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Diffstat (limited to 'include/irrMath.h')
| -rw-r--r-- | include/irrMath.h | 685 |
1 files changed, 685 insertions, 0 deletions
diff --git a/include/irrMath.h b/include/irrMath.h new file mode 100644 index 0000000..b97e270 --- /dev/null +++ b/include/irrMath.h @@ -0,0 +1,685 @@ +// Copyright (C) 2002-2012 Nikolaus Gebhardt
+// This file is part of the "Irrlicht Engine".
+// For conditions of distribution and use, see copyright notice in irrlicht.h
+
+#ifndef __IRR_MATH_H_INCLUDED__
+#define __IRR_MATH_H_INCLUDED__
+
+#include "IrrCompileConfig.h"
+#include "irrTypes.h"
+#include <math.h>
+#include <float.h>
+#include <stdlib.h> // for abs() etc.
+#include <limits.h> // For INT_MAX / UINT_MAX
+
+#if defined(_IRR_SOLARIS_PLATFORM_) || defined(__BORLANDC__) || defined (__BCPLUSPLUS__) || defined (_WIN32_WCE)
+ #define sqrtf(X) (irr::f32)sqrt((irr::f64)(X))
+ #define sinf(X) (irr::f32)sin((irr::f64)(X))
+ #define cosf(X) (irr::f32)cos((irr::f64)(X))
+ #define asinf(X) (irr::f32)asin((irr::f64)(X))
+ #define acosf(X) (irr::f32)acos((irr::f64)(X))
+ #define atan2f(X,Y) (irr::f32)atan2((irr::f64)(X),(irr::f64)(Y))
+ #define ceilf(X) (irr::f32)ceil((irr::f64)(X))
+ #define floorf(X) (irr::f32)floor((irr::f64)(X))
+ #define powf(X,Y) (irr::f32)pow((irr::f64)(X),(irr::f64)(Y))
+ #define fmodf(X,Y) (irr::f32)fmod((irr::f64)(X),(irr::f64)(Y))
+ #define fabsf(X) (irr::f32)fabs((irr::f64)(X))
+ #define logf(X) (irr::f32)log((irr::f64)(X))
+#endif
+
+#ifndef FLT_MAX
+#define FLT_MAX 3.402823466E+38F
+#endif
+
+#ifndef FLT_MIN
+#define FLT_MIN 1.17549435e-38F
+#endif
+
+namespace irr
+{
+namespace core
+{
+
+ //! Rounding error constant often used when comparing f32 values.
+
+ const s32 ROUNDING_ERROR_S32 = 0;
+
+#ifdef __IRR_HAS_S64
+ const s64 ROUNDING_ERROR_S64 = 0;
+#endif
+ const f32 ROUNDING_ERROR_f32 = 0.000001f;
+ const f64 ROUNDING_ERROR_f64 = 0.00000001;
+
+#ifdef PI // make sure we don't collide with a define
+#undef PI
+#endif
+ //! Constant for PI.
+ const f32 PI = 3.14159265359f;
+
+ //! Constant for reciprocal of PI.
+ const f32 RECIPROCAL_PI = 1.0f/PI;
+
+ //! Constant for half of PI.
+ const f32 HALF_PI = PI/2.0f;
+
+#ifdef PI64 // make sure we don't collide with a define
+#undef PI64
+#endif
+ //! Constant for 64bit PI.
+ const f64 PI64 = 3.1415926535897932384626433832795028841971693993751;
+
+ //! Constant for 64bit reciprocal of PI.
+ const f64 RECIPROCAL_PI64 = 1.0/PI64;
+
+ //! 32bit Constant for converting from degrees to radians
+ const f32 DEGTORAD = PI / 180.0f;
+
+ //! 32bit constant for converting from radians to degrees (formally known as GRAD_PI)
+ const f32 RADTODEG = 180.0f / PI;
+
+ //! 64bit constant for converting from degrees to radians (formally known as GRAD_PI2)
+ const f64 DEGTORAD64 = PI64 / 180.0;
+
+ //! 64bit constant for converting from radians to degrees
+ const f64 RADTODEG64 = 180.0 / PI64;
+
+ //! Utility function to convert a radian value to degrees
+ /** Provided as it can be clearer to write radToDeg(X) than RADTODEG * X
+ \param radians The radians value to convert to degrees.
+ */
+ inline f32 radToDeg(f32 radians)
+ {
+ return RADTODEG * radians;
+ }
+
+ //! Utility function to convert a radian value to degrees
+ /** Provided as it can be clearer to write radToDeg(X) than RADTODEG * X
+ \param radians The radians value to convert to degrees.
+ */
+ inline f64 radToDeg(f64 radians)
+ {
+ return RADTODEG64 * radians;
+ }
+
+ //! Utility function to convert a degrees value to radians
+ /** Provided as it can be clearer to write degToRad(X) than DEGTORAD * X
+ \param degrees The degrees value to convert to radians.
+ */
+ inline f32 degToRad(f32 degrees)
+ {
+ return DEGTORAD * degrees;
+ }
+
+ //! Utility function to convert a degrees value to radians
+ /** Provided as it can be clearer to write degToRad(X) than DEGTORAD * X
+ \param degrees The degrees value to convert to radians.
+ */
+ inline f64 degToRad(f64 degrees)
+ {
+ return DEGTORAD64 * degrees;
+ }
+
+ //! returns minimum of two values. Own implementation to get rid of the STL (VS6 problems)
+ template<class T>
+ inline const T& min_(const T& a, const T& b)
+ {
+ return a < b ? a : b;
+ }
+
+ //! returns minimum of three values. Own implementation to get rid of the STL (VS6 problems)
+ template<class T>
+ inline const T& min_(const T& a, const T& b, const T& c)
+ {
+ return a < b ? min_(a, c) : min_(b, c);
+ }
+
+ //! returns maximum of two values. Own implementation to get rid of the STL (VS6 problems)
+ template<class T>
+ inline const T& max_(const T& a, const T& b)
+ {
+ return a < b ? b : a;
+ }
+
+ //! returns maximum of three values. Own implementation to get rid of the STL (VS6 problems)
+ template<class T>
+ inline const T& max_(const T& a, const T& b, const T& c)
+ {
+ return a < b ? max_(b, c) : max_(a, c);
+ }
+
+ //! returns abs of two values. Own implementation to get rid of STL (VS6 problems)
+ template<class T>
+ inline T abs_(const T& a)
+ {
+ return a < (T)0 ? -a : a;
+ }
+
+ //! returns linear interpolation of a and b with ratio t
+ //! \return: a if t==0, b if t==1, and the linear interpolation else
+ template<class T>
+ inline T lerp(const T& a, const T& b, const f32 t)
+ {
+ return (T)(a*(1.f-t)) + (b*t);
+ }
+
+ //! clamps a value between low and high
+ template <class T>
+ inline const T clamp (const T& value, const T& low, const T& high)
+ {
+ return min_ (max_(value,low), high);
+ }
+
+ //! swaps the content of the passed parameters
+ // Note: We use the same trick as boost and use two template arguments to
+ // avoid ambiguity when swapping objects of an Irrlicht type that has not
+ // it's own swap overload. Otherwise we get conflicts with some compilers
+ // in combination with stl.
+ template <class T1, class T2>
+ inline void swap(T1& a, T2& b)
+ {
+ T1 c(a);
+ a = b;
+ b = c;
+ }
+
+ template <class T>
+ inline T roundingError();
+
+ template <>
+ inline f32 roundingError()
+ {
+ return ROUNDING_ERROR_f32;
+ }
+
+ template <>
+ inline f64 roundingError()
+ {
+ return ROUNDING_ERROR_f64;
+ }
+
+ template <>
+ inline s32 roundingError()
+ {
+ return ROUNDING_ERROR_S32;
+ }
+
+ template <>
+ inline u32 roundingError()
+ {
+ return ROUNDING_ERROR_S32;
+ }
+
+#ifdef __IRR_HAS_S64
+ template <>
+ inline s64 roundingError()
+ {
+ return ROUNDING_ERROR_S64;
+ }
+
+ template <>
+ inline u64 roundingError()
+ {
+ return ROUNDING_ERROR_S64;
+ }
+#endif
+
+ template <class T>
+ inline T relativeErrorFactor()
+ {
+ return 1;
+ }
+
+ template <>
+ inline f32 relativeErrorFactor()
+ {
+ return 4;
+ }
+
+ template <>
+ inline f64 relativeErrorFactor()
+ {
+ return 8;
+ }
+
+ //! returns if a equals b, taking possible rounding errors into account
+ template <class T>
+ inline bool equals(const T a, const T b, const T tolerance = roundingError<T>())
+ {
+ return (a + tolerance >= b) && (a - tolerance <= b);
+ }
+
+
+ //! returns if a equals b, taking relative error in form of factor
+ //! this particular function does not involve any division.
+ template <class T>
+ inline bool equalsRelative( const T a, const T b, const T factor = relativeErrorFactor<T>())
+ {
+ //https://eagergames.wordpress.com/2017/04/01/fast-parallel-lines-and-vectors-test/
+
+ const T maxi = max_( a, b);
+ const T mini = min_( a, b);
+ const T maxMagnitude = max_( maxi, -mini);
+
+ return (maxMagnitude*factor + maxi) == (maxMagnitude*factor + mini); // MAD Wise
+ }
+
+ union FloatIntUnion32
+ {
+ FloatIntUnion32(float f1 = 0.0f) : f(f1) {}
+ // Portable sign-extraction
+ bool sign() const { return (i >> 31) != 0; }
+
+ irr::s32 i;
+ irr::f32 f;
+ };
+
+ //! We compare the difference in ULP's (spacing between floating-point numbers, aka ULP=1 means there exists no float between).
+ //\result true when numbers have a ULP <= maxUlpDiff AND have the same sign.
+ inline bool equalsByUlp(f32 a, f32 b, int maxUlpDiff)
+ {
+ // Based on the ideas and code from Bruce Dawson on
+ // http://www.altdevblogaday.com/2012/02/22/comparing-floating-point-numbers-2012-edition/
+ // When floats are interpreted as integers the two nearest possible float numbers differ just
+ // by one integer number. Also works the other way round, an integer of 1 interpreted as float
+ // is for example the smallest possible float number.
+
+ const FloatIntUnion32 fa(a);
+ const FloatIntUnion32 fb(b);
+
+ // Different signs, we could maybe get difference to 0, but so close to 0 using epsilons is better.
+ if ( fa.sign() != fb.sign() )
+ {
+ // Check for equality to make sure +0==-0
+ if (fa.i == fb.i)
+ return true;
+ return false;
+ }
+
+ // Find the difference in ULPs.
+ const int ulpsDiff = abs_(fa.i- fb.i);
+ if (ulpsDiff <= maxUlpDiff)
+ return true;
+
+ return false;
+ }
+
+ //! returns if a equals zero, taking rounding errors into account
+ inline bool iszero(const f64 a, const f64 tolerance = ROUNDING_ERROR_f64)
+ {
+ return fabs(a) <= tolerance;
+ }
+
+ //! returns if a equals zero, taking rounding errors into account
+ inline bool iszero(const f32 a, const f32 tolerance = ROUNDING_ERROR_f32)
+ {
+ return fabsf(a) <= tolerance;
+ }
+
+ //! returns if a equals not zero, taking rounding errors into account
+ inline bool isnotzero(const f32 a, const f32 tolerance = ROUNDING_ERROR_f32)
+ {
+ return fabsf(a) > tolerance;
+ }
+
+ //! returns if a equals zero, taking rounding errors into account
+ inline bool iszero(const s32 a, const s32 tolerance = 0)
+ {
+ return ( a & 0x7ffffff ) <= tolerance;
+ }
+
+ //! returns if a equals zero, taking rounding errors into account
+ inline bool iszero(const u32 a, const u32 tolerance = 0)
+ {
+ return a <= tolerance;
+ }
+
+#ifdef __IRR_HAS_S64
+ //! returns if a equals zero, taking rounding errors into account
+ inline bool iszero(const s64 a, const s64 tolerance = 0)
+ {
+ return abs_(a) <= tolerance;
+ }
+#endif
+
+ inline s32 s32_min(s32 a, s32 b)
+ {
+ const s32 mask = (a - b) >> 31;
+ return (a & mask) | (b & ~mask);
+ }
+
+ inline s32 s32_max(s32 a, s32 b)
+ {
+ const s32 mask = (a - b) >> 31;
+ return (b & mask) | (a & ~mask);
+ }
+
+ inline s32 s32_clamp (s32 value, s32 low, s32 high)
+ {
+ return s32_min(s32_max(value,low), high);
+ }
+
+ /*
+ float IEEE-754 bit representation
+
+ 0 0x00000000
+ 1.0 0x3f800000
+ 0.5 0x3f000000
+ 3 0x40400000
+ +inf 0x7f800000
+ -inf 0xff800000
+ +NaN 0x7fc00000 or 0x7ff00000
+ in general: number = (sign ? -1:1) * 2^(exponent) * 1.(mantissa bits)
+ */
+
+ typedef union { u32 u; s32 s; f32 f; } inttofloat;
+
+ #define F32_AS_S32(f) (*((s32 *) &(f)))
+ #define F32_AS_U32(f) (*((u32 *) &(f)))
+ #define F32_AS_U32_POINTER(f) ( ((u32 *) &(f)))
+
+ #define F32_VALUE_0 0x00000000
+ #define F32_VALUE_1 0x3f800000
+ #define F32_SIGN_BIT 0x80000000U
+ #define F32_EXPON_MANTISSA 0x7FFFFFFFU
+
+ //! code is taken from IceFPU
+ //! Integer representation of a floating-point value.
+#ifdef IRRLICHT_FAST_MATH
+ #define IR(x) ((u32&)(x))
+#else
+ inline u32 IR(f32 x) {inttofloat tmp; tmp.f=x; return tmp.u;}
+#endif
+
+ //! Absolute integer representation of a floating-point value
+ #define AIR(x) (IR(x)&0x7fffffff)
+
+ //! Floating-point representation of an integer value.
+#ifdef IRRLICHT_FAST_MATH
+ #define FR(x) ((f32&)(x))
+#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 positive to mask
+ //s32 conmask = -condition >> 31;
+ state ^= ( ( -condition >> 31 ) ^ state ) & mask;
+ }
+
+ // NOTE: This is not as exact as the c99/c++11 round function, especially at high numbers starting with 8388609
+ // (only low number which seems to go wrong is 0.49999997 which is rounded to 1)
+ // 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)
+ inline f32 round_( f32 x )
+ {
+ return floorf( x + 0.5f );
+ }
+
+ // 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 )
+ // NOTE: Unlike comment below says I found inaccuracies already at 4'th significant bit.
+ // p.E: Input 1, expected 1, got 0.999755859
+
+ #if defined(_MSC_VER) && !defined(_WIN64)
+ // 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)
+ // NOTE: Unlike with 1.f / f the values very close to 0 return -nan instead of inf
+
+ // SSE Newton-Raphson reciprocal estimate, accurate to 23 significant
+ // bi ts of the mantissa
+ // One Newton-Raphson Iteration:
+ // f(i+1) = 2 * rcpss(f) - f * rcpss(f) * rcpss(f)
+#if defined(_MSC_VER) && !defined(_WIN64)
+ 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;
+#else // no support yet for other compilers
+ return 1.f / f;
+#endif
+ //! 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 Newton-Raphson Iteration:
+ // f(i+1) = 2 * rcpss(f) - f * rcpss(f) * rcpss(f)
+#if defined(_MSC_VER) && !defined(_WIN64)
+ 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;
+#else // no support yet for other compilers
+ return 1.f / f;
+#endif
+
+/*
+ // 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)
+ {
+ return (s32) floorf ( x );
+ }
+
+ REALINLINE s32 ceil32 ( f32 x )
+ {
+ return (s32) ceilf ( x );
+ }
+
+ // NOTE: Please check round_ documentation about some inaccuracies in this compared to standard library round function.
+ REALINLINE s32 round32(f32 x)
+ {
+ return (s32) round_(x);
+ }
+
+ 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
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