Math.h File Reference

#include <Eigen/Core>
#include <cmath>
#include <vector>

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Namespaces
namespace	autopas
	This is the main namespace of AutoPas.
namespace	autopas::utils
	In this namespace some helper classes and functions can be found used inside of AutoPas.

Functions
template<class Int_t , std::enable_if_t< std::is_integral_v< Int_t >, bool > = true>
Int_t	autopas::utils::Math::safeAdd (const Int_t &a, const Int_t &b, const Int_t &valUnderflow=std::numeric_limits< Int_t >::min(), const Int_t &valOverflow=std::numeric_limits< Int_t >::max())
	Addition function for integer types that is safe against over and underflow.
template<class Float_t , std::enable_if_t< std::is_floating_point_v< Float_t >, bool > = true>
Float_t	autopas::utils::Math::safeAdd (const Float_t &a, const Float_t &b, const Float_t &valUnderflow=-std::numeric_limits< Float_t >::max(), const Float_t &valOverflow=std::numeric_limits< Float_t >::max())
	Addition function for floating point types that is safe against over and underflow.
template<class Int_t , std::enable_if_t< std::is_integral_v< Int_t >, bool > = true>
Int_t	autopas::utils::Math::safeSub (const Int_t &a, const Int_t &b, const Int_t &valUnderflow=std::numeric_limits< Int_t >::min(), const Int_t &valOverflow=std::numeric_limits< Int_t >::max())
	Subtraction function for integer types that is safe against over and underflow.
template<class Float_t , std::enable_if_t< std::is_floating_point_v< Float_t >, bool > = true>
Float_t	autopas::utils::Math::safeSub (const Float_t &a, const Float_t &b, const Float_t &valUnderflow=-std::numeric_limits< Float_t >::max(), const Float_t &valOverflow=std::numeric_limits< Float_t >::max())
	Addition function for floating point types that is safe against over and underflow.
template<class Int_t , std::enable_if_t< std::is_integral_v< Int_t >, bool > = true>
Int_t	autopas::utils::Math::safeMul (const Int_t &a, const Int_t &b, const Int_t &valUnderflow=std::numeric_limits< Int_t >::min(), const Int_t &valOverflow=std::numeric_limits< Int_t >::max())
	Multiplication function for integer types that is safe against over and underflow.
template<class Float_t , std::enable_if_t< std::is_floating_point_v< Float_t >, bool > = true>
Float_t	autopas::utils::Math::safeMul (const Float_t &a, const Float_t &b, const Float_t &valUnderflow=-std::numeric_limits< Float_t >::max(), const Float_t &valOverflow=std::numeric_limits< Float_t >::max())
	Multiplication function for floating point types that is safe against over and underflow.
template<size_t exponent, class T >
T	autopas::utils::Math::pow (const T &base)
	No-overhead power function with exponent known at compile time.
double	autopas::utils::Math::normalPDF (double x)
	Probability density function PDF of the standard normal distribution.
double	autopas::utils::Math::normalCDF (double x)
	Cumulative distribution function CDF of the standard normal distribution.
double	autopas::utils::Math::sigmoid (double x)
	Sigmoid logistic function.
bool	autopas::utils::Math::isNearRel (double a, double b, double maxRelativeDifference=1e-9)
	Determines if two doubles are near each other.
bool	autopas::utils::Math::isNearAbs (double a, double b, double maxAbsoluteDifference)
	Determines if two doubles are near each other.
double	autopas::utils::Math::roundFixed (double d, int fixedPrecision)
	Round a floating point number to a given number of decimal digits.
double	autopas::utils::Math::roundFloating (double d, int floatingPrecision)
	Round a floating point number to a given floating precision.
Eigen::VectorXd	autopas::utils::Math::makeVectorXd (const std::vector< double > &elements)
	Create a vector of doubles from given elements.
Eigen::VectorXi	autopas::utils::Math::makeVectorXi (const std::vector< int > &elements)
	Create a vector of ints from given elements.

Variables
const double	autopas::utils::Math::normalScale = 1. / std::sqrt(2 * M_PI)
	Factor of PDF of standard normal distribution.

Detailed Description

Author

Jan Nguyen

Date

18.08.19

Function Documentation

isNearAbs()

bool autopas::utils::Math::isNearAbs	(	double	a,
		double	b,
		double	maxAbsoluteDifference
	)

Determines if two doubles are near each other.

This function should be preferred to comparing with ==.

Parameters

a
b
maxAbsoluteDifference	inclusive

Returns

isNearRel()

bool autopas::utils::Math::isNearRel	(	double	a,
		double	b,
		double	maxRelativeDifference = 1e-9
	)

Determines if two doubles are near each other.

This function should be preferred to comparing with ==.

Parameters

a
b
maxRelativeDifference	inclusive, relative to max(|a|, |b|).

Returns

makeVectorXd()

Eigen::VectorXd autopas::utils::Math::makeVectorXd

(

const std::vector< double > &

elements

)

Create a vector of doubles from given elements.

Parameters

elements

Returns

makeVectorXi()

Eigen::VectorXi autopas::utils::Math::makeVectorXi

(

const std::vector< int > &

elements

)

Create a vector of ints from given elements.

Parameters

elements

Returns

normalCDF()

double autopas::utils::Math::normalCDF

(

double

x

)

Cumulative distribution function CDF of the standard normal distribution.

Parameters

x

Returns

CDF(x)

normalPDF()

double autopas::utils::Math::normalPDF

(

double

x

)

Probability density function PDF of the standard normal distribution.

Parameters

x

Returns

PDF(x)

pow()

template<size_t exponent, class T >

T autopas::utils::Math::pow

(

const T &

base

)

No-overhead power function with exponent known at compile time.

Template Parameters

exponent
T

Parameters

base

Returns

roundFixed()

double autopas::utils::Math::roundFixed	(	double	d,
		int	fixedPrecision
	)

Round a floating point number to a given number of decimal digits.

Parameters

d	Number to round.
fixedPrecision	Number of decimal digits. Negative values lead to rounding of digits left of the decimal.

Returns

d rounded to the given number of digits.

roundFloating()

double autopas::utils::Math::roundFloating	(	double	d,
		int	floatingPrecision
	)

Round a floating point number to a given floating precision.

Parameters

d	Number to round.
floatingPrecision	Number of significant digits. Values <0 will return in 0.

Returns

d rounded to the given number of digits.

safeAdd() [1/2]

template<class Float_t , std::enable_if_t< std::is_floating_point_v< Float_t >, bool > = true>

Float_t autopas::utils::Math::safeAdd	(	const Float_t &	a,
		const Float_t &	b,
		const Float_t &	valUnderflow = -std::numeric_limits<Float_t>::max(),
		const Float_t &	valOverflow = std::numeric_limits<Float_t>::max()
	)

Addition function for floating point types that is safe against over and underflow.

If over or underflow is detected, the function returns the specified values.

Note

Underflow here refers to a value more negative than representable and not the underflow gap around zero.

Template Parameters

Float_t

Parameters

a
b
valUnderflow	Return value in case of underflow.
valOverflow	Return value in case of overflow.

Returns

Sum or valUnderflow or valOverflow.

safeAdd() [2/2]

template<class Int_t , std::enable_if_t< std::is_integral_v< Int_t >, bool > = true>

Int_t autopas::utils::Math::safeAdd	(	const Int_t &	a,
		const Int_t &	b,
		const Int_t &	valUnderflow = std::numeric_limits<Int_t>::min(),
		const Int_t &	valOverflow = std::numeric_limits<Int_t>::max()
	)

Addition function for integer types that is safe against over and underflow.

If over or underflow is detected, the function returns the specified values.

Template Parameters

Int_t

Parameters

a
b
valUnderflow	Return value in case of underflow.
valOverflow	Return value in case of overflow.

Returns

Sum or valOverflow or valUnderflow.

safeMul() [1/2]

template<class Float_t , std::enable_if_t< std::is_floating_point_v< Float_t >, bool > = true>

Float_t autopas::utils::Math::safeMul	(	const Float_t &	a,
		const Float_t &	b,
		const Float_t &	valUnderflow = -std::numeric_limits<Float_t>::max(),
		const Float_t &	valOverflow = std::numeric_limits<Float_t>::max()
	)

Multiplication function for floating point types that is safe against over and underflow.

If over or underflow is detected, the function returns the specified values.

Note

Underflow here refers to a value more negative than representable and not the underflow gap around zero.

Template Parameters

Float_t

Parameters

a
b
valUnderflow	Return value in case of underflow.
valOverflow	Return value in case of overflow.

Returns

Product or valUnderflow or valOverflow.

safeMul() [2/2]

template<class Int_t , std::enable_if_t< std::is_integral_v< Int_t >, bool > = true>

Int_t autopas::utils::Math::safeMul	(	const Int_t &	a,
		const Int_t &	b,
		const Int_t &	valUnderflow = std::numeric_limits<Int_t>::min(),
		const Int_t &	valOverflow = std::numeric_limits<Int_t>::max()
	)

Multiplication function for integer types that is safe against over and underflow.

If over or underflow is detected, the function returns the specified values.

Template Parameters

Int_t

Parameters

a
b
valUnderflow	Return value in case of underflow.
valOverflow	Return value in case of overflow.

Returns

Product or valUnderflow or valOverflow.

safeSub() [1/2]

template<class Float_t , std::enable_if_t< std::is_floating_point_v< Float_t >, bool > = true>

Float_t autopas::utils::Math::safeSub	(	const Float_t &	a,
		const Float_t &	b,
		const Float_t &	valUnderflow = -std::numeric_limits<Float_t>::max(),
		const Float_t &	valOverflow = std::numeric_limits<Float_t>::max()
	)

Addition function for floating point types that is safe against over and underflow.

If over or underflow is detected, the function returns the specified values.

Note

Underflow here refers to a value more negative than representable and not the underflow gap around zero.

Template Parameters

Float_t

Parameters

a
b
valUnderflow	Return value in case of underflow.
valOverflow	Return value in case of overflow.

Returns

Sum or valUnderflow or valOverflow.

safeSub() [2/2]

template<class Int_t , std::enable_if_t< std::is_integral_v< Int_t >, bool > = true>

Int_t autopas::utils::Math::safeSub	(	const Int_t &	a,
		const Int_t &	b,
		const Int_t &	valUnderflow = std::numeric_limits<Int_t>::min(),
		const Int_t &	valOverflow = std::numeric_limits<Int_t>::max()
	)

Subtraction function for integer types that is safe against over and underflow.

If over or underflow is detected, the function returns the specified values.

Template Parameters

Int_t

Parameters

a
b
valUnderflow	Return value in case of underflow.
valOverflow	Return value in case of overflow.

Returns

Difference or valOverflow or valUnderflow.

sigmoid()

double autopas::utils::Math::sigmoid

(

double

x

)

Sigmoid logistic function.

Parameters

x

Returns

S(x)