text: /* 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
  