Namespace of constexpr variables and functions. More...

Namespaces
namespace	impl
	Namespace of internal implementations.

Functions
template<typename T >
constexpr auto	cbrt (T x)
	Calculate cubic root \( \sqrt[3]{x} \).

template<typename T >
constexpr auto	ceil (T x) -> T
	Calculate the smallest integer not less than x, \( \lceil x \rceil \).

template<typename T , typename = std::enable_if_t<std::is_floating_point_v<T>>>
constexpr auto	exp (T x) -> T
	Calculate exponential function \( e^x \).

template<typename T , typename = std::enable_if_t<std::is_floating_point_v<T>>>
constexpr auto	expm1 (T x) -> T
	Calculate exponential function minus one \( e^x - 1 \).

template<typename T >
constexpr auto	floor (T x) -> T
	Calculate the largest integer not greater than x, \( \lfloor x \rfloor \).

template<typename T , typename = std::enable_if_t<std::is_floating_point_v<T>>>
constexpr auto	log (T x) -> T
	Calculate logarithm \( \log(x) \).

template<typename T , typename = std::enable_if_t<std::is_floating_point_v<T>>>
constexpr auto	log1p (T x) -> T
	Calculate natural logarithm of 1 + x, \( \log(1 + x) \).

template<typename B , typename E , std::enable_if_t< std::is_integral_v< E >, void * > = nullptr>
constexpr auto	pow (B base, E exp) -> B
	Calculate power \( {base}^{exp} \).

template<typename T , std::enable_if_t< std::is_floating_point_v< T >, void * > = nullptr>
constexpr auto	pow (T base, T exp) -> T
	Calculate power \( {base}^{exp} \).

template<typename F , typename I , std::enable_if_t< std::is_floating_point_v< F > &&std::is_integral_v< I >, void * > = nullptr>
constexpr auto	root (F x, I n) -> F
	Calculate n-th root \( \sqrt[n]{x} \).

template<typename IB , typename IE , std::enable_if_t< std::is_integral_v< IB > &&std::is_integral_v< IE >, void * > = nullptr>
constexpr auto	root (IB x, IE n) -> double
	Calculate n-th root \( \sqrt[n]{x} \).

template<typename F , std::enable_if_t< std::is_floating_point_v< F >, void * > = nullptr>
constexpr auto	sqrt (F x) -> F
	Calculate square root \( \sqrt{x} \).

template<typename I , std::enable_if_t< std::is_integral_v< I >, void * > = nullptr>
constexpr auto	sqrt (I x) -> double
	Calculate square root \( \sqrt{x} \).

template<typename T >
constexpr auto	trunc (T x) -> T
	Truncate the decimal part of a number x.

Variables
template<typename T >
constexpr T	half = static_cast<T>(0.5)
	Value 0.5.

template<typename T >
constexpr T	napier = static_cast<T>(NUM_COLLECT_NAPIER)
	Value of Napier's constant (or Euler's number), \( e = 2.7182818284590452 \ldots \).

template<typename T >
constexpr T	one = static_cast<T>(1)
	Value 1.

template<typename T >
constexpr T	pi = static_cast<T>(NUM_COLLECT_PI)
	Value of pi, \( \pi = 3.141592653589793238462 \dots \).

constexpr double	pid = pi<double>
	Value of pi.

constexpr float	pif = pi<float>
	Value of pi.

template<typename T >
constexpr T	two = static_cast<T>(2)
	Value 2.

template<typename T >
constexpr T	zero = static_cast<T>(0)
	Value 0.

Detailed Description

Namespace of constexpr variables and functions.

Function Documentation

◆ cbrt()

template<typename T >

auto num_collect::constants::cbrt ( T x )

constexpr

Calculate cubic root \( \sqrt[3]{x} \).

This function calculates similar values as cbrt function in C++ standard library in constexpr.

Template Parameters

T	Value type.

Parameters

[in] x Value to calculate cubic root of.

Returns: Cubic root.

Definition at line 38 of file cbrt.h.

◆ ceil()

template<typename T >

auto num_collect::constants::ceil ( T x ) -> T

constexpr

Calculate the smallest integer not less than x, \( \lceil x \rceil \).

This function calculates similar values as ceil function in C++ standard library in constexpr.

Note: This function assumes that inputs are floating-point numbers.

Template Parameters

T	Number type.

Parameters

[in] x Number.

Returns: Smallest integer not less than x.

Definition at line 43 of file ceil.h.

◆ exp()

template<typename T , typename = std::enable_if_t<std::is_floating_point_v<T>>>

auto num_collect::constants::exp ( T x ) -> T

constexpr

Calculate exponential function \( e^x \).

This function calculates similar values as exp function in C++ standard library in constexpr.

Template Parameters

T	Number type.

Parameters

[in] x Number.

Returns: Exponential function value.

Definition at line 46 of file exp.h.

◆ expm1()

template<typename T , typename = std::enable_if_t<std::is_floating_point_v<T>>>

auto num_collect::constants::expm1 ( T x ) -> T

constexpr

Calculate exponential function minus one \( e^x - 1 \).

This function calculates similar values as expm1 function in C++ standard library in constexpr.

This function has following optimization for small values:

for \( 0 \le x \le 1 \), Maclaurin series for \( e^x - 1 \) is used.
for \( -1 \le x < 0 \), \( e^x - 1 = - (e^{-x} - 1) / e^{-x} \) is calculated.

Template Parameters

T	Number type.

Parameters

[in] x Number.

Returns: Exponential function minus one.

Definition at line 49 of file expm1.h.

◆ floor()

template<typename T >

auto num_collect::constants::floor ( T x ) -> T

constexpr

Calculate the largest integer not greater than x, \( \lfloor x \rfloor \).

This function calculates similar values as floor function in C++ standard library in constexpr.

Note: This function assumes that inputs are floating-point numbers.

Template Parameters

T	Number type.

Parameters

[in] x Number.

Returns: Largest integer not greater than x.

Definition at line 43 of file floor.h.

◆ log()

template<typename T , typename = std::enable_if_t<std::is_floating_point_v<T>>>

auto num_collect::constants::log ( T x ) -> T

constexpr

Calculate logarithm \( \log(x) \).

This function calculates similar values as log function in C++ standard library in constexpr.

Template Parameters

T	Number type.

Parameters

[in] x Number.

Returns: Logarithm

Definition at line 43 of file log.h.

◆ log1p()

template<typename T , typename = std::enable_if_t<std::is_floating_point_v<T>>>

auto num_collect::constants::log1p ( T x ) -> T

constexpr

Calculate natural logarithm of 1 + x, \( \log(1 + x) \).

This function calculates similar values as log1p function in C++ standard library in constexpr.

This function can calculate natural logarithm of numbers near to 1 more accurately.

Template Parameters

T	Number type.

Parameters

[in] x Number.

Returns: Logarithm of 1 - x.

Definition at line 47 of file log1p.h.

◆ pow() [1/2]

template<typename B , typename E , std::enable_if_t< std::is_integral_v< E >, void * > = nullptr>

auto num_collect::constants::pow	(	B	base,
		E	exp ) -> B

constexpr

Calculate power \( {base}^{exp} \).

This function calculates similar values as pow function in C++ standard library in constexpr.

Template Parameters

B	Base type.
E	Exponent type.

Parameters

[in]	base	Base.
[in]	exp	Exponent.

Returns: Power.

Definition at line 47 of file pow.h.

◆ pow() [2/2]

template<typename T , std::enable_if_t< std::is_floating_point_v< T >, void * > = nullptr>

auto num_collect::constants::pow	(	T	base,
		T	exp ) -> T

constexpr

Calculate power \( {base}^{exp} \).

This function calculates similar values as pow function in C++ standard library in constexpr.

Template Parameters

T	Number type.

Parameters

[in]	base	Base.
[in]	exp	Exponent.

Returns: Power.

Definition at line 70 of file pow.h.

◆ root() [1/2]

template<typename F , typename I , std::enable_if_t< std::is_floating_point_v< F > &&std::is_integral_v< I >, void * > = nullptr>

auto num_collect::constants::root	(	F	x,
		I	n ) -> F

constexpr

Calculate n-th root \( \sqrt[n]{x} \).

Template Parameters

F	Value type.
I	Integer type for n.

Parameters

[in]	x	Value to calculate n-th root of.
[in]	n	Exponent.

Returns: n-th root of x.

Definition at line 44 of file root.h.

◆ root() [2/2]

template<typename IB , typename IE , std::enable_if_t< std::is_integral_v< IB > &&std::is_integral_v< IE >, void * > = nullptr>

auto num_collect::constants::root	(	IB	x,
		IE	n ) -> double

constexpr

Calculate n-th root \( \sqrt[n]{x} \).

Template Parameters

IB	Value type.
IE	Integer type for n.

Parameters

[in]	x	Value to calculate n-th root of.
[in]	n	Exponent.

Returns: n-th root of x.

Definition at line 86 of file root.h.

◆ sqrt() [1/2]

template<typename F , std::enable_if_t< std::is_floating_point_v< F >, void * > = nullptr>

auto num_collect::constants::sqrt ( F x ) -> F

constexpr

Calculate square root \( \sqrt{x} \).

This function calculates similar values as sqrt function in C++ standard library in constexpr.

Template Parameters

F	Value type.

Parameters

[in] x Value to calculate square root of.

Returns: Square root.

Definition at line 44 of file sqrt.h.

◆ sqrt() [2/2]

template<typename I , std::enable_if_t< std::is_integral_v< I >, void * > = nullptr>

auto num_collect::constants::sqrt ( I x ) -> double

constexpr

Calculate square root \( \sqrt{x} \).

This function calculates similar values as sqrt function in C++ standard library in constexpr.

Template Parameters

I	Value type.

Parameters

[in] x Value to calculate square root of.

Returns: Square root.

Definition at line 78 of file sqrt.h.

◆ trunc()

template<typename T >

auto num_collect::constants::trunc ( T x ) -> T

constexpr

Truncate the decimal part of a number x.

This function calculates similar values as trunc function in C++ standard library in constexpr.

Note: This function assumes that inputs are floating-point numbers.

Template Parameters

T	Number type.

Parameters

[in] x Number to truncate.

Returns: Truncated number.

Definition at line 43 of file trunc.h.

Variable Documentation

◆ half

template<typename T >

T num_collect::constants::half = static_cast<T>(0.5)

constexpr

Value 0.5.

Template Parameters

T	Value type.

Definition at line 30 of file half.h.

◆ napier

template<typename T >

T num_collect::constants::napier = static_cast<T>(NUM_COLLECT_NAPIER)

constexpr

Value of Napier's constant (or Euler's number), \( e = 2.7182818284590452 \ldots \).

Template Parameters

T	Value type.

Definition at line 41 of file napier.h.

◆ one

template<typename T >

T num_collect::constants::one = static_cast<T>(1)

constexpr

Value 1.

Template Parameters

T	Value type.

Definition at line 30 of file one.h.

◆ pi

template<typename T >

T num_collect::constants::pi = static_cast<T>(NUM_COLLECT_PI)

constexpr

Value of pi, \( \pi = 3.141592653589793238462 \dots \).

Template Parameters

T	Value type.

Definition at line 40 of file pi.h.

◆ pid

double num_collect::constants::pid = pi<double>

constexpr

Value of pi.

Definition at line 45 of file pi.h.

◆ pif

float num_collect::constants::pif = pi<float>

constexpr

Value of pi.

Definition at line 50 of file pi.h.

◆ two

template<typename T >

T num_collect::constants::two = static_cast<T>(2)

constexpr

Value 2.

Template Parameters

T	Value type.

Definition at line 30 of file two.h.

◆ zero

template<typename T >

T num_collect::constants::zero = static_cast<T>(0)

constexpr

Value 0.

Template Parameters

T	Value type.

Definition at line 30 of file zero.h.

Namespaces

Functions

Variables

Detailed Description

Function Documentation

◆ cbrt()

◆ ceil()

◆ exp()

◆ expm1()

◆ floor()

◆ log()

◆ log1p()

◆ pow() [1/2]

◆ pow() [2/2]

◆ root() [1/2]

◆ root() [2/2]

◆ sqrt() [1/2]

◆ sqrt() [2/2]

◆ trunc()

Variable Documentation

◆ half

◆ napier

◆ one

◆ pi

◆ pid

◆ pif

◆ two

◆ zero