Math.h File Reference

constexpr math implementations More...

#include "Molassembler/Temple/Preprocessor.h"
#include <cmath>
#include <limits>
#include <type_traits>

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Namespaces
	Scine::Molassembler
	Central library namespace.
	Scine::Molassembler::Temple
	Template shorthands, optimizers and constexpr data types.

Typedefs
template<typename T , typename U >
using	Scine::Molassembler::Temple::Math::Traits::enableIfFloatingWithReturn = std::enable_if_t< std::is_floating_point< T >::value, U >
template<typename T , typename U >
using	Scine::Molassembler::Temple::Math::Traits::enableIfIntegralWithReturn = std::enable_if_t< std::is_integral< T >::value, U >
template<typename T , typename U >
using	Scine::Molassembler::Temple::Math::Traits::enableIfArithmeticWithReturn = std::enable_if_t< std::is_arithmetic< T >::value, U >

Functions
template<typename FloatingPoint >
constexpr PURITY_STRONG std::enable_if_t< std::is_floating_point< FloatingPoint >::value, bool >	Scine::Molassembler::Temple::Math::Traits::isnan (const FloatingPoint x)
template<typename ... Bools>
constexpr bool	Scine::Molassembler::Temple::Math::XOR (Bools ... bools)
	Template parameter-pack exclusive or of booleans.
template<typename T >
constexpr Traits::enableIfArithmeticWithReturn< T, T >	Scine::Molassembler::Temple::Math::abs (T x) noexcept
	Absolute value.
template<typename T >
constexpr Traits::enableIfArithmeticWithReturn< T, T >	Scine::Molassembler::Temple::Math::max (T a, T b) noexcept
	Maximum of two values.
template<typename T >
constexpr Traits::enableIfArithmeticWithReturn< T, T >	Scine::Molassembler::Temple::Math::min (T a, T b) noexcept
	Minimum of two values.
template<typename T >
constexpr Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::toRadians (T inDegrees) noexcept
	Convert angular degrees to radians.
template<typename T >
constexpr Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::toDegrees (T inRadians) noexcept
	Convert angular radians to degrees.
template<typename T , typename U >
constexpr Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::fmod (T value, U divider) noexcept
	module function for arbitrary types
template<typename T >
constexpr Traits::enableIfFloatingWithReturn< T, long >	Scine::Molassembler::Temple::Math::ceil (T value) noexcept
	Ceiling function, no overflow check.
template<typename T >
constexpr Traits::enableIfFloatingWithReturn< T, int >	Scine::Molassembler::Temple::Math::floor (T value) noexcept
	Floor function.
template<typename T >
constexpr Traits::enableIfArithmeticWithReturn< T, T >	Scine::Molassembler::Temple::Math::pow (T base, unsigned exponent) noexcept
	Power of a number.
template<typename T >
constexpr Traits::enableIfArithmeticWithReturn< T, double >	Scine::Molassembler::Temple::Math::pow (T base, int exponent) noexcept
	Integer version that just calls the unsigned power function and inverts the result. More...
template<typename T >
constexpr Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::sqrt (T x)
	Square root.
template<typename T >
constexpr Traits::enableIfIntegralWithReturn< T, T >	Scine::Molassembler::Temple::Math::factorial (T x)
	Factorial.
template<typename T >
constexpr Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::ln (T x)
	Natural logarithm.
template<typename T >
constexpr Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::log10 (T x)
	Base-10 logarithm.
template<typename T >
constexpr Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::log (T x, T base)
	Arbitrary base logarithm.
template<typename T >
constexpr Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::asin (T x)
template<typename T >
constexpr Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::acos (T x)
	Inverse cosine.
template<typename T >
constexpr Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::atan (T x)
	Inverse tangens.
template<typename T >
constexpr PURITY_STRONG Traits::enableIfArithmeticWithReturn< T, T >	Scine::Molassembler::Temple::Math::abs (const T x) noexcept
	Absolute value.
template<typename T >
constexpr PURITY_STRONG Traits::enableIfArithmeticWithReturn< T, T >	Scine::Molassembler::Temple::Math::max (const T a, const T b) noexcept
	Maximum of two values.
template<typename T >
constexpr PURITY_STRONG Traits::enableIfArithmeticWithReturn< T, T >	Scine::Molassembler::Temple::Math::min (const T a, const T b) noexcept
	Minimum of two values.
template<typename T >
constexpr PURITY_STRONG Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::toRadians (const T inDegrees) noexcept
	Convert angular degrees to radians.
template<typename T >
constexpr PURITY_STRONG Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::toDegrees (const T inRadians) noexcept
	Convert angular radians to degrees.
template<typename T , typename U >
constexpr PURITY_STRONG Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::fmod (const T value, const U divider) noexcept
	module function for arbitrary types
template<typename T >
constexpr PURITY_STRONG Traits::enableIfFloatingWithReturn< T, long >	Scine::Molassembler::Temple::Math::ceil (const T value) noexcept
	Ceiling function, no overflow check.
template<typename T >
constexpr PURITY_STRONG Traits::enableIfFloatingWithReturn< T, int >	Scine::Molassembler::Temple::Math::floor (const T value) noexcept
	Floor function.
template<typename T >
constexpr PURITY_STRONG Traits::enableIfArithmeticWithReturn< T, T >	Scine::Molassembler::Temple::Math::pow (const T base, const unsigned exponent) noexcept
	Power of a number.
template<typename T >
constexpr PURITY_STRONG T	Scine::Molassembler::Temple::Math::recPow (const T base, const unsigned exponent) noexcept
template<typename T >
constexpr PURITY_STRONG Traits::enableIfArithmeticWithReturn< T, double >	Scine::Molassembler::Temple::Math::pow (const T base, const int exponent) noexcept
	Integer version that just calls the unsigned power function and inverts the result. More...
template<typename T >
constexpr PURITY_STRONG Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::sqrt (const T x)
	Square root.
template<typename T >
constexpr PURITY_STRONG Traits::enableIfIntegralWithReturn< T, T >	Scine::Molassembler::Temple::Math::factorial (const T x)
	Factorial.
template<typename T >
constexpr PURITY_STRONG Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::ln (const T x)
	Natural logarithm.
template<typename T >
constexpr PURITY_STRONG Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::log10 (const T x)
	Base-10 logarithm.
template<typename T >
constexpr PURITY_STRONG Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::log (const T x, const T base)
	Arbitrary base logarithm.
template<typename T >
constexpr PURITY_STRONG Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::asin (const T x)
template<typename T >
constexpr PURITY_STRONG Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::acos (const T x)
	Inverse cosine.
template<typename T >
constexpr PURITY_STRONG Traits::enableIfFloatingWithReturn< T, T >	Scine::Molassembler::Temple::Math::atan (const T x)
	Inverse tangens.

Detailed Description

constexpr math implementations

Copyright

This code is licensed under the 3-clause BSD license. Copyright ETH Zurich, Department of Chemistry and Applied Biosciences, Reiher Group. See LICENSE.txt for details.

Provides constexpr basic mathematical function implementations, some logical functions and floating-point comparison helpers.

Warning

Do not use these math functions for anything other than constexpr evaluations. The standard library implementations are most definitely better. In many cases, even though it is not required by the standard, the supplied STL functions are constexpr.

Function Documentation

asin() [1/2]

template<typename T >

constexpr PURITY_STRONG Traits::enableIfFloatingWithReturn<T, T> Scine::Molassembler::Temple::Math::asin ( T  x )

constexpr

Computes the inverse sine function.

NOTE: Accurate to only ~1e-9 absolute deviation close to domain boundaries

asin() [2/2]

template<typename T >

constexpr Traits::enableIfFloatingWithReturn<T, T> Scine::Molassembler::Temple::Math::asin ( T  x )

constexpr

Computes the inverse sine function.

NOTE: Accurate to only ~1e-9 absolute deviation close to domain boundaries

pow() [1/2]

template<typename T >

constexpr PURITY_STRONG Traits::enableIfArithmeticWithReturn<T, double> Scine::Molassembler::Temple::Math::pow ( const T  base, const int  exponent  )

constexprnoexcept

Integer version that just calls the unsigned power function and inverts the result.

Warning

lots can go wrong here!

pow() [2/2]

template<typename T >

constexpr Traits::enableIfArithmeticWithReturn<T, double> Scine::Molassembler::Temple::Math::pow ( const T  base, const int  exponent  )

constexprnoexcept

Integer version that just calls the unsigned power function and inverts the result.

Warning

lots can go wrong here!