483 lines
12 KiB
C++
483 lines
12 KiB
C++
// 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 "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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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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const s64 ROUNDING_ERROR_S64 = 0;
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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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template <class T>
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inline T roundingError();
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template <>
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inline f32 roundingError()
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{
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return ROUNDING_ERROR_f32;
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}
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template <>
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inline f64 roundingError()
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{
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return ROUNDING_ERROR_f64;
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}
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template <>
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inline s32 roundingError()
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{
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return ROUNDING_ERROR_S32;
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}
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template <>
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inline u32 roundingError()
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{
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return ROUNDING_ERROR_S32;
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}
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template <>
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inline s64 roundingError()
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{
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return ROUNDING_ERROR_S64;
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}
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template <>
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inline u64 roundingError()
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{
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return ROUNDING_ERROR_S64;
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}
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template <class T>
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inline T relativeErrorFactor()
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{
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return 1;
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}
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template <>
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inline f32 relativeErrorFactor()
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{
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return 4;
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}
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template <>
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inline f64 relativeErrorFactor()
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{
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return 8;
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}
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//! returns if a equals b, taking possible rounding errors into account
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template <class T>
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inline bool equals(const T a, const T b, const T tolerance = roundingError<T>())
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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 relative error in form of factor
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//! this particular function does not involve any division.
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template <class T>
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inline bool equalsRelative( const T a, const T b, const T factor = relativeErrorFactor<T>())
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{
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//https://eagergames.wordpress.com/2017/04/01/fast-parallel-lines-and-vectors-test/
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const T maxi = max_( a, b);
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const T mini = min_( a, b);
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const T maxMagnitude = max_( maxi, -mini);
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return (maxMagnitude*factor + maxi) == (maxMagnitude*factor + mini); // MAD Wise
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}
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union FloatIntUnion32
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{
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FloatIntUnion32(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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irr::s32 i;
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irr::f32 f;
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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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const FloatIntUnion32 fa(a);
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const FloatIntUnion32 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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const 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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//! 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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//! 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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inline s32 s32_min(s32 a, s32 b)
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{
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return min_(a, b);
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}
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inline s32 s32_max(s32 a, s32 b)
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{
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return max_(a, b);
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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 clamp(value, low, high);
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}
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/*
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float IEEE-754 bit representation
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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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//! code is taken from IceFPU
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//! Integer representation of a floating-point value.
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inline u32 IR(f32 x) {inttofloat tmp; tmp.f=x; return tmp.u;}
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//! Floating-point representation of an integer value.
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inline f32 FR(u32 x) {inttofloat tmp; tmp.u=x; return tmp.f;}
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inline f32 FR(s32 x) {inttofloat tmp; tmp.s=x; return tmp.f;}
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#define F32_LOWER_0(n) ((n) < 0.0f)
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#define F32_LOWER_EQUAL_0(n) ((n) <= 0.0f)
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#define F32_GREATER_0(n) ((n) > 0.0f)
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#define F32_GREATER_EQUAL_0(n) ((n) >= 0.0f)
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#define F32_EQUAL_1(n) ((n) == 1.0f)
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#define F32_EQUAL_0(n) ((n) == 0.0f)
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#define F32_A_GREATER_B(a,b) ((a) > (b))
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#ifndef REALINLINE
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#ifdef _MSC_VER
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#define REALINLINE __forceinline
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#else
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#define REALINLINE inline
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#endif
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#endif
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// NOTE: This is not as exact as the c99/c++11 round function, especially at high numbers starting with 8388609
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// (only low number which seems to go wrong is 0.49999997 which is rounded to 1)
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// Also negative 0.5 is rounded up not down unlike with the standard function (p.E. input -0.5 will be 0 and not -1)
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inline f32 round_( f32 x )
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{
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return floorf( x + 0.5f );
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}
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// calculate: sqrt ( x )
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REALINLINE f32 squareroot(const f32 f)
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{
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return sqrtf(f);
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}
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// calculate: sqrt ( x )
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REALINLINE f64 squareroot(const f64 f)
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{
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return sqrt(f);
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}
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// calculate: sqrt ( x )
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REALINLINE s32 squareroot(const s32 f)
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{
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return static_cast<s32>(squareroot(static_cast<f32>(f)));
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}
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// calculate: sqrt ( x )
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REALINLINE s64 squareroot(const s64 f)
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{
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return static_cast<s64>(squareroot(static_cast<f64>(f)));
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}
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// calculate: 1 / sqrt ( x )
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REALINLINE f64 reciprocal_squareroot(const f64 x)
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{
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return 1.0 / sqrt(x);
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}
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// calculate: 1 / sqrtf ( x )
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REALINLINE f32 reciprocal_squareroot(const f32 f)
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{
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return 1.f / sqrtf(f);
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}
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// calculate: 1 / sqrtf( x )
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REALINLINE s32 reciprocal_squareroot(const s32 x)
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{
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return static_cast<s32>(reciprocal_squareroot(static_cast<f32>(x)));
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}
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// calculate: 1 / x
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REALINLINE f32 reciprocal( const f32 f )
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{
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return 1.f / f;
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}
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// calculate: 1 / x
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REALINLINE f64 reciprocal ( const f64 f )
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{
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return 1.0 / f;
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}
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// calculate: 1 / x, low precision allowed
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REALINLINE f32 reciprocal_approxim ( const f32 f )
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{
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return 1.f / f;
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}
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REALINLINE s32 floor32(f32 x)
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{
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return (s32) floorf ( x );
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}
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REALINLINE s32 ceil32 ( f32 x )
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{
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return (s32) ceilf ( x );
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}
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// NOTE: Please check round_ documentation about some inaccuracies in this compared to standard library round function.
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REALINLINE s32 round32(f32 x)
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{
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return (s32) round_(x);
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}
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inline f32 f32_max3(const f32 a, const f32 b, const f32 c)
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{
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return a > b ? (a > c ? a : c) : (b > c ? b : c);
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}
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inline f32 f32_min3(const f32 a, const f32 b, const f32 c)
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{
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return a < b ? (a < c ? a : c) : (b < c ? b : c);
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}
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inline f32 fract ( f32 x )
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{
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return x - floorf ( x );
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}
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} // end namespace core
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} // end namespace irr
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using irr::core::IR;
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using irr::core::FR;
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#endif
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