732 lines
19 KiB
C
732 lines
19 KiB
C
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// Copyright (C) 2002-2012 Nikolaus Gebhardt
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// This file is part of the "Irrlicht Engine".
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// For conditions of distribution and use, see copyright notice in irrlicht.h
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#ifndef __IRR_MATH_H_INCLUDED__
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#define __IRR_MATH_H_INCLUDED__
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#include "IrrCompileConfig.h"
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#include "irrTypes.h"
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#include <math.h>
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#include <float.h>
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#include <stdlib.h> // for abs() etc.
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#include <limits.h> // For INT_MAX / UINT_MAX
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#if defined(_IRR_SOLARIS_PLATFORM_) || defined(__BORLANDC__) || defined (__BCPLUSPLUS__) || defined (_WIN32_WCE)
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#define sqrtf(X) (irr::f32)sqrt((irr::f64)(X))
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#define sinf(X) (irr::f32)sin((irr::f64)(X))
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#define cosf(X) (irr::f32)cos((irr::f64)(X))
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#define asinf(X) (irr::f32)asin((irr::f64)(X))
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#define acosf(X) (irr::f32)acos((irr::f64)(X))
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#define atan2f(X,Y) (irr::f32)atan2((irr::f64)(X),(irr::f64)(Y))
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#define ceilf(X) (irr::f32)ceil((irr::f64)(X))
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#define floorf(X) (irr::f32)floor((irr::f64)(X))
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#define powf(X,Y) (irr::f32)pow((irr::f64)(X),(irr::f64)(Y))
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#define fmodf(X,Y) (irr::f32)fmod((irr::f64)(X),(irr::f64)(Y))
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#define fabsf(X) (irr::f32)fabs((irr::f64)(X))
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#define logf(X) (irr::f32)log((irr::f64)(X))
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#endif
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#ifndef FLT_MAX
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#define FLT_MAX 3.402823466E+38F
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#endif
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#ifndef FLT_MIN
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#define FLT_MIN 1.17549435e-38F
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#endif
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namespace irr
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{
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namespace core
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{
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//! Rounding error constant often used when comparing f32 values.
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const s32 ROUNDING_ERROR_S32 = 0;
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#ifdef __IRR_HAS_S64
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const s64 ROUNDING_ERROR_S64 = 0;
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#endif
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const f32 ROUNDING_ERROR_f32 = 0.000001f;
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const f64 ROUNDING_ERROR_f64 = 0.00000001;
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#ifdef PI // make sure we don't collide with a define
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#undef PI
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#endif
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//! Constant for PI.
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const f32 PI = 3.14159265359f;
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//! Constant for reciprocal of PI.
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const f32 RECIPROCAL_PI = 1.0f/PI;
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//! Constant for half of PI.
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const f32 HALF_PI = PI/2.0f;
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#ifdef PI64 // make sure we don't collide with a define
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#undef PI64
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#endif
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//! Constant for 64bit PI.
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const f64 PI64 = 3.1415926535897932384626433832795028841971693993751;
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//! Constant for 64bit reciprocal of PI.
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const f64 RECIPROCAL_PI64 = 1.0/PI64;
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//! 32bit Constant for converting from degrees to radians
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const f32 DEGTORAD = PI / 180.0f;
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//! 32bit constant for converting from radians to degrees (formally known as GRAD_PI)
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const f32 RADTODEG = 180.0f / PI;
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//! 64bit constant for converting from degrees to radians (formally known as GRAD_PI2)
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const f64 DEGTORAD64 = PI64 / 180.0;
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//! 64bit constant for converting from radians to degrees
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const f64 RADTODEG64 = 180.0 / PI64;
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//! Utility function to convert a radian value to degrees
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/** Provided as it can be clearer to write radToDeg(X) than RADTODEG * X
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\param radians The radians value to convert to degrees.
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*/
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inline f32 radToDeg(f32 radians)
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{
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return RADTODEG * radians;
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}
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//! Utility function to convert a radian value to degrees
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/** Provided as it can be clearer to write radToDeg(X) than RADTODEG * X
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\param radians The radians value to convert to degrees.
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*/
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inline f64 radToDeg(f64 radians)
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{
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return RADTODEG64 * radians;
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}
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//! Utility function to convert a degrees value to radians
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/** Provided as it can be clearer to write degToRad(X) than DEGTORAD * X
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\param degrees The degrees value to convert to radians.
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*/
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inline f32 degToRad(f32 degrees)
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{
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return DEGTORAD * degrees;
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}
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//! Utility function to convert a degrees value to radians
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/** Provided as it can be clearer to write degToRad(X) than DEGTORAD * X
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\param degrees The degrees value to convert to radians.
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*/
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inline f64 degToRad(f64 degrees)
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{
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return DEGTORAD64 * degrees;
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}
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//! returns minimum of two values. Own implementation to get rid of the STL (VS6 problems)
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template<class T>
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inline const T& min_(const T& a, const T& b)
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{
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return a < b ? a : b;
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}
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//! returns minimum of three values. Own implementation to get rid of the STL (VS6 problems)
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template<class T>
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inline const T& min_(const T& a, const T& b, const T& c)
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{
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return a < b ? min_(a, c) : min_(b, c);
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}
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//! returns maximum of two values. Own implementation to get rid of the STL (VS6 problems)
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template<class T>
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inline const T& max_(const T& a, const T& b)
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{
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return a < b ? b : a;
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}
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//! returns maximum of three values. Own implementation to get rid of the STL (VS6 problems)
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template<class T>
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inline const T& max_(const T& a, const T& b, const T& c)
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{
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return a < b ? max_(b, c) : max_(a, c);
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}
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//! returns abs of two values. Own implementation to get rid of STL (VS6 problems)
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template<class T>
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inline T abs_(const T& a)
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{
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return a < (T)0 ? -a : a;
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}
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//! returns linear interpolation of a and b with ratio t
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//! \return: a if t==0, b if t==1, and the linear interpolation else
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template<class T>
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inline T lerp(const T& a, const T& b, const f32 t)
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{
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return (T)(a*(1.f-t)) + (b*t);
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}
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//! clamps a value between low and high
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template <class T>
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inline const T clamp (const T& value, const T& low, const T& high)
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{
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return min_ (max_(value,low), high);
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}
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//! swaps the content of the passed parameters
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// Note: We use the same trick as boost and use two template arguments to
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// avoid ambiguity when swapping objects of an Irrlicht type that has not
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// it's own swap overload. Otherwise we get conflicts with some compilers
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// in combination with stl.
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template <class T1, class T2>
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inline void swap(T1& a, T2& b)
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{
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T1 c(a);
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a = b;
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b = c;
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}
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//! returns if a equals b, taking possible rounding errors into account
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inline bool equals(const f64 a, const f64 b, const f64 tolerance = ROUNDING_ERROR_f64)
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{
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return (a + tolerance >= b) && (a - tolerance <= b);
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}
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//! returns if a equals b, taking possible rounding errors into account
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inline bool equals(const f32 a, const f32 b, const f32 tolerance = ROUNDING_ERROR_f32)
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{
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return (a + tolerance >= b) && (a - tolerance <= b);
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}
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//! We compare the difference in ULP's (spacing between floating-point numbers, aka ULP=1 means there exists no float between).
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//\result true when numbers have a ULP <= maxUlpDiff AND have the same sign.
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inline bool equalsByUlp(f32 a, f32 b, int maxUlpDiff)
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{
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// Based on the ideas and code from Bruce Dawson on
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// http://www.altdevblogaday.com/2012/02/22/comparing-floating-point-numbers-2012-edition/
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// When floats are interpreted as integers the two nearest possible float numbers differ just
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// by one integer number. Also works the other way round, an integer of 1 interpreted as float
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// is for example the smallest possible float number.
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union Float_t
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{
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Float_t(float f1 = 0.0f) : f(f1) {}
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// Portable sign-extraction
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bool sign() const { return (i >> 31) != 0; }
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int i;
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float f;
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};
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Float_t fa(a);
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Float_t fb(b);
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// Different signs, we could maybe get difference to 0, but so close to 0 using epsilons is better.
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if ( fa.sign() != fb.sign() )
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{
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// Check for equality to make sure +0==-0
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if (fa.i == fb.i)
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return true;
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return false;
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}
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// Find the difference in ULPs.
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int ulpsDiff = abs_(fa.i- fb.i);
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if (ulpsDiff <= maxUlpDiff)
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return true;
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return false;
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}
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#if 0
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//! returns if a equals b, not using any rounding tolerance
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inline bool equals(const s32 a, const s32 b)
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{
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return (a == b);
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}
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//! returns if a equals b, not using any rounding tolerance
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inline bool equals(const u32 a, const u32 b)
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{
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return (a == b);
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}
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#endif
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//! returns if a equals b, taking an explicit rounding tolerance into account
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inline bool equals(const s32 a, const s32 b, const s32 tolerance = ROUNDING_ERROR_S32)
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{
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return (a + tolerance >= b) && (a - tolerance <= b);
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}
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//! returns if a equals b, taking an explicit rounding tolerance into account
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inline bool equals(const u32 a, const u32 b, const s32 tolerance = ROUNDING_ERROR_S32)
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{
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return (a + tolerance >= b) && (a - tolerance <= b);
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}
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#ifdef __IRR_HAS_S64
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//! returns if a equals b, taking an explicit rounding tolerance into account
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inline bool equals(const s64 a, const s64 b, const s64 tolerance = ROUNDING_ERROR_S64)
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{
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return (a + tolerance >= b) && (a - tolerance <= b);
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}
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#endif
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//! returns if a equals zero, taking rounding errors into account
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inline bool iszero(const f64 a, const f64 tolerance = ROUNDING_ERROR_f64)
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{
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return fabs(a) <= tolerance;
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}
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//! returns if a equals zero, taking rounding errors into account
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inline bool iszero(const f32 a, const f32 tolerance = ROUNDING_ERROR_f32)
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{
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return fabsf(a) <= tolerance;
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}
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//! returns if a equals not zero, taking rounding errors into account
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inline bool isnotzero(const f32 a, const f32 tolerance = ROUNDING_ERROR_f32)
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{
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return fabsf(a) > tolerance;
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}
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//! returns if a equals zero, taking rounding errors into account
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inline bool iszero(const s32 a, const s32 tolerance = 0)
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{
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return ( a & 0x7ffffff ) <= tolerance;
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}
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//! returns if a equals zero, taking rounding errors into account
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inline bool iszero(const u32 a, const u32 tolerance = 0)
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{
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return a <= tolerance;
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}
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#ifdef __IRR_HAS_S64
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//! returns if a equals zero, taking rounding errors into account
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inline bool iszero(const s64 a, const s64 tolerance = 0)
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{
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return abs_(a) > tolerance;
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}
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#endif
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inline s32 s32_min(s32 a, s32 b)
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{
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const s32 mask = (a - b) >> 31;
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return (a & mask) | (b & ~mask);
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}
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inline s32 s32_max(s32 a, s32 b)
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{
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const s32 mask = (a - b) >> 31;
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return (b & mask) | (a & ~mask);
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}
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inline s32 s32_clamp (s32 value, s32 low, s32 high)
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{
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return s32_min(s32_max(value,low), high);
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}
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/*
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float IEEE-754 bit represenation
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0 0x00000000
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1.0 0x3f800000
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0.5 0x3f000000
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3 0x40400000
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+inf 0x7f800000
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-inf 0xff800000
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+NaN 0x7fc00000 or 0x7ff00000
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in general: number = (sign ? -1:1) * 2^(exponent) * 1.(mantissa bits)
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*/
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typedef union { u32 u; s32 s; f32 f; } inttofloat;
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#define F32_AS_S32(f) (*((s32 *) &(f)))
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#define F32_AS_U32(f) (*((u32 *) &(f)))
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#define F32_AS_U32_POINTER(f) ( ((u32 *) &(f)))
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#define F32_VALUE_0 0x00000000
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#define F32_VALUE_1 0x3f800000
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#define F32_SIGN_BIT 0x80000000U
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#define F32_EXPON_MANTISSA 0x7FFFFFFFU
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//! code is taken from IceFPU
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//! Integer representation of a floating-point value.
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#ifdef IRRLICHT_FAST_MATH
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#define IR(x) ((u32&)(x))
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#else
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inline u32 IR(f32 x) {inttofloat tmp; tmp.f=x; return tmp.u;}
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#endif
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//! Absolute integer representation of a floating-point value
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#define AIR(x) (IR(x)&0x7fffffff)
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//! Floating-point representation of an integer value.
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#ifdef IRRLICHT_FAST_MATH
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#define FR(x) ((f32&)(x))
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|
|
#else
|
||
|
|
inline f32 FR(u32 x) {inttofloat tmp; tmp.u=x; return tmp.f;}
|
||
|
|
inline f32 FR(s32 x) {inttofloat tmp; tmp.s=x; return tmp.f;}
|
||
|
|
#endif
|
||
|
|
|
||
|
|
//! integer representation of 1.0
|
||
|
|
#define IEEE_1_0 0x3f800000
|
||
|
|
//! integer representation of 255.0
|
||
|
|
#define IEEE_255_0 0x437f0000
|
||
|
|
|
||
|
|
#ifdef IRRLICHT_FAST_MATH
|
||
|
|
#define F32_LOWER_0(f) (F32_AS_U32(f) > F32_SIGN_BIT)
|
||
|
|
#define F32_LOWER_EQUAL_0(f) (F32_AS_S32(f) <= F32_VALUE_0)
|
||
|
|
#define F32_GREATER_0(f) (F32_AS_S32(f) > F32_VALUE_0)
|
||
|
|
#define F32_GREATER_EQUAL_0(f) (F32_AS_U32(f) <= F32_SIGN_BIT)
|
||
|
|
#define F32_EQUAL_1(f) (F32_AS_U32(f) == F32_VALUE_1)
|
||
|
|
#define F32_EQUAL_0(f) ( (F32_AS_U32(f) & F32_EXPON_MANTISSA ) == F32_VALUE_0)
|
||
|
|
|
||
|
|
// only same sign
|
||
|
|
#define F32_A_GREATER_B(a,b) (F32_AS_S32((a)) > F32_AS_S32((b)))
|
||
|
|
|
||
|
|
#else
|
||
|
|
|
||
|
|
#define F32_LOWER_0(n) ((n) < 0.0f)
|
||
|
|
#define F32_LOWER_EQUAL_0(n) ((n) <= 0.0f)
|
||
|
|
#define F32_GREATER_0(n) ((n) > 0.0f)
|
||
|
|
#define F32_GREATER_EQUAL_0(n) ((n) >= 0.0f)
|
||
|
|
#define F32_EQUAL_1(n) ((n) == 1.0f)
|
||
|
|
#define F32_EQUAL_0(n) ((n) == 0.0f)
|
||
|
|
#define F32_A_GREATER_B(a,b) ((a) > (b))
|
||
|
|
#endif
|
||
|
|
|
||
|
|
|
||
|
|
#ifndef REALINLINE
|
||
|
|
#ifdef _MSC_VER
|
||
|
|
#define REALINLINE __forceinline
|
||
|
|
#else
|
||
|
|
#define REALINLINE inline
|
||
|
|
#endif
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#if defined(__BORLANDC__) || defined (__BCPLUSPLUS__)
|
||
|
|
|
||
|
|
// 8-bit bools in borland builder
|
||
|
|
|
||
|
|
//! conditional set based on mask and arithmetic shift
|
||
|
|
REALINLINE u32 if_c_a_else_b ( const c8 condition, const u32 a, const u32 b )
|
||
|
|
{
|
||
|
|
return ( ( -condition >> 7 ) & ( a ^ b ) ) ^ b;
|
||
|
|
}
|
||
|
|
|
||
|
|
//! conditional set based on mask and arithmetic shift
|
||
|
|
REALINLINE u32 if_c_a_else_0 ( const c8 condition, const u32 a )
|
||
|
|
{
|
||
|
|
return ( -condition >> 31 ) & a;
|
||
|
|
}
|
||
|
|
#else
|
||
|
|
|
||
|
|
//! conditional set based on mask and arithmetic shift
|
||
|
|
REALINLINE u32 if_c_a_else_b ( const s32 condition, const u32 a, const u32 b )
|
||
|
|
{
|
||
|
|
return ( ( -condition >> 31 ) & ( a ^ b ) ) ^ b;
|
||
|
|
}
|
||
|
|
|
||
|
|
//! conditional set based on mask and arithmetic shift
|
||
|
|
REALINLINE u16 if_c_a_else_b ( const s16 condition, const u16 a, const u16 b )
|
||
|
|
{
|
||
|
|
return ( ( -condition >> 15 ) & ( a ^ b ) ) ^ b;
|
||
|
|
}
|
||
|
|
|
||
|
|
//! conditional set based on mask and arithmetic shift
|
||
|
|
REALINLINE u32 if_c_a_else_0 ( const s32 condition, const u32 a )
|
||
|
|
{
|
||
|
|
return ( -condition >> 31 ) & a;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
|
||
|
|
/*
|
||
|
|
if (condition) state |= m; else state &= ~m;
|
||
|
|
*/
|
||
|
|
REALINLINE void setbit_cond ( u32 &state, s32 condition, u32 mask )
|
||
|
|
{
|
||
|
|
// 0, or any postive to mask
|
||
|
|
//s32 conmask = -condition >> 31;
|
||
|
|
state ^= ( ( -condition >> 31 ) ^ state ) & mask;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline f32 round_( f32 x )
|
||
|
|
{
|
||
|
|
return floorf( x + 0.5f );
|
||
|
|
}
|
||
|
|
|
||
|
|
REALINLINE void clearFPUException ()
|
||
|
|
{
|
||
|
|
#ifdef IRRLICHT_FAST_MATH
|
||
|
|
return;
|
||
|
|
#ifdef feclearexcept
|
||
|
|
feclearexcept(FE_ALL_EXCEPT);
|
||
|
|
#elif defined(_MSC_VER)
|
||
|
|
__asm fnclex;
|
||
|
|
#elif defined(__GNUC__) && defined(__x86__)
|
||
|
|
__asm__ __volatile__ ("fclex \n\t");
|
||
|
|
#else
|
||
|
|
# warn clearFPUException not supported.
|
||
|
|
#endif
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
// calculate: sqrt ( x )
|
||
|
|
REALINLINE f32 squareroot(const f32 f)
|
||
|
|
{
|
||
|
|
return sqrtf(f);
|
||
|
|
}
|
||
|
|
|
||
|
|
// calculate: sqrt ( x )
|
||
|
|
REALINLINE f64 squareroot(const f64 f)
|
||
|
|
{
|
||
|
|
return sqrt(f);
|
||
|
|
}
|
||
|
|
|
||
|
|
// calculate: sqrt ( x )
|
||
|
|
REALINLINE s32 squareroot(const s32 f)
|
||
|
|
{
|
||
|
|
return static_cast<s32>(squareroot(static_cast<f32>(f)));
|
||
|
|
}
|
||
|
|
|
||
|
|
#ifdef __IRR_HAS_S64
|
||
|
|
// calculate: sqrt ( x )
|
||
|
|
REALINLINE s64 squareroot(const s64 f)
|
||
|
|
{
|
||
|
|
return static_cast<s64>(squareroot(static_cast<f64>(f)));
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
|
||
|
|
// calculate: 1 / sqrt ( x )
|
||
|
|
REALINLINE f64 reciprocal_squareroot(const f64 x)
|
||
|
|
{
|
||
|
|
return 1.0 / sqrt(x);
|
||
|
|
}
|
||
|
|
|
||
|
|
// calculate: 1 / sqrtf ( x )
|
||
|
|
REALINLINE f32 reciprocal_squareroot(const f32 f)
|
||
|
|
{
|
||
|
|
#if defined ( IRRLICHT_FAST_MATH )
|
||
|
|
#if defined(_MSC_VER)
|
||
|
|
// SSE reciprocal square root estimate, accurate to 12 significant
|
||
|
|
// bits of the mantissa
|
||
|
|
f32 recsqrt;
|
||
|
|
__asm rsqrtss xmm0, f // xmm0 = rsqrtss(f)
|
||
|
|
__asm movss recsqrt, xmm0 // return xmm0
|
||
|
|
return recsqrt;
|
||
|
|
|
||
|
|
/*
|
||
|
|
// comes from Nvidia
|
||
|
|
u32 tmp = (u32(IEEE_1_0 << 1) + IEEE_1_0 - *(u32*)&x) >> 1;
|
||
|
|
f32 y = *(f32*)&tmp;
|
||
|
|
return y * (1.47f - 0.47f * x * y * y);
|
||
|
|
*/
|
||
|
|
#else
|
||
|
|
return 1.f / sqrtf(f);
|
||
|
|
#endif
|
||
|
|
#else // no fast math
|
||
|
|
return 1.f / sqrtf(f);
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
// calculate: 1 / sqrtf( x )
|
||
|
|
REALINLINE s32 reciprocal_squareroot(const s32 x)
|
||
|
|
{
|
||
|
|
return static_cast<s32>(reciprocal_squareroot(static_cast<f32>(x)));
|
||
|
|
}
|
||
|
|
|
||
|
|
// calculate: 1 / x
|
||
|
|
REALINLINE f32 reciprocal( const f32 f )
|
||
|
|
{
|
||
|
|
#if defined (IRRLICHT_FAST_MATH)
|
||
|
|
|
||
|
|
// SSE Newton-Raphson reciprocal estimate, accurate to 23 significant
|
||
|
|
// bi ts of the mantissa
|
||
|
|
// One Newtown-Raphson Iteration:
|
||
|
|
// f(i+1) = 2 * rcpss(f) - f * rcpss(f) * rcpss(f)
|
||
|
|
f32 rec;
|
||
|
|
__asm rcpss xmm0, f // xmm0 = rcpss(f)
|
||
|
|
__asm movss xmm1, f // xmm1 = f
|
||
|
|
__asm mulss xmm1, xmm0 // xmm1 = f * rcpss(f)
|
||
|
|
__asm mulss xmm1, xmm0 // xmm2 = f * rcpss(f) * rcpss(f)
|
||
|
|
__asm addss xmm0, xmm0 // xmm0 = 2 * rcpss(f)
|
||
|
|
__asm subss xmm0, xmm1 // xmm0 = 2 * rcpss(f)
|
||
|
|
// - f * rcpss(f) * rcpss(f)
|
||
|
|
__asm movss rec, xmm0 // return xmm0
|
||
|
|
return rec;
|
||
|
|
|
||
|
|
|
||
|
|
//! i do not divide through 0.. (fpu expection)
|
||
|
|
// instead set f to a high value to get a return value near zero..
|
||
|
|
// -1000000000000.f.. is use minus to stay negative..
|
||
|
|
// must test's here (plane.normal dot anything ) checks on <= 0.f
|
||
|
|
//u32 x = (-(AIR(f) != 0 ) >> 31 ) & ( IR(f) ^ 0xd368d4a5 ) ^ 0xd368d4a5;
|
||
|
|
//return 1.f / FR ( x );
|
||
|
|
|
||
|
|
#else // no fast math
|
||
|
|
return 1.f / f;
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
// calculate: 1 / x
|
||
|
|
REALINLINE f64 reciprocal ( const f64 f )
|
||
|
|
{
|
||
|
|
return 1.0 / f;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// calculate: 1 / x, low precision allowed
|
||
|
|
REALINLINE f32 reciprocal_approxim ( const f32 f )
|
||
|
|
{
|
||
|
|
#if defined( IRRLICHT_FAST_MATH)
|
||
|
|
|
||
|
|
// SSE Newton-Raphson reciprocal estimate, accurate to 23 significant
|
||
|
|
// bi ts of the mantissa
|
||
|
|
// One Newtown-Raphson Iteration:
|
||
|
|
// f(i+1) = 2 * rcpss(f) - f * rcpss(f) * rcpss(f)
|
||
|
|
f32 rec;
|
||
|
|
__asm rcpss xmm0, f // xmm0 = rcpss(f)
|
||
|
|
__asm movss xmm1, f // xmm1 = f
|
||
|
|
__asm mulss xmm1, xmm0 // xmm1 = f * rcpss(f)
|
||
|
|
__asm mulss xmm1, xmm0 // xmm2 = f * rcpss(f) * rcpss(f)
|
||
|
|
__asm addss xmm0, xmm0 // xmm0 = 2 * rcpss(f)
|
||
|
|
__asm subss xmm0, xmm1 // xmm0 = 2 * rcpss(f)
|
||
|
|
// - f * rcpss(f) * rcpss(f)
|
||
|
|
__asm movss rec, xmm0 // return xmm0
|
||
|
|
return rec;
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
// SSE reciprocal estimate, accurate to 12 significant bits of
|
||
|
|
f32 rec;
|
||
|
|
__asm rcpss xmm0, f // xmm0 = rcpss(f)
|
||
|
|
__asm movss rec , xmm0 // return xmm0
|
||
|
|
return rec;
|
||
|
|
*/
|
||
|
|
/*
|
||
|
|
register u32 x = 0x7F000000 - IR ( p );
|
||
|
|
const f32 r = FR ( x );
|
||
|
|
return r * (2.0f - p * r);
|
||
|
|
*/
|
||
|
|
#else // no fast math
|
||
|
|
return 1.f / f;
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
REALINLINE s32 floor32(f32 x)
|
||
|
|
{
|
||
|
|
#ifdef IRRLICHT_FAST_MATH
|
||
|
|
const f32 h = 0.5f;
|
||
|
|
|
||
|
|
s32 t;
|
||
|
|
|
||
|
|
#if defined(_MSC_VER)
|
||
|
|
__asm
|
||
|
|
{
|
||
|
|
fld x
|
||
|
|
fsub h
|
||
|
|
fistp t
|
||
|
|
}
|
||
|
|
#elif defined(__GNUC__)
|
||
|
|
__asm__ __volatile__ (
|
||
|
|
"fsub %2 \n\t"
|
||
|
|
"fistpl %0"
|
||
|
|
: "=m" (t)
|
||
|
|
: "t" (x), "f" (h)
|
||
|
|
: "st"
|
||
|
|
);
|
||
|
|
#else
|
||
|
|
# warn IRRLICHT_FAST_MATH not supported.
|
||
|
|
return (s32) floorf ( x );
|
||
|
|
#endif
|
||
|
|
return t;
|
||
|
|
#else // no fast math
|
||
|
|
return (s32) floorf ( x );
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
REALINLINE s32 ceil32 ( f32 x )
|
||
|
|
{
|
||
|
|
#ifdef IRRLICHT_FAST_MATH
|
||
|
|
const f32 h = 0.5f;
|
||
|
|
|
||
|
|
s32 t;
|
||
|
|
|
||
|
|
#if defined(_MSC_VER)
|
||
|
|
__asm
|
||
|
|
{
|
||
|
|
fld x
|
||
|
|
fadd h
|
||
|
|
fistp t
|
||
|
|
}
|
||
|
|
#elif defined(__GNUC__)
|
||
|
|
__asm__ __volatile__ (
|
||
|
|
"fadd %2 \n\t"
|
||
|
|
"fistpl %0 \n\t"
|
||
|
|
: "=m"(t)
|
||
|
|
: "t"(x), "f"(h)
|
||
|
|
: "st"
|
||
|
|
);
|
||
|
|
#else
|
||
|
|
# warn IRRLICHT_FAST_MATH not supported.
|
||
|
|
return (s32) ceilf ( x );
|
||
|
|
#endif
|
||
|
|
return t;
|
||
|
|
#else // not fast math
|
||
|
|
return (s32) ceilf ( x );
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
REALINLINE s32 round32(f32 x)
|
||
|
|
{
|
||
|
|
#if defined(IRRLICHT_FAST_MATH)
|
||
|
|
s32 t;
|
||
|
|
|
||
|
|
#if defined(_MSC_VER)
|
||
|
|
__asm
|
||
|
|
{
|
||
|
|
fld x
|
||
|
|
fistp t
|
||
|
|
}
|
||
|
|
#elif defined(__GNUC__)
|
||
|
|
__asm__ __volatile__ (
|
||
|
|
"fistpl %0 \n\t"
|
||
|
|
: "=m"(t)
|
||
|
|
: "t"(x)
|
||
|
|
: "st"
|
||
|
|
);
|
||
|
|
#else
|
||
|
|
# warn IRRLICHT_FAST_MATH not supported.
|
||
|
|
return (s32) round_(x);
|
||
|
|
#endif
|
||
|
|
return t;
|
||
|
|
#else // no fast math
|
||
|
|
return (s32) round_(x);
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
inline f32 f32_max3(const f32 a, const f32 b, const f32 c)
|
||
|
|
{
|
||
|
|
return a > b ? (a > c ? a : c) : (b > c ? b : c);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline f32 f32_min3(const f32 a, const f32 b, const f32 c)
|
||
|
|
{
|
||
|
|
return a < b ? (a < c ? a : c) : (b < c ? b : c);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline f32 fract ( f32 x )
|
||
|
|
{
|
||
|
|
return x - floorf ( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
} // end namespace core
|
||
|
|
} // end namespace irr
|
||
|
|
|
||
|
|
#ifndef IRRLICHT_FAST_MATH
|
||
|
|
using irr::core::IR;
|
||
|
|
using irr::core::FR;
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#endif
|
||
|
|
|