457 lines
11 KiB
C++
457 lines
11 KiB
C++
// Copyright (C) 2002-2007 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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#if defined(_IRR_SOLARIS_PLATFORM_) || defined(__BORLANDC__) || defined (__BCPLUSPLUS__) || defined (_WIN32_WCE)
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#define sqrtf(X) (f32)sqrt((f64)(X))
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#define sinf(X) (f32)sin((f64)(X))
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#define cosf(X) (f32)cos((f64)(X))
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#define asinf(X) (f32)asin((f64)(X))
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#define acosf(X) (f32)acos((f64)(X))
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#define atan2f(X,Y) (f32)atan2((f64)(X),(f64)(Y))
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#define ceilf(X) (f32)ceil((f64)(X))
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#define floorf(X) (f32)floor((f64)(X))
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#define powf(X,Y) (f32)pow((f64)(X),(f64)(Y))
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#define fmodf(X,Y) (f32)fmod((f64)(X),(f64)(Y))
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#define fabsf(X) (f32)fabs((f64)(X))
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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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#ifdef IRRLICHT_FAST_MATH
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const f32 ROUNDING_ERROR_32 = 0.00005f;
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const f64 ROUNDING_ERROR_64 = 0.000005f;
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#else
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const f32 ROUNDING_ERROR_32 = 0.000001f;
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const f64 ROUNDING_ERROR_64 = 0.00000001f;
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#endif
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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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//! 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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//! 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_32)
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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 s32 a, const s32 b, const s32 tolerance = 0)
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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 u32 a, const u32 b, const u32 tolerance = 0)
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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 zero, taking rounding errors into account
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inline bool iszero(const f32 a, const f32 tolerance = ROUNDING_ERROR_32)
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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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inline s32 s32_min ( s32 a, s32 b)
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{
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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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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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#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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#define IR(x) ((u32&)(x))
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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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#define FR(x) ((f32&)(x))
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#define IEEE_1_0 0x3f800000 //!< integer representation of 1.0
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#define IEEE_255_0 0x437f0000 //!< integer representation of 255.0
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#ifdef IRRLICHT_FAST_MATH
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#define F32_LOWER_0(f) (F32_AS_U32(f) > F32_SIGN_BIT)
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#define F32_LOWER_EQUAL_0(f) (F32_AS_S32(f) <= F32_VALUE_0)
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#define F32_GREATER_0(f) (F32_AS_S32(f) > F32_VALUE_0)
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#define F32_GREATER_EQUAL_0(f) (F32_AS_U32(f) <= F32_SIGN_BIT)
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#define F32_EQUAL_1(f) (F32_AS_U32(f) == F32_VALUE_1)
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#define F32_EQUAL_0(f) ( (F32_AS_U32(f) & F32_EXPON_MANTISSA ) == F32_VALUE_0)
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// only same sign
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#define F32_A_GREATER_B(a,b) (F32_AS_S32((a)) > F32_AS_S32((b)))
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#else
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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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#endif
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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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//! conditional set based on mask and arithmetic shift
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REALINLINE u32 if_c_a_else_b ( const s32 condition, const u32 a, const u32 b )
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{
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return ( ( -condition >> 31 ) & ( a ^ b ) ) ^ b;
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}
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//! conditional set based on mask and arithmetic shift
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REALINLINE u32 if_c_a_else_0 ( const s32 condition, const u32 a )
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{
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return ( -condition >> 31 ) & a;
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}
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/*
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if (condition) state |= m; else state &= ~m;
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*/
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REALINLINE void setbit_cond ( u32 &state, s32 condition, u32 mask )
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{
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// 0, or any postive to mask
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//s32 conmask = -condition >> 31;
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state ^= ( ( -condition >> 31 ) ^ state ) & mask;
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}
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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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REALINLINE void clearFPUException ()
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{
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#ifdef IRRLICHT_FAST_MATH
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#ifdef feclearexcept
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feclearexcept(FE_ALL_EXCEPT);
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#elif defined(_MSC_VER)
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__asm fnclex;
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#elif defined(__GNUC__) && defined(__x86__)
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__asm__ __volatile__ ("fclex \n\t");
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#else
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# warn clearFPUException not supported.
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#endif
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#endif
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}
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REALINLINE f32 reciprocal_squareroot(const f32 x)
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{
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#ifdef IRRLICHT_FAST_MATH
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// comes from Nvidia
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#if 1
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u32 tmp = (u32(IEEE_1_0 << 1) + IEEE_1_0 - *(u32*)&x) >> 1;
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f32 y = *(f32*)&tmp;
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return y * (1.47f - 0.47f * x * y * y);
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#elif defined(_MSC_VER)
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// an sse2 version
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__asm
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{
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movss xmm0, x
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rsqrtss xmm0, xmm0
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movss x, xmm0
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}
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return x;
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#endif
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#else // no fast math
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return 1.f / sqrtf ( x );
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#endif
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}
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REALINLINE f32 reciprocal ( const f32 f )
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{
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#ifdef IRRLICHT_FAST_MATH
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//! i do not divide through 0.. (fpu expection)
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// instead set f to a high value to get a return value near zero..
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// -1000000000000.f.. is use minus to stay negative..
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// must test's here (plane.normal dot anything ) checks on <= 0.f
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return 1.f / f;
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//u32 x = (-(AIR(f) != 0 ) >> 31 ) & ( IR(f) ^ 0xd368d4a5 ) ^ 0xd368d4a5;
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//return 1.f / FR ( x );
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#else // no fast math
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return 1.f / f;
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#endif
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}
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REALINLINE f32 reciprocal_approxim ( const f32 p )
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{
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#ifdef IRRLICHT_FAST_MATH
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register u32 x = 0x7F000000 - IR ( p );
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const f32 r = FR ( x );
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return r * (2.0f - p * r);
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#else // no fast math
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return 1.f / p;
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#endif
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}
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REALINLINE s32 floor32(f32 x)
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{
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#ifdef IRRLICHT_FAST_MATH
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const f32 h = 0.5f;
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s32 t;
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#if defined(_MSC_VER)
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__asm
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{
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fld x
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fsub h
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fistp t
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}
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#elif defined(__GNUC__)
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__asm__ __volatile__ (
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"fsub %2 \n\t"
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"fistpl %0"
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: "=m" (t)
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: "t" (x), "f" (h)
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: "st"
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);
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#else
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# warn IRRLICHT_FAST_MATH not supported.
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return (s32) floorf ( x );
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#endif
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return t;
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#else // no fast math
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return (s32) floorf ( x );
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#endif
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}
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REALINLINE s32 ceil32 ( f32 x )
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{
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#ifdef IRRLICHT_FAST_MATH
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const f32 h = 0.5f;
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s32 t;
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#if defined(_MSC_VER)
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__asm
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{
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fld x
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fadd h
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fistp t
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}
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#elif defined(__GNUC__)
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__asm__ __volatile__ (
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"fadd %2 \n\t"
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"fistpl %0 \n\t"
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: "=m"(t)
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: "t"(x), "f"(h)
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: "st"
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);
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#else
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# warn IRRLICHT_FAST_MATH not supported.
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return (s32) ceilf ( x );
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#endif
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return t;
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#else // not fast math
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return (s32) ceilf ( x );
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#endif
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}
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REALINLINE s32 round32(f32 x)
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{
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#if defined(IRRLICHT_FAST_MATH)
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s32 t;
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#if defined(_MSC_VER)
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__asm
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{
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fld x
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fistp t
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}
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#elif defined(__GNUC__)
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__asm__ __volatile__ (
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"fistpl %0 \n\t"
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: "=m"(t)
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: "t"(x)
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: "st"
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);
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#else
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# warn IRRLICHT_FAST_MATH not supported.
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return (s32) round_(x);
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#endif
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return t;
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#else // no fast math
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return (s32) round_(x);
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#endif
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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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#endif
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