text: /*
   * Copyright 2011-2013 Blender Foundation
   *
   * Licensed under the Apache License, Version 2.0 (the "License");
   * you may not use this file except in compliance with the License.
   * You may obtain a copy of the License at
   *
   * http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License
   */
  
  #ifndef __UTIL_MATH_H__
  #define __UTIL_MATH_H__
  
  /* Math
   *
   * Basic math functions on scalar and vector types. This header is used by
   * both the kernel code when compiled as C++, and other C++ non-kernel code. */
  
  #ifndef __KERNEL_OPENCL__
  
  #ifdef _MSC_VER
  #  define _USE_MATH_DEFINES
  #endif
  
  #include <float.h>
  #include <math.h>
  #include <stdio.h>
  
  #endif
  
  #include "util_types.h"
  
  CCL_NAMESPACE_BEGIN
  
  /* Float Pi variations */
  
  /* Division */
  #ifndef M_PI_F
  #define M_PI_F		((float)3.14159265358979323846264338327950288) 		/* pi */
  #endif
  #ifndef M_PI_2_F
  #define M_PI_2_F	((float)1.57079632679489661923132169163975144) 		/* pi/2 */
  #endif
  #ifndef M_PI_4_F
  #define M_PI_4_F	((float)0.785398163397448309615660845819875721) 	/* pi/4 */
  #endif
  #ifndef M_1_PI_F
  #define M_1_PI_F	((float)0.318309886183790671537767526745028724) 	/* 1/pi */
  #endif
  #ifndef M_2_PI_F
  #define M_2_PI_F	((float)0.636619772367581343075535053490057448) 	/* 2/pi */
  #endif
  
  /* Multiplication */
  #ifndef M_2PI_F
  #define M_2PI_F		((float)6.283185307179586476925286766559005768)		/* 2*pi */
  #endif
  #ifndef M_4PI_F
  #define M_4PI_F		((float)12.56637061435917295385057353311801153)		/* 4*pi */
  #endif
  
  /* Float sqrt variations */
  
  #ifndef M_SQRT2_F
  #define M_SQRT2_F	((float)1.41421356237309504880) 					/* sqrt(2) */
  #endif
  
  
  /* Scalar */
  
  #ifdef _WIN32
  
  #ifndef __KERNEL_OPENCL__
  
  ccl_device_inline float fmaxf(float a, float b)
  {
  	return (a > b)? a: b;
  }
  
  ccl_device_inline float fminf(float a, float b)
  {
  	return (a < b)? a: b;
  }
  
  #endif
  
  #endif
  
  #ifndef __KERNEL_GPU__
  
  ccl_device_inline int max(int a, int b)
  {
  	return (a > b)? a: b;
  }
  
  ccl_device_inline int min(int a, int b)
  {
  	return (a < b)? a: b;
  }
  
  ccl_device_inline float max(float a, float b)
  {
  	return (a > b)? a: b;
  }
  
  ccl_device_inline float min(float a, float b)
  {
  	return (a < b)? a: b;
  }
  
  ccl_device_inline double max(double a, double b)
  {
  	return (a > b)? a: b;
  }
  
  ccl_device_inline double min(double a, double b)
  {
  	return (a < b)? a: b;
  }
  
  #endif
  
  ccl_device_inline float min4(float a, float b, float c, float d)
  {
  	return min(min(a, b), min(c, d));
  }
  
  ccl_device_inline float max4(float a, float b, float c, float d)
  {
  	return max(max(a, b), max(c, d));
  }
  
  #ifndef __KERNEL_OPENCL__
  
  ccl_device_inline int clamp(int a, int mn, int mx)
  {
  	return min(max(a, mn), mx);
  }
  
  ccl_device_inline float clamp(float a, float mn, float mx)
  {
  	return min(max(a, mn), mx);
  }
  
  #endif
  
  ccl_device_inline int float_to_int(float f)
  {
  	return (int)f;
  }
  
  ccl_device_inline int floor_to_int(float f)
  {
  	return float_to_int(floorf(f));
  }
  
  ccl_device_inline int ceil_to_int(float f)
  {
  	return float_to_int(ceilf(f));
  }
  
  ccl_device_inline float signf(float f)
  {
  	return (f < 0.0f)? -1.0f: 1.0f;
  }
  
  ccl_device_inline float nonzerof(float f, float eps)
  {
  	if(fabsf(f) < eps)
  		return signf(f)*eps;
  	else
  		return f;
  }
  
  ccl_device_inline float smoothstepf(float f)
  {
  	float ff = f*f;
  	return (3.0f*ff - 2.0f*ff*f);
  }
  
  /* Float2 Vector */
  
  #ifndef __KERNEL_OPENCL__
  
  ccl_device_inline bool is_zero(const float2 a)
  {
  	return (a.x == 0.0f && a.y == 0.0f);
  }
  
  #endif
  
  #ifndef __KERNEL_OPENCL__
  
  ccl_device_inline float average(const float2 a)
  {
  	return (a.x + a.y)*(1.0f/2.0f);
  }
  
  #endif
  
  #ifndef __KERNEL_OPENCL__
  
  ccl_device_inline float2 operator-(const float2 a)
  {
  	return make_float2(-a.x, -a.y);
  }
  
  ccl_device_inline float2 operator*(const float2 a, const float2 b)
  {
  	return make_float2(a.x*b.x, a.y*b.y);
  }
  
  ccl_device_inline float2 operator*(const float2 a, float f)
  {
  	return make_float2(a.x*f, a.y*f);
  }
  
  ccl_device_inline float2 operator*(float f, const float2 a)
  {
  	return make_float2(a.x*f, a.y*f);
  }
  
  ccl_device_inline float2 operator/(float f, const float2 a)
  {
  	return make_float2(f/a.x, f/a.y);
  }
  
  ccl_device_inline float2 operator/(const float2 a, float f)
  {
  	float invf = 1.0f/f;
  	return make_float2(a.x*invf, a.y*invf);
  }
  
  ccl_device_inline float2 operator/(const float2 a, const float2 b)
  {
  	return make_float2(a.x/b.x, a.y/b.y);
  }
  
  ccl_device_inline float2 operator+(const float2 a, const float2 b)
  {
  	return make_float2(a.x+b.x, a.y+b.y);
  }
  
  ccl_device_inline float2 operator-(const float2 a, const float2 b)
  {
  	return make_float2(a.x-b.x, a.y-b.y);
  }
  
  ccl_device_inline float2 operator+=(float2& a, const float2 b)
  {
  	return a = a + b;
  }
  
  ccl_device_inline float2 operator*=(float2& a, const float2 b)
  {
  	return a = a * b;
  }
  
  ccl_device_inline float2 operator*=(float2& a, float f)
  {
  	return a = a * f;
  }
  
  ccl_device_inline float2 operator/=(float2& a, const float2 b)
  {
  	return a = a / b;
  }
  
  ccl_device_inline float2 operator/=(float2& a, float f)
  {
  	float invf = 1.0f/f;
  	return a = a * invf;
  }
  
  
  ccl_device_inline float dot(const float2 a, const float2 b)
  {
  	return a.x*b.x + a.y*b.y;
  }
  
  ccl_device_inline float cross(const float2 a, const float2 b)
  {
  	return (a.x*b.y - a.y*b.x);
  }
  
  #endif
  
  #ifndef __KERNEL_OPENCL__
  
  ccl_device_inline bool operator==(const int2 a, const int2 b)
  {
  	return (a.x == b.x && a.y == b.y);
  }
  
  ccl_device_inline float len(const float2 a)
  {
  	return sqrtf(dot(a, a));
  }
  
  ccl_device_inline float2 normalize(const float2 a)
  {
  	return a/len(a);
  }
  
  ccl_device_inline float2 normalize_len(const float2 a, float *t)
  {
  	*t = len(a);
  	return a/(*t);
  }
  
  ccl_device_inline float2 safe_normalize(const float2 a)
  {
  	float t = len(a);
  	return (t)? a/t: a;
  }
  
  ccl_device_inline bool operator==(const float2 a, const float2 b)
  {
  	return (a.x == b.x && a.y == b.y);
  }
  
  ccl_device_inline bool operator!=(const float2 a, const float2 b)
  {
  	return !(a == b);
  }
  
  ccl_device_inline float2 min(float2 a, float2 b)
  {
  	return make_float2(min(a.x, b.x), min(a.y, b.y));
  }
  
  ccl_device_inline float2 max(float2 a, float2 b)
  {
  	return make_float2(max(a.x, b.x), max(a.y, b.y));
  }
  
  ccl_device_inline float2 clamp(float2 a, float2 mn, float2 mx)
  {
  	return min(max(a, mn), mx);
  }
  
  ccl_device_inline float2 fabs(float2 a)
  {
  	return make_float2(fabsf(a.x), fabsf(a.y));
  }
  
  ccl_device_inline float2 as_float2(const float4 a)
  {
  	return make_float2(a.x, a.y);
  }
  
  #endif
  
  #ifndef __KERNEL_GPU__
  
  ccl_device_inline void print_float2(const char *label, const float2& a)
  {
  	printf("%s: %.8f %.8f\n", label, (double)a.x, (double)a.y);
  }
  
  #endif
  
  #ifndef __KERNEL_OPENCL__
  
  ccl_device_inline float2 interp(float2 a, float2 b, float t)
  {
  	return a + t*(b - a);
  }
  
  #endif
  
  /* Float3 Vector */
  
  #ifndef __KERNEL_OPENCL__
  
  ccl_device_inline float3 operator-(const float3 a)
  {
  	return make_float3(-a.x, -a.y, -a.z);
  }
  
  ccl_device_inline float3 operator*(const float3 a, const float3 b)
  {
  	return make_float3(a.x*b.x, a.y*b.y, a.z*b.z);
  }
  
  ccl_device_inline float3 operator*(const float3 a, float f)
  {
  	return make_float3(a.x*f, a.y*f, a.z*f);
  }
  
  ccl_device_inline float3 operator*(float f, const float3 a)
  {
  	return make_float3(a.x*f, a.y*f, a.z*f);
  }
  
  ccl_device_inline float3 operator/(float f, const float3 a)
  {
  	return make_float3(f/a.x, f/a.y, f/a.z);
  }
  
  ccl_device_inline float3 operator/(const float3 a, float f)
  {
  	float invf = 1.0f/f;
  	return make_float3(a.x*invf, a.y*invf, a.z*invf);
  }
  
  ccl_device_inline float3 operator/(const float3 a, const float3 b)
  {
  	return make_float3(a.x/b.x, a.y/b.y, a.z/b.z);
  }
  
  ccl_device_inline float3 operator+(const float3 a, const float3 b)
  {
  	return make_float3(a.x+b.x, a.y+b.y, a.z+b.z);
  }
  
  ccl_device_inline float3 operator-(const float3 a, const float3 b)
  {
  	return make_float3(a.x-b.x, a.y-b.y, a.z-b.z);
  }
  
  ccl_device_inline float3 operator+=(float3& a, const float3 b)
  {
  	return a = a + b;
  }
  
  ccl_device_inline float3 operator*=(float3& a, const float3 b)
  {
  	return a = a * b;
  }
  
  ccl_device_inline float3 operator*=(float3& a, float f)
  {
  	return a = a * f;
  }
  
  ccl_device_inline float3 operator/=(float3& a, const float3 b)
  {
  	return a = a / b;
  }
  
  ccl_device_inline float3 operator/=(float3& a, float f)
  {
  	float invf = 1.0f/f;
  	return a = a * invf;
  }
  
  ccl_device_inline float dot(const float3 a, const float3 b)
  {
  #if defined(__KERNEL_SSE41__) && defined(__KERNEL_SSE__)
  	return _mm_cvtss_f32(_mm_dp_ps(a, b, 0x7F));
  #else	
  	return a.x*b.x + a.y*b.y + a.z*b.z;
  #endif
  }
  
  ccl_device_inline float dot(const float4 a, const float4 b)
  {
  #if defined(__KERNEL_SSE41__) && defined(__KERNEL_SSE__)
  	return _mm_cvtss_f32(_mm_dp_ps(a, b, 0xFF));
  #else	
  	return (a.x*b.x + a.y*b.y) + (a.z*b.z + a.w*b.w);
  #endif
  }
  
  ccl_device_inline float3 cross(const float3 a, const float3 b)
  {
  	float3 r = 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);
  	return r;
  }
  
  #endif
  
  ccl_device_inline float len(const float3 a)
  {
  #if defined(__KERNEL_SSE41__) && defined(__KERNEL_SSE__)
  	return _mm_cvtss_f32(_mm_sqrt_ss(_mm_dp_ps(a.m128, a.m128, 0x7F)));
  #else
  	return sqrtf(dot(a, a));
  #endif
  }
  
  ccl_device_inline float len_squared(const float3 a)
  {
  	return dot(a, a);
  }
  
  #ifndef __KERNEL_OPENCL__
  
  ccl_device_inline float len_squared(const float4 a)
  {
  	return dot(a, a);
  }
  
  ccl_device_inline float3 normalize(const float3 a)
  {
  #if defined(__KERNEL_SSE41__) && defined(__KERNEL_SSE__)
  	__m128 norm = _mm_sqrt_ps(_mm_dp_ps(a.m128, a.m128, 0x7F));
  	return _mm_div_ps(a.m128, norm);
  #else
  	return a/len(a);
  #endif
  }
  
  #endif
  
  ccl_device_inline float3 normalize_len(const float3 a, float *t)
  {
  	*t = len(a);
  	return a/(*t);
  }
  
  ccl_device_inline float3 safe_normalize(const float3 a)
  {
  	float t = len(a);
  	return (t)? a/t: a;
  }
  
  #ifndef __KERNEL_OPENCL__
  
  ccl_device_inline bool operator==(const float3 a, const float3 b)
  {
  #ifdef __KERNEL_SSE__
  	return (_mm_movemask_ps(_mm_cmpeq_ps(a.m128, b.m128)) & 7) == 7;
  #else
  	return (a.x == b.x && a.y == b.y && a.z == b.z);
  #endif
  }
  
  ccl_device_inline bool operator!=(const float3 a, const float3 b)
  {
  	return !(a == b);
  }
  
  ccl_device_inline float3 min(float3 a, float3 b)
  {
  #ifdef __KERNEL_SSE__
  	return _mm_min_ps(a.m128, b.m128);
  #else
  	return make_float3(min(a.x, b.x), min(a.y, b.y), min(a.z, b.z));
  #endif
  }
  
  ccl_device_inline float3 max(float3 a, float3 b)
  {
  #ifdef __KERNEL_SSE__
  	return _mm_max_ps(a.m128, b.m128);
  #else
  	return make_float3(max(a.x, b.x), max(a.y, b.y), max(a.z, b.z));
  #endif
  }
  
  ccl_device_inline float3 clamp(float3 a, float3 mn, float3 mx)
  {
  	return min(max(a, mn), mx);
  }
  
  ccl_device_inline float3 fabs(float3 a)
  {
  #ifdef __KERNEL_SSE__
  	__m128 mask = _mm_castsi128_ps(_mm_set1_epi32(0x7fffffff));
  	return _mm_and_ps(a.m128, mask);
  #else
  	return make_float3(fabsf(a.x), fabsf(a.y), fabsf(a.z));
  #endif
  }
  
  #endif
  
  ccl_device_inline float3 float2_to_float3(const float2 a)
  {
  	return make_float3(a.x, a.y, 0.0f);
  }
  
  ccl_device_inline float3 float4_to_float3(const float4 a)
  {
  	return make_float3(a.x, a.y, a.z);
  }
  
  ccl_device_inline float4 float3_to_float4(const float3 a)
  {
  	return make_float4(a.x, a.y, a.z, 1.0f);
  }
  
  #ifndef __KERNEL_GPU__
  
  ccl_device_inline void print_float3(const char *label, const float3& a)
  {
  	printf("%s: %.8f %.8f %.8f\n", label, (double)a.x, (double)a.y, (double)a.z);
  }
  
  ccl_device_inline float3 rcp(const float3& a)
  {
  #ifdef __KERNEL_SSE__
  	float4 r = _mm_rcp_ps(a.m128);
  	return _mm_sub_ps(_mm_add_ps(r, r), _mm_mul_ps(_mm_mul_ps(r, r), a));
  #else
  	return make_float3(1.0f/a.x, 1.0f/a.y, 1.0f/a.z);
  #endif
  }
  
  #endif
  
  ccl_device_inline float3 interp(float3 a, float3 b, float t)
  {
  	return a + t*(b - a);
  }
  
  ccl_device_inline bool is_zero(const float3 a)
  {
  #ifdef __KERNEL_SSE__
  	return a == make_float3(0.0f);
  #else
  	return (a.x == 0.0f && a.y == 0.0f && a.z == 0.0f);
  #endif
  }
  
  ccl_device_inline float reduce_add(const float3 a)
  {
  	return (a.x + a.y + a.z);
  }
  
  ccl_device_inline float average(const float3 a)
  {
  	return reduce_add(a)*(1.0f/3.0f);
  }
  
  /* Float4 Vector */
  
  #ifdef __KERNEL_SSE__
  
  template<size_t index_0, size_t index_1, size_t index_2, size_t index_3> __forceinline const float4 shuffle(const float4& b)
  {
  	return _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(b), _MM_SHUFFLE(index_3, index_2, index_1, index_0)));
  }
  
  template<> __forceinline const float4 shuffle<0, 0, 2, 2>(const float4& b)
  {
  	return _mm_moveldup_ps(b);
  }
  
  template<> __forceinline const float4 shuffle<1, 1, 3, 3>(const float4& b)
  {
  	return _mm_movehdup_ps(b);
  }
  
  template<> __forceinline const float4 shuffle<0, 1, 0, 1>(const float4& b)
  {
  	return _mm_castpd_ps(_mm_movedup_pd(_mm_castps_pd(b)));
  }
  
  #endif
  
  #ifndef __KERNEL_OPENCL__
  
  ccl_device_inline float4 operator-(const float4& a)
  {
  #ifdef __KERNEL_SSE__
  	__m128 mask = _mm_castsi128_ps(_mm_set1_epi32(0x80000000));
  	return _mm_xor_ps(a.m128, mask);
  #else
  	return make_float4(-a.x, -a.y, -a.z, -a.w);
  #endif
  }
  
  ccl_device_inline float4 operator*(const float4& a, const float4& b)
  {
  #ifdef __KERNEL_SSE__
  	return _mm_mul_ps(a.m128, b.m128);
  #else
  	return make_float4(a.x*b.x, a.y*b.y, a.z*b.z, a.w*b.w);
  #endif
  }
  
  ccl_device_inline float4 operator*(const float4& a, float f)
  {
  #ifdef __KERNEL_SSE__
  	return a * make_float4(f);
  #else
  	return make_float4(a.x*f, a.y*f, a.z*f, a.w*f);
  #endif
  }
  
  ccl_device_inline float4 operator*(float f, const float4& a)
  {
  	return a * f;
  }
  
  ccl_device_inline float4 rcp(const float4& a)
  {
  #ifdef __KERNEL_SSE__
  	float4 r = _mm_rcp_ps(a.m128);
  	return _mm_sub_ps(_mm_add_ps(r, r), _mm_mul_ps(_mm_mul_ps(r, r), a));
  #else
  	return make_float4(1.0f/a.x, 1.0f/a.y, 1.0f/a.z, 1.0f/a.w);
  #endif
  }
  
  ccl_device_inline float4 operator/(const float4& a, float f)
  {
  	return a * (1.0f/f);
  }
  
  ccl_device_inline float4 operator/(const float4& a, const float4& b)
  {
  #ifdef __KERNEL_SSE__
  	return a * rcp(b);
  #else
  	return make_float4(a.x/b.x, a.y/b.y, a.z/b.z, a.w/b.w);
  #endif
  
  }
  
  ccl_device_inline float4 operator+(const float4& a, const float4& b)
  {
  #ifdef __KERNEL_SSE__
  	return _mm_add_ps(a.m128, b.m128);
  #else
  	return make_float4(a.x+b.x, a.y+b.y, a.z+b.z, a.w+b.w);
  #endif
  }
  
  ccl_device_inline float4 operator-(const float4& a, const float4& b)
  {
  #ifdef __KERNEL_SSE__
  	return _mm_sub_ps(a.m128, b.m128);
  #else
  	return make_float4(a.x-b.x, a.y-b.y, a.z-b.z, a.w-b.w);
  #endif
  }
  
  ccl_device_inline float4 operator+=(float4& a, const float4& b)
  {
  	return a = a + b;
  }
  
  ccl_device_inline float4 operator*=(float4& a, const float4& b)
  {
  	return a = a * b;
  }
  
  ccl_device_inline float4 operator/=(float4& a, float f)
  {
  	return a = a / f;
  }
  
  ccl_device_inline int4 operator<(const float4& a, const float4& b)
  {
  #ifdef __KERNEL_SSE__
  	return _mm_cvtps_epi32(_mm_cmplt_ps(a.m128, b.m128)); /* todo: avoid cvt */
  #else
  	return make_int4(a.x < b.x, a.y < b.y, a.z < b.z, a.w < b.w);
  #endif
  }
  
  ccl_device_inline int4 operator>=(float4 a, float4 b)
  {
  #ifdef __KERNEL_SSE__
  	return _mm_cvtps_epi32(_mm_cmpge_ps(a.m128, b.m128)); /* todo: avoid cvt */
  #else
  	return make_int4(a.x >= b.x, a.y >= b.y, a.z >= b.z, a.w >= b.w);
  #endif
  }
  
  ccl_device_inline int4 operator<=(const float4& a, const float4& b)
  {
  #ifdef __KERNEL_SSE__
  	return _mm_cvtps_epi32(_mm_cmple_ps(a.m128, b.m128)); /* todo: avoid cvt */
  #else
  	return make_int4(a.x <= b.x, a.y <= b.y, a.z <= b.z, a.w <= b.w);
  #endif
  }
  
  ccl_device_inline bool operator==(const float4 a, const float4 b)
  {
  #ifdef __KERNEL_SSE__
  	return (_mm_movemask_ps(_mm_cmpeq_ps(a.m128, b.m128)) & 15) == 15;
  #else
  	return (a.x == b.x && a.y == b.y && a.z == b.z && a.w == b.w);
  #endif
  }
  
  ccl_device_inline float4 cross(const float4& a, const float4& b)
  {
  #ifdef __KERNEL_SSE__
  	return (shuffle<1,2,0,0>(a)*shuffle<2,0,1,0>(b)) - (shuffle<2,0,1,0>(a)*shuffle<1,2,0,0>(b));
  #else
  	return make_float4(a.y*b.z - a.z*b.y, a.z*b.x - a.x*b.z, a.x*b.y - a.y*b.x, 0.0f);
  #endif
  }
  
  ccl_device_inline bool is_zero(const float4& a)
  {
  #ifdef __KERNEL_SSE__
  	return a == make_float4(0.0f);
  #else
  	return (a.x == 0.0f && a.y == 0.0f && a.z == 0.0f && a.w == 0.0f);
  #endif
  }
  
  ccl_device_inline float reduce_add(const float4& a)
  {
  #ifdef __KERNEL_SSE__
  	float4 h = shuffle<1,0,3,2>(a) + a;
  	return _mm_cvtss_f32(shuffle<2,3,0,1>(h) + h); /* todo: efficiency? */
  #else
  	return ((a.x + a.y) + (a.z + a.w));
  #endif
  }
  
  ccl_device_inline float average(const float4& a)
  {
  	return reduce_add(a) * 0.25f;
  }
  
  ccl_device_inline float len(const float4 a)
  {
  	return sqrtf(dot(a, a));
  }
  
  ccl_device_inline float4 normalize(const float4 a)
  {
  	return a/len(a);
  }
  
  ccl_device_inline float4 safe_normalize(const float4 a)
  {
  	float t = len(a);
  	return (t)? a/t: a;
  }
  
  ccl_device_inline float4 min(float4 a, float4 b)
  {
  #ifdef __KERNEL_SSE__
  	return _mm_min_ps(a.m128, b.m128);
  #else
  	return make_float4(min(a.x, b.x), min(a.y, b.y), min(a.z, b.z), min(a.w, b.w));
  #endif
  }
  
  ccl_device_inline float4 max(float4 a, float4 b)
  {
  #ifdef __KERNEL_SSE__
  	return _mm_max_ps(a.m128, b.m128);
  #else
  	return make_float4(max(a.x, b.x), max(a.y, b.y), max(a.z, b.z), max(a.w, b.w));
  #endif
  }
  
  #endif
  
  #ifndef __KERNEL_GPU__
  
  ccl_device_inline float4 select(const int4& mask, const float4& a, const float4& b)
  {
  #ifdef __KERNEL_SSE__
  	return _mm_or_ps(_mm_and_ps(_mm_cvtepi32_ps(mask), a), _mm_andnot_ps(_mm_cvtepi32_ps(mask), b)); /* todo: avoid cvt */
  #else
  	return make_float4((mask.x)? a.x: b.x, (mask.y)? a.y: b.y, (mask.z)? a.z: b.z, (mask.w)? a.w: b.w);
  #endif
  }
  
  ccl_device_inline float4 reduce_min(const float4& a)
  {
  #ifdef __KERNEL_SSE__
  	float4 h = min(shuffle<1,0,3,2>(a), a);
  	return min(shuffle<2,3,0,1>(h), h);
  #else
  	return make_float4(min(min(a.x, a.y), min(a.z, a.w)));
  #endif
  }
  
  ccl_device_inline float4 reduce_max(const float4& a)
  {
  #ifdef __KERNEL_SSE__
  	float4 h = max(shuffle<1,0,3,2>(a), a);
  	return max(shuffle<2,3,0,1>(h), h);
  #else
  	return make_float4(max(max(a.x, a.y), max(a.z, a.w)));
  #endif
  }
  
  #if 0
  ccl_device_inline float4 reduce_add(const float4& a)
  {
  #ifdef __KERNEL_SSE__
  	float4 h = shuffle<1,0,3,2>(a) + a;
  	return shuffle<2,3,0,1>(h) + h;
  #else
  	return make_float4((a.x + a.y) + (a.z + a.w));
  #endif
  }
  #endif
  
  ccl_device_inline void print_float4(const char *label, const float4& a)
  {
  	printf("%s: %.8f %.8f %.8f %.8f\n", label, (double)a.x, (double)a.y, (double)a.z, (double)a.w);
  }
  
  #endif
  
  /* Int3 */
  
  #ifndef __KERNEL_OPENCL__
  
  ccl_device_inline int3 min(int3 a, int3 b)
  {
  #if defined(__KERNEL_SSE__) && defined(__KERNEL_SSE41__)
  	return _mm_min_epi32(a.m128, b.m128);
  #else
  	return make_int3(min(a.x, b.x), min(a.y, b.y), min(a.z, b.z));
  #endif
  }
  
  ccl_device_inline int3 max(int3 a, int3 b)
  {
  #if defined(__KERNEL_SSE__) && defined(__KERNEL_SSE41__)
  	return _mm_max_epi32(a.m128, b.m128);
  #else
  	return make_int3(max(a.x, b.x), max(a.y, b.y), max(a.z, b.z));
  #endif
  }
  
  ccl_device_inline int3 clamp(const int3& a, int mn, int mx)
  {
  #ifdef __KERNEL_SSE__
  	return min(max(a, make_int3(mn)), make_int3(mx));
  #else
  	return make_int3(clamp(a.x, mn, mx), clamp(a.y, mn, mx), clamp(a.z, mn, mx));
  #endif
  }
  
  ccl_device_inline int3 clamp(const int3& a, int3& mn, int mx)
  {
  #ifdef __KERNEL_SSE__
  	return min(max(a, mn), make_int3(mx));
  #else
  	return make_int3(clamp(a.x, mn.x, mx), clamp(a.y, mn.y, mx), clamp(a.z, mn.z, mx));
  #endif
  }
  
  #endif
  
  #ifndef __KERNEL_GPU__
  
  ccl_device_inline void print_int3(const char *label, const int3& a)
  {
  	printf("%s: %d %d %d\n", label, a.x, a.y, a.z);
  }
  
  #endif
  
  /* Int4 */
  
  #ifndef __KERNEL_GPU__
  
  ccl_device_inline int4 operator+(const int4& a, const int4& b)
  {
  #ifdef __KERNEL_SSE__
  	return _mm_add_epi32(a.m128, b.m128);
  #else
  	return make_int4(a.x+b.x, a.y+b.y, a.z+b.z, a.w+b.w);
  #endif
  }
  
  ccl_device_inline int4 operator+=(int4& a, const int4& b)
  {
  	return a = a + b;
  }
  
  ccl_device_inline int4 operator>>(const int4& a, int i)
  {
  #ifdef __KERNEL_SSE__
  	return _mm_srai_epi32(a.m128, i);
  #else
  	return make_int4(a.x >> i, a.y >> i, a.z >> i, a.w >> i);
  #endif
  }
  
  ccl_device_inline int4 min(int4 a, int4 b)
  {
  #if defined(__KERNEL_SSE__) && defined(__KERNEL_SSE41__)
  	return _mm_min_epi32(a.m128, b.m128);
  #else
  	return make_int4(min(a.x, b.x), min(a.y, b.y), min(a.z, b.z), min(a.w, b.w));
  #endif
  }
  
  ccl_device_inline int4 max(int4 a, int4 b)
  {
  #if defined(__KERNEL_SSE__) && defined(__KERNEL_SSE41__)
  	return _mm_max_epi32(a.m128, b.m128);
  #else
  	return make_int4(max(a.x, b.x), max(a.y, b.y), max(a.z, b.z), max(a.w, b.w));
  #endif
  }
  
  ccl_device_inline int4 clamp(const int4& a, const int4& mn, const int4& mx)
  {
  	return min(max(a, mn), mx);
  }
  
  ccl_device_inline int4 select(const int4& mask, const int4& a, const int4& b)
  {
  #ifdef __KERNEL_SSE__
  	__m128 m = _mm_cvtepi32_ps(mask);
  	return _mm_castps_si128(_mm_or_ps(_mm_and_ps(m, _mm_castsi128_ps(a)), _mm_andnot_ps(m, _mm_castsi128_ps(b)))); /* todo: avoid cvt */
  #else
  	return make_int4((mask.x)? a.x: b.x, (mask.y)? a.y: b.y, (mask.z)? a.z: b.z, (mask.w)? a.w: b.w);
  #endif
  }
  
  ccl_device_inline void print_int4(const char *label, const int4& a)
  {
  	printf("%s: %d %d %d %d\n", label, a.x, a.y, a.z, a.w);
  }
  
  #endif
  
  /* Int/Float conversion */
  
  #ifndef __KERNEL_OPENCL__
  
  ccl_device_inline int as_int(uint i)
  {
  	union { uint ui; int i; } u;
  	u.ui = i;
  	return u.i;
  }
  
  ccl_device_inline uint as_uint(int i)
  {
  	union { uint ui; int i; } u;
  	u.i = i;
  	return u.ui;
  }
  
  ccl_device_inline uint as_uint(float f)
  {
  	union { uint i; float f; } u;
  	u.f = f;
  	return u.i;
  }
  
  ccl_device_inline int __float_as_int(float f)
  {
  	union { int i; float f; } u;
  	u.f = f;
  	return u.i;
  }
  
  ccl_device_inline float __int_as_float(int i)
  {
  	union { int i; float f; } u;
  	u.i = i;
  	return u.f;
  }
  
  ccl_device_inline uint __float_as_uint(float f)
  {
  	union { uint i; float f; } u;
  	u.f = f;
  	return u.i;
  }
  
  ccl_device_inline float __uint_as_float(uint i)
  {
  	union { uint i; float f; } u;
  	u.i = i;
  	return u.f;
  }
  
  /* Interpolation */
  
  template<class A, class B> A lerp(const A& a, const A& b, const B& t)
  {
  	return (A)(a * ((B)1 - t) + b * t);
  }
  
  /* Triangle */
  
  ccl_device_inline float triangle_area(const float3 v1, const float3 v2, const float3 v3)
  {
  	return len(cross(v3 - v2, v1 - v2))*0.5f;
  }
  
  #endif
  
  /* Orthonormal vectors */
  
  ccl_device_inline void make_orthonormals(const float3 N, float3 *a, float3 *b)
  {
  #if 0
  	if(fabsf(N.y) >= 0.999f) {
  		*a = make_float3(1, 0, 0);
  		*b = make_float3(0, 0, 1);
  		return;
  	}
  	if(fabsf(N.z) >= 0.999f) {
  		*a = make_float3(1, 0, 0);
  		*b = make_float3(0, 1, 0);
  		return;
  	}
  #endif
  
  	if(N.x != N.y || N.x != N.z)
  		*a = make_float3(N.z-N.y, N.x-N.z, N.y-N.x);  //(1,1,1)x N
  	else
  		*a = make_float3(N.z-N.y, N.x+N.z, -N.y-N.x);  //(-1,1,1)x N
  
  	*a = normalize(*a);
  	*b = cross(N, *a);
  }
  
  /* Color division */
  
  ccl_device_inline float3 safe_invert_color(float3 a)
  {
  	float x, y, z;
  
  	x = (a.x != 0.0f)? 1.0f/a.x: 0.0f;
  	y = (a.y != 0.0f)? 1.0f/a.y: 0.0f;
  	z = (a.z != 0.0f)? 1.0f/a.z: 0.0f;
  
  	return make_float3(x, y, z);
  }
  
  ccl_device_inline float3 safe_divide_color(float3 a, float3 b)
  {
  	float x, y, z;
  
  	x = (b.x != 0.0f)? a.x/b.x: 0.0f;
  	y = (b.y != 0.0f)? a.y/b.y: 0.0f;
  	z = (b.z != 0.0f)? a.z/b.z: 0.0f;
  
  	return make_float3(x, y, z);
  }
  
  ccl_device_inline float3 safe_divide_even_color(float3 a, float3 b)
  {
  	float x, y, z;
  
  	x = (b.x != 0.0f)? a.x/b.x: 0.0f;
  	y = (b.y != 0.0f)? a.y/b.y: 0.0f;
  	z = (b.z != 0.0f)? a.z/b.z: 0.0f;
  
  	/* try to get grey even if b is zero */
  	if(b.x == 0.0f) {
  		if(b.y == 0.0f) {
  			x = z;
  			y = z;
  		}
  		else if(b.z == 0.0f) {
  			x = y;
  			z = y;
  		}
  		else
  			x = 0.5f*(y + z);
  	}
  	else if(b.y == 0.0f) {
  		if(b.z == 0.0f) {
  			y = x;
  			z = x;
  		}
  		else
  			y = 0.5f*(x + z);
  	}
  	else if(b.z == 0.0f) {
  		z = 0.5f*(x + y);
  	}
  
  	return make_float3(x, y, z);
  }
  
  /* Rotation of point around axis and angle */
  
  ccl_device_inline float3 rotate_around_axis(float3 p, float3 axis, float angle)
  {
  	float costheta = cosf(angle);
  	float sintheta = sinf(angle);
  	float3 r;
  
  	r.x = ((costheta + (1 - costheta) * axis.x * axis.x) * p.x) +
  		(((1 - costheta) * axis.x * axis.y - axis.z * sintheta) * p.y) +
  		(((1 - costheta) * axis.x * axis.z + axis.y * sintheta) * p.z);
  
  	r.y = (((1 - costheta) * axis.x * axis.y + axis.z * sintheta) * p.x) +
  		((costheta + (1 - costheta) * axis.y * axis.y) * p.y) +
  		(((1 - costheta) * axis.y * axis.z - axis.x * sintheta) * p.z);
  
  	r.z = (((1 - costheta) * axis.x * axis.z - axis.y * sintheta) * p.x) +
  		(((1 - costheta) * axis.y * axis.z + axis.x * sintheta) * p.y) +
  		((costheta + (1 - costheta) * axis.z * axis.z) * p.z);
  
  	return r;
  }
  
  /* NaN-safe math ops */
  
  ccl_device_inline float safe_sqrtf(float f)
  {
  	return sqrtf(max(f, 0.0f));
  }
  
  ccl_device float safe_asinf(float a)
  {
  	return asinf(clamp(a, -1.0f, 1.0f));
  }
  
  ccl_device float safe_acosf(float a)
  {
  	return acosf(clamp(a, -1.0f, 1.0f));
  }
  
  ccl_device float compatible_powf(float x, float y)
  {
  #ifdef __KERNEL_GPU__
  	if(y == 0.0f) /* x^0 -> 1, including 0^0 */
  		return 1.0f;
  
  	/* GPU pow doesn't accept negative x, do manual checks here */
  	if(x < 0.0f) {
  		if(fmodf(-y, 2.0f) == 0.0f)
  			return powf(-x, y);
  		else
  			return -powf(-x, y);
  	}
  	else if(x == 0.0f)
  		return 0.0f;
  #endif
  	return powf(x, y);
  }
  
  ccl_device float safe_powf(float a, float b)
  {
  	if(UNLIKELY(a < 0.0f && b != float_to_int(b)))
  		return 0.0f;
  
  	return compatible_powf(a, b);
  }
  
  ccl_device float safe_logf(float a, float b)
  {
  	if(UNLIKELY(a < 0.0f || b < 0.0f))
  		return 0.0f;
  
  	return logf(a)/logf(b);
  }
  
  ccl_device float safe_divide(float a, float b)
  {
  	return (b != 0.0f)? a/b: 0.0f;
  }
  
  ccl_device float safe_modulo(float a, float b)
  {
  	return (b != 0.0f)? fmodf(a, b): 0.0f;
  }
  
  /* Ray Intersection */
  
  ccl_device bool ray_sphere_intersect(
  	float3 ray_P, float3 ray_D, float ray_t,
  	float3 sphere_P, float sphere_radius,
  	float3 *isect_P, float *isect_t)
  {
  	float3 d = sphere_P - ray_P;
  	float radiussq = sphere_radius*sphere_radius;
  	float tsq = dot(d, d);
  
  	if(tsq > radiussq) { /* ray origin outside sphere */
  		float tp = dot(d, ray_D);
  
  		if(tp < 0.0f) /* dir points away from sphere */
  			return false;
  
  		float dsq = tsq - tp*tp; /* pythagoras */
  
  		if(dsq > radiussq) /* closest point on ray outside sphere */
  			return false;
  
  		float t = tp - sqrtf(radiussq - dsq); /* pythagoras */
  
  		if(t < ray_t) {
  			*isect_t = t;
  			*isect_P = ray_P + ray_D*t;
  			return true;
  		}
  	}
  
  	return false;
  }
  
  ccl_device bool ray_aligned_disk_intersect(
  	float3 ray_P, float3 ray_D, float ray_t,
  	float3 disk_P, float disk_radius,
  	float3 *isect_P, float *isect_t)
  {
  	/* aligned disk normal */
  	float disk_t;
  	float3 disk_N = normalize_len(ray_P - disk_P, &disk_t);
  	float div = dot(ray_D, disk_N);
  
  	if(UNLIKELY(div == 0.0f))
  		return false;
  
  	/* compute t to intersection point */
  	float t = -disk_t/div;
  	if(t < 0.0f || t > ray_t)
  		return false;
  	
  	/* test if within radius */
  	float3 P = ray_P + ray_D*t;
  	if(len_squared(P - disk_P) > disk_radius*disk_radius)
  		return false;
  
  	*isect_P = P;
  	*isect_t = t;
  
  	return true;
  }
  
  ccl_device bool ray_triangle_intersect(
  	float3 ray_P, float3 ray_D, float ray_t,
  	float3 v0, float3 v1, float3 v2,
  	float3 *isect_P, float *isect_t)
  {
  	/* Calculate intersection */
  	float3 e1 = v1 - v0;
  	float3 e2 = v2 - v0;
  	float3 s1 = cross(ray_D, e2);
  
  	const float divisor = dot(s1, e1);
  	if(UNLIKELY(divisor == 0.0f))
  		return false;
  
  	const float invdivisor = 1.0f/divisor;
  
  	/* compute first barycentric coordinate */
  	const float3 d = ray_P - v0;
  	const float u = dot(d, s1)*invdivisor;
  	if(u < 0.0f)
  		return false;
  
  	/* Compute second barycentric coordinate */
  	const float3 s2 = cross(d, e1);
  	const float v = dot(ray_D, s2)*invdivisor;
  	if(v < 0.0f)
  		return false;
  
  	const float b0 = 1.0f - u - v;
  	if(b0 < 0.0f)
  		return false;
  
  	/* compute t to intersection point */
  	const float t = dot(e2, s2)*invdivisor;
  	if(t < 0.0f || t > ray_t)
  		return false;
  
  	*isect_t = t;
  	*isect_P = ray_P + ray_D*t;
  
  	return true;
  }
  
  ccl_device bool ray_triangle_intersect_uv(
  	float3 ray_P, float3 ray_D, float ray_t,
  	float3 v0, float3 v1, float3 v2,
  	float *isect_u, float *isect_v, float *isect_t)
  {
  	/* Calculate intersection */
  	float3 e1 = v1 - v0;
  	float3 e2 = v2 - v0;
  	float3 s1 = cross(ray_D, e2);
  
  	const float divisor = dot(s1, e1);
  	if(UNLIKELY(divisor == 0.0f))
  		return false;
  
  	const float invdivisor = 1.0f/divisor;
  
  	/* compute first barycentric coordinate */
  	const float3 d = ray_P - v0;
  	const float u = dot(d, s1)*invdivisor;
  	if(u < 0.0f)
  		return false;
  
  	/* Compute second barycentric coordinate */
  	const float3 s2 = cross(d, e1);
  	const float v = dot(ray_D, s2)*invdivisor;
  	if(v < 0.0f)
  		return false;
  
  	const float b0 = 1.0f - u - v;
  	if(b0 < 0.0f)
  		return false;
  
  	/* compute t to intersection point */
  	const float t = dot(e2, s2)*invdivisor;
  	if(t < 0.0f || t > ray_t)
  		return false;
  
  	*isect_u = u;
  	*isect_v = v;
  	*isect_t = t;
  
  	return true;
  }
  
  ccl_device bool ray_quad_intersect(
  	float3 ray_P, float3 ray_D, float ray_t,
  	float3 quad_P, float3 quad_u, float3 quad_v,
  	float3 *isect_P, float *isect_t)
  {
  	float3 v0 = quad_P - quad_u*0.5f - quad_v*0.5f;
  	float3 v1 = quad_P + quad_u*0.5f - quad_v*0.5f;
  	float3 v2 = quad_P + quad_u*0.5f + quad_v*0.5f;
  	float3 v3 = quad_P - quad_u*0.5f + quad_v*0.5f;
  
  	if(ray_triangle_intersect(ray_P, ray_D, ray_t, v0, v1, v2, isect_P, isect_t))
  		return true;
  	else if(ray_triangle_intersect(ray_P, ray_D, ray_t, v0, v2, v3, isect_P, isect_t))
  		return true;
  	
  	return false;
  }
  
  /* projections */
  ccl_device bool map_to_sphere(float *r_u, float *r_v,
                                const float x, const float y, const float z)
  {
  	float len = sqrtf(x * x + y * y + z * z);
  	if(len > 0.0f) {
  		if(UNLIKELY(x == 0.0f && y == 0.0f)) {
  			*r_u = 0.0f;  /* othwise domain error */
  		}
  		else {
  			*r_u = (1.0f - atan2f(x, y) / M_PI_F) / 2.0f;
  		}
  		*r_v = 1.0f - safe_acosf(z / len) / M_PI_F;
  		return true;
  	}
  	else {
  		*r_v = *r_u = 0.0f; /* to avoid un-initialized variables */
  		return false;
  	}
  }
  
  CCL_NAMESPACE_END
  
  #endif /* __UTIL_MATH_H__ */
  
  