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/*
* 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_GPU__
# include <cmath>
#endif
#ifndef __KERNEL_OPENCL__
# include <float.h>
# include <math.h>
# include <stdio.h>
#endif /* __KERNEL_OPENCL__ */
#include "util/util_types.h"
CCL_NAMESPACE_BEGIN
/* Float Pi variations */
/* Division */
#ifndef M_PI_F
# define M_PI_F (3.1415926535897932f) /* pi */
#endif
#ifndef M_PI_2_F
# define M_PI_2_F (1.5707963267948966f) /* pi/2 */
#endif
#ifndef M_PI_4_F
# define M_PI_4_F (0.7853981633974830f) /* pi/4 */
#endif
#ifndef M_1_PI_F
# define M_1_PI_F (0.3183098861837067f) /* 1/pi */
#endif
#ifndef M_2_PI_F
# define M_2_PI_F (0.6366197723675813f) /* 2/pi */
#endif
/* Multiplication */
#ifndef M_2PI_F
# define M_2PI_F (6.2831853071795864f) /* 2*pi */
#endif
#ifndef M_4PI_F
# define M_4PI_F (12.566370614359172f) /* 4*pi */
#endif
/* Float sqrt variations */
#ifndef M_SQRT2_F
# define M_SQRT2_F (1.4142135623730950f) /* sqrt(2) */
#endif
#ifndef M_LN2_F
# define M_LN2_F (0.6931471805599453f) /* ln(2) */
#endif
#ifndef M_LN10_F
# define M_LN10_F (2.3025850929940457f) /* ln(10) */
#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 /* !__KERNEL_OPENCL__ */
#endif /* _WIN32 */
#ifndef __KERNEL_GPU__
using std::isfinite;
using std::isnan;
using std::sqrt;
ccl_device_inline int abs(int x)
{
return (x > 0)? x: -x;
}
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;
}
/* These 2 guys are templated for usage with registers data.
*
* NOTE: Since this is CPU-only functions it is ok to use references here.
* But for other devices we'll need to be careful about this.
*/
template<typename T>
ccl_device_inline T min4(const T& a, const T& b, const T& c, const T& d)
{
return min(min(a,b),min(c,d));
}
template<typename T>
ccl_device_inline T max4(const T& a, const T& b, const T& c, const T& d)
{
return max(max(a,b),max(c,d));
}
#endif /* __KERNEL_GPU__ */
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__
/* Int/Float conversion */
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;
}
#endif /* __KERNEL_OPENCL__ */
/* Versions of functions which are safe for fast math. */
ccl_device_inline bool isnan_safe(float f)
{
unsigned int x = __float_as_uint(f);
return (x << 1) > 0xff000000u;
}
ccl_device_inline bool isfinite_safe(float f)
{
/* By IEEE 754 rule, 2*Inf equals Inf */
unsigned int x = __float_as_uint(f);
return (f == f) && (x == 0 || x == (1 << 31) || (f != 2.0f*f)) && !((x << 1) > 0xff000000u);
}
ccl_device_inline float ensure_finite(float v)
{
return isfinite_safe(v)? v : 0.0f;
}
#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);
}
ccl_device_inline float mix(float a, float b, float t)
{
return a + t*(b - a);
}
#endif /* __KERNEL_OPENCL__ */
#ifndef __KERNEL_CUDA__
ccl_device_inline float saturate(float a)
{
return clamp(a, 0.0f, 1.0f);
}
#endif /* __KERNEL_CUDA__ */
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);
}
ccl_device_inline int mod(int x, int m)
{
return (x % m + m) % m;
}
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);
}
CCL_NAMESPACE_END
#include "util/util_math_int2.h"
#include "util/util_math_int3.h"
#include "util/util_math_int4.h"
#include "util/util_math_float2.h"
#include "util/util_math_float3.h"
#include "util/util_math_float4.h"
CCL_NAMESPACE_BEGIN
#ifndef __KERNEL_OPENCL__
/* 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);
}
#endif /* __KERNEL_OPENCL__ */
/* Triangle */
#ifndef __KERNEL_OPENCL__
ccl_device_inline float triangle_area(const float3& v1,
const float3& v2,
const float3& v3)
#else
ccl_device_inline float triangle_area(const float3 v1,
const float3 v2,
const float3 v3)
#endif
{
return len(cross(v3 - v2, v1 - v2))*0.5f;
}
/* 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 gray 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_divide(float a, float b)
{
return (b != 0.0f)? a/b: 0.0f;
}
ccl_device float safe_logf(float a, float b)
{
if(UNLIKELY(a <= 0.0f || b <= 0.0f))
return 0.0f;
return safe_divide(logf(a),logf(b));
}
ccl_device float safe_modulo(float a, float b)
{
return (b != 0.0f)? fmodf(a, b): 0.0f;
}
ccl_device_inline float beta(float x, float y)
{
#ifndef __KERNEL_OPENCL__
return expf(lgammaf(x) + lgammaf(y) - lgammaf(x+y));
#else
return expf(lgamma(x) + lgamma(y) - lgamma(x+y));
#endif
}
ccl_device_inline float xor_signmask(float x, int y)
{
return __int_as_float(__float_as_int(x) ^ y);
}
/* projections */
ccl_device_inline float2 map_to_tube(const float3 co)
{
float len, u, v;
len = sqrtf(co.x * co.x + co.y * co.y);
if(len > 0.0f) {
u = (1.0f - (atan2f(co.x / len, co.y / len) / M_PI_F)) * 0.5f;
v = (co.z + 1.0f) * 0.5f;
}
else {
u = v = 0.0f;
}
return make_float2(u, v);
}
ccl_device_inline float2 map_to_sphere(const float3 co)
{
float l = len(co);
float u, v;
if(l > 0.0f) {
if(UNLIKELY(co.x == 0.0f && co.y == 0.0f)) {
u = 0.0f; /* othwise domain error */
}
else {
u = (1.0f - atan2f(co.x, co.y) / M_PI_F) / 2.0f;
}
v = 1.0f - safe_acosf(co.z / l) / M_PI_F;
}
else {
u = v = 0.0f;
}
return make_float2(u, v);
}
CCL_NAMESPACE_END
#endif /* __UTIL_MATH_H__ */
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