Namespaces
	Detail

Functions
template<typename TReturn , typename TInput >
TReturn	CastWithRangeCheck (TInput x)

template<TReturn , typename TInput >
	Ceil (TInput x)

template<typename T >
bool	FloatAlmostEqual (T x1, T x2, typename Detail::FloatIEEE< T >::IntType maxUlps=4, typename Detail::FloatIEEE< T >::FloatType maxAbsoluteDifference=0.1 *NumericTraits< T >::epsilon())

template<typename T >
Detail::FloatIEEE< T >::IntType	FloatDifferenceULP (T x1, T x2)

template<TReturn , typename TInput >
	Floor (TInput x)

template<typename TReturn , typename TInput >
TReturn	Round (TInput x)

template<TReturn , typename TInput >
	RoundHalfIntegerToEven (TInput x)

template<TReturn , typename TInput >
	RoundHalfIntegerUp (TInput x)

Variables
static const double	e = 2.7182818284590452354

static const double	ln10 = 2.30258509299404568402

static const double	ln2 = 0.69314718055994530942

static const double	log10e = 0.43429448190325182765

static const double	log2e = 1.4426950408889634074

static const double	one_over_pi = 0.31830988618379067154

static const double	one_over_sqrt2pi = 0.39894228040143267794

static const double	pi = 3.14159265358979323846

static const double	pi_over_2 = 1.57079632679489661923

static const double	pi_over_4 = 0.78539816339744830962

static const double	sqrt1_2 = 0.70710678118654752440

static const double	sqrt2 = 1.41421356237309504880

static const double	two_over_pi = 0.63661977236758134308

static const double	two_over_sqrtpi = 1.12837916709551257390

Function Documentation

template<typename TReturn , typename TInput >

TReturn itk::Math::CastWithRangeCheck ( TInput x )

inline

This class requires OnlyDefinedForIntegerTypes1 in the form of ( itk::Concept::IsInteger< TReturn > )

This class requires OnlyDefinedForIntegerTypes2 in the form of ( itk::Concept::IsInteger< TInput > )

Definition at line 180 of file itkMath.h.

References itk::NumericTraits< T >::IsPositive(), and itkConceptMacro.

template<TReturn , typename TInput >

itk::Math::Ceil ( TInput x )

Round towards plus infinity.

The behavior of overflow is undefined due to numerous implementations.

Warning: argument absolute value must be less than INT_MAX/2 for vnl_math_ceil to be guaranteed to work.; We also assume that the rounding mode is not changed from the default one (or at least that it is always restored to the default one).

template<typename T >

bool itk::Math::FloatAlmostEqual	(	T	x1,
		T	x2,
		typename Detail::FloatIEEE< T >::IntType	maxUlps = `4`,
		typename Detail::FloatIEEE< T >::FloatType	maxAbsoluteDifference = `0.1*NumericTraits<T>::epsilon()`
	)

inline

Compare two floats and return if they are effectively equal.

Determining when floats are almost equal is difficult because of their IEEE bit representation. This function uses the integer representation of the float to determine if they are almost equal.

The implementation is based off the explanation in the white papers:

This function is not a cure-all, and reading those articles is important to understand its appropriate use in the context of ULPs, zeros, subnormals, infinities, and NANs. For example, it is preferable to use this function on two floats directly instead of subtracting them and comparing them to zero.

The tolerance is specified in ULPs (units in the last place), i.e. how many floats there are in between the numbers. Therefore, the tolerance depends on the magnitude of the values that are being compared. A second tolerance is a maximum difference allowed, which is important when comparing numbers close to zero.

A NAN compares as not equal to a number, but two NAN's may compare as equal to each other.

Parameters

x1	first floating value to compare
x2	second floating values to compare
maxUlps	maximum units in the last place to be considered equal
maxAbsoluteDifference	maximum absolute difference to be considered equal

Definition at line 259 of file itkMath.h.

References FloatDifferenceULP().

template<typename T >

Detail::FloatIEEE<T>::IntType itk::Math::FloatDifferenceULP	(	T	x1,
		T	x2
	)

inline

Return the signed distance in ULPs (units in the last place) between two floats.

This is the signed distance, i.e., if x1 > x2, then the result is positive.

See Also: FloatAlmostEqual

Definition at line 220 of file itkMath.h.

References itk::Math::Detail::FloatIEEE< T >::AsULP().

Referenced by FloatAlmostEqual().

template<TReturn , typename TInput >

itk::Math::Floor ( TInput x )

Round towards minus infinity.

The behavior of overflow is undefined due to numerous implementations.

Warning: argument absolute value must be less than NumbericTraits<TReturn>::max()/2 for vnl_math_floor to be guaranteed to work.; We also assume that the rounding mode is not changed from the default one (or at least that it is always restored to the default one).

template<typename TReturn , typename TInput >

TReturn itk::Math::Round ( TInput x )

inline

Round towards nearest integer (This is a synonym for RoundHalfIntegerUp)

Template Parameters

TReturn	must be an integer type
TInput	must be float or double

See Also: RoundHalfIntegerUp<TReturn, TInput>()

Definition at line 149 of file itkMath.h.

template<TReturn , typename TInput >

itk::Math::RoundHalfIntegerToEven ( TInput x )

Round towards nearest integer.

Template Parameters

TReturn	must be an integer type
TInput	must be float or double halfway cases are rounded towards the nearest even integer, e.g. * RoundHalfIntegerToEven( 1.5) == 2 * RoundHalfIntegerToEven(-1.5) == -2 * RoundHalfIntegerToEven( 2.5) == 2 * RoundHalfIntegerToEven( 3.5) == 4 *

The behavior of overflow is undefined due to numerous implementations.

Warning: We assume that the rounding mode is not changed from the default one (or at least that it is always restored to the default one).

template<TReturn , typename TInput >

itk::Math::RoundHalfIntegerUp ( TInput x )

Round towards nearest integer.

Template Parameters

TReturn	must be an integer type
TInput	must be float or double halfway cases are rounded upward, e.g. * RoundHalfIntegerUp( 1.5) == 2 * RoundHalfIntegerUp(-1.5) == -1 * RoundHalfIntegerUp( 2.5) == 3 *

The behavior of overflow is undefined due to numerous implementations.

Warning: The argument absolute value must be less than NumbericTraits<TReturn>::max()/2 for RoundHalfIntegerUp to be guaranteed to work.; We also assume that the rounding mode is not changed from the default one (or at least that it is always restored to the default one).