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

Include dependency graph for Math.h:

This graph shows which files directly or indirectly include this file:

Classes
struct	autopas::utils::Math::internal::int_t_impl< FloatType >
	Helper struct to get the correspondingly sized integer for a given floating type. More...

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.

Typedefs
template<std::floating_point FloatType>
using	autopas::utils::Math::int_t = typename internal::int_t_impl< FloatType >::type
	Returns the correspondingly sized integer type for a given float.

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.

template<std::floating_point FloatType>
bool	autopas::utils::Math::isInUlp (FloatType lhs, FloatType rhs, unsigned int ulpDistance=MAX_ULP_DISTANCE)
	Function for comparing closeness of two floating point numbers using ULP (Units in the Last Place) method.

template<std::floating_point FloatType>
bool	autopas::utils::Math::isNearRel (FloatType a, FloatType b, double maxRelativeDifference=EPSILON_RELATIVE_EQUALITY)
	Determines if two doubles are near each other.

template<std::floating_point FloatType>
bool	autopas::utils::Math::isNearAbs (FloatType a, FloatType 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.

constexpr double	autopas::utils::Math::EPSILON_RELATIVE_EQUALITY = 1e-9
	This default relative EPSILON used for the `isNearRel` function.

constexpr unsigned int	autopas::utils::Math::MAX_ULP_DISTANCE = 4
	The default maximal allowed ULP (Units in the Last Place) distance utilized for FloatingPoint comparisons.

template<typename T >
constexpr size_t	autopas::utils::Math::internal::bit_size_v = sizeof(T) * 8
	Helper to find out the bit size of a given type.

Detailed Description

Author: Jan Nguyen

Date: 18.08.19

Typedef Documentation

◆ int_t

template<std::floating_point FloatType>

using autopas::utils::Math::int_t = typedef typename internal::int_t_impl<FloatType>::type

Returns the correspondingly sized integer type for a given float.

E.g. int_t of float would be int32_t.

Function Documentation

◆ isInUlp()

template<std::floating_point FloatType>

bool autopas::utils::Math::isInUlp	(	FloatType	lhs,
		FloatType	rhs,
		unsigned int	ulpDistance = `MAX_ULP_DISTANCE`
	)

Function for comparing closeness of two floating point numbers using ULP (Units in the Last Place) method.

Template Parameters

FloatType must be either double or float

Parameters

lhs	The left hand side floating point number to compare.
rhs	The right hand side floating point number to compare.
ulpDistance	The maximum acceptable ULP distance between the two floating points for which they would be considered near each other, defaults to `autopas::utils::Math::MAX_ULP_DISTANCE`

Returns: true if the ULP distance between lhs and rhs is less than or equal to the provided ulpDistance value, otherwise, false. Returns true if both numbers are exactly the same. Returns false if the signs do not match.

Note: The ULP distance between 3.0 and std::nextafter(3.0, INFINITY) would be 1, the ULP distance of 3.0 and std::nextafter(std::nextafter(3.0, INFINITY), INFINITY) would be 2, etc.

See also: https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/

◆ isNearAbs()

template<std::floating_point FloatType>

bool autopas::utils::Math::isNearAbs	(	FloatType	a,
		FloatType	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()

template<std::floating_point FloatType>

bool autopas::utils::Math::isNearRel	(	FloatType	a,
		FloatType	b,
		double	maxRelativeDifference = `EPSILON_RELATIVE_EQUALITY`
	)

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\|), defaults to `autopas::utils::Math::EPSILON_RELATIVE_EQUALITY`

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)

Variable Documentation

◆ bit_size_v

template<typename T >

constexpr size_t autopas::utils::Math::internal::bit_size_v = sizeof(T) * 8

constexpr

Helper to find out the bit size of a given type.

Template Parameters

T	any type T

◆ MAX_ULP_DISTANCE

constexpr unsigned int autopas::utils::Math::MAX_ULP_DISTANCE = 4

constexpr

The default maximal allowed ULP (Units in the Last Place) distance utilized for FloatingPoint comparisons.

This is also the value utilized in GoogleTest for their DoubleEq() and FloatEq() Matchers.

See also: https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/

Classes

Namespaces

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ int_t

Function Documentation

◆ isInUlp()

◆ isNearAbs()

◆ isNearRel()

◆ makeVectorXd()

◆ makeVectorXi()

◆ normalCDF()

◆ normalPDF()

◆ pow()

◆ roundFixed()

◆ roundFloating()

◆ safeAdd() [1/2]

◆ safeAdd() [2/2]

◆ safeMul() [1/2]

◆ safeMul() [2/2]

◆ safeSub() [1/2]

◆ safeSub() [2/2]

◆ sigmoid()

Variable Documentation

◆ bit_size_v

◆ MAX_ULP_DISTANCE