log.hpp File Reference

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Namespaces
namespace	internal

Functions
template<typename T >
constexpr T	internal::log_cf_main (const T xx, const int depth) noexcept
template<typename T >
constexpr T	internal::log_cf_begin (const T x) noexcept
template<typename T >
constexpr T	internal::log_main (const T x) noexcept
constexpr long double	internal::log_mantissa_integer (const int x) noexcept
template<typename T >
constexpr T	internal::log_mantissa (const T x) noexcept
template<typename T >
constexpr T	internal::log_breakup (const T x) noexcept
template<typename T >
constexpr T	internal::log_check (const T x) noexcept
template<typename T >
constexpr return_t< T >	internal::log_integral_check (const T x) noexcept
template<typename T >
constexpr return_t< T >	log (const T x) noexcept
	Compile-time natural logarithm function. More...

Function Documentation

log()

template<typename T >

constexpr return_t< T > log ( const T  x )

constexprnoexcept

Compile-time natural logarithm function.

Parameters

x	a real-valued input.

Returns

\( \log_e(x) \) using

\[ \log\left(\frac{1+x}{1-x}\right) = \dfrac{2x}{1-\dfrac{x^2}{3-\dfrac{4x^2}{5 - \dfrac{9x^3}{7 - \ddots}}}}, \ \ x \in [-1,1] \]

The continued fraction argument is split into two parts: \( x = a \times 10^c \), where \( c \) is an integer.