diff --git a/09/01_texture/01/main.cu b/09/01_texture/01/main.cu
index 9080c6cf..30b0b065 100644
--- a/09/01_texture/01/main.cu
+++ b/09/01_texture/01/main.cu
@@ -2,32 +2,51 @@
 #include <vector>
 #include <cuda_runtime.h>
 #include "helper_cuda.h"
+#include "helper_math.h"
 #include "CudaAllocator.cuh"
 #include "CudaArray.cuh"
 #include "ticktock.h"
 #include "writevdb.h"
 
-__global__ void kernel(cudaTextureObject_t vel, cudaSurfaceObject_t loc, unsigned int n) {
+__global__ void kernel(cudaTextureObject_t texVel, cudaSurfaceObject_t sufLoc, unsigned int n) {
     unsigned int x = threadIdx.x + blockDim.x * blockIdx.x;
     unsigned int y = threadIdx.y + blockDim.y * blockIdx.y;
     unsigned int z = threadIdx.z + blockDim.z * blockIdx.z;
-    float vel = tex3D<float>(vel, x, y, z);
-    surf3Dwrite<float>(value, clr_nxt, x, y, z, cudaBoundaryModeTrap);
+    float4 vel = tex3D<float4>(texVel, x, y, z);
+    float4 loc = make_float4(x + 0.5f, y + 0.5f, z + 0.5f, 0.f) - vel;
+    surf3Dwrite<float4>(loc, sufLoc, x, y, z, cudaBoundaryModeTrap);
 }
 
 int main() {
-    unsigned int n = 32;
+    unsigned int n = 4;
 
-    auto loc = CudaArray<float>::make({{n, n, n}, 0});
-    auto loc_s = CudaSurface<float>::make(loc);
-    auto vel = CudaArray<float>::make({{n, n, n}, 0});
-    auto vel_t = CudaTexture<float>::make(vel);
+    auto arrLoc = CudaArray<float4>::make({{n, n, n}, 0});
+    auto sufLoc = CudaSurface<float4>::make(arrLoc);
+    auto arrVel = CudaArray<float4>::make({{n, n, n}, 0});
+    auto texVel = CudaTexture<float4>::make(arrVel);
 
-    kernel<<<dim3(n / 8, n / 8, n / 8), dim3(8, 8, 8)>>>(vel_t.get(), loc_s.get(), n);
+    std::vector<float4> cpuVel(n * n * n);
+    for (int z = 0; z < n; z++) {
+        for (int y = 0; y < n; y++) {
+            for (int x = 0; x < n; x++) {
+                cpuVel[x + n * (y + n * z)] = make_float4(1.f, 0.f, 0.f, 0.f);
+            }
+        }
+    }
+    arrVel.copyIn(cpuVel.data());
 
-    std::vector<float> arr(n * n * n);
-    clr.getArray().copyOut(arr.data());
-    writevdb<float>("/tmp/a.vdb", n, n, n, arr.data());
+    kernel<<<dim3(n / 8, n / 8, n / 8), dim3(8, 8, 8)>>>(texVel.get(), sufLoc.get(), n);
+
+    std::vector<float4> cpuLoc(n * n * n);
+    arrLoc.copyOut(cpuLoc.data());
+    for (int z = 0; z < n; z++) {
+        for (int y = 0; y < n; y++) {
+            for (int x = 0; x < n; x++) {
+                printf("%d,%d,%d: %f\n", x, y, z, cpuLoc[x + n * (y + n * z)]);
+            }
+        }
+    }
+    //writevdb<float, 3>("/tmp/a.vdb", n, n, n, arr.data());
 
     return 0;
 }
diff --git a/09/include/helper_math.h b/09/include/helper_math.h
new file mode 100644
index 00000000..c9c07c3e
--- /dev/null
+++ b/09/include/helper_math.h
@@ -0,0 +1,1453 @@
+/**
+ * Copyright 1993-2013 NVIDIA Corporation.  All rights reserved.
+ *
+ * Please refer to the NVIDIA end user license agreement (EULA) associated
+ * with this source code for terms and conditions that govern your use of
+ * this software. Any use, reproduction, disclosure, or distribution of
+ * this software and related documentation outside the terms of the EULA
+ * is strictly prohibited.
+ *
+ */
+
+/*
+ *  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