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igl/external/embree/common/math/math.h
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// ======================================================================== //
// Copyright 2009-2014 Intel Corporation //
// //
// 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. //
// ======================================================================== //
#pragma once
#include "sys/platform.h"
#include "sys/intrinsics.h"
#define _USE_MATH_DEFINES
#include <math.h>
#include <cmath>
#include <float.h>
#include <emmintrin.h>
#include <xmmintrin.h>
namespace embree
{
#if defined(__WIN32__)
__forceinline bool finite ( const float x ) { return _finite(x) != 0; }
#endif
__forceinline float sign ( const float x ) { return x<0?-1.0f:1.0f; }
__forceinline float sqr ( const float x ) { return x*x; }
#ifndef __MIC__
__forceinline float rcp ( const float x )
{
const __m128 vx = _mm_set_ss(x);
const __m128 r = _mm_rcp_ps(vx);
return _mm_cvtss_f32(_mm_sub_ps(_mm_add_ps(r, r), _mm_mul_ps(_mm_mul_ps(r, r), vx)));
}
__forceinline float signmsk ( const float x ) {
return _mm_cvtss_f32(_mm_and_ps(_mm_set_ss(x),_mm_castsi128_ps(_mm_set1_epi32(0x80000000))));
}
__forceinline float xorf( const float x, const float y ) {
return _mm_cvtss_f32(_mm_xor_ps(_mm_set_ss(x),_mm_set_ss(y)));
}
__forceinline float andf( const float x, const unsigned y ) {
return _mm_cvtss_f32(_mm_and_ps(_mm_set_ss(x),_mm_castsi128_ps(_mm_set1_epi32(y))));
}
__forceinline float rsqrt( const float x ) {
const __m128 a = _mm_set_ss(x);
const __m128 r = _mm_rsqrt_ps(a);
const __m128 c = _mm_add_ps(_mm_mul_ps(_mm_set_ps(1.5f, 1.5f, 1.5f, 1.5f), r),
_mm_mul_ps(_mm_mul_ps(_mm_mul_ps(a, _mm_set_ps(-0.5f, -0.5f, -0.5f, -0.5f)), r), _mm_mul_ps(r, r)));
return _mm_cvtss_f32(c);
}
#else
__forceinline float rcp ( const float x ) { return 1.0f/x; }
__forceinline float signmsk ( const float x ) { return cast_i2f(cast_f2i(x)&0x80000000); }
__forceinline float xorf( const float x, const float y ) { return cast_i2f(cast_f2i(x) ^ cast_f2i(y)); }
__forceinline float andf( const float x, const float y ) { return cast_i2f(cast_f2i(x) & cast_f2i(y)); }
__forceinline float rsqrt( const float x ) { return 1.0f/sqrtf(x); }
#endif
#if !defined(__WIN32__)
__forceinline float abs ( const float x ) { return ::fabsf(x); }
__forceinline float acos ( const float x ) { return ::acosf (x); }
__forceinline float asin ( const float x ) { return ::asinf (x); }
__forceinline float atan ( const float x ) { return ::atanf (x); }
__forceinline float atan2( const float y, const float x ) { return ::atan2f(y, x); }
__forceinline float cos ( const float x ) { return ::cosf (x); }
__forceinline float cosh ( const float x ) { return ::coshf (x); }
__forceinline float exp ( const float x ) { return ::expf (x); }
__forceinline float fmod ( const float x, const float y ) { return ::fmodf (x, y); }
__forceinline float log ( const float x ) { return ::logf (x); }
__forceinline float log10( const float x ) { return ::log10f(x); }
__forceinline float pow ( const float x, const float y ) { return ::powf (x, y); }
__forceinline float sin ( const float x ) { return ::sinf (x); }
__forceinline float sinh ( const float x ) { return ::sinhf (x); }
__forceinline float sqrt ( const float x ) { return ::sqrtf (x); }
__forceinline float tan ( const float x ) { return ::tanf (x); }
__forceinline float tanh ( const float x ) { return ::tanhf (x); }
__forceinline float floor( const float x ) { return ::floorf (x); }
__forceinline float ceil ( const float x ) { return ::ceilf (x); }
#endif
__forceinline double abs ( const double x ) { return ::fabs(x); }
__forceinline double sign ( const double x ) { return x<0?-1.0:1.0; }
__forceinline double acos ( const double x ) { return ::acos (x); }
__forceinline double asin ( const double x ) { return ::asin (x); }
__forceinline double atan ( const double x ) { return ::atan (x); }
__forceinline double atan2( const double y, const double x ) { return ::atan2(y, x); }
__forceinline double cos ( const double x ) { return ::cos (x); }
__forceinline double cosh ( const double x ) { return ::cosh (x); }
__forceinline double exp ( const double x ) { return ::exp (x); }
__forceinline double fmod ( const double x, const double y ) { return ::fmod (x, y); }
__forceinline double log ( const double x ) { return ::log (x); }
__forceinline double log10( const double x ) { return ::log10(x); }
__forceinline double pow ( const double x, const double y ) { return ::pow (x, y); }
__forceinline double rcp ( const double x ) { return 1.0/x; }
__forceinline double rsqrt( const double x ) { return 1.0/::sqrt(x); }
__forceinline double sin ( const double x ) { return ::sin (x); }
__forceinline double sinh ( const double x ) { return ::sinh (x); }
__forceinline double sqr ( const double x ) { return x*x; }
__forceinline double sqrt ( const double x ) { return ::sqrt (x); }
__forceinline double tan ( const double x ) { return ::tan (x); }
__forceinline double tanh ( const double x ) { return ::tanh (x); }
__forceinline double floor( const double x ) { return ::floor (x); }
__forceinline double ceil ( const double x ) { return ::ceil (x); }
#if defined(__SSE4_1__)
__forceinline float mini(float a, float b) {
const __m128i ai = _mm_castps_si128(_mm_set_ss(a));
const __m128i bi = _mm_castps_si128(_mm_set_ss(b));
const __m128i ci = _mm_min_epi32(ai,bi);
return _mm_cvtss_f32(_mm_castsi128_ps(ci));
}
#endif
#if defined(__SSE4_1__)
__forceinline float maxi(float a, float b) {
const __m128i ai = _mm_castps_si128(_mm_set_ss(a));
const __m128i bi = _mm_castps_si128(_mm_set_ss(b));
const __m128i ci = _mm_max_epi32(ai,bi);
return _mm_cvtss_f32(_mm_castsi128_ps(ci));
}
#endif
__forceinline int min(int a, int b) { return a<b? a:b; }
__forceinline int64 min(int64 a, int64 b) { return a<b? a:b; }
__forceinline size_t min(size_t a, size_t b) { return a<b? a:b; }
#if !defined(__WIN32__)
__forceinline ssize_t min(ssize_t a, ssize_t b) { return a<b? a:b; }
#endif
__forceinline float min(float a, float b) { return a<b? a:b; }
__forceinline double min(double a, double b) { return a<b? a:b; }
template<typename T> __forceinline T min(const T& a, const T& b, const T& c) { return min(min(a,b),c); }
template<typename T> __forceinline T min(const T& a, const T& b, const T& c, const T& d) { return min(min(a,b),min(c,d)); }
template<typename T> __forceinline T min(const T& a, const T& b, const T& c, const T& d, const T& e) { return min(min(min(a,b),min(c,d)),e); }
__forceinline int max(int a, int b) { return a<b? b:a; }
__forceinline int64 max(int64 a, int64 b) { return a<b? b:a; }
__forceinline size_t max(size_t a, size_t b) { return a<b? b:a; }
#if !defined(__WIN32__)
__forceinline ssize_t max(ssize_t a, ssize_t b) { return a<b? b:a; }
#endif
__forceinline float max(float a, float b) { return a<b? b:a; }
__forceinline double max(double a, double b) { return a<b? b:a; }
template<typename T> __forceinline T max(const T& a, const T& b, const T& c) { return max(max(a,b),c); }
template<typename T> __forceinline T max(const T& a, const T& b, const T& c, const T& d) { return max(max(a,b),max(c,d)); }
template<typename T> __forceinline T max(const T& a, const T& b, const T& c, const T& d, const T& e) { return max(max(max(a,b),max(c,d)),e); }
template<typename T> __forceinline T clamp(const T& x, const T& lower = T(zero), const T& upper = T(one)) { return max(min(x,upper),lower); }
template<typename T> __forceinline T clampz(const T& x, const T& upper) { return max(T(zero), min(x,upper)); }
template<typename T> __forceinline T deg2rad ( const T& x ) { return x * T(1.74532925199432957692e-2f); }
template<typename T> __forceinline T rad2deg ( const T& x ) { return x * T(5.72957795130823208768e1f); }
template<typename T> __forceinline T sin2cos ( const T& x ) { return sqrt(max(T(zero),T(one)-x*x)); }
template<typename T> __forceinline T cos2sin ( const T& x ) { return sin2cos(x); }
#if defined(__AVX2__)
__forceinline float madd ( const float a, const float b, const float c) { return _mm_cvtss_f32(_mm_fmadd_ss(_mm_set_ss(a),_mm_set_ss(b),_mm_set_ss(c))); }
__forceinline float msub ( const float a, const float b, const float c) { return _mm_cvtss_f32(_mm_fmsub_ss(_mm_set_ss(a),_mm_set_ss(b),_mm_set_ss(c))); }
__forceinline float nmadd ( const float a, const float b, const float c) { return _mm_cvtss_f32(_mm_fnmadd_ss(_mm_set_ss(a),_mm_set_ss(b),_mm_set_ss(c))); }
__forceinline float nmsub ( const float a, const float b, const float c) { return _mm_cvtss_f32(_mm_fnmsub_ss(_mm_set_ss(a),_mm_set_ss(b),_mm_set_ss(c))); }
#else
__forceinline float madd ( const float a, const float b, const float c) { return a*b+c; }
__forceinline float msub ( const float a, const float b, const float c) { return a*b-c; }
__forceinline float nmadd ( const float a, const float b, const float c) { return -a*b-c;}
__forceinline float nmsub ( const float a, const float b, const float c) { return c-a*b; }
#endif
/*! random functions */
template<typename T> T random() { return T(0); }
template<> __forceinline int random() { return int(rand()); }
template<> __forceinline uint32 random() { return uint32(rand()); }
template<> __forceinline float random() { return random<uint32>()/float(RAND_MAX); }
template<> __forceinline double random() { return random<uint32>()/double(RAND_MAX); }
/*! selects */
__forceinline bool select(bool s, bool t , bool f) { return s ? t : f; }
__forceinline int select(bool s, int t, int f) { return s ? t : f; }
__forceinline float select(bool s, float t, float f) { return s ? t : f; }
/*! exchange */
template<typename T> __forceinline void xchg ( T& a, T& b ) { const T tmp = a; a = b; b = tmp; }
/*! bit reverse operation */
template<class T>
__forceinline T bitReverse(const T& vin)
{
T v = vin;
v = ((v >> 1) & 0x55555555) | ((v & 0x55555555) << 1);
v = ((v >> 2) & 0x33333333) | ((v & 0x33333333) << 2);
v = ((v >> 4) & 0x0F0F0F0F) | ((v & 0x0F0F0F0F) << 4);
v = ((v >> 8) & 0x00FF00FF) | ((v & 0x00FF00FF) << 8);
v = ( v >> 16 ) | ( v << 16);
return v;
}
/*! bit interleave operation */
template<class T>
__forceinline T bitInterleave(const T& xin, const T& yin, const T& zin)
{
T x = xin, y = yin, z = zin;
x = (x | (x << 16)) & 0x030000FF;
x = (x | (x << 8)) & 0x0300F00F;
x = (x | (x << 4)) & 0x030C30C3;
x = (x | (x << 2)) & 0x09249249;
y = (y | (y << 16)) & 0x030000FF;
y = (y | (y << 8)) & 0x0300F00F;
y = (y | (y << 4)) & 0x030C30C3;
y = (y | (y << 2)) & 0x09249249;
z = (z | (z << 16)) & 0x030000FF;
z = (z | (z << 8)) & 0x0300F00F;
z = (z | (z << 4)) & 0x030C30C3;
z = (z | (z << 2)) & 0x09249249;
return x | (y << 1) | (z << 2);
}
/*! bit interleave operation for 64bit data types*/
template<class T>
__forceinline T bitInterleave64(const T& xin, const T& yin, const T& zin){
T x = xin & 0x1fffff;
T y = yin & 0x1fffff;
T z = zin & 0x1fffff;
x = (x | x << 32) & 0x1f00000000ffff;
x = (x | x << 16) & 0x1f0000ff0000ff;
x = (x | x << 8) & 0x100f00f00f00f00f;
x = (x | x << 4) & 0x10c30c30c30c30c3;
x = (x | x << 2) & 0x1249249249249249;
y = (y | y << 32) & 0x1f00000000ffff;
y = (y | y << 16) & 0x1f0000ff0000ff;
y = (y | y << 8) & 0x100f00f00f00f00f;
y = (y | y << 4) & 0x10c30c30c30c30c3;
y = (y | y << 2) & 0x1249249249249249;
z = (z | z << 32) & 0x1f00000000ffff;
z = (z | z << 16) & 0x1f0000ff0000ff;
z = (z | z << 8) & 0x100f00f00f00f00f;
z = (z | z << 4) & 0x10c30c30c30c30c3;
z = (z | z << 2) & 0x1249249249249249;
return x | (y << 1) | (z << 2);
}
#if _WIN32
__forceinline double drand48() {
return double(rand())/double(RAND_MAX);
}
#endif
}
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