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/*
    This file implements common mathematical operations on vector types
    (float3, float4 etc.) since these are not provided as standard by CUDA.

    The syntax is modelled on the Cg standard library.
*/

#ifndef CUTIL_MATH_H
#define CUTIL_MATH_H

#include "foundation/PxPreprocessor.h"

#if PX_LINUX && PX_CLANG
#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Wdocumentation"
#endif
#include <vector_types.h>
#include "vector_functions.h" // why does this pull in the runtime api?
#if PX_LINUX && PX_CLANG
#pragma clang diagnostic pop
#endif

////////////////////////////////////////////////////////////////////////////////
typedef unsigned int uint;
typedef unsigned short ushort;
typedef unsigned char uchar;

// float functions
////////////////////////////////////////////////////////////////////////////////

#if !PX_CUDA_COMPILER
#ifndef PX_MIN_MAX
#define PX_MIN_MAX
#if PX_VC
PX_FORCE_INLINE __device__ __host__ float fmaxf(float a, float b) { return a > b ? a : b; }
PX_FORCE_INLINE __device__ __host__ float fminf(float a, float b) { return a < b ? a : b; }
#endif
PX_FORCE_INLINE __device__ __host__ int max(int a, int b) { return a > b ? a : b; }
PX_FORCE_INLINE __device__ __host__ unsigned int max(unsigned int a, unsigned int b) { return a > b ? a : b; }
PX_FORCE_INLINE __device__ __host__ int min(int a, int b) { return a < b ? a : b; }
PX_FORCE_INLINE __device__ __host__ unsigned int min(unsigned int a, unsigned int b) { return a < b ? a : b; }
#endif
#endif

// lerp
inline __device__ __host__ float lerp(float a, float b, float t)
{
    return a + t*(b-a);
}

template <typename T>
__device__ inline T bilerp(const T f00, const T f10, const T f01, const T f11, const float tx, const float ty)
{
	return lerp(lerp(f00, f10, tx), lerp(f01, f11, tx), ty);
}

template <typename T>
__device__ inline T trilerp(const T f000, const T f100, const T f010, const T f110, const T f001, const T f101, const T f011, const T f111,
							const float tx, const float ty, const float tz)
{
	return lerp(bilerp(f000, f100, f010, f110, tx, ty), bilerp(f001, f101, f011, f111, tx, ty), tz);
}

// clamp
inline __device__ __host__ float clamp(float f, float a, float b)
{
    return fmaxf(a, fminf(f, b));
}

// int2 functions
////////////////////////////////////////////////////////////////////////////////

// addition
inline __host__ __device__ int2 operator+(int2 a, int2 b)
{
    return make_int2(a.x + b.x, a.y + b.y);
}
inline __host__ __device__ void operator+=(int2 &a, int2 b)
{
    a.x += b.x; a.y += b.y;
}

// subtract
inline __host__ __device__ int2 operator-(int2 a, int2 b)
{
    return make_int2(a.x - b.x, a.y - b.y);
}
inline __host__ __device__ void operator-=(int2 &a, int2 b)
{
    a.x -= b.x; a.y -= b.y;
}

// multiply
inline __host__ __device__ int2 operator*(int2 a, int2 b)
{
    return make_int2(a.x * b.x, a.y * b.y);
}
inline __host__ __device__ int2 operator*(int2 a, int s)
{
    return make_int2(a.x * s, a.y * s);
}
inline __host__ __device__ int2 operator*(int s, int2 a)
{
    return make_int2(a.x * s, a.y * s);
}
inline __host__ __device__ void operator*=(int2 &a, int s)
{
    a.x *= s; a.y *= s;
}

// float2 functions
////////////////////////////////////////////////////////////////////////////////

// additional constructors
inline __host__ __device__ float2 make_float2(float s)
{
    return make_float2(s, s);
}
inline __host__ __device__ float2 make_float2(int2 a)
{
    return make_float2(float(a.x), float(a.y));
}

// addition
inline __host__ __device__ float2 operator+(float2 a, float2 b)
{
    return make_float2(a.x + b.x, a.y + b.y);
}
inline __host__ __device__ void operator+=(float2 &a, float2 b)
{
    a.x += b.x; a.y += b.y;
}

// subtract
inline __host__ __device__ float2 operator-(float2 a, float2 b)
{
    return make_float2(a.x - b.x, a.y - b.y);
}
inline __host__ __device__ void operator-=(float2 &a, float2 b)
{
    a.x -= b.x; a.y -= b.y;
}

// multiply
inline __host__ __device__ float2 operator*(float2 a, float2 b)
{
    return make_float2(a.x * b.x, a.y * b.y);
}
inline __host__ __device__ float2 operator*(float2 a, float s)
{
    return make_float2(a.x * s, a.y * s);
}
inline __host__ __device__ float2 operator*(float s, float2 a)
{
    return make_float2(a.x * s, a.y * s);
}
inline __host__ __device__ void operator*=(float2 &a, float s)
{
    a.x *= s; a.y *= s;
}

// divide
inline __host__ __device__ float2 operator/(float2 a, float2 b)
{
    return make_float2(a.x / b.x, a.y / b.y);
}
inline __host__ __device__ float2 operator/(float2 a, float s)
{
    float inv = 1.0f / s;
    return a * inv;
}
inline __host__ __device__ float2 operator/(float s, float2 a)
{
    float inv = 1.0f / s;
    return a * inv;
}
inline __host__ __device__ void operator/=(float2 &a, float s)
{
    float inv = 1.0f / s;
    a *= inv;
}

// lerp
inline __device__ __host__ float2 lerp(float2 a, float2 b, float t)
{
    return a + t*(b-a);
}

// clamp
inline __device__ __host__ float2 clamp(float2 v, float a, float b)
{
    return make_float2(clamp(v.x, a, b), clamp(v.y, a, b));
}

inline __device__ __host__ float2 clamp(float2 v, float2 a, float2 b)
{
    return make_float2(clamp(v.x, a.x, b.x), clamp(v.y, a.y, b.y));
}

// dot product
inline __host__ __device__ float dot(float2 a, float2 b)
{ 
    return a.x * b.x + a.y * b.y;
}

// length
inline __host__ __device__ float length(float2 v)
{
    return sqrtf(dot(v, v));
}

// normalize
inline __host__ __device__ float2 normalize(float2 v)
{
    float invLen = 1.0f / sqrtf(dot(v, v));
    return v * invLen;
}

// floor
inline __host__ __device__ float2 floor(const float2 v)
{
    return make_float2(floorf(v.x), floorf(v.y));
}

//validate
inline __host__ __device__ bool validate(const float2 v0, const float2 v1)
{
    return (v0.x == v1.x && v0.y == v1.y);
}


// float3 functions
////////////////////////////////////////////////////////////////////////////////

// additional constructors
inline __host__ __device__ float3 make_float3(float s)
{
    return make_float3(s, s, s);
}
inline __host__ __device__ float3 make_float3(float2 a)
{
    return make_float3(a.x, a.y, 0.0f);
}
inline __host__ __device__ float3 make_float3(float2 a, float s)
{
    return make_float3(a.x, a.y, s);
}
inline __host__ __device__ float3 make_float3(float4 a)
{
    return make_float3(a.x, a.y, a.z);  // discards w
}
inline __host__ __device__ float3 make_float3(int3 a)
{
    return make_float3(float(a.x), float(a.y), float(a.z));
}

// min
static __inline__ __host__ __device__ float3 fminf(float3 a, float3 b)
{
	return make_float3(fminf(a.x,b.x), fminf(a.y,b.y), fminf(a.z,b.z));
}

// max
static __inline__ __host__ __device__ float3 fmaxf(float3 a, float3 b)
{
	return make_float3(fmaxf(a.x,b.x), fmaxf(a.y,b.y), fmaxf(a.z,b.z));
}

// addition
inline __host__ __device__ float3 operator+(float3 a, float3 b)
{
    return make_float3(a.x + b.x, a.y + b.y, a.z + b.z);
}
inline __host__ __device__ void operator+=(float3 &a, float3 b)
{
    a.x += b.x; a.y += b.y; a.z += b.z;
}

// subtract
inline __host__ __device__ float3 operator-(float3 a, float3 b)
{
    return make_float3(a.x - b.x, a.y - b.y, a.z - b.z);
}
inline __host__ __device__ void operator-=(float3 &a, float3 b)
{
    a.x -= b.x; a.y -= b.y; a.z -= b.z;
}

// multiply
inline __host__ __device__ float3 operator*(float3 a, float3 b)
{
    return make_float3(a.x * b.x, a.y * b.y, a.z * b.z);
}
inline __host__ __device__ float3 operator*(float3 a, float s)
{
    return make_float3(a.x * s, a.y * s, a.z * s);
}
inline __host__ __device__ float3 operator*(float s, float3 a)
{
    return make_float3(a.x * s, a.y * s, a.z * s);
}
inline __host__ __device__ void operator*=(float3 &a, float s)
{
    a.x *= s; a.y *= s; a.z *= s;
}

// divide
inline __host__ __device__ float3 operator/(float3 a, float3 b)
{
    return make_float3(a.x / b.x, a.y / b.y, a.z / b.z);
}
inline __host__ __device__ float3 operator/(float3 a, float s)
{
    float inv = 1.0f / s;
    return a * inv;
}
inline __host__ __device__ float3 operator/(float s, float3 a)
{
    float inv = 1.0f / s;
    return a * inv;
}
inline __host__ __device__ void operator/=(float3 &a, float s)
{
    float inv = 1.0f / s;
    a *= inv;
}

// lerp
inline __device__ __host__ float3 lerp(float3 a, float3 b, float t)
{
    return a + t*(b-a);
}

// clamp
inline __device__ __host__ float3 clamp(float3 v, float a, float b)
{
    return make_float3(clamp(v.x, a, b), clamp(v.y, a, b), clamp(v.z, a, b));
}

inline __device__ __host__ float3 clamp(float3 v, float3 a, float3 b)
{
    return make_float3(clamp(v.x, a.x, b.x), clamp(v.y, a.y, b.y), clamp(v.z, a.z, b.z));
}

// dot product
inline __host__ __device__ float dot(float3 a, float3 b)
{ 
    return a.x * b.x + a.y * b.y + a.z * b.z;
}

// cross product
inline __host__ __device__ float3 cross(float3 a, float3 b)
{ 
    return make_float3(a.y*b.z - a.z*b.y, a.z*b.x - a.x*b.z, a.x*b.y - a.y*b.x); 
}

// length
inline __host__ __device__ float length(float3 v)
{
    return sqrtf(dot(v, v));
}

// normalize
inline __host__ __device__ float3 normalize(float3 v)
{
    float invLen = 1.0f / sqrtf(dot(v, v));
    return v * invLen;
}

// floor
inline __host__ __device__ float3 floor(const float3 v)
{
    return make_float3(floorf(v.x), floorf(v.y), floorf(v.z));
}

//validate
inline __host__ __device__ bool validate(const float3 v0, const float3 v1)
{
    return (v0.x == v1.x && v0.y == v1.y && v0.z == v1.z);
}


// float4 functions
////////////////////////////////////////////////////////////////////////////////

// additional constructors
inline __host__ __device__ float4 make_float4(float s)
{
    return make_float4(s, s, s, s);
}
inline __host__ __device__ float4 make_float4(float3 a)
{
    return make_float4(a.x, a.y, a.z, 0.0f);
}
inline __host__ __device__ float4 make_float4(float3 a, float w)
{
    return make_float4(a.x, a.y, a.z, w);
}
inline __host__ __device__ float4 make_float4(int4 a)
{
    return make_float4(float(a.x), float(a.y), float(a.z), float(a.w));
}

// min
static __inline__ __host__ __device__ float4 fminf(float4 a, float4 b)
{
	return make_float4(fminf(a.x,b.x), fminf(a.y,b.y), fminf(a.z,b.z), fminf(a.w,b.w));
}

// max
static __inline__ __host__ __device__ float4 fmaxf(float4 a, float4 b)
{
	return make_float4(fmaxf(a.x,b.x), fmaxf(a.y,b.y), fmaxf(a.z,b.z), fmaxf(a.w,b.w));
}

// addition
inline __host__ __device__ float4 operator+(float4 a, float4 b)
{
    return make_float4(a.x + b.x, a.y + b.y, a.z + b.z, a.w + b.w);
}
inline __host__ __device__ void operator+=(float4 &a, float4 b)
{
    a.x += b.x; a.y += b.y; a.z += b.z; a.w += b.w;
}

// subtract
inline __host__ __device__ float4 operator-(float4 a, float4 b)
{
    return make_float4(a.x - b.x, a.y - b.y, a.z - b.z, a.w - b.w);
}
inline __host__ __device__ void operator-=(float4 &a, float4 b)
{
    a.x -= b.x; a.y -= b.y; a.z -= b.z; a.w -= b.w;
}

// multiply
inline __host__ __device__ float4 operator*(float4 a, float s)
{
    return make_float4(a.x * s, a.y * s, a.z * s, a.w * s);
}
inline __host__ __device__ float4 operator*(float s, float4 a)
{
    return make_float4(a.x * s, a.y * s, a.z * s, a.w * s);
}
inline __host__ __device__ void operator*=(float4 &a, float s)
{
    a.x *= s; a.y *= s; a.z *= s; a.w *= s;
}

// divide
inline __host__ __device__ float4 operator/(float4 a, float4 b)
{
    return make_float4(a.x / b.x, a.y / b.y, a.z / b.z, a.w / b.w);
}
inline __host__ __device__ float4 operator/(float4 a, float s)
{
    float inv = 1.0f / s;
    return a * inv;
}
inline __host__ __device__ float4 operator/(float s, float4 a)
{
    float inv = 1.0f / s;
    return a * inv;
}
inline __host__ __device__ void operator/=(float4 &a, float s)
{
    float inv = 1.0f / s;
    a *= inv;
}

// lerp
inline __device__ __host__ float4 lerp(float4 a, float4 b, float t)
{
    return a + t*(b-a);
}

// clamp
inline __device__ __host__ float4 clamp(float4 v, float a, float b)
{
    return make_float4(clamp(v.x, a, b), clamp(v.y, a, b), clamp(v.z, a, b), clamp(v.w, a, b));
}

inline __device__ __host__ float4 clamp(float4 v, float4 a, float4 b)
{
    return make_float4(clamp(v.x, a.x, b.x), clamp(v.y, a.y, b.y), clamp(v.z, a.z, b.z), clamp(v.w, a.w, b.w));
}

// dot product
inline __host__ __device__ float dot(float4 a, float4 b)
{ 
    return a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w;
}

// length
inline __host__ __device__ float length(float4 r)
{
    return sqrtf(dot(r, r));
}

// normalize
inline __host__ __device__ float4 normalize(float4 v)
{
    float invLen = 1.0f / sqrtf(dot(v, v));
    return v * invLen;
}

// floor
inline __host__ __device__ float4 floor(const float4 v)
{
    return make_float4(floorf(v.x), floorf(v.y), floorf(v.z), floorf(v.w));
}

//validate
inline __host__ __device__ bool validate(const float4 v0, const float4 v1)
{
    return (v0.x == v1.x && v0.y == v1.y && v0.z == v1.z && v0.w == v1.w);
}

// int3 functions
////////////////////////////////////////////////////////////////////////////////

// additional constructors
inline __host__ __device__ int3 make_int3(int s)
{
    return make_int3(s, s, s);
}
inline __host__ __device__ int3 make_int3(float3 a)
{
    return make_int3(int(a.x), int(a.y), int(a.z));
}

// min
inline __host__ __device__ int3 min(int3 a, int3 b)
{
    return make_int3(min(a.x,b.x), min(a.y,b.y), min(a.z,b.z));
}

// max
inline __host__ __device__ int3 max(int3 a, int3 b)
{
    return make_int3(max(a.x,b.x), max(a.y,b.y), max(a.z,b.z));
}

// addition
inline __host__ __device__ int3 operator+(int3 a, int3 b)
{
    return make_int3(a.x + b.x, a.y + b.y, a.z + b.z);
}
inline __host__ __device__ void operator+=(int3 &a, int3 b)
{
    a.x += b.x; a.y += b.y; a.z += b.z;
}

// subtract
inline __host__ __device__ int3 operator-(int3 a, int3 b)
{
    return make_int3(a.x - b.x, a.y - b.y, a.z - b.z);
}

inline __host__ __device__ void operator-=(int3 &a, int3 b)
{
    a.x -= b.x; a.y -= b.y; a.z -= b.z;
}

// multiply
inline __host__ __device__ int3 operator*(int3 a, int3 b)
{
    return make_int3(a.x * b.x, a.y * b.y, a.z * b.z);
}
inline __host__ __device__ int3 operator*(int3 a, int s)
{
    return make_int3(a.x * s, a.y * s, a.z * s);
}
inline __host__ __device__ int3 operator*(int s, int3 a)
{
    return make_int3(a.x * s, a.y * s, a.z * s);
}
inline __host__ __device__ void operator*=(int3 &a, int s)
{
    a.x *= s; a.y *= s; a.z *= s;
}

// divide
inline __host__ __device__ int3 operator/(int3 a, int3 b)
{
    return make_int3(a.x / b.x, a.y / b.y, a.z / b.z);
}
inline __host__ __device__ int3 operator/(int3 a, int s)
{
    return make_int3(a.x / s, a.y / s, a.z / s);
}
inline __host__ __device__ int3 operator/(int s, int3 a)
{
    return make_int3(a.x / s, a.y / s, a.z / s);
}
inline __host__ __device__ void operator/=(int3 &a, int s)
{
    a.x /= s; a.y /= s; a.z /= s;
}

// clamp
inline __device__ __host__ int clamp(int f, int a, int b)
{
    return max(a, min(f, b));
}

inline __device__ __host__ int3 clamp(int3 v, int a, int b)
{
    return make_int3(clamp(v.x, a, b), clamp(v.y, a, b), clamp(v.z, a, b));
}

inline __device__ __host__ int3 clamp(int3 v, int3 a, int3 b)
{
    return make_int3(clamp(v.x, a.x, b.x), clamp(v.y, a.y, b.y), clamp(v.z, a.z, b.z));
}

//validate
inline __host__ __device__ bool validate(const int3 v0, const int3 v1)
{
    return (v0.x == v1.x && v0.y == v1.y && v0.z == v1.z);
}

// uint3 functions
////////////////////////////////////////////////////////////////////////////////

// additional constructors
inline __host__ __device__ uint3 make_uint3(uint s)
{
    return make_uint3(s, s, s);
}

inline __host__ __device__ uint4 make_uint4(uint s)
{
    return make_uint4(s, s, s, s);
}

inline __host__ __device__ uint3 make_uint3(float3 a)
{
    return make_uint3(uint(a.x), uint(a.y), uint(a.z));
}

// min
inline __host__ __device__ uint3 min(uint3 a, uint3 b)
{
    return make_uint3(min(a.x,b.x), min(a.y,b.y), min(a.z,b.z));
}

// max
inline __host__ __device__ uint3 max(uint3 a, uint3 b)
{
    return make_uint3(max(a.x,b.x), max(a.y,b.y), max(a.z,b.z));
}

// addition
inline __host__ __device__ uint3 operator+(uint3 a, uint3 b)
{
    return make_uint3(a.x + b.x, a.y + b.y, a.z + b.z);
}
inline __host__ __device__ void operator+=(uint3 &a, uint3 b)
{
    a.x += b.x; a.y += b.y; a.z += b.z;
}

// subtract
inline __host__ __device__ uint3 operator-(uint3 a, uint3 b)
{
    return make_uint3(a.x - b.x, a.y - b.y, a.z - b.z);
}

inline __host__ __device__ void operator-=(uint3 &a, uint3 b)
{
    a.x -= b.x; a.y -= b.y; a.z -= b.z;
}

// multiply
inline __host__ __device__ uint3 operator*(uint3 a, uint3 b)
{
    return make_uint3(a.x * b.x, a.y * b.y, a.z * b.z);
}
inline __host__ __device__ uint3 operator*(uint3 a, uint s)
{
    return make_uint3(a.x * s, a.y * s, a.z * s);
}
inline __host__ __device__ uint3 operator*(uint s, uint3 a)
{
    return make_uint3(a.x * s, a.y * s, a.z * s);
}
inline __host__ __device__ void operator*=(uint3 &a, uint s)
{
    a.x *= s; a.y *= s; a.z *= s;
}

// divide
inline __host__ __device__ uint3 operator/(uint3 a, uint3 b)
{
    return make_uint3(a.x / b.x, a.y / b.y, a.z / b.z);
}
inline __host__ __device__ uint3 operator/(uint3 a, uint s)
{
    return make_uint3(a.x / s, a.y / s, a.z / s);
}
inline __host__ __device__ uint3 operator/(uint s, uint3 a)
{
    return make_uint3(a.x / s, a.y / s, a.z / s);
}
inline __host__ __device__ void operator/=(uint3 &a, uint s)
{
    a.x /= s; a.y /= s; a.z /= s;
}


// clamp
inline __device__ __host__ uint clamp(uint f, uint a, uint b)
{
    return max(a, min(f, b));
}

inline __device__ __host__ uint3 clamp(uint3 v, uint a, uint b)
{
    return make_uint3(clamp(v.x, a, b), clamp(v.y, a, b), clamp(v.z, a, b));
}

inline __device__ __host__ uint3 clamp(uint3 v, uint3 a, uint3 b)
{
    return make_uint3(clamp(v.x, a.x, b.x), clamp(v.y, a.y, b.y), clamp(v.z, a.z, b.z));
}

//validate
inline __host__ __device__ bool validate(const uint3 v0, const uint3 v1)
{
    return (v0.x == v1.x && v0.y == v1.y && v0.z == v1.z);
}

//other 
inline __device__ __host__ ushort u32High(uint val)
{
	return ushort(val >> 16);
}

inline __device__ __host__ ushort u32Low(uint val)
{
	return ushort(val & ((1 << 16u) - 1));
}

inline __device__ __host__  uint merge(ushort hi, ushort lo)
{
	return uint((uint(hi) << 16) | uint(lo)); 
}

inline __device__ __host__ uchar u16High(ushort val)
{
	return uchar(val >> 8);
}

inline __device__ __host__ uchar u16Low(ushort val)
{
	return uchar(val & ((1 << 8u) - 1));
}

inline __device__ __host__ ushort merge(uchar hi, uchar lo)
{
	return ushort((ushort(hi) << 8) | ushort(lo)); 
}

#endif