/*
 * Copyright 2011-2023 Branimir Karadzic. All rights reserved.
 * License: https://github.com/bkaradzic/bx/blob/master/LICENSE
 */

// FPU math lib

#ifndef BX_MATH_H_HEADER_GUARD
#	error "Must be included from bx/math.h!"
#endif // BX_MATH_H_HEADER_GUARD

#include <bx/simd_t.h>
#include <bx/uint32_t.h>

namespace bx
{
	inline BX_CONSTEXPR_FUNC float toRad(float _deg)
	{
		return _deg * kPi / 180.0f;
	}

	inline BX_CONSTEXPR_FUNC float toDeg(float _rad)
	{
		return _rad * 180.0f / kPi;
	}

	inline BX_CONST_FUNC uint32_t floatToBits(float _a)
	{
		union { float f; uint32_t ui; } u = { _a };
		return u.ui;
	}

	inline BX_CONST_FUNC float bitsToFloat(uint32_t _a)
	{
		union { uint32_t ui; float f; } u = { _a };
		return u.f;
	}

	inline BX_CONST_FUNC uint64_t doubleToBits(double _a)
	{
		union { double f; uint64_t ui; } u = { _a };
		return u.ui;
	}

	inline BX_CONST_FUNC double bitsToDouble(uint64_t _a)
	{
		union { uint64_t ui; double f; } u = { _a };
		return u.f;
	}

	inline BX_CONST_FUNC uint32_t floatFlip(uint32_t _value)
	{
		// Reference(s):
		// - http://archive.fo/2012.12.08-212402/http://stereopsis.com/radix.html
		//
		const uint32_t tmp0   = uint32_sra(_value, 31);
		const uint32_t tmp1   = uint32_neg(tmp0);
		const uint32_t mask   = uint32_or(tmp1, kFloatSignMask);
		const uint32_t result = uint32_xor(_value, mask);
		return result;
	}

	inline BX_CONST_FUNC bool isNan(float _f)
	{
		const uint32_t tmp = floatToBits(_f) & INT32_MAX;
		return tmp > kFloatExponentMask;
	}

	inline BX_CONST_FUNC bool isNan(double _f)
	{
		const uint64_t tmp = doubleToBits(_f) & INT64_MAX;
		return tmp > kDoubleExponentMask;
	}

	inline BX_CONST_FUNC bool isFinite(float _f)
	{
		const uint32_t tmp = floatToBits(_f) & INT32_MAX;
		return tmp < kFloatExponentMask;
	}

	inline BX_CONST_FUNC bool isFinite(double _f)
	{
		const uint64_t tmp = doubleToBits(_f) & INT64_MAX;
		return tmp < kDoubleExponentMask;
	}

	inline BX_CONST_FUNC bool isInfinite(float _f)
	{
		const uint32_t tmp = floatToBits(_f) & INT32_MAX;
		return tmp == kFloatExponentMask;
	}

	inline BX_CONST_FUNC bool isInfinite(double _f)
	{
		const uint64_t tmp = doubleToBits(_f) & INT64_MAX;
		return tmp == kDoubleExponentMask;
	}

	inline BX_CONSTEXPR_FUNC float floor(float _a)
	{
		if (_a < 0.0f)
		{
			const float fr = fract(-_a);
			const float tr = trunc(-_a);

			return -tr - float(0.0f != fr);
		}

		return _a - fract(_a);
	}

	inline BX_CONSTEXPR_FUNC float ceil(float _a)
	{
		return -floor(-_a);
	}

	inline BX_CONSTEXPR_FUNC float round(float _f)
	{
		return floor(_f + 0.5f);
	}

	inline BX_CONSTEXPR_FUNC float lerp(float _a, float _b, float _t)
	{
		// Reference(s):
		// - Linear interpolation past, present and future
		//   https://web.archive.org/web/20200404165201/https://fgiesen.wordpress.com/2012/08/15/linear-interpolation-past-present-and-future/
		//
		return mad(_t, _b, nms(_t, _a, _a) );
	}

	inline BX_CONSTEXPR_FUNC float invLerp(float _a, float _b, float _value)
	{
		return (_value - _a) / (_b - _a);
	}

	inline BX_CONSTEXPR_FUNC float sign(float _a)
	{
		return float( (0.0f < _a) - (0.0f > _a) );
	}

	inline BX_CONSTEXPR_FUNC bool signbit(float _a)
	{
		return -0.0f == _a ? 0.0f != _a : 0.0f > _a;
	}

	inline BX_CONSTEXPR_FUNC float copysign(float _value, float _sign)
	{
#if BX_COMPILER_MSVC
		return signbit(_value) != signbit(_sign) ? -_value : _value;
#else
		return __builtin_copysign(_value, _sign);
#endif // BX_COMPILER_MSVC
	}

	inline BX_CONSTEXPR_FUNC float abs(float _a)
	{
		return _a < 0.0f ? -_a : _a;
	}

	inline BX_CONSTEXPR_FUNC float square(float _a)
	{
		return _a * _a;
	}

	inline BX_CONST_FUNC float sin(float _a)
	{
		return cos(_a - kPiHalf);
	}

	inline BX_CONST_FUNC float sinh(float _a)
	{
		return 0.5f*(exp(_a) - exp(-_a) );
	}

	inline BX_CONST_FUNC float asin(float _a)
	{
		return kPiHalf - acos(_a);
	}

	inline BX_CONST_FUNC float cosh(float _a)
	{
		return 0.5f*(exp(_a) + exp(-_a) );
	}

	inline BX_CONST_FUNC float tan(float _a)
	{
		return sin(_a) / cos(_a);
	}

	inline BX_CONST_FUNC float tanh(float _a)
	{
		const float tmp0   = exp(2.0f*_a);
		const float tmp1   = tmp0 - 1.0f;
		const float tmp2   = tmp0 + 1.0f;
		const float result = tmp1 / tmp2;

		return result;
	}

	inline BX_CONST_FUNC float atan(float _a)
	{
		return atan2(_a, 1.0f);
	}

	inline BX_CONST_FUNC float pow(float _a, float _b)
	{
		return exp(_b * log(_a) );
	}

	inline BX_CONST_FUNC float exp2(float _a)
	{
		return pow(2.0f, _a);
	}

	template<>
	inline BX_CONST_FUNC float log2(float _a)
	{
		return log(_a) * kInvLogNat2;
	}

	template<>
	inline BX_CONST_FUNC int32_t log2(int32_t _a)
	{
		return 31 - uint32_cntlz(_a);
	}

	inline BX_CONST_FUNC float rsqrtRef(float _a)
	{
		if (_a < kNearZero)
		{
			return kFloatInfinity;
		}

		return pow(_a, -0.5f);
	}

	inline BX_CONST_FUNC float rsqrtSimd(float _a)
	{
		if (_a < kNearZero)
		{
			return kFloatInfinity;
		}

		const simd128_t aa = simd_splat(_a);
#if BX_SIMD_NEON
		const simd128_t rsqrta = simd_rsqrt_nr(aa);
#else
		const simd128_t rsqrta = simd_rsqrt_ni(aa);
#endif // BX_SIMD_NEON

		float result;
		simd_stx(&result, rsqrta);

		return result;
	}

	inline BX_CONST_FUNC float sqrtRef(float _a)
	{
		if (_a < 0.0F)
		{
			return bitsToFloat(kFloatExponentMask | kFloatMantissaMask);
		}

		return _a * pow(_a, -0.5f);
	}

	inline BX_CONST_FUNC float sqrtSimd(float _a)
	{
		if (_a < 0.0F)
		{
			return bitsToFloat(kFloatExponentMask | kFloatMantissaMask);
		}
		else if (_a < kNearZero)
		{
			return 0.0f;
		}

		const simd128_t aa   = simd_splat(_a);
		const simd128_t sqrt = simd_sqrt(aa);

		float result;
		simd_stx(&result, sqrt);

		return result;
	}

	inline BX_CONST_FUNC float rsqrt(float _a)
	{
#if BX_CONFIG_SUPPORTS_SIMD
		return rsqrtSimd(_a);
#else
		return rsqrtRef(_a);
#endif // BX_CONFIG_SUPPORTS_SIMD
	}

	inline BX_CONST_FUNC float sqrt(float _a)
	{
#if BX_CONFIG_SUPPORTS_SIMD
		return sqrtSimd(_a);
#else
		return sqrtRef(_a);
#endif // BX_CONFIG_SUPPORTS_SIMD
	}

	inline BX_CONSTEXPR_FUNC float trunc(float _a)
	{
		return float(int(_a) );
	}

	inline BX_CONSTEXPR_FUNC float fract(float _a)
	{
		return _a - trunc(_a);
	}

	inline BX_CONSTEXPR_FUNC float nms(float _a, float _b, float _c)
	{
		return _c - _a * _b;
	}

	inline BX_CONSTEXPR_FUNC float add(float _a, float _b)
	{
		return _a + _b;
	}

	inline BX_CONSTEXPR_FUNC float sub(float _a, float _b)
	{
		return _a - _b;
	}

	inline BX_CONSTEXPR_FUNC float mul(float _a, float _b)
	{
		return _a * _b;
	}

	inline BX_CONSTEXPR_FUNC float mad(float _a, float _b, float _c)
	{
		return add(mul(_a, _b), _c);
	}

	inline BX_CONSTEXPR_FUNC float rcp(float _a)
	{
		return 1.0f / _a;
	}

	inline BX_CONSTEXPR_FUNC float mod(float _a, float _b)
	{
		return _a - _b * floor(_a / _b);
	}

	inline BX_CONSTEXPR_FUNC bool isEqual(float _a, float _b, float _epsilon)
	{
		// Reference(s):
		// - Floating-point tolerances revisited
		//   https://web.archive.org/web/20181103180318/http://realtimecollisiondetection.net/blog/?p=89
		//
		const float lhs = abs(_a - _b);
		const float rhs = _epsilon * max(1.0f, abs(_a), abs(_b) );
		return lhs <= rhs;
	}

	inline BX_CONST_FUNC bool isEqual(const float* _a, const float* _b, uint32_t _num, float _epsilon)
	{
		bool result = isEqual(_a[0], _b[0], _epsilon);
		for (uint32_t ii = 1; result && ii < _num; ++ii)
		{
			result = isEqual(_a[ii], _b[ii], _epsilon);
		}
		return result;
	}

	inline BX_CONSTEXPR_FUNC float wrap(float _a, float _wrap)
	{
		const float tmp0   = mod(_a, _wrap);
		const float result = tmp0 < 0.0f ? _wrap + tmp0 : tmp0;
		return result;
	}

	inline BX_CONSTEXPR_FUNC float step(float _edge, float _a)
	{
		return _a < _edge ? 0.0f : 1.0f;
	}

	inline BX_CONSTEXPR_FUNC float pulse(float _a, float _start, float _end)
	{
		return step(_a, _start) - step(_a, _end);
	}

	inline BX_CONSTEXPR_FUNC float smoothStep(float _a)
	{
		return square(_a)*(3.0f - 2.0f*_a);
	}

	inline BX_CONST_FUNC float invSmoothStep(float _a)
	{
		return 0.5f - sin(asin(1.0f - 2.0f * _a) / 3.0f);
	}

	inline BX_CONSTEXPR_FUNC float bias(float _time, float _bias)
	{
		return _time / ( ( (1.0f/_bias - 2.0f)*(1.0f - _time) ) + 1.0f);
	}

	inline BX_CONSTEXPR_FUNC float gain(float _time, float _gain)
	{
		// Reference(s):
		// - Bias And Gain Are Your Friend
		//   https://web.archive.org/web/20181126040535/https://blog.demofox.org/2012/09/24/bias-and-gain-are-your-friend/
		//   https://web.archive.org/web/20181126040558/http://demofox.org/biasgain.html
		//
		if (_time < 0.5f)
		{
			return bias(_time * 2.0f, _gain) * 0.5f;
		}

		return bias(_time * 2.0f - 1.0f, 1.0f - _gain) * 0.5f + 0.5f;
	}

	inline BX_CONSTEXPR_FUNC float angleDiff(float _a, float _b)
	{
		const float dist = wrap(_b - _a, kPi2);
		return wrap(dist*2.0f, kPi2) - dist;
	}

	inline BX_CONSTEXPR_FUNC float angleLerp(float _a, float _b, float _t)
	{
		return _a + angleDiff(_a, _b) * _t;
	}

	template<typename Ty>
	inline Ty load(const void* _ptr)
	{
		Ty result(InitNone);
		memCopy(&result, _ptr, sizeof(Ty) );
		return result;
	}

	template<typename Ty>
	inline void store(void* _ptr, const Ty& _a)
	{
		memCopy(_ptr, &_a, sizeof(Ty) );
	}

	inline Vec3::Vec3(InitNoneTag)
	{
	}

	constexpr Vec3::Vec3(InitZeroTag)
		: x(0.0f)
		, y(0.0f)
		, z(0.0f)
	{
	}

	constexpr Vec3::Vec3(InitIdentityTag)
		: x(0.0f)
		, y(0.0f)
		, z(0.0f)
	{
	}

	constexpr Vec3::Vec3(float _v)
		: x(_v)
		, y(_v)
		, z(_v)
	{
	}

	constexpr Vec3::Vec3(float _x, float _y, float _z)
		: x(_x)
		, y(_y)
		, z(_z)
	{
	}

	inline Plane::Plane(InitNoneTag)
		: normal(InitNone)
	{
	}

	constexpr Plane::Plane(InitZeroTag)
		: normal(InitZero)
		, dist(0.0f)
	{
	}

	constexpr Plane::Plane(InitIdentityTag)
		: normal(0.0f, 1.0f, 0.0f)
		, dist(0.0f)
	{
	}

	constexpr Plane::Plane(Vec3 _normal, float _dist)
		: normal(_normal)
		, dist(_dist)
	{
	}

	inline Quaternion::Quaternion(InitNoneTag)
	{
	}

	constexpr Quaternion::Quaternion(InitZeroTag)
		: x(0.0f)
		, y(0.0f)
		, z(0.0f)
		, w(0.0f)
	{
	}

	constexpr Quaternion::Quaternion(InitIdentityTag)
		: x(0.0f)
		, y(0.0f)
		, z(0.0f)
		, w(1.0f)
	{
	}

	constexpr Quaternion::Quaternion(float _x, float _y, float _z, float _w)
		: x(_x)
		, y(_y)
		, z(_z)
		, w(_w)
	{
	}

	inline BX_CONSTEXPR_FUNC Vec3 round(const Vec3 _a)
	{
		return
		{
			round(_a.x),
			round(_a.y),
			round(_a.z),
		};
	}

	inline BX_CONSTEXPR_FUNC Vec3 abs(const Vec3 _a)
	{
		return
		{
			abs(_a.x),
			abs(_a.y),
			abs(_a.z),
		};
	}

	inline BX_CONSTEXPR_FUNC Vec3 neg(const Vec3 _a)
	{
		return
		{
			-_a.x,
			-_a.y,
			-_a.z,
		};
	}

	inline BX_CONSTEXPR_FUNC Vec3 add(const Vec3 _a, const Vec3 _b)
	{
		return
		{
			_a.x + _b.x,
			_a.y + _b.y,
			_a.z + _b.z,
		};
	}

	inline BX_CONSTEXPR_FUNC Vec3 add(const Vec3 _a, float _b)
	{
		return
		{
			_a.x + _b,
			_a.y + _b,
			_a.z + _b,
		};
	}

	inline BX_CONSTEXPR_FUNC Vec3 sub(const Vec3 _a, const Vec3 _b)
	{
		return
		{
			_a.x - _b.x,
			_a.y - _b.y,
			_a.z - _b.z,
		};
	}

	inline BX_CONSTEXPR_FUNC Vec3 sub(const Vec3 _a, float _b)
	{
		return
		{
			_a.x - _b,
			_a.y - _b,
			_a.z - _b,
		};
	}

	inline BX_CONSTEXPR_FUNC Vec3 mul(const Vec3 _a, const Vec3 _b)
	{
		return
		{
			_a.x * _b.x,
			_a.y * _b.y,
			_a.z * _b.z,
		};
	}

	inline BX_CONSTEXPR_FUNC Vec3 mul(const Vec3 _a, float _b)
	{
		return
		{
			_a.x * _b,
			_a.y * _b,
			_a.z * _b,
		};
	}

	inline BX_CONSTEXPR_FUNC Vec3 div(const Vec3 _a, const Vec3 _b)
	{
		return mul(_a, rcp(_b) );
	}

	inline BX_CONSTEXPR_FUNC Vec3 div(const Vec3 _a, float _b)
	{
		return mul(_a, rcp(_b) );
	}

	inline BX_CONSTEXPR_FUNC Vec3 nms(const Vec3 _a, const float _b, const Vec3 _c)
	{
		return sub(_c, mul(_a, _b) );
	}

	inline BX_CONSTEXPR_FUNC Vec3 nms(const Vec3 _a, const Vec3 _b, const Vec3 _c)
	{
		return sub(_c, mul(_a, _b) );
	}

	inline BX_CONSTEXPR_FUNC Vec3 mad(const Vec3 _a, const float _b, const Vec3 _c)
	{
		return add(mul(_a, _b), _c);
	}

	inline BX_CONSTEXPR_FUNC Vec3 mad(const Vec3 _a, const Vec3 _b, const Vec3 _c)
	{
		return add(mul(_a, _b), _c);
	}

	inline BX_CONSTEXPR_FUNC float dot(const Vec3 _a, const Vec3 _b)
	{
		return _a.x*_b.x + _a.y*_b.y + _a.z*_b.z;
	}

	inline BX_CONSTEXPR_FUNC Vec3 cross(const Vec3 _a, const Vec3 _b)
	{
		return
		{
			_a.y*_b.z - _a.z*_b.y,
			_a.z*_b.x - _a.x*_b.z,
			_a.x*_b.y - _a.y*_b.x,
		};
	}

	inline BX_CONST_FUNC float length(const Vec3 _a)
	{
		return sqrt(dot(_a, _a) );
	}

	inline BX_CONST_FUNC float distanceSq(const Vec3 _a, const Vec3 _b)
	{
		const Vec3 ba = sub(_b, _a);
		return dot(ba, ba);
	}

	inline BX_CONST_FUNC float distance(const Vec3 _a, const Vec3 _b)
	{
		return length(sub(_b, _a) );
	}

	inline BX_CONSTEXPR_FUNC Vec3 lerp(const Vec3 _a, const Vec3 _b, float _t)
	{
		return
		{
			lerp(_a.x, _b.x, _t),
			lerp(_a.y, _b.y, _t),
			lerp(_a.z, _b.z, _t),
		};
	}

	inline BX_CONSTEXPR_FUNC Vec3 lerp(const Vec3 _a, const Vec3 _b, const Vec3 _t)
	{
		return
		{
			lerp(_a.x, _b.x, _t.x),
			lerp(_a.y, _b.y, _t.y),
			lerp(_a.z, _b.z, _t.z),
		};
	}

	inline BX_CONST_FUNC Vec3 normalize(const Vec3 _a)
	{
		const float invLen = 1.0f/length(_a);
		const Vec3 result = mul(_a, invLen);
		return result;
	}

	inline BX_CONSTEXPR_FUNC Vec3 min(const Vec3 _a, const Vec3 _b)
	{
		return
		{
			min(_a.x, _b.x),
			min(_a.y, _b.y),
			min(_a.z, _b.z),
		};
	}

	inline BX_CONSTEXPR_FUNC Vec3 max(const Vec3 _a, const Vec3 _b)
	{
		return
		{
			max(_a.x, _b.x),
			max(_a.y, _b.y),
			max(_a.z, _b.z),
		};
	}

	inline BX_CONSTEXPR_FUNC Vec3 rcp(const Vec3 _a)
	{
		return
		{
			1.0f / _a.x,
			1.0f / _a.y,
			1.0f / _a.z,
		};
	}

	inline BX_CONSTEXPR_FUNC bool isEqual(const Vec3 _a, const Vec3 _b, float _epsilon)
	{
		return isEqual(_a.x, _b.x, _epsilon)
			&& isEqual(_a.y, _b.y, _epsilon)
			&& isEqual(_a.z, _b.z, _epsilon)
			;
	}

	inline void calcTangentFrame(Vec3& _outT, Vec3& _outB, const Vec3 _n)
	{
		const float nx = _n.x;
		const float ny = _n.y;
		const float nz = _n.z;

		if (abs(nx) > abs(nz) )
		{
			float invLen = 1.0f / sqrt(nx*nx + nz*nz);
			_outT.x = -nz * invLen;
			_outT.y =  0.0f;
			_outT.z =  nx * invLen;
		}
		else
		{
			float invLen = 1.0f / sqrt(ny*ny + nz*nz);
			_outT.x =  0.0f;
			_outT.y =  nz * invLen;
			_outT.z = -ny * invLen;
		}

		_outB = cross(_n, _outT);
	}

	inline void calcTangentFrame(Vec3& _outT, Vec3& _outB, const Vec3 _n, float _angle)
	{
		calcTangentFrame(_outT, _outB, _n);

		const float sa = sin(_angle);
		const float ca = cos(_angle);

		_outT.x = -sa * _outB.x + ca * _outT.x;
		_outT.y = -sa * _outB.y + ca * _outT.y;
		_outT.z = -sa * _outB.z + ca * _outT.z;

		_outB = cross(_n, _outT);
	}

	inline BX_CONST_FUNC Vec3 fromLatLong(float _u, float _v)
	{
		Vec3 result(InitNone);
		const float phi   = _u * kPi2;
		const float theta = _v * kPi;

		const float st = sin(theta);
		const float sp = sin(phi);
		const float ct = cos(theta);
		const float cp = cos(phi);

		result.x = -st*sp;
		result.y =  ct;
		result.z = -st*cp;
		return result;
	}

	inline void toLatLong(float* _outU, float* _outV, const Vec3 _dir)
	{
		const float phi   = atan2(_dir.x, _dir.z);
		const float theta = acos(_dir.y);

		*_outU = (kPi + phi)/kPi2;
		*_outV = theta*kInvPi;
	}

	inline BX_CONSTEXPR_FUNC Quaternion invert(const Quaternion _a)
	{
		return
		{
			-_a.x,
			-_a.y,
			-_a.z,
			 _a.w,
		};
	}

	inline BX_CONSTEXPR_FUNC Vec3 mulXyz(const Quaternion _a, const Quaternion _b)
	{
		const float ax = _a.x;
		const float ay = _a.y;
		const float az = _a.z;
		const float aw = _a.w;

		const float bx = _b.x;
		const float by = _b.y;
		const float bz = _b.z;
		const float bw = _b.w;

		return
		{
			aw * bx + ax * bw + ay * bz - az * by,
			aw * by - ax * bz + ay * bw + az * bx,
			aw * bz + ax * by - ay * bx + az * bw,
		};
	}

	inline BX_CONSTEXPR_FUNC Quaternion add(const Quaternion _a, const Quaternion _b)
	{
		return
		{
			_a.x + _b.x,
			_a.y + _b.y,
			_a.z + _b.z,
			_a.w + _b.w,
		};
	}

	inline BX_CONSTEXPR_FUNC Quaternion sub(const Quaternion _a, const Quaternion _b)
	{
		return
		{
			_a.x - _b.x,
			_a.y - _b.y,
			_a.z - _b.z,
			_a.w - _b.w,
		};
	}

	inline BX_CONSTEXPR_FUNC Quaternion mul(const Quaternion _a, float _b)
	{
		return
		{
			_a.x * _b,
			_a.y * _b,
			_a.z * _b,
			_a.w * _b,
		};
	}

	inline BX_CONSTEXPR_FUNC Quaternion mul(const Quaternion _a, const Quaternion _b)
	{
		const float ax = _a.x;
		const float ay = _a.y;
		const float az = _a.z;
		const float aw = _a.w;

		const float bx = _b.x;
		const float by = _b.y;
		const float bz = _b.z;
		const float bw = _b.w;

		return
		{
			aw * bx + ax * bw + ay * bz - az * by,
			aw * by - ax * bz + ay * bw + az * bx,
			aw * bz + ax * by - ay * bx + az * bw,
			aw * bw - ax * bx - ay * by - az * bz,
		};
	}

	inline BX_CONSTEXPR_FUNC Vec3 mul(const Vec3 _v, const Quaternion _q)
	{
		const Quaternion tmp0 = invert(_q);
		const Quaternion qv   = { _v.x, _v.y, _v.z, 0.0f };
		const Quaternion tmp1 = mul(tmp0, qv);
		const Vec3 result     = mulXyz(tmp1, _q);

		return result;
	}

	inline BX_CONSTEXPR_FUNC float dot(const Quaternion _a, const Quaternion _b)
	{
		return
			  _a.x * _b.x
			+ _a.y * _b.y
			+ _a.z * _b.z
			+ _a.w * _b.w
			;
	}

	inline BX_CONSTEXPR_FUNC Quaternion normalize(const Quaternion _a)
	{
		const float norm = dot(_a, _a);
		if (0.0f < norm)
		{
			const float invNorm = rsqrt(norm);

			return mul(_a, invNorm);
		}

		return
		{
			0.0f,
			0.0f,
			0.0f,
			1.0f,
		};
	}

	inline BX_CONSTEXPR_FUNC Quaternion lerp(const Quaternion _a, const Quaternion _b, float _t)
	{
		const float sa    = 1.0f - _t;
		const float adotb = dot(_a, _b);
		const float sb    = sign(adotb) * _t;

		const Quaternion aa = mul(_a, sa);
		const Quaternion bb = mul(_b, sb);
		const Quaternion qq = add(aa, bb);

		return normalize(qq);
	}

	inline BX_CONST_FUNC Quaternion fromEuler(const Vec3 _euler)
	{
		const float sx = sin(_euler.x * 0.5f);
		const float cx = cos(_euler.x * 0.5f);
		const float sy = sin(_euler.y * 0.5f);
		const float cy = cos(_euler.y * 0.5f);
		const float sz = sin(_euler.z * 0.5f);
		const float cz = cos(_euler.z * 0.5f);

		return
		{
			sx * cy * cz - cx * sy * sz,
			cx * sy * cz + sx * cy * sz,
			cx * cy * sz - sx * sy * cz,
			cx * cy * cz + sx * sy * sz,
		};
	}

	inline BX_CONST_FUNC Vec3 toEuler(const Quaternion _a)
	{
		const float xx  = _a.x;
		const float yy  = _a.y;
		const float zz  = _a.z;
		const float ww  = _a.w;
		const float xsq = square(xx);
		const float ysq = square(yy);
		const float zsq = square(zz);

		return
		{
			atan2(2.0f * (xx * ww - yy * zz), 1.0f - 2.0f * (xsq + zsq) ),
			atan2(2.0f * (yy * ww + xx * zz), 1.0f - 2.0f * (ysq + zsq) ),
			asin( 2.0f * (xx * yy + zz * ww) ),
		};
	}

	inline BX_CONST_FUNC Vec3 toXAxis(const Quaternion _a)
	{
		const float xx  = _a.x;
		const float yy  = _a.y;
		const float zz  = _a.z;
		const float ww  = _a.w;
		const float ysq = square(yy);
		const float zsq = square(zz);

		return
		{
			1.0f - 2.0f * ysq     - 2.0f * zsq,
			       2.0f * xx * yy + 2.0f * zz * ww,
			       2.0f * xx * zz - 2.0f * yy * ww,
		};
	}

	inline BX_CONST_FUNC Vec3 toYAxis(const Quaternion _a)
	{
		const float xx  = _a.x;
		const float yy  = _a.y;
		const float zz  = _a.z;
		const float ww  = _a.w;
		const float xsq = square(xx);
		const float zsq = square(zz);

		return
		{
			       2.0f * xx * yy - 2.0f * zz * ww,
			1.0f - 2.0f * xsq     - 2.0f * zsq,
			       2.0f * yy * zz + 2.0f * xx * ww,
		};
	}

	inline BX_CONST_FUNC Vec3 toZAxis(const Quaternion _a)
	{
		const float xx  = _a.x;
		const float yy  = _a.y;
		const float zz  = _a.z;
		const float ww  = _a.w;
		const float xsq = square(xx);
		const float ysq = square(yy);

		return
		{
			       2.0f * xx * zz + 2.0f * yy * ww,
			       2.0f * yy * zz - 2.0f * xx * ww,
			1.0f - 2.0f * xsq     - 2.0f * ysq,
		};
	}

	inline BX_CONST_FUNC Quaternion fromAxisAngle(const Vec3 _axis, float _angle)
	{
		const float ha = _angle * 0.5f;
		const float sa = sin(ha);

		return
		{
			_axis.x * sa,
			_axis.y * sa,
			_axis.z * sa,
			cos(ha),
		};
	}

	inline void toAxisAngle(Vec3& _outAxis, float& _outAngle, const Quaternion _a)
	{
		const float ww = _a.w;
		const float sa = sqrt(1.0f - square(ww) );

		_outAngle = 2.0f * acos(ww);

		if (0.001f > sa)
		{
			_outAxis = { _a.x, _a.y, _a.z };
			return;
		}

		const float invSa = 1.0f/sa;

		_outAxis = { _a.x * invSa, _a.y * invSa, _a.z * invSa };
	}

	inline BX_CONST_FUNC Quaternion rotateX(float _ax)
	{
		const float hx = _ax * 0.5f;

		return
		{
			sin(hx),
			0.0f,
			0.0f,
			cos(hx),
		};
	}

	inline BX_CONST_FUNC Quaternion rotateY(float _ay)
	{
		const float hy = _ay * 0.5f;

		return
		{
			0.0f,
			sin(hy),
			0.0f,
			cos(hy),
		};
	}

	inline BX_CONST_FUNC Quaternion rotateZ(float _az)
	{
		const float hz = _az * 0.5f;

		return
		{
			0.0f,
			0.0f,
			sin(hz),
			cos(hz),
		};
	}

	inline BX_CONSTEXPR_FUNC bool isEqual(const Quaternion _a, const Quaternion _b, float _epsilon)
	{
		return isEqual(_a.x, _b.x, _epsilon)
			&& isEqual(_a.y, _b.y, _epsilon)
			&& isEqual(_a.z, _b.z, _epsilon)
			&& isEqual(_a.w, _b.w, _epsilon)
			;
	}

	inline void mtxIdentity(float* _result)
	{
		memSet(_result, 0, sizeof(float)*16);
		_result[0] = _result[5] = _result[10] = _result[15] = 1.0f;
	}

	inline void mtxTranslate(float* _result, float _tx, float _ty, float _tz)
	{
		mtxIdentity(_result);
		_result[12] = _tx;
		_result[13] = _ty;
		_result[14] = _tz;
	}

	inline void mtxScale(float* _result, float _sx, float _sy, float _sz)
	{
		memSet(_result, 0, sizeof(float) * 16);
		_result[0]  = _sx;
		_result[5]  = _sy;
		_result[10] = _sz;
		_result[15] = 1.0f;
	}

	inline void mtxScale(float* _result, float _scale)
	{
		mtxScale(_result, _scale, _scale, _scale);
	}

	inline void mtxFromNormal(float* _result, const Vec3& _normal, float _scale, const Vec3& _pos)
	{
		Vec3 tangent(InitNone);
		Vec3 bitangent(InitNone);
		calcTangentFrame(tangent, bitangent, _normal);

		store(&_result[ 0], mul(bitangent, _scale) );
		store(&_result[ 4], mul(_normal,   _scale) );
		store(&_result[ 8], mul(tangent,   _scale) );

		_result[ 3] = 0.0f;
		_result[ 7] = 0.0f;
		_result[11] = 0.0f;
		_result[12] = _pos.x;
		_result[13] = _pos.y;
		_result[14] = _pos.z;
		_result[15] = 1.0f;
	}

	inline void mtxFromNormal(float* _result, const Vec3& _normal, float _scale, const Vec3& _pos, float _angle)
	{
		Vec3 tangent(InitNone);
		Vec3 bitangent(InitNone);
		calcTangentFrame(tangent, bitangent, _normal, _angle);

		store(&_result[0], mul(bitangent, _scale) );
		store(&_result[4], mul(_normal,   _scale) );
		store(&_result[8], mul(tangent,   _scale) );

		_result[ 3] = 0.0f;
		_result[ 7] = 0.0f;
		_result[11] = 0.0f;
		_result[12] = _pos.x;
		_result[13] = _pos.y;
		_result[14] = _pos.z;
		_result[15] = 1.0f;
	}

	inline void mtxFromQuaternion(float* _result, const Quaternion& _rotation)
	{
		const float qx = _rotation.x;
		const float qy = _rotation.y;
		const float qz = _rotation.z;
		const float qw = _rotation.w;

		const float x2  = qx + qx;
		const float y2  = qy + qy;
		const float z2  = qz + qz;
		const float x2x = x2 * qx;
		const float x2y = x2 * qy;
		const float x2z = x2 * qz;
		const float x2w = x2 * qw;
		const float y2y = y2 * qy;
		const float y2z = y2 * qz;
		const float y2w = y2 * qw;
		const float z2z = z2 * qz;
		const float z2w = z2 * qw;

		_result[ 0] = 1.0f - (y2y + z2z);
		_result[ 1] =         x2y - z2w;
		_result[ 2] =         x2z + y2w;
		_result[ 3] = 0.0f;

		_result[ 4] =         x2y + z2w;
		_result[ 5] = 1.0f - (x2x + z2z);
		_result[ 6] =         y2z - x2w;
		_result[ 7] = 0.0f;

		_result[ 8] =         x2z - y2w;
		_result[ 9] =         y2z + x2w;
		_result[10] = 1.0f - (x2x + y2y);
		_result[11] = 0.0f;

		_result[12] = 0.0f;
		_result[13] = 0.0f;
		_result[14] = 0.0f;
		_result[15] = 1.0f;
	}

	inline void mtxFromQuaternion(float* _result, const Quaternion& _rotation, const Vec3& _translation)
	{
		mtxFromQuaternion(_result, _rotation);
		store(&_result[12], neg(mulXyz0(_translation, _result) ) );
	}

	inline Vec3 mul(const Vec3& _vec, const float* _mat)
	{
		Vec3 result(InitNone);
		result.x = _vec.x * _mat[0] + _vec.y * _mat[4] + _vec.z * _mat[ 8] + _mat[12];
		result.y = _vec.x * _mat[1] + _vec.y * _mat[5] + _vec.z * _mat[ 9] + _mat[13];
		result.z = _vec.x * _mat[2] + _vec.y * _mat[6] + _vec.z * _mat[10] + _mat[14];
		return result;
	}

	inline Vec3 mulXyz0(const Vec3& _vec, const float* _mat)
	{
		Vec3 result(InitNone);
		result.x = _vec.x * _mat[0] + _vec.y * _mat[4] + _vec.z * _mat[ 8];
		result.y = _vec.x * _mat[1] + _vec.y * _mat[5] + _vec.z * _mat[ 9];
		result.z = _vec.x * _mat[2] + _vec.y * _mat[6] + _vec.z * _mat[10];
		return result;
	}

	inline Vec3 mulH(const Vec3& _vec, const float* _mat)
	{
		const float xx   = _vec.x * _mat[0] + _vec.y * _mat[4] + _vec.z * _mat[ 8] + _mat[12];
		const float yy   = _vec.x * _mat[1] + _vec.y * _mat[5] + _vec.z * _mat[ 9] + _mat[13];
		const float zz   = _vec.x * _mat[2] + _vec.y * _mat[6] + _vec.z * _mat[10] + _mat[14];
		const float ww   = _vec.x * _mat[3] + _vec.y * _mat[7] + _vec.z * _mat[11] + _mat[15];
		const float invW = sign(ww) / ww;

		Vec3 result =
		{
			xx * invW,
			yy * invW,
			zz * invW,
		};

		return result;
	}

	inline void vec4MulMtx(float* _result, const float* _vec, const float* _mat)
	{
		_result[0] = _vec[0] * _mat[ 0] + _vec[1] * _mat[4] + _vec[2] * _mat[ 8] + _vec[3] * _mat[12];
		_result[1] = _vec[0] * _mat[ 1] + _vec[1] * _mat[5] + _vec[2] * _mat[ 9] + _vec[3] * _mat[13];
		_result[2] = _vec[0] * _mat[ 2] + _vec[1] * _mat[6] + _vec[2] * _mat[10] + _vec[3] * _mat[14];
		_result[3] = _vec[0] * _mat[ 3] + _vec[1] * _mat[7] + _vec[2] * _mat[11] + _vec[3] * _mat[15];
	}

	inline void mtxMul(float* _result, const float* _a, const float* _b)
	{
		vec4MulMtx(&_result[ 0], &_a[ 0], _b);
		vec4MulMtx(&_result[ 4], &_a[ 4], _b);
		vec4MulMtx(&_result[ 8], &_a[ 8], _b);
		vec4MulMtx(&_result[12], &_a[12], _b);
	}

	inline void mtxTranspose(float* _result, const float* _a)
	{
		_result[ 0] = _a[ 0];
		_result[ 4] = _a[ 1];
		_result[ 8] = _a[ 2];
		_result[12] = _a[ 3];
		_result[ 1] = _a[ 4];
		_result[ 5] = _a[ 5];
		_result[ 9] = _a[ 6];
		_result[13] = _a[ 7];
		_result[ 2] = _a[ 8];
		_result[ 6] = _a[ 9];
		_result[10] = _a[10];
		_result[14] = _a[11];
		_result[ 3] = _a[12];
		_result[ 7] = _a[13];
		_result[11] = _a[14];
		_result[15] = _a[15];
	}

	inline Vec3 calcNormal(const Vec3& _va, const Vec3& _vb, const Vec3& _vc)
	{
		const Vec3 ba    = sub(_vb, _va);
		const Vec3 ca    = sub(_vc, _va);
		const Vec3 baxca = cross(ba, ca);

		return normalize(baxca);
	}

	inline void calcPlane(Plane& _outPlane, const Vec3& _va, const Vec3& _vb, const Vec3& _vc)
	{
		Vec3 normal = calcNormal(_va, _vb, _vc);
		calcPlane(_outPlane, normal, _va);
	}

	inline void calcPlane(Plane& _outPlane, const Vec3& _normal, const Vec3& _pos)
	{
		_outPlane.normal = _normal;
		_outPlane.dist   = -dot(_normal, _pos);
	}

	inline BX_CONSTEXPR_FUNC float distance(const Plane& _plane, const Vec3& _pos)
	{
		return dot(_plane.normal, _pos) + _plane.dist;
	}

	inline BX_CONSTEXPR_FUNC bool isEqual(const Plane& _a, const Plane& _b, float _epsilon)
	{
		return isEqual(_a.normal, _b.normal, _epsilon)
			&& isEqual(_a.dist,   _b.dist,   _epsilon)
			;
	}

	inline BX_CONST_FUNC float toLinear(float _a)
	{
		const float lo     = _a / 12.92f;
		const float hi     = pow( (_a + 0.055f) / 1.055f, 2.4f);
		const float result = lerp(hi, lo, _a <= 0.04045f);
		return result;
	}

	inline BX_CONST_FUNC float toGamma(float _a)
	{
		const float lo     = _a * 12.92f;
		const float hi     = pow(abs(_a), 1.0f/2.4f) * 1.055f - 0.055f;
		const float result = lerp(hi, lo, _a <= 0.0031308f);
		return result;
	}

} // namespace bx
