/**
 * This file defines vector operations to simplify code elsewhere.
 */

// Versions of make_x() that take a single value and set all components to that.

inline __device__ int2 make_int2(int a) {
    return make_int2(a, a);
}

inline __device__ int3 make_int3(int a) {
    return make_int3(a, a, a);
}

inline __device__ int4 make_int4(int a) {
    return make_int4(a, a, a, a);
}

inline __device__ float2 make_float2(float a) {
    return make_float2(a, a);
}

inline __device__ float3 make_float3(float a) {
    return make_float3(a, a, a);
}

inline __device__ float4 make_float4(float a) {
    return make_float4(a, a, a, a);
}

inline __device__ double2 make_double2(double a) {
    return make_double2(a, a);
}

inline __device__ double3 make_double3(double a) {
    return make_double3(a, a, a);
}

inline __device__ double4 make_double4(double a) {
    return make_double4(a, a, a, a);
}

// Negate a vector.

inline __device__ int2 operator-(int2 a) {
    return make_int2(-a.x, -a.y);
}

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

inline __device__ int4 operator-(int4 a) {
    return make_int4(-a.x, -a.y, -a.z, -a.w);
}

inline __device__ float2 operator-(float2 a) {
    return make_float2(-a.x, -a.y);
}

inline __device__ float3 operator-(float3 a) {
    return make_float3(-a.x, -a.y, -a.z);
}

inline __device__ float4 operator-(float4 a) {
    return make_float4(-a.x, -a.y, -a.z, -a.w);
}

inline __device__ double2 operator-(double2 a) {
    return make_double2(-a.x, -a.y);
}

inline __device__ double3 operator-(double3 a) {
    return make_double3(-a.x, -a.y, -a.z);
}

inline __device__ double4 operator-(double4 a) {
    return make_double4(-a.x, -a.y, -a.z, -a.w);
}

// Add two vectors.

inline __device__ int2 operator+(int2 a, int2 b) {
    return make_int2(a.x+b.x, a.y+b.y);
}

inline __device__ int3 operator+(int3 a, int3 b) {
    return make_int3(a.x+b.x, a.y+b.y, a.z+b.z);
}

inline __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 __device__ float2 operator+(float2 a, float2 b) {
    return make_float2(a.x+b.x, a.y+b.y);
}

inline __device__ float3 operator+(float3 a, float3 b) {
    return make_float3(a.x+b.x, a.y+b.y, a.z+b.z);
}

inline __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 __device__ double2 operator+(double2 a, double2 b) {
    return make_double2(a.x+b.x, a.y+b.y);
}

inline __device__ double3 operator+(double3 a, double3 b) {
    return make_double3(a.x+b.x, a.y+b.y, a.z+b.z);
}

inline __device__ double4 operator+(double4 a, double4 b) {
    return make_double4(a.x+b.x, a.y+b.y, a.z+b.z, a.w+b.w);
}

// Subtract two vectors.

inline __device__ int2 operator-(int2 a, int2 b) {
    return make_int2(a.x-b.x, a.y-b.y);
}

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

inline __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 __device__ float2 operator-(float2 a, float2 b) {
    return make_float2(a.x-b.x, a.y-b.y);
}

inline __device__ float3 operator-(float3 a, float3 b) {
    return make_float3(a.x-b.x, a.y-b.y, a.z-b.z);
}

inline __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 __device__ double2 operator-(double2 a, double2 b) {
    return make_double2(a.x-b.x, a.y-b.y);
}

inline __device__ double3 operator-(double3 a, double3 b) {
    return make_double3(a.x-b.x, a.y-b.y, a.z-b.z);
}

inline __device__ double4 operator-(double4 a, double4 b) {
    return make_double4(a.x-b.x, a.y-b.y, a.z-b.z, a.w-b.w);
}

// Multiply two vectors.

inline __device__ int2 operator*(int2 a, int2 b) {
    return make_int2(a.x*b.x, a.y*b.y);
}

inline __device__ int3 operator*(int3 a, int3 b) {
    return make_int3(a.x*b.x, a.y*b.y, a.z*b.z);
}

inline __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 __device__ float2 operator*(float2 a, float2 b) {
    return make_float2(a.x*b.x, a.y*b.y);
}

inline __device__ float3 operator*(float3 a, float3 b) {
    return make_float3(a.x*b.x, a.y*b.y, a.z*b.z);
}

inline __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 __device__ double2 operator*(double2 a, double2 b) {
    return make_double2(a.x*b.x, a.y*b.y);
}

inline __device__ double3 operator*(double3 a, double3 b) {
    return make_double3(a.x*b.x, a.y*b.y, a.z*b.z);
}

inline __device__ double4 operator*(double4 a, double4 b) {
    return make_double4(a.x*b.x, a.y*b.y, a.z*b.z, a.w*b.w);
}

// Divide two vectors.

inline __device__ int2 operator/(int2 a, int2 b) {
    return make_int2(a.x/b.x, a.y/b.y);
}

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

inline __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 __device__ float2 operator/(float2 a, float2 b) {
    return make_float2(a.x/b.x, a.y/b.y);
}

inline __device__ float3 operator/(float3 a, float3 b) {
    return make_float3(a.x/b.x, a.y/b.y, a.z/b.z);
}

inline __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 __device__ double2 operator/(double2 a, double2 b) {
    return make_double2(a.x/b.x, a.y/b.y);
}

inline __device__ double3 operator/(double3 a, double3 b) {
    return make_double3(a.x/b.x, a.y/b.y, a.z/b.z);
}

inline __device__ double4 operator/(double4 a, double4 b) {
    return make_double4(a.x/b.x, a.y/b.y, a.z/b.z, a.w/b.w);
}

// += operator

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

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

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

inline __device__ void operator+=(float2& a, float2 b) {
    a.x += b.x; a.y += b.y;
}

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

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

inline __device__ void operator+=(double2& a, double2 b) {
    a.x += b.x; a.y += b.y;
}

inline __device__ void operator+=(double3& a, double3 b) {
    a.x += b.x; a.y += b.y; a.z += b.z;
}

inline __device__ void operator+=(double4& a, double4 b) {
    a.x += b.x; a.y += b.y; a.z += b.z; a.w += b.w;
}

// -= operator

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

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

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

inline __device__ void operator-=(float2& a, float2 b) {
    a.x -= b.x; a.y -= b.y;
}

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

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

inline __device__ void operator-=(double2& a, double2 b) {
    a.x -= b.x; a.y -= b.y;
}

inline __device__ void operator-=(double3& a, double3 b) {
    a.x -= b.x; a.y -= b.y; a.z -= b.z;
}

inline __device__ void operator-=(double4& a, double4 b) {
    a.x -= b.x; a.y -= b.y; a.z -= b.z; a.w -= b.w;
}

// *= operator

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

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

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

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

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

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

inline __device__ void operator*=(double2& a, double2 b) {
    a.x *= b.x; a.y *= b.y;
}

inline __device__ void operator*=(double3& a, double3 b) {
    a.x *= b.x; a.y *= b.y; a.z *= b.z;
}

inline __device__ void operator*=(double4& a, double4 b) {
    a.x *= b.x; a.y *= b.y; a.z *= b.z; a.w *= b.w;
}

// /= operator

inline __device__ void operator/=(int2& a, int2 b) {
    a.x /= b.x; a.y /= b.y;
}

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

inline __device__ void operator/=(int4& a, int4 b) {
    a.x /= b.x; a.y /= b.y; a.z /= b.z; a.w /= b.w;
}

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

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

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

inline __device__ void operator/=(double2& a, double2 b) {
    a.x /= b.x; a.y /= b.y;
}

inline __device__ void operator/=(double3& a, double3 b) {
    a.x /= b.x; a.y /= b.y; a.z /= b.z;
}

inline __device__ void operator/=(double4& a, double4 b) {
    a.x /= b.x; a.y /= b.y; a.z /= b.z; a.w /= b.w;
}

// Multiply a vector by a constant.

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

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

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

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

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

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

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

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

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

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

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

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

inline __device__ double2 operator*(double2 a, double b) {
    return make_double2(a.x*b, a.y*b);
}

inline __device__ double3 operator*(double3 a, double b) {
    return make_double3(a.x*b, a.y*b, a.z*b);
}

inline __device__ double4 operator*(double4 a, double b) {
    return make_double4(a.x*b, a.y*b, a.z*b, a.w*b);
}

inline __device__ double2 operator*(double a, double2 b) {
    return make_double2(a*b.x, a*b.y);
}

inline __device__ double3 operator*(double a, double3 b) {
    return make_double3(a*b.x, a*b.y, a*b.z);
}

inline __device__ double4 operator*(double a, double4 b) {
    return make_double4(a*b.x, a*b.y, a*b.z, a*b.w);
}

// *= operator (multiply vector by constant)

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

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

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

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

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

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

inline __device__ void operator*=(double2& a, double b) {
    a.x *= b; a.y *= b;
}

inline __device__ void operator*=(double3& a, double b) {
    a.x *= b; a.y *= b; a.z *= b;
}

inline __device__ void operator*=(double4& a, double b) {
    a.x *= b; a.y *= b; a.z *= b; a.w *= b;
}

// Dot product

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

inline __device__ double dot(double3 a, double3 b) {
    return a.x*b.x+a.y*b.y+a.z*b.z;
}

// Cross product

inline __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);
}

inline __device__ float3 cross(float4 a, float4 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);
}

inline __device__ double3 cross(double3 a, double3 b) {
    return make_double3(a.y*b.z-a.z*b.y, a.z*b.x-a.x*b.z, a.x*b.y-a.y*b.x);
}

inline __device__ double3 cross(double4 a, double4 b) {
    return make_double3(a.y*b.z-a.z*b.y, a.z*b.x-a.x*b.z, a.x*b.y-a.y*b.x);
}

// Normalize a vector

inline __device__ float2 normalize(float2 a) {
    return a*rsqrtf(a.x*a.x+a.y*a.y);
}

inline __device__ float3 normalize(float3 a) {
    return a*rsqrtf(a.x*a.x+a.y*a.y+a.z*a.z);
}

inline __device__ float4 normalize(float4 a) {
    return a*rsqrtf(a.x*a.x+a.y*a.y+a.z*a.z+a.w*a.w);
}

inline __device__ double2 normalize(double2 a) {
    return a*rsqrt(a.x*a.x+a.y*a.y);
}

inline __device__ double3 normalize(double3 a) {
    return a*rsqrt(a.x*a.x+a.y*a.y+a.z*a.z);
}

inline __device__ double4 normalize(double4 a) {
    return a*rsqrt(a.x*a.x+a.y*a.y+a.z*a.z+a.w*a.w);
}