This class provides basic numeric functionalities. More...

Public Member Functions
constexpr double	eps ()
	Specialization of NumericT::eps(). More...

constexpr float	eps ()
	Specialization of NumericT::eps(). More...

constexpr signed char	eps ()
	Specialization of NumericT::eps(). More...

constexpr unsigned char	eps ()
	Specialization of NumericT::eps(). More...

constexpr short	eps ()
	Specialization of NumericT::eps(). More...

constexpr unsigned short	eps ()
	Specialization of NumericT::eps(). More...

constexpr int	eps ()
	Specialization of NumericT::eps(). More...

constexpr unsigned int	eps ()
	Specialization of NumericT::eps(). More...

constexpr long	eps ()
	Specialization of NumericT::eps(). More...

constexpr unsigned long	eps ()
	Specialization of NumericT::eps(). More...

constexpr long long	eps ()
	Specialization of NumericT::eps(). More...

constexpr unsigned long long	eps ()
	Specialization of NumericT::eps(). More...

constexpr double	weakEps ()
	Specialization of NumericT::weakEps(). More...

constexpr float	weakEps ()
	Specialization of NumericT::weakEps(). More...

constexpr signed char	weakEps ()
	Specialization of NumericT::weakEps(). More...

constexpr unsigned char	weakEps ()
	Specialization of NumericT::weakEps(). More...

constexpr short	weakEps ()
	Specialization of NumericT::weakEps(). More...

constexpr unsigned short	weakEps ()
	Specialization of NumericT::weakEps(). More...

constexpr int	weakEps ()
	Specialization of NumericT::weakEps(). More...

constexpr unsigned int	weakEps ()
	Specialization of NumericT::weakEps(). More...

constexpr long	weakEps ()
	Specialization of NumericT::weakEps(). More...

constexpr unsigned long	weakEps ()
	Specialization of NumericT::weakEps(). More...

constexpr long long	weakEps ()
	Specialization of NumericT::weakEps(). More...

constexpr unsigned long long	weakEps ()
	Specialization of NumericT::weakEps(). More...

signed char	abs (const signed char value)
	Specialization of NumericT::abs(). More...

unsigned char	abs (const unsigned char value)
	Specialization of NumericT::abs(). More...

short	abs (const short value)
	Specialization of NumericT::abs(). More...

unsigned short	abs (const unsigned short value)
	Specialization of NumericT::abs(). More...

int	abs (const int value)
	Specialization of NumericT::abs(). More...

unsigned int	abs (const unsigned int value)
	Specialization of NumericT::abs(). More...

long	abs (const long value)
	Specialization of NumericT::abs(). More...

unsigned long	abs (const unsigned long value)
	Specialization of NumericT::abs(). More...

long long	abs (const long long value)
	Specialization of NumericT::abs(). More...

unsigned long long	abs (const unsigned long long value)
	Specialization of NumericT::abs(). More...

double	abs (const double value)
	Specialization of NumericT::abs(). More...

float	abs (const float value)
	Specialization of NumericT::abs(). More...

unsigned char	secureAbs (const signed char value)
	Specialization of NumericT::secureAbs(). More...

unsigned char	secureAbs (const unsigned char value)
	Specialization of NumericT::secureAbs(). More...

unsigned short	secureAbs (const short value)
	Specialization of NumericT::secureAbs(). More...

unsigned short	secureAbs (const unsigned short value)
	Specialization of NumericT::secureAbs(). More...

unsigned int	secureAbs (const int value)
	Specialization of NumericT::secureAbs(). More...

unsigned int	secureAbs (const unsigned int value)
	Specialization of NumericT::secureAbs(). More...

unsigned long	secureAbs (const long value)
	Specialization of NumericT::secureAbs(). More...

unsigned long	secureAbs (const unsigned long value)
	Specialization of NumericT::secureAbs(). More...

unsigned long long	secureAbs (const long long value)
	Specialization of NumericT::secureAbs(). More...

unsigned long long	secureAbs (const unsigned long long value)
	Specialization of NumericT::secureAbs(). More...

double	secureAbs (const double value)
	Specialization of NumericT::secureAbs(). More...

float	secureAbs (const float value)
	Specialization of NumericT::secureAbs(). More...

float	sqrt (const float value)
	Specialization of NumericT::sqrt(). More...

int	sqrt (const int value)
	Specialization of NumericT::sqrt(). More...

float	sin (const float value)
	Specialization of NumericT::sin(). More...

float	cos (const float value)
	Specialization of NumericT::cos(). More...

float	tan (const float value)
	Specialization of NumericT::tan(). More...

float	atan (const float value)
	Specialization of NumericT::atan(). More...

float	exp (const float value)

float	log (const float value)

float	log1p (const float value)

float	log2 (const float value)
	Specialization of NumericT::log2(). More...

float	log10 (const float value)

float	atan2 (const float y, const float x)
	Specialization of NumericT::atan2(). More...

float	fmod (const float valueA, const float valueB)
	Specialization of NumericT::fmod(). More...

float	pow (const float x, const float y)
	Specialization of NumericT::pow(). More...

constexpr unsigned int	factorial (const unsigned int &value)

float	ceil (const float value)
	Specialization of NumericT::ceil(). More...

double	ceil (const double value)
	Specialization of NumericT::ceil(). More...

long double	ceil (const long double value)
	Specialization of NumericT::ceil(). More...

float	floor (const float value)
	Specialization of NumericT::floor(). More...

double	floor (const double value)
	Specialization of NumericT::floor(). More...

long double	floor (const long double value)
	Specialization of NumericT::floor(). More...

constexpr bool	isEqualEps (const signed char value)

constexpr bool	isEqualEps (const unsigned char value)

constexpr bool	isEqualEps (const short value)

constexpr bool	isEqualEps (const unsigned short value)

constexpr bool	isEqualEps (const int value)

constexpr bool	isEqualEps (const unsigned int value)

constexpr bool	isEqualEps (const long value)

constexpr bool	isEqualEps (const unsigned long value)

constexpr bool	isEqualEps (const long long value)

constexpr bool	isEqualEps (const unsigned long long value)

constexpr bool	isWeakEqualEps (const signed char value)

constexpr bool	isWeakEqualEps (const unsigned char value)

constexpr bool	isWeakEqualEps (const short value)

constexpr bool	isWeakEqualEps (const unsigned short value)

constexpr bool	isWeakEqualEps (const int value)

constexpr bool	isWeakEqualEps (const unsigned int value)

constexpr bool	isWeakEqualEps (const long value)

constexpr bool	isWeakEqualEps (const unsigned long value)

constexpr bool	isWeakEqualEps (const long long value)

constexpr bool	isWeakEqualEps (const unsigned long long value)

constexpr bool	isNotEqualEps (const signed char value)

constexpr bool	isNotEqualEps (const unsigned char value)

constexpr bool	isNotEqualEps (const short value)

constexpr bool	isNotEqualEps (const unsigned short value)

constexpr bool	isNotEqualEps (const int value)

constexpr bool	isNotEqualEps (const unsigned int value)

constexpr bool	isNotEqualEps (const long value)

constexpr bool	isNotEqualEps (const unsigned long value)

constexpr bool	isNotEqualEps (const long long value)

constexpr bool	isNotEqualEps (const unsigned long long value)

constexpr bool	isNotWeakEqualEps (const signed char value)

constexpr bool	isNotWeakEqualEps (const unsigned char value)

constexpr bool	isNotWeakEqualEps (const short value)

constexpr bool	isNotWeakEqualEps (const unsigned short value)

constexpr bool	isNotWeakEqualEps (const int value)

constexpr bool	isNotWeakEqualEps (const unsigned int value)

constexpr bool	isNotWeakEqualEps (const long value)

constexpr bool	isNotWeakEqualEps (const unsigned long value)

constexpr bool	isNotWeakEqualEps (const long long value)

constexpr bool	isNotWeakEqualEps (const unsigned long long value)

bool	isEqual (const signed char first, const signed char second)

bool	isEqual (const unsigned char first, const unsigned char second)

bool	isEqual (const short first, const short second)

bool	isEqual (const unsigned short first, const unsigned short second)

bool	isEqual (const int first, const int second)

bool	isEqual (const unsigned int first, const unsigned int second)

bool	isEqual (const long first, const long second)

bool	isEqual (const unsigned long first, const unsigned long second)

bool	isEqual (const long long first, const long long second)

bool	isEqual (const unsigned long long first, const unsigned long long second)

bool	isEqual (const signed char first, const signed char second, const signed char epsilon)

bool	isEqual (const short first, const short second, const short epsilon)

bool	isEqual (const int first, const int second, const int epsilon)

bool	isEqual (const long first, const long second, const long epsilon)

bool	isEqual (const long long first, const long long second, const long long epsilon)

bool	isEqual (const unsigned char first, const unsigned char second, const unsigned char epsilon)

bool	isEqual (const unsigned short first, const unsigned short second, const unsigned short epsilon)

bool	isEqual (const unsigned int first, const unsigned int second, const unsigned int epsilon)

bool	isEqual (const unsigned long first, const unsigned long second, const unsigned long epsilon)

bool	isEqual (const unsigned long long first, const unsigned long long second, const unsigned long long epsilon)

bool	isWeakEqual (const int first, const int second)

bool	isNotEqual (const signed char first, const signed char second)

bool	isNotEqual (const unsigned char first, const unsigned char second)

bool	isNotEqual (const short first, const short second)

bool	isNotEqual (const unsigned short first, const unsigned short second)

bool	isNotEqual (const int first, const int second)

bool	isNotEqual (const unsigned int first, const unsigned int second)

bool	isNotEqual (const long first, const long second)

bool	isNotEqual (const unsigned long first, const unsigned long second)

bool	isNotEqual (const long long first, const long long second)

bool	isNotEqual (const unsigned long long first, const unsigned long long second)

bool	isNotWeakEqual (const signed char first, const signed char second)

bool	isNotWeakEqual (const unsigned char first, const unsigned char second)

bool	isNotWeakEqual (const short first, const short second)

bool	isNotWeakEqual (const unsigned short first, const unsigned short second)

bool	isNotWeakEqual (const int first, const int second)

bool	isNotWeakEqual (const unsigned int first, const unsigned int second)

bool	isNotWeakEqual (const long first, const long second)

bool	isNotWeakEqual (const unsigned long first, const unsigned long second)

bool	isNotWeakEqual (const long long first, const long long second)

bool	isNotWeakEqual (const unsigned long long first, const unsigned long long second)

bool	isNotEqual (const signed char first, const signed char second, const signed char epsilon)

bool	isNotEqual (const short first, const short second, const short epsilon)

bool	isNotEqual (const int first, const int second, const int epsilon)

bool	isNotEqual (const long first, const long second, const long epsilon)

bool	isNotEqual (const long long first, const long long second, const long long epsilon)

bool	isNotEqual (const unsigned char first, const unsigned char second, const unsigned char epsilon)

bool	isNotEqual (const unsigned short first, const unsigned short second, const unsigned short epsilon)

bool	isNotEqual (const unsigned int first, const unsigned int second, const unsigned int epsilon)

bool	isNotEqual (const unsigned long first, const unsigned long second, const unsigned long epsilon)

bool	isNotEqual (const unsigned long long first, const unsigned long long second, const unsigned long long epsilon)

float	asin (const float value)
	Specialization of NumericT::asin(). More...

float	acos (const float value)
	Specialization of NumericT::acos(). More...

bool	isNan (const float value)

bool	isNan (const double value)

bool	isInf (const float value)

bool	isInf (const double value)

bool	isInf (const long double value)

constexpr double	copySign (const double first, const double second)
	Specialization of NumericT::copySign(). More...

constexpr float	copySign (const float first, const float second)
	Specialization of NumericT::copySign(). More...

constexpr double	invertSign (const double first, const double second)
	Specialization of NumericT::invertSign(). More...

constexpr float	invertSign (const float first, const float second)
	Specialization of NumericT::invertSign(). More...

Static Public Member Functions
static constexpr T	pi ()
	Returns PI which is equivalent to 180 degree. More...

static constexpr T	pi2 ()
	Returns 2*PI which is equivalent to 360 degree. More...

static constexpr T	pi_2 ()
	Returns PI/2 which is equivalent to 90 degree. More...

static constexpr T	pi_3 ()
	Returns PI/3 which is equivalent to 60 degree. More...

static constexpr T	pi_4 ()
	Returns PI/4 which is equivalent to 45 degree. More...

static constexpr T	squarePi ()
	Returns the square of PI i.e., PI^2. More...

static constexpr T	squarePi2 ()
	Returns the square of two PI i.e., (2*PI)^2. More...

static constexpr T	squarePi_2 ()
	Returns the square of PI half i.e., (PI/2)^2. More...

static constexpr T	e ()
	Returns the euler's number. More...

static constexpr T	eps ()
	Returns a small epsilon. More...

static constexpr T	weakEps ()
	Returns a weak epsilon. More...

static T	abs (const T value)
	Returns the absolute value of a given value. More...

static UnsignedTyper< T >::Type	secureAbs (const T value)
	Returns the absolute value of a given value while the return value is guaranteed to be the absolute value of the input value. More...

static constexpr T	sqr (const T value)
	Returns the square of a given value. More...

static T	sum (const T *values, const size_t number)
	Returns the sum of given values. More...

static T	summedSqr (const T *values, const size_t number)
	Returns the summed squares of a given values. More...

static constexpr T	sqrDistance (const T value0, const T value1)
	Returns the square distance between two values. More...

static T	sqrt (const T value)
	Returns the square root of a given value. More...

static std::complex< T >	sqrt (const std::complex< T > &value)
	Returns the square root of a given value. More...

static T	sin (const T value)
	Returns the sine of a given value. More...

static T	cos (const T value)
	Returns the cosine of a given value. More...

static T	tan (const T value)
	Returns the tangent of a given value. More...

static T	asin (const T value)
	Returns the arcsine of a given value. More...

static T	acos (const T value)
	Returns the arccosine of a given value. More...

static T	atan (const T value)
	Returns the arctangent of a given value. More...

static T	atan2 (const T y, const T x)
	Returns the arctangent of a given value in radian. More...

static T	exp (const T value)
	Returns the base-e exponential function of a given value. More...

static T	log (const T value)
	Returns the natural logarithm of a given value (the logarithm to the base e). More...

static T	log1p (const T value)
	Returns the natural logarithm of a given value plus 1 (the logarithm to the base e). More...

static T	log2 (const T value)
	Returns the logarithm to base 2 of a given value. More...

static T	log10 (const T value)
	Returns the logarithm to base 10 of a given value. More...

static T	fmod (const T valueA, const T valueB)
	Returns the floating-point remainder of a given value. More...

static T	dot (const T vectorA, const T vectorB, const size_t size)
	Returns the dot product for two vectors. More...

static T	angleAdjustPositive (const T angle)
	Adjusts an arbitrary angle into the range of [0.0, 2PI). More...

static T	angleAdjustPositiveHalf (const T angle)
	Adjusts an arbitrary angle into the range of [0.0, PI). More...

static T	angleAdjustNull (const T angle)
	Adjusts an arbitrary angle into the range of (-PI, PI]. More...

static bool	angleIsEqual (const T angleA, const T angleB)
	Returns whether two angles represent the same angle up to a small epsilon. More...

static bool	angleIsWeakEqual (const T angleA, const T angleB)
	Returns whether two angles represent the same angle up to a weak epsilon. More...

static bool	angleIsEqual (const T angleA, const T angleB, const T epsilon)
	Returns whether two angles represent the same angle up to a given epsilon. More...

static bool	angleIsBelowThreshold (const T angleA, const T angleB, const T threshold)
	Returns whether the angular difference (distance) between two angles is smaller than a specified threshold. More...

static T	angleDistance (const T angleA, const T angleB)
	Returns the angular difference (distance between two angles). More...

static T	pow (const T x, const T y)
	Returns x raised to the power of y. More...

static std::complex< T >	pow (const std::complex< T > &x, const T y)
	Returns x raised to the power of y. More...

static constexpr T	integerPow (const T x, const unsigned int y)
	Returns x raised to the power of y while y is an integer. More...

static constexpr T	factorial (const T &value)
	Returns the factorial for a given value. More...

static constexpr T	binomialCoefficient (const T &n, const T &k)
	Returns the binomial coefficient for two binomial parameters. More...

static T	ceil (const T value)
	Returns the smallest integer value that is not less than the given value. More...

static T	floor (const T value)
	Returns the largest integer value that is not greater than the given value. More...

static constexpr int32_t	round32 (const T value)
	Returns the rounded 32 bit integer value of a given value. More...

static constexpr int64_t	round64 (const T value)
	Returns the rounded 64 bit integer value of a given value. More...

static constexpr T	ratio (const T nominator, const T denominator, const T fallback=T(1))
	Returns the ratio between two values if the denominator is not equal a small epsilon. More...

static constexpr bool	isEqualEps (const T value)
	Returns whether a value is smaller than or equal to a small epsilon. More...

static constexpr bool	isEqualEps (const std::complex< T > &value)
	Returns whether a complex value is smaller than or equal to a small epsilon. More...

static constexpr bool	isWeakEqualEps (const T value)
	Returns whether a value is smaller than or equal to a weak epsilon. More...

static constexpr bool	isWeakEqualEps (const std::complex< T > &value)
	Returns whether a complex value is smaller than or equal to a weak epsilon. More...

static constexpr bool	isNotEqualEps (const T value)
	Returns whether a value is not smaller than or equal to a small epsilon. More...

static constexpr bool	isNotEqualEps (const std::complex< T > &value)
	Returns whether a complex value is not smaller than or equal to a small epsilon. More...

static constexpr bool	isNotWeakEqualEps (const T value)
	Returns whether a value is not smaller than or equal to a weak epsilon. More...

static constexpr bool	isNotWeakEqualEps (const std::complex< T > &value)
	Returns whether a complex value is not smaller than or equal to a weak epsilon. More...

static bool	isEqual (const T first, const T second)
	Returns whether two values are equal up to a small epsilon. More...

static bool	isEqual (const std::complex< T > &first, const std::complex< T > &second)
	Returns whether two complex values are equal up to a small epsilon. More...

static bool	isWeakEqual (const T first, const T second)
	Returns whether two values a equal up to a weak epsilon. More...

static bool	isWeakEqual (const std::complex< T > &first, const std::complex< T > &second)
	Returns whether two complex values are equal up to a weak epsilon. More...

static bool	isEqual (const T first, const T second, const T epsilon)
	Returns whether two values are equal up to a given epsilon. More...

static bool	isEqual (const std::complex< T > &first, const std::complex< T > &second, const T epsilon)
	Returns whether two complex values are equal up to a given epsilon. More...

template<int tMagnitude>
static bool	isEqual (const T first, const T second, const T referenceEpsilon)
	Returns whether two values are equal up to a dynamic epsilon which is adjusted due to the magnitude of both values and the reference magnitude. More...

static bool	isNotEqual (const T first, const T second)
	Returns whether two values are not equal up to a small epsilon. More...

static bool	isNotEqual (const std::complex< T > &first, const std::complex< T > &second)
	Returns whether two complex values are not equal up to a small epsilon. More...

static bool	isNotWeakEqual (const T first, const T second)
	Returns whether two values are not equal up to a weak epsilon. More...

static bool	isNotWeakEqual (const std::complex< T > &first, const std::complex< T > &second)
	Returns whether two complex values are not equal up to a weak epsilon. More...

static bool	isNotEqual (const T first, const T second, const T epsilon)
	Returns whether two values are not equal up to a given epsilon. More...

static bool	isNotEqual (const std::complex< T > &first, const std::complex< T > &second, const T epsilon)
	Returns whether two complex values are not equal up to a given epsilon. More...

static constexpr bool	isInsideRange (const T lower, const T value, const T upper, const T epsilon=NumericT< T >::eps())
	Returns whether a value lies between a given range up to a provided epsilon border. More...

static constexpr bool	isInsideWeakRange (const T lower, const T value, const T upper)
	Returns whether a value lies between a given range up to a weak epsilon border. More...

static constexpr bool	isBelow (const T value, const T upper, const T epsilon=NumericT< T >::eps())
	Returns whether a parameter lies on or below a given border tolerating a small epsilon. More...

static constexpr bool	isAbove (const T value, const T lower, const T epsilon=NumericT< T >::eps())
	Returns whether a parameter lies on or above a given border tolerating a small epsilon. More...

static constexpr T	nan ()
	Returns a value which is not a number (nan). More...

static bool	isNan (const T value)
	Returns whether a given value is not a number. More...

static bool	isNan (const std::complex< T > &value)
	Returns whether a given value is not a number. More...

static constexpr T	inf ()
	Returns a value which is positive infinity. More...

static bool	isInf (const T value)
	Returns whether a given value is positive or negative infinity. More...

static bool	isInf (const std::complex< T > &value)
	Returns whether a given value is positive or negative infinity. More...

template<typename TValue >
static bool	isInsideValueRange (const TValue &value)
	Returns whether a given value of an arbitrary data type fits into the value range of 'T'. More...

static constexpr T	deg2rad (const T deg)
	Converts deg to rad. More...

static constexpr T	rad2deg (const T rad)
	Converts rad to deg. More...

static constexpr T	maxValue ()
	Returns the max scalar value. More...

static constexpr T	minValue ()
	Returns the min scalar value. More...

static constexpr T	sign (const T &value)
	Returns the sign of a given value by either returning -1, 0, or +1. More...

static constexpr T	copySign (const T signReceiver, const T signProvider)
	Copies the sign of a given value to another one. More...

static constexpr T	invertSign (const T signReceiver, const T signProvider)
	Copies the inverted sign of a given value to another one. More...

static T	pythagoras (const T a, const T b)
	Returns the length of the hypotenuse of a given right-angled triangle. More...

static T	gaussianDistribution (const T x, const T sigma)
	Returns a value of the univariate Gaussian distribution centered around the origin. More...

static T	gaussianDistribution (const T x, const T x0, const T sigma)
	Returns a value of the univariate Gaussian distribution centered around a given position x0. More...

static T	normalizedGaussianDistribution (const T x, const T sigma)
	Returns a value of the normalized univariate Gaussian distribution centered around the origin. More...

static T	normalizedGaussianDistribution (const T x, const T x0, const T sigma)
	Returns a value of the normalized univariate Gaussian distribution around a given position x0. More...

static T	gaussianDistribution2 (const T x, const T y, const T sigmaX, const T sigmaY)
	Returns a value of the bivariate Gaussian distribution centered around the origin. More...

static T	gaussianDistribution2 (const T x, const T y, const T x0, const T y0, const T sigmaX, const T sigmaY)
	Returns a value of the bivariate Gaussian distribution centered around a given position (x0, y0). More...

static T	normalizedGaussianDistribution2 (const T x, const T y, const T sigmaX, const T sigmaY)
	Returns a value of the normalized bivariate Gaussian distribution centered around the origin. More...

static T	normalizedGaussianDistribution2 (const T x, const T y, const T x0, const T y0, const T sigmaX, const T sigmaY)
	Returns a value of the normalized bivariate Gaussian distribution centered around a given position (x0, y0). More...

static T	gaussianDistribution3 (const T x, const T y, const T z, const T sigmaX, const T sigmaY, const T sigmaZ)
	Returns a value of the trivariate Gaussian distribution centered around the origin. More...

static T	gaussianDistribution3 (const T x, const T y, const T z, const T x0, const T y0, const T z0, const T sigmaX, const T sigmaY, const T sigmaZ)
	Returns a value of the trivariate Gaussian distribution centered around a given position (x0, y0, z0). More...

static T	normalizedGaussianDistribution3 (const T x, const T y, const T z, const T sigmaX, const T sigmaY, const T sigmaZ)
	Returns a value of the normalized trivariate Gaussian distribution centered around the origin. More...

static T	normalizedGaussianDistribution3 (const T x, const T y, const T z, const T x0, const T y0, const T z0, const T sigmaX, const T sigmaY, const T sigmaZ)
	Returns a value of the normalized trivariate Gaussian distribution centered around a given position (x0, y0, z0). More...

Detailed Description

template<typename T>
class Ocean::NumericT< T >

This class provides basic numeric functionalities.

Template Parameters

T	Data type of the numeric elements

See also: Numeric, NumericF, NumericD.

Member Function Documentation

◆ abs() [1/13]

double Ocean::NumericT< double >::abs ( const double value )

inline

Specialization of NumericT::abs().

See also: NumericT::abs().

◆ abs() [2/13]

float Ocean::NumericT< float >::abs ( const float value )

inline

Specialization of NumericT::abs().

See also: NumericT::abs().

◆ abs() [3/13]

int Ocean::NumericT< int >::abs ( const int value )

inline

Specialization of NumericT::abs().

See also: NumericT::abs().

◆ abs() [4/13]

long long Ocean::NumericT< long long >::abs ( const long long value )

inline

Specialization of NumericT::abs().

See also: NumericT::abs().

◆ abs() [5/13]

long Ocean::NumericT< long >::abs ( const long value )

inline

Specialization of NumericT::abs().

See also: NumericT::abs().

◆ abs() [6/13]

short Ocean::NumericT< short >::abs ( const short value )

inline

Specialization of NumericT::abs().

See also: NumericT::abs().

◆ abs() [7/13]

signed char Ocean::NumericT< signed char >::abs ( const signed char value )

inline

Specialization of NumericT::abs().

See also: NumericT::abs().

◆ abs() [8/13]

template<typename T >

T Ocean::NumericT< T >::abs ( const T value )

inlinestatic

Returns the absolute value of a given value.

Beware some values do not have a corresponding absolute value e.g., -128 for (8bit signed chars), -32768 for (16bit signed chars), and so on.

Parameters

value The value for which the absolute value will be returned

Returns: Absolute value

See also: secureAbs().

◆ abs() [9/13]

unsigned char Ocean::NumericT< unsigned char >::abs ( const unsigned char value )

inline

Specialization of NumericT::abs().

See also: NumericT::abs().

◆ abs() [10/13]

unsigned int Ocean::NumericT< unsigned int >::abs ( const unsigned int value )

inline

Specialization of NumericT::abs().

See also: NumericT::abs().

◆ abs() [11/13]

unsigned long long Ocean::NumericT< unsigned long long >::abs ( const unsigned long long value )

inline

Specialization of NumericT::abs().

See also: NumericT::abs().

◆ abs() [12/13]

unsigned long Ocean::NumericT< unsigned long >::abs ( const unsigned long value )

inline

Specialization of NumericT::abs().

See also: NumericT::abs().

◆ abs() [13/13]

unsigned short Ocean::NumericT< unsigned short >::abs ( const unsigned short value )

inline

Specialization of NumericT::abs().

See also: NumericT::abs().

◆ acos() [1/2]

float Ocean::NumericT< float >::acos ( const float value )

inline

Specialization of NumericT::acos().

See also: NumericT::acos().

◆ acos() [2/2]

template<typename T >

T Ocean::NumericT< T >::acos ( const T value )

inlinestatic

Returns the arccosine of a given value.

Parameters

value The value to return the arc cosine from, with range [-1, 1]

Returns: Arccosine value in radian, with range [0, PI]

◆ angleAdjustNull()

template<typename T >

T Ocean::NumericT< T >::angleAdjustNull ( const T angle )

inlinestatic

Adjusts an arbitrary angle into the range of (-PI, PI].

Parameters

angle The angle to be adjusted, defined in radian, with range (-infinity, infinity)

Returns: Adjusted angle with range (-PI, PI]

◆ angleAdjustPositive()

template<typename T >

T Ocean::NumericT< T >::angleAdjustPositive ( const T angle )

inlinestatic

Adjusts an arbitrary angle into the range of [0.0, 2PI).

Parameters

angle The angle to be adjusted, defined in radian, with range (-infinity, infinity)

Returns: Adjusted angle with range [0.0, 2PI)

◆ angleAdjustPositiveHalf()

template<typename T >

T Ocean::NumericT< T >::angleAdjustPositiveHalf ( const T angle )

inlinestatic

Adjusts an arbitrary angle into the range of [0.0, PI).

Parameters

angle The angle to be adjusted, defined in radian, with range (-infinity, infinity)

Returns: Adjusted angle with range [0.0, PI)

◆ angleDistance()

template<typename T >

T Ocean::NumericT< T >::angleDistance	(	const T	angleA,
		const T	angleB
	)

inlinestatic

Returns the angular difference (distance between two angles).

Parameters

angleA	First angle specified in radian, with range (-infinity, infinity)
angleB	Second angle specified in radian, with range (-infinity, infinity)

Returns: Absolute distance between both angles, in radian

◆ angleIsBelowThreshold()

template<typename T >

bool Ocean::NumericT< T >::angleIsBelowThreshold	(	const T	angleA,
		const T	angleB,
		const T	threshold
	)

inlinestatic

Returns whether the angular difference (distance) between two angles is smaller than a specified threshold.

Parameters

angleA	First angle specified in radian, with range (-infinity, infinity)
angleB	Second angle specified in radian, with range (-infinity, infinity)
threshold	Positive angular threshold in radian with range [0, PI)

Returns: True, if so

◆ angleIsEqual() [1/2]

template<typename T >

bool Ocean::NumericT< T >::angleIsEqual	(	const T	angleA,
		const T	angleB
	)

inlinestatic

Returns whether two angles represent the same angle up to a small epsilon.

Parameters

angleA	First angle specified in radian, with range (-infinity, infinity)
angleB	Second angle specified in radian, with range (-infinity, infinity)

Returns: True, if so

◆ angleIsEqual() [2/2]

template<typename T >

bool Ocean::NumericT< T >::angleIsEqual	(	const T	angleA,
		const T	angleB,
		const T	epsilon
	)

inlinestatic

Returns whether two angles represent the same angle up to a given epsilon.

Parameters

angleA	First angle specified in radian, with range (-infinity, infinity)
angleB	Second angle specified in radian, with range (-infinity, infinity)
epsilon	Accuracy epsilon in radian, with range [0, infinity)

Returns: True, if so

◆ angleIsWeakEqual()

template<typename T >

bool Ocean::NumericT< T >::angleIsWeakEqual	(	const T	angleA,
		const T	angleB
	)

inlinestatic

Returns whether two angles represent the same angle up to a weak epsilon.

Parameters

angleA	First angle specified in radian, with range (-infinity, infinity)
angleB	Second angle specified in radian, with range (-infinity, infinity)

Returns: True, if so

◆ asin() [1/2]

float Ocean::NumericT< float >::asin ( const float value )

inline

Specialization of NumericT::asin().

See also: NumericT::asin().

◆ asin() [2/2]

template<typename T >

T Ocean::NumericT< T >::asin ( const T value )

inlinestatic

Returns the arcsine of a given value.

Parameters

value The value to return the arc sine from, with range [-1, 1]

Returns: Arcsine value, with range [-PI/2, PI/2]

◆ atan() [1/2]

float Ocean::NumericT< float >::atan ( const float value )

inline

Specialization of NumericT::atan().

See also: NumericT::atan().

◆ atan() [2/2]

template<typename T >

T Ocean::NumericT< T >::atan ( const T value )

inlinestatic

Returns the arctangent of a given value.

Parameters

value The value to return the arctangent from

Returns: Arctangent value, with range [-PI/2, PI/2]

◆ atan2() [1/2]

float Ocean::NumericT< float >::atan2	(	const float	y,
		const float	x
	)

inline

Specialization of NumericT::atan2().

See also: NumericT::atan2().

◆ atan2() [2/2]

template<typename T >

T Ocean::NumericT< T >::atan2	(	const T	y,
		const T	x
	)

inlinestatic

Returns the arctangent of a given value in radian.

Parameters

y	Opposite value, must not be zero if x is zero
x	Adjacent value, must not be zero if y is zero

Returns: Arctangent value, with range [-PI, PI]

◆ binomialCoefficient()

template<typename T >

constexpr T Ocean::NumericT< T >::binomialCoefficient	(	const T &	n,
		const T &	k
	)

inlinestaticconstexpr

Returns the binomial coefficient for two binomial parameters.

This function calculates: n! / (k! * (n - k)!).

Parameters

n	Upper binomial coefficient parameter, with range [0, infinity)
k	Lower binomial coefficient parameter, with range [0, n]

Returns: Resulting binomial coefficient

◆ ceil() [1/4]

double Ocean::NumericT< double >::ceil ( const double value )

inline

Specialization of NumericT::ceil().

See also: NumericT::ceil().

◆ ceil() [2/4]

float Ocean::NumericT< float >::ceil ( const float value )

inline

Specialization of NumericT::ceil().

See also: NumericT::ceil().

◆ ceil() [3/4]

long double Ocean::NumericT< long double >::ceil ( const long double value )

inline

Specialization of NumericT::ceil().

See also: NumericT::ceil().

◆ ceil() [4/4]

template<typename T >

T Ocean::NumericT< T >::ceil ( const T value )

inlinestatic

Returns the smallest integer value that is not less than the given value.

Parameters

value The value to handle, with range (-infinity, infinity)

Returns: Smallest integer value

◆ copySign() [1/3]

constexpr double Ocean::NumericT< double >::copySign	(	const double	first,
		const double	second
	)

inlineconstexpr

Specialization of NumericT::copySign().

See also: NumericT::copySign().

◆ copySign() [2/3]

constexpr float Ocean::NumericT< float >::copySign	(	const float	first,
		const float	second
	)

inlineconstexpr

Specialization of NumericT::copySign().

See also: NumericT::copySign().

◆ copySign() [3/3]

template<typename T >

constexpr T Ocean::NumericT< T >::copySign	(	const T	signReceiver,
		const T	signProvider
	)

inlinestaticconstexpr

Copies the sign of a given value to another one.

Parameters

signReceiver	First value receiving the sign from the second value
signProvider	Second value providing the sign for the first one

Returns: First value with the sign of the second one

◆ cos() [1/2]

float Ocean::NumericT< float >::cos ( const float value )

inline

Specialization of NumericT::cos().

See also: NumericT::cos().

◆ cos() [2/2]

template<typename T >

T Ocean::NumericT< T >::cos ( const T value )

inlinestatic

Returns the cosine of a given value.

Parameters

value The value to return the cosine from, with range (-infinity, infinity)

Returns: Cosine value

◆ deg2rad()

template<typename T >

constexpr T Ocean::NumericT< T >::deg2rad ( const T deg )

inlinestaticconstexpr

Converts deg to rad.

Parameters

deg	Angle in deg, with range (-infinity, infinity)

Returns: Angle in radian

◆ dot()

template<typename T >

T Ocean::NumericT< T >::dot	(	const T *	vectorA,
		const T *	vectorB,
		const size_t	size
	)

inlinestatic

Returns the dot product for two vectors.

Parameters

vectorA	The first vector, can be nullptr if size is 0
vectorB	The second vector, can be nullptr if size is 0
size	The size/dimension of both vector (the number of elements each vector holds), with range [0, infinity)

Returns: The resulting dot product

◆ e()

template<typename T >

constexpr T Ocean::NumericT< T >::e

staticconstexpr

Returns the euler's number.

Returns: Euler's number

◆ eps() [1/13]

template<typename T >

static constexpr T Ocean::NumericT< T >::eps ( )

staticconstexpr

Returns a small epsilon.

Returns: Small epsilon

◆ eps() [2/13]

constexpr double Ocean::NumericT< double >::eps ( )

constexpr

Specialization of NumericT::eps().

See also: NumericT::eps().

◆ eps() [3/13]

constexpr float Ocean::NumericT< float >::eps ( )

constexpr

Specialization of NumericT::eps().

See also: NumericT::eps().

◆ eps() [4/13]

constexpr signed char Ocean::NumericT< signed char >::eps ( )

constexpr

Specialization of NumericT::eps().

See also: NumericT::eps().

◆ eps() [5/13]

constexpr unsigned char Ocean::NumericT< unsigned char >::eps ( )

constexpr

Specialization of NumericT::eps().

See also: NumericT::eps().

◆ eps() [6/13]

constexpr short Ocean::NumericT< short >::eps ( )

constexpr

Specialization of NumericT::eps().

See also: NumericT::eps().

◆ eps() [7/13]

constexpr unsigned short Ocean::NumericT< unsigned short >::eps ( )

constexpr

Specialization of NumericT::eps().

See also: NumericT::eps().

◆ eps() [8/13]

constexpr int Ocean::NumericT< int >::eps ( )

constexpr

Specialization of NumericT::eps().

See also: NumericT::eps().

◆ eps() [9/13]

constexpr unsigned int Ocean::NumericT< unsigned int >::eps ( )

constexpr

Specialization of NumericT::eps().

See also: NumericT::eps().

◆ eps() [10/13]

constexpr long Ocean::NumericT< long >::eps ( )

constexpr

Specialization of NumericT::eps().

See also: NumericT::eps().

◆ eps() [11/13]

constexpr unsigned long Ocean::NumericT< unsigned long >::eps ( )

constexpr

Specialization of NumericT::eps().

See also: NumericT::eps().

◆ eps() [12/13]

constexpr long long Ocean::NumericT< long long >::eps ( )

constexpr

Specialization of NumericT::eps().

See also: NumericT::eps().

◆ eps() [13/13]

constexpr unsigned long long Ocean::NumericT< unsigned long long >::eps ( )

constexpr

Specialization of NumericT::eps().

See also: NumericT::eps().

◆ exp() [1/2]

float Ocean::NumericT< float >::exp ( const float value )

inline

◆ exp() [2/2]

template<typename T >

T Ocean::NumericT< T >::exp ( const T value )

inlinestatic

Returns the base-e exponential function of a given value.

Parameters

value The value to determine the exponential value for, with range (-infinity, infinity)

Returns: Exponential value

◆ factorial() [1/2]

template<typename T >

constexpr T Ocean::NumericT< T >::factorial ( const T & value )

inlinestaticconstexpr

Returns the factorial for a given value.

Parameters

value The value for that the factorial will be determined, with range [0, infinity) for floating point types; with range [0, 12] for 32 bit integer types

Returns: Resulting factorial, with range [0, infinity)

◆ factorial() [2/2]

constexpr unsigned int Ocean::NumericT< unsigned int >::factorial ( const unsigned int & value )

inlineconstexpr

◆ floor() [1/4]

double Ocean::NumericT< double >::floor ( const double value )

inline

Specialization of NumericT::floor().

See also: NumericT::floor().

◆ floor() [2/4]

float Ocean::NumericT< float >::floor ( const float value )

inline

Specialization of NumericT::floor().

See also: NumericT::floor().

◆ floor() [3/4]

long double Ocean::NumericT< long double >::floor ( const long double value )

inline

Specialization of NumericT::floor().

See also: NumericT::floor().

◆ floor() [4/4]

template<typename T >

T Ocean::NumericT< T >::floor ( const T value )

inlinestatic

Returns the largest integer value that is not greater than the given value.

Parameters

value The value to handle, with range (-infinity, infinity)

Returns: Largest integer value

◆ fmod() [1/2]

float Ocean::NumericT< float >::fmod	(	const float	valueA,
		const float	valueB
	)

inline

Specialization of NumericT::fmod().

See also: NumericT::fmod().

◆ fmod() [2/2]

template<typename T >

T Ocean::NumericT< T >::fmod	(	const T	valueA,
		const T	valueB
	)

inlinestatic

Returns the floating-point remainder of a given value.

Parameters

valueA	Value to return the floating-point remainder from
valueB	Divisor value

Returns: Floating-point remainder

◆ gaussianDistribution() [1/2]

template<typename T >

T Ocean::NumericT< T >::gaussianDistribution	(	const T	x,
		const T	sigma
	)

inlinestatic

Returns a value of the univariate Gaussian distribution centered around the origin.

Parameters

x	Value to return the Gaussian distribution value for
sigma	The sigma parameter defining the standard deviation of the Gaussian distribution, with range (0, infinity)

Returns: Function value

◆ gaussianDistribution() [2/2]

template<typename T >

T Ocean::NumericT< T >::gaussianDistribution	(	const T	x,
		const T	x0,
		const T	sigma
	)

inlinestatic

Returns a value of the univariate Gaussian distribution centered around a given position x0.

Parameters

x	Value to return the Gaussian distribution value for
x0	X value for the center of the Gaussian distribution
sigma	The sigma parameter defining the standard deviation of the Gaussian distribution, with range (0, infinity)

Returns: Function value

◆ gaussianDistribution2() [1/2]

template<typename T >

T Ocean::NumericT< T >::gaussianDistribution2	(	const T	x,
		const T	y,
		const T	sigmaX,
		const T	sigmaY
	)

inlinestatic

Returns a value of the bivariate Gaussian distribution centered around the origin.

Parameters

x	X value for the function
y	Y value for the function
sigmaX	Sigma parameter defining the standard deviation for the x-axis of the Gaussian distribution, with range (0, infinity)
sigmaY	Sigma parameter defining the standard deviation for the y-axis of the Gaussian distribution, with range (0, infinity)

Returns: Function value

◆ gaussianDistribution2() [2/2]

template<typename T >

T Ocean::NumericT< T >::gaussianDistribution2	(	const T	x,
		const T	y,
		const T	x0,
		const T	y0,
		const T	sigmaX,
		const T	sigmaY
	)

inlinestatic

Returns a value of the bivariate Gaussian distribution centered around a given position (x0, y0).

Parameters

x	X value for the function
y	Y value for the function
x0	X value for the center of the Gaussian distribution
y0	Y value for the center of the Gaussian distribution
sigmaX	Sigma parameter defining the standard deviation for the x-axis of the Gaussian distribution, with range (0, infinity)
sigmaY	Sigma parameter defining the standard deviation for the y-axis of the Gaussian distribution, with range (0, infinity)

Returns: Function value

◆ gaussianDistribution3() [1/2]

template<typename T >

T Ocean::NumericT< T >::gaussianDistribution3	(	const T	x,
		const T	y,
		const T	z,
		const T	sigmaX,
		const T	sigmaY,
		const T	sigmaZ
	)

inlinestatic

Returns a value of the trivariate Gaussian distribution centered around the origin.

Parameters

x	X value for the function
y	Y value for the function
z	Z value for the function
sigmaX	Sigma parameter defining the standard deviation for the x-axis of the Gaussian distribution, with range (0, infinity)
sigmaY	Sigma parameter defining the standard deviation for the y-axis of the Gaussian distribution, with range (0, infinity)
sigmaZ	Sigma parameter defining the standard deviation for the z-axis of the Gaussian distribution, with range (0, infinity)

Returns: Function value

◆ gaussianDistribution3() [2/2]

template<typename T >

T Ocean::NumericT< T >::gaussianDistribution3	(	const T	x,
		const T	y,
		const T	z,
		const T	x0,
		const T	y0,
		const T	z0,
		const T	sigmaX,
		const T	sigmaY,
		const T	sigmaZ
	)

inlinestatic

Returns a value of the trivariate Gaussian distribution centered around a given position (x0, y0, z0).

Parameters

x	X value for the function
y	Y value for the function
z	Z value for the function
x0	X value for the center of the Gaussian distribution
y0	Y value for the center of the Gaussian distribution
z0	Z value for the center of the Gaussian distribution
sigmaX	Sigma parameter defining the standard deviation for the x-axis of the Gaussian distribution, with range (0, infinity)
sigmaY	Sigma parameter defining the standard deviation for the y-axis of the Gaussian distribution, with range (0, infinity)
sigmaZ	Sigma parameter defining the standard deviation for the z-axis of the Gaussian distribution, with range (0, infinity)

Returns: Function value

◆ inf()

template<typename T >

constexpr T Ocean::NumericT< T >::inf

inlinestaticconstexpr

Returns a value which is positive infinity.

Returns: Positive infinity

◆ integerPow()

template<typename T >

constexpr T Ocean::NumericT< T >::integerPow	(	const T	x,
		const unsigned int	y
	)

staticconstexpr

Returns x raised to the power of y while y is an integer.

Parameters

x	X value, with range [0, infinity)
y	Y value, with range (-infinity, infinity)

Returns: The power result

◆ invertSign() [1/3]

constexpr double Ocean::NumericT< double >::invertSign	(	const double	first,
		const double	second
	)

inlineconstexpr

Specialization of NumericT::invertSign().

See also: NumericT::invertedSign().

◆ invertSign() [2/3]

constexpr float Ocean::NumericT< float >::invertSign	(	const float	first,
		const float	second
	)

inlineconstexpr

Specialization of NumericT::invertSign().

See also: NumericT::invertSign().

◆ invertSign() [3/3]

template<typename T >

constexpr T Ocean::NumericT< T >::invertSign	(	const T	signReceiver,
		const T	signProvider
	)

inlinestaticconstexpr

Copies the inverted sign of a given value to another one.

Parameters

signReceiver	First value receiving the inverted sign from the second value
signProvider	Second value providing the inverted sign for the first one

Returns: First value with the inverted sign of the second one

◆ isAbove()

template<typename T >

constexpr bool Ocean::NumericT< T >::isAbove	(	const T	value,
		const T	lower,
		const T	epsilon = `NumericT<T>::eps()`
	)

staticconstexpr

Returns whether a parameter lies on or above a given border tolerating a small epsilon.

Parameters

value	The value to check, with range (-infinity, infinity)
lower	The lower border, with range (-infinity, infinity)
epsilon	Accuracy epsilon, with range [0, infinity)

Returns: True, if 'lower - epsilon <= value'

◆ isBelow()

template<typename T >

constexpr bool Ocean::NumericT< T >::isBelow	(	const T	value,
		const T	upper,
		const T	epsilon = `NumericT<T>::eps()`
	)

staticconstexpr

Returns whether a parameter lies on or below a given border tolerating a small epsilon.

Parameters

value	The value to check, with range (-infinity, infinity)
upper	The upper border, with range (-infinity, infinity)
epsilon	Accuracy epsilon, with range [0, infinity)

Returns: True, if 'value <= upper + epsilon'

◆ isEqual() [1/25]

bool Ocean::NumericT< int >::isEqual	(	const int	first,
		const int	second
	)

inline

◆ isEqual() [2/25]

bool Ocean::NumericT< int >::isEqual	(	const int	first,
		const int	second,
		const int	epsilon
	)

inline

◆ isEqual() [3/25]

bool Ocean::NumericT< long >::isEqual	(	const long	first,
		const long	second
	)

inline

◆ isEqual() [4/25]

bool Ocean::NumericT< long >::isEqual	(	const long	first,
		const long	second,
		const long	epsilon
	)

inline

◆ isEqual() [5/25]

bool Ocean::NumericT< long long >::isEqual	(	const long long	first,
		const long long	second
	)

inline

◆ isEqual() [6/25]

bool Ocean::NumericT< long long >::isEqual	(	const long long	first,
		const long long	second,
		const long long	epsilon
	)

inline

◆ isEqual() [7/25]

bool Ocean::NumericT< short >::isEqual	(	const short	first,
		const short	second
	)

inline

◆ isEqual() [8/25]

bool Ocean::NumericT< short >::isEqual	(	const short	first,
		const short	second,
		const short	epsilon
	)

inline

◆ isEqual() [9/25]

bool Ocean::NumericT< signed char >::isEqual	(	const signed char	first,
		const signed char	second
	)

inline

◆ isEqual() [10/25]

bool Ocean::NumericT< signed char >::isEqual	(	const signed char	first,
		const signed char	second,
		const signed char	epsilon
	)

inline

◆ isEqual() [11/25]

template<typename T >

bool Ocean::NumericT< T >::isEqual	(	const std::complex< T > &	first,
		const std::complex< T > &	second
	)

inlinestatic

Returns whether two complex values are equal up to a small epsilon.

Parameters

first	The first value to check
second	The second value to check

Returns: True, if so

◆ isEqual() [12/25]

template<typename T >

bool Ocean::NumericT< T >::isEqual	(	const std::complex< T > &	first,
		const std::complex< T > &	second,
		const T	epsilon
	)

inlinestatic

Returns whether two complex values are equal up to a given epsilon.

Parameters

first	The first value to check
second	The second value to check
epsilon	Accuracy epsilon, with range [0, infinity)

Returns: True, if so

◆ isEqual() [13/25]

template<typename T >

bool Ocean::NumericT< T >::isEqual	(	const T	first,
		const T	second
	)

inlinestatic

Returns whether two values are equal up to a small epsilon.

Parameters

first	The first value to check, with range (-infinity, infinity)
second	The second value to check, with range (-infinity, infinity)

Returns: True, if so

◆ isEqual() [14/25]

template<typename T >

bool Ocean::NumericT< T >::isEqual	(	const T	first,
		const T	second,
		const T	epsilon
	)

inlinestatic

Returns whether two values are equal up to a given epsilon.

Parameters

first	The first value to check, with range (-infinity, infinity)
second	The second value to check, with range (-infinity, infinity)
epsilon	Accuracy epsilon, with range [0, infinity)

Returns: True, if so

◆ isEqual() [15/25]

template<typename T >

template<int tMagnitude>

static bool Ocean::NumericT< T >::isEqual	(	const T	first,
		const T	second,
		const T	referenceEpsilon
	)

inlinestatic

Returns whether two values are equal up to a dynamic epsilon which is adjusted due to the magnitude of both values and the reference magnitude.

The reference magnitude (provided as template parameter) corresponds to the provided reference epsilon.
That means that if the magnitude of both values to compare is equal to the defined reference magnitude the given epsilon value is used for comparison.
Otherwise the given epsilon is increased by 10 times the difference between the magnitude of the values and the reference magnitude, the epsilon value will not be decreased if the actual magnitude is smaller than the reference magnitude.

Parameters

first	The first value to check, with range (-infinity, infinity)
second	The second value to check, with range (-infinity, infinity)
referenceEpsilon	The accuracy epsilon for the specified magnitude, with range [0, infinity)

Returns: True, if so

Template Parameters

tMagnitude The reference magnitude for which the specified epsilon must hold so that both values count as equal, with range [-20, 20]

◆ isEqual() [16/25]

bool Ocean::NumericT< unsigned char >::isEqual	(	const unsigned char	first,
		const unsigned char	second
	)

inline

◆ isEqual() [17/25]

bool Ocean::NumericT< unsigned char >::isEqual	(	const unsigned char	first,
		const unsigned char	second,
		const unsigned char	epsilon
	)

inline

◆ isEqual() [18/25]

bool Ocean::NumericT< unsigned int >::isEqual	(	const unsigned int	first,
		const unsigned int	second
	)

inline

◆ isEqual() [19/25]

bool Ocean::NumericT< unsigned int >::isEqual	(	const unsigned int	first,
		const unsigned int	second,
		const unsigned int	epsilon
	)

inline

◆ isEqual() [20/25]

bool Ocean::NumericT< unsigned long >::isEqual	(	const unsigned long	first,
		const unsigned long	second
	)

inline

◆ isEqual() [21/25]

bool Ocean::NumericT< unsigned long >::isEqual	(	const unsigned long	first,
		const unsigned long	second,
		const unsigned long	epsilon
	)

inline

◆ isEqual() [22/25]

bool Ocean::NumericT< unsigned long long >::isEqual	(	const unsigned long long	first,
		const unsigned long long	second
	)

inline

◆ isEqual() [23/25]

bool Ocean::NumericT< unsigned long long >::isEqual	(	const unsigned long long	first,
		const unsigned long long	second,
		const unsigned long long	epsilon
	)

inline

◆ isEqual() [24/25]

bool Ocean::NumericT< unsigned short >::isEqual	(	const unsigned short	first,
		const unsigned short	second
	)

inline

◆ isEqual() [25/25]

bool Ocean::NumericT< unsigned short >::isEqual	(	const unsigned short	first,
		const unsigned short	second,
		const unsigned short	epsilon
	)

inline

◆ isEqualEps() [1/12]

constexpr bool Ocean::NumericT< int >::isEqualEps ( const int value )

inlineconstexpr

◆ isEqualEps() [2/12]

constexpr bool Ocean::NumericT< long long >::isEqualEps ( const long long value )

inlineconstexpr

◆ isEqualEps() [3/12]

constexpr bool Ocean::NumericT< long >::isEqualEps ( const long value )

inlineconstexpr

◆ isEqualEps() [4/12]

constexpr bool Ocean::NumericT< short >::isEqualEps ( const short value )

inlineconstexpr

◆ isEqualEps() [5/12]

constexpr bool Ocean::NumericT< signed char >::isEqualEps ( const signed char value )

inlineconstexpr

◆ isEqualEps() [6/12]

template<typename T >

constexpr bool Ocean::NumericT< T >::isEqualEps ( const std::complex< T > & value )

inlinestaticconstexpr

Returns whether a complex value is smaller than or equal to a small epsilon.

Parameters

value Complex value to check

Returns: True, if so

◆ isEqualEps() [7/12]

template<typename T >

constexpr bool Ocean::NumericT< T >::isEqualEps ( const T value )

inlinestaticconstexpr

Returns whether a value is smaller than or equal to a small epsilon.

Parameters

value The value to check, with range (-infinity, infinity)

Returns: True, if so

◆ isEqualEps() [8/12]

constexpr bool Ocean::NumericT< unsigned char >::isEqualEps ( const unsigned char value )

inlineconstexpr

◆ isEqualEps() [9/12]

constexpr bool Ocean::NumericT< unsigned int >::isEqualEps ( const unsigned int value )

inlineconstexpr

◆ isEqualEps() [10/12]

constexpr bool Ocean::NumericT< unsigned long long >::isEqualEps ( const unsigned long long value )

inlineconstexpr

◆ isEqualEps() [11/12]

constexpr bool Ocean::NumericT< unsigned long >::isEqualEps ( const unsigned long value )

inlineconstexpr

◆ isEqualEps() [12/12]

constexpr bool Ocean::NumericT< unsigned short >::isEqualEps ( const unsigned short value )

inlineconstexpr

◆ isInf() [1/5]

bool Ocean::NumericT< double >::isInf ( const double value )

inline

◆ isInf() [2/5]

bool Ocean::NumericT< float >::isInf ( const float value )

inline

◆ isInf() [3/5]

bool Ocean::NumericT< long double >::isInf ( const long double value )

inline

◆ isInf() [4/5]

template<typename T >

bool Ocean::NumericT< T >::isInf ( const std::complex< T > & value )

inlinestatic

Returns whether a given value is positive or negative infinity.

Only floating point values can be infinity.

Parameters

value The value to check

Returns: True, if so

◆ isInf() [5/5]

template<typename T >

bool Ocean::NumericT< T >::isInf ( const T value )

inlinestatic

Returns whether a given value is positive or negative infinity.

Only floating point values can be infinity.

Parameters

value The value to check

Returns: True, if so

◆ isInsideRange()

template<typename T >

constexpr bool Ocean::NumericT< T >::isInsideRange	(	const T	lower,
		const T	value,
		const T	upper,
		const T	epsilon = `NumericT<T>::eps()`
	)

staticconstexpr

Returns whether a value lies between a given range up to a provided epsilon border.

Parameters

lower	The lower border, with range (-infinity, infinity)
value	The value to check, with range (-infinity, infinity)
upper	The upper border, with range [lower, infinity)
epsilon	Accuracy epsilon, with range [0, infinity)

Returns: True, if so

◆ isInsideValueRange()

template<typename T >

template<typename TValue >

bool Ocean::NumericT< T >::isInsideValueRange ( const TValue & value )

inlinestatic

Returns whether a given value of an arbitrary data type fits into the value range of 'T'.

Below the behavior for individual data types:

T           TValue           return
A           A                true
float       float            true
double      double           true
uint8_t     int8_t           >= 0
int8_t      uint8_t          <= 127
uint8_t     uint16_t         true
uint8_t     uint32_t         true
...
float       Integral         false
double      Integral         false
Integral    float            false
Integral    double           false

Parameters

value The value to check, with range (-infinity, infinity)

Returns: True, if value fits into 'T', or 'T' is same as 'TValue'

Template Parameters

TValue The data type of the given value

◆ isInsideWeakRange()

template<typename T >

constexpr bool Ocean::NumericT< T >::isInsideWeakRange	(	const T	lower,
		const T	value,
		const T	upper
	)

staticconstexpr

Returns whether a value lies between a given range up to a weak epsilon border.

Parameters

lower	The lower border, with range (-infinity, infinity)
value	The value to check, with range (-infinity, infinity)
upper	The upper border, with range [lower, infinity)

Returns: True, if so

◆ isNan() [1/4]

bool Ocean::NumericT< double >::isNan ( const double value )

inline

◆ isNan() [2/4]

bool Ocean::NumericT< float >::isNan ( const float value )

inline

◆ isNan() [3/4]

template<typename T >

bool Ocean::NumericT< T >::isNan ( const std::complex< T > & value )

inlinestatic

Returns whether a given value is not a number.

Parameters

value The value to check

Returns: True, if so

◆ isNan() [4/4]

template<typename T >

bool Ocean::NumericT< T >::isNan ( const T value )

inlinestatic

Returns whether a given value is not a number.

Parameters

value The value to check

Returns: True, if so

◆ isNotEqual() [1/24]

bool Ocean::NumericT< int >::isNotEqual	(	const int	first,
		const int	second
	)

inline

◆ isNotEqual() [2/24]

bool Ocean::NumericT< int >::isNotEqual	(	const int	first,
		const int	second,
		const int	epsilon
	)

inline

◆ isNotEqual() [3/24]

bool Ocean::NumericT< long >::isNotEqual	(	const long	first,
		const long	second
	)

inline

◆ isNotEqual() [4/24]

bool Ocean::NumericT< long >::isNotEqual	(	const long	first,
		const long	second,
		const long	epsilon
	)

inline

◆ isNotEqual() [5/24]

bool Ocean::NumericT< long long >::isNotEqual	(	const long long	first,
		const long long	second
	)

inline

◆ isNotEqual() [6/24]

bool Ocean::NumericT< long long >::isNotEqual	(	const long long	first,
		const long long	second,
		const long long	epsilon
	)

inline

◆ isNotEqual() [7/24]

bool Ocean::NumericT< short >::isNotEqual	(	const short	first,
		const short	second
	)

inline

◆ isNotEqual() [8/24]

bool Ocean::NumericT< short >::isNotEqual	(	const short	first,
		const short	second,
		const short	epsilon
	)

inline

◆ isNotEqual() [9/24]

bool Ocean::NumericT< signed char >::isNotEqual	(	const signed char	first,
		const signed char	second
	)

inline

◆ isNotEqual() [10/24]

bool Ocean::NumericT< signed char >::isNotEqual	(	const signed char	first,
		const signed char	second,
		const signed char	epsilon
	)

inline

◆ isNotEqual() [11/24]

template<typename T >

bool Ocean::NumericT< T >::isNotEqual	(	const std::complex< T > &	first,
		const std::complex< T > &	second
	)

inlinestatic

Returns whether two complex values are not equal up to a small epsilon.

Parameters

first	The first value to check
second	The second value to check

Returns: True, if so

◆ isNotEqual() [12/24]

template<typename T >

bool Ocean::NumericT< T >::isNotEqual	(	const std::complex< T > &	first,
		const std::complex< T > &	second,
		const T	epsilon
	)

inlinestatic

Returns whether two complex values are not equal up to a given epsilon.

Parameters

first	The first value to check
second	The second value to check
epsilon	Accuracy epsilon, with range [0, infinity)

Returns: True, if so

◆ isNotEqual() [13/24]

template<typename T >

bool Ocean::NumericT< T >::isNotEqual	(	const T	first,
		const T	second
	)

inlinestatic

Returns whether two values are not equal up to a small epsilon.

Parameters

first	The first value to check, with range (-infinity, infinity)
second	The second value to check, with range (-infinity, infinity)

Returns: True, if so

◆ isNotEqual() [14/24]

template<typename T >

bool Ocean::NumericT< T >::isNotEqual	(	const T	first,
		const T	second,
		const T	epsilon
	)

inlinestatic

Returns whether two values are not equal up to a given epsilon.

Parameters

first	The first value to check, with range (-infinity, infinity)
second	The second value to check, with range (-infinity, infinity)
epsilon	Accuracy epsilon, with range [0, infinity)

Returns: True, if so

◆ isNotEqual() [15/24]

bool Ocean::NumericT< unsigned char >::isNotEqual	(	const unsigned char	first,
		const unsigned char	second
	)

inline

◆ isNotEqual() [16/24]

bool Ocean::NumericT< unsigned char >::isNotEqual	(	const unsigned char	first,
		const unsigned char	second,
		const unsigned char	epsilon
	)

inline

◆ isNotEqual() [17/24]

bool Ocean::NumericT< unsigned int >::isNotEqual	(	const unsigned int	first,
		const unsigned int	second
	)

inline

◆ isNotEqual() [18/24]

bool Ocean::NumericT< unsigned int >::isNotEqual	(	const unsigned int	first,
		const unsigned int	second,
		const unsigned int	epsilon
	)

inline

◆ isNotEqual() [19/24]

bool Ocean::NumericT< unsigned long >::isNotEqual	(	const unsigned long	first,
		const unsigned long	second
	)

inline

◆ isNotEqual() [20/24]

bool Ocean::NumericT< unsigned long >::isNotEqual	(	const unsigned long	first,
		const unsigned long	second,
		const unsigned long	epsilon
	)

inline

◆ isNotEqual() [21/24]

bool Ocean::NumericT< unsigned long long >::isNotEqual	(	const unsigned long long	first,
		const unsigned long long	second
	)

inline

◆ isNotEqual() [22/24]

bool Ocean::NumericT< unsigned long long >::isNotEqual	(	const unsigned long long	first,
		const unsigned long long	second,
		const unsigned long long	epsilon
	)

inline

◆ isNotEqual() [23/24]

bool Ocean::NumericT< unsigned short >::isNotEqual	(	const unsigned short	first,
		const unsigned short	second
	)

inline

◆ isNotEqual() [24/24]

bool Ocean::NumericT< unsigned short >::isNotEqual	(	const unsigned short	first,
		const unsigned short	second,
		const unsigned short	epsilon
	)

inline

◆ isNotEqualEps() [1/12]

constexpr bool Ocean::NumericT< int >::isNotEqualEps ( const int value )

inlineconstexpr

◆ isNotEqualEps() [2/12]

constexpr bool Ocean::NumericT< long long >::isNotEqualEps ( const long long value )

inlineconstexpr

◆ isNotEqualEps() [3/12]

constexpr bool Ocean::NumericT< long >::isNotEqualEps ( const long value )

inlineconstexpr

◆ isNotEqualEps() [4/12]

constexpr bool Ocean::NumericT< short >::isNotEqualEps ( const short value )

inlineconstexpr

◆ isNotEqualEps() [5/12]

constexpr bool Ocean::NumericT< signed char >::isNotEqualEps ( const signed char value )

inlineconstexpr

◆ isNotEqualEps() [6/12]

template<typename T >

constexpr bool Ocean::NumericT< T >::isNotEqualEps ( const std::complex< T > & value )

inlinestaticconstexpr

Returns whether a complex value is not smaller than or equal to a small epsilon.

Parameters

value Complex value to check

Returns: True, if so

◆ isNotEqualEps() [7/12]

template<typename T >

constexpr bool Ocean::NumericT< T >::isNotEqualEps ( const T value )

inlinestaticconstexpr

Returns whether a value is not smaller than or equal to a small epsilon.

Parameters

value The value to check, with range (-infinity, infinity)

Returns: True, if so

◆ isNotEqualEps() [8/12]

constexpr bool Ocean::NumericT< unsigned char >::isNotEqualEps ( const unsigned char value )

inlineconstexpr

◆ isNotEqualEps() [9/12]

constexpr bool Ocean::NumericT< unsigned int >::isNotEqualEps ( const unsigned int value )

inlineconstexpr

◆ isNotEqualEps() [10/12]

constexpr bool Ocean::NumericT< unsigned long long >::isNotEqualEps ( const unsigned long long value )

inlineconstexpr

◆ isNotEqualEps() [11/12]

constexpr bool Ocean::NumericT< unsigned long >::isNotEqualEps ( const unsigned long value )

inlineconstexpr

◆ isNotEqualEps() [12/12]

constexpr bool Ocean::NumericT< unsigned short >::isNotEqualEps ( const unsigned short value )

inlineconstexpr

◆ isNotWeakEqual() [1/12]

bool Ocean::NumericT< int >::isNotWeakEqual	(	const int	first,
		const int	second
	)

inline

◆ isNotWeakEqual() [2/12]

bool Ocean::NumericT< long >::isNotWeakEqual	(	const long	first,
		const long	second
	)

inline

◆ isNotWeakEqual() [3/12]

bool Ocean::NumericT< long long >::isNotWeakEqual	(	const long long	first,
		const long long	second
	)

inline

◆ isNotWeakEqual() [4/12]

bool Ocean::NumericT< short >::isNotWeakEqual	(	const short	first,
		const short	second
	)

inline

◆ isNotWeakEqual() [5/12]

bool Ocean::NumericT< signed char >::isNotWeakEqual	(	const signed char	first,
		const signed char	second
	)

inline

◆ isNotWeakEqual() [6/12]

template<typename T >

bool Ocean::NumericT< T >::isNotWeakEqual	(	const std::complex< T > &	first,
		const std::complex< T > &	second
	)

inlinestatic

Returns whether two complex values are not equal up to a weak epsilon.

Parameters

first	The first value to check
second	The second value to check

Returns: True, if so

◆ isNotWeakEqual() [7/12]

template<typename T >

bool Ocean::NumericT< T >::isNotWeakEqual	(	const T	first,
		const T	second
	)

inlinestatic

Returns whether two values are not equal up to a weak epsilon.

Parameters

first	The first value to check, with range (-infinity, infinity)
second	The second value to check, with range (-infinity, infinity)

Returns: True, if so

◆ isNotWeakEqual() [8/12]

bool Ocean::NumericT< unsigned char >::isNotWeakEqual	(	const unsigned char	first,
		const unsigned char	second
	)

inline

◆ isNotWeakEqual() [9/12]

bool Ocean::NumericT< unsigned int >::isNotWeakEqual	(	const unsigned int	first,
		const unsigned int	second
	)

inline

◆ isNotWeakEqual() [10/12]

bool Ocean::NumericT< unsigned long >::isNotWeakEqual	(	const unsigned long	first,
		const unsigned long	second
	)

inline

◆ isNotWeakEqual() [11/12]

bool Ocean::NumericT< unsigned long long >::isNotWeakEqual	(	const unsigned long long	first,
		const unsigned long long	second
	)

inline

◆ isNotWeakEqual() [12/12]

bool Ocean::NumericT< unsigned short >::isNotWeakEqual	(	const unsigned short	first,
		const unsigned short	second
	)

inline

◆ isNotWeakEqualEps() [1/12]

constexpr bool Ocean::NumericT< int >::isNotWeakEqualEps ( const int value )

inlineconstexpr

◆ isNotWeakEqualEps() [2/12]

constexpr bool Ocean::NumericT< long long >::isNotWeakEqualEps ( const long long value )

inlineconstexpr

◆ isNotWeakEqualEps() [3/12]

constexpr bool Ocean::NumericT< long >::isNotWeakEqualEps ( const long value )

inlineconstexpr

◆ isNotWeakEqualEps() [4/12]

constexpr bool Ocean::NumericT< short >::isNotWeakEqualEps ( const short value )

inlineconstexpr

◆ isNotWeakEqualEps() [5/12]

constexpr bool Ocean::NumericT< signed char >::isNotWeakEqualEps ( const signed char value )

inlineconstexpr

◆ isNotWeakEqualEps() [6/12]

template<typename T >

constexpr bool Ocean::NumericT< T >::isNotWeakEqualEps ( const std::complex< T > & value )

inlinestaticconstexpr

Returns whether a complex value is not smaller than or equal to a weak epsilon.

Parameters

value Complex value to check

Returns: True, if so

◆ isNotWeakEqualEps() [7/12]

template<typename T >

constexpr bool Ocean::NumericT< T >::isNotWeakEqualEps ( const T value )

inlinestaticconstexpr

Returns whether a value is not smaller than or equal to a weak epsilon.

Parameters

value The value to check, with range (-infinity, infinity)

Returns: True, if so

◆ isNotWeakEqualEps() [8/12]

constexpr bool Ocean::NumericT< unsigned char >::isNotWeakEqualEps ( const unsigned char value )

inlineconstexpr

◆ isNotWeakEqualEps() [9/12]

constexpr bool Ocean::NumericT< unsigned int >::isNotWeakEqualEps ( const unsigned int value )

inlineconstexpr

◆ isNotWeakEqualEps() [10/12]

constexpr bool Ocean::NumericT< unsigned long long >::isNotWeakEqualEps ( const unsigned long long value )

inlineconstexpr

◆ isNotWeakEqualEps() [11/12]

constexpr bool Ocean::NumericT< unsigned long >::isNotWeakEqualEps ( const unsigned long value )

inlineconstexpr

◆ isNotWeakEqualEps() [12/12]

constexpr bool Ocean::NumericT< unsigned short >::isNotWeakEqualEps ( const unsigned short value )

inlineconstexpr

◆ isWeakEqual() [1/3]

bool Ocean::NumericT< int >::isWeakEqual	(	const int	first,
		const int	second
	)

inline

◆ isWeakEqual() [2/3]

template<typename T >

bool Ocean::NumericT< T >::isWeakEqual	(	const std::complex< T > &	first,
		const std::complex< T > &	second
	)

inlinestatic

Returns whether two complex values are equal up to a weak epsilon.

Parameters

first	The first value to check
second	The second value to check

Returns: True, if so

◆ isWeakEqual() [3/3]

template<typename T >

bool Ocean::NumericT< T >::isWeakEqual	(	const T	first,
		const T	second
	)

inlinestatic

Returns whether two values a equal up to a weak epsilon.

Parameters

first	The first value to check, with range (-infinity, infinity)
second	The second value to check, with range (-infinity, infinity)

Returns: True, if so

◆ isWeakEqualEps() [1/12]

constexpr bool Ocean::NumericT< int >::isWeakEqualEps ( const int value )

inlineconstexpr

◆ isWeakEqualEps() [2/12]

constexpr bool Ocean::NumericT< long long >::isWeakEqualEps ( const long long value )

inlineconstexpr

◆ isWeakEqualEps() [3/12]

constexpr bool Ocean::NumericT< long >::isWeakEqualEps ( const long value )

inlineconstexpr

◆ isWeakEqualEps() [4/12]

constexpr bool Ocean::NumericT< short >::isWeakEqualEps ( const short value )

inlineconstexpr

◆ isWeakEqualEps() [5/12]

constexpr bool Ocean::NumericT< signed char >::isWeakEqualEps ( const signed char value )

inlineconstexpr

◆ isWeakEqualEps() [6/12]

template<typename T >

constexpr bool Ocean::NumericT< T >::isWeakEqualEps ( const std::complex< T > & value )

inlinestaticconstexpr

Returns whether a complex value is smaller than or equal to a weak epsilon.

Parameters

value Complex value to check

Returns: True, if so

◆ isWeakEqualEps() [7/12]

template<typename T >

constexpr bool Ocean::NumericT< T >::isWeakEqualEps ( const T value )

inlinestaticconstexpr

Returns whether a value is smaller than or equal to a weak epsilon.

Parameters

value The value to check, with range (-infinity, infinity)

Returns: True, if so

◆ isWeakEqualEps() [8/12]

constexpr bool Ocean::NumericT< unsigned char >::isWeakEqualEps ( const unsigned char value )

inlineconstexpr

◆ isWeakEqualEps() [9/12]

constexpr bool Ocean::NumericT< unsigned int >::isWeakEqualEps ( const unsigned int value )

inlineconstexpr

◆ isWeakEqualEps() [10/12]

constexpr bool Ocean::NumericT< unsigned long long >::isWeakEqualEps ( const unsigned long long value )

inlineconstexpr

◆ isWeakEqualEps() [11/12]

constexpr bool Ocean::NumericT< unsigned long >::isWeakEqualEps ( const unsigned long value )

inlineconstexpr

◆ isWeakEqualEps() [12/12]

constexpr bool Ocean::NumericT< unsigned short >::isWeakEqualEps ( const unsigned short value )

inlineconstexpr

◆ log() [1/2]

float Ocean::NumericT< float >::log ( const float value )

inline

◆ log() [2/2]

template<typename T >

T Ocean::NumericT< T >::log ( const T value )

inlinestatic

Returns the natural logarithm of a given value (the logarithm to the base e).

Parameters

value The value to return the logarithm for, with range (0, infinity)

Returns: Natural logarithm

◆ log10() [1/2]

float Ocean::NumericT< float >::log10 ( const float value )

inline

◆ log10() [2/2]

template<typename T >

T Ocean::NumericT< T >::log10 ( const T value )

inlinestatic

Returns the logarithm to base 10 of a given value.

Parameters

value The value to return the logarithm for, with range (0, infinity)

Returns: Logarithm to base 10

◆ log1p() [1/2]

float Ocean::NumericT< float >::log1p ( const float value )

inline

◆ log1p() [2/2]

template<typename T >

T Ocean::NumericT< T >::log1p ( const T value )

inlinestatic

Returns the natural logarithm of a given value plus 1 (the logarithm to the base e).

This function has better precision than log(1 + value) when value is close to 0.

Parameters

value Input for which logarithm of (1 + value) will be returned, with range (-1, infinity)

Returns: Natural logarithm

◆ log2() [1/2]

float Ocean::NumericT< float >::log2 ( const float value )

inline

Specialization of NumericT::log2().

See also: NumericT::log2().

◆ log2() [2/2]

template<typename T >

T Ocean::NumericT< T >::log2 ( const T value )

inlinestatic

Returns the logarithm to base 2 of a given value.

Parameters

value The value to return the logarithm for, with range (0, infinity)

Returns: Logarithm to base 2

◆ maxValue()

template<typename T >

constexpr T Ocean::NumericT< T >::maxValue

inlinestaticconstexpr

Returns the max scalar value.

Returns: Max value

◆ minValue()

template<typename T >

constexpr T Ocean::NumericT< T >::minValue

inlinestaticconstexpr

Returns the min scalar value.

Returns: Min value

◆ nan()

template<typename T >

constexpr T Ocean::NumericT< T >::nan

inlinestaticconstexpr

Returns a value which is not a number (nan).

Returns: The nan value

◆ normalizedGaussianDistribution() [1/2]

template<typename T >

T Ocean::NumericT< T >::normalizedGaussianDistribution	(	const T	x,
		const T	sigma
	)

inlinestatic

Returns a value of the normalized univariate Gaussian distribution centered around the origin.

As the result is normalized, the resulting Gaussian distribution value is 1 at the origin.

Parameters

x	Value to return the Gaussian distribution value for
sigma	The sigma parameter defining the standard deviation of the Gaussian distribution, with range (0, infinity)

Returns: Function value

◆ normalizedGaussianDistribution() [2/2]

template<typename T >

T Ocean::NumericT< T >::normalizedGaussianDistribution	(	const T	x,
		const T	x0,
		const T	sigma
	)

inlinestatic

Returns a value of the normalized univariate Gaussian distribution around a given position x0.

As the result is normalized, the resulting Gaussian distribution value is 1 at the given position x0.

Parameters

x	Value to return the Gaussian distribution value for
x0	X value for the center of the Gaussian distribution
sigma	The sigma parameter defining the standard deviation of the Gaussian distribution, with range (0, infinity)

Returns: Function value

◆ normalizedGaussianDistribution2() [1/2]

template<typename T >

T Ocean::NumericT< T >::normalizedGaussianDistribution2	(	const T	x,
		const T	y,
		const T	sigmaX,
		const T	sigmaY
	)

inlinestatic

Returns a value of the normalized bivariate Gaussian distribution centered around the origin.

As the result is normalized, the resulting Gaussian distribution value is 1 at the origin.

Parameters

x	X value for the function
y	Y value for the function
sigmaX	Sigma parameter defining the standard deviation for the x-axis of the Gaussian distribution, with range (0, infinity)
sigmaY	Sigma parameter defining the standard deviation for the y-axis of the Gaussian distribution, with range (0, infinity)

Returns: Function value

◆ normalizedGaussianDistribution2() [2/2]

template<typename T >

T Ocean::NumericT< T >::normalizedGaussianDistribution2	(	const T	x,
		const T	y,
		const T	x0,
		const T	y0,
		const T	sigmaX,
		const T	sigmaY
	)

inlinestatic

Returns a value of the normalized bivariate Gaussian distribution centered around a given position (x0, y0).

As the result is normalized, the resulting Gaussian distribution value is 1 at the given position (x0, y0).

Parameters

x	X value for the function
y	Y value for the function
x0	X value for the center of the Gaussian distribution
y0	Y value for the center of the Gaussian distribution
sigmaX	Sigma parameter defining the standard deviation for the x-axis of the Gaussian distribution, with range (0, infinity)
sigmaY	Sigma parameter defining the standard deviation for the y-axis of the Gaussian distribution, with range (0, infinity)

Returns: Function value

◆ normalizedGaussianDistribution3() [1/2]

template<typename T >

T Ocean::NumericT< T >::normalizedGaussianDistribution3	(	const T	x,
		const T	y,
		const T	z,
		const T	sigmaX,
		const T	sigmaY,
		const T	sigmaZ
	)

inlinestatic

Returns a value of the normalized trivariate Gaussian distribution centered around the origin.

As the result is normalized, the resulting Gaussian distribution value is 1 at the origin.

Parameters

x	X value for the function
y	Y value for the function
z	Z value for the function
sigmaX	Sigma parameter defining the standard deviation for the x-axis of the Gaussian distribution, with range (0, infinity)
sigmaY	Sigma parameter defining the standard deviation for the y-axis of the Gaussian distribution, with range (0, infinity)
sigmaZ	Sigma parameter defining the standard deviation for the z-axis of the Gaussian distribution, with range (0, infinity)

Returns: Function value

◆ normalizedGaussianDistribution3() [2/2]

template<typename T >

T Ocean::NumericT< T >::normalizedGaussianDistribution3	(	const T	x,
		const T	y,
		const T	z,
		const T	x0,
		const T	y0,
		const T	z0,
		const T	sigmaX,
		const T	sigmaY,
		const T	sigmaZ
	)

inlinestatic

Returns a value of the normalized trivariate Gaussian distribution centered around a given position (x0, y0, z0).

As the result is normalized, the resulting Gaussian distribution value is 1 at the given position (x0, y0, z0).

Parameters

x	X value for the function
y	Y value for the function
z	Z value for the function
x0	X value for the center of the Gaussian distribution
y0	Y value for the center of the Gaussian distribution
z0	Z value for the center of the Gaussian distribution
sigmaX	Sigma parameter defining the standard deviation for the x-axis of the Gaussian distribution, with range (0, infinity)
sigmaY	Sigma parameter defining the standard deviation for the y-axis of the Gaussian distribution, with range (0, infinity)
sigmaZ	Sigma parameter defining the standard deviation for the z-axis of the Gaussian distribution, with range (0, infinity)

Returns: Function value

◆ pi()

template<typename T >

constexpr T Ocean::NumericT< T >::pi

staticconstexpr

Returns PI which is equivalent to 180 degree.

Returns: PI

◆ pi2()

template<typename T >

constexpr T Ocean::NumericT< T >::pi2

staticconstexpr

Returns 2*PI which is equivalent to 360 degree.

Returns: 2*PI

◆ pi_2()

template<typename T >

constexpr T Ocean::NumericT< T >::pi_2

staticconstexpr

Returns PI/2 which is equivalent to 90 degree.

Returns: PI/2

◆ pi_3()

template<typename T >

constexpr T Ocean::NumericT< T >::pi_3

staticconstexpr

Returns PI/3 which is equivalent to 60 degree.

Returns: PI/3

◆ pi_4()

template<typename T >

constexpr T Ocean::NumericT< T >::pi_4

staticconstexpr

Returns PI/4 which is equivalent to 45 degree.

Returns: PI/4

◆ pow() [1/3]

float Ocean::NumericT< float >::pow	(	const float	x,
		const float	y
	)

inline

Specialization of NumericT::pow().

See also: NumericT::pow().

◆ pow() [2/3]

template<typename T >

std::complex< T > Ocean::NumericT< T >::pow	(	const std::complex< T > &	x,
		const T	y
	)

inlinestatic

Returns x raised to the power of y.

Parameters

x	X value
y	Y value

Returns: The power result

◆ pow() [3/3]

template<typename T >

T Ocean::NumericT< T >::pow	(	const T	x,
		const T	y
	)

inlinestatic

Returns x raised to the power of y.

Parameters

x	X value, with range (-infinity, infinity), must not be negative if y < 1
y	Y value, with range (-infinity, infinity)

Returns: The power result

◆ pythagoras()

template<typename T >

T Ocean::NumericT< T >::pythagoras	(	const T	a,
		const T	b
	)

static

Returns the length of the hypotenuse of a given right-angled triangle.

This function avoids the calculation of square values of a and b.

Parameters

a	Length of the first leg
b	Length of the second leg

Returns: (a^2 + b^2)^0.5

◆ rad2deg()

template<typename T >

constexpr T Ocean::NumericT< T >::rad2deg ( const T rad )

inlinestaticconstexpr

Converts rad to deg.

Parameters

rad	Angle in radian, with range (-infinity, infinity)

Returns: Angle in deg

◆ ratio()

template<typename T >

constexpr T Ocean::NumericT< T >::ratio	(	const T	nominator,
		const T	denominator,
		const T	fallback = `T(1)`
	)

inlinestaticconstexpr

Returns the ratio between two values if the denominator is not equal a small epsilon.

Parameters

nominator	The nominator of the resulting ratio
denominator	The denominator of the resulting ratio
fallback	The fallback value if the denominator is equal eps()

Returns: The ratio between both values, the 'fallback' if the denominator is equal eps()

◆ round32()

template<typename T >

constexpr int32_t Ocean::NumericT< T >::round32 ( const T value )

inlinestaticconstexpr

Returns the rounded 32 bit integer value of a given value.

The function applies a symmetric rounding:

Input:     -1.50   -1.49  -0.50   -0.49   |   0.49   0.50    1.49   1.50
Output:    -2      -1     -1       0      |   0      1       1      2

So that for positive integer x:
x  <-  [x - 0.5, x + 0.5)

and for negative integer x:
x  <-  (x - 0.5, x + 0.5]

Parameters

value The value to handle, with range (-infinity, infinity)

Returns: Rounded value

◆ round64()

template<typename T >

constexpr int64_t Ocean::NumericT< T >::round64 ( const T value )

inlinestaticconstexpr

Returns the rounded 64 bit integer value of a given value.

The function applies a symmetric rounding:

Input:     -1.50   -1.49  -0.50   -0.49   |   0.49   0.50    1.49   1.50
Output:    -2      -1     -1       0      |   0      1       1      2

So that for positive integer x:
x  <-  [x - 0.5, x + 0.5)

and for negative integer x:
x  <-  (x - 0.5, x + 0.5]

Parameters

value The value to handle, with range (-infinity, infinity)

Returns: Rounded value

◆ secureAbs() [1/13]

double Ocean::NumericT< double >::secureAbs ( const double value )

inline

Specialization of NumericT::secureAbs().

See also: NumericT::secureAbs().

◆ secureAbs() [2/13]

float Ocean::NumericT< float >::secureAbs ( const float value )

inline

Specialization of NumericT::secureAbs().

See also: NumericT::secureAbs().

◆ secureAbs() [3/13]

unsigned int Ocean::NumericT< int >::secureAbs ( const int value )

inline

Specialization of NumericT::secureAbs().

See also: NumericT::secureAbs().

◆ secureAbs() [4/13]

unsigned long long Ocean::NumericT< long long >::secureAbs ( const long long value )

inline

Specialization of NumericT::secureAbs().

See also: NumericT::secureAbs().

◆ secureAbs() [5/13]

unsigned long Ocean::NumericT< long >::secureAbs ( const long value )

inline

Specialization of NumericT::secureAbs().

See also: NumericT::secureAbs().

◆ secureAbs() [6/13]

unsigned short Ocean::NumericT< short >::secureAbs ( const short value )

inline

Specialization of NumericT::secureAbs().

See also: NumericT::secureAbs().

◆ secureAbs() [7/13]

unsigned char Ocean::NumericT< signed char >::secureAbs ( const signed char value )

inline

Specialization of NumericT::secureAbs().

See also: NumericT::secureAbs().

◆ secureAbs() [8/13]

template<typename T >

UnsignedTyper< T >::Type Ocean::NumericT< T >::secureAbs ( const T value )

inlinestatic

Returns the absolute value of a given value while the return value is guaranteed to be the absolute value of the input value.

This function returns the unsigned data type T (if possible) and ensures that the absolute value of the minimal integer value is correct.

Parameters

value The value for which the absolute value will be returned

Returns: Absolute value

See also: abs().

◆ secureAbs() [9/13]

unsigned char Ocean::NumericT< unsigned char >::secureAbs ( const unsigned char value )

inline

Specialization of NumericT::secureAbs().

See also: NumericT::secureAbs().

◆ secureAbs() [10/13]

unsigned int Ocean::NumericT< unsigned int >::secureAbs ( const unsigned int value )

inline

Specialization of NumericT::secureAbs().

See also: NumericT::secureAbs().

◆ secureAbs() [11/13]

unsigned long long Ocean::NumericT< unsigned long long >::secureAbs ( const unsigned long long value )

inline

Specialization of NumericT::secureAbs().

See also: NumericT::secureAbs().

◆ secureAbs() [12/13]

unsigned long Ocean::NumericT< unsigned long >::secureAbs ( const unsigned long value )

inline

Specialization of NumericT::secureAbs().

See also: NumericT::secureAbs().

◆ secureAbs() [13/13]

unsigned short Ocean::NumericT< unsigned short >::secureAbs ( const unsigned short value )

inline

Specialization of NumericT::secureAbs().

See also: NumericT::secureAbs().

◆ sign()

template<typename T >

constexpr T Ocean::NumericT< T >::sign ( const T & value )

inlinestaticconstexpr

Returns the sign of a given value by either returning -1, 0, or +1.

Negative values have return value -1, 0 has return value 0, and positive values have return value +1.

Parameters

value The value for which the sign will be returned

◆ sin() [1/2]

float Ocean::NumericT< float >::sin ( const float value )

inline

Specialization of NumericT::sin().

See also: NumericT::sin().

◆ sin() [2/2]

template<typename T >

T Ocean::NumericT< T >::sin ( const T value )

inlinestatic

Returns the sine of a given value.

Parameters

value The value to return the sine from, with range (-infinity, infinity)

Returns: Sine value

◆ sqr()

template<typename T >

constexpr T Ocean::NumericT< T >::sqr ( const T value )

inlinestaticconstexpr

Returns the square of a given value.

Parameters

value The value to return the square from

Returns: Square value

◆ sqrDistance()

template<typename T >

constexpr T Ocean::NumericT< T >::sqrDistance	(	const T	value0,
		const T	value1
	)

inlinestaticconstexpr

Returns the square distance between two values.

Parameters

value0	First value
value1	Second value

Returns: Square distance

◆ sqrt() [1/4]

float Ocean::NumericT< float >::sqrt ( const float value )

inline

Specialization of NumericT::sqrt().

See also: NumericT::sqrt().

◆ sqrt() [2/4]

int Ocean::NumericT< int >::sqrt ( const int value )

inline

Specialization of NumericT::sqrt().

See also: NumericT::sqrt().

◆ sqrt() [3/4]

template<typename T >

std::complex< T > Ocean::NumericT< T >::sqrt ( const std::complex< T > & value )

inlinestatic

Returns the square root of a given value.

Parameters

value The value to return the square root from

Returns: Square root

◆ sqrt() [4/4]

template<typename T >

T Ocean::NumericT< T >::sqrt ( const T value )

inlinestatic

Returns the square root of a given value.

Parameters

value The value to return the square root from, with range [0, infinity)

Returns: Square root

◆ squarePi()

template<typename T >

constexpr T Ocean::NumericT< T >::squarePi

staticconstexpr

Returns the square of PI i.e., PI^2.

Returns: PI^2

◆ squarePi2()

template<typename T >

constexpr T Ocean::NumericT< T >::squarePi2

staticconstexpr

Returns the square of two PI i.e., (2*PI)^2.

Returns: (2*PI)^2

◆ squarePi_2()

template<typename T >

constexpr T Ocean::NumericT< T >::squarePi_2

staticconstexpr

Returns the square of PI half i.e., (PI/2)^2.

Returns: (PI/2)^2

◆ sum()

template<typename T >

T Ocean::NumericT< T >::sum	(	const T *	values,
		const size_t	number
	)

inlinestatic

Returns the sum of given values.

Parameters

values	The values to return the sum from
number	The number of given values

Returns: Sum of elements

◆ summedSqr()

template<typename T >

T Ocean::NumericT< T >::summedSqr	(	const T *	values,
		const size_t	number
	)

inlinestatic

Returns the summed squares of a given values.

Parameters

values	The values to return the summed squares from
number	The number of given values

Returns: Summed squared result

◆ tan() [1/2]

float Ocean::NumericT< float >::tan ( const float value )

inline

Specialization of NumericT::tan().

See also: NumericT::tan().

◆ tan() [2/2]

template<typename T >

T Ocean::NumericT< T >::tan ( const T value )

inlinestatic

Returns the tangent of a given value.

Parameters

value The value to return the tangent from, with range (-infinity, infinity)

Returns: Tangent value

◆ weakEps() [1/13]

template<typename T >

static constexpr T Ocean::NumericT< T >::weakEps ( )

staticconstexpr

Returns a weak epsilon.

Returns: Weak epsilon

◆ weakEps() [2/13]

constexpr double Ocean::NumericT< double >::weakEps ( )

constexpr

Specialization of NumericT::weakEps().

See also: NumericT::weakEps().

◆ weakEps() [3/13]

constexpr float Ocean::NumericT< float >::weakEps ( )

constexpr

Specialization of NumericT::weakEps().

See also: NumericT::weakEps().

◆ weakEps() [4/13]

constexpr signed char Ocean::NumericT< signed char >::weakEps ( )

constexpr

Specialization of NumericT::weakEps().

See also: NumericT::weakEps().

◆ weakEps() [5/13]

constexpr unsigned char Ocean::NumericT< unsigned char >::weakEps ( )

constexpr

Specialization of NumericT::weakEps().

See also: NumericT::weakEps().

◆ weakEps() [6/13]

constexpr short Ocean::NumericT< short >::weakEps ( )

constexpr

Specialization of NumericT::weakEps().

See also: NumericT::weakEps().

◆ weakEps() [7/13]

constexpr unsigned short Ocean::NumericT< unsigned short >::weakEps ( )

constexpr

Specialization of NumericT::weakEps().

See also: NumericT::weakEps().

◆ weakEps() [8/13]

constexpr int Ocean::NumericT< int >::weakEps ( )

constexpr

Specialization of NumericT::weakEps().

See also: NumericT::weakEps().

◆ weakEps() [9/13]

constexpr unsigned int Ocean::NumericT< unsigned int >::weakEps ( )

constexpr

Specialization of NumericT::weakEps().

See also: NumericT::weakEps().

◆ weakEps() [10/13]

constexpr long Ocean::NumericT< long >::weakEps ( )

constexpr

Specialization of NumericT::weakEps().

See also: NumericT::weakEps().

◆ weakEps() [11/13]

constexpr unsigned long Ocean::NumericT< unsigned long >::weakEps ( )

constexpr

Specialization of NumericT::weakEps().

See also: NumericT::weakEps().

◆ weakEps() [12/13]

constexpr long long Ocean::NumericT< long long >::weakEps ( )

constexpr

Specialization of NumericT::weakEps().

See also: NumericT::weakEps().

◆ weakEps() [13/13]

constexpr unsigned long long Ocean::NumericT< unsigned long long >::weakEps ( )

constexpr

Specialization of NumericT::weakEps().

See also: NumericT::weakEps().

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

Numeric.h

Public Member Functions

Static Public Member Functions

Detailed Description

template<typename T> class Ocean::NumericT< T >

Member Function Documentation

◆ abs() [1/13]

◆ abs() [2/13]

◆ abs() [3/13]

◆ abs() [4/13]

◆ abs() [5/13]

◆ abs() [6/13]

◆ abs() [7/13]

◆ abs() [8/13]

◆ abs() [9/13]

◆ abs() [10/13]

◆ abs() [11/13]

◆ abs() [12/13]

◆ abs() [13/13]

◆ acos() [1/2]

◆ acos() [2/2]

◆ angleAdjustNull()

◆ angleAdjustPositive()

◆ angleAdjustPositiveHalf()

◆ angleDistance()

◆ angleIsBelowThreshold()

◆ angleIsEqual() [1/2]

◆ angleIsEqual() [2/2]

◆ angleIsWeakEqual()

◆ asin() [1/2]

◆ asin() [2/2]

◆ atan() [1/2]

◆ atan() [2/2]

◆ atan2() [1/2]

◆ atan2() [2/2]

◆ binomialCoefficient()

◆ ceil() [1/4]

◆ ceil() [2/4]

◆ ceil() [3/4]

◆ ceil() [4/4]

◆ copySign() [1/3]

◆ copySign() [2/3]

◆ copySign() [3/3]

◆ cos() [1/2]

◆ cos() [2/2]

◆ deg2rad()

◆ dot()

◆ e()

◆ eps() [1/13]

◆ eps() [2/13]

◆ eps() [3/13]

◆ eps() [4/13]

◆ eps() [5/13]

◆ eps() [6/13]

◆ eps() [7/13]

◆ eps() [8/13]

◆ eps() [9/13]

◆ eps() [10/13]

◆ eps() [11/13]

◆ eps() [12/13]

◆ eps() [13/13]

◆ exp() [1/2]

◆ exp() [2/2]

◆ factorial() [1/2]

◆ factorial() [2/2]

◆ floor() [1/4]

◆ floor() [2/4]

◆ floor() [3/4]

◆ floor() [4/4]

◆ fmod() [1/2]

◆ fmod() [2/2]

◆ gaussianDistribution() [1/2]

◆ gaussianDistribution() [2/2]

◆ gaussianDistribution2() [1/2]

◆ gaussianDistribution2() [2/2]

◆ gaussianDistribution3() [1/2]

◆ gaussianDistribution3() [2/2]

◆ inf()

◆ integerPow()

◆ invertSign() [1/3]

◆ invertSign() [2/3]

template<typename T>
class Ocean::NumericT< T >