PxUnixSse2InlineAoS.h

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// Copyright (c) 2008-2022 NVIDIA Corporation. All rights reserved.
// Copyright (c) 2004-2008 AGEIA Technologies, Inc. All rights reserved.
// Copyright (c) 2001-2004 NovodeX AG. All rights reserved.
 
#ifndef PXFOUNDATION_PXUNIXSSE2INLINEAOS_H
#define PXFOUNDATION_PXUNIXSSE2INLINEAOS_H
 
#if !COMPILE_VECTOR_INTRINSICS
#error Vector intrinsics should not be included when using scalar implementation.
#endif
 
#ifdef __SSE4_2__
#include "smmintrin.h"
#endif
 
#include "../../PxVecMathSSE.h"
 
namespace physx
{
namespace aos
{
 
#define PX_FPCLASS_SNAN 0x0001 /* signaling NaN */
#define PX_FPCLASS_QNAN 0x0002 /* quiet NaN */
#define PX_FPCLASS_NINF 0x0004 /* negative infinity */
#define PX_FPCLASS_PINF 0x0200 /* positive infinity */
 
PX_FORCE_INLINE __m128 m128_I2F(__m128i n)
{
    return _mm_castsi128_ps(n);
}
PX_FORCE_INLINE __m128i m128_F2I(__m128 n)
{
    return _mm_castps_si128(n);
}
 
//Test that Vec3V and FloatV are legal
 
#define FLOAT_COMPONENTS_EQUAL_THRESHOLD 0.01f
PX_FORCE_INLINE static bool isValidFloatV(const FloatV a)
{
    const PxF32 x = V4ReadX(a);
    const PxF32 y = V4ReadY(a);
    const PxF32 z = V4ReadZ(a);
    const PxF32 w = V4ReadW(a);
 
    return (x == y && x == z && x == w);
 
    /*if (
        (PxAbs(x - y) < FLOAT_COMPONENTS_EQUAL_THRESHOLD) &&
        (PxAbs(x - z) < FLOAT_COMPONENTS_EQUAL_THRESHOLD) &&
        (PxAbs(x - w) < FLOAT_COMPONENTS_EQUAL_THRESHOLD)
        )
    {
        return true;
    }
 
    if (
        (PxAbs((x - y) / x) < FLOAT_COMPONENTS_EQUAL_THRESHOLD) &&
        (PxAbs((x - z) / x) < FLOAT_COMPONENTS_EQUAL_THRESHOLD) &&
        (PxAbs((x - w) / x) < FLOAT_COMPONENTS_EQUAL_THRESHOLD)
        )
    {
        return true;
    }
 
    return false;*/
}
 
PX_FORCE_INLINE bool isValidVec3V(const Vec3V a)
{
    PX_ALIGN(16, PxF32 f[4]);
    V4StoreA(a, f);
    return (f[3] == 0.0f);
}
 
PX_FORCE_INLINE bool isFiniteLength(const Vec3V a)
{
    return !FAllEq(V4LengthSq(a), FZero());
}
 
PX_FORCE_INLINE bool isAligned16(void* a)
{
    return(0 == (size_t(a) & 0x0f));
}
 
//ASSERT_FINITELENGTH is deactivated because there is a lot of code that calls a simd normalisation function with zero length but then ignores the result.
 
#if PX_DEBUG
#define ASSERT_ISVALIDVEC3V(a) PX_ASSERT(isValidVec3V(a))
#define ASSERT_ISVALIDFLOATV(a) PX_ASSERT(isValidFloatV(a))
#define ASSERT_ISALIGNED16(a) PX_ASSERT(isAligned16(reinterpret_cast<void*>(a)))
#define ASSERT_ISFINITELENGTH(a) //PX_ASSERT(isFiniteLength(a))
#else
#define ASSERT_ISVALIDVEC3V(a)
#define ASSERT_ISVALIDFLOATV(a) 
#define ASSERT_ISALIGNED16(a)
#define ASSERT_ISFINITELENGTH(a)
#endif
 
 
namespace internalUnitSSE2Simd
{
PX_FORCE_INLINE PxU32 BAllTrue4_R(const BoolV a)
{
    const PxI32 moveMask = _mm_movemask_ps(a);
    return PxU32(moveMask == 0xf);
}
 
PX_FORCE_INLINE PxU32 BAllTrue3_R(const BoolV a)
{
    const PxI32 moveMask = _mm_movemask_ps(a);
    return PxU32((moveMask & 0x7) == 0x7);
}
 
PX_FORCE_INLINE PxU32 BAnyTrue4_R(const BoolV a)
{
    const PxI32 moveMask = _mm_movemask_ps(a);
    return PxU32(moveMask != 0x0);
}
 
PX_FORCE_INLINE PxU32 BAnyTrue3_R(const BoolV a)
{
    const PxI32 moveMask = _mm_movemask_ps(a);
    return PxU32((moveMask & 0x7) != 0x0);
}
 
PX_FORCE_INLINE PxU32 FiniteTestEq(const Vec4V a, const Vec4V b)
{
    // This is a bit of a bodge.
    //_mm_comieq_ss returns 1 if either value is nan so we need to re-cast a and b with true encoded as a non-nan
    // number.
    // There must be a better way of doing this in sse.
    const BoolV one = FOne();
    const BoolV zero = FZero();
    const BoolV a1 = V4Sel(a, one, zero);
    const BoolV b1 = V4Sel(b, one, zero);
    return (
        _mm_comieq_ss(a1, b1) &&
        _mm_comieq_ss(_mm_shuffle_ps(a1, a1, _MM_SHUFFLE(1, 1, 1, 1)), _mm_shuffle_ps(b1, b1, _MM_SHUFFLE(1, 1, 1, 1))) &&
        _mm_comieq_ss(_mm_shuffle_ps(a1, a1, _MM_SHUFFLE(2, 2, 2, 2)), _mm_shuffle_ps(b1, b1, _MM_SHUFFLE(2, 2, 2, 2))) &&
        _mm_comieq_ss(_mm_shuffle_ps(a1, a1, _MM_SHUFFLE(3, 3, 3, 3)), _mm_shuffle_ps(b1, b1, _MM_SHUFFLE(3, 3, 3, 3))));
}
 
#if !PX_EMSCRIPTEN
#if PX_CLANG
#if PX_LINUX
#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Wglobal-constructors"
#endif
#endif
const PX_ALIGN(16, PxF32 gMaskXYZ[4]) = { physx::PxUnionCast<PxF32>(0xffffffff), physx::PxUnionCast<PxF32>(0xffffffff),
                                          physx::PxUnionCast<PxF32>(0xffffffff), 0 };
#if PX_CLANG
#if PX_LINUX
#pragma clang diagnostic pop
#endif
#endif
#else
// emscripten doesn't like the PxUnionCast data structure
// the following is what windows and xbox does -- using these for emscripten
const PX_ALIGN(16, PxU32 gMaskXYZ[4]) = { 0xffffffff, 0xffffffff, 0xffffffff, 0 };
#endif
}
 
namespace vecMathTests
{
// PT: this function returns an invalid Vec3V (W!=0.0f) just for unit-testing 'isValidVec3V'
PX_FORCE_INLINE Vec3V getInvalidVec3V()
{
    const float f = 1.0f;
    return _mm_load1_ps(&f);
}
 
PX_FORCE_INLINE bool allElementsEqualFloatV(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    return _mm_comieq_ss(a, b) != 0;
}
 
PX_FORCE_INLINE bool allElementsEqualVec3V(const Vec3V a, const Vec3V b)
{
    return V3AllEq(a, b) != 0;
}
 
PX_FORCE_INLINE bool allElementsEqualVec4V(const Vec4V a, const Vec4V b)
{
    return V4AllEq(a, b) != 0;
}
 
PX_FORCE_INLINE bool allElementsEqualBoolV(const BoolV a, const BoolV b)
{
    return internalUnitSSE2Simd::BAllTrue4_R(VecI32V_IsEq(m128_F2I(a), m128_F2I(b))) != 0;
}
 
PX_FORCE_INLINE bool allElementsEqualVecU32V(const VecU32V a, const VecU32V b)
{
    return internalUnitSSE2Simd::BAllTrue4_R(V4IsEqU32(a, b)) != 0;
}
 
PX_FORCE_INLINE bool allElementsEqualVecI32V(const VecI32V a, const VecI32V b)
{
    BoolV c = m128_I2F(_mm_cmpeq_epi32(a, b));
    return internalUnitSSE2Simd::BAllTrue4_R(c) != 0;
}
 
#define VECMATH_AOS_EPSILON (1e-3f)
 
PX_FORCE_INLINE bool allElementsNearEqualFloatV(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    const FloatV c = FSub(a, b);
    const FloatV minError = FLoad(-VECMATH_AOS_EPSILON);
    const FloatV maxError = FLoad(VECMATH_AOS_EPSILON);
    return _mm_comigt_ss(c, minError) && _mm_comilt_ss(c, maxError);
}
 
PX_FORCE_INLINE bool allElementsNearEqualVec3V(const Vec3V a, const Vec3V b)
{
    const Vec3V c = V3Sub(a, b);
    const Vec3V minError = V3Load(-VECMATH_AOS_EPSILON);
    const Vec3V maxError = V3Load(VECMATH_AOS_EPSILON);
    return (_mm_comigt_ss(_mm_shuffle_ps(c, c, _MM_SHUFFLE(0, 0, 0, 0)), minError) &&
            _mm_comilt_ss(_mm_shuffle_ps(c, c, _MM_SHUFFLE(0, 0, 0, 0)), maxError) &&
            _mm_comigt_ss(_mm_shuffle_ps(c, c, _MM_SHUFFLE(1, 1, 1, 1)), minError) &&
            _mm_comilt_ss(_mm_shuffle_ps(c, c, _MM_SHUFFLE(1, 1, 1, 1)), maxError) &&
            _mm_comigt_ss(_mm_shuffle_ps(c, c, _MM_SHUFFLE(2, 2, 2, 2)), minError) &&
            _mm_comilt_ss(_mm_shuffle_ps(c, c, _MM_SHUFFLE(2, 2, 2, 2)), maxError));
}
 
PX_FORCE_INLINE bool allElementsNearEqualVec4V(const Vec4V a, const Vec4V b)
{
    const Vec4V c = V4Sub(a, b);
    const Vec4V minError = V4Load(-VECMATH_AOS_EPSILON);
    const Vec4V maxError = V4Load(VECMATH_AOS_EPSILON);
    return (_mm_comigt_ss(_mm_shuffle_ps(c, c, _MM_SHUFFLE(0, 0, 0, 0)), minError) &&
            _mm_comilt_ss(_mm_shuffle_ps(c, c, _MM_SHUFFLE(0, 0, 0, 0)), maxError) &&
            _mm_comigt_ss(_mm_shuffle_ps(c, c, _MM_SHUFFLE(1, 1, 1, 1)), minError) &&
            _mm_comilt_ss(_mm_shuffle_ps(c, c, _MM_SHUFFLE(1, 1, 1, 1)), maxError) &&
            _mm_comigt_ss(_mm_shuffle_ps(c, c, _MM_SHUFFLE(2, 2, 2, 2)), minError) &&
            _mm_comilt_ss(_mm_shuffle_ps(c, c, _MM_SHUFFLE(2, 2, 2, 2)), maxError) &&
            _mm_comigt_ss(_mm_shuffle_ps(c, c, _MM_SHUFFLE(3, 3, 3, 3)), minError) &&
            _mm_comilt_ss(_mm_shuffle_ps(c, c, _MM_SHUFFLE(3, 3, 3, 3)), maxError));
}
}
 
 
PX_FORCE_INLINE bool isFiniteFloatV(const FloatV a)
{
    PxF32 badNumber =
        physx::PxUnionCast<PxF32, PxU32>(PX_FPCLASS_SNAN | PX_FPCLASS_QNAN | PX_FPCLASS_NINF | PX_FPCLASS_PINF);
    const FloatV vBadNum = FLoad(badNumber);
    const BoolV vMask = BAnd(vBadNum, a);
    return internalUnitSSE2Simd::FiniteTestEq(vMask, BFFFF()) == 1;
}
 
PX_FORCE_INLINE bool isFiniteVec3V(const Vec3V a)
{
    PxF32 badNumber =
        physx::PxUnionCast<PxF32, PxU32>(PX_FPCLASS_SNAN | PX_FPCLASS_QNAN | PX_FPCLASS_NINF | PX_FPCLASS_PINF);
    const Vec3V vBadNum = V3Load(badNumber);
    const BoolV vMask = BAnd(BAnd(vBadNum, a), BTTTF());
    return internalUnitSSE2Simd::FiniteTestEq(vMask, BFFFF()) == 1;
}
 
PX_FORCE_INLINE bool isFiniteVec4V(const Vec4V a)
{
    /*Vec4V a;
    PX_ALIGN(16, PxF32 f[4]);
    F32Array_Aligned_From_Vec4V(a, f);
    return PxIsFinite(f[0])
            && PxIsFinite(f[1])
            && PxIsFinite(f[2])
            && PxIsFinite(f[3]);*/
 
    PxF32 badNumber =
        physx::PxUnionCast<PxF32, PxU32>(PX_FPCLASS_SNAN | PX_FPCLASS_QNAN | PX_FPCLASS_NINF | PX_FPCLASS_PINF);
    const Vec4V vBadNum = V4Load(badNumber);
    const BoolV vMask = BAnd(vBadNum, a);
 
    return internalUnitSSE2Simd::FiniteTestEq(vMask, BFFFF()) == 1;
}
 
PX_FORCE_INLINE bool hasZeroElementinFloatV(const FloatV a)
{
    ASSERT_ISVALIDFLOATV(a);
    return _mm_comieq_ss(_mm_shuffle_ps(a, a, _MM_SHUFFLE(0, 0, 0, 0)), FZero()) ? true : false;
}
 
PX_FORCE_INLINE bool hasZeroElementInVec3V(const Vec3V a)
{
    return (_mm_comieq_ss(_mm_shuffle_ps(a, a, _MM_SHUFFLE(0, 0, 0, 0)), FZero()) ||
            _mm_comieq_ss(_mm_shuffle_ps(a, a, _MM_SHUFFLE(1, 1, 1, 1)), FZero()) ||
            _mm_comieq_ss(_mm_shuffle_ps(a, a, _MM_SHUFFLE(2, 2, 2, 2)), FZero()));
}
 
PX_FORCE_INLINE bool hasZeroElementInVec4V(const Vec4V a)
{
    return (_mm_comieq_ss(_mm_shuffle_ps(a, a, _MM_SHUFFLE(0, 0, 0, 0)), FZero()) ||
            _mm_comieq_ss(_mm_shuffle_ps(a, a, _MM_SHUFFLE(1, 1, 1, 1)), FZero()) ||
            _mm_comieq_ss(_mm_shuffle_ps(a, a, _MM_SHUFFLE(2, 2, 2, 2)), FZero()) ||
            _mm_comieq_ss(_mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 3, 3, 3)), FZero()));
}
 
 
PX_FORCE_INLINE FloatV FLoad(const PxF32 f)
{
    return _mm_load1_ps(&f);
}
 
PX_FORCE_INLINE Vec3V V3Load(const PxF32 f)
{
    return _mm_set_ps(0.0f, f, f, f);
}
 
PX_FORCE_INLINE Vec4V V4Load(const PxF32 f)
{
    return _mm_load1_ps(&f);
}
 
PX_FORCE_INLINE BoolV BLoad(const bool f)
{
    const PxU32 i = PxU32(-PxI32(f));
    return _mm_load1_ps(reinterpret_cast<const float*>(&i));
}
 
PX_FORCE_INLINE Vec3V V3LoadA(const PxVec3& f)
{
    ASSERT_ISALIGNED16(const_cast<PxVec3*>(&f));
#if !PX_EMSCRIPTEN
    return _mm_and_ps(reinterpret_cast<const Vec3V&>(f), V4LoadA(internalUnitSSE2Simd::gMaskXYZ));
#else
    return _mm_and_ps((Vec3V&)f, (VecI32V&)internalUnitSSE2Simd::gMaskXYZ);
#endif
}
 
PX_FORCE_INLINE Vec3V V3LoadU(const PxVec3& f)
{
    return _mm_set_ps(0.0f, f.z, f.y, f.x);
}
 
PX_FORCE_INLINE Vec3V V3LoadUnsafeA(const PxVec3& f)
{
    ASSERT_ISALIGNED16(const_cast<PxVec3*>(&f));
    return _mm_set_ps(0.0f, f.z, f.y, f.x);
}
 
PX_FORCE_INLINE Vec3V V3LoadA(const PxF32* const f)
{
    ASSERT_ISALIGNED16(const_cast<PxF32*>(f));
#if !PX_EMSCRIPTEN
    return _mm_and_ps(V4LoadA(f), V4LoadA(internalUnitSSE2Simd::gMaskXYZ));
#else
    return _mm_and_ps((Vec3V&)*f, (VecI32V&)internalUnitSSE2Simd::gMaskXYZ);
#endif
}
 
PX_FORCE_INLINE Vec3V V3LoadU(const PxF32* const i)
{
    return _mm_set_ps(0.0f, i[2], i[1], i[0]);
}
 
PX_FORCE_INLINE Vec3V Vec3V_From_Vec4V(Vec4V v)
{
    return V4ClearW(v);
}
 
PX_FORCE_INLINE Vec3V Vec3V_From_Vec4V_WUndefined(const Vec4V v)
{
    return v;
}
 
PX_FORCE_INLINE Vec4V Vec4V_From_Vec3V(Vec3V f)
{
    ASSERT_ISVALIDVEC3V(f);
    return f; // ok if it is implemented as the same type.
}
 
PX_FORCE_INLINE Vec4V Vec4V_From_PxVec3_WUndefined(const PxVec3& f)
{
    return _mm_set_ps(0.0f, f.z, f.y, f.x);
}
 
PX_FORCE_INLINE Vec4V Vec4V_From_FloatV(FloatV f)
{
    return f;
}
 
PX_FORCE_INLINE Vec3V Vec3V_From_FloatV(FloatV f)
{
    ASSERT_ISVALIDFLOATV(f);
    return Vec3V_From_Vec4V(Vec4V_From_FloatV(f));
}
 
PX_FORCE_INLINE Vec3V Vec3V_From_FloatV_WUndefined(FloatV f)
{
    ASSERT_ISVALIDVEC3V(f);
    return Vec3V_From_Vec4V_WUndefined(Vec4V_From_FloatV(f));
}
 
PX_FORCE_INLINE Mat33V Mat33V_From_PxMat33(const PxMat33& m)
{
    return Mat33V(V3LoadU(m.column0), V3LoadU(m.column1), V3LoadU(m.column2));
}
 
PX_FORCE_INLINE void PxMat33_From_Mat33V(const Mat33V& m, PxMat33& out)
{
    V3StoreU(m.col0, out.column0);
    V3StoreU(m.col1, out.column1);
    V3StoreU(m.col2, out.column2);
}
 
PX_FORCE_INLINE Vec4V V4LoadA(const PxF32* const f)
{
    ASSERT_ISALIGNED16(const_cast<PxF32*>(f));
    return _mm_load_ps(f);
}
 
PX_FORCE_INLINE void V4StoreA(Vec4V a, PxF32* f)
{
    ASSERT_ISALIGNED16(f);
    _mm_store_ps(f, a);
}
 
PX_FORCE_INLINE void V4StoreU(const Vec4V a, PxF32* f)
{
    _mm_storeu_ps(f, a);
}
 
PX_FORCE_INLINE void BStoreA(const BoolV a, PxU32* f)
{
    ASSERT_ISALIGNED16(f);
    _mm_store_ps(reinterpret_cast<PxF32*>(f), a);
}
 
PX_FORCE_INLINE void U4StoreA(const VecU32V uv, PxU32* u)
{
    ASSERT_ISALIGNED16(u);
    _mm_store_ps(reinterpret_cast<float*>(u), uv);
}
 
PX_FORCE_INLINE VecI32V I4LoadXYZW(const PxI32& x, const PxI32& y, const PxI32& z, const PxI32& w)
{
    return _mm_set_epi32(w, z, y, x);
}
 
PX_FORCE_INLINE void I4StoreA(const VecI32V iv, PxI32* i)
{
    ASSERT_ISALIGNED16(i);
    _mm_store_ps(reinterpret_cast<float*>(i), m128_I2F(iv));
}
 
PX_FORCE_INLINE Vec4V V4LoadU(const PxF32* const f)
{
    return _mm_loadu_ps(f);
}
 
PX_FORCE_INLINE BoolV BLoad(const bool* const f)
{
    const PX_ALIGN(16, PxI32) b[4] = { -PxI32(f[0]), -PxI32(f[1]), -PxI32(f[2]), -PxI32(f[3]) };
    return _mm_load_ps(reinterpret_cast<const float*>(&b));
}
 
PX_FORCE_INLINE void FStore(const FloatV a, PxF32* PX_RESTRICT f)
{
    ASSERT_ISVALIDFLOATV(a);
    _mm_store_ss(f, a);
}
 
PX_FORCE_INLINE void V3StoreA(const Vec3V a, PxVec3& f)
{
    ASSERT_ISALIGNED16(&f);
    PX_ALIGN(16, PxF32) f2[4];
    _mm_store_ps(f2, a);
    f = PxVec3(f2[0], f2[1], f2[2]);
}
 
PX_FORCE_INLINE void V3StoreU(const Vec3V a, PxVec3& f)
{
    PX_ALIGN(16, PxF32) f2[4];
    _mm_store_ps(f2, a);
    f = PxVec3(f2[0], f2[1], f2[2]);
}
 
PX_FORCE_INLINE void Store_From_BoolV(const BoolV b, PxU32* b2)
{
    _mm_store_ss(reinterpret_cast<PxF32*>(b2), b);
}
 
PX_FORCE_INLINE VecU32V U4Load(const PxU32 i)
{
    return _mm_load1_ps(reinterpret_cast<const PxF32*>(&i));
}
 
PX_FORCE_INLINE VecU32V U4LoadU(const PxU32* i)
{
    return _mm_loadu_ps(reinterpret_cast<const PxF32*>(i));
}
 
PX_FORCE_INLINE VecU32V U4LoadA(const PxU32* i)
{
    ASSERT_ISALIGNED16(const_cast<PxU32*>(i));
    return _mm_load_ps(reinterpret_cast<const PxF32*>(i));
}
 
// FLOATV
 
PX_FORCE_INLINE FloatV FZero()
{
    return FLoad(0.0f);
}
 
PX_FORCE_INLINE FloatV FOne()
{
    return FLoad(1.0f);
}
 
PX_FORCE_INLINE FloatV FHalf()
{
    return FLoad(0.5f);
}
 
PX_FORCE_INLINE FloatV FEps()
{
    return FLoad(PX_EPS_REAL);
}
 
PX_FORCE_INLINE FloatV FEps6()
{
    return FLoad(1e-6f);
}
 
PX_FORCE_INLINE FloatV FMax()
{
    return FLoad(PX_MAX_REAL);
}
 
PX_FORCE_INLINE FloatV FNegMax()
{
    return FLoad(-PX_MAX_REAL);
}
 
PX_FORCE_INLINE FloatV IZero()
{
    const PxU32 zero = 0;
    return _mm_load1_ps(reinterpret_cast<const PxF32*>(&zero));
}
 
PX_FORCE_INLINE FloatV IOne()
{
    const PxU32 one = 1;
    return _mm_load1_ps(reinterpret_cast<const PxF32*>(&one));
}
 
PX_FORCE_INLINE FloatV ITwo()
{
    const PxU32 two = 2;
    return _mm_load1_ps(reinterpret_cast<const PxF32*>(&two));
}
 
PX_FORCE_INLINE FloatV IThree()
{
    const PxU32 three = 3;
    return _mm_load1_ps(reinterpret_cast<const PxF32*>(&three));
}
 
PX_FORCE_INLINE FloatV IFour()
{
    PxU32 four = 4;
    return _mm_load1_ps(reinterpret_cast<const PxF32*>(&four));
}
 
PX_FORCE_INLINE FloatV FNeg(const FloatV f)
{
    ASSERT_ISVALIDFLOATV(f);
    return _mm_sub_ps(_mm_setzero_ps(), f);
}
 
PX_FORCE_INLINE FloatV FAdd(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
/*
    if(!isValidFloatV(a))
    {
assert(false);
    }
    if(!isValidFloatV(b))
    {
assert(false);
    }
*/
    return _mm_add_ps(a, b);
}
 
PX_FORCE_INLINE FloatV FSub(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    return _mm_sub_ps(a, b);
}
 
PX_FORCE_INLINE FloatV FMul(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    return _mm_mul_ps(a, b);
}
 
PX_FORCE_INLINE FloatV FDiv(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    return _mm_div_ps(a, b);
}
 
PX_FORCE_INLINE FloatV FDivFast(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    return _mm_mul_ps(a, _mm_rcp_ps(b));
}
 
PX_FORCE_INLINE FloatV FRecip(const FloatV a)
{
    ASSERT_ISVALIDFLOATV(a);
    return _mm_div_ps(FOne(), a);
}
 
PX_FORCE_INLINE FloatV FRecipFast(const FloatV a)
{
    ASSERT_ISVALIDFLOATV(a);
    return _mm_rcp_ps(a);
}
 
PX_FORCE_INLINE FloatV FRsqrt(const FloatV a)
{
    ASSERT_ISVALIDFLOATV(a);
    return _mm_div_ps(FOne(), _mm_sqrt_ps(a));
}
 
PX_FORCE_INLINE FloatV FSqrt(const FloatV a)
{
    ASSERT_ISVALIDFLOATV(a);
    return _mm_sqrt_ps(a);
}
 
PX_FORCE_INLINE FloatV FRsqrtFast(const FloatV a)
{
    ASSERT_ISVALIDFLOATV(a);
    return _mm_rsqrt_ps(a);
}
 
PX_FORCE_INLINE FloatV FScaleAdd(const FloatV a, const FloatV b, const FloatV c)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    ASSERT_ISVALIDFLOATV(c);
    return FAdd(FMul(a, b), c);
}
 
PX_FORCE_INLINE FloatV FNegScaleSub(const FloatV a, const FloatV b, const FloatV c)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    ASSERT_ISVALIDFLOATV(c);
    return FSub(c, FMul(a, b));
}
 
PX_FORCE_INLINE FloatV FAbs(const FloatV a)
{
    ASSERT_ISVALIDFLOATV(a);
    PX_ALIGN(16, const PxU32) absMask[4] = { 0x7fFFffFF, 0x7fFFffFF, 0x7fFFffFF, 0x7fFFffFF };
    return _mm_and_ps(a, _mm_load_ps(reinterpret_cast<const PxF32*>(absMask)));
}
 
PX_FORCE_INLINE FloatV FSel(const BoolV c, const FloatV a, const FloatV b)
{
    PX_ASSERT(vecMathTests::allElementsEqualBoolV(c,BTTTT()) ||
              vecMathTests::allElementsEqualBoolV(c,BFFFF()));
    ASSERT_ISVALIDFLOATV(_mm_or_ps(_mm_andnot_ps(c, b), _mm_and_ps(c, a)));
    return _mm_or_ps(_mm_andnot_ps(c, b), _mm_and_ps(c, a));
}
 
PX_FORCE_INLINE BoolV FIsGrtr(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    return _mm_cmpgt_ps(a, b);
}
 
PX_FORCE_INLINE BoolV FIsGrtrOrEq(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    return _mm_cmpge_ps(a, b);
}
 
PX_FORCE_INLINE BoolV FIsEq(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    return _mm_cmpeq_ps(a, b);
}
 
PX_FORCE_INLINE FloatV FMax(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    return _mm_max_ps(a, b);
}
 
PX_FORCE_INLINE FloatV FMin(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    return _mm_min_ps(a, b);
}
 
PX_FORCE_INLINE FloatV FClamp(const FloatV a, const FloatV minV, const FloatV maxV)
{
    ASSERT_ISVALIDFLOATV(minV);
    ASSERT_ISVALIDFLOATV(maxV);
    return _mm_max_ps(_mm_min_ps(a, maxV), minV);
}
 
PX_FORCE_INLINE PxU32 FAllGrtr(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    return PxU32(_mm_comigt_ss(a, b));
}
 
PX_FORCE_INLINE PxU32 FAllGrtrOrEq(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    return PxU32(_mm_comige_ss(a, b));
}
 
PX_FORCE_INLINE PxU32 FAllEq(const FloatV a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(b);
    return PxU32(_mm_comieq_ss(a, b));
}
 
PX_FORCE_INLINE FloatV FRound(const FloatV a)
{
    ASSERT_ISVALIDFLOATV(a);
#ifdef __SSE4_2__
    return _mm_round_ps(a, _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
#else
    // return _mm_round_ps(a, 0x0);
    const FloatV half = FLoad(0.5f);
    const __m128 signBit = _mm_cvtepi32_ps(_mm_srli_epi32(_mm_cvtps_epi32(a), 31));
    const FloatV aRound = FSub(FAdd(a, half), signBit);
    __m128i tmp = _mm_cvttps_epi32(aRound);
    return _mm_cvtepi32_ps(tmp);
#endif
}
 
PX_FORCE_INLINE FloatV FSin(const FloatV a)
{
    ASSERT_ISVALIDFLOATV(a);
 
    // Modulo the range of the given angles such that -XM_2PI <= Angles < XM_2PI
    const FloatV recipTwoPi = V4LoadA(g_PXReciprocalTwoPi.f);
    const FloatV twoPi = V4LoadA(g_PXTwoPi.f);
    const FloatV tmp = FMul(a, recipTwoPi);
    const FloatV b = FRound(tmp);
    const FloatV V1 = FNegScaleSub(twoPi, b, a);
 
    // sin(V) ~= V - V^3 / 3! + V^5 / 5! - V^7 / 7! + V^9 / 9! - V^11 / 11! + V^13 / 13! -
    //           V^15 / 15! + V^17 / 17! - V^19 / 19! + V^21 / 21! - V^23 / 23! (for -PI <= V < PI)
    const FloatV V2 = FMul(V1, V1);
    const FloatV V3 = FMul(V2, V1);
    const FloatV V5 = FMul(V3, V2);
    const FloatV V7 = FMul(V5, V2);
    const FloatV V9 = FMul(V7, V2);
    const FloatV V11 = FMul(V9, V2);
    const FloatV V13 = FMul(V11, V2);
    const FloatV V15 = FMul(V13, V2);
    const FloatV V17 = FMul(V15, V2);
    const FloatV V19 = FMul(V17, V2);
    const FloatV V21 = FMul(V19, V2);
    const FloatV V23 = FMul(V21, V2);
 
    const Vec4V sinCoefficients0 = V4LoadA(g_PXSinCoefficients0.f);
    const Vec4V sinCoefficients1 = V4LoadA(g_PXSinCoefficients1.f);
    const Vec4V sinCoefficients2 = V4LoadA(g_PXSinCoefficients2.f);
 
    const FloatV S1 = V4GetY(sinCoefficients0);
    const FloatV S2 = V4GetZ(sinCoefficients0);
    const FloatV S3 = V4GetW(sinCoefficients0);
    const FloatV S4 = V4GetX(sinCoefficients1);
    const FloatV S5 = V4GetY(sinCoefficients1);
    const FloatV S6 = V4GetZ(sinCoefficients1);
    const FloatV S7 = V4GetW(sinCoefficients1);
    const FloatV S8 = V4GetX(sinCoefficients2);
    const FloatV S9 = V4GetY(sinCoefficients2);
    const FloatV S10 = V4GetZ(sinCoefficients2);
    const FloatV S11 = V4GetW(sinCoefficients2);
 
    FloatV Result;
    Result = FScaleAdd(S1, V3, V1);
    Result = FScaleAdd(S2, V5, Result);
    Result = FScaleAdd(S3, V7, Result);
    Result = FScaleAdd(S4, V9, Result);
    Result = FScaleAdd(S5, V11, Result);
    Result = FScaleAdd(S6, V13, Result);
    Result = FScaleAdd(S7, V15, Result);
    Result = FScaleAdd(S8, V17, Result);
    Result = FScaleAdd(S9, V19, Result);
    Result = FScaleAdd(S10, V21, Result);
    Result = FScaleAdd(S11, V23, Result);
 
    return Result;
}
 
PX_FORCE_INLINE FloatV FCos(const FloatV a)
{
    ASSERT_ISVALIDFLOATV(a);
 
    // Modulo the range of the given angles such that -XM_2PI <= Angles < XM_2PI
    const FloatV recipTwoPi = V4LoadA(g_PXReciprocalTwoPi.f);
    const FloatV twoPi = V4LoadA(g_PXTwoPi.f);
    const FloatV tmp = FMul(a, recipTwoPi);
    const FloatV b = FRound(tmp);
    const FloatV V1 = FNegScaleSub(twoPi, b, a);
 
    // cos(V) ~= 1 - V^2 / 2! + V^4 / 4! - V^6 / 6! + V^8 / 8! - V^10 / 10! + V^12 / 12! -
    //           V^14 / 14! + V^16 / 16! - V^18 / 18! + V^20 / 20! - V^22 / 22! (for -PI <= V < PI)
    const FloatV V2 = FMul(V1, V1);
    const FloatV V4 = FMul(V2, V2);
    const FloatV V6 = FMul(V4, V2);
    const FloatV V8 = FMul(V4, V4);
    const FloatV V10 = FMul(V6, V4);
    const FloatV V12 = FMul(V6, V6);
    const FloatV V14 = FMul(V8, V6);
    const FloatV V16 = FMul(V8, V8);
    const FloatV V18 = FMul(V10, V8);
    const FloatV V20 = FMul(V10, V10);
    const FloatV V22 = FMul(V12, V10);
 
    const Vec4V cosCoefficients0 = V4LoadA(g_PXCosCoefficients0.f);
    const Vec4V cosCoefficients1 = V4LoadA(g_PXCosCoefficients1.f);
    const Vec4V cosCoefficients2 = V4LoadA(g_PXCosCoefficients2.f);
 
    const FloatV C1 = V4GetY(cosCoefficients0);
    const FloatV C2 = V4GetZ(cosCoefficients0);
    const FloatV C3 = V4GetW(cosCoefficients0);
    const FloatV C4 = V4GetX(cosCoefficients1);
    const FloatV C5 = V4GetY(cosCoefficients1);
    const FloatV C6 = V4GetZ(cosCoefficients1);
    const FloatV C7 = V4GetW(cosCoefficients1);
    const FloatV C8 = V4GetX(cosCoefficients2);
    const FloatV C9 = V4GetY(cosCoefficients2);
    const FloatV C10 = V4GetZ(cosCoefficients2);
    const FloatV C11 = V4GetW(cosCoefficients2);
 
    FloatV Result;
    Result = FScaleAdd(C1, V2, V4One());
    Result = FScaleAdd(C2, V4, Result);
    Result = FScaleAdd(C3, V6, Result);
    Result = FScaleAdd(C4, V8, Result);
    Result = FScaleAdd(C5, V10, Result);
    Result = FScaleAdd(C6, V12, Result);
    Result = FScaleAdd(C7, V14, Result);
    Result = FScaleAdd(C8, V16, Result);
    Result = FScaleAdd(C9, V18, Result);
    Result = FScaleAdd(C10, V20, Result);
    Result = FScaleAdd(C11, V22, Result);
 
    return Result;
}
 
PX_FORCE_INLINE PxU32 FOutOfBounds(const FloatV a, const FloatV min, const FloatV max)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(min);
    ASSERT_ISVALIDFLOATV(max);
    const BoolV c = BOr(FIsGrtr(a, max), FIsGrtr(min, a));
    return !BAllEqFFFF(c);
}
 
PX_FORCE_INLINE PxU32 FInBounds(const FloatV a, const FloatV min, const FloatV max)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(min);
    ASSERT_ISVALIDFLOATV(max)
    const BoolV c = BAnd(FIsGrtrOrEq(a, min), FIsGrtrOrEq(max, a));
    return BAllEqTTTT(c);
}
 
PX_FORCE_INLINE PxU32 FOutOfBounds(const FloatV a, const FloatV bounds)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(bounds);
    return FOutOfBounds(a, FNeg(bounds), bounds);
}
 
PX_FORCE_INLINE PxU32 FInBounds(const FloatV a, const FloatV bounds)
{
    ASSERT_ISVALIDFLOATV(a);
    ASSERT_ISVALIDFLOATV(bounds);
    return FInBounds(a, FNeg(bounds), bounds);
}
 
// VEC3V
 
PX_FORCE_INLINE Vec3V V3Splat(const FloatV f)
{
    ASSERT_ISVALIDFLOATV(f);
    const __m128 zero = FZero();
    const __m128 fff0 = _mm_move_ss(f, zero);
    return _mm_shuffle_ps(fff0, fff0, _MM_SHUFFLE(0, 1, 2, 3));
}
 
PX_FORCE_INLINE Vec3V V3Merge(const FloatVArg x, const FloatVArg y, const FloatVArg z)
{
    ASSERT_ISVALIDFLOATV(x);
    ASSERT_ISVALIDFLOATV(y);
    ASSERT_ISVALIDFLOATV(z);
    // static on zero causes compiler crash on x64 debug_opt
    const __m128 zero = FZero();
    const __m128 xy = _mm_move_ss(x, y);
    const __m128 z0 = _mm_move_ss(zero, z);
 
    return _mm_shuffle_ps(xy, z0, _MM_SHUFFLE(1, 0, 0, 1));
}
 
PX_FORCE_INLINE Vec3V V3UnitX()
{
    const PX_ALIGN(16, PxF32) x[4] = { 1.0f, 0.0f, 0.0f, 0.0f };
    const __m128 x128 = _mm_load_ps(x);
    return x128;
}
 
PX_FORCE_INLINE Vec3V V3UnitY()
{
    const PX_ALIGN(16, PxF32) y[4] = { 0.0f, 1.0f, 0.0f, 0.0f };
    const __m128 y128 = _mm_load_ps(y);
    return y128;
}
 
PX_FORCE_INLINE Vec3V V3UnitZ()
{
    const PX_ALIGN(16, PxF32) z[4] = { 0.0f, 0.0f, 1.0f, 0.0f };
    const __m128 z128 = _mm_load_ps(z);
    return z128;
}
 
PX_FORCE_INLINE FloatV V3GetX(const Vec3V f)
{
    ASSERT_ISVALIDVEC3V(f);
    return _mm_shuffle_ps(f, f, _MM_SHUFFLE(0, 0, 0, 0));
}
 
PX_FORCE_INLINE FloatV V3GetY(const Vec3V f)
{
    ASSERT_ISVALIDVEC3V(f)
    return _mm_shuffle_ps(f, f, _MM_SHUFFLE(1, 1, 1, 1));
}
 
PX_FORCE_INLINE FloatV V3GetZ(const Vec3V f)
{
    ASSERT_ISVALIDVEC3V(f);
    return _mm_shuffle_ps(f, f, _MM_SHUFFLE(2, 2, 2, 2));
}
 
PX_FORCE_INLINE Vec3V V3SetX(const Vec3V v, const FloatV f)
{
    ASSERT_ISVALIDVEC3V(v);
    ASSERT_ISVALIDFLOATV(f);
    return V4Sel(BFTTT(), v, f);
}
 
PX_FORCE_INLINE Vec3V V3SetY(const Vec3V v, const FloatV f)
{
    ASSERT_ISVALIDVEC3V(v);
    ASSERT_ISVALIDFLOATV(f);
    return V4Sel(BTFTT(), v, f);
}
 
PX_FORCE_INLINE Vec3V V3SetZ(const Vec3V v, const FloatV f)
{
    ASSERT_ISVALIDVEC3V(v);
    ASSERT_ISVALIDFLOATV(f);
    return V4Sel(BTTFT(), v, f);
}
 
PX_FORCE_INLINE Vec3V V3ColX(const Vec3V a, const Vec3V b, const Vec3V c)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    ASSERT_ISVALIDVEC3V(c);
    Vec3V r = _mm_shuffle_ps(a, c, _MM_SHUFFLE(3, 0, 3, 0));
    return V3SetY(r, V3GetX(b));
}
 
PX_FORCE_INLINE Vec3V V3ColY(const Vec3V a, const Vec3V b, const Vec3V c)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    ASSERT_ISVALIDVEC3V(c)
    Vec3V r = _mm_shuffle_ps(a, c, _MM_SHUFFLE(3, 1, 3, 1));
    return V3SetY(r, V3GetY(b));
}
 
PX_FORCE_INLINE Vec3V V3ColZ(const Vec3V a, const Vec3V b, const Vec3V c)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    ASSERT_ISVALIDVEC3V(c);
    Vec3V r = _mm_shuffle_ps(a, c, _MM_SHUFFLE(3, 2, 3, 2));
    return V3SetY(r, V3GetZ(b));
}
 
PX_FORCE_INLINE Vec3V V3Zero()
{
    return V3Load(0.0f);
}
 
PX_FORCE_INLINE Vec3V V3Eps()
{
    return V3Load(PX_EPS_REAL);
}
PX_FORCE_INLINE Vec3V V3One()
{
    return V3Load(1.0f);
}
 
PX_FORCE_INLINE Vec3V V3Neg(const Vec3V f)
{
    ASSERT_ISVALIDVEC3V(f);
    return _mm_sub_ps(_mm_setzero_ps(), f);
}
 
PX_FORCE_INLINE Vec3V V3Add(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    return _mm_add_ps(a, b);
}
 
PX_FORCE_INLINE Vec3V V3Sub(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    return _mm_sub_ps(a, b);
}
 
PX_FORCE_INLINE Vec3V V3Scale(const Vec3V a, const FloatV b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDFLOATV(b);
    return _mm_mul_ps(a, b);
}
 
PX_FORCE_INLINE Vec3V V3Mul(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    return _mm_mul_ps(a, b);
}
 
PX_FORCE_INLINE Vec3V V3ScaleInv(const Vec3V a, const FloatV b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDFLOATV(b);
    return _mm_div_ps(a, b);
}
 
PX_FORCE_INLINE Vec3V V3Div(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    return V4ClearW(_mm_div_ps(a, b));
}
 
PX_FORCE_INLINE Vec3V V3ScaleInvFast(const Vec3V a, const FloatV b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDFLOATV(b);
    return _mm_mul_ps(a, _mm_rcp_ps(b));
}
 
PX_FORCE_INLINE Vec3V V3DivFast(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    return V4ClearW(_mm_mul_ps(a, _mm_rcp_ps(b)));
}
 
PX_FORCE_INLINE Vec3V V3Recip(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    const __m128 zero = V3Zero();
    const __m128 tttf = BTTTF();
    const __m128 recipA = _mm_div_ps(V3One(), a);
    return V4Sel(tttf, recipA, zero);
}
 
PX_FORCE_INLINE Vec3V V3RecipFast(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    const __m128 zero = V3Zero();
    const __m128 tttf = BTTTF();
    const __m128 recipA = _mm_rcp_ps(a);
    return V4Sel(tttf, recipA, zero);
}
 
PX_FORCE_INLINE Vec3V V3Rsqrt(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    const __m128 zero = V3Zero();
    const __m128 tttf = BTTTF();
    const __m128 recipA = _mm_div_ps(V3One(), _mm_sqrt_ps(a));
    return V4Sel(tttf, recipA, zero);
}
 
PX_FORCE_INLINE Vec3V V3RsqrtFast(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    const __m128 zero = V3Zero();
    const __m128 tttf = BTTTF();
    const __m128 recipA = _mm_rsqrt_ps(a);
    return V4Sel(tttf, recipA, zero);
}
 
PX_FORCE_INLINE Vec3V V3ScaleAdd(const Vec3V a, const FloatV b, const Vec3V c)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDFLOATV(b);
    ASSERT_ISVALIDVEC3V(c);
    return V3Add(V3Scale(a, b), c);
}
 
PX_FORCE_INLINE Vec3V V3NegScaleSub(const Vec3V a, const FloatV b, const Vec3V c)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDFLOATV(b);
    ASSERT_ISVALIDVEC3V(c);
    return V3Sub(c, V3Scale(a, b));
}
 
PX_FORCE_INLINE Vec3V V3MulAdd(const Vec3V a, const Vec3V b, const Vec3V c)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    ASSERT_ISVALIDVEC3V(c);
    return V3Add(V3Mul(a, b), c);
}
 
PX_FORCE_INLINE Vec3V V3NegMulSub(const Vec3V a, const Vec3V b, const Vec3V c)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    ASSERT_ISVALIDVEC3V(c);
    return V3Sub(c, V3Mul(a, b));
}
 
PX_FORCE_INLINE Vec3V V3Abs(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    return V3Max(a, V3Neg(a));
}
 
PX_FORCE_INLINE FloatV V3Dot(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
#ifdef __SSE4_2__
    return _mm_dp_ps(a, b, 0x7f);
#else
    const __m128 t0 = _mm_mul_ps(a, b);                             //  aw*bw | az*bz | ay*by | ax*bx
    const __m128 t1 = _mm_shuffle_ps(t0, t0, _MM_SHUFFLE(1,0,3,2)); //  ay*by | ax*bx | aw*bw | az*bz
    const __m128 t2 = _mm_add_ps(t0, t1);                           //  ay*by + aw*bw | ax*bx + az*bz | aw*bw + ay*by | az*bz + ax*bx
    const __m128 t3 = _mm_shuffle_ps(t2, t2, _MM_SHUFFLE(2,3,0,1)); //  ax*bx + az*bz | ay*by + aw*bw | az*bz + ax*bx | aw*bw + ay*by
    return _mm_add_ps(t3, t2);                                      //  ax*bx + az*bz + ay*by + aw*bw 
                                                                    //  ay*by + aw*bw + ax*bx + az*bz
                                                                    //  az*bz + ax*bx + aw*bw + ay*by
                                                                    //  aw*bw + ay*by + az*bz + ax*bx
#endif
}
 
PX_FORCE_INLINE Vec3V V3Cross(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    const __m128 r1 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 1, 0, 2)); // z,x,y,w
    const __m128 r2 = _mm_shuffle_ps(b, b, _MM_SHUFFLE(3, 0, 2, 1)); // y,z,x,w
    const __m128 l1 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 0, 2, 1)); // y,z,x,w
    const __m128 l2 = _mm_shuffle_ps(b, b, _MM_SHUFFLE(3, 1, 0, 2)); // z,x,y,w
    return _mm_sub_ps(_mm_mul_ps(l1, l2), _mm_mul_ps(r1, r2));
}
 
PX_FORCE_INLINE VecCrossV V3PrepareCross(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    VecCrossV v;
    v.mR1 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 1, 0, 2)); // z,x,y,w
    v.mL1 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 0, 2, 1)); // y,z,x,w
    return v;
}
 
PX_FORCE_INLINE Vec3V V3Cross(const VecCrossV& a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(b);
    const __m128 r2 = _mm_shuffle_ps(b, b, _MM_SHUFFLE(3, 0, 2, 1)); // y,z,x,w
    const __m128 l2 = _mm_shuffle_ps(b, b, _MM_SHUFFLE(3, 1, 0, 2)); // z,x,y,w
    return _mm_sub_ps(_mm_mul_ps(a.mL1, l2), _mm_mul_ps(a.mR1, r2));
}
 
PX_FORCE_INLINE Vec3V V3Cross(const Vec3V a, const VecCrossV& b)
{
    ASSERT_ISVALIDVEC3V(a);
    const __m128 r2 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 0, 2, 1)); // y,z,x,w
    const __m128 l2 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 1, 0, 2)); // z,x,y,w
    return _mm_sub_ps(_mm_mul_ps(b.mR1, r2), _mm_mul_ps(b.mL1, l2));
}
 
PX_FORCE_INLINE Vec3V V3Cross(const VecCrossV& a, const VecCrossV& b)
{
    return _mm_sub_ps(_mm_mul_ps(a.mL1, b.mR1), _mm_mul_ps(a.mR1, b.mL1));
}
 
PX_FORCE_INLINE FloatV V3Length(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    return _mm_sqrt_ps(V3Dot(a, a));
}
 
PX_FORCE_INLINE FloatV V3LengthSq(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    return V3Dot(a, a);
}
 
PX_FORCE_INLINE Vec3V V3Normalize(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISFINITELENGTH(a);
    return V3ScaleInv(a, _mm_sqrt_ps(V3Dot(a, a)));
}
 
PX_FORCE_INLINE Vec3V V3NormalizeFast(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISFINITELENGTH(a);
    return V3Scale(a, _mm_rsqrt_ps(V3Dot(a, a)));
}
 
PX_FORCE_INLINE Vec3V V3NormalizeSafe(const Vec3V a, const Vec3V unsafeReturnValue)
{
    ASSERT_ISVALIDVEC3V(a);
    const __m128 eps = V4Eps();
    const __m128 length = V3Length(a);
    const __m128 isGreaterThanZero = FIsGrtr(length, eps);
    return V3Sel(isGreaterThanZero, V3ScaleInv(a, length), unsafeReturnValue);
}
 
PX_FORCE_INLINE Vec3V V3Sel(const BoolV c, const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(_mm_or_ps(_mm_andnot_ps(c, b), _mm_and_ps(c, a)));
    return _mm_or_ps(_mm_andnot_ps(c, b), _mm_and_ps(c, a));
}
 
PX_FORCE_INLINE BoolV V3IsGrtr(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    return _mm_cmpgt_ps(a, b);
}
 
PX_FORCE_INLINE BoolV V3IsGrtrOrEq(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    return _mm_cmpge_ps(a, b);
}
 
PX_FORCE_INLINE BoolV V3IsEq(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    return _mm_cmpeq_ps(a, b);
}
 
PX_FORCE_INLINE Vec3V V3Max(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    return _mm_max_ps(a, b);
}
 
PX_FORCE_INLINE Vec3V V3Min(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    return _mm_min_ps(a, b);
}
 
PX_FORCE_INLINE FloatV V3ExtractMax(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    const __m128 shuf1 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(0, 0, 0, 0));
    const __m128 shuf2 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(1, 1, 1, 1));
    const __m128 shuf3 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(2, 2, 2, 2));
 
    return _mm_max_ps(_mm_max_ps(shuf1, shuf2), shuf3);
}
 
PX_FORCE_INLINE FloatV V3ExtractMin(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
 
    const __m128 shuf1 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(0, 0, 0, 0));
    const __m128 shuf2 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(1, 1, 1, 1));
    const __m128 shuf3 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(2, 2, 2, 2));
 
    return _mm_min_ps(_mm_min_ps(shuf1, shuf2), shuf3);
}
 
// return (a >= 0.0f) ? 1.0f : -1.0f;
PX_FORCE_INLINE Vec3V V3Sign(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    const __m128 zero = V3Zero();
    const __m128 one = V3One();
    const __m128 none = V3Neg(one);
    return V3Sel(V3IsGrtrOrEq(a, zero), one, none);
}
 
PX_FORCE_INLINE Vec3V V3Clamp(const Vec3V a, const Vec3V minV, const Vec3V maxV)
{
    ASSERT_ISVALIDVEC3V(maxV);
    ASSERT_ISVALIDVEC3V(minV);
    return V3Max(V3Min(a, maxV), minV);
}
 
PX_FORCE_INLINE PxU32 V3AllGrtr(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    return internalUnitSSE2Simd::BAllTrue3_R(V4IsGrtr(a, b));
}
 
PX_FORCE_INLINE PxU32 V3AllGrtrOrEq(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    return internalUnitSSE2Simd::BAllTrue3_R(V4IsGrtrOrEq(a, b));
}
 
PX_FORCE_INLINE PxU32 V3AllEq(const Vec3V a, const Vec3V b)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(b);
    return internalUnitSSE2Simd::BAllTrue3_R(V4IsEq(a, b));
}
 
PX_FORCE_INLINE Vec3V V3Round(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
#ifdef __SSE4_2__
    return _mm_round_ps(a, _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
#else
    // return _mm_round_ps(a, 0x0);
    const Vec3V half = V3Load(0.5f);
    const __m128 signBit = _mm_cvtepi32_ps(_mm_srli_epi32(_mm_cvtps_epi32(a), 31));
    const Vec3V aRound = V3Sub(V3Add(a, half), signBit);
    __m128i tmp = _mm_cvttps_epi32(aRound);
    return _mm_cvtepi32_ps(tmp);
#endif
}
 
PX_FORCE_INLINE Vec3V V3Sin(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    // Modulo the range of the given angles such that -XM_2PI <= Angles < XM_2PI
    const Vec4V recipTwoPi = V4LoadA(g_PXReciprocalTwoPi.f);
    const Vec4V twoPi = V4LoadA(g_PXTwoPi.f);
    const Vec3V tmp = V3Scale(a, recipTwoPi);
    const Vec3V b = V3Round(tmp);
    const Vec3V V1 = V3NegScaleSub(b, twoPi, a);
 
    // sin(V) ~= V - V^3 / 3! + V^5 / 5! - V^7 / 7! + V^9 / 9! - V^11 / 11! + V^13 / 13! -
    //           V^15 / 15! + V^17 / 17! - V^19 / 19! + V^21 / 21! - V^23 / 23! (for -PI <= V < PI)
    const Vec3V V2 = V3Mul(V1, V1);
    const Vec3V V3 = V3Mul(V2, V1);
    const Vec3V V5 = V3Mul(V3, V2);
    const Vec3V V7 = V3Mul(V5, V2);
    const Vec3V V9 = V3Mul(V7, V2);
    const Vec3V V11 = V3Mul(V9, V2);
    const Vec3V V13 = V3Mul(V11, V2);
    const Vec3V V15 = V3Mul(V13, V2);
    const Vec3V V17 = V3Mul(V15, V2);
    const Vec3V V19 = V3Mul(V17, V2);
    const Vec3V V21 = V3Mul(V19, V2);
    const Vec3V V23 = V3Mul(V21, V2);
 
    const Vec4V sinCoefficients0 = V4LoadA(g_PXSinCoefficients0.f);
    const Vec4V sinCoefficients1 = V4LoadA(g_PXSinCoefficients1.f);
    const Vec4V sinCoefficients2 = V4LoadA(g_PXSinCoefficients2.f);
 
    const FloatV S1 = V4GetY(sinCoefficients0);
    const FloatV S2 = V4GetZ(sinCoefficients0);
    const FloatV S3 = V4GetW(sinCoefficients0);
    const FloatV S4 = V4GetX(sinCoefficients1);
    const FloatV S5 = V4GetY(sinCoefficients1);
    const FloatV S6 = V4GetZ(sinCoefficients1);
    const FloatV S7 = V4GetW(sinCoefficients1);
    const FloatV S8 = V4GetX(sinCoefficients2);
    const FloatV S9 = V4GetY(sinCoefficients2);
    const FloatV S10 = V4GetZ(sinCoefficients2);
    const FloatV S11 = V4GetW(sinCoefficients2);
 
    Vec3V Result;
    Result = V3ScaleAdd(V3, S1, V1);
    Result = V3ScaleAdd(V5, S2, Result);
    Result = V3ScaleAdd(V7, S3, Result);
    Result = V3ScaleAdd(V9, S4, Result);
    Result = V3ScaleAdd(V11, S5, Result);
    Result = V3ScaleAdd(V13, S6, Result);
    Result = V3ScaleAdd(V15, S7, Result);
    Result = V3ScaleAdd(V17, S8, Result);
    Result = V3ScaleAdd(V19, S9, Result);
    Result = V3ScaleAdd(V21, S10, Result);
    Result = V3ScaleAdd(V23, S11, Result);
 
    ASSERT_ISVALIDVEC3V(Result);
    return Result;
}
 
PX_FORCE_INLINE Vec3V V3Cos(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
 
    // Modulo the range of the given angles such that -XM_2PI <= Angles < XM_2PI
    const Vec4V recipTwoPi = V4LoadA(g_PXReciprocalTwoPi.f);
    const Vec4V twoPi = V4LoadA(g_PXTwoPi.f);
    const Vec3V tmp = V3Scale(a, recipTwoPi);
    const Vec3V b = V3Round(tmp);
    const Vec3V V1 = V3NegScaleSub(b, twoPi, a);
 
    // cos(V) ~= 1 - V^2 / 2! + V^4 / 4! - V^6 / 6! + V^8 / 8! - V^10 / 10! + V^12 / 12! -
    //           V^14 / 14! + V^16 / 16! - V^18 / 18! + V^20 / 20! - V^22 / 22! (for -PI <= V < PI)
    const Vec3V V2 = V3Mul(V1, V1);
    const Vec3V V4 = V3Mul(V2, V2);
    const Vec3V V6 = V3Mul(V4, V2);
    const Vec3V V8 = V3Mul(V4, V4);
    const Vec3V V10 = V3Mul(V6, V4);
    const Vec3V V12 = V3Mul(V6, V6);
    const Vec3V V14 = V3Mul(V8, V6);
    const Vec3V V16 = V3Mul(V8, V8);
    const Vec3V V18 = V3Mul(V10, V8);
    const Vec3V V20 = V3Mul(V10, V10);
    const Vec3V V22 = V3Mul(V12, V10);
 
    const Vec4V cosCoefficients0 = V4LoadA(g_PXCosCoefficients0.f);
    const Vec4V cosCoefficients1 = V4LoadA(g_PXCosCoefficients1.f);
    const Vec4V cosCoefficients2 = V4LoadA(g_PXCosCoefficients2.f);
 
    const FloatV C1 = V4GetY(cosCoefficients0);
    const FloatV C2 = V4GetZ(cosCoefficients0);
    const FloatV C3 = V4GetW(cosCoefficients0);
    const FloatV C4 = V4GetX(cosCoefficients1);
    const FloatV C5 = V4GetY(cosCoefficients1);
    const FloatV C6 = V4GetZ(cosCoefficients1);
    const FloatV C7 = V4GetW(cosCoefficients1);
    const FloatV C8 = V4GetX(cosCoefficients2);
    const FloatV C9 = V4GetY(cosCoefficients2);
    const FloatV C10 = V4GetZ(cosCoefficients2);
    const FloatV C11 = V4GetW(cosCoefficients2);
 
    Vec3V Result;
    Result = V3ScaleAdd(V2, C1, V3One());
    Result = V3ScaleAdd(V4, C2, Result);
    Result = V3ScaleAdd(V6, C3, Result);
    Result = V3ScaleAdd(V8, C4, Result);
    Result = V3ScaleAdd(V10, C5, Result);
    Result = V3ScaleAdd(V12, C6, Result);
    Result = V3ScaleAdd(V14, C7, Result);
    Result = V3ScaleAdd(V16, C8, Result);
    Result = V3ScaleAdd(V18, C9, Result);
    Result = V3ScaleAdd(V20, C10, Result);
    Result = V3ScaleAdd(V22, C11, Result);
 
    ASSERT_ISVALIDVEC3V(Result);
    return Result;
}
 
PX_FORCE_INLINE Vec3V V3PermYZZ(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    return _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 2, 2, 1));
}
 
PX_FORCE_INLINE Vec3V V3PermXYX(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    return _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 0, 1, 0));
}
 
PX_FORCE_INLINE Vec3V V3PermYZX(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    return _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 0, 2, 1));
}
 
PX_FORCE_INLINE Vec3V V3PermZXY(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    return _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 1, 0, 2));
}
 
PX_FORCE_INLINE Vec3V V3PermZZY(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    return _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 1, 2, 2));
}
 
PX_FORCE_INLINE Vec3V V3PermYXX(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
    return _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 0, 0, 1));
}
 
PX_FORCE_INLINE Vec3V V3Perm_Zero_1Z_0Y(const Vec3V v0, const Vec3V v1)
{
    ASSERT_ISVALIDVEC3V(v0);
    ASSERT_ISVALIDVEC3V(v1);
    return _mm_shuffle_ps(v1, v0, _MM_SHUFFLE(3, 1, 2, 3));
}
 
PX_FORCE_INLINE Vec3V V3Perm_0Z_Zero_1X(const Vec3V v0, const Vec3V v1)
{
    ASSERT_ISVALIDVEC3V(v0);
    ASSERT_ISVALIDVEC3V(v1);
    return _mm_shuffle_ps(v0, v1, _MM_SHUFFLE(3, 0, 3, 2));
}
 
PX_FORCE_INLINE Vec3V V3Perm_1Y_0X_Zero(const Vec3V v0, const Vec3V v1)
{
    ASSERT_ISVALIDVEC3V(v0);
    ASSERT_ISVALIDVEC3V(v1);
    // There must be a better way to do this.
    Vec3V v2 = V3Zero();
    FloatV y1 = V3GetY(v1);
    FloatV x0 = V3GetX(v0);
    v2 = V3SetX(v2, y1);
    return V3SetY(v2, x0);
}
 
PX_FORCE_INLINE FloatV V3SumElems(const Vec3V a)
{
    ASSERT_ISVALIDVEC3V(a);
#ifdef __SSE4_2__
    Vec3V r = _mm_hadd_ps(a, a);
    r = _mm_hadd_ps(r, r);
    return r;
#else
    __m128 shuf1 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(0, 0, 0, 0)); // z,y,x,w
    __m128 shuf2 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(1, 1, 1, 1)); // y,x,w,z
    __m128 shuf3 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(2, 2, 2, 2)); // x,w,z,y
    return _mm_add_ps(_mm_add_ps(shuf1, shuf2), shuf3);
#endif
}
 
PX_FORCE_INLINE PxU32 V3OutOfBounds(const Vec3V a, const Vec3V min, const Vec3V max)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(min);
    ASSERT_ISVALIDVEC3V(max);
    const BoolV c = BOr(V3IsGrtr(a, max), V3IsGrtr(min, a));
    return !BAllEqFFFF(c);
}
 
PX_FORCE_INLINE PxU32 V3InBounds(const Vec3V a, const Vec3V min, const Vec3V max)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(min);
    ASSERT_ISVALIDVEC3V(max);
    const BoolV c = BAnd(V3IsGrtrOrEq(a, min), V3IsGrtrOrEq(max, a));
    return BAllEqTTTT(c);
}
 
PX_FORCE_INLINE PxU32 V3OutOfBounds(const Vec3V a, const Vec3V bounds)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(bounds);
    return V3OutOfBounds(a, V3Neg(bounds), bounds);
}
 
PX_FORCE_INLINE PxU32 V3InBounds(const Vec3V a, const Vec3V bounds)
{
    ASSERT_ISVALIDVEC3V(a);
    ASSERT_ISVALIDVEC3V(bounds)
    return V3InBounds(a, V3Neg(bounds), bounds);
}
 
PX_FORCE_INLINE void V3Transpose(Vec3V& col0, Vec3V& col1, Vec3V& col2)
{
    ASSERT_ISVALIDVEC3V(col0);
    ASSERT_ISVALIDVEC3V(col1);
    ASSERT_ISVALIDVEC3V(col2);
 
    const Vec3V col3 = _mm_setzero_ps();
    Vec3V tmp0 = _mm_unpacklo_ps(col0, col1);
    Vec3V tmp2 = _mm_unpacklo_ps(col2, col3);
    Vec3V tmp1 = _mm_unpackhi_ps(col0, col1);
    Vec3V tmp3 = _mm_unpackhi_ps(col2, col3);
    col0 = _mm_movelh_ps(tmp0, tmp2);
    col1 = _mm_movehl_ps(tmp2, tmp0);
    col2 = _mm_movelh_ps(tmp1, tmp3);
}
 
// VEC4V
 
PX_FORCE_INLINE Vec4V V4Splat(const FloatV f)
{
    ASSERT_ISVALIDFLOATV(f);
    // return _mm_shuffle_ps(f, f, _MM_SHUFFLE(0,0,0,0));
    return f;
}
 
PX_FORCE_INLINE Vec4V V4Merge(const FloatV* const floatVArray)
{
    ASSERT_ISVALIDFLOATV(floatVArray[0]);
    ASSERT_ISVALIDFLOATV(floatVArray[1]);
    ASSERT_ISVALIDFLOATV(floatVArray[2]);
    ASSERT_ISVALIDFLOATV(floatVArray[3]);
    const __m128 xw = _mm_move_ss(floatVArray[1], floatVArray[0]); // y, y, y, x
    const __m128 yz = _mm_move_ss(floatVArray[2], floatVArray[3]); // z, z, z, w
    return _mm_shuffle_ps(xw, yz, _MM_SHUFFLE(0, 2, 1, 0));
}
 
PX_FORCE_INLINE Vec4V V4Merge(const FloatVArg x, const FloatVArg y, const FloatVArg z, const FloatVArg w)
{
    ASSERT_ISVALIDFLOATV(x);
    ASSERT_ISVALIDFLOATV(y);
    ASSERT_ISVALIDFLOATV(z);
    ASSERT_ISVALIDFLOATV(w);
    const __m128 xw = _mm_move_ss(y, x); // y, y, y, x
    const __m128 yz = _mm_move_ss(z, w); // z, z, z, w
    return _mm_shuffle_ps(xw, yz, _MM_SHUFFLE(0, 2, 1, 0));
}
 
PX_FORCE_INLINE Vec4V V4MergeW(const Vec4VArg x, const Vec4VArg y, const Vec4VArg z, const Vec4VArg w)
{
    const Vec4V xz = _mm_unpackhi_ps(x, z);
    const Vec4V yw = _mm_unpackhi_ps(y, w);
    return _mm_unpackhi_ps(xz, yw);
}
 
PX_FORCE_INLINE Vec4V V4MergeZ(const Vec4VArg x, const Vec4VArg y, const Vec4VArg z, const Vec4VArg w)
{
    const Vec4V xz = _mm_unpackhi_ps(x, z);
    const Vec4V yw = _mm_unpackhi_ps(y, w);
    return _mm_unpacklo_ps(xz, yw);
}
 
PX_FORCE_INLINE Vec4V V4MergeY(const Vec4VArg x, const Vec4VArg y, const Vec4VArg z, const Vec4VArg w)
{
    const Vec4V xz = _mm_unpacklo_ps(x, z);
    const Vec4V yw = _mm_unpacklo_ps(y, w);
    return _mm_unpackhi_ps(xz, yw);
}
 
PX_FORCE_INLINE Vec4V V4MergeX(const Vec4VArg x, const Vec4VArg y, const Vec4VArg z, const Vec4VArg w)
{
    const Vec4V xz = _mm_unpacklo_ps(x, z);
    const Vec4V yw = _mm_unpacklo_ps(y, w);
    return _mm_unpacklo_ps(xz, yw);
}
 
PX_FORCE_INLINE Vec4V V4UnpackXY(const Vec4VArg a, const Vec4VArg b)
{
    return _mm_unpacklo_ps(a, b);
}
 
PX_FORCE_INLINE Vec4V V4UnpackZW(const Vec4VArg a, const Vec4VArg b)
{
    return _mm_unpackhi_ps(a, b);
}
 
PX_FORCE_INLINE Vec4V V4UnitW()
{
    const PX_ALIGN(16, PxF32) w[4] = { 0.0f, 0.0f, 0.0f, 1.0f };
    const __m128 w128 = _mm_load_ps(w);
    return w128;
}
 
PX_FORCE_INLINE Vec4V V4UnitX()
{
    const PX_ALIGN(16, PxF32) x[4] = { 1.0f, 0.0f, 0.0f, 0.0f };
    const __m128 x128 = _mm_load_ps(x);
    return x128;
}
 
PX_FORCE_INLINE Vec4V V4UnitY()
{
    const PX_ALIGN(16, PxF32) y[4] = { 0.0f, 1.0f, 0.0f, 0.0f };
    const __m128 y128 = _mm_load_ps(y);
    return y128;
}
 
PX_FORCE_INLINE Vec4V V4UnitZ()
{
    const PX_ALIGN(16, PxF32) z[4] = { 0.0f, 0.0f, 1.0f, 0.0f };
    const __m128 z128 = _mm_load_ps(z);
    return z128;
}
 
PX_FORCE_INLINE FloatV V4GetW(const Vec4V f)
{
    return _mm_shuffle_ps(f, f, _MM_SHUFFLE(3, 3, 3, 3));
}
 
PX_FORCE_INLINE FloatV V4GetX(const Vec4V f)
{
    return _mm_shuffle_ps(f, f, _MM_SHUFFLE(0, 0, 0, 0));
}
 
PX_FORCE_INLINE FloatV V4GetY(const Vec4V f)
{
    return _mm_shuffle_ps(f, f, _MM_SHUFFLE(1, 1, 1, 1));
}
 
PX_FORCE_INLINE FloatV V4GetZ(const Vec4V f)
{
    return _mm_shuffle_ps(f, f, _MM_SHUFFLE(2, 2, 2, 2));
}
 
PX_FORCE_INLINE Vec4V V4SetW(const Vec4V v, const FloatV f)
{
    ASSERT_ISVALIDFLOATV(f);
    return V4Sel(BTTTF(), v, f);
}
 
PX_FORCE_INLINE Vec4V V4SetX(const Vec4V v, const FloatV f)
{
    ASSERT_ISVALIDFLOATV(f);
    return V4Sel(BFTTT(), v, f);
}
 
PX_FORCE_INLINE Vec4V V4SetY(const Vec4V v, const FloatV f)
{
    ASSERT_ISVALIDFLOATV(f);
    return V4Sel(BTFTT(), v, f);
}
 
PX_FORCE_INLINE Vec4V V4SetZ(const Vec4V v, const FloatV f)
{
    ASSERT_ISVALIDFLOATV(f);
    return V4Sel(BTTFT(), v, f);
}
 
PX_FORCE_INLINE Vec4V V4ClearW(const Vec4V v)
{
#if !PX_EMSCRIPTEN
    return _mm_and_ps(v, V4LoadA(internalUnitSSE2Simd::gMaskXYZ));
#else
    return _mm_and_ps(v, (VecI32V&)internalUnitSSE2Simd::gMaskXYZ);
#endif
}
 
PX_FORCE_INLINE Vec4V V4PermYXWZ(const Vec4V a)
{
    return _mm_shuffle_ps(a, a, _MM_SHUFFLE(2, 3, 0, 1));
}
 
PX_FORCE_INLINE Vec4V V4PermXZXZ(const Vec4V a)
{
    return _mm_shuffle_ps(a, a, _MM_SHUFFLE(2, 0, 2, 0));
}
 
PX_FORCE_INLINE Vec4V V4PermYWYW(const Vec4V a)
{
    return _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 1, 3, 1));
}
 
PX_FORCE_INLINE Vec4V V4PermYZXW(const Vec4V a)
{
    return _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 0, 2, 1));
}
 
PX_FORCE_INLINE Vec4V V4PermZWXY(const Vec4V a)
{
    return _mm_shuffle_ps(a, a, _MM_SHUFFLE(1, 0, 3, 2));
}
 
template <PxU8 x, PxU8 y, PxU8 z, PxU8 w>
PX_FORCE_INLINE Vec4V V4Perm(const Vec4V a)
{
    return _mm_shuffle_ps(a, a, _MM_SHUFFLE(w, z, y, x));
}
 
PX_FORCE_INLINE Vec4V V4Zero()
{
    return V4Load(0.0f);
}
 
PX_FORCE_INLINE Vec4V V4One()
{
    return V4Load(1.0f);
}
 
PX_FORCE_INLINE Vec4V V4Eps()
{
    return V4Load(PX_EPS_REAL);
}
 
PX_FORCE_INLINE Vec4V V4Neg(const Vec4V f)
{
    return _mm_sub_ps(_mm_setzero_ps(), f);
}
 
PX_FORCE_INLINE Vec4V V4Add(const Vec4V a, const Vec4V b)
{
    return _mm_add_ps(a, b);
}
 
PX_FORCE_INLINE Vec4V V4Sub(const Vec4V a, const Vec4V b)
{
    return _mm_sub_ps(a, b);
}
 
PX_FORCE_INLINE Vec4V V4Scale(const Vec4V a, const FloatV b)
{
    return _mm_mul_ps(a, b);
}
 
PX_FORCE_INLINE Vec4V V4Mul(const Vec4V a, const Vec4V b)
{
    return _mm_mul_ps(a, b);
}
 
PX_FORCE_INLINE Vec4V V4ScaleInv(const Vec4V a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(b);
    return _mm_div_ps(a, b);
}
 
PX_FORCE_INLINE Vec4V V4Div(const Vec4V a, const Vec4V b)
{
    return _mm_div_ps(a, b);
}
 
PX_FORCE_INLINE Vec4V V4ScaleInvFast(const Vec4V a, const FloatV b)
{
    ASSERT_ISVALIDFLOATV(b);
    return _mm_mul_ps(a, _mm_rcp_ps(b));
}
 
PX_FORCE_INLINE Vec4V V4DivFast(const Vec4V a, const Vec4V b)
{
    return _mm_mul_ps(a, _mm_rcp_ps(b));
}
 
PX_FORCE_INLINE Vec4V V4Recip(const Vec4V a)
{
    return _mm_div_ps(V4One(), a);
}
 
PX_FORCE_INLINE Vec4V V4RecipFast(const Vec4V a)
{
    return _mm_rcp_ps(a);
}
 
PX_FORCE_INLINE Vec4V V4Rsqrt(const Vec4V a)
{
    return _mm_div_ps(V4One(), _mm_sqrt_ps(a));
}
 
PX_FORCE_INLINE Vec4V V4RsqrtFast(const Vec4V a)
{
    return _mm_rsqrt_ps(a);
}
 
PX_FORCE_INLINE Vec4V V4Sqrt(const Vec4V a)
{
    return _mm_sqrt_ps(a);
}
 
PX_FORCE_INLINE Vec4V V4ScaleAdd(const Vec4V a, const FloatV b, const Vec4V c)
{
    ASSERT_ISVALIDFLOATV(b);
    return V4Add(V4Scale(a, b), c);
}
 
PX_FORCE_INLINE Vec4V V4NegScaleSub(const Vec4V a, const FloatV b, const Vec4V c)
{
    ASSERT_ISVALIDFLOATV(b);
    return V4Sub(c, V4Scale(a, b));
}
 
PX_FORCE_INLINE Vec4V V4MulAdd(const Vec4V a, const Vec4V b, const Vec4V c)
{
    return V4Add(V4Mul(a, b), c);
}
 
PX_FORCE_INLINE Vec4V V4NegMulSub(const Vec4V a, const Vec4V b, const Vec4V c)
{
    return V4Sub(c, V4Mul(a, b));
}
 
PX_FORCE_INLINE Vec4V V4Abs(const Vec4V a)
{
    return V4Max(a, V4Neg(a));
}
 
PX_FORCE_INLINE FloatV V4SumElements(const Vec4V a)
{
#ifdef __SSE4_2__
    Vec4V r = _mm_hadd_ps(a, a);
    r = _mm_hadd_ps(r, r);
    return r;
#else
    const Vec4V xy = V4UnpackXY(a, a);                                        // x,x,y,y
    const Vec4V zw = V4UnpackZW(a, a);                                        // z,z,w,w
    const Vec4V xz_yw = V4Add(xy, zw);                                        // x+z,x+z,y+w,y+w
    const FloatV xz = V4GetX(xz_yw);                                          // x+z
    const FloatV yw = V4GetZ(xz_yw);                                          // y+w
    return FAdd(xz, yw);                                                      // sum
#endif
}
 
PX_FORCE_INLINE FloatV V4Dot(const Vec4V a, const Vec4V b)
{
#ifdef __SSE4_2__
    return _mm_dp_ps(a, b, 0xff);
#else
    //const __m128 dot1 = _mm_mul_ps(a, b);                                     // x,y,z,w
    //const __m128 shuf1 = _mm_shuffle_ps(dot1, dot1, _MM_SHUFFLE(2, 1, 0, 3)); // w,x,y,z
    //const __m128 shuf2 = _mm_shuffle_ps(dot1, dot1, _MM_SHUFFLE(1, 0, 3, 2)); // z,w,x,y
    //const __m128 shuf3 = _mm_shuffle_ps(dot1, dot1, _MM_SHUFFLE(0, 3, 2, 1)); // y,z,w,x
    //return _mm_add_ps(_mm_add_ps(shuf2, shuf3), _mm_add_ps(dot1, shuf1));
 
    // aw*bw | az*bz | ay*by | ax*bx
    const __m128 t0 = _mm_mul_ps(a, b);
    // ay*by | ax*bx | aw*bw | az*bz
    const __m128 t1 = _mm_shuffle_ps(t0, t0, _MM_SHUFFLE(1, 0, 3, 2));
    // ay*by + aw*bw | ax*bx + az*bz | aw*bw + ay*by | az*bz + ax*bx
    const __m128 t2 = _mm_add_ps(t0, t1);
    // ax*bx + az*bz | ay*by + aw*bw | az*bz + ax*bx | aw*bw + ay*by
    const __m128 t3 = _mm_shuffle_ps(t2, t2, _MM_SHUFFLE(2, 3, 0, 1));
    // ax*bx + az*bz + ay*by + aw*bw
    return _mm_add_ps(t3, t2);
#endif
}
 
PX_FORCE_INLINE FloatV V4Dot3(const Vec4V a, const Vec4V b)
{
#ifdef __SSE4_2__
    return _mm_dp_ps(a, b, 0x7f);
#else
    const __m128 dot1 = _mm_mul_ps(a, b);                                     // w,z,y,x
    const __m128 shuf1 = _mm_shuffle_ps(dot1, dot1, _MM_SHUFFLE(0, 0, 0, 0)); // z,y,x,w
    const __m128 shuf2 = _mm_shuffle_ps(dot1, dot1, _MM_SHUFFLE(1, 1, 1, 1)); // y,x,w,z
    const __m128 shuf3 = _mm_shuffle_ps(dot1, dot1, _MM_SHUFFLE(2, 2, 2, 2)); // x,w,z,y
    return _mm_add_ps(_mm_add_ps(shuf1, shuf2), shuf3);
#endif
}
 
PX_FORCE_INLINE Vec4V V4Cross(const Vec4V a, const Vec4V b)
{
    const __m128 r1 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 1, 0, 2)); // z,x,y,w
    const __m128 r2 = _mm_shuffle_ps(b, b, _MM_SHUFFLE(3, 0, 2, 1)); // y,z,x,w
    const __m128 l1 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(3, 0, 2, 1)); // y,z,x,w
    const __m128 l2 = _mm_shuffle_ps(b, b, _MM_SHUFFLE(3, 1, 0, 2)); // z,x,y,w
    return _mm_sub_ps(_mm_mul_ps(l1, l2), _mm_mul_ps(r1, r2));
}
 
PX_FORCE_INLINE FloatV V4Length(const Vec4V a)
{
    return _mm_sqrt_ps(V4Dot(a, a));
}
 
PX_FORCE_INLINE FloatV V4LengthSq(const Vec4V a)
{
    return V4Dot(a, a);
}
 
PX_FORCE_INLINE Vec4V V4Normalize(const Vec4V a)
{
    ASSERT_ISFINITELENGTH(a);
    return V4ScaleInv(a, _mm_sqrt_ps(V4Dot(a, a)));
}
 
PX_FORCE_INLINE Vec4V V4NormalizeFast(const Vec4V a)
{
    ASSERT_ISFINITELENGTH(a);
    return V4ScaleInvFast(a, _mm_sqrt_ps(V4Dot(a, a)));
}
 
PX_FORCE_INLINE Vec4V V4NormalizeSafe(const Vec4V a, const Vec3V unsafeReturnValue)
{
    const __m128 eps = V3Eps();
    const __m128 length = V4Length(a);
    const __m128 isGreaterThanZero = V4IsGrtr(length, eps);
    return V4Sel(isGreaterThanZero, V4ScaleInv(a, length), unsafeReturnValue);
}
 
PX_FORCE_INLINE BoolV V4IsEqU32(const VecU32V a, const VecU32V b)
{
    return m128_I2F(_mm_cmpeq_epi32(m128_F2I(a), m128_F2I(b)));
}
 
PX_FORCE_INLINE Vec4V V4Sel(const BoolV c, const Vec4V a, const Vec4V b)
{
    return _mm_or_ps(_mm_andnot_ps(c, b), _mm_and_ps(c, a));
}
 
PX_FORCE_INLINE BoolV V4IsGrtr(const Vec4V a, const Vec4V b)
{
    return _mm_cmpgt_ps(a, b);
}
 
PX_FORCE_INLINE BoolV V4IsGrtrOrEq(const Vec4V a, const Vec4V b)
{
    return _mm_cmpge_ps(a, b);
}
 
PX_FORCE_INLINE BoolV V4IsEq(const Vec4V a, const Vec4V b)
{
    return _mm_cmpeq_ps(a, b);
}
 
PX_FORCE_INLINE Vec4V V4Max(const Vec4V a, const Vec4V b)
{
    return _mm_max_ps(a, b);
}
 
PX_FORCE_INLINE Vec4V V4Min(const Vec4V a, const Vec4V b)
{
    return _mm_min_ps(a, b);
}
 
PX_FORCE_INLINE FloatV V4ExtractMax(const Vec4V a)
{
    const __m128 shuf1 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(2, 1, 0, 3));
    const __m128 shuf2 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(1, 0, 3, 2));
    const __m128 shuf3 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(0, 3, 2, 1));
 
    return _mm_max_ps(_mm_max_ps(a, shuf1), _mm_max_ps(shuf2, shuf3));
}
 
PX_FORCE_INLINE FloatV V4ExtractMin(const Vec4V a)
{
    const __m128 shuf1 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(2, 1, 0, 3));
    const __m128 shuf2 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(1, 0, 3, 2));
    const __m128 shuf3 = _mm_shuffle_ps(a, a, _MM_SHUFFLE(0, 3, 2, 1));
 
    return _mm_min_ps(_mm_min_ps(a, shuf1), _mm_min_ps(shuf2, shuf3));
}
 
PX_FORCE_INLINE Vec4V V4Clamp(const Vec4V a, const Vec4V minV, const Vec4V maxV)
{
    return V4Max(V4Min(a, maxV), minV);
}
 
PX_FORCE_INLINE PxU32 V4AllGrtr(const Vec4V a, const Vec4V b)
{
    return internalUnitSSE2Simd::BAllTrue4_R(V4IsGrtr(a, b));
}
 
PX_FORCE_INLINE PxU32 V4AllGrtrOrEq(const Vec4V a, const Vec4V b)
{
    return internalUnitSSE2Simd::BAllTrue4_R(V4IsGrtrOrEq(a, b));
}
 
PX_FORCE_INLINE PxU32 V4AllGrtrOrEq3(const Vec4V a, const Vec4V b)
{
    return internalUnitSSE2Simd::BAllTrue3_R(V4IsGrtrOrEq(a, b));
}
 
PX_FORCE_INLINE PxU32 V4AllEq(const Vec4V a, const Vec4V b)
{
    return internalUnitSSE2Simd::BAllTrue4_R(V4IsEq(a, b));
}
 
PX_FORCE_INLINE PxU32 V4AnyGrtr3(const Vec4V a, const Vec4V b)
{
    return internalUnitSSE2Simd::BAnyTrue3_R(V4IsGrtr(a, b));
}
 
PX_FORCE_INLINE Vec4V V4Round(const Vec4V a)
{
#ifdef __SSE4_2__
    return _mm_round_ps(a, _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
#else
    // return _mm_round_ps(a, 0x0);
    const Vec4V half = V4Load(0.5f);
    const __m128 signBit = _mm_cvtepi32_ps(_mm_srli_epi32(_mm_cvtps_epi32(a), 31));
    const Vec4V aRound = V4Sub(V4Add(a, half), signBit);
    __m128i tmp = _mm_cvttps_epi32(aRound);
    return _mm_cvtepi32_ps(tmp);
#endif
}
 
PX_FORCE_INLINE Vec4V V4Sin(const Vec4V a)
{
    const Vec4V recipTwoPi = V4LoadA(g_PXReciprocalTwoPi.f);
    const Vec4V twoPi = V4LoadA(g_PXTwoPi.f);
    const Vec4V tmp = V4Mul(a, recipTwoPi);
    const Vec4V b = V4Round(tmp);
    const Vec4V V1 = V4NegMulSub(twoPi, b, a);
 
    // sin(V) ~= V - V^3 / 3! + V^5 / 5! - V^7 / 7! + V^9 / 9! - V^11 / 11! + V^13 / 13! -
    //           V^15 / 15! + V^17 / 17! - V^19 / 19! + V^21 / 21! - V^23 / 23! (for -PI <= V < PI)
    const Vec4V V2 = V4Mul(V1, V1);
    const Vec4V V3 = V4Mul(V2, V1);
    const Vec4V V5 = V4Mul(V3, V2);
    const Vec4V V7 = V4Mul(V5, V2);
    const Vec4V V9 = V4Mul(V7, V2);
    const Vec4V V11 = V4Mul(V9, V2);
    const Vec4V V13 = V4Mul(V11, V2);
    const Vec4V V15 = V4Mul(V13, V2);
    const Vec4V V17 = V4Mul(V15, V2);
    const Vec4V V19 = V4Mul(V17, V2);
    const Vec4V V21 = V4Mul(V19, V2);
    const Vec4V V23 = V4Mul(V21, V2);
 
    const Vec4V sinCoefficients0 = V4LoadA(g_PXSinCoefficients0.f);
    const Vec4V sinCoefficients1 = V4LoadA(g_PXSinCoefficients1.f);
    const Vec4V sinCoefficients2 = V4LoadA(g_PXSinCoefficients2.f);
 
    const FloatV S1 = V4GetY(sinCoefficients0);
    const FloatV S2 = V4GetZ(sinCoefficients0);
    const FloatV S3 = V4GetW(sinCoefficients0);
    const FloatV S4 = V4GetX(sinCoefficients1);
    const FloatV S5 = V4GetY(sinCoefficients1);
    const FloatV S6 = V4GetZ(sinCoefficients1);
    const FloatV S7 = V4GetW(sinCoefficients1);
    const FloatV S8 = V4GetX(sinCoefficients2);
    const FloatV S9 = V4GetY(sinCoefficients2);
    const FloatV S10 = V4GetZ(sinCoefficients2);
    const FloatV S11 = V4GetW(sinCoefficients2);
 
    Vec4V Result;
    Result = V4MulAdd(S1, V3, V1);
    Result = V4MulAdd(S2, V5, Result);
    Result = V4MulAdd(S3, V7, Result);
    Result = V4MulAdd(S4, V9, Result);
    Result = V4MulAdd(S5, V11, Result);
    Result = V4MulAdd(S6, V13, Result);
    Result = V4MulAdd(S7, V15, Result);
    Result = V4MulAdd(S8, V17, Result);
    Result = V4MulAdd(S9, V19, Result);
    Result = V4MulAdd(S10, V21, Result);
    Result = V4MulAdd(S11, V23, Result);
 
    return Result;
}
 
PX_FORCE_INLINE Vec4V V4Cos(const Vec4V a)
{
    const Vec4V recipTwoPi = V4LoadA(g_PXReciprocalTwoPi.f);
    const Vec4V twoPi = V4LoadA(g_PXTwoPi.f);
    const Vec4V tmp = V4Mul(a, recipTwoPi);
    const Vec4V b = V4Round(tmp);
    const Vec4V V1 = V4NegMulSub(twoPi, b, a);
 
    // cos(V) ~= 1 - V^2 / 2! + V^4 / 4! - V^6 / 6! + V^8 / 8! - V^10 / 10! + V^12 / 12! -
    //           V^14 / 14! + V^16 / 16! - V^18 / 18! + V^20 / 20! - V^22 / 22! (for -PI <= V < PI)
    const Vec4V V2 = V4Mul(V1, V1);
    const Vec4V V4 = V4Mul(V2, V2);
    const Vec4V V6 = V4Mul(V4, V2);
    const Vec4V V8 = V4Mul(V4, V4);
    const Vec4V V10 = V4Mul(V6, V4);
    const Vec4V V12 = V4Mul(V6, V6);
    const Vec4V V14 = V4Mul(V8, V6);
    const Vec4V V16 = V4Mul(V8, V8);
    const Vec4V V18 = V4Mul(V10, V8);
    const Vec4V V20 = V4Mul(V10, V10);
    const Vec4V V22 = V4Mul(V12, V10);
 
    const Vec4V cosCoefficients0 = V4LoadA(g_PXCosCoefficients0.f);
    const Vec4V cosCoefficients1 = V4LoadA(g_PXCosCoefficients1.f);
    const Vec4V cosCoefficients2 = V4LoadA(g_PXCosCoefficients2.f);
 
    const FloatV C1 = V4GetY(cosCoefficients0);
    const FloatV C2 = V4GetZ(cosCoefficients0);
    const FloatV C3 = V4GetW(cosCoefficients0);
    const FloatV C4 = V4GetX(cosCoefficients1);
    const FloatV C5 = V4GetY(cosCoefficients1);
    const FloatV C6 = V4GetZ(cosCoefficients1);
    const FloatV C7 = V4GetW(cosCoefficients1);
    const FloatV C8 = V4GetX(cosCoefficients2);
    const FloatV C9 = V4GetY(cosCoefficients2);
    const FloatV C10 = V4GetZ(cosCoefficients2);
    const FloatV C11 = V4GetW(cosCoefficients2);
 
    Vec4V Result;
    Result = V4MulAdd(C1, V2, V4One());
    Result = V4MulAdd(C2, V4, Result);
    Result = V4MulAdd(C3, V6, Result);
    Result = V4MulAdd(C4, V8, Result);
    Result = V4MulAdd(C5, V10, Result);
    Result = V4MulAdd(C6, V12, Result);
    Result = V4MulAdd(C7, V14, Result);
    Result = V4MulAdd(C8, V16, Result);
    Result = V4MulAdd(C9, V18, Result);
    Result = V4MulAdd(C10, V20, Result);
    Result = V4MulAdd(C11, V22, Result);
 
    return Result;
}
 
PX_FORCE_INLINE void V4Transpose(Vec4V& col0, Vec4V& col1, Vec4V& col2, Vec4V& col3)
{
    Vec4V tmp0 = _mm_unpacklo_ps(col0, col1);
    Vec4V tmp2 = _mm_unpacklo_ps(col2, col3);
    Vec4V tmp1 = _mm_unpackhi_ps(col0, col1);
    Vec4V tmp3 = _mm_unpackhi_ps(col2, col3);
    col0 = _mm_movelh_ps(tmp0, tmp2);
    col1 = _mm_movehl_ps(tmp2, tmp0);
    col2 = _mm_movelh_ps(tmp1, tmp3);
    col3 = _mm_movehl_ps(tmp3, tmp1);
}
 
// BoolV
 
PX_FORCE_INLINE BoolV BFFFF()
{
    return _mm_setzero_ps();
}
 
PX_FORCE_INLINE BoolV BFFFT()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0,0,0,0xFFFFFFFF};
    const __m128 ffft=_mm_load_ps((float*)&f);
    return ffft;*/
    return m128_I2F(_mm_set_epi32(-1, 0, 0, 0));
}
 
PX_FORCE_INLINE BoolV BFFTF()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0,0,0xFFFFFFFF,0};
    const __m128 fftf=_mm_load_ps((float*)&f);
    return fftf;*/
    return m128_I2F(_mm_set_epi32(0, -1, 0, 0));
}
 
PX_FORCE_INLINE BoolV BFFTT()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0,0,0xFFFFFFFF,0xFFFFFFFF};
    const __m128 fftt=_mm_load_ps((float*)&f);
    return fftt;*/
    return m128_I2F(_mm_set_epi32(-1, -1, 0, 0));
}
 
PX_FORCE_INLINE BoolV BFTFF()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0,0xFFFFFFFF,0,0};
    const __m128 ftff=_mm_load_ps((float*)&f);
    return ftff;*/
    return m128_I2F(_mm_set_epi32(0, 0, -1, 0));
}
 
PX_FORCE_INLINE BoolV BFTFT()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0,0xFFFFFFFF,0,0xFFFFFFFF};
    const __m128 ftft=_mm_load_ps((float*)&f);
    return ftft;*/
    return m128_I2F(_mm_set_epi32(-1, 0, -1, 0));
}
 
PX_FORCE_INLINE BoolV BFTTF()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0,0xFFFFFFFF,0xFFFFFFFF,0};
    const __m128 fttf=_mm_load_ps((float*)&f);
    return fttf;*/
    return m128_I2F(_mm_set_epi32(0, -1, -1, 0));
}
 
PX_FORCE_INLINE BoolV BFTTT()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF};
    const __m128 fttt=_mm_load_ps((float*)&f);
    return fttt;*/
    return m128_I2F(_mm_set_epi32(-1, -1, -1, 0));
}
 
PX_FORCE_INLINE BoolV BTFFF()
{
    // const PX_ALIGN(16, PxU32 f[4])={0xFFFFFFFF,0,0,0};
    // const __m128 tfff=_mm_load_ps((float*)&f);
    // return tfff;
    return m128_I2F(_mm_set_epi32(0, 0, 0, -1));
}
 
PX_FORCE_INLINE BoolV BTFFT()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0xFFFFFFFF,0,0,0xFFFFFFFF};
    const __m128 tfft=_mm_load_ps((float*)&f);
    return tfft;*/
    return m128_I2F(_mm_set_epi32(-1, 0, 0, -1));
}
 
PX_FORCE_INLINE BoolV BTFTF()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0xFFFFFFFF,0,0xFFFFFFFF,0};
    const __m128 tftf=_mm_load_ps((float*)&f);
    return tftf;*/
    return m128_I2F(_mm_set_epi32(0, -1, 0, -1));
}
 
PX_FORCE_INLINE BoolV BTFTT()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0xFFFFFFFF,0,0xFFFFFFFF,0xFFFFFFFF};
    const __m128 tftt=_mm_load_ps((float*)&f);
    return tftt;*/
    return m128_I2F(_mm_set_epi32(-1, -1, 0, -1));
}
 
PX_FORCE_INLINE BoolV BTTFF()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0xFFFFFFFF,0xFFFFFFFF,0,0};
    const __m128 ttff=_mm_load_ps((float*)&f);
    return ttff;*/
    return m128_I2F(_mm_set_epi32(0, 0, -1, -1));
}
 
PX_FORCE_INLINE BoolV BTTFT()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0xFFFFFFFF,0xFFFFFFFF,0,0xFFFFFFFF};
    const __m128 ttft=_mm_load_ps((float*)&f);
    return ttft;*/
    return m128_I2F(_mm_set_epi32(-1, 0, -1, -1));
}
 
PX_FORCE_INLINE BoolV BTTTF()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0};
    const __m128 tttf=_mm_load_ps((float*)&f);
    return tttf;*/
    return m128_I2F(_mm_set_epi32(0, -1, -1, -1));
}
 
PX_FORCE_INLINE BoolV BTTTT()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF};
    const __m128 tttt=_mm_load_ps((float*)&f);
    return tttt;*/
    return m128_I2F(_mm_set_epi32(-1, -1, -1, -1));
}
 
PX_FORCE_INLINE BoolV BXMask()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0xFFFFFFFF,0,0,0};
    const __m128 tfff=_mm_load_ps((float*)&f);
    return tfff;*/
    return m128_I2F(_mm_set_epi32(0, 0, 0, -1));
}
 
PX_FORCE_INLINE BoolV BYMask()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0,0xFFFFFFFF,0,0};
    const __m128 ftff=_mm_load_ps((float*)&f);
    return ftff;*/
    return m128_I2F(_mm_set_epi32(0, 0, -1, 0));
}
 
PX_FORCE_INLINE BoolV BZMask()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0,0,0xFFFFFFFF,0};
    const __m128 fftf=_mm_load_ps((float*)&f);
    return fftf;*/
    return m128_I2F(_mm_set_epi32(0, -1, 0, 0));
}
 
PX_FORCE_INLINE BoolV BWMask()
{
    /*const PX_ALIGN(16, PxU32 f[4])={0,0,0,0xFFFFFFFF};
    const __m128 ffft=_mm_load_ps((float*)&f);
    return ffft;*/
    return m128_I2F(_mm_set_epi32(-1, 0, 0, 0));
}
 
PX_FORCE_INLINE BoolV BGetX(const BoolV f)
{
    return _mm_shuffle_ps(f, f, _MM_SHUFFLE(0, 0, 0, 0));
}
 
PX_FORCE_INLINE BoolV BGetY(const BoolV f)
{
    return _mm_shuffle_ps(f, f, _MM_SHUFFLE(1, 1, 1, 1));
}
 
PX_FORCE_INLINE BoolV BGetZ(const BoolV f)
{
    return _mm_shuffle_ps(f, f, _MM_SHUFFLE(2, 2, 2, 2));
}
 
PX_FORCE_INLINE BoolV BGetW(const BoolV f)
{
    return _mm_shuffle_ps(f, f, _MM_SHUFFLE(3, 3, 3, 3));
}
 
PX_FORCE_INLINE BoolV BSetX(const BoolV v, const BoolV f)
{
    return V4Sel(BFTTT(), v, f);
}
 
PX_FORCE_INLINE BoolV BSetY(const BoolV v, const BoolV f)
{
    return V4Sel(BTFTT(), v, f);
}
 
PX_FORCE_INLINE BoolV BSetZ(const BoolV v, const BoolV f)
{
    return V4Sel(BTTFT(), v, f);
}
 
PX_FORCE_INLINE BoolV BSetW(const BoolV v, const BoolV f)
{
    return V4Sel(BTTTF(), v, f);
}
 
PX_FORCE_INLINE BoolV BAnd(const BoolV a, const BoolV b)
{
    return _mm_and_ps(a, b);
}
 
PX_FORCE_INLINE BoolV BNot(const BoolV a)
{
    const BoolV bAllTrue(BTTTT());
    return _mm_xor_ps(a, bAllTrue);
}
 
PX_FORCE_INLINE BoolV BAndNot(const BoolV a, const BoolV b)
{
    return _mm_andnot_ps(b, a);
}
 
PX_FORCE_INLINE BoolV BOr(const BoolV a, const BoolV b)
{
    return _mm_or_ps(a, b);
}
 
PX_FORCE_INLINE BoolV BAllTrue4(const BoolV a)
{
    const BoolV bTmp =
        _mm_and_ps(_mm_shuffle_ps(a, a, _MM_SHUFFLE(0, 1, 0, 1)), _mm_shuffle_ps(a, a, _MM_SHUFFLE(2, 3, 2, 3)));
    return _mm_and_ps(_mm_shuffle_ps(bTmp, bTmp, _MM_SHUFFLE(0, 0, 0, 0)),
                      _mm_shuffle_ps(bTmp, bTmp, _MM_SHUFFLE(1, 1, 1, 1)));
}
 
PX_FORCE_INLINE BoolV BAnyTrue4(const BoolV a)
{
    const BoolV bTmp =
        _mm_or_ps(_mm_shuffle_ps(a, a, _MM_SHUFFLE(0, 1, 0, 1)), _mm_shuffle_ps(a, a, _MM_SHUFFLE(2, 3, 2, 3)));
    return _mm_or_ps(_mm_shuffle_ps(bTmp, bTmp, _MM_SHUFFLE(0, 0, 0, 0)),
                     _mm_shuffle_ps(bTmp, bTmp, _MM_SHUFFLE(1, 1, 1, 1)));
}
 
PX_FORCE_INLINE BoolV BAllTrue3(const BoolV a)
{
    const BoolV bTmp =
        _mm_and_ps(_mm_shuffle_ps(a, a, _MM_SHUFFLE(0, 1, 0, 1)), _mm_shuffle_ps(a, a, _MM_SHUFFLE(2, 2, 2, 2)));
    return _mm_and_ps(_mm_shuffle_ps(bTmp, bTmp, _MM_SHUFFLE(0, 0, 0, 0)),
                      _mm_shuffle_ps(bTmp, bTmp, _MM_SHUFFLE(1, 1, 1, 1)));
}
 
PX_FORCE_INLINE BoolV BAnyTrue3(const BoolV a)
{
    const BoolV bTmp =
        _mm_or_ps(_mm_shuffle_ps(a, a, _MM_SHUFFLE(0, 1, 0, 1)), _mm_shuffle_ps(a, a, _MM_SHUFFLE(2, 2, 2, 2)));
    return _mm_or_ps(_mm_shuffle_ps(bTmp, bTmp, _MM_SHUFFLE(0, 0, 0, 0)),
                     _mm_shuffle_ps(bTmp, bTmp, _MM_SHUFFLE(1, 1, 1, 1)));
}
 
PX_FORCE_INLINE PxU32 BAllEq(const BoolV a, const BoolV b)
{
    const BoolV bTest = m128_I2F(_mm_cmpeq_epi32(m128_F2I(a), m128_F2I(b)));
    return internalUnitSSE2Simd::BAllTrue4_R(bTest);
}
 
PX_FORCE_INLINE PxU32 BAllEqTTTT(const BoolV a)
{
    return PxU32(_mm_movemask_ps(a)==15);
}
 
PX_FORCE_INLINE PxU32 BAllEqFFFF(const BoolV a)
{
    return PxU32(_mm_movemask_ps(a)==0);
}
 
PX_FORCE_INLINE PxU32 BGetBitMask(const BoolV a)
{
    return PxU32(_mm_movemask_ps(a));
}
 
// MAT33V
 
PX_FORCE_INLINE Vec3V M33MulV3(const Mat33V& a, const Vec3V b)
{
    const FloatV x = V3GetX(b);
    const FloatV y = V3GetY(b);
    const FloatV z = V3GetZ(b);
    const Vec3V v0 = V3Scale(a.col0, x);
    const Vec3V v1 = V3Scale(a.col1, y);
    const Vec3V v2 = V3Scale(a.col2, z);
    const Vec3V v0PlusV1 = V3Add(v0, v1);
    return V3Add(v0PlusV1, v2);
}
 
PX_FORCE_INLINE Vec3V M33TrnspsMulV3(const Mat33V& a, const Vec3V b)
{
    const FloatV x = V3Dot(a.col0, b);
    const FloatV y = V3Dot(a.col1, b);
    const FloatV z = V3Dot(a.col2, b);
    return V3Merge(x, y, z);
}
 
PX_FORCE_INLINE Vec3V M33MulV3AddV3(const Mat33V& A, const Vec3V b, const Vec3V c)
{
    const FloatV x = V3GetX(b);
    const FloatV y = V3GetY(b);
    const FloatV z = V3GetZ(b);
    Vec3V result = V3ScaleAdd(A.col0, x, c);
    result = V3ScaleAdd(A.col1, y, result);
    return V3ScaleAdd(A.col2, z, result);
}
 
PX_FORCE_INLINE Mat33V M33MulM33(const Mat33V& a, const Mat33V& b)
{
    return Mat33V(M33MulV3(a, b.col0), M33MulV3(a, b.col1), M33MulV3(a, b.col2));
}
 
PX_FORCE_INLINE Mat33V M33Add(const Mat33V& a, const Mat33V& b)
{
    return Mat33V(V3Add(a.col0, b.col0), V3Add(a.col1, b.col1), V3Add(a.col2, b.col2));
}
 
PX_FORCE_INLINE Mat33V M33Scale(const Mat33V& a, const FloatV& b)
{
    return Mat33V(V3Scale(a.col0, b), V3Scale(a.col1, b), V3Scale(a.col2, b));
}
 
PX_FORCE_INLINE Mat33V M33Inverse(const Mat33V& a)
{
    const BoolV tfft = BTFFT();
    const BoolV tttf = BTTTF();
    const FloatV zero = FZero();
    const Vec3V cross01 = V3Cross(a.col0, a.col1);
    const Vec3V cross12 = V3Cross(a.col1, a.col2);
    const Vec3V cross20 = V3Cross(a.col2, a.col0);
    const FloatV dot = V3Dot(cross01, a.col2);
    const FloatV invDet = _mm_rcp_ps(dot);
    const Vec3V mergeh = _mm_unpacklo_ps(cross12, cross01);
    const Vec3V mergel = _mm_unpackhi_ps(cross12, cross01);
    Vec3V colInv0 = _mm_unpacklo_ps(mergeh, cross20);
    colInv0 = _mm_or_ps(_mm_andnot_ps(tttf, zero), _mm_and_ps(tttf, colInv0));
    const Vec3V zppd = _mm_shuffle_ps(mergeh, cross20, _MM_SHUFFLE(3, 0, 0, 2));
    const Vec3V pbwp = _mm_shuffle_ps(cross20, mergeh, _MM_SHUFFLE(3, 3, 1, 0));
    const Vec3V colInv1 = _mm_or_ps(_mm_andnot_ps(BTFFT(), pbwp), _mm_and_ps(BTFFT(), zppd));
    const Vec3V xppd = _mm_shuffle_ps(mergel, cross20, _MM_SHUFFLE(3, 0, 0, 0));
    const Vec3V pcyp = _mm_shuffle_ps(cross20, mergel, _MM_SHUFFLE(3, 1, 2, 0));
    const Vec3V colInv2 = _mm_or_ps(_mm_andnot_ps(tfft, pcyp), _mm_and_ps(tfft, xppd));
 
    return Mat33V(_mm_mul_ps(colInv0, invDet), _mm_mul_ps(colInv1, invDet), _mm_mul_ps(colInv2, invDet));
}
 
PX_FORCE_INLINE Mat33V M33Trnsps(const Mat33V& a)
{
    return Mat33V(V3Merge(V3GetX(a.col0), V3GetX(a.col1), V3GetX(a.col2)),
                  V3Merge(V3GetY(a.col0), V3GetY(a.col1), V3GetY(a.col2)),
                  V3Merge(V3GetZ(a.col0), V3GetZ(a.col1), V3GetZ(a.col2)));
}
 
PX_FORCE_INLINE Mat33V M33Identity()
{
    return Mat33V(V3UnitX(), V3UnitY(), V3UnitZ());
}
 
PX_FORCE_INLINE Mat33V M33Sub(const Mat33V& a, const Mat33V& b)
{
    return Mat33V(V3Sub(a.col0, b.col0), V3Sub(a.col1, b.col1), V3Sub(a.col2, b.col2));
}
 
PX_FORCE_INLINE Mat33V M33Neg(const Mat33V& a)
{
    return Mat33V(V3Neg(a.col0), V3Neg(a.col1), V3Neg(a.col2));
}
 
PX_FORCE_INLINE Mat33V M33Abs(const Mat33V& a)
{
    return Mat33V(V3Abs(a.col0), V3Abs(a.col1), V3Abs(a.col2));
}
 
PX_FORCE_INLINE Mat33V PromoteVec3V(const Vec3V v)
{
    const BoolV bTFFF = BTFFF();
    const BoolV bFTFF = BFTFF();
    const BoolV bFFTF = BTFTF();
 
    const Vec3V zero = V3Zero();
 
    return Mat33V(V3Sel(bTFFF, v, zero), V3Sel(bFTFF, v, zero), V3Sel(bFFTF, v, zero));
}
 
PX_FORCE_INLINE Mat33V M33Diagonal(const Vec3VArg d)
{
    const FloatV x = V3Mul(V3UnitX(), d);
    const FloatV y = V3Mul(V3UnitY(), d);
    const FloatV z = V3Mul(V3UnitZ(), d);
    return Mat33V(x, y, z);
}
 
// MAT34V
 
PX_FORCE_INLINE Vec3V M34MulV3(const Mat34V& a, const Vec3V b)
{
    const FloatV x = V3GetX(b);
    const FloatV y = V3GetY(b);
    const FloatV z = V3GetZ(b);
    const Vec3V v0 = V3Scale(a.col0, x);
    const Vec3V v1 = V3Scale(a.col1, y);
    const Vec3V v2 = V3Scale(a.col2, z);
    const Vec3V v0PlusV1 = V3Add(v0, v1);
    const Vec3V v0PlusV1Plusv2 = V3Add(v0PlusV1, v2);
    return V3Add(v0PlusV1Plusv2, a.col3);
}
 
PX_FORCE_INLINE Vec3V M34Mul33V3(const Mat34V& a, const Vec3V b)
{
    const FloatV x = V3GetX(b);
    const FloatV y = V3GetY(b);
    const FloatV z = V3GetZ(b);
    const Vec3V v0 = V3Scale(a.col0, x);
    const Vec3V v1 = V3Scale(a.col1, y);
    const Vec3V v2 = V3Scale(a.col2, z);
    const Vec3V v0PlusV1 = V3Add(v0, v1);
    return V3Add(v0PlusV1, v2);
}
 
PX_FORCE_INLINE Vec3V M34TrnspsMul33V3(const Mat34V& a, const Vec3V b)
{
    const FloatV x = V3Dot(a.col0, b);
    const FloatV y = V3Dot(a.col1, b);
    const FloatV z = V3Dot(a.col2, b);
    return V3Merge(x, y, z);
}
 
PX_FORCE_INLINE Mat34V M34MulM34(const Mat34V& a, const Mat34V& b)
{
    return Mat34V(M34Mul33V3(a, b.col0), M34Mul33V3(a, b.col1), M34Mul33V3(a, b.col2), M34MulV3(a, b.col3));
}
 
PX_FORCE_INLINE Mat33V M34MulM33(const Mat34V& a, const Mat33V& b)
{
    return Mat33V(M34Mul33V3(a, b.col0), M34Mul33V3(a, b.col1), M34Mul33V3(a, b.col2));
}
 
PX_FORCE_INLINE Mat33V M34Mul33MM34(const Mat34V& a, const Mat34V& b)
{
    return Mat33V(M34Mul33V3(a, b.col0), M34Mul33V3(a, b.col1), M34Mul33V3(a, b.col2));
}
 
PX_FORCE_INLINE Mat34V M34Add(const Mat34V& a, const Mat34V& b)
{
    return Mat34V(V3Add(a.col0, b.col0), V3Add(a.col1, b.col1), V3Add(a.col2, b.col2), V3Add(a.col3, b.col3));
}
 
PX_FORCE_INLINE Mat33V M34Trnsps33(const Mat34V& a)
{
    return Mat33V(V3Merge(V3GetX(a.col0), V3GetX(a.col1), V3GetX(a.col2)),
                  V3Merge(V3GetY(a.col0), V3GetY(a.col1), V3GetY(a.col2)),
                  V3Merge(V3GetZ(a.col0), V3GetZ(a.col1), V3GetZ(a.col2)));
}
 
// MAT44V
 
PX_FORCE_INLINE Vec4V M44MulV4(const Mat44V& a, const Vec4V b)
{
    const FloatV x = V4GetX(b);
    const FloatV y = V4GetY(b);
    const FloatV z = V4GetZ(b);
    const FloatV w = V4GetW(b);
 
    const Vec4V v0 = V4Scale(a.col0, x);
    const Vec4V v1 = V4Scale(a.col1, y);
    const Vec4V v2 = V4Scale(a.col2, z);
    const Vec4V v3 = V4Scale(a.col3, w);
    const Vec4V v0PlusV1 = V4Add(v0, v1);
    const Vec4V v0PlusV1Plusv2 = V4Add(v0PlusV1, v2);
    return V4Add(v0PlusV1Plusv2, v3);
}
 
PX_FORCE_INLINE Vec4V M44TrnspsMulV4(const Mat44V& a, const Vec4V b)
{
    PX_ALIGN(16, FloatV) dotProdArray[4] = { V4Dot(a.col0, b), V4Dot(a.col1, b), V4Dot(a.col2, b), V4Dot(a.col3, b) };
    return V4Merge(dotProdArray);
}
 
PX_FORCE_INLINE Mat44V M44MulM44(const Mat44V& a, const Mat44V& b)
{
    return Mat44V(M44MulV4(a, b.col0), M44MulV4(a, b.col1), M44MulV4(a, b.col2), M44MulV4(a, b.col3));
}
 
PX_FORCE_INLINE Mat44V M44Add(const Mat44V& a, const Mat44V& b)
{
    return Mat44V(V4Add(a.col0, b.col0), V4Add(a.col1, b.col1), V4Add(a.col2, b.col2), V4Add(a.col3, b.col3));
}
 
PX_FORCE_INLINE Mat44V M44Trnsps(const Mat44V& a)
{
    const Vec4V v0 = _mm_unpacklo_ps(a.col0, a.col2);
    const Vec4V v1 = _mm_unpackhi_ps(a.col0, a.col2);
    const Vec4V v2 = _mm_unpacklo_ps(a.col1, a.col3);
    const Vec4V v3 = _mm_unpackhi_ps(a.col1, a.col3);
    return Mat44V(_mm_unpacklo_ps(v0, v2), _mm_unpackhi_ps(v0, v2), _mm_unpacklo_ps(v1, v3), _mm_unpackhi_ps(v1, v3));
}
 
PX_FORCE_INLINE Mat44V M44Inverse(const Mat44V& a)
{
    __m128 minor0, minor1, minor2, minor3;
    __m128 row0, row1, row2, row3;
    __m128 det, tmp1;
 
    tmp1 = V4Zero();
    row1 = V4Zero();
    row3 = V4Zero();
 
    row0 = a.col0;
    row1 = _mm_shuffle_ps(a.col1, a.col1, _MM_SHUFFLE(1, 0, 3, 2));
    row2 = a.col2;
    row3 = _mm_shuffle_ps(a.col3, a.col3, _MM_SHUFFLE(1, 0, 3, 2));
 
    tmp1 = _mm_mul_ps(row2, row3);
    tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1);
    minor0 = _mm_mul_ps(row1, tmp1);
    minor1 = _mm_mul_ps(row0, tmp1);
    tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E);
    minor0 = _mm_sub_ps(_mm_mul_ps(row1, tmp1), minor0);
    minor1 = _mm_sub_ps(_mm_mul_ps(row0, tmp1), minor1);
    minor1 = _mm_shuffle_ps(minor1, minor1, 0x4E);
 
    tmp1 = _mm_mul_ps(row1, row2);
    tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1);
    minor0 = _mm_add_ps(_mm_mul_ps(row3, tmp1), minor0);
    minor3 = _mm_mul_ps(row0, tmp1);
    tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E);
    minor0 = _mm_sub_ps(minor0, _mm_mul_ps(row3, tmp1));
    minor3 = _mm_sub_ps(_mm_mul_ps(row0, tmp1), minor3);
    minor3 = _mm_shuffle_ps(minor3, minor3, 0x4E);
 
    tmp1 = _mm_mul_ps(_mm_shuffle_ps(row1, row1, 0x4E), row3);
    tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1);
    row2 = _mm_shuffle_ps(row2, row2, 0x4E);
    minor0 = _mm_add_ps(_mm_mul_ps(row2, tmp1), minor0);
    minor2 = _mm_mul_ps(row0, tmp1);
    tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E);
    minor0 = _mm_sub_ps(minor0, _mm_mul_ps(row2, tmp1));
    minor2 = _mm_sub_ps(_mm_mul_ps(row0, tmp1), minor2);
    minor2 = _mm_shuffle_ps(minor2, minor2, 0x4E);
 
    tmp1 = _mm_mul_ps(row0, row1);
    tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1);
    minor2 = _mm_add_ps(_mm_mul_ps(row3, tmp1), minor2);
    minor3 = _mm_sub_ps(_mm_mul_ps(row2, tmp1), minor3);
    tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E);
    minor2 = _mm_sub_ps(_mm_mul_ps(row3, tmp1), minor2);
    minor3 = _mm_sub_ps(minor3, _mm_mul_ps(row2, tmp1));
 
    tmp1 = _mm_mul_ps(row0, row3);
    tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1);
    minor1 = _mm_sub_ps(minor1, _mm_mul_ps(row2, tmp1));
    minor2 = _mm_add_ps(_mm_mul_ps(row1, tmp1), minor2);
    tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E);
    minor1 = _mm_add_ps(_mm_mul_ps(row2, tmp1), minor1);
    minor2 = _mm_sub_ps(minor2, _mm_mul_ps(row1, tmp1));
 
    tmp1 = _mm_mul_ps(row0, row2);
    tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1);
    minor1 = _mm_add_ps(_mm_mul_ps(row3, tmp1), minor1);
    minor3 = _mm_sub_ps(minor3, _mm_mul_ps(row1, tmp1));
    tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E);
    minor1 = _mm_sub_ps(minor1, _mm_mul_ps(row3, tmp1));
    minor3 = _mm_add_ps(_mm_mul_ps(row1, tmp1), minor3);
 
    det = _mm_mul_ps(row0, minor0);
    det = _mm_add_ps(_mm_shuffle_ps(det, det, 0x4E), det);
    det = _mm_add_ss(_mm_shuffle_ps(det, det, 0xB1), det);
    tmp1 = _mm_rcp_ss(det);
#if 0
    det = _mm_sub_ss(_mm_add_ss(tmp1, tmp1), _mm_mul_ss(det, _mm_mul_ss(tmp1, tmp1)));
    det = _mm_shuffle_ps(det, det, 0x00);
#else
    det = _mm_shuffle_ps(tmp1, tmp1, _MM_SHUFFLE(0, 0, 0, 0));
#endif
 
    minor0 = _mm_mul_ps(det, minor0);
    minor1 = _mm_mul_ps(det, minor1);
    minor2 = _mm_mul_ps(det, minor2);
    minor3 = _mm_mul_ps(det, minor3);
    Mat44V invTrans(minor0, minor1, minor2, minor3);
    return M44Trnsps(invTrans);
}
 
PX_FORCE_INLINE Vec4V V4LoadXYZW(const PxF32& x, const PxF32& y, const PxF32& z, const PxF32& w)
{
    return _mm_set_ps(w, z, y, x);
}
 
/*
// AP: work in progress - use proper SSE intrinsics where possible
PX_FORCE_INLINE VecU16V V4U32PK(VecU32V a, VecU32V b)
{
    VecU16V result;
    result.m128_u16[0] = PxU16(PxClamp<PxU32>((a).m128_u32[0], 0, 0xFFFF));
    result.m128_u16[1] = PxU16(PxClamp<PxU32>((a).m128_u32[1], 0, 0xFFFF));
    result.m128_u16[2] = PxU16(PxClamp<PxU32>((a).m128_u32[2], 0, 0xFFFF));
    result.m128_u16[3] = PxU16(PxClamp<PxU32>((a).m128_u32[3], 0, 0xFFFF));
    result.m128_u16[4] = PxU16(PxClamp<PxU32>((b).m128_u32[0], 0, 0xFFFF));
    result.m128_u16[5] = PxU16(PxClamp<PxU32>((b).m128_u32[1], 0, 0xFFFF));
    result.m128_u16[6] = PxU16(PxClamp<PxU32>((b).m128_u32[2], 0, 0xFFFF));
    result.m128_u16[7] = PxU16(PxClamp<PxU32>((b).m128_u32[3], 0, 0xFFFF));
    return result;
}
*/
 
PX_FORCE_INLINE VecU32V V4U32Sel(const BoolV c, const VecU32V a, const VecU32V b)
{
    return m128_I2F(_mm_or_si128(_mm_andnot_si128(m128_F2I(c), m128_F2I(b)), _mm_and_si128(m128_F2I(c), m128_F2I(a))));
}
 
PX_FORCE_INLINE VecU32V V4U32or(VecU32V a, VecU32V b)
{
    return m128_I2F(_mm_or_si128(m128_F2I(a), m128_F2I(b)));
}
 
PX_FORCE_INLINE VecU32V V4U32xor(VecU32V a, VecU32V b)
{
    return m128_I2F(_mm_xor_si128(m128_F2I(a), m128_F2I(b)));
}
 
PX_FORCE_INLINE VecU32V V4U32and(VecU32V a, VecU32V b)
{
    return m128_I2F(_mm_and_si128(m128_F2I(a), m128_F2I(b)));
}
 
PX_FORCE_INLINE VecU32V V4U32Andc(VecU32V a, VecU32V b)
{
    return m128_I2F(_mm_andnot_si128(m128_F2I(b), m128_F2I(a)));
}
 
/*
PX_FORCE_INLINE VecU16V V4U16Or(VecU16V a, VecU16V b)
{
    return m128_I2F(_mm_or_si128(m128_F2I(a), m128_F2I(b)));
}
*/
 
/*
PX_FORCE_INLINE VecU16V V4U16And(VecU16V a, VecU16V b)
{
    return m128_I2F(_mm_and_si128(m128_F2I(a), m128_F2I(b)));
}
*/
 
/*
PX_FORCE_INLINE VecU16V V4U16Andc(VecU16V a, VecU16V b)
{
    return m128_I2F(_mm_andnot_si128(m128_F2I(b), m128_F2I(a)));
}
*/
 
PX_FORCE_INLINE VecI32V I4Load(const PxI32 i)
{
    return m128_F2I(_mm_load1_ps(reinterpret_cast<const PxF32*>(&i)));
}
 
PX_FORCE_INLINE VecI32V I4LoadU(const PxI32* i)
{
    return m128_F2I(_mm_loadu_ps(reinterpret_cast<const PxF32*>(i)));
}
 
PX_FORCE_INLINE VecI32V I4LoadA(const PxI32* i)
{
    return m128_F2I(_mm_load_ps(reinterpret_cast<const PxF32*>(i)));
}
 
PX_FORCE_INLINE VecI32V VecI32V_Add(const VecI32VArg a, const VecI32VArg b)
{
    return _mm_add_epi32(a, b);
}
 
PX_FORCE_INLINE VecI32V VecI32V_Sub(const VecI32VArg a, const VecI32VArg b)
{
    return _mm_sub_epi32(a, b);
}
 
PX_FORCE_INLINE BoolV VecI32V_IsGrtr(const VecI32VArg a, const VecI32VArg b)
{
    return m128_I2F(_mm_cmpgt_epi32(a, b));
}
 
PX_FORCE_INLINE BoolV VecI32V_IsEq(const VecI32VArg a, const VecI32VArg b)
{
    return m128_I2F(_mm_cmpeq_epi32(a, b));
}
 
PX_FORCE_INLINE VecI32V V4I32Sel(const BoolV c, const VecI32V a, const VecI32V b)
{
    return _mm_or_si128(_mm_andnot_si128(m128_F2I(c), b), _mm_and_si128(m128_F2I(c), a));
}
 
PX_FORCE_INLINE VecI32V VecI32V_Zero()
{
    return _mm_setzero_si128();
}
 
PX_FORCE_INLINE VecI32V VecI32V_One()
{
    return I4Load(1);
}
 
PX_FORCE_INLINE VecI32V VecI32V_Two()
{
    return I4Load(2);
}
 
PX_FORCE_INLINE VecI32V VecI32V_MinusOne()
{
    return I4Load(-1);
}
 
PX_FORCE_INLINE VecU32V U4Zero()
{
    return U4Load(0);
}
 
PX_FORCE_INLINE VecU32V U4One()
{
    return U4Load(1);
}
 
PX_FORCE_INLINE VecU32V U4Two()
{
    return U4Load(2);
}
 
PX_FORCE_INLINE VecI32V VecI32V_Sel(const BoolV c, const VecI32VArg a, const VecI32VArg b)
{
    return _mm_or_si128(_mm_andnot_si128(m128_F2I(c), b), _mm_and_si128(m128_F2I(c), a));
}
 
PX_FORCE_INLINE VecShiftV VecI32V_PrepareShift(const VecI32VArg shift)
{
    VecShiftV s;
    s.shift = VecI32V_Sel(BTFFF(), shift, VecI32V_Zero());
    return s;
}
 
PX_FORCE_INLINE VecI32V VecI32V_LeftShift(const VecI32VArg a, const VecShiftVArg count)
{
    return _mm_sll_epi32(a, count.shift);
}
 
PX_FORCE_INLINE VecI32V VecI32V_RightShift(const VecI32VArg a, const VecShiftVArg count)
{
    return _mm_srl_epi32(a, count.shift);
}
 
PX_FORCE_INLINE VecI32V VecI32V_LeftShift(const VecI32VArg a, const PxU32 count)
{
    return _mm_slli_epi32(a, PxI32(count));
}
 
PX_FORCE_INLINE VecI32V VecI32V_RightShift(const VecI32VArg a, const PxU32 count)
{
    return _mm_srai_epi32(a, PxI32(count));
}
 
PX_FORCE_INLINE VecI32V VecI32V_And(const VecI32VArg a, const VecI32VArg b)
{
    return _mm_and_si128(a, b);
}
 
PX_FORCE_INLINE VecI32V VecI32V_Or(const VecI32VArg a, const VecI32VArg b)
{
    return _mm_or_si128(a, b);
}
 
PX_FORCE_INLINE VecI32V VecI32V_GetX(const VecI32VArg a)
{
    return m128_F2I(_mm_shuffle_ps(m128_I2F(a), m128_I2F(a), _MM_SHUFFLE(0, 0, 0, 0)));
}
 
PX_FORCE_INLINE VecI32V VecI32V_GetY(const VecI32VArg a)
{
    return m128_F2I(_mm_shuffle_ps(m128_I2F(a), m128_I2F(a), _MM_SHUFFLE(1, 1, 1, 1)));
}
 
PX_FORCE_INLINE VecI32V VecI32V_GetZ(const VecI32VArg a)
{
    return m128_F2I(_mm_shuffle_ps(m128_I2F(a), m128_I2F(a), _MM_SHUFFLE(2, 2, 2, 2)));
}
 
PX_FORCE_INLINE VecI32V VecI32V_GetW(const VecI32VArg a)
{
    return m128_F2I(_mm_shuffle_ps(m128_I2F(a), m128_I2F(a), _MM_SHUFFLE(3, 3, 3, 3)));
}
 
PX_FORCE_INLINE void PxI32_From_VecI32V(const VecI32VArg a, PxI32* i)
{
    _mm_store_ss(reinterpret_cast<PxF32*>(i), m128_I2F(a));
}
 
PX_FORCE_INLINE VecI32V VecI32V_Merge(const VecI32VArg x, const VecI32VArg y, const VecI32VArg z, const VecI32VArg w)
{
    const __m128 xw = _mm_move_ss(m128_I2F(y), m128_I2F(x)); // y, y, y, x
    const __m128 yz = _mm_move_ss(m128_I2F(z), m128_I2F(w)); // z, z, z, w
    return m128_F2I(_mm_shuffle_ps(xw, yz, _MM_SHUFFLE(0, 2, 1, 0)));
}
 
PX_FORCE_INLINE VecI32V VecI32V_From_BoolV(const BoolVArg a)
{
    return m128_F2I(a);
}
 
PX_FORCE_INLINE VecU32V VecU32V_From_BoolV(const BoolVArg a)
{
    return a;
}
 
/*
template<int a> PX_FORCE_INLINE VecI32V V4ISplat()
{
    VecI32V result;
    result.m128_i32[0] = a;
    result.m128_i32[1] = a;
    result.m128_i32[2] = a;
    result.m128_i32[3] = a;
    return result;
}
 
template<PxU32 a> PX_FORCE_INLINE VecU32V V4USplat()
{
    VecU32V result;
    result.m128_u32[0] = a;
    result.m128_u32[1] = a;
    result.m128_u32[2] = a;
    result.m128_u32[3] = a;
    return result;
}
*/
 
/*
PX_FORCE_INLINE void V4U16StoreAligned(VecU16V val, VecU16V* address)
{
    *address = val;
}
*/
 
PX_FORCE_INLINE void V4U32StoreAligned(VecU32V val, VecU32V* address)
{
    *address = val;
}
 
PX_FORCE_INLINE Vec4V V4LoadAligned(Vec4V* addr)
{
    return *addr;
}
 
PX_FORCE_INLINE Vec4V V4LoadUnaligned(Vec4V* addr)
{
    return V4LoadU(reinterpret_cast<float*>(addr));
}
 
PX_FORCE_INLINE Vec4V V4Andc(const Vec4V a, const VecU32V b)
{
    VecU32V result32(a);
    result32 = V4U32Andc(result32, b);
    return Vec4V(result32);
}
 
PX_FORCE_INLINE VecU32V V4IsGrtrV32u(const Vec4V a, const Vec4V b)
{
    return V4IsGrtr(a, b);
}
 
PX_FORCE_INLINE VecU16V V4U16LoadAligned(VecU16V* addr)
{
    return *addr;
}
 
PX_FORCE_INLINE VecU16V V4U16LoadUnaligned(VecU16V* addr)
{
    return *addr;
}
 
PX_FORCE_INLINE VecU16V V4U16CompareGt(VecU16V a, VecU16V b)
{
    // _mm_cmpgt_epi16 doesn't work for unsigned values unfortunately
    // return m128_I2F(_mm_cmpgt_epi16(m128_F2I(a), m128_F2I(b)));
    VecU16V result;
    result.m128_u16[0] = (a).m128_u16[0] > (b).m128_u16[0];
    result.m128_u16[1] = (a).m128_u16[1] > (b).m128_u16[1];
    result.m128_u16[2] = (a).m128_u16[2] > (b).m128_u16[2];
    result.m128_u16[3] = (a).m128_u16[3] > (b).m128_u16[3];
    result.m128_u16[4] = (a).m128_u16[4] > (b).m128_u16[4];
    result.m128_u16[5] = (a).m128_u16[5] > (b).m128_u16[5];
    result.m128_u16[6] = (a).m128_u16[6] > (b).m128_u16[6];
    result.m128_u16[7] = (a).m128_u16[7] > (b).m128_u16[7];
    return result;
}
 
PX_FORCE_INLINE VecU16V V4I16CompareGt(VecU16V a, VecU16V b)
{
    return m128_I2F(_mm_cmpgt_epi16(m128_F2I(a), m128_F2I(b)));
}
 
PX_FORCE_INLINE Vec4V Vec4V_From_VecU32V(VecU32V a)
{
    Vec4V result = V4LoadXYZW(PxF32(a.m128_u32[0]), PxF32(a.m128_u32[1]), PxF32(a.m128_u32[2]), PxF32(a.m128_u32[3]));
    return result;
}
 
PX_FORCE_INLINE Vec4V Vec4V_From_VecI32V(VecI32V in)
{
    return _mm_cvtepi32_ps(in);
}
 
PX_FORCE_INLINE VecI32V VecI32V_From_Vec4V(Vec4V a)
{
    return _mm_cvttps_epi32(a);
}
 
PX_FORCE_INLINE Vec4V Vec4V_ReinterpretFrom_VecU32V(VecU32V a)
{
    return Vec4V(a);
}
 
PX_FORCE_INLINE Vec4V Vec4V_ReinterpretFrom_VecI32V(VecI32V a)
{
    return m128_I2F(a);
}
 
PX_FORCE_INLINE VecU32V VecU32V_ReinterpretFrom_Vec4V(Vec4V a)
{
    return VecU32V(a);
}
 
PX_FORCE_INLINE VecI32V VecI32V_ReinterpretFrom_Vec4V(Vec4V a)
{
    return m128_F2I(a);
}
 
/*
template<int index> PX_FORCE_INLINE BoolV BSplatElement(BoolV a)
{
    BoolV result;
    result[0] = result[1] = result[2] = result[3] = a[index];
    return result;
}
*/
 
template <int index>
BoolV BSplatElement(BoolV a)
{
    float* data = reinterpret_cast<float*>(&a);
    return V4Load(data[index]);
}
 
template <int index>
PX_FORCE_INLINE VecU32V V4U32SplatElement(VecU32V a)
{
    VecU32V result;
    result.m128_u32[0] = result.m128_u32[1] = result.m128_u32[2] = result.m128_u32[3] = a.m128_u32[index];
    return result;
}
 
template <int index>
PX_FORCE_INLINE Vec4V V4SplatElement(Vec4V a)
{
    float* data = reinterpret_cast<float*>(&a);
    return V4Load(data[index]);
}
 
PX_FORCE_INLINE VecU32V U4LoadXYZW(PxU32 x, PxU32 y, PxU32 z, PxU32 w)
{
    VecU32V result;
    result.m128_u32[0] = x;
    result.m128_u32[1] = y;
    result.m128_u32[2] = z;
    result.m128_u32[3] = w;
    return result;
}
 
PX_FORCE_INLINE Vec4V V4Ceil(const Vec4V in)
{
    UnionM128 a(in);
    return V4LoadXYZW(PxCeil(a.m128_f32[0]), PxCeil(a.m128_f32[1]), PxCeil(a.m128_f32[2]), PxCeil(a.m128_f32[3]));
}
 
PX_FORCE_INLINE Vec4V V4Floor(const Vec4V in)
{
    UnionM128 a(in);
    return V4LoadXYZW(PxFloor(a.m128_f32[0]), PxFloor(a.m128_f32[1]), PxFloor(a.m128_f32[2]), PxFloor(a.m128_f32[3]));
}
 
PX_FORCE_INLINE VecU32V V4ConvertToU32VSaturate(const Vec4V in, PxU32 power)
{
    PX_ASSERT(power == 0 && "Non-zero power not supported in convertToU32VSaturate");
    PX_UNUSED(power); // prevent warning in release builds
    PxF32 ffffFFFFasFloat = PxF32(0xFFFF0000);
    UnionM128 a(in);
    VecU32V result;
    result.m128_u32[0] = PxU32(PxClamp<PxF32>((a).m128_f32[0], 0.0f, ffffFFFFasFloat));
    result.m128_u32[1] = PxU32(PxClamp<PxF32>((a).m128_f32[1], 0.0f, ffffFFFFasFloat));
    result.m128_u32[2] = PxU32(PxClamp<PxF32>((a).m128_f32[2], 0.0f, ffffFFFFasFloat));
    result.m128_u32[3] = PxU32(PxClamp<PxF32>((a).m128_f32[3], 0.0f, ffffFFFFasFloat));
    return result;
}
 
} // namespace aos
} // namespace physx
 
#endif // PXFOUNDATION_PXUNIXSSE2INLINEAOS_H