num_collect::constants::impl Namespace Reference

Namespace of internal implementations. More...

Functions
template<typename T >
constexpr auto	exp_maclaurin (T x) -> T
	Calculate exponential function with Maclaurin series.
template<typename T >
constexpr auto	expm1_maclaurin (T x) -> T
	Calculate exponential function minus one with Maclaurin series.
template<typename T >
constexpr auto	log1m_maclaurin (T x) -> T
	Calculate logarithm of 1 - x.
template<typename T , typename I >
constexpr auto	pow_pos_int (T base, I exp) -> T
	Calculate the value of base raised to the power exp.

Detailed Description

Namespace of internal implementations.

Function Documentation

exp_maclaurin()

template<typename T >

auto num_collect::constants::impl::exp_maclaurin ( T x ) -> T

constexpr

Calculate exponential function with Maclaurin series.

This calculates the following series:

\[ e^x = \sum_{k=0}^\infty \frac{x^k}{k!} \]

Note

This function is suitable for small positive numbers.

Template Parameters

T	Number type (assumed as floating-point number types).

Parameters

[in]

x

Number.

Returns

Exponential function.

Definition at line 41 of file exp_maclaurin.h.

expm1_maclaurin()

template<typename T >

auto num_collect::constants::impl::expm1_maclaurin ( T x ) -> T

constexpr

Calculate exponential function minus one with Maclaurin series.

This calculates the following series:

\[ e^x - 1 = \sum_{k=1}^\infty \frac{x^k}{k!} \]

Note

This function is suitable for small positive numbers.

Template Parameters

T	Number type (assumed as floating-point number types).

Parameters

[in]

x

Number.

Returns

Exponential function minus one.

Definition at line 42 of file expm1_maclaurin.h.

log1m_maclaurin()

template<typename T >

auto num_collect::constants::impl::log1m_maclaurin ( T x ) -> T

constexpr

Calculate logarithm of 1 - x.

This calculates the following series:

\[ log(1 - x) = -\sum_{k=1}^\infty \frac{x^k}{k} \]

Note

This function is suitable for small positive numbers.

Template Parameters

T	Number type.

Parameters

[in]

x

Number.

Returns

logarithm of 1 - x.

Definition at line 42 of file log1m_maclaurin.h.

pow_pos_int()

template<typename T , typename I >

auto num_collect::constants::impl::pow_pos_int ( T base, I exp ) -> T

constexpr

Calculate the value of base raised to the power exp.

Warning

Exponent is assumed to be a positive integer.

Template Parameters

T	Base type.
I	Integer type for exponent.

Parameters

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

Returns

Value of base raised to the power exp.

Definition at line 40 of file pow_pos_int.h.