/* Copyright (c) 2019, NVIDIA CORPORATION. All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *  * Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *  * Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *  * Neither the name of NVIDIA CORPORATION nor the names of its
 *    contributors may be used to endorse or promote products derived
 *    from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
 * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

/*
 *  This file implements common mathematical operations on vector types
 *  (float3, float4 etc.) since these are not provided as standard by CUDA.
 *
 *  The syntax is modeled on the Cg standard library.
 *
 *  This is part of the Helper library includes
 *
 *    Thanks to Linh Hah for additions and fixes.
 */

#ifndef HELPER_MATH_H
#define HELPER_MATH_H

#include "cuda_runtime.h"

typedef unsigned int uint;
typedef unsigned short ushort;

#ifndef EXIT_WAIVED
  #define EXIT_WAIVED 2
#endif

#ifndef __CUDACC__
  #include <math.h>

////////////////////////////////////////////////////////////////////////////////
// host implementations of CUDA functions
////////////////////////////////////////////////////////////////////////////////

inline float
fminf(float a, float b) {
  return a < b ? a : b;
}

inline float
fmaxf(float a, float b) {
  return a > b ? a : b;
}

inline int
max(int a, int b) {
  return a > b ? a : b;
}

inline int
min(int a, int b) {
  return a < b ? a : b;
}

inline float
rsqrtf(float x) {
  return 1.0f / sqrtf(x);
}
#endif

////////////////////////////////////////////////////////////////////////////////
// constructors
////////////////////////////////////////////////////////////////////////////////

inline __host__ __device__ float2
make_float2(float s) {
  return make_float2(s, s);
}
inline __host__ __device__ float2
make_float2(float3 a) {
  return make_float2(a.x, a.y);
}
inline __host__ __device__ float2
make_float2(int2 a) {
  return make_float2(float(a.x), float(a.y));
}
inline __host__ __device__ float2
make_float2(uint2 a) {
  return make_float2(float(a.x), float(a.y));
}

inline __host__ __device__ int2
make_int2(int s) {
  return make_int2(s, s);
}
inline __host__ __device__ int2
make_int2(int3 a) {
  return make_int2(a.x, a.y);
}
inline __host__ __device__ int2
make_int2(uint2 a) {
  return make_int2(int(a.x), int(a.y));
}
inline __host__ __device__ int2
make_int2(float2 a) {
  return make_int2(int(a.x), int(a.y));
}

inline __host__ __device__ uint2
make_uint2(uint s) {
  return make_uint2(s, s);
}
inline __host__ __device__ uint2
make_uint2(uint3 a) {
  return make_uint2(a.x, a.y);
}
inline __host__ __device__ uint2
make_uint2(int2 a) {
  return make_uint2(uint(a.x), uint(a.y));
}

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);
}
inline __host__ __device__ float3
make_float3(int3 a) {
  return make_float3(float(a.x), float(a.y), float(a.z));
}
inline __host__ __device__ float3
make_float3(uint3 a) {
  return make_float3(float(a.x), float(a.y), float(a.z));
}

inline __host__ __device__ int3
make_int3(int s) {
  return make_int3(s, s, s);
}
inline __host__ __device__ int3
make_int3(int2 a) {
  return make_int3(a.x, a.y, 0);
}
inline __host__ __device__ int3
make_int3(int2 a, int s) {
  return make_int3(a.x, a.y, s);
}
inline __host__ __device__ int3
make_int3(uint3 a) {
  return make_int3(int(a.x), int(a.y), int(a.z));
}
inline __host__ __device__ int3
make_int3(float3 a) {
  return make_int3(int(a.x), int(a.y), int(a.z));
}

inline __host__ __device__ uint3
make_uint3(uint s) {
  return make_uint3(s, s, s);
}
inline __host__ __device__ uint3
make_uint3(uint2 a) {
  return make_uint3(a.x, a.y, 0);
}
inline __host__ __device__ uint3
make_uint3(uint2 a, uint s) {
  return make_uint3(a.x, a.y, s);
}
inline __host__ __device__ uint3
make_uint3(uint4 a) {
  return make_uint3(a.x, a.y, a.z);
}
inline __host__ __device__ uint3
make_uint3(int3 a) {
  return make_uint3(uint(a.x), uint(a.y), uint(a.z));
}

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));
}
inline __host__ __device__ float4
make_float4(uint4 a) {
  return make_float4(float(a.x), float(a.y), float(a.z), float(a.w));
}

inline __host__ __device__ int4
make_int4(int s) {
  return make_int4(s, s, s, s);
}
inline __host__ __device__ int4
make_int4(int3 a) {
  return make_int4(a.x, a.y, a.z, 0);
}
inline __host__ __device__ int4
make_int4(int3 a, int w) {
  return make_int4(a.x, a.y, a.z, w);
}
inline __host__ __device__ int4
make_int4(uint4 a) {
  return make_int4(int(a.x), int(a.y), int(a.z), int(a.w));
}
inline __host__ __device__ int4
make_int4(float4 a) {
  return make_int4(int(a.x), int(a.y), int(a.z), int(a.w));
}

inline __host__ __device__ uint4
make_uint4(uint s) {
  return make_uint4(s, s, s, s);
}
inline __host__ __device__ uint4
make_uint4(uint3 a) {
  return make_uint4(a.x, a.y, a.z, 0);
}
inline __host__ __device__ uint4
make_uint4(uint3 a, uint w) {
  return make_uint4(a.x, a.y, a.z, w);
}
inline __host__ __device__ uint4
make_uint4(int4 a) {
  return make_uint4(uint(a.x), uint(a.y), uint(a.z), uint(a.w));
}

////////////////////////////////////////////////////////////////////////////////
// negate
////////////////////////////////////////////////////////////////////////////////

inline __host__ __device__ float2
operator-(float2 &a) {
  return make_float2(-a.x, -a.y);
}
inline __host__ __device__ int2
operator-(int2 &a) {
  return make_int2(-a.x, -a.y);
}
inline __host__ __device__ float3
operator-(float3 &a) {
  return make_float3(-a.x, -a.y, -a.z);
}
inline __host__ __device__ int3
operator-(int3 &a) {
  return make_int3(-a.x, -a.y, -a.z);
}
inline __host__ __device__ float4
operator-(float4 &a) {
  return make_float4(-a.x, -a.y, -a.z, -a.w);
}
inline __host__ __device__ int4
operator-(int4 &a) {
  return make_int4(-a.x, -a.y, -a.z, -a.w);
}

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

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

inline __host__ __device__ uint2
operator+(uint2 a, uint2 b) {
  return make_uint2(a.x + b.x, a.y + b.y);
}
inline __host__ __device__ void
operator+=(uint2 &a, uint2 b) {
  a.x += b.x;
  a.y += b.y;
}
inline __host__ __device__ uint2
operator+(uint2 a, uint b) {
  return make_uint2(a.x + b, a.y + b);
}
inline __host__ __device__ uint2
operator+(uint b, uint2 a) {
  return make_uint2(a.x + b, a.y + b);
}
inline __host__ __device__ void
operator+=(uint2 &a, uint b) {
  a.x += b;
  a.y += b;
}

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

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

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

inline __host__ __device__ int3
operator+(int b, int3 a) {
  return make_int3(a.x + b, a.y + b, a.z + b);
}
inline __host__ __device__ uint3
operator+(uint b, uint3 a) {
  return make_uint3(a.x + b, a.y + b, a.z + b);
}
inline __host__ __device__ float3
operator+(float b, float3 a) {
  return make_float3(a.x + b, a.y + b, a.z + b);
}

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

inline __host__ __device__ int4
operator+(int4 a, int4 b) {
  return make_int4(a.x + b.x, a.y + b.y, a.z + b.z, a.w + b.w);
}
inline __host__ __device__ void
operator+=(int4 &a, int4 b) {
  a.x += b.x;
  a.y += b.y;
  a.z += b.z;
  a.w += b.w;
}
inline __host__ __device__ int4
operator+(int4 a, int b) {
  return make_int4(a.x + b, a.y + b, a.z + b, a.w + b);
}
inline __host__ __device__ int4
operator+(int b, int4 a) {
  return make_int4(a.x + b, a.y + b, a.z + b, a.w + b);
}
inline __host__ __device__ void
operator+=(int4 &a, int b) {
  a.x += b;
  a.y += b;
  a.z += b;
  a.w += b;
}

inline __host__ __device__ uint4
operator+(uint4 a, uint4 b) {
  return make_uint4(a.x + b.x, a.y + b.y, a.z + b.z, a.w + b.w);
}
inline __host__ __device__ void
operator+=(uint4 &a, uint4 b) {
  a.x += b.x;
  a.y += b.y;
  a.z += b.z;
  a.w += b.w;
}
inline __host__ __device__ uint4
operator+(uint4 a, uint b) {
  return make_uint4(a.x + b, a.y + b, a.z + b, a.w + b);
}
inline __host__ __device__ uint4
operator+(uint b, uint4 a) {
  return make_uint4(a.x + b, a.y + b, a.z + b, a.w + b);
}
inline __host__ __device__ void
operator+=(uint4 &a, uint b) {
  a.x += b;
  a.y += b;
  a.z += b;
  a.w += b;
}

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

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

inline __host__ __device__ uint2
operator-(uint2 a, uint2 b) {
  return make_uint2(a.x - b.x, a.y - b.y);
}
inline __host__ __device__ void
operator-=(uint2 &a, uint2 b) {
  a.x -= b.x;
  a.y -= b.y;
}
inline __host__ __device__ uint2
operator-(uint2 a, uint b) {
  return make_uint2(a.x - b, a.y - b);
}
inline __host__ __device__ uint2
operator-(uint b, uint2 a) {
  return make_uint2(b - a.x, b - a.y);
}
inline __host__ __device__ void
operator-=(uint2 &a, uint b) {
  a.x -= b;
  a.y -= b;
}

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

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

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

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

inline __host__ __device__ int4
operator-(int4 a, int4 b) {
  return make_int4(a.x - b.x, a.y - b.y, a.z - b.z, a.w - b.w);
}
inline __host__ __device__ void
operator-=(int4 &a, int4 b) {
  a.x -= b.x;
  a.y -= b.y;
  a.z -= b.z;
  a.w -= b.w;
}
inline __host__ __device__ int4
operator-(int4 a, int b) {
  return make_int4(a.x - b, a.y - b, a.z - b, a.w - b);
}
inline __host__ __device__ int4
operator-(int b, int4 a) {
  return make_int4(b - a.x, b - a.y, b - a.z, b - a.w);
}
inline __host__ __device__ void
operator-=(int4 &a, int b) {
  a.x -= b;
  a.y -= b;
  a.z -= b;
  a.w -= b;
}

inline __host__ __device__ uint4
operator-(uint4 a, uint4 b) {
  return make_uint4(a.x - b.x, a.y - b.y, a.z - b.z, a.w - b.w);
}
inline __host__ __device__ void
operator-=(uint4 &a, uint4 b) {
  a.x -= b.x;
  a.y -= b.y;
  a.z -= b.z;
  a.w -= b.w;
}
inline __host__ __device__ uint4
operator-(uint4 a, uint b) {
  return make_uint4(a.x - b, a.y - b, a.z - b, a.w - b);
}
inline __host__ __device__ uint4
operator-(uint b, uint4 a) {
  return make_uint4(b - a.x, b - a.y, b - a.z, b - a.w);
}
inline __host__ __device__ void
operator-=(uint4 &a, uint b) {
  a.x -= b;
  a.y -= b;
  a.z -= b;
  a.w -= b;
}

////////////////////////////////////////////////////////////////////////////////
// multiply
////////////////////////////////////////////////////////////////////////////////

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

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

inline __host__ __device__ uint2
operator*(uint2 a, uint2 b) {
  return make_uint2(a.x * b.x, a.y * b.y);
}
inline __host__ __device__ void
operator*=(uint2 &a, uint2 b) {
  a.x *= b.x;
  a.y *= b.y;
}
inline __host__ __device__ uint2
operator*(uint2 a, uint b) {
  return make_uint2(a.x * b, a.y * b);
}
inline __host__ __device__ uint2
operator*(uint b, uint2 a) {
  return make_uint2(b * a.x, b * a.y);
}
inline __host__ __device__ void
operator*=(uint2 &a, uint b) {
  a.x *= b;
  a.y *= b;
}

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

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

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

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

inline __host__ __device__ int4
operator*(int4 a, int4 b) {
  return make_int4(a.x * b.x, a.y * b.y, a.z * b.z, a.w * b.w);
}
inline __host__ __device__ void
operator*=(int4 &a, int4 b) {
  a.x *= b.x;
  a.y *= b.y;
  a.z *= b.z;
  a.w *= b.w;
}
inline __host__ __device__ int4
operator*(int4 a, int b) {
  return make_int4(a.x * b, a.y * b, a.z * b, a.w * b);
}
inline __host__ __device__ int4
operator*(int b, int4 a) {
  return make_int4(b * a.x, b * a.y, b * a.z, b * a.w);
}
inline __host__ __device__ void
operator*=(int4 &a, int b) {
  a.x *= b;
  a.y *= b;
  a.z *= b;
  a.w *= b;
}

inline __host__ __device__ uint4
operator*(uint4 a, uint4 b) {
  return make_uint4(a.x * b.x, a.y * b.y, a.z * b.z, a.w * b.w);
}
inline __host__ __device__ void
operator*=(uint4 &a, uint4 b) {
  a.x *= b.x;
  a.y *= b.y;
  a.z *= b.z;
  a.w *= b.w;
}
inline __host__ __device__ uint4
operator*(uint4 a, uint b) {
  return make_uint4(a.x * b, a.y * b, a.z * b, a.w * b);
}
inline __host__ __device__ uint4
operator*(uint b, uint4 a) {
  return make_uint4(b * a.x, b * a.y, b * a.z, b * a.w);
}
inline __host__ __device__ void
operator*=(uint4 &a, uint b) {
  a.x *= b;
  a.y *= b;
  a.z *= b;
  a.w *= b;
}

////////////////////////////////////////////////////////////////////////////////
// divide
////////////////////////////////////////////////////////////////////////////////

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

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

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

////////////////////////////////////////////////////////////////////////////////
// min
////////////////////////////////////////////////////////////////////////////////

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

inline __host__ __device__ int2
min(int2 a, int2 b) {
  return make_int2(min(a.x, b.x), min(a.y, b.y));
}
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));
}
inline __host__ __device__ int4
min(int4 a, int4 b) {
  return make_int4(min(a.x, b.x), min(a.y, b.y), min(a.z, b.z), min(a.w, b.w));
}

inline __host__ __device__ uint2
min(uint2 a, uint2 b) {
  return make_uint2(min(a.x, b.x), min(a.y, b.y));
}
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));
}
inline __host__ __device__ uint4
min(uint4 a, uint4 b) {
  return make_uint4(min(a.x, b.x), min(a.y, b.y), min(a.z, b.z), min(a.w, b.w));
}

////////////////////////////////////////////////////////////////////////////////
// max
////////////////////////////////////////////////////////////////////////////////

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

inline __host__ __device__ int2
max(int2 a, int2 b) {
  return make_int2(max(a.x, b.x), max(a.y, b.y));
}
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));
}
inline __host__ __device__ int4
max(int4 a, int4 b) {
  return make_int4(max(a.x, b.x), max(a.y, b.y), max(a.z, b.z), max(a.w, b.w));
}

inline __host__ __device__ uint2
max(uint2 a, uint2 b) {
  return make_uint2(max(a.x, b.x), max(a.y, b.y));
}
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));
}
inline __host__ __device__ uint4
max(uint4 a, uint4 b) {
  return make_uint4(max(a.x, b.x), max(a.y, b.y), max(a.z, b.z), max(a.w, b.w));
}

////////////////////////////////////////////////////////////////////////////////
// lerp
// - linear interpolation between a and b, based on value t in [0, 1] range
////////////////////////////////////////////////////////////////////////////////

inline __device__ __host__ float
lerp(float a, float b, float t) {
  return a + t * (b - a);
}
inline __device__ __host__ float2
lerp(float2 a, float2 b, float t) {
  return a + t * (b - a);
}
inline __device__ __host__ float3
lerp(float3 a, float3 b, float t) {
  return a + t * (b - a);
}
inline __device__ __host__ float4
lerp(float4 a, float4 b, float t) {
  return a + t * (b - a);
}

////////////////////////////////////////////////////////////////////////////////
// clamp
// - clamp the value v to be in the range [a, b]
////////////////////////////////////////////////////////////////////////////////

inline __device__ __host__ float
clamp(float f, float a, float b) {
  return fmaxf(a, fminf(f, b));
}
inline __device__ __host__ int
clamp(int f, int a, int b) {
  return max(a, min(f, b));
}
inline __device__ __host__ uint
clamp(uint f, uint a, uint b) {
  return max(a, min(f, b));
}

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));
}
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));
}
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));
}

inline __device__ __host__ int2
clamp(int2 v, int a, int b) {
  return make_int2(clamp(v.x, a, b), clamp(v.y, a, b));
}
inline __device__ __host__ int2
clamp(int2 v, int2 a, int2 b) {
  return make_int2(clamp(v.x, a.x, b.x), clamp(v.y, a.y, b.y));
}
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));
}
inline __device__ __host__ int4
clamp(int4 v, int a, int b) {
  return make_int4(clamp(v.x, a, b), clamp(v.y, a, b), clamp(v.z, a, b), clamp(v.w, a, b));
}
inline __device__ __host__ int4
clamp(int4 v, int4 a, int4 b) {
  return make_int4(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));
}

inline __device__ __host__ uint2
clamp(uint2 v, uint a, uint b) {
  return make_uint2(clamp(v.x, a, b), clamp(v.y, a, b));
}
inline __device__ __host__ uint2
clamp(uint2 v, uint2 a, uint2 b) {
  return make_uint2(clamp(v.x, a.x, b.x), clamp(v.y, a.y, b.y));
}
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));
}
inline __device__ __host__ uint4
clamp(uint4 v, uint a, uint b) {
  return make_uint4(clamp(v.x, a, b), clamp(v.y, a, b), clamp(v.z, a, b), clamp(v.w, a, b));
}
inline __device__ __host__ uint4
clamp(uint4 v, uint4 a, uint4 b) {
  return make_uint4(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(float2 a, float2 b) {
  return a.x * b.x + a.y * b.y;
}
inline __host__ __device__ float
dot(float3 a, float3 b) {
  return a.x * b.x + a.y * b.y + a.z * b.z;
}
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;
}

inline __host__ __device__ int
dot(int2 a, int2 b) {
  return a.x * b.x + a.y * b.y;
}
inline __host__ __device__ int
dot(int3 a, int3 b) {
  return a.x * b.x + a.y * b.y + a.z * b.z;
}
inline __host__ __device__ int
dot(int4 a, int4 b) {
  return a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w;
}

inline __host__ __device__ uint
dot(uint2 a, uint2 b) {
  return a.x * b.x + a.y * b.y;
}
inline __host__ __device__ uint
dot(uint3 a, uint3 b) {
  return a.x * b.x + a.y * b.y + a.z * b.z;
}
inline __host__ __device__ uint
dot(uint4 a, uint4 b) {
  return a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w;
}

////////////////////////////////////////////////////////////////////////////////
// length
////////////////////////////////////////////////////////////////////////////////

inline __host__ __device__ float
length(float2 v) {
  return sqrtf(dot(v, v));
}
inline __host__ __device__ float
length(float3 v) {
  return sqrtf(dot(v, v));
}
inline __host__ __device__ float
length(float4 v) {
  return sqrtf(dot(v, v));
}

////////////////////////////////////////////////////////////////////////////////
// normalize
////////////////////////////////////////////////////////////////////////////////

inline __host__ __device__ float2
normalize(float2 v) {
  float invLen = rsqrtf(dot(v, v));
  return v * invLen;
}
inline __host__ __device__ float3
normalize(float3 v) {
  float invLen = rsqrtf(dot(v, v));
  return v * invLen;
}
inline __host__ __device__ float4
normalize(float4 v) {
  float invLen = rsqrtf(dot(v, v));
  return v * invLen;
}

////////////////////////////////////////////////////////////////////////////////
// floor
////////////////////////////////////////////////////////////////////////////////

inline __host__ __device__ float2
floorf(float2 v) {
  return make_float2(floorf(v.x), floorf(v.y));
}
inline __host__ __device__ float3
floorf(float3 v) {
  return make_float3(floorf(v.x), floorf(v.y), floorf(v.z));
}
inline __host__ __device__ float4
floorf(float4 v) {
  return make_float4(floorf(v.x), floorf(v.y), floorf(v.z), floorf(v.w));
}

////////////////////////////////////////////////////////////////////////////////
// frac - returns the fractional portion of a scalar or each vector component
////////////////////////////////////////////////////////////////////////////////

inline __host__ __device__ float
fracf(float v) {
  return v - floorf(v);
}
inline __host__ __device__ float2
fracf(float2 v) {
  return make_float2(fracf(v.x), fracf(v.y));
}
inline __host__ __device__ float3
fracf(float3 v) {
  return make_float3(fracf(v.x), fracf(v.y), fracf(v.z));
}
inline __host__ __device__ float4
fracf(float4 v) {
  return make_float4(fracf(v.x), fracf(v.y), fracf(v.z), fracf(v.w));
}

////////////////////////////////////////////////////////////////////////////////
// fmod
////////////////////////////////////////////////////////////////////////////////

inline __host__ __device__ float2
fmodf(float2 a, float2 b) {
  return make_float2(fmodf(a.x, b.x), fmodf(a.y, b.y));
}
inline __host__ __device__ float3
fmodf(float3 a, float3 b) {
  return make_float3(fmodf(a.x, b.x), fmodf(a.y, b.y), fmodf(a.z, b.z));
}
inline __host__ __device__ float4
fmodf(float4 a, float4 b) {
  return make_float4(fmodf(a.x, b.x), fmodf(a.y, b.y), fmodf(a.z, b.z), fmodf(a.w, b.w));
}

////////////////////////////////////////////////////////////////////////////////
// absolute value
////////////////////////////////////////////////////////////////////////////////

inline __host__ __device__ float2
fabs(float2 v) {
  return make_float2(fabs(v.x), fabs(v.y));
}
inline __host__ __device__ float3
fabs(float3 v) {
  return make_float3(fabs(v.x), fabs(v.y), fabs(v.z));
}
inline __host__ __device__ float4
fabs(float4 v) {
  return make_float4(fabs(v.x), fabs(v.y), fabs(v.z), fabs(v.w));
}

inline __host__ __device__ int2
abs(int2 v) {
  return make_int2(abs(v.x), abs(v.y));
}
inline __host__ __device__ int3
abs(int3 v) {
  return make_int3(abs(v.x), abs(v.y), abs(v.z));
}
inline __host__ __device__ int4
abs(int4 v) {
  return make_int4(abs(v.x), abs(v.y), abs(v.z), abs(v.w));
}

////////////////////////////////////////////////////////////////////////////////
// reflect
// - returns reflection of incident ray I around surface normal N
// - N should be normalized, reflected vector's length is equal to length of I
////////////////////////////////////////////////////////////////////////////////

inline __host__ __device__ float3
reflect(float3 i, float3 n) {
  return i - 2.0f * n * dot(n, i);
}

////////////////////////////////////////////////////////////////////////////////
// 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);
}

////////////////////////////////////////////////////////////////////////////////
// smoothstep
// - returns 0 if x < a
// - returns 1 if x > b
// - otherwise returns smooth interpolation between 0 and 1 based on x
////////////////////////////////////////////////////////////////////////////////

inline __device__ __host__ float
smoothstep(float a, float b, float x) {
  float y = clamp((x - a) / (b - a), 0.0f, 1.0f);
  return (y * y * (3.0f - (2.0f * y)));
}
inline __device__ __host__ float2
smoothstep(float2 a, float2 b, float2 x) {
  float2 y = clamp((x - a) / (b - a), 0.0f, 1.0f);
  return (y * y * (make_float2(3.0f) - (make_float2(2.0f) * y)));
}
inline __device__ __host__ float3
smoothstep(float3 a, float3 b, float3 x) {
  float3 y = clamp((x - a) / (b - a), 0.0f, 1.0f);
  return (y * y * (make_float3(3.0f) - (make_float3(2.0f) * y)));
}
inline __device__ __host__ float4
smoothstep(float4 a, float4 b, float4 x) {
  float4 y = clamp((x - a) / (b - a), 0.0f, 1.0f);
  return (y * y * (make_float4(3.0f) - (make_float4(2.0f) * y)));
}

#endif
