#include <FastMath.h>

Public Member Functions
template<typename T >
MCORE_INLINE T	Align (T inValue, T alignment)

Static Public Member Functions
static MCORE_INLINE float	Floor (float x)

static MCORE_INLINE bool	IsPositive (float x)

static MCORE_INLINE bool	IsNegative (float x)

static MCORE_INLINE bool	IsFloatZero (float x)

static MCORE_INLINE bool	IsFloatEqual (float x, float y)

static MCORE_INLINE float	SignOfFloat (float x)

static MCORE_INLINE float	Abs (float x)

static MCORE_INLINE float	Ceil (float x)

static MCORE_INLINE float	RadiansToDegrees (float rad)

static MCORE_INLINE float	DegreesToRadians (float deg)

static MCORE_INLINE float	Sin (float x)

static MCORE_INLINE float	Cos (float x)

static MCORE_INLINE float	Tan (float x)

static MCORE_INLINE float	ASin (float x)

static MCORE_INLINE float	ACos (float x)

static MCORE_INLINE float	ATan (float x)

static MCORE_INLINE float	ATan2 (float y, float x)

static MCORE_INLINE float	SignOfCos (float y)

static MCORE_INLINE float	SignOfSin (float y)

static MCORE_INLINE float	Exp (float x)

static MCORE_INLINE float	Log (float x)

static MCORE_INLINE float	Log2 (float x)

static MCORE_INLINE float	Pow (float base, float exponent)

static MCORE_INLINE float	Sqrt (float x)

static MCORE_INLINE float	SafeSqrt (float x)

static MCORE_INLINE float	FastSqrt (float x)

static MCORE_INLINE float	FastSqrt2 (float x)

static MCORE_INLINE float	InvSqrt (float x)

static MCORE_INLINE float	FastInvSqrt (float x)

static MCORE_INLINE uint32	NextPowerOfTwo (uint32 x)

static MCORE_INLINE float	FMod (float x, float y)

static MCORE_INLINE float	SafeFMod (float x, float y)

template<typename T >
static MCORE_INLINE T	Align (T inValue, T alignment)

static MCORE_INLINE void	MulSign (float &dest, float const &source)

Static Public Attributes
static const float	pi

static const float	twoPi

static const float	halfPi

static const float	invPi

static const float	epsilon

static const float	sqrtHalf

static const float	sqrt2

static const float	sqrt3

static const float	halfSqrt2

static const float	halfSqrt3

Detailed Description

The math class. All methods and attributes are static.

Member Function Documentation

◆ Abs()

MCORE_INLINE float Math::Abs ( float x )

static

Calculates the absolute value. The Abs function returns the absolute value of its parameter. Examples: The absolute value of -4 is 4 The absolute value of -41567 is 41567 The absolute value of -3.141593 is 3.141593

Parameters

x	The value to calculate the absolute value from.

Returns: The absolute value of the parameter.

◆ ACos()

MCORE_INLINE float Math::ACos ( float x )

static

Arccosine function.

Parameters

x	Angle in radians.

Returns: The arccosine of x.

◆ Align()

template<typename T >

static MCORE_INLINE T MCore::Math::Align	(	T	inValue,
		T	alignment
	)

static

Align a given size_t value to a given alignment. For example when the input value of inOutValue contains a value of 50, and the alignment is set to 16, then the aligned return value would be 64.

Parameters

inValue	The input value, which would be 50 in our above example.
alignment	The alignment touse, which would be 16 in our above example.

Returns: The value returned is the input value aligned to the given alignment. In our example it would return a value of 64.

◆ ASin()

MCORE_INLINE float Math::ASin ( float x )

static

Arcsine function.

Parameters

x	Angle in radians.

Returns: The arcsine of x.

◆ ATan()

MCORE_INLINE float Math::ATan ( float x )

static

Arctangent function.

Parameters

x	Angle in radians.

Returns: The arctangent of x.

◆ ATan2()

MCORE_INLINE float Math::ATan2	(	float	y,
		float	x
	)

static

Calculate the arctangent of y/x.

Parameters

y	The value of y.
x	The value of x.

Returns: The arctangent of y/x.

◆ Ceil()

MCORE_INLINE float Math::Ceil ( float x )

static

Calculates the ceiling of a value. The ceil function returns a value representing the smallest integer that is greater than or equal to x. Examples: The ceil of 2.8 is 3.000000 The ceil of -2.8 is -2.000000

Parameters

x	The value to ceil.

Returns: The value representing the smallest integer that is greater than or equal to x.

◆ Cos()

MCORE_INLINE float Math::Cos ( float x )

static

Cosine function.

Parameters

x	Angle in radians.

Returns: The cosine of x.

◆ DegreesToRadians()

MCORE_INLINE float Math::DegreesToRadians ( float deg )

static

Degree to radians Conversion.

Parameters

deg	The angle (degrees) to convert.

Returns: The converted angle in radians.

◆ Exp()

MCORE_INLINE float Math::Exp ( float x )

static

Calculates the exponential.

Parameters

x	The value.

Returns: The exponential of x.

◆ FastInvSqrt()

MCORE_INLINE float Math::FastInvSqrt ( float x )

static

Calculates a fast approximation (very good approx) to 1/sqrt(x). This one is more accurate than FastInvSqrt2, but a bit slower, but still much faster than the standard 1.0f / sqrt(x).

Parameters

x	The value in the equation 1/sqrt(x).

Returns: The inverse square root of x.

◆ FastSqrt()

MCORE_INLINE float Math::FastSqrt ( float x )

static

Fast square root. On the PC and MSVC compiler an optimized SSE version is used. On other platforms or other compilers it uses the standard square root. The precision is 22 bits here.

Returns: The square root of x.

◆ FastSqrt2()

MCORE_INLINE float Math::FastSqrt2 ( float x )

static

Fast square root method 2. On the PC and MSVC compiler an optimized SSE version is used. On other platforms or other compilers it uses the standard square root. The precision is 11 bits here.

Returns: The square root of x.

◆ Floor()

MCORE_INLINE float Math::Floor ( float x )

static

Calculates the floored version of a value. The floor function returns a value representing the largest integer that is less than or equal to x. Examples: The floor of 2.8 is 2.000000 The floor of -2.8 is -3.000000

Parameters

x	The value to floor.

Returns: The value representing the largest integer that is less than or equal to x.

◆ FMod()

MCORE_INLINE float Math::FMod	(	float	x,
		float	y
	)

static

Perform the modulus calculation on a float. Please keep in mind that the value of y is not allowed to be zero. If you don't know if y will be zero, use SafeFMod instead.

Parameters

x	The value to take the modulus on.
y	The modulus value, which is NOT allowed to be zero.

Returns: The result of the calculation.

◆ InvSqrt()

MCORE_INLINE float Math::InvSqrt ( float x )

static

Calculates the inverse square root (1 / Sqrt(x)). Parameter has to be nonnegative.

Parameters

x	Nonnegative value.

Returns: The inverse square root.

◆ IsFloatEqual()

MCORE_INLINE bool Math::IsFloatEqual	(	float	x,
		float	y
	)

static

Tests if two numbers are equal to each other. This uses the epsilon value as tolerance. Basically it does "return (Abs(x-y) < epsilon)".

Parameters

x	The first value.
y	The second value.

Returns: True if x is equal to y, otherwise false is returned.

◆ IsFloatZero()

MCORE_INLINE bool Math::IsFloatZero ( float x )

static

Tests if a number is equal to zero. This uses the epsilon value as tolerance. Basically it does "return (Abs(x) < epsilon)".

Parameters

x	The tested value.

Returns: True if x is zero, otherwise false is returned.

◆ IsNegative()

MCORE_INLINE bool Math::IsNegative ( float x )

static

Tests if a number is negative.

Parameters

x	The tested value.

Returns: True if the number is negative, false if it is positive or zero.

◆ IsPositive()

MCORE_INLINE bool Math::IsPositive ( float x )

static

Tests if a number is positive.

Parameters

x	The tested value.

Returns: True if the number is positive, false if it is negative or zero.

◆ Log()

MCORE_INLINE float Math::Log ( float x )

static

Calculates logarithms. The log functions return the logarithm of x. If x is negative, these functions return an indefinite, by default. If x is 0, they return INF (infinite).

Parameters

x	The value.

Returns: The logarithm of x.

◆ Log2()

MCORE_INLINE float Math::Log2 ( float x )

static

Calculates logarithms. The log2 functions return the logarithm of x. If x is negative, these functions return an indefinite, by default. If x is 0, they return INF (infinite).

Parameters

x	The value.

Returns: The logarithm of x.

◆ MulSign()

MCORE_INLINE void Math::MulSign	(	float &	dest,
		float const &	source
	)

static

Multiply a float value by its sign. This basically does:

dest = source > 0.0f ? source : -source;
or
dest = source * sgn(source);

Using bit operations the required if statement is eliminated.

◆ NextPowerOfTwo()

MCORE_INLINE uint32 Math::NextPowerOfTwo ( uint32 x )

static

Calculates a fast (but less accurate) approximation to 1/sqrt(x). The precision starts to show changes after the second digit in most cases.

Parameters

x	The value in the equation 1/sqrt(x).

Returns: The inverse square root of x. Calculates a fast (but less accurate) approximation to 1/sqrt(x). This version is more accurate (but a little slower) than the FastInvSqrt2.

Parameters

x	The value in the equation 1/sqrt(x).

Returns: The inverse square root of x. Calculates the next power of two.

Parameters

x	The value.

Returns: The next power of two of the parameter.

◆ Pow()

MCORE_INLINE float Math::Pow	(	float	base,
		float	exponent
	)

static

Calculates x raised to the power of y.

Parameters

base	The base.
exponent	The exponent.

Returns: X raised to the power of y.

◆ RadiansToDegrees()

MCORE_INLINE float Math::RadiansToDegrees ( float rad )

static

Radians to degree Conversion.

Parameters

rad	The angle(rads) to convert.

Returns: The converted angle in degrees.

◆ SafeFMod()

MCORE_INLINE float Math::SafeFMod	(	float	x,
		float	y
	)

static

Perform the modulus calculation on a float. The value of y is allowed to be zero. If you know that the value of y will never be zero, please use FMod instead, as that is a bit faster.

Parameters

x	The value to take the modulus on.
y	The modulus value, which is allowed to be zero as well.

Returns: The result of the calculation.

◆ SafeSqrt()

MCORE_INLINE float Math::SafeSqrt ( float x )

static

Calculates the square root. Parameter has to be nonnegative. The difference between Sqrt and SafeSqrt is that SafeSqrt checks if the parameter value is bigger than epsilon or not, otherwise it returns zero.

Parameters

x	Nonnegative value.

Returns: The square root of x.

◆ SignOfCos()

MCORE_INLINE float Math::SignOfCos ( float y )

static

Returns the sign of the cosine of the argument.

◆ SignOfFloat()

MCORE_INLINE float Math::SignOfFloat ( float x )

static

Returns the sign of a real number.

Parameters

x	The tested number.

Returns: 1 for positive, -1 for negative, 0 for zero.

◆ SignOfSin()

MCORE_INLINE float Math::SignOfSin ( float y )

static

Returns the sign of the sine of the argument.

◆ Sin()

MCORE_INLINE float Math::Sin ( float x )

static

Sine function.

Parameters

x	Angle in radians.

Returns: The sine of x.

◆ Sqrt()

MCORE_INLINE float Math::Sqrt ( float x )

static

Calculates the square root. Parameter has to be nonnegative and non-zero.

Parameters

x	Nonnegative value.

Returns: The square root of x.

◆ Tan()

MCORE_INLINE float Math::Tan ( float x )

static

Tangent function.

Parameters

x	Angle in radians.

Returns: The tangent of x.

Member Data Documentation

◆ epsilon

const float MCore::Math::epsilon

static

A very small number, almost equal to zero (0.000001).

◆ halfPi

const float MCore::Math::halfPi

static

PI divided by two

◆ halfSqrt2

const float MCore::Math::halfSqrt2

static

Half the square root of two.

◆ halfSqrt3

const float MCore::Math::halfSqrt3

static

Half the square root of three.

◆ invPi

const float MCore::Math::invPi

static

1.0 divided by PI

◆ pi

const float MCore::Math::pi

static

Check if a given float is positive.

Parameters

f	The float to check.

Returns: Returns true when positive, otherwise false is returned. Check if a given float is negative.

Parameters

f	The float to check.

Returns: Returns true when negative, otherwise false is returned. The value of PI, which is 3.1415926

◆ sqrt2

const float MCore::Math::sqrt2

static

The square root of 2.

◆ sqrt3

const float MCore::Math::sqrt3

static

The square root of 3.

◆ sqrtHalf

const float MCore::Math::sqrtHalf

static

The square root of 0.5.

◆ twoPi

const float MCore::Math::twoPi

static

PI multiplied by two

The documentation for this class was generated from the following files:

Gems/EMotionFX/Code/MCore/Source/FastMath.h
Gems/EMotionFX/Code/MCore/Source/FastMath.inl

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation

◆ Abs()

◆ ACos()

◆ Align()

◆ ASin()

◆ ATan()

◆ ATan2()

◆ Ceil()

◆ Cos()

◆ DegreesToRadians()

◆ Exp()

◆ FastInvSqrt()

◆ FastSqrt()

◆ FastSqrt2()

◆ Floor()

◆ FMod()

◆ InvSqrt()

◆ IsFloatEqual()

◆ IsFloatZero()

◆ IsNegative()

◆ IsPositive()

◆ Log()

◆ Log2()

◆ MulSign()

◆ NextPowerOfTwo()

◆ Pow()

◆ RadiansToDegrees()

◆ SafeFMod()

◆ SafeSqrt()

◆ SignOfCos()

◆ SignOfFloat()

◆ SignOfSin()

◆ Sin()

◆ Sqrt()

◆ Tan()

Member Data Documentation

◆ epsilon

◆ halfPi

◆ halfSqrt2

◆ halfSqrt3

◆ invPi

◆ pi

◆ sqrt2

◆ sqrt3

◆ sqrtHalf

◆ twoPi