Functions
template<typename T >
T	constantE ()
	Constant \(e\). More...

template<typename T >
T	constantLog2e ()
	Constant \(log2(e)\). More...

template<typename T >
T	constantLog10e ()
	Constant \(log10(e)\). More...

template<typename T >
T	constantLn2 ()
	Constant \(ln(2)\). More...

template<typename T >
T	constantLn10 ()
	Constant \(ln(10)\). More...

template<typename T >
T	constantPi ()
	Constant \(\pi\). More...

template<typename T >
T	constantPiBy2 ()
	Constant \(\pi / 2\). More...

template<typename T >
T	constantPiBy4 ()
	Constant \(\pi / 4\). More...

template<typename T >
T	constant1ByPi ()
	Constant \(1 / \pi\). More...

template<typename T >
T	constant2ByPi ()
	Constant \(2 / \pi\). More...

template<typename T >
T	constant2BySqrtPi ()
	Constant \(2 / \sqrt{\pi}\). More...

template<typename T >
T	constantSqrt2 ()
	Constant \(\sqrt{2}\). More...

template<typename T >
T	constant1BySqrt2 ()
	Constant \(1 / \sqrt{2}\). More...

template<typename T >
T	constantMaxIncrementable ()
	Maximal value that can be incremented to give a different value. More...

template<typename T >
T	constantMinDecrementable ()
	Minimal value that can be decremented to give a different value. More...

template<typename T >
bool	sameSign (T x, T y)
	Tells whether `x` and `y` are of the same sign. More...

template<typename T >
T	clamp (T value, T minVal, T maxVal)
	Clamps a value to a range. More...

template<typename T >
T	roundX (T number, size_t digits)
	Rounds a number to the specified number of fractional digits. More...

template<typename T >
T	round2 (T number)
	Rounds a number to 2 fractional digits. More...

template<typename T >
T	factorial (T n)
	Returns the factorial of a given number. More...

template<typename VALUES_TYPE , typename INCREASE_TYPE = VALUES_TYPE>
INCREASE_TYPE	proportionalIncrease (VALUES_TYPE initialValue, VALUES_TYPE finalValue)
	Returns the proportional increase from an initial value to a final value. More...

template<typename T >
T	increaseRate (T overallIncrease, size_t numPeriods)
	Converts an proportional increase over a number of periods to an increase rate per period. More...

template<typename VALUES_TYPE , typename INCREASE_TYPE = VALUES_TYPE>
INCREASE_TYPE	increaseRate (VALUES_TYPE initialValue, VALUES_TYPE finalValue, size_t numPeriods)
	Returns the increase rate per period giving a final value from an initial value over a given number of periods. More...

Detailed Description

Set of helper constants and functions.

Function Documentation

◆ constantE()

template<typename T >

T shlublu::Math::constantE ( )

inline

Constant \(e\).

As per the legacy <math.h> C header.

Template Parameters

T	the type of the returned value. This type should be floating point.

Returns: \(e\)

◆ constantLog2e()

template<typename T >

T shlublu::Math::constantLog2e ( )

inline

Constant \(log2(e)\).

As per the legacy <math.h> C header.

Template Parameters

T	the type of the returned value. This type should be floating point.

Returns: \(log2(e)\)

◆ constantLog10e()

template<typename T >

T shlublu::Math::constantLog10e ( )

inline

Constant \(log10(e)\).

As per the legacy <math.h> C header.

Template Parameters

T	the type of the returned value. This type should be floating point.

Returns: \(log10(e)\)

◆ constantLn2()

template<typename T >

T shlublu::Math::constantLn2 ( )

inline

Constant \(ln(2)\).

As per the legacy <math.h> C header.

Template Parameters

T	the type of the returned value. This type should be floating point.

Returns: \(ln(2)\)

◆ constantLn10()

template<typename T >

T shlublu::Math::constantLn10 ( )

inline

Constant \(ln(10)\).

As per the legacy <math.h> C header.

Template Parameters

T	the type of the returned value. This type should be floating point.

Returns: \(ln(10)\)

◆ constantPi()

template<typename T >

T shlublu::Math::constantPi ( )

inline

Constant \(\pi\).

As per the legacy <math.h> C header.

Template Parameters

T	the type of the returned value. This type should be floating point.

Returns: \(\pi\)

◆ constantPiBy2()

template<typename T >

T shlublu::Math::constantPiBy2 ( )

inline

Constant \(\pi / 2\).

As per the legacy <math.h> C header.

Template Parameters

T	the type of the returned value. This type should be floating point.

Returns: \(\pi / 2\)

◆ constantPiBy4()

template<typename T >

T shlublu::Math::constantPiBy4 ( )

inline

Constant \(\pi / 4\).

As per the legacy <math.h> C header.

Template Parameters

T	the type of the returned value. This type should be floating point.

Returns: \(\pi / 4\)

◆ constant1ByPi()

template<typename T >

T shlublu::Math::constant1ByPi ( )

inline

Constant \(1 / \pi\).

As per the legacy <math.h> C header.

Template Parameters

T	the type of the returned value. This type should be floating point.

Returns: \(1 / \pi\)

◆ constant2ByPi()

template<typename T >

T shlublu::Math::constant2ByPi ( )

inline

Constant \(2 / \pi\).

As per the legacy <math.h> C header.

Template Parameters

T	the type of the returned value. This type should be floating point.

Returns: \(2 / \pi\)

◆ constant2BySqrtPi()

template<typename T >

T shlublu::Math::constant2BySqrtPi ( )

inline

Constant \(2 / \sqrt{\pi}\).

As per the legacy <math.h> C header.

Template Parameters

T	the type of the returned value. This type should be floating point.

Returns: \(2 / \sqrt{\pi}\)

◆ constantSqrt2()

template<typename T >

T shlublu::Math::constantSqrt2 ( )

inline

Constant \(\sqrt{2}\).

As per the legacy <math.h> C header.

Template Parameters

T	the type of the returned value. This type should be floating point.

Returns: \(\sqrt{2}\)

◆ constant1BySqrt2()

template<typename T >

T shlublu::Math::constant1BySqrt2 ( )

inline

Constant \(1 / \sqrt{2}\).

As per the legacy <math.h> C header.

Template Parameters

T	the type of the returned value. This type should be floating point.

Returns: \(1 / \sqrt{2}\)

◆ constantMaxIncrementable()

template<typename T >

T shlublu::Math::constantMaxIncrementable ( )

inline

Maximal value that can be incremented to give a different value.

Determined as \(f + 1 \neq f\).

Template Parameters

T	the type to apply this function to. This type should be floating point.

Returns: the value applicable to T

Note: Linux long double is currently handled as double though it would support higher values.

◆ constantMinDecrementable()

template<typename T >

T shlublu::Math::constantMinDecrementable ( )

inline

Minimal value that can be decremented to give a different value.

Determined as \(f - 1 \neq f\).

Template Parameters

T	the type to apply this function to. This type should be floating point.

Returns: the value applicable to T

Note: Linux long double is currently handled as double though it would support lower values.

◆ sameSign()

template<typename T >

bool shlublu::Math::sameSign	(	T	x,
		T	y
	)

Tells whether x and y are of the same sign.

Template Parameters

the	type of `x` and `y`. This type should be arithmetic.

Parameters

x	a value
y	another value

Returns: true if x and y are of the same sign, false otherwise

◆ clamp()

template<typename T >

T shlublu::Math::clamp	(	T	value,
		T	minVal,
		T	maxVal
	)

Clamps a value to a range.

Template Parameters

T	The type of the value and the range. This type should be non-boolean arithmetic.

Parameters

value	the value to clamp
minVal	the lower inclusive bound of the range
maxVal	the upper inclusive bound of the range

Returns: value if \(value \in [minVal, maxVal]\), minVal if \(value < minVal\), and maxVal if \(value > maxVal\)

Exceptions

std::invalid_argument if minVal > maxVal

◆ roundX()

template<typename T >

T shlublu::Math::roundX	(	T	number,
		size_t	digits
	)

Rounds a number to the specified number of fractional digits.

Template Parameters

T	the type of the number to round and of the returned value. This type should be floating point.

Parameters

number	the number to round
digits	the number of fractional digits to round `number` to

Returns: the rounded value of number

◆ round2()

template<typename T >

T shlublu::Math::round2 ( T number )

Rounds a number to 2 fractional digits.

Template Parameters

T	the type of the number to round and of the returned value. This type should be floating point.

Parameters

number the number to round

Returns: the rounded value of number

See also: roundX()

◆ factorial()

template<typename T >

T shlublu::Math::factorial ( T n )

Returns the factorial of a given number.

This function is only defined for \(n \in \mathbb{N+}\)

Template Parameters

T	the type of `n` and of the returned value

Parameters

n	the number whose factorial is to be calculated

Returns: the factorial of n

Exceptions

std::domain_error if \(n \notin \mathbb{N+}\)

◆ proportionalIncrease()

template<typename VALUES_TYPE , typename INCREASE_TYPE = VALUES_TYPE>

INCREASE_TYPE shlublu::Math::proportionalIncrease	(	VALUES_TYPE	initialValue,
		VALUES_TYPE	finalValue
	)

inline

Returns the proportional increase from an initial value to a final value.

The increase I is defined as \(Vfinal = Vinitial + (Vinitial \times I)\), leading to \(I = (Vfinal / Vinitial) - 1\).

If I be negative, this is a decrease.

Template Parameters

VALUES_TYPE	the type of the initial and final values. This type should be arithmetic.
INCREASE_TYPE	the type of the resulting increase. This type should be floating point.

Parameters

initialValue	the initial value
finalValue	the final value

Returns: The proportional increase \((Vfinal / Vinitial) - 1\). initialValue is converted to INCREASE_TYPE to ensure this is a floating point division.

Exceptions

std::invalid_argument if initialValue is zero

◆ increaseRate() [1/2]

template<typename T >

T shlublu::Math::increaseRate	(	T	overallIncrease,
		size_t	numPeriods
	)

inline

Converts an proportional increase over a number of periods to an increase rate per period.

This is the increase rate that produces the overall increase when applied to each period.
This rate R is defined as \((R + 1) ^ N = O + 1\), where N is the number of periods and O the overall increase. This leads to \(R = \sqrt[N]{O + 1} - 1\).

This function only applies to \(O > -1\) as -1 or less would correspond to a decrease of 100% or more, leading the result R not to be a real number.

Template Parameters

T	the type of the overall increase and the returned rate. This type should be floating point.

Parameters

overallIncrease	the proportional increase over all the periods of times
numPeriods	the number of periods of time that are covered

Returns: the increase rate \(\sqrt[N]{O + 1} - 1\)

Exceptions

std::invalid_argument	if `numPeriods` is zero
std::domain_error	if `overallIncrease <= -1`

◆ increaseRate() [2/2]

template<typename VALUES_TYPE , typename INCREASE_TYPE = VALUES_TYPE>

INCREASE_TYPE shlublu::Math::increaseRate	(	VALUES_TYPE	initialValue,
		VALUES_TYPE	finalValue,
		size_t	numPeriods
	)

inline

Returns the increase rate per period giving a final value from an initial value over a given number of periods.

This rate R is defined as \(Vfinal = Vinitial \times (R + 1)^N\) where N is the number of periods. This leads to \(R = \sqrt[N]{Vfinal / Vinitial} - 1\).

This function only applies to:

\(Vinitial > 0\) and
\(Vfinal / Vinitial > 0\) as zero or less would correspond to a decrease of 100% or more, leading the result R not to be a real number.

Template Parameters

VALUES_TYPE	the type of the initial and final values. This type should be arithmetic.
INCREASE_TYPE	the type of the resulting increase. This type should be floating point.

Parameters

initialValue	the initial value
finalValue	the final value
numPeriods	the number of periods of time that are covered

Returns: the increase rate \(\sqrt[N]{Vfinal / Vinitial} - 1\)

Exceptions

std::invalid_argument	if `initialValue` is zero or if `numPeriods` is zero
std::domain_error	if `initialValue` is zero, or if `finalValue / initialValue <= 0`

Functions

Detailed Description

Function Documentation

◆ constantE()

◆ constantLog2e()

◆ constantLog10e()

◆ constantLn2()

◆ constantLn10()

◆ constantPi()

◆ constantPiBy2()

◆ constantPiBy4()

◆ constant1ByPi()

◆ constant2ByPi()

◆ constant2BySqrtPi()

◆ constantSqrt2()

◆ constant1BySqrt2()

◆ constantMaxIncrementable()

◆ constantMinDecrementable()

◆ sameSign()

◆ clamp()

◆ roundX()

◆ round2()

◆ factorial()

◆ proportionalIncrease()

◆ increaseRate() [1/2]

◆ increaseRate() [2/2]