PxVecMath.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 PX_VEC_MATH_H
#define PX_VEC_MATH_H
 
#include "foundation/Px.h"
#include "foundation/PxIntrinsics.h"
#include "foundation/PxVec3.h"
#include "foundation/PxVec4.h"
#include "foundation/PxMat33.h"
#include "foundation/PxUnionCast.h"
 
// We can opt to use the scalar version of vectorised functions.
// This can catch type safety issues and might even work out more optimal on pc.
// It will also be useful for benchmarking and testing.
// NEVER submit with vector intrinsics deactivated without good reason.
// AM: deactivating SIMD for debug win64 just so autobuild will also exercise
// non-SIMD path, until a dedicated non-SIMD platform sich as Arm comes online.
// TODO: dima: reference all platforms with SIMD support here,
// all unknown/experimental cases should better default to NO SIMD.
 
// enable/disable SIMD
#if !defined(PX_SIMD_DISABLED)
#if PX_INTEL_FAMILY && (!defined(__EMSCRIPTEN__) || defined(__SSE2__))
    #define COMPILE_VECTOR_INTRINSICS 1
#elif PX_SWITCH
    #define COMPILE_VECTOR_INTRINSICS 1
#else
    #define COMPILE_VECTOR_INTRINSICS 0
#endif
#else
    #define COMPILE_VECTOR_INTRINSICS 0
#endif
 
#if COMPILE_VECTOR_INTRINSICS && PX_INTEL_FAMILY && PX_UNIX_FAMILY
// only SSE2 compatible platforms should reach this
#if PX_EMSCRIPTEN
    #include <emmintrin.h>
#endif
    #include <xmmintrin.h>
#endif
 
#if COMPILE_VECTOR_INTRINSICS
    #include "PxAoS.h"
#else
    #include "PxVecMathAoSScalar.h"
#endif
 
#if !PX_DOXYGEN
namespace physx
{
#endif
namespace aos
{
 
// Basic AoS types are
// FloatV   - 16-byte aligned representation of float.
// Vec3V        - 16-byte aligned representation of PxVec3 stored as (x y z 0).
// Vec4V        - 16-byte aligned representation of vector of 4 floats stored as (x y z w).
// BoolV        - 16-byte aligned representation of vector of 4 bools stored as (x y z w).
// VecU32V  - 16-byte aligned representation of 4 unsigned ints stored as (x y z w).
// VecI32V  - 16-byte aligned representation of 4 signed ints stored as (x y z w).
// Mat33V   - 16-byte aligned representation of any 3x3 matrix.
// Mat34V   - 16-byte aligned representation of transformation matrix (rotation in col1,col2,col3 and translation in
// col4).
// Mat44V   - 16-byte aligned representation of any 4x4 matrix.
 
// Construct a simd type from a scalar type
 
// FloatV
//(f,f,f,f)
PX_FORCE_INLINE FloatV FLoad(const PxF32 f);
 
// Vec3V
//(f,f,f,0)
PX_FORCE_INLINE Vec3V V3Load(const PxF32 f);
//(f.x,f.y,f.z,0)
PX_FORCE_INLINE Vec3V V3LoadU(const PxVec3& f);
//(f.x,f.y,f.z,0), f must be 16-byte aligned
PX_FORCE_INLINE Vec3V V3LoadA(const PxVec3& f);
//(f.x,f.y,f.z,w_undefined), f must be 16-byte aligned
PX_FORCE_INLINE Vec3V V3LoadUnsafeA(const PxVec3& f);
//(f.x,f.y,f.z,0)
PX_FORCE_INLINE Vec3V V3LoadU(const PxF32* f);
//(f.x,f.y,f.z,0), f must be 16-byte aligned
PX_FORCE_INLINE Vec3V V3LoadA(const PxF32* f);
 
// Vec4V
//(f,f,f,f)
PX_FORCE_INLINE Vec4V V4Load(const PxF32 f);
//(f[0],f[1],f[2],f[3])
PX_FORCE_INLINE Vec4V V4LoadU(const PxF32* const f);
//(f[0],f[1],f[2],f[3]), f must be 16-byte aligned
PX_FORCE_INLINE Vec4V V4LoadA(const PxF32* const f);
//(x,y,z,w)
PX_FORCE_INLINE Vec4V V4LoadXYZW(const PxF32& x, const PxF32& y, const PxF32& z, const PxF32& w);
 
// BoolV
//(f,f,f,f)
PX_FORCE_INLINE BoolV BLoad(const bool f);
//(f[0],f[1],f[2],f[3])
PX_FORCE_INLINE BoolV BLoad(const bool* const f);
 
// VecU32V
//(f,f,f,f)
PX_FORCE_INLINE VecU32V U4Load(const PxU32 f);
//(f[0],f[1],f[2],f[3])
PX_FORCE_INLINE VecU32V U4LoadU(const PxU32* f);
//(f[0],f[1],f[2],f[3]), f must be 16-byte aligned
PX_FORCE_INLINE VecU32V U4LoadA(const PxU32* f);
//((U32)x, (U32)y, (U32)z, (U32)w)
PX_FORCE_INLINE VecU32V U4LoadXYZW(PxU32 x, PxU32 y, PxU32 z, PxU32 w);
 
// VecI32V
//(i,i,i,i)
PX_FORCE_INLINE VecI32V I4Load(const PxI32 i);
//(i,i,i,i)
PX_FORCE_INLINE VecI32V I4LoadU(const PxI32* i);
//(i,i,i,i)
PX_FORCE_INLINE VecI32V I4LoadA(const PxI32* i);
 
// QuatV
//(x = v[0], y=v[1], z=v[2], w=v3[3]) and array don't need to aligned
PX_FORCE_INLINE QuatV QuatVLoadU(const PxF32* v);
//(x = v[0], y=v[1], z=v[2], w=v3[3]) and array need to aligned, fast load
PX_FORCE_INLINE QuatV QuatVLoadA(const PxF32* v);
//(x, y, z, w)
PX_FORCE_INLINE QuatV QuatVLoadXYZW(const PxF32 x, const PxF32 y, const PxF32 z, const PxF32 w);
 
// not added to public api
Vec4V Vec4V_From_PxVec3_WUndefined(const PxVec3& v);
 
// Construct a simd type from a different simd type
 
// Vec3V
//(v.x,v.y,v.z,0)
PX_FORCE_INLINE Vec3V Vec3V_From_Vec4V(Vec4V v);
//(v.x,v.y,v.z,undefined) - be very careful with w!=0 because many functions require w==0 for correct operation eg V3Dot, V3Length, V3Cross etc etc.
PX_FORCE_INLINE Vec3V Vec3V_From_Vec4V_WUndefined(const Vec4V v);
 
// Vec4V
//(f.x,f.y,f.z,f.w)
PX_FORCE_INLINE Vec4V Vec4V_From_Vec3V(Vec3V f);
//((PxF32)f.x, (PxF32)f.y, (PxF32)f.z, (PxF32)f.w)
PX_FORCE_INLINE Vec4V Vec4V_From_VecU32V(VecU32V a);
//((PxF32)f.x, (PxF32)f.y, (PxF32)f.z, (PxF32)f.w)
PX_FORCE_INLINE Vec4V Vec4V_From_VecI32V(VecI32V a);
//(*(reinterpret_cast<PxF32*>(&f.x), (reinterpret_cast<PxF32*>(&f.y), (reinterpret_cast<PxF32*>(&f.z),
//(reinterpret_cast<PxF32*>(&f.w))
PX_FORCE_INLINE Vec4V Vec4V_ReinterpretFrom_VecU32V(VecU32V a);
//(*(reinterpret_cast<PxF32*>(&f.x), (reinterpret_cast<PxF32*>(&f.y), (reinterpret_cast<PxF32*>(&f.z),
//(reinterpret_cast<PxF32*>(&f.w))
PX_FORCE_INLINE Vec4V Vec4V_ReinterpretFrom_VecI32V(VecI32V a);
 
// VecU32V
//(*(reinterpret_cast<PxU32*>(&f.x), (reinterpret_cast<PxU32*>(&f.y), (reinterpret_cast<PxU32*>(&f.z),
//(reinterpret_cast<PxU32*>(&f.w))
PX_FORCE_INLINE VecU32V VecU32V_ReinterpretFrom_Vec4V(Vec4V a);
//(b[0], b[1], b[2], b[3])
PX_FORCE_INLINE VecU32V VecU32V_From_BoolV(const BoolVArg b);
 
// VecI32V
//(*(reinterpret_cast<PxI32*>(&f.x), (reinterpret_cast<PxI32*>(&f.y), (reinterpret_cast<PxI32*>(&f.z),
//(reinterpret_cast<PxI32*>(&f.w))
PX_FORCE_INLINE VecI32V VecI32V_ReinterpretFrom_Vec4V(Vec4V a);
//((I32)a.x, (I32)a.y, (I32)a.z, (I32)a.w)
PX_FORCE_INLINE VecI32V VecI32V_From_Vec4V(Vec4V a);
//((I32)b.x, (I32)b.y, (I32)b.z, (I32)b.w)
PX_FORCE_INLINE VecI32V VecI32V_From_BoolV(const BoolVArg b);
 
// Convert from a simd type back to a scalar type
 
// FloatV
// a.x
PX_FORCE_INLINE void FStore(const FloatV a, PxF32* PX_RESTRICT f);
 
// Vec3V
//(a.x,a.y,a.z)
PX_FORCE_INLINE void V3StoreA(const Vec3V a, PxVec3& f);
//(a.x,a.y,a.z)
PX_FORCE_INLINE void V3StoreU(const Vec3V a, PxVec3& f);
 
// Vec4V
PX_FORCE_INLINE void V4StoreA(const Vec4V a, PxF32* f);
PX_FORCE_INLINE void V4StoreU(const Vec4V a, PxF32* f);
 
// BoolV
PX_FORCE_INLINE void BStoreA(const BoolV b, PxU32* f);
 
// VecU32V
PX_FORCE_INLINE void U4StoreA(const VecU32V uv, PxU32* u);
 
// VecI32V
PX_FORCE_INLINE void I4StoreA(const VecI32V iv, PxI32* i);
 
// Test that simd types have elements in the floating point range
 
// check for each component is valid ie in floating point range
PX_FORCE_INLINE bool isFiniteFloatV(const FloatV a);
// check for each component is valid ie in floating point range
PX_FORCE_INLINE bool isFiniteVec3V(const Vec3V a);
// check for each component is valid ie in floating point range
PX_FORCE_INLINE bool isFiniteVec4V(const Vec4V a);
 
// Check that w-component is zero.
PX_FORCE_INLINE bool isValidVec3V(const Vec3V a);
 
// Tests that all elements of two 16-byte types are completely equivalent.
// Use these tests for unit testing and asserts only.
 
namespace vecMathTests
{
PX_FORCE_INLINE Vec3V getInvalidVec3V();
PX_FORCE_INLINE bool allElementsEqualFloatV(const FloatV a, const FloatV b);
PX_FORCE_INLINE bool allElementsEqualVec3V(const Vec3V a, const Vec3V b);
PX_FORCE_INLINE bool allElementsEqualVec4V(const Vec4V a, const Vec4V b);
PX_FORCE_INLINE bool allElementsEqualBoolV(const BoolV a, const BoolV b);
PX_FORCE_INLINE bool allElementsEqualVecU32V(const VecU32V a, const VecU32V b);
PX_FORCE_INLINE bool allElementsEqualVecI32V(const VecI32V a, const VecI32V b);
 
PX_FORCE_INLINE bool allElementsEqualMat33V(const Mat33V& a, const Mat33V& b)
{
    return (allElementsEqualVec3V(a.col0, b.col0) && allElementsEqualVec3V(a.col1, b.col1) &&
            allElementsEqualVec3V(a.col2, b.col2));
}
PX_FORCE_INLINE bool allElementsEqualMat34V(const Mat34V& a, const Mat34V& b)
{
    return (allElementsEqualVec3V(a.col0, b.col0) && allElementsEqualVec3V(a.col1, b.col1) &&
            allElementsEqualVec3V(a.col2, b.col2) && allElementsEqualVec3V(a.col3, b.col3));
}
PX_FORCE_INLINE bool allElementsEqualMat44V(const Mat44V& a, const Mat44V& b)
{
    return (allElementsEqualVec4V(a.col0, b.col0) && allElementsEqualVec4V(a.col1, b.col1) &&
            allElementsEqualVec4V(a.col2, b.col2) && allElementsEqualVec4V(a.col3, b.col3));
}
 
PX_FORCE_INLINE bool allElementsNearEqualFloatV(const FloatV a, const FloatV b);
PX_FORCE_INLINE bool allElementsNearEqualVec3V(const Vec3V a, const Vec3V b);
PX_FORCE_INLINE bool allElementsNearEqualVec4V(const Vec4V a, const Vec4V b);
PX_FORCE_INLINE bool allElementsNearEqualMat33V(const Mat33V& a, const Mat33V& b)
{
    return (allElementsNearEqualVec3V(a.col0, b.col0) && allElementsNearEqualVec3V(a.col1, b.col1) &&
            allElementsNearEqualVec3V(a.col2, b.col2));
}
PX_FORCE_INLINE bool allElementsNearEqualMat34V(const Mat34V& a, const Mat34V& b)
{
    return (allElementsNearEqualVec3V(a.col0, b.col0) && allElementsNearEqualVec3V(a.col1, b.col1) &&
            allElementsNearEqualVec3V(a.col2, b.col2) && allElementsNearEqualVec3V(a.col3, b.col3));
}
PX_FORCE_INLINE bool allElementsNearEqualMat44V(const Mat44V& a, const Mat44V& b)
{
    return (allElementsNearEqualVec4V(a.col0, b.col0) && allElementsNearEqualVec4V(a.col1, b.col1) &&
            allElementsNearEqualVec4V(a.col2, b.col2) && allElementsNearEqualVec4V(a.col3, b.col3));
}
}
 
// Math operations on FloatV
 
//(0,0,0,0)
PX_FORCE_INLINE FloatV FZero();
//(1,1,1,1)
PX_FORCE_INLINE FloatV FOne();
//(0.5,0.5,0.5,0.5)
PX_FORCE_INLINE FloatV FHalf();
//(PX_EPS_REAL,PX_EPS_REAL,PX_EPS_REAL,PX_EPS_REAL)
PX_FORCE_INLINE FloatV FEps();
//(PX_MAX_REAL, PX_MAX_REAL, PX_MAX_REAL PX_MAX_REAL)
PX_FORCE_INLINE FloatV FMax();
//(-PX_MAX_REAL, -PX_MAX_REAL, -PX_MAX_REAL -PX_MAX_REAL)
PX_FORCE_INLINE FloatV FNegMax();
//(1e-6f, 1e-6f, 1e-6f, 1e-6f)
PX_FORCE_INLINE FloatV FEps6();
//((PxF32*)&1, (PxF32*)&1, (PxF32*)&1, (PxF32*)&1)
 
//-f (per component)
PX_FORCE_INLINE FloatV FNeg(const FloatV f);
// a+b (per component)
PX_FORCE_INLINE FloatV FAdd(const FloatV a, const FloatV b);
// a-b (per component)
PX_FORCE_INLINE FloatV FSub(const FloatV a, const FloatV b);
// a*b (per component)
PX_FORCE_INLINE FloatV FMul(const FloatV a, const FloatV b);
// a/b (per component)
PX_FORCE_INLINE FloatV FDiv(const FloatV a, const FloatV b);
// a/b (per component)
PX_FORCE_INLINE FloatV FDivFast(const FloatV a, const FloatV b);
// 1.0f/a
PX_FORCE_INLINE FloatV FRecip(const FloatV a);
// 1.0f/a
PX_FORCE_INLINE FloatV FRecipFast(const FloatV a);
// 1.0f/sqrt(a)
PX_FORCE_INLINE FloatV FRsqrt(const FloatV a);
// 1.0f/sqrt(a)
PX_FORCE_INLINE FloatV FRsqrtFast(const FloatV a);
// sqrt(a)
PX_FORCE_INLINE FloatV FSqrt(const FloatV a);
// a*b+c
PX_FORCE_INLINE FloatV FScaleAdd(const FloatV a, const FloatV b, const FloatV c);
// c-a*b
PX_FORCE_INLINE FloatV FNegScaleSub(const FloatV a, const FloatV b, const FloatV c);
// fabs(a)
PX_FORCE_INLINE FloatV FAbs(const FloatV a);
// c ? a : b (per component)
PX_FORCE_INLINE FloatV FSel(const BoolV c, const FloatV a, const FloatV b);
// a>b (per component)
PX_FORCE_INLINE BoolV FIsGrtr(const FloatV a, const FloatV b);
// a>=b (per component)
PX_FORCE_INLINE BoolV FIsGrtrOrEq(const FloatV a, const FloatV b);
// a==b (per component)
PX_FORCE_INLINE BoolV FIsEq(const FloatV a, const FloatV b);
// Max(a,b) (per component)
PX_FORCE_INLINE FloatV FMax(const FloatV a, const FloatV b);
// Min(a,b) (per component)
PX_FORCE_INLINE FloatV FMin(const FloatV a, const FloatV b);
// Clamp(a,b) (per component)
PX_FORCE_INLINE FloatV FClamp(const FloatV a, const FloatV minV, const FloatV maxV);
 
// a.x>b.x
PX_FORCE_INLINE PxU32 FAllGrtr(const FloatV a, const FloatV b);
// a.x>=b.x
PX_FORCE_INLINE PxU32 FAllGrtrOrEq(const FloatV a, const FloatV b);
// a.x==b.x
PX_FORCE_INLINE PxU32 FAllEq(const FloatV a, const FloatV b);
// a<min || a>max
PX_FORCE_INLINE PxU32 FOutOfBounds(const FloatV a, const FloatV min, const FloatV max);
// a>=min && a<=max
PX_FORCE_INLINE PxU32 FInBounds(const FloatV a, const FloatV min, const FloatV max);
// a<-bounds || a>bounds
PX_FORCE_INLINE PxU32 FOutOfBounds(const FloatV a, const FloatV bounds);
// a>=-bounds && a<=bounds
PX_FORCE_INLINE PxU32 FInBounds(const FloatV a, const FloatV bounds);
 
// round float a to the near int
PX_FORCE_INLINE FloatV FRound(const FloatV a);
// calculate the sin of float a
PX_FORCE_INLINE FloatV FSin(const FloatV a);
// calculate the cos of float b
PX_FORCE_INLINE FloatV FCos(const FloatV a);
 
// Math operations on Vec3V
 
//(f,f,f,f)
PX_FORCE_INLINE Vec3V V3Splat(const FloatV f);
 
//(x,y,z)
PX_FORCE_INLINE Vec3V V3Merge(const FloatVArg x, const FloatVArg y, const FloatVArg z);
 
//(1,0,0,0)
PX_FORCE_INLINE Vec3V V3UnitX();
//(0,1,0,0)
PX_FORCE_INLINE Vec3V V3UnitY();
//(0,0,1,0)
PX_FORCE_INLINE Vec3V V3UnitZ();
 
//(f.x,f.x,f.x,f.x)
PX_FORCE_INLINE FloatV V3GetX(const Vec3V f);
//(f.y,f.y,f.y,f.y)
PX_FORCE_INLINE FloatV V3GetY(const Vec3V f);
//(f.z,f.z,f.z,f.z)
PX_FORCE_INLINE FloatV V3GetZ(const Vec3V f);
 
//(f,v.y,v.z,v.w)
PX_FORCE_INLINE Vec3V V3SetX(const Vec3V v, const FloatV f);
//(v.x,f,v.z,v.w)
PX_FORCE_INLINE Vec3V V3SetY(const Vec3V v, const FloatV f);
//(v.x,v.y,f,v.w)
PX_FORCE_INLINE Vec3V V3SetZ(const Vec3V v, const FloatV f);
 
// v.x=f
PX_FORCE_INLINE void V3WriteX(Vec3V& v, const PxF32 f);
// v.y=f
PX_FORCE_INLINE void V3WriteY(Vec3V& v, const PxF32 f);
// v.z=f
PX_FORCE_INLINE void V3WriteZ(Vec3V& v, const PxF32 f);
// v.x=f.x, v.y=f.y, v.z=f.z
PX_FORCE_INLINE void V3WriteXYZ(Vec3V& v, const PxVec3& f);
// return v.x
PX_FORCE_INLINE PxF32 V3ReadX(const Vec3V& v);
// return v.y
PX_FORCE_INLINE PxF32 V3ReadY(const Vec3V& v);
// return v.y
PX_FORCE_INLINE PxF32 V3ReadZ(const Vec3V& v);
// return (v.x,v.y,v.z)
PX_FORCE_INLINE const PxVec3& V3ReadXYZ(const Vec3V& v);
 
//(a.x, b.x, c.x)
PX_FORCE_INLINE Vec3V V3ColX(const Vec3V a, const Vec3V b, const Vec3V c);
//(a.y, b.y, c.y)
PX_FORCE_INLINE Vec3V V3ColY(const Vec3V a, const Vec3V b, const Vec3V c);
//(a.z, b.z, c.z)
PX_FORCE_INLINE Vec3V V3ColZ(const Vec3V a, const Vec3V b, const Vec3V c);
 
//(0,0,0,0)
PX_FORCE_INLINE Vec3V V3Zero();
//(1,1,1,1)
PX_FORCE_INLINE Vec3V V3One();
//(PX_EPS_REAL,PX_EPS_REAL,PX_EPS_REAL,PX_EPS_REAL)
PX_FORCE_INLINE Vec3V V3Eps();
//-c (per component)
PX_FORCE_INLINE Vec3V V3Neg(const Vec3V c);
// a+b (per component)
PX_FORCE_INLINE Vec3V V3Add(const Vec3V a, const Vec3V b);
// a-b (per component)
PX_FORCE_INLINE Vec3V V3Sub(const Vec3V a, const Vec3V b);
// a*b (per component)
PX_FORCE_INLINE Vec3V V3Scale(const Vec3V a, const FloatV b);
// a*b (per component)
PX_FORCE_INLINE Vec3V V3Mul(const Vec3V a, const Vec3V b);
// a/b (per component)
PX_FORCE_INLINE Vec3V V3ScaleInv(const Vec3V a, const FloatV b);
// a/b (per component)
PX_FORCE_INLINE Vec3V V3Div(const Vec3V a, const Vec3V b);
// a/b (per component)
PX_FORCE_INLINE Vec3V V3ScaleInvFast(const Vec3V a, const FloatV b);
// a/b (per component)
PX_FORCE_INLINE Vec3V V3DivFast(const Vec3V a, const Vec3V b);
// 1.0f/a
PX_FORCE_INLINE Vec3V V3Recip(const Vec3V a);
// 1.0f/a
PX_FORCE_INLINE Vec3V V3RecipFast(const Vec3V a);
// 1.0f/sqrt(a)
PX_FORCE_INLINE Vec3V V3Rsqrt(const Vec3V a);
// 1.0f/sqrt(a)
PX_FORCE_INLINE Vec3V V3RsqrtFast(const Vec3V a);
// a*b+c
PX_FORCE_INLINE Vec3V V3ScaleAdd(const Vec3V a, const FloatV b, const Vec3V c);
// c-a*b
PX_FORCE_INLINE Vec3V V3NegScaleSub(const Vec3V a, const FloatV b, const Vec3V c);
// a*b+c
PX_FORCE_INLINE Vec3V V3MulAdd(const Vec3V a, const Vec3V b, const Vec3V c);
// c-a*b
PX_FORCE_INLINE Vec3V V3NegMulSub(const Vec3V a, const Vec3V b, const Vec3V c);
// fabs(a)
PX_FORCE_INLINE Vec3V V3Abs(const Vec3V a);
 
// a.b 
// Note: a.w and b.w must have value zero
PX_FORCE_INLINE FloatV V3Dot(const Vec3V a, const Vec3V b);
// aXb
// Note: a.w and b.w must have value zero
PX_FORCE_INLINE Vec3V V3Cross(const Vec3V a, const Vec3V b);
// |a.a|^1/2
// Note: a.w must have value zero
PX_FORCE_INLINE FloatV V3Length(const Vec3V a);
// a.a
// Note: a.w must have value zero
PX_FORCE_INLINE FloatV V3LengthSq(const Vec3V a);
// a*|a.a|^-1/2
// Note: a.w must have value zero
PX_FORCE_INLINE Vec3V V3Normalize(const Vec3V a);
// a.a>0 ? a*|a.a|^-1/2 : (0,0,0,0)
// Note: a.w must have value zero
PX_FORCE_INLINE FloatV V3Length(const Vec3V a);
// a.a>0 ? a*|a.a|^-1/2 : unsafeReturnValue 
// Note: a.w must have value zero
PX_FORCE_INLINE Vec3V V3NormalizeSafe(const Vec3V a, const Vec3V unsafeReturnValue);
// a.x + a.y + a.z
// Note: a.w must have value zero
PX_FORCE_INLINE FloatV V3SumElems(const Vec3V a);
 
// c ? a : b (per component)
PX_FORCE_INLINE Vec3V V3Sel(const BoolV c, const Vec3V a, const Vec3V b);
// a>b (per component)
PX_FORCE_INLINE BoolV V3IsGrtr(const Vec3V a, const Vec3V b);
// a>=b (per component)
PX_FORCE_INLINE BoolV V3IsGrtrOrEq(const Vec3V a, const Vec3V b);
// a==b (per component)
PX_FORCE_INLINE BoolV V3IsEq(const Vec3V a, const Vec3V b);
// Max(a,b) (per component)
PX_FORCE_INLINE Vec3V V3Max(const Vec3V a, const Vec3V b);
// Min(a,b) (per component)
PX_FORCE_INLINE Vec3V V3Min(const Vec3V a, const Vec3V b);
 
// Extract the maximum value from a
// Note: a.w must have value zero
PX_FORCE_INLINE FloatV V3ExtractMax(const Vec3V a);
 
// Extract the minimum value from a
// Note: a.w must have value zero
PX_FORCE_INLINE FloatV V3ExtractMin(const Vec3V a);
 
// Clamp(a,b) (per component)
PX_FORCE_INLINE Vec3V V3Clamp(const Vec3V a, const Vec3V minV, const Vec3V maxV);
 
// Extract the sign for each component
PX_FORCE_INLINE Vec3V V3Sign(const Vec3V a);
 
// Test all components.
// (a.x>b.x && a.y>b.y && a.z>b.z)
// Note: a.w and b.w must have value zero
PX_FORCE_INLINE PxU32 V3AllGrtr(const Vec3V a, const Vec3V b);
// (a.x>=b.x && a.y>=b.y && a.z>=b.z)
// Note: a.w and b.w must have value zero
PX_FORCE_INLINE PxU32 V3AllGrtrOrEq(const Vec3V a, const Vec3V b);
// (a.x==b.x && a.y==b.y && a.z==b.z)
// Note: a.w and b.w must have value zero
PX_FORCE_INLINE PxU32 V3AllEq(const Vec3V a, const Vec3V b);
// a.x<min.x || a.y<min.y || a.z<min.z || a.x>max.x || a.y>max.y || a.z>max.z
// Note: a.w and min.w and max.w must have value zero
PX_FORCE_INLINE PxU32 V3OutOfBounds(const Vec3V a, const Vec3V min, const Vec3V max);
// a.x>=min.x && a.y>=min.y && a.z>=min.z && a.x<=max.x && a.y<=max.y && a.z<=max.z
// Note: a.w and min.w and max.w must have value zero
PX_FORCE_INLINE PxU32 V3InBounds(const Vec3V a, const Vec3V min, const Vec3V max);
// a.x<-bounds.x || a.y<=-bounds.y || a.z<bounds.z || a.x>bounds.x || a.y>bounds.y || a.z>bounds.z
// Note: a.w and bounds.w must have value zero
PX_FORCE_INLINE PxU32 V3OutOfBounds(const Vec3V a, const Vec3V bounds);
// a.x>=-bounds.x && a.y>=-bounds.y && a.z>=-bounds.z && a.x<=bounds.x && a.y<=bounds.y && a.z<=bounds.z
// Note: a.w and bounds.w must have value zero
PX_FORCE_INLINE PxU32 V3InBounds(const Vec3V a, const Vec3V bounds);
 
//(floor(a.x + 0.5f), floor(a.y + 0.5f), floor(a.z + 0.5f))
PX_FORCE_INLINE Vec3V V3Round(const Vec3V a);
 
//(sinf(a.x), sinf(a.y), sinf(a.z))
PX_FORCE_INLINE Vec3V V3Sin(const Vec3V a);
//(cosf(a.x), cosf(a.y), cosf(a.z))
PX_FORCE_INLINE Vec3V V3Cos(const Vec3V a);
 
//(a.y,a.z,a.z)
PX_FORCE_INLINE Vec3V V3PermYZZ(const Vec3V a);
//(a.x,a.y,a.x)
PX_FORCE_INLINE Vec3V V3PermXYX(const Vec3V a);
//(a.y,a.z,a.x)
PX_FORCE_INLINE Vec3V V3PermYZX(const Vec3V a);
//(a.z, a.x, a.y)
PX_FORCE_INLINE Vec3V V3PermZXY(const Vec3V a);
//(a.z,a.z,a.y)
PX_FORCE_INLINE Vec3V V3PermZZY(const Vec3V a);
//(a.y,a.x,a.x)
PX_FORCE_INLINE Vec3V V3PermYXX(const Vec3V a);
//(0, v1.z, v0.y)
PX_FORCE_INLINE Vec3V V3Perm_Zero_1Z_0Y(const Vec3V v0, const Vec3V v1);
//(v0.z, 0, v1.x)
PX_FORCE_INLINE Vec3V V3Perm_0Z_Zero_1X(const Vec3V v0, const Vec3V v1);
//(v1.y, v0.x, 0)
PX_FORCE_INLINE Vec3V V3Perm_1Y_0X_Zero(const Vec3V v0, const Vec3V v1);
 
// Transpose 3 Vec3Vs inplace. Sets the w component to zero
// [ x0, y0, z0, w0] [ x1, y1, z1, w1]  [ x2, y2, z2, w2]  -> [x0 x1 x2 0] [y0 y1 y2 0] [z0 z1 z2 0]
PX_FORCE_INLINE void V3Transpose(Vec3V& col0, Vec3V& col1, Vec3V& col2);
 
// Math operations on Vec4V
 
//(f,f,f,f)
PX_FORCE_INLINE Vec4V V4Splat(const FloatV f);
 
//(f[0],f[1],f[2],f[3])
PX_FORCE_INLINE Vec4V V4Merge(const FloatV* const f);
//(x,y,z,w)
PX_FORCE_INLINE Vec4V V4Merge(const FloatVArg x, const FloatVArg y, const FloatVArg z, const FloatVArg w);
//(x.w, y.w, z.w, w.w)
PX_FORCE_INLINE Vec4V V4MergeW(const Vec4VArg x, const Vec4VArg y, const Vec4VArg z, const Vec4VArg w);
//(x.z, y.z, z.z, w.z)
PX_FORCE_INLINE Vec4V V4MergeZ(const Vec4VArg x, const Vec4VArg y, const Vec4VArg z, const Vec4VArg w);
//(x.y, y.y, z.y, w.y)
PX_FORCE_INLINE Vec4V V4MergeY(const Vec4VArg x, const Vec4VArg y, const Vec4VArg z, const Vec4VArg w);
//(x.x, y.x, z.x, w.x)
PX_FORCE_INLINE Vec4V V4MergeX(const Vec4VArg x, const Vec4VArg y, const Vec4VArg z, const Vec4VArg w);
 
//(a.x, b.x, a.y, b.y)
PX_FORCE_INLINE Vec4V V4UnpackXY(const Vec4VArg a, const Vec4VArg b);
//(a.z, b.z, a.w, b.w)
PX_FORCE_INLINE Vec4V V4UnpackZW(const Vec4VArg a, const Vec4VArg b);
 
//(1,0,0,0)
PX_FORCE_INLINE Vec4V V4UnitW();
//(0,1,0,0)
PX_FORCE_INLINE Vec4V V4UnitY();
//(0,0,1,0)
PX_FORCE_INLINE Vec4V V4UnitZ();
//(0,0,0,1)
PX_FORCE_INLINE Vec4V V4UnitW();
 
//(f.x,f.x,f.x,f.x)
PX_FORCE_INLINE FloatV V4GetX(const Vec4V f);
//(f.y,f.y,f.y,f.y)
PX_FORCE_INLINE FloatV V4GetY(const Vec4V f);
//(f.z,f.z,f.z,f.z)
PX_FORCE_INLINE FloatV V4GetZ(const Vec4V f);
//(f.w,f.w,f.w,f.w)
PX_FORCE_INLINE FloatV V4GetW(const Vec4V f);
 
//(f,v.y,v.z,v.w)
PX_FORCE_INLINE Vec4V V4SetX(const Vec4V v, const FloatV f);
//(v.x,f,v.z,v.w)
PX_FORCE_INLINE Vec4V V4SetY(const Vec4V v, const FloatV f);
//(v.x,v.y,f,v.w)
PX_FORCE_INLINE Vec4V V4SetZ(const Vec4V v, const FloatV f);
//(v.x,v.y,v.z,f)
PX_FORCE_INLINE Vec4V V4SetW(const Vec4V v, const FloatV f);
 
//(v.x,v.y,v.z,0)
PX_FORCE_INLINE Vec4V V4ClearW(const Vec4V v);
 
//(a[elementIndex], a[elementIndex], a[elementIndex], a[elementIndex])
template <int elementIndex>
PX_FORCE_INLINE Vec4V V4SplatElement(Vec4V a);
 
// v.x=f
PX_FORCE_INLINE void V4WriteX(Vec4V& v, const PxF32 f);
// v.y=f
PX_FORCE_INLINE void V4WriteY(Vec4V& v, const PxF32 f);
// v.z=f
PX_FORCE_INLINE void V4WriteZ(Vec4V& v, const PxF32 f);
// v.w=f
PX_FORCE_INLINE void V4WriteW(Vec4V& v, const PxF32 f);
// v.x=f.x, v.y=f.y, v.z=f.z
PX_FORCE_INLINE void V4WriteXYZ(Vec4V& v, const PxVec3& f);
// return v.x
PX_FORCE_INLINE PxF32 V4ReadX(const Vec4V& v);
// return v.y
PX_FORCE_INLINE PxF32 V4ReadY(const Vec4V& v);
// return v.z
PX_FORCE_INLINE PxF32 V4ReadZ(const Vec4V& v);
// return v.w
PX_FORCE_INLINE PxF32 V4ReadW(const Vec4V& v);
// return (v.x,v.y,v.z)
PX_FORCE_INLINE const PxVec3& V4ReadXYZ(const Vec4V& v);
 
//(0,0,0,0)
PX_FORCE_INLINE Vec4V V4Zero();
//(1,1,1,1)
PX_FORCE_INLINE Vec4V V4One();
//(PX_EPS_REAL,PX_EPS_REAL,PX_EPS_REAL,PX_EPS_REAL)
PX_FORCE_INLINE Vec4V V4Eps();
 
//-c (per component)
PX_FORCE_INLINE Vec4V V4Neg(const Vec4V c);
// a+b (per component)
PX_FORCE_INLINE Vec4V V4Add(const Vec4V a, const Vec4V b);
// a-b (per component)
PX_FORCE_INLINE Vec4V V4Sub(const Vec4V a, const Vec4V b);
// a*b (per component)
PX_FORCE_INLINE Vec4V V4Scale(const Vec4V a, const FloatV b);
// a*b (per component)
PX_FORCE_INLINE Vec4V V4Mul(const Vec4V a, const Vec4V b);
// a/b (per component)
PX_FORCE_INLINE Vec4V V4ScaleInv(const Vec4V a, const FloatV b);
// a/b (per component)
PX_FORCE_INLINE Vec4V V4Div(const Vec4V a, const Vec4V b);
// a/b (per component)
PX_FORCE_INLINE Vec4V V4ScaleInvFast(const Vec4V a, const FloatV b);
// a/b (per component)
PX_FORCE_INLINE Vec4V V4DivFast(const Vec4V a, const Vec4V b);
// 1.0f/a
PX_FORCE_INLINE Vec4V V4Recip(const Vec4V a);
// 1.0f/a
PX_FORCE_INLINE Vec4V V4RecipFast(const Vec4V a);
// 1.0f/sqrt(a)
PX_FORCE_INLINE Vec4V V4Rsqrt(const Vec4V a);
// 1.0f/sqrt(a)
PX_FORCE_INLINE Vec4V V4RsqrtFast(const Vec4V a);
// a*b+c
PX_FORCE_INLINE Vec4V V4ScaleAdd(const Vec4V a, const FloatV b, const Vec4V c);
// c-a*b
PX_FORCE_INLINE Vec4V V4NegScaleSub(const Vec4V a, const FloatV b, const Vec4V c);
// a*b+c
PX_FORCE_INLINE Vec4V V4MulAdd(const Vec4V a, const Vec4V b, const Vec4V c);
// c-a*b
PX_FORCE_INLINE Vec4V V4NegMulSub(const Vec4V a, const Vec4V b, const Vec4V c);
 
// fabs(a)
PX_FORCE_INLINE Vec4V V4Abs(const Vec4V a);
// bitwise a & ~b
PX_FORCE_INLINE Vec4V V4Andc(const Vec4V a, const VecU32V b);
 
// a.b (W is taken into account)
PX_FORCE_INLINE FloatV V4Dot(const Vec4V a, const Vec4V b);
// a.b (same computation as V3Dot. W is ignored in input)
PX_FORCE_INLINE FloatV V4Dot3(const Vec4V a, const Vec4V b);
// aXb (same computation as V3Cross. W is ignored in input and undefined in output)
PX_FORCE_INLINE Vec4V V4Cross(const Vec4V a, const Vec4V b);
 
//|a.a|^1/2
PX_FORCE_INLINE FloatV V4Length(const Vec4V a);
// a.a
PX_FORCE_INLINE FloatV V4LengthSq(const Vec4V a);
 
// a*|a.a|^-1/2
PX_FORCE_INLINE Vec4V V4Normalize(const Vec4V a);
// a.a>0 ? a*|a.a|^-1/2 : unsafeReturnValue 
PX_FORCE_INLINE Vec4V V4NormalizeSafe(const Vec4V a, const Vec4V unsafeReturnValue);
// a*|a.a|^-1/2
PX_FORCE_INLINE Vec4V V4NormalizeFast(const Vec4V a);
 
// c ? a : b (per component)
PX_FORCE_INLINE Vec4V V4Sel(const BoolV c, const Vec4V a, const Vec4V b);
// a>b (per component)
PX_FORCE_INLINE BoolV V4IsGrtr(const Vec4V a, const Vec4V b);
// a>=b (per component)
PX_FORCE_INLINE BoolV V4IsGrtrOrEq(const Vec4V a, const Vec4V b);
// a==b (per component)
PX_FORCE_INLINE BoolV V4IsEq(const Vec4V a, const Vec4V b);
// Max(a,b) (per component)
PX_FORCE_INLINE Vec4V V4Max(const Vec4V a, const Vec4V b);
// Min(a,b) (per component)
PX_FORCE_INLINE Vec4V V4Min(const Vec4V a, const Vec4V b);
// Get the maximum component from a
PX_FORCE_INLINE FloatV V4ExtractMax(const Vec4V a);
// Get the minimum component from a
PX_FORCE_INLINE FloatV V4ExtractMin(const Vec4V a);
 
// Clamp(a,b) (per component)
PX_FORCE_INLINE Vec4V V4Clamp(const Vec4V a, const Vec4V minV, const Vec4V maxV);
 
// return 1 if all components of a are greater than all components of b.
PX_FORCE_INLINE PxU32 V4AllGrtr(const Vec4V a, const Vec4V b);
// return 1 if all components of a are greater than or equal to all components of b
PX_FORCE_INLINE PxU32 V4AllGrtrOrEq(const Vec4V a, const Vec4V b);
// return 1 if XYZ components of a are greater than or equal to XYZ components of b. W is ignored.
PX_FORCE_INLINE PxU32 V4AllGrtrOrEq3(const Vec4V a, const Vec4V b);
// return 1 if all components of a are equal to all components of b
PX_FORCE_INLINE PxU32 V4AllEq(const Vec4V a, const Vec4V b);
// return 1 if any XYZ component of a is greater than the corresponding component of b. W is ignored.
PX_FORCE_INLINE PxU32 V4AnyGrtr3(const Vec4V a, const Vec4V b);
 
// round(a)(per component)
PX_FORCE_INLINE Vec4V V4Round(const Vec4V a);
// sin(a) (per component)
PX_FORCE_INLINE Vec4V V4Sin(const Vec4V a);
// cos(a) (per component)
PX_FORCE_INLINE Vec4V V4Cos(const Vec4V a);
 
// Permute v into a new vec4v with YXWZ format
PX_FORCE_INLINE Vec4V V4PermYXWZ(const Vec4V v);
// Permute v into a new vec4v with XZXZ format
PX_FORCE_INLINE Vec4V V4PermXZXZ(const Vec4V v);
// Permute v into a new vec4v with YWYW format
PX_FORCE_INLINE Vec4V V4PermYWYW(const Vec4V v);
// Permute v into a new vec4v with YZXW format
PX_FORCE_INLINE Vec4V V4PermYZXW(const Vec4V v);
// Permute v into a new vec4v with ZWXY format - equivalent to a swap of the two 64bit parts of the vector
PX_FORCE_INLINE Vec4V V4PermZWXY(const Vec4V a);
 
// Permute v into a new vec4v with format {a[x], a[y], a[z], a[w]}
// V4Perm<1,3,1,3> is equal to V4PermYWYW
// V4Perm<0,2,0,2> is equal to V4PermXZXZ
// V3Perm<1,0,3,2> is equal to V4PermYXWZ
template <PxU8 x, PxU8 y, PxU8 z, PxU8 w>
PX_FORCE_INLINE Vec4V V4Perm(const Vec4V a);
 
// Transpose 4 Vec4Vs inplace.
// [ x0, y0, z0, w0] [ x1, y1, z1, w1] [ x2, y2, z2, w2] [ x3, y3, z3, w3] ->
// [ x0, x1, x2, x3] [ y0, y1, y2, y3] [ z0, z1, z2, z3] [ w0, w1, w2, w3]
PX_FORCE_INLINE void V3Transpose(Vec3V& col0, Vec3V& col1, Vec3V& col2);
 
// q = cos(a/2) + u*sin(a/2)
PX_FORCE_INLINE QuatV QuatV_From_RotationAxisAngle(const Vec3V u, const FloatV a);
// convert q to a unit quaternion
PX_FORCE_INLINE QuatV QuatNormalize(const QuatV q);
//|q.q|^1/2
PX_FORCE_INLINE FloatV QuatLength(const QuatV q);
// q.q
PX_FORCE_INLINE FloatV QuatLengthSq(const QuatV q);
// a.b
PX_FORCE_INLINE FloatV QuatDot(const QuatV a, const QuatV b);
//(-q.x, -q.y, -q.z, q.w)
PX_FORCE_INLINE QuatV QuatConjugate(const QuatV q);
//(q.x, q.y, q.z)
PX_FORCE_INLINE Vec3V QuatGetImaginaryPart(const QuatV q);
// convert quaternion to matrix 33
PX_FORCE_INLINE Mat33V QuatGetMat33V(const QuatVArg q);
// convert quaternion to matrix 33
PX_FORCE_INLINE void QuatGetMat33V(const QuatVArg q, Vec3V& column0, Vec3V& column1, Vec3V& column2);
// convert matrix 33 to quaternion
PX_FORCE_INLINE QuatV Mat33GetQuatV(const Mat33V& a);
// brief computes rotation of x-axis
PX_FORCE_INLINE Vec3V QuatGetBasisVector0(const QuatV q);
// brief computes rotation of y-axis
PX_FORCE_INLINE Vec3V QuatGetBasisVector1(const QuatV q);
// brief computes rotation of z-axis
PX_FORCE_INLINE Vec3V QuatGetBasisVector2(const QuatV q);
// calculate the rotation vector from q and v
PX_FORCE_INLINE Vec3V QuatRotate(const QuatV q, const Vec3V v);
// calculate the rotation vector from the conjugate quaternion and v
PX_FORCE_INLINE Vec3V QuatRotateInv(const QuatV q, const Vec3V v);
// quaternion multiplication
PX_FORCE_INLINE QuatV QuatMul(const QuatV a, const QuatV b);
// quaternion add
PX_FORCE_INLINE QuatV QuatAdd(const QuatV a, const QuatV b);
// (-q.x, -q.y, -q.z, -q.w)
PX_FORCE_INLINE QuatV QuatNeg(const QuatV q);
// (a.x - b.x, a.y-b.y, a.z-b.z, a.w-b.w )
PX_FORCE_INLINE QuatV QuatSub(const QuatV a, const QuatV b);
// (a.x*b, a.y*b, a.z*b, a.w*b)
PX_FORCE_INLINE QuatV QuatScale(const QuatV a, const FloatV b);
// (x = v[0], y = v[1], z = v[2], w =v[3])
PX_FORCE_INLINE QuatV QuatMerge(const FloatV* const v);
// (x = v[0], y = v[1], z = v[2], w =v[3])
PX_FORCE_INLINE QuatV QuatMerge(const FloatVArg x, const FloatVArg y, const FloatVArg z, const FloatVArg w);
// (x = 0.f, y = 0.f, z = 0.f, w = 1.f)
PX_FORCE_INLINE QuatV QuatIdentity();
// check for each component is valid
PX_FORCE_INLINE bool isFiniteQuatV(const QuatV q);
// check for each component is valid
PX_FORCE_INLINE bool isValidQuatV(const QuatV q);
// check for each component is valid
PX_FORCE_INLINE bool isSaneQuatV(const QuatV q);
 
// Math operations on 16-byte aligned booleans.
// x=false  y=false     z=false     w=false
PX_FORCE_INLINE BoolV BFFFF();
// x=false  y=false     z=false     w=true
PX_FORCE_INLINE BoolV BFFFT();
// x=false  y=false     z=true      w=false
PX_FORCE_INLINE BoolV BFFTF();
// x=false  y=false     z=true      w=true
PX_FORCE_INLINE BoolV BFFTT();
// x=false  y=true      z=false     w=false
PX_FORCE_INLINE BoolV BFTFF();
// x=false  y=true      z=false     w=true
PX_FORCE_INLINE BoolV BFTFT();
// x=false  y=true      z=true      w=false
PX_FORCE_INLINE BoolV BFTTF();
// x=false  y=true      z=true      w=true
PX_FORCE_INLINE BoolV BFTTT();
// x=true   y=false     z=false     w=false
PX_FORCE_INLINE BoolV BTFFF();
// x=true   y=false     z=false     w=true
PX_FORCE_INLINE BoolV BTFFT();
// x=true   y=false     z=true      w=false
PX_FORCE_INLINE BoolV BTFTF();
// x=true   y=false     z=true      w=true
PX_FORCE_INLINE BoolV BTFTT();
// x=true   y=true      z=false     w=false
PX_FORCE_INLINE BoolV BTTFF();
// x=true   y=true      z=false     w=true
PX_FORCE_INLINE BoolV BTTFT();
// x=true   y=true      z=true      w=false
PX_FORCE_INLINE BoolV BTTTF();
// x=true   y=true      z=true      w=true
PX_FORCE_INLINE BoolV BTTTT();
 
// x=false  y=false     z=false     w=true
PX_FORCE_INLINE BoolV BWMask();
// x=true   y=false     z=false     w=false
PX_FORCE_INLINE BoolV BXMask();
// x=false  y=true      z=false     w=false
PX_FORCE_INLINE BoolV BYMask();
// x=false  y=false     z=true      w=false
PX_FORCE_INLINE BoolV BZMask();
 
// get x component
PX_FORCE_INLINE BoolV BGetX(const BoolV f);
// get y component
PX_FORCE_INLINE BoolV BGetY(const BoolV f);
// get z component
PX_FORCE_INLINE BoolV BGetZ(const BoolV f);
// get w component
PX_FORCE_INLINE BoolV BGetW(const BoolV f);
 
// Use elementIndex to splat xxxx or yyyy or zzzz or wwww
template <int elementIndex>
PX_FORCE_INLINE BoolV BSplatElement(Vec4V a);
 
// component-wise && (AND)
PX_FORCE_INLINE BoolV BAnd(const BoolV a, const BoolV b);
// component-wise || (OR)
PX_FORCE_INLINE BoolV BOr(const BoolV a, const BoolV b);
// component-wise not
PX_FORCE_INLINE BoolV BNot(const BoolV a);
 
// if all four components are true, return true, otherwise return false
PX_FORCE_INLINE BoolV BAllTrue4(const BoolV a);
 
// if any four components is true, return true, otherwise return false
PX_FORCE_INLINE BoolV BAnyTrue4(const BoolV a);
 
// if all three(0, 1, 2) components are true, return true, otherwise return false
PX_FORCE_INLINE BoolV BAllTrue3(const BoolV a);
 
// if any three (0, 1, 2) components is true, return true, otherwise return false
PX_FORCE_INLINE BoolV BAnyTrue3(const BoolV a);
 
// Return 1 if all components equal, zero otherwise.
PX_FORCE_INLINE PxU32 BAllEq(const BoolV a, const BoolV b);
 
// Specialized/faster BAllEq function for b==TTTT
PX_FORCE_INLINE PxU32 BAllEqTTTT(const BoolV a);
// Specialized/faster BAllEq function for b==FFFF
PX_FORCE_INLINE PxU32 BAllEqFFFF(const BoolV a);
 
PX_FORCE_INLINE PxU32 BGetBitMask(const BoolV a);
 
// VecI32V stuff
 
PX_FORCE_INLINE VecI32V VecI32V_Zero();
 
PX_FORCE_INLINE VecI32V VecI32V_One();
 
PX_FORCE_INLINE VecI32V VecI32V_Two();
 
PX_FORCE_INLINE VecI32V VecI32V_MinusOne();
 
// Compute a shift parameter for VecI32V_LeftShift and VecI32V_RightShift
// Each element of shift must be identical ie the vector must have form {count, count, count, count} with count>=0
PX_FORCE_INLINE VecShiftV VecI32V_PrepareShift(const VecI32VArg shift);
 
// Shift each element of a leftwards by the same amount
// Compute shift with VecI32V_PrepareShift
//{a.x<<shift[0], a.y<<shift[0], a.z<<shift[0], a.w<<shift[0]}
PX_FORCE_INLINE VecI32V VecI32V_LeftShift(const VecI32VArg a, const VecShiftVArg shift);
 
// Shift each element of a rightwards by the same amount
// Compute shift with VecI32V_PrepareShift
//{a.x>>shift[0], a.y>>shift[0], a.z>>shift[0], a.w>>shift[0]}
PX_FORCE_INLINE VecI32V VecI32V_RightShift(const VecI32VArg a, const VecShiftVArg shift);
 
PX_FORCE_INLINE VecI32V VecI32V_Add(const VecI32VArg a, const VecI32VArg b);
 
PX_FORCE_INLINE VecI32V VecI32V_Or(const VecI32VArg a, const VecI32VArg b);
 
PX_FORCE_INLINE VecI32V VecI32V_GetX(const VecI32VArg a);
 
PX_FORCE_INLINE VecI32V VecI32V_GetY(const VecI32VArg a);
 
PX_FORCE_INLINE VecI32V VecI32V_GetZ(const VecI32VArg a);
 
PX_FORCE_INLINE VecI32V VecI32V_GetW(const VecI32VArg a);
 
PX_FORCE_INLINE VecI32V VecI32V_Sub(const VecI32VArg a, const VecI32VArg b);
 
PX_FORCE_INLINE BoolV VecI32V_IsGrtr(const VecI32VArg a, const VecI32VArg b);
 
PX_FORCE_INLINE BoolV VecI32V_IsEq(const VecI32VArg a, const VecI32VArg b);
 
PX_FORCE_INLINE VecI32V V4I32Sel(const BoolV c, const VecI32V a, const VecI32V b);
 
// VecU32V stuff
 
PX_FORCE_INLINE VecU32V U4Zero();
 
PX_FORCE_INLINE VecU32V U4One();
 
PX_FORCE_INLINE VecU32V U4Two();
 
PX_FORCE_INLINE BoolV V4IsEqU32(const VecU32V a, const VecU32V b);
 
PX_FORCE_INLINE VecU32V V4U32Sel(const BoolV c, const VecU32V a, const VecU32V b);
 
PX_FORCE_INLINE VecU32V V4U32or(VecU32V a, VecU32V b);
 
PX_FORCE_INLINE VecU32V V4U32xor(VecU32V a, VecU32V b);
 
PX_FORCE_INLINE VecU32V V4U32and(VecU32V a, VecU32V b);
 
PX_FORCE_INLINE VecU32V V4U32Andc(VecU32V a, VecU32V b);
 
// VecU32 - why does this not return a bool?
PX_FORCE_INLINE VecU32V V4IsGrtrV32u(const Vec4V a, const Vec4V b);
 
// Math operations on 16-byte aligned Mat33s (represents any 3x3 matrix)
PX_FORCE_INLINE Mat33V M33Load(const PxMat33& m) 
{
    return Mat33V(Vec3V_From_Vec4V(V4LoadU(&m.column0.x)), 
    Vec3V_From_Vec4V(V4LoadU(&m.column1.x)), V3LoadU(m.column2)); 
}
// a*b
PX_FORCE_INLINE Vec3V M33MulV3(const Mat33V& a, const Vec3V b);
// A*x + b
PX_FORCE_INLINE Vec3V M33MulV3AddV3(const Mat33V& A, const Vec3V b, const Vec3V c);
// transpose(a) * b
PX_FORCE_INLINE Vec3V M33TrnspsMulV3(const Mat33V& a, const Vec3V b);
// a*b
PX_FORCE_INLINE Mat33V M33MulM33(const Mat33V& a, const Mat33V& b);
// a+b
PX_FORCE_INLINE Mat33V M33Add(const Mat33V& a, const Mat33V& b);
// a+b
PX_FORCE_INLINE Mat33V M33Sub(const Mat33V& a, const Mat33V& b);
//-a
PX_FORCE_INLINE Mat33V M33Neg(const Mat33V& a);
// absolute value of the matrix
PX_FORCE_INLINE Mat33V M33Abs(const Mat33V& a);
// inverse mat
PX_FORCE_INLINE Mat33V M33Inverse(const Mat33V& a);
// transpose(a)
PX_FORCE_INLINE Mat33V M33Trnsps(const Mat33V& a);
// create an identity matrix
PX_FORCE_INLINE Mat33V M33Identity();
 
// create a vec3 to store the diagonal element of the M33
PX_FORCE_INLINE Mat33V M33Diagonal(const Vec3VArg);
 
// Not implemented
// return 1 if all components of a are equal to all components of b
// PX_FORCE_INLINE PxU32 V4U32AllEq(const VecU32V a, const VecU32V b);
// v.w=f
// PX_FORCE_INLINE void V3WriteW(Vec3V& v, const PxF32 f);
// PX_FORCE_INLINE PxF32 V3ReadW(const Vec3V& v);
 
// Not used
// PX_FORCE_INLINE Vec4V V4LoadAligned(Vec4V* addr);
// PX_FORCE_INLINE Vec4V V4LoadUnaligned(Vec4V* addr);
// floor(a)(per component)
// PX_FORCE_INLINE Vec4V V4Floor(Vec4V a);
// ceil(a) (per component)
// PX_FORCE_INLINE Vec4V V4Ceil(Vec4V a);
// PX_FORCE_INLINE VecU32V V4ConvertToU32VSaturate(const Vec4V a, PxU32 power);
 
// Math operations on 16-byte aligned Mat34s (represents transformation matrix - rotation and translation).
// namespace _Mat34V
//{
//  //a*b
//  PX_FORCE_INLINE Vec3V multiplyV(const Mat34V& a, const Vec3V b);
//  //a_rotation * b
//  PX_FORCE_INLINE Vec3V multiply3X3V(const Mat34V& a, const Vec3V b);
//  //transpose(a_rotation)*b
//  PX_FORCE_INLINE Vec3V multiplyTranspose3X3V(const Mat34V& a, const Vec3V b);
//  //a*b
//  PX_FORCE_INLINE Mat34V multiplyV(const Mat34V& a, const Mat34V& b);
//  //a_rotation*b
//  PX_FORCE_INLINE Mat33V multiply3X3V(const Mat34V& a, const Mat33V& b);
//  //a_rotation*b_rotation
//  PX_FORCE_INLINE Mat33V multiply3X3V(const Mat34V& a, const Mat34V& b);
//  //a+b
//  PX_FORCE_INLINE Mat34V addV(const Mat34V& a, const Mat34V& b);
//  //a^-1
//  PX_FORCE_INLINE Mat34V getInverseV(const Mat34V& a);
//  //transpose(a_rotation)
//  PX_FORCE_INLINE Mat33V getTranspose3X3(const Mat34V& a);
//}; //namespace _Mat34V
 
// a*b
//#define M34MulV3(a,b)         (M34MulV3(a,b))
//#define M34Mul33V3(a,b)           (M34Mul33V3(a,b))
//#define M34TrnspsMul33V3(a,b) (M34TrnspsMul33V3(a,b))
//#define M34MulM34(a,b)            (_Mat34V::multiplyV(a,b))
// a_rotation*b
//#define M34MulM33(a,b)            (M34MulM33(a,b))
// a_rotation*b_rotation
//#define M34Mul33MM34(a,b)     (M34MulM33(a,b))
// a+b
//#define M34Add(a,b)               (M34Add(a,b))
//#define M34Inverse(a,b)           (M34Inverse(a))
// transpose(a_rotation)
//#define M34Trnsps33(a)            (M33Trnsps3X3(a))
 
// Math operations on 16-byte aligned Mat44s (represents any 4x4 matrix)
// namespace _Mat44V
//{
//  //a*b
//  PX_FORCE_INLINE Vec4V multiplyV(const Mat44V& a, const Vec4V b);
//  //transpose(a)*b
//  PX_FORCE_INLINE Vec4V multiplyTransposeV(const Mat44V& a, const Vec4V b);
//  //a*b
//  PX_FORCE_INLINE Mat44V multiplyV(const Mat44V& a, const Mat44V& b);
//  //a+b
//  PX_FORCE_INLINE Mat44V addV(const Mat44V& a, const Mat44V& b);
//  //a&-1
//  PX_FORCE_INLINE Mat44V getInverseV(const Mat44V& a);
//  //transpose(a)
//  PX_FORCE_INLINE Mat44V getTransposeV(const Mat44V& a);
//}; //namespace _Mat44V
 
// namespace _VecU32V
//{
//  // pack 8 U32s to 8 U16s with saturation
//  PX_FORCE_INLINE VecU16V pack2U32VToU16VSaturate(VecU32V a, VecU32V b);
//  PX_FORCE_INLINE VecU32V orV(VecU32V a, VecU32V b);
//  PX_FORCE_INLINE VecU32V andV(VecU32V a, VecU32V b);
//  PX_FORCE_INLINE VecU32V andcV(VecU32V a, VecU32V b);
//  // conversion from integer to float
//  PX_FORCE_INLINE Vec4V convertToVec4V(VecU32V a);
//  // splat a[elementIndex] into all fields of a
//  template<int elementIndex>
//  PX_FORCE_INLINE VecU32V splatElement(VecU32V a);
//  PX_FORCE_INLINE void storeAligned(VecU32V a, VecU32V* address);
//};
 
// namespace _VecI32V
//{
//  template<int a> PX_FORCE_INLINE VecI32V splatI32();
//};
//
// namespace _VecU16V
//{
//  PX_FORCE_INLINE VecU16V orV(VecU16V a, VecU16V b);
//  PX_FORCE_INLINE VecU16V andV(VecU16V a, VecU16V b);
//  PX_FORCE_INLINE VecU16V andcV(VecU16V a, VecU16V b);
//  PX_FORCE_INLINE void storeAligned(VecU16V val, VecU16V *address);
//  PX_FORCE_INLINE VecU16V loadAligned(VecU16V* addr);
//  PX_FORCE_INLINE VecU16V loadUnaligned(VecU16V* addr);
//  PX_FORCE_INLINE VecU16V compareGt(VecU16V a, VecU16V b);
//  template<int elementIndex>
//  PX_FORCE_INLINE VecU16V splatElement(VecU16V a);
//  PX_FORCE_INLINE VecU16V subtractModulo(VecU16V a, VecU16V b);
//  PX_FORCE_INLINE VecU16V addModulo(VecU16V a, VecU16V b);
//  PX_FORCE_INLINE VecU32V getLo16(VecU16V a); // [0,2,4,6] 16-bit values to [0,1,2,3] 32-bit vector
//  PX_FORCE_INLINE VecU32V getHi16(VecU16V a); // [1,3,5,7] 16-bit values to [0,1,2,3] 32-bit vector
//};
//
// namespace _VecI16V
//{
//  template <int val> PX_FORCE_INLINE VecI16V splatImmediate();
//};
//
// namespace _VecU8V
//{
//};
 
// a*b
//#define M44MulV4(a,b)     (M44MulV4(a,b))
//#define M44TrnspsMulV4(a,b) (M44TrnspsMulV4(a,b))
//#define M44MulM44(a,b)        (M44MulM44(a,b))
//#define M44Add(a,b)           (M44Add(a,b))
//#define M44Inverse(a)     (M44Inverse(a))
//#define M44Trnsps(a)      (M44Trnsps(a))
 
// dsequeira: these used to be assert'd out in SIMD builds, but they're necessary if
// we want to be able to write some scalar functions which run using SIMD data structures
 
PX_FORCE_INLINE void V3WriteX(Vec3V& v, const PxF32 f)
{
    reinterpret_cast<PxVec3&>(v).x = f;
}
 
PX_FORCE_INLINE void V3WriteY(Vec3V& v, const PxF32 f)
{
    reinterpret_cast<PxVec3&>(v).y = f;
}
 
PX_FORCE_INLINE void V3WriteZ(Vec3V& v, const PxF32 f)
{
    reinterpret_cast<PxVec3&>(v).z = f;
}
 
PX_FORCE_INLINE void V3WriteXYZ(Vec3V& v, const PxVec3& f)
{
    reinterpret_cast<PxVec3&>(v) = f;
}
 
PX_FORCE_INLINE PxF32 V3ReadX(const Vec3V& v)
{
    return reinterpret_cast<const PxVec3&>(v).x;
}
 
PX_FORCE_INLINE PxF32 V3ReadY(const Vec3V& v)
{
    return reinterpret_cast<const PxVec3&>(v).y;
}
 
PX_FORCE_INLINE PxF32 V3ReadZ(const Vec3V& v)
{
    return reinterpret_cast<const PxVec3&>(v).z;
}
 
PX_FORCE_INLINE const PxVec3& V3ReadXYZ(const Vec3V& v)
{
    return reinterpret_cast<const PxVec3&>(v);
}
 
PX_FORCE_INLINE void V4WriteX(Vec4V& v, const PxF32 f)
{
    reinterpret_cast<PxVec4&>(v).x = f;
}
 
PX_FORCE_INLINE void V4WriteY(Vec4V& v, const PxF32 f)
{
    reinterpret_cast<PxVec4&>(v).y = f;
}
 
PX_FORCE_INLINE void V4WriteZ(Vec4V& v, const PxF32 f)
{
    reinterpret_cast<PxVec4&>(v).z = f;
}
 
PX_FORCE_INLINE void V4WriteW(Vec4V& v, const PxF32 f)
{
    reinterpret_cast<PxVec4&>(v).w = f;
}
 
PX_FORCE_INLINE void V4WriteXYZ(Vec4V& v, const PxVec3& f)
{
    reinterpret_cast<PxVec3&>(v) = f;
}
 
PX_FORCE_INLINE PxF32 V4ReadX(const Vec4V& v)
{
    return reinterpret_cast<const PxVec4&>(v).x;
}
 
PX_FORCE_INLINE PxF32 V4ReadY(const Vec4V& v)
{
    return reinterpret_cast<const PxVec4&>(v).y;
}
 
PX_FORCE_INLINE PxF32 V4ReadZ(const Vec4V& v)
{
    return reinterpret_cast<const PxVec4&>(v).z;
}
 
PX_FORCE_INLINE PxF32 V4ReadW(const Vec4V& v)
{
    return reinterpret_cast<const PxVec4&>(v).w;
}
 
PX_FORCE_INLINE const PxVec3& V4ReadXYZ(const Vec4V& v)
{
    return reinterpret_cast<const PxVec3&>(v);
}
 
// this macro transposes 4 Vec4V into 3 Vec4V (assuming that the W component can be ignored
#define PX_TRANSPOSE_44_34(inA, inB, inC, inD, outA, outB, outC)                                                       \
outA = V4UnpackXY(inA, inC);                                                                                           \
inA = V4UnpackZW(inA, inC);                                                                                            \
inC = V4UnpackXY(inB, inD);                                                                                            \
inB = V4UnpackZW(inB, inD);                                                                                            \
outB = V4UnpackZW(outA, inC);                                                                                          \
outA = V4UnpackXY(outA, inC);                                                                                          \
outC = V4UnpackXY(inA, inB);
 
// this macro transposes 3 Vec4V into 4 Vec4V (with W components as garbage!)
#define PX_TRANSPOSE_34_44(inA, inB, inC, outA, outB, outC, outD)                                                      \
    outA = V4UnpackXY(inA, inC);                                                                                       \
    inA = V4UnpackZW(inA, inC);                                                                                        \
    outC = V4UnpackXY(inB, inB);                                                                                       \
    inC = V4UnpackZW(inB, inB);                                                                                        \
    outB = V4UnpackZW(outA, outC);                                                                                     \
    outA = V4UnpackXY(outA, outC);                                                                                     \
    outC = V4UnpackXY(inA, inC);                                                                                       \
    outD = V4UnpackZW(inA, inC);
 
#define PX_TRANSPOSE_44(inA, inB, inC, inD, outA, outB, outC, outD)                                                    \
    outA = V4UnpackXY(inA, inC);                                                                                       \
    inA = V4UnpackZW(inA, inC);                                                                                        \
    inC = V4UnpackXY(inB, inD);                                                                                        \
    inB = V4UnpackZW(inB, inD);                                                                                        \
    outB = V4UnpackZW(outA, inC);                                                                                      \
    outA = V4UnpackXY(outA, inC);                                                                                      \
    outC = V4UnpackXY(inA, inB);                                                                                       \
    outD = V4UnpackZW(inA, inB);
 
// This function returns a Vec4V, where each element is the dot product of one pair of Vec3Vs. On PC, each element in
// the result should be identical to the results if V3Dot was performed
// for each pair of Vec3V.
// However, on other platforms, the result might diverge by some small margin due to differences in FP rounding, e.g. if
// _mm_dp_ps was used or some other approximate dot product or fused madd operations
// were used.
// Where there does not exist a hw-accelerated dot-product operation, this approach should be the fastest way to compute
// the dot product of 4 vectors.
PX_FORCE_INLINE Vec4V V3Dot4(const Vec3VArg a0, const Vec3VArg b0, const Vec3VArg a1, const Vec3VArg b1,
                             const Vec3VArg a2, const Vec3VArg b2, const Vec3VArg a3, const Vec3VArg b3)
{
    Vec4V a0b0 = Vec4V_From_Vec3V(V3Mul(a0, b0));
    Vec4V a1b1 = Vec4V_From_Vec3V(V3Mul(a1, b1));
    Vec4V a2b2 = Vec4V_From_Vec3V(V3Mul(a2, b2));
    Vec4V a3b3 = Vec4V_From_Vec3V(V3Mul(a3, b3));
 
    Vec4V aTrnsps, bTrnsps, cTrnsps;
 
    PX_TRANSPOSE_44_34(a0b0, a1b1, a2b2, a3b3, aTrnsps, bTrnsps, cTrnsps);
 
    return V4Add(V4Add(aTrnsps, bTrnsps), cTrnsps);
}
 
//(f.x,f.y,f.z,0) - Alternative/faster V3LoadU implementation when it is safe to read "W", i.e. the 32bits after the PxVec3.
PX_FORCE_INLINE Vec3V V3LoadU_SafeReadW(const PxVec3& f)
{
    return Vec3V_From_Vec4V(V4LoadU(&f.x));
}
 
} // namespace aos
#if !PX_DOXYGEN
} // namespace physx
#endif
 
// Now for the cross-platform implementations of the 16-byte aligned maths functions (win32/360/ppu/spu etc).
#if COMPILE_VECTOR_INTRINSICS
#include "PxInlineAoS.h"
#else // #if COMPILE_VECTOR_INTRINSICS
#include "PxVecMathAoSScalarInline.h"
#endif // #if !COMPILE_VECTOR_INTRINSICS
#include "PxVecQuat.h"
 
#endif