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Basic functionality used frequently throughout the whole library. More...
Concepts | |
| concept | ntlib::HasAdditiveNeutral |
| Restricts to types with an additive neutral element. | |
| concept | ntlib::HasMultiplicativeNeutral |
| Restricts to types with a multiplicative neutral element. | |
| concept | ntlib::AdditiveSemigroup |
| Restricts to types modeling an additive semigroup. | |
| concept | ntlib::MultiplicativeSemigroup |
| Restricts to types modeling a multiplication semigroup. | |
| concept | ntlib::AdditiveMonoid |
| Restricts to types modeling an additive monoid. | |
| concept | ntlib::MultiplicativeMonoid |
| Restricts to types modeling a multiplicative monoid. | |
| concept | ntlib::HasAdditiveInverses |
| concept | ntlib::HasMultiplicativeInverses |
| Restricts to types with multiplicative inverse elements. | |
| concept | ntlib::AdditiveGroup |
| Restricts to types modeling an additive group. | |
| concept | ntlib::MultiplicativeGroup |
| Restricts to types modeling a multiplicative group. | |
| concept | ntlib::IsAdditiveCommutative |
| Restricts to types with a commutative addition operation. | |
| concept | ntlib::IsMultiplicativeCommutative |
| Restricts to types with a commutative multiplication operation. | |
| concept | ntlib::AdditiveCommutativeGroup |
| Restricts to types modeling an additive commutative group. | |
| concept | ntlib::MultiplicativeCommutativeGroup |
| Restricts to types modeling a multiplicative commutative group. | |
| concept | ntlib::Ring |
| Restricts to types modeling a ring. | |
| concept | ntlib::CommutativeRing |
| Restricts to types modeling a commutative ring. | |
| concept | ntlib::Field |
| Restricts to types modeling a field. | |
| concept | ntlib::HasDivisionWithRemainder |
| Restricts to types supporting division with remainder. | |
| concept | ntlib::Integer |
| Restricts to types modeling the integers. | |
Classes | |
| class | ntlib::algebra_traits< typename > |
| Traits class for algebraic types. More... | |
| class | ntlib::algebra_traits< T > |
| Specialization of ntlib::algebra_traits for integral types. More... | |
Functions | |
| template<Integer T> | |
| constexpr bool | ntlib::is_odd (T n) noexcept |
| Checks whether a given number is odd. | |
| template<Integer T> | |
| constexpr bool | ntlib::is_even (T n) noexcept |
| Checks whether a given number is even. | |
| template<AdditiveGroup T> | |
| constexpr T | ntlib::abs (T n) noexcept |
| Computes the absolute value of a given number. | |
| template<AdditiveGroup T> | |
| constexpr T | ntlib::difference (T a, T b) noexcept |
| Computes the difference between two numbers. | |
| template<std::totally_ordered T> | |
| constexpr int | ntlib::sgn (T n) noexcept |
| Computes the sign of a given number. | |
| template<Integer T> | |
| constexpr std::pair< T, T > | ntlib::odd_part (T n) noexcept |
| Given a number n, computes a pair (e, o), such that n=2^e*o. | |
| template<Integer T> | |
| constexpr T | ntlib::gcd (T a, T b) noexcept |
| Computes the greatest common divisor of two numbers using the Euclidean algorithm. | |
| template<Integer T> | |
| constexpr T | ntlib::gcd (std::initializer_list< T > list) noexcept |
| Computes the greatest common divisor of a list of numbers. | |
| template<Integer T> | |
| constexpr T | ntlib::lcm (T a, T b) noexcept |
| Computes the least common multiple of two numbers. | |
| template<Integer T> | |
| constexpr T | ntlib::lcm (std::initializer_list< T > list) noexcept |
| Computes the least common multiple of a list of numbers. | |
| template<Integer T> | |
| constexpr std::tuple< T, T, T > | ntlib::extended_euclid (T a, T b) noexcept |
| Extended Euclidean algorithm. | |
| template<MultiplicativeMonoid A, Integer B> | |
| constexpr A | ntlib::pow (A a, B b) noexcept |
| Binary exponentation. | |
| template<Integer T> | |
| constexpr T | ntlib::ilog2 (T n) noexcept |
| Computes the integer part of the binary logarithm of a given number. | |
| template<Integer T> | |
| constexpr T | ntlib::isqrt (T n) noexcept |
| Computes the integer square root of a given number. | |
| template<Integer T> | |
| constexpr bool | ntlib::is_square (T n) noexcept |
| Tests, if a given number is a perfect square. | |
| template<Integer T> | |
| constexpr T | ntlib::factorial (T n) noexcept |
| Computes the factorial of a given number. | |
| template<typename T> | |
| constexpr T | ntlib::zero () noexcept |
| Returns the additive neutral element of a given type. | |
| template<typename T> | |
| constexpr T | ntlib::one () noexcept |
| Returns the multiplicative neutral element of a given type. | |
Variables | |
| template<Integer T> | |
| constexpr auto | ntlib::SMALL_PRIMES |
| A list with all prime numbers up to ntlib::SMALL_PRIMES_BIGGEST. | |
| template<Integer T> | |
| constexpr T | ntlib::SMALL_PRIMES_BIGGEST |
| Helper constant to get the biggest among the small primes in ntlib::SMALL_PRIMES. | |
Detailed Description
Basic functionality used frequently throughout the whole library.
Functionality contained in this module has no further dependencies and only depends on the C++ standard library.
Files | |
| file | modules/base/base.cpp |
| Primary module interface unit for module base. | |
| file | modules/base/concepts.cpp |
| Module interface unit for module base, partition concepts. | |
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