			c0 = xx;
			c2 = kSinC2;
			c4 = kSinC4;
			c6 = kSinC6;
			c8 = kSinC8;
			c10 = kSinC10;
		}

		const float xsq = square(xx);
		const float tmp0 = mad(c10, xsq, c8 );
		const float tmp1 = mad(tmp0, xsq, c6 );
		const float tmp2 = mad(tmp1, xsq, c4 );
		const float tmp3 = mad(tmp2, xsq, c2 );
		const float tmp4 = mad(tmp3, xsq, 1.0);
		const float result = tmp4 * c0;

		return bits == 1 || bits == 2
			? -result
			: result
			;
	}

	namespace
	{
		static const float kAcosC0 = 1.5707288f;
		static const float kAcosC1 = -0.2121144f;
		static const float kAcosC2 = 0.0742610f;
		static const float kAcosC3 = -0.0187293f;

	} // namespace

	BX_CONST_FUNC float acos(float _a)
	{
		const float absa = abs(_a);
		const float tmp0 = mad(kAcosC3, absa, kAcosC2);
		const float tmp1 = mad(tmp0, absa, kAcosC1);
		const float tmp2 = mad(tmp1, absa, kAcosC0);
		const float tmp3 = tmp2 * sqrt(1.0f - absa);
		const float negate = float(_a < 0.0f);
		const float tmp4 = tmp3 - 2.0f*negate*tmp3;
		const float result = negate*kPi + tmp4;

		return result;
	}

	namespace
	{
		static const float kAtan2C0 = -0.013480470f;
		static const float kAtan2C1 = 0.057477314f;
		static const float kAtan2C2 = -0.121239071f;
		static const float kAtan2C3 = 0.195635925f;
		static const float kAtan2C4 = -0.332994597f;
		static const float kAtan2C5 = 0.999995630f;

	} // namespace

	BX_CONST_FUNC float atan2(float _y, float _x)
	{
		const float ax = abs(_x);
		const float ay = abs(_y);
		const float maxaxy = max(ax, ay);
		const float minaxy = min(ax, ay);

		if (maxaxy == 0.0f)
		{
			return 0.0f*sign(_y);
		}

		const float mxy = minaxy / maxaxy;
		const float mxysq = square(mxy);
		const float tmp0 = mad(kAtan2C0, mxysq, kAtan2C1);
		const float tmp1 = mad(tmp0, mxysq, kAtan2C2);
		const float tmp2 = mad(tmp1, mxysq, kAtan2C3);
		const float tmp3 = mad(tmp2, mxysq, kAtan2C4);
		const float tmp4 = mad(tmp3, mxysq, kAtan2C5);
		const float tmp5 = tmp4 * mxy;
		const float tmp6 = ay > ax ? kPiHalf - tmp5 : tmp5;
		const float tmp7 = _x < 0.0f ? kPi - tmp6 : tmp6;
		const float result = sign(_y)*tmp7;

		return result;
	}

	BX_CONST_FUNC float ldexp(float _a, int32_t _b)
	{
		const uint32_t ftob = floatToBits(_a);
		const uint32_t masked = uint32_and(ftob, UINT32_C(0xff800000) );
		const uint32_t expsign0 = uint32_sra(masked, 23);
		const uint32_t tmp = uint32_iadd(expsign0, _b);
		const uint32_t expsign1 = uint32_sll(tmp, 23);
		const uint32_t mantissa = uint32_and(ftob, UINT32_C(0x007fffff) );
		const uint32_t bits = uint32_or(mantissa, expsign1);
		const float result = bitsToFloat(bits);

		return result;
	}

	float frexp(float _a, int32_t* _outExp)
	{
		const uint32_t ftob = floatToBits(_a);
		const uint32_t masked0 = uint32_and(ftob, UINT32_C(0x7f800000) );
		const uint32_t exp0 = uint32_srl(masked0, 23);
		const uint32_t masked1 = uint32_and(ftob, UINT32_C(0x807fffff) );
		const uint32_t bits = uint32_or(masked1, UINT32_C(0x3f000000) );
		const float result = bitsToFloat(bits);

		*_outExp = int32_t(exp0 - 0x7e);

		return result;
	}

	namespace
	{
		static const float kExpC0 = 1.66666666666666019037e-01f;
		static const float kExpC1 = -2.77777777770155933842e-03f;
		static const float kExpC2 = 6.61375632143793436117e-05f;
		static const float kExpC3 = -1.65339022054652515390e-06f;
		static const float kExpC4 = 4.13813679705723846039e-08f;

	} // namespace

	BX_CONST_FUNC float exp(float _a)
	{
		if (abs(_a) <= kNearZero)
		{
			return _a + 1.0f;
		}

		const float kk = round(_a*kInvLogNat2);
		const float hi = _a - kk*kLogNat2Hi;
		const float lo = kk*kLogNat2Lo;
		const float hml = hi - lo;
		const float hmlsq = square(hml);
		const float tmp0 = mad(kExpC4, hmlsq, kExpC3);
		const float tmp1 = mad(tmp0, hmlsq, kExpC2);
		const float tmp2 = mad(tmp1, hmlsq, kExpC1);
		const float tmp3 = mad(tmp2, hmlsq, kExpC0);
		const float tmp4 = hml - hmlsq * tmp3;
		const float tmp5 = hml*tmp4/(2.0f-tmp4);
		const float tmp6 = 1.0f - ( (lo - tmp5) - hi);
		const float result = ldexp(tmp6, int32_t(kk) );

		return result;
	}

	namespace
	{
		static const float kLogC0 = 6.666666666666735130e-01f;
		static const float kLogC1 = 3.999999999940941908e-01f;
		static const float kLogC2 = 2.857142874366239149e-01f;
		static const float kLogC3 = 2.222219843214978396e-01f;
		static const float kLogC4 = 1.818357216161805012e-01f;
		static const float kLogC5 = 1.531383769920937332e-01f;
		static const float kLogC6 = 1.479819860511658591e-01f;

	} // namespace

	BX_CONST_FUNC float log(float _a)
	{
		int32_t exp;
		float ff = frexp(_a, &exp);
		if (ff < kSqrt2*0.5f)
		{
			ff *= 2.0f;
			--exp;
		}

		ff -= 1.0f;
		const float kk = float(exp);
		const float hi = kk*kLogNat2Hi;
		const float lo = kk*kLogNat2Lo;
		const float ss = ff / (2.0f + ff);
		const float s2 = square(ss);
		const float s4 = square(s2);

		const float tmp0 = mad(kLogC6, s4, kLogC4);
		const float tmp1 = mad(tmp0, s4, kLogC2);
		const float tmp2 = mad(tmp1, s4, kLogC0);
		const float t1 = s2*tmp2;

		const float tmp3 = mad(kLogC5, s4, kLogC3);
		const float tmp4 = mad(tmp3, s4, kLogC1);
		const float t2 = s4*tmp4;

		const float t12 = t1 + t2;
		const float hfsq = 0.5f*square(ff);
		const float result = hi - ( (hfsq - (ss*(hfsq+t12) + lo) ) - ff);

		return result;
	}

	BX_CONST_FUNC float floor(float _a)
	{
		if (_a < 0.0f)
		{
			const float fr = fract(-_a);
			const float result = -_a - fr;

			return -(0.0f != fr
				? result + 1.0f
				: result)
				;
		}

		return _a - fract(_a);
	}

	void mtxLookAtImpl(float* _result, const float* _eye, const float* _view, const float* _up)
	{
		float up[3] = { 0.0f, 1.0f, 0.0f };
		if (NULL != _up)
		{
			up[0] = _up[0];
			up[1] = _up[1];
			up[2] = _up[2];
		}

		float tmp[4];
		vec3Cross(tmp, up, _view);

		float right[4];
		vec3Norm(right, tmp);

		vec3Cross(up, _view, right);

		memSet(_result, 0, sizeof(float)*16);
		_result[ 0] = right[0];
		_result[ 1] = up[0];
		_result[ 2] = _view[0];

		_result[ 4] = right[1];
		_result[ 5] = up[1];
		_result[ 6] = _view[1];

		_result[ 8] = right[2];
		_result[ 9] = up[2];
		_result[10] = _view[2];

		_result[12] = -vec3Dot(right, _eye);
		_result[13] = -vec3Dot(up, _eye);
		_result[14] = -vec3Dot(_view, _eye);
		_result[15] = 1.0f;
	}

	void mtxLookAtLh(float* _result, const float* _eye, const float* _at, const float* _up)
	{
		float tmp[4];
		vec3Sub(tmp, _at, _eye);

		float view[4];
		vec3Norm(view, tmp);

		mtxLookAtImpl(_result, _eye, view, _up);
	}

	void mtxLookAtRh(float* _result, const float* _eye, const float* _at, const float* _up)
	{
		float tmp[4];
		vec3Sub(tmp, _eye, _at);

		float view[4];
		vec3Norm(view, tmp);

		mtxLookAtImpl(_result, _eye, view, _up);
	}

	void mtxLookAt(float* _result, const float* _eye, const float* _at, const float* _up)
	{
		mtxLookAtLh(_result, _eye, _at, _up);
	}

	template<Handness::Enum HandnessT>
	void mtxProjXYWH(float* _result, float _x, float _y, float _width, float _height, float _near, float _far, bool _oglNdc)
	{
		const float diff = _far-_near;
		const float aa = _oglNdc ? ( _far+_near)/diff : _far/diff;
		const float bb = _oglNdc ? (2.0f*_far*_near)/diff : _near*aa;

		memSet(_result, 0, sizeof(float)*16);
		_result[ 0] = _width;
		_result[ 5] = _height;
		_result[ 8] = (Handness::Right == HandnessT) ? _x : -_x;
		_result[ 9] = (Handness::Right == HandnessT) ? _y : -_y;
		_result[10] = (Handness::Right == HandnessT) ? -aa : aa;
		_result[11] = (Handness::Right == HandnessT) ? -1.0f : 1.0f;
		_result[14] = -bb;
	}

	template<Handness::Enum HandnessT>
	void mtxProjImpl(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, float _far, bool _oglNdc)
	{
		const float invDiffRl = 1.0f/(_rt - _lt);
		const float invDiffUd = 1.0f/(_ut - _dt);
		const float width = 2.0f*_near * invDiffRl;
		const float height = 2.0f*_near * invDiffUd;
		const float xx = (_rt + _lt) * invDiffRl;
		const float yy = (_ut + _dt) * invDiffUd;
		mtxProjXYWH<HandnessT>(_result, xx, yy, width, height, _near, _far, _oglNdc);
	}

	template<Handness::Enum HandnessT>
	void mtxProjImpl(float* _result, const float _fov[4], float _near, float _far, bool _oglNdc)
	{
		mtxProjImpl<HandnessT>(_result, _fov[0], _fov[1], _fov[2], _fov[3], _near, _far, _oglNdc);
	}

	template<Handness::Enum HandnessT>
	void mtxProjImpl(float* _result, float _fovy, float _aspect, float _near, float _far, bool _oglNdc)
	{
		const float height = 1.0f/tan(toRad(_fovy)*0.5f);
		const float width = height * 1.0f/_aspect;
		mtxProjXYWH<HandnessT>(_result, 0.0f, 0.0f, width, height, _near, _far, _oglNdc);
	}

	void mtxProj(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, float _far, bool _oglNdc)
	{
		mtxProjImpl<Handness::Left>(_result, _ut, _dt, _lt, _rt, _near, _far, _oglNdc);
	}

	void mtxProj(float* _result, const float _fov[4], float _near, float _far, bool _oglNdc)
	{
		mtxProjImpl<Handness::Left>(_result, _fov, _near, _far, _oglNdc);
	}

	void mtxProj(float* _result, float _fovy, float _aspect, float _near, float _far, bool _oglNdc)
	{
		mtxProjImpl<Handness::Left>(_result, _fovy, _aspect, _near, _far, _oglNdc);
	}

	void mtxProjLh(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, float _far, bool _oglNdc)
	{
		mtxProjImpl<Handness::Left>(_result, _ut, _dt, _lt, _rt, _near, _far, _oglNdc);
	}

	void mtxProjLh(float* _result, const float _fov[4], float _near, float _far, bool _oglNdc)
	{
		mtxProjImpl<Handness::Left>(_result, _fov, _near, _far, _oglNdc);
	}

	void mtxProjLh(float* _result, float _fovy, float _aspect, float _near, float _far, bool _oglNdc)
	{
		mtxProjImpl<Handness::Left>(_result, _fovy, _aspect, _near, _far, _oglNdc);
	}

	void mtxProjRh(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, float _far, bool _oglNdc)
	{
		mtxProjImpl<Handness::Right>(_result, _ut, _dt, _lt, _rt, _near, _far, _oglNdc);
	}

	void mtxProjRh(float* _result, const float _fov[4], float _near, float _far, bool _oglNdc)
	{
		mtxProjImpl<Handness::Right>(_result, _fov, _near, _far, _oglNdc);
	}

	void mtxProjRh(float* _result, float _fovy, float _aspect, float _near, float _far, bool _oglNdc)
	{
		mtxProjImpl<Handness::Right>(_result, _fovy, _aspect, _near, _far, _oglNdc);
	}

	template<NearFar::Enum NearFarT, Handness::Enum HandnessT>
	void mtxProjInfXYWH(float* _result, float _x, float _y, float _width, float _height, float _near, bool _oglNdc)
	{
		float aa;
		float bb;
		if (BX_ENABLED(NearFar::Reverse == NearFarT) )
		{
			aa = _oglNdc ? -1.0f : 0.0f;
			bb = _oglNdc ? -2.0f*_near : -_near;
		}
		else
		{
			aa = 1.0f;
			bb = _oglNdc ? 2.0f*_near : _near;
		}

		memSet(_result, 0, sizeof(float)*16);
		_result[ 0] = _width;
		_result[ 5] = _height;
		_result[ 8] = (Handness::Right == HandnessT) ? _x : -_x;
		_result[ 9] = (Handness::Right == HandnessT) ? _y : -_y;
		_result[10] = (Handness::Right == HandnessT) ? -aa : aa;
		_result[11] = (Handness::Right == HandnessT) ? -1.0f : 1.0f;
		_result[14] = -bb;
	}

	template<NearFar::Enum NearFarT, Handness::Enum HandnessT>
	void mtxProjInfImpl(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, bool _oglNdc)
	{
		const float invDiffRl = 1.0f/(_rt - _lt);
		const float invDiffUd = 1.0f/(_ut - _dt);
		const float width = 2.0f*_near * invDiffRl;
		const float height = 2.0f*_near * invDiffUd;
		const float xx = (_rt + _lt) * invDiffRl;
		const float yy = (_ut + _dt) * invDiffUd;
		mtxProjInfXYWH<NearFarT,HandnessT>(_result, xx, yy, width, height, _near, _oglNdc);
	}

	template<NearFar::Enum NearFarT, Handness::Enum HandnessT>
	void mtxProjInfImpl(float* _result, const float _fov[4], float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFarT,HandnessT>(_result, _fov[0], _fov[1], _fov[2], _fov[3], _near, _oglNdc);
	}

	template<NearFar::Enum NearFarT, Handness::Enum HandnessT>
	void mtxProjInfImpl(float* _result, float _fovy, float _aspect, float _near, bool _oglNdc)
	{
		const float height = 1.0f/tan(toRad(_fovy)*0.5f);
		const float width = height * 1.0f/_aspect;
		mtxProjInfXYWH<NearFarT,HandnessT>(_result, 0.0f, 0.0f, width, height, _near, _oglNdc);
	}

	void mtxProjInf(float* _result, const float _fov[4], float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Default,Handness::Left>(_result, _fov, _near, _oglNdc);
	}

	void mtxProjInf(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Default,Handness::Left>(_result, _ut, _dt, _lt, _rt, _near, _oglNdc);
	}

	void mtxProjInf(float* _result, float _fovy, float _aspect, float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Default,Handness::Left>(_result, _fovy, _aspect, _near, _oglNdc);
	}

	void mtxProjInfLh(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Default,Handness::Left>(_result, _ut, _dt, _lt, _rt, _near, _oglNdc);
	}

	void mtxProjInfLh(float* _result, const float _fov[4], float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Default,Handness::Left>(_result, _fov, _near, _oglNdc);
	}

	void mtxProjInfLh(float* _result, float _fovy, float _aspect, float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Default,Handness::Left>(_result, _fovy, _aspect, _near, _oglNdc);
	}

	void mtxProjInfRh(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Default,Handness::Right>(_result, _ut, _dt, _lt, _rt, _near, _oglNdc);
	}

	void mtxProjInfRh(float* _result, const float _fov[4], float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Default,Handness::Right>(_result, _fov, _near, _oglNdc);
	}

	void mtxProjInfRh(float* _result, float _fovy, float _aspect, float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Default,Handness::Right>(_result, _fovy, _aspect, _near, _oglNdc);
	}

	void mtxProjRevInfLh(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Reverse,Handness::Left>(_result, _ut, _dt, _lt, _rt, _near, _oglNdc);
	}

	void mtxProjRevInfLh(float* _result, const float _fov[4], float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Reverse,Handness::Left>(_result, _fov, _near, _oglNdc);
	}

	void mtxProjRevInfLh(float* _result, float _fovy, float _aspect, float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Reverse,Handness::Left>(_result, _fovy, _aspect, _near, _oglNdc);
	}

	void mtxProjRevInfRh(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Reverse,Handness::Right>(_result, _ut, _dt, _lt, _rt, _near, _oglNdc);
	}

	void mtxProjRevInfRh(float* _result, const float _fov[4], float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Reverse,Handness::Right>(_result, _fov, _near, _oglNdc);
	}

	void mtxProjRevInfRh(float* _result, float _fovy, float _aspect, float _near, bool _oglNdc)
	{
		mtxProjInfImpl<NearFar::Reverse,Handness::Right>(_result, _fovy, _aspect, _near, _oglNdc);
	}

	template<Handness::Enum HandnessT>
	void mtxOrthoImpl(float* _result, float _left, float _right, float _bottom, float _top, float _near, float _far, float _offset, bool _oglNdc)
	{
		const float aa = 2.0f/(_right - _left);
		const float bb = 2.0f/(_top - _bottom);
		const float cc = (_oglNdc ? 2.0f : 1.0f) / (_far - _near);
		const float dd = (_left + _right )/(_left - _right);
		const float ee = (_top + _bottom)/(_bottom - _top );
		const float ff = _oglNdc
			? (_near + _far)/(_near - _far)
			: _near /(_near - _far)
			;

		memSet(_result, 0, sizeof(float)*16);
		_result[ 0] = aa;
		_result[ 5] = bb;
		_result[10] = (Handness::Right == HandnessT) ? -cc : cc;
		_result[12] = dd + _offset;
		_result[13] = ee;
		_result[14] = ff;
		_result[15] = 1.0f;
	}

	void mtxOrtho(float* _result, float _left, float _right, float _bottom, float _top, float _near, float _far, float _offset, bool _oglNdc)
	{
		mtxOrthoImpl<Handness::Left>(_result, _left, _right, _bottom, _top, _near, _far, _offset, _oglNdc);
	}

	void mtxOrthoLh(float* _result, float _left, float _right, float _bottom, float _top, float _near, float _far, float _offset, bool _oglNdc)
	{
		mtxOrthoImpl<Handness::Left>(_result, _left, _right, _bottom, _top, _near, _far, _offset, _oglNdc);
	}

	void mtxOrthoRh(float* _result, float _left, float _right, float _bottom, float _top, float _near, float _far, float _offset, bool _oglNdc)
	{
		mtxOrthoImpl<Handness::Right>(_result, _left, _right, _bottom, _top, _near, _far, _offset, _oglNdc);
	}

	void mtxRotateX(float* _result, float _ax)
	{
		const float sx = sin(_ax);
		const float cx = cos(_ax);

		memSet(_result, 0, sizeof(float)*16);
		_result[ 0] = 1.0f;
		_result[ 5] = cx;
		_result[ 6] = -sx;
		_result[ 9] = sx;
		_result[10] = cx;
		_result[15] = 1.0f;
	}

	void mtxRotateY(float* _result, float _ay)
	{
		const float sy = sin(_ay);
		const float cy = cos(_ay);

		memSet(_result, 0, sizeof(float)*16);
		_result[ 0] = cy;
		_result[ 2] = sy;
		_result[ 5] = 1.0f;
		_result[ 8] = -sy;
		_result[10] = cy;
		_result[15] = 1.0f;
	}

	void mtxRotateZ(float* _result, float _az)
	{
		const float sz = sin(_az);
		const float cz = cos(_az);

		memSet(_result, 0, sizeof(float)*16);
		_result[ 0] = cz;
		_result[ 1] = -sz;
		_result[ 4] = sz;
		_result[ 5] = cz;
		_result[10] = 1.0f;
		_result[15] = 1.0f;
	}

	void mtxRotateXY(float* _result, float _ax, float _ay)
	{
		const float sx = sin(_ax);
		const float cx = cos(_ax);
		const float sy = sin(_ay);
		const float cy = cos(_ay);

		memSet(_result, 0, sizeof(float)*16);
		_result[ 0] = cy;
		_result[ 2] = sy;
		_result[ 4] = sx*sy;
		_result[ 5] = cx;
		_result[ 6] = -sx*cy;
		_result[ 8] = -cx*sy;
		_result[ 9] = sx;
		_result[10] = cx*cy;
		_result[15] = 1.0f;
	}

	void mtxRotateXYZ(float* _result, float _ax, float _ay, float _az)
	{
		const float sx = sin(_ax);
		const float cx = cos(_ax);
		const float sy = sin(_ay);
		const float cy = cos(_ay);
		const float sz = sin(_az);
		const float cz = cos(_az);

		memSet(_result, 0, sizeof(float)*16);
		_result[ 0] = cy*cz;
		_result[ 1] = -cy*sz;
		_result[ 2] = sy;
		_result[ 4] = cz*sx*sy + cx*sz;
		_result[ 5] = cx*cz - sx*sy*sz;
		_result[ 6] = -cy*sx;
		_result[ 8] = -cx*cz*sy + sx*sz;
		_result[ 9] = cz*sx + cx*sy*sz;
		_result[10] = cx*cy;
		_result[15] = 1.0f;
	}

	void mtxRotateZYX(float* _result, float _ax, float _ay, float _az)
	{
		const float sx = sin(_ax);
		const float cx = cos(_ax);
		const float sy = sin(_ay);
		const float cy = cos(_ay);
		const float sz = sin(_az);
		const float cz = cos(_az);

		memSet(_result, 0, sizeof(float)*16);
		_result[ 0] = cy*cz;
		_result[ 1] = cz*sx*sy-cx*sz;
		_result[ 2] = cx*cz*sy+sx*sz;
		_result[ 4] = cy*sz;
		_result[ 5] = cx*cz + sx*sy*sz;
		_result[ 6] = -cz*sx + cx*sy*sz;
		_result[ 8] = -sy;
		_result[ 9] = cy*sx;
		_result[10] = cx*cy;
		_result[15] = 1.0f;
	};

	void mtxSRT(float* _result, float _sx, float _sy, float _sz, float _ax, float _ay, float _az, float _tx, float _ty, float _tz)
	{
		const float sx = sin(_ax);
		const float cx = cos(_ax);
		const float sy = sin(_ay);
		const float cy = cos(_ay);
		const float sz = sin(_az);
		const float cz = cos(_az);

		const float sxsz = sx*sz;
		const float cycz = cy*cz;

		_result[ 0] = _sx * (cycz - sxsz*sy);
		_result[ 1] = _sx * -cx*sz;
		_result[ 2] = _sx * (cz*sy + cy*sxsz);
		_result[ 3] = 0.0f;

		_result[ 4] = _sy * (cz*sx*sy + cy*sz);
		_result[ 5] = _sy * cx*cz;
		_result[ 6] = _sy * (sy*sz -cycz*sx);
		_result[ 7] = 0.0f;

		_result[ 8] = _sz * -cx*sy;
		_result[ 9] = _sz * sx;
		_result[10] = _sz * cx*cy;
		_result[11] = 0.0f;

		_result[12] = _tx;
		_result[13] = _ty;
		_result[14] = _tz;
		_result[15] = 1.0f;
	}

	void mtx3Inverse(float* _result, const float* _a)
	{
		float xx = _a[0];
		float xy = _a[1];
		float xz = _a[2];
		float yx = _a[3];
		float yy = _a[4];
		float yz = _a[5];
		float zx = _a[6];
		float zy = _a[7];
		float zz = _a[8];

		float det = 0.0f;
		det += xx * (yy*zz - yz*zy);
		det -= xy * (yx*zz - yz*zx);
		det += xz * (yx*zy - yy*zx);

		float invDet = 1.0f/det;

		_result[0] = +(yy*zz - yz*zy) * invDet;
		_result[1] = -(xy*zz - xz*zy) * invDet;
		_result[2] = +(xy*yz - xz*yy) * invDet;

		_result[3] = -(yx*zz - yz*zx) * invDet;
		_result[4] = +(xx*zz - xz*zx) * invDet;
		_result[5] = -(xx*yz - xz*yx) * invDet;

		_result[6] = +(yx*zy - yy*zx) * invDet;
		_result[7] = -(xx*zy - xy*zx) * invDet;
		_result[8] = +(xx*yy - xy*yx) * invDet;
	}

	void mtxInverse(float* _result, const float* _a)
	{
		float xx = _a[ 0];
		float xy = _a[ 1];
		float xz = _a[ 2];
		float xw = _a[ 3];
		float yx = _a[ 4];
		float yy = _a[ 5];
		float yz = _a[ 6];
		float yw = _a[ 7];
		float zx = _a[ 8];
		float zy = _a[ 9];
		float zz = _a[10];
		float zw = _a[11];
		float wx = _a[12];
		float wy = _a[13];
		float wz = _a[14];
		float ww = _a[15];

		float det = 0.0f;
		det += xx * (yy*(zz*ww - zw*wz) - yz*(zy*ww - zw*wy) + yw*(zy*wz - zz*wy) );
		det -= xy * (yx*(zz*ww - zw*wz) - yz*(zx*ww - zw*wx) + yw*(zx*wz - zz*wx) );
		det += xz * (yx*(zy*ww - zw*wy) - yy*(zx*ww - zw*wx) + yw*(zx*wy - zy*wx) );
		det -= xw * (yx*(zy*wz - zz*wy) - yy*(zx*wz - zz*wx) + yz*(zx*wy - zy*wx) );

		float invDet = 1.0f/det;

		_result[ 0] = +(yy*(zz*ww - wz*zw) - yz*(zy*ww - wy*zw) + yw*(zy*wz - wy*zz) ) * invDet;
		_result[ 1] = -(xy*(zz*ww - wz*zw) - xz*(zy*ww - wy*zw) + xw*(zy*wz - wy*zz) ) * invDet;
		_result[ 2] = +(xy*(yz*ww - wz*yw) - xz*(yy*ww - wy*yw) + xw*(yy*wz - wy*yz) ) * invDet;
		_result[ 3] = -(xy*(yz*zw - zz*yw) - xz*(yy*zw - zy*yw) + xw*(yy*zz - zy*yz) ) * invDet;

		_result[ 4] = -(yx*(zz*ww - wz*zw) - yz*(zx*ww - wx*zw) + yw*(zx*wz - wx*zz) ) * invDet;
		_result[ 5] = +(xx*(zz*ww - wz*zw) - xz*(zx*ww - wx*zw) + xw*(zx*wz - wx*zz) ) * invDet;
		_result[ 6] = -(xx*(yz*ww - wz*yw) - xz*(yx*ww - wx*yw) + xw*(yx*wz - wx*yz) ) * invDet;
		_result[ 7] = +(xx*(yz*zw - zz*yw) - xz*(yx*zw - zx*yw) + xw*(yx*zz - zx*yz) ) * invDet;

		_result[ 8] = +(yx*(zy*ww - wy*zw) - yy*(zx*ww - wx*zw) + yw*(zx*wy - wx*zy) ) * invDet;
		_result[ 9] = -(xx*(zy*ww - wy*zw) - xy*(zx*ww - wx*zw) + xw*(zx*wy - wx*zy) ) * invDet;
		_result[10] = +(xx*(yy*ww - wy*yw) - xy*(yx*ww - wx*yw) + xw*(yx*wy - wx*yy) ) * invDet;
		_result[11] = -(xx*(yy*zw - zy*yw) - xy*(yx*zw - zx*yw) + xw*(yx*zy - zx*yy) ) * invDet;

		_result[12] = -(yx*(zy*wz - wy*zz) - yy*(zx*wz - wx*zz) + yz*(zx*wy - wx*zy) ) * invDet;
		_result[13] = +(xx*(zy*wz - wy*zz) - xy*(zx*wz - wx*zz) + xz*(zx*wy - wx*zy) ) * invDet;
		_result[14] = -(xx*(yy*wz - wy*yz) - xy*(yx*wz - wx*yz) + xz*(yx*wy - wx*yy) ) * invDet;
		_result[15] = +(xx*(yy*zz - zy*yz) - xy*(yx*zz - zx*yz) + xz*(yx*zy - zx*yy) ) * invDet;
	}

	void calcLinearFit2D(float _result[2], const void* _points, uint32_t _stride, uint32_t _numPoints)
	{
		float sumX = 0.0f;
		float sumY = 0.0f;
		float sumXX = 0.0f;
		float sumXY = 0.0f;

		const uint8_t* ptr = (const uint8_t*)_points;
		for (uint32_t ii = 0; ii < _numPoints; ++ii, ptr += _stride)
		{
			const float* point = (const float*)ptr;
			float xx = point[0];
			float yy = point[1];
			sumX += xx;
			sumY += yy;
			sumXX += xx*xx;
			sumXY += xx*yy;
		}

		// [ sum(x^2) sum(x) ] [ A ] = [ sum(x*y) ]
		// [ sum(x) numPoints ] [ B ] [ sum(y) ]

		float det = (sumXX*_numPoints - sumX*sumX);
		float invDet = 1.0f/det;

		_result[0] = (-sumX * sumY + _numPoints * sumXY) * invDet;
		_result[1] = (sumXX * sumY - sumX * sumXY) * invDet;
	}

	void calcLinearFit3D(float _result[3], const void* _points, uint32_t _stride, uint32_t _numPoints)
	{
		float sumX = 0.0f;
		float sumY = 0.0f;
		float sumZ = 0.0f;
		float sumXX = 0.0f;
		float sumXY = 0.0f;
		float sumXZ = 0.0f;
		float sumYY = 0.0f;
		float sumYZ = 0.0f;

		const uint8_t* ptr = (const uint8_t*)_points;
		for (uint32_t ii = 0; ii < _numPoints; ++ii, ptr += _stride)
		{
			const float* point = (const float*)ptr;
			float xx = point[0];
			float yy = point[1];
			float zz = point[2];

			sumX += xx;
			sumY += yy;
			sumZ += zz;
			sumXX += xx*xx;
			sumXY += xx*yy;
			sumXZ += xx*zz;
			sumYY += yy*yy;
			sumYZ += yy*zz;
		}

		// [ sum(x^2) sum(x*y) sum(x) ] [ A ] [ sum(x*z) ]
		// [ sum(x*y) sum(y^2) sum(y) ] [ B ] = [ sum(y*z) ]
		// [ sum(x) sum(y) numPoints ] [ C ] [ sum(z) ]

		float mtx[9] =
		{
			sumXX, sumXY, sumX,
			sumXY, sumYY, sumY,
			sumX, sumY, float(_numPoints),
		};
		float invMtx[9];
		mtx3Inverse(invMtx, mtx);

		_result[0] = invMtx[0]*sumXZ + invMtx[1]*sumYZ + invMtx[2]*sumZ;
		_result[1] = invMtx[3]*sumXZ + invMtx[4]*sumYZ + invMtx[5]*sumZ;
		_result[2] = invMtx[6]*sumXZ + invMtx[7]*sumYZ + invMtx[8]*sumZ;
	}

	void rgbToHsv(float _hsv[3], const float _rgb[3])
	{
		const float rr = _rgb[0];
		const float gg = _rgb[1];
		const float bb = _rgb[2];

		const float s0 = step(bb, gg);

		const float px = lerp(bb, gg, s0);
		const float py = lerp(gg, bb, s0);
		const float pz = lerp(-1.0f, 0.0f, s0);
		const float pw = lerp(2.0f/3.0f, -1.0f/3.0f, s0);

		const float s1 = step(px, rr);

		const float qx = lerp(px, rr, s1);
		const float qy = py;
		const float qz = lerp(pw, pz, s1);
		const float qw = lerp(rr, px, s1);

		const float dd = qx - min(qw, qy);
		const float ee = 1.0e-10f;

		_hsv[0] = abs(qz + (qw - qy) / (6.0f * dd + ee) );
		_hsv[1] = dd / (qx + ee);
		_hsv[2] = qx;
	}

	void hsvToRgb(float _rgb[3], const float _hsv[3])
	{
		const float hh = _hsv[0];
		const float ss = _hsv[1];
		const float vv = _hsv[2];

		const float px = abs(fract(hh + 1.0f ) * 6.0f - 3.0f);
		const float py = abs(fract(hh + 2.0f/3.0f) * 6.0f - 3.0f);
		const float pz = abs(fract(hh + 1.0f/3.0f) * 6.0f - 3.0f);

		_rgb[0] = vv * lerp(1.0f, clamp(px - 1.0f, 0.0f, 1.0f), ss);
		_rgb[1] = vv * lerp(1.0f, clamp(py - 1.0f, 0.0f, 1.0f), ss);
		_rgb[2] = vv * lerp(1.0f, clamp(pz - 1.0f, 0.0f, 1.0f), ss);
	}

} // namespace bx