intalg.hpp File Reference

#include "config.hpp"
#include <cmath>
#include "exception.hpp"
#include "type_traits.hpp"
#include "factory.hpp"
#include "cmp.hpp"
#include "gcd.hpp"
#include "powerest.hpp"
#include "std_import.hpp"
#include "intalg.cpp"

Go to the source code of this file.

Namespaces
namespace	Arageli
namespace	Arageli::_Internal
namespace	std
Jacobi symbol.
template<typename T, typename T_factory>
int	Arageli::jacobi (T a, T n, const T_factory &tfctr)
	Computes the Jacobi symbol (a/n).
template<typename T>
int	Arageli::jacobi (const T &a, const T &n)
	Computes the Jacobi symbol (a/n).
Specialization of std::sqrt for all integer type as Arageli::intsqrt.
char	std::sqrt (char a)
unsigned char	std::sqrt (unsigned char a)
signed char	std::sqrt (signed char a)
unsigned short	std::sqrt (unsigned short a)
signed short	std::sqrt (signed short a)
unsigned int	std::sqrt (unsigned int a)
signed int	std::sqrt (signed int a)
unsigned long	std::sqrt (unsigned long a)
signed long	std::sqrt (signed long a)
Defines
#define	ARAGELI_INCLUDE_CPP_WITH_EXPORT_TEMPLATE_INTALG
Functions
template<typename T, typename T_factory>
T	Arageli::inverse_mod (const T &a, const T &m, const T_factory &tfctr)
	Returns inversion of a modulo n.
template<typename T>
T	Arageli::inverse_mod (const T &a, const T &n)
	Returns inversion of a modulo n.
template<typename T, typename I, typename T_factory>
T	Arageli::power_mod (T a, I n, const T &m, const T_factory &tfctr)
	Exponentiates a in to power n modulo m via squaring and adding.
template<typename T, typename I>
T	Arageli::power_mod (const T &a, const I &n, const T &m)
	Exponentiates a in to power n modulo m via squaring and adding.
template<typename T>
T	Arageli::_Internal::conditioner (const T &a, const T &b, const T &N)
template<typename T, typename V>
T	Arageli::_Internal::conditioner (const T &_a, const T &_b, const T &N, V &d)
template<typename T1, typename T2, typename T3>
T3	Arageli::mod (const T1 &a, const T2 &b, const T3 &d)
template<typename T1, typename T2>
T2	Arageli::mod (const T1 &a, const T2 &b)
	Compute a modulo b.
template<typename T1, typename T2, typename T3>
T3	Arageli::div_mod (const T1 &a, const T2 &b, const T3 &d)
	Compute a/b modulo d.
template<typename T1, typename T2, typename T3>
T3	Arageli::rem_mod (const T1 &a, const T2 &b, const T3 &d)
	Compute residue of division a by b modulo d.
template<typename T1, typename T2>
T2	Arageli::ann (const T1 &a, const T2 &n)
	Compute n/gcd(a, n).
template<typename T1, typename T2, typename T3>
T3	Arageli::quo_mod (const T1 &a, const T2 &b, const T3 &d)
template<typename T>
T	Arageli::split (const T &a, const T &d)
template<typename T>
T	Arageli::stab (const T &a, const T &b, const T &N)
template<typename T>
T	Arageli::split_stab (const T &a, const T &b, const T &N)
template<typename T>
T	Arageli::unit (const T &a, const T &N)
template<typename T>
T	Arageli::stab (const T &a, const T &b, const T &N, const T &d)
template<typename T>
T	Arageli::split_stab (const T &a, const T &b, const T &N, const T &d)
template<typename T>
T	Arageli::split_mod (const T &a, const T &d)
template<typename T>
T	Arageli::stab_mod (const T &a, const T &b, const T &N)
template<typename T>
T	Arageli::stab_mod (const T &a, const T &b, const T &N, const T &d)
template<typename T>
bool	Arageli::is_invertible_mod (const T &a, const T &N)
	Returns true iff a is invertible element modulo N.
template<typename T>
std::size_t	Arageli::nbits (const T &a)
	Compute number of bit in binary notation of a.
template<typename T, typename T_factory>
std::size_t	Arageli::nbits (T a, const T_factory &tfctr)
	Compute number of bit in binary notation of a.
template<typename T, typename T_factory>
T	Arageli::factorial_successive_multiplication (T a, const T_factory &tfctr)
	Computes factorial via just successive multiplication (by definition).
template<typename T>
T	Arageli::factorial_successive_multiplication (const T &a)
	Computes factorial via just successive multiplication (by definition).
template<typename T, typename T_factory>
T	Arageli::factorial_even_odd_multiplication (T a, const T_factory &tfctr)
	Computes factorial via even and odd multiplier separation.
template<typename T>
T	Arageli::factorial_even_odd_multiplication (const T &a)
	Computes factorial via even and odd multiplier separation.
template<typename T, typename T_factory>
T	Arageli::factorial (const T &a, const T_factory &tfctr)
	Computes factorial of a via apropriate algorithm.
template<typename T>
T	Arageli::factorial (const T &a)
	Computes factorial of a via apropriate algorithm.
template<typename T>
T	Arageli::intsqrt (const T &a)
	Integer square root of a.
template<typename T, typename TT>
T	Arageli::sqrt_mod_shenks (const T &a, const T &n, const TT &tt)
	The Shenks algorithm (square root of a modulo n, for n = 1 (mod 4)).
template<typename T>
T	Arageli::sqrt_mod_shenks (const T &a, const T &n)
	The Shenks algorithm (square root of a modulo n, for n = 1 (mod 4)).

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Define Documentation

#define ARAGELI_INCLUDE_CPP_WITH_EXPORT_TEMPLATE_INTALG

Definition at line 347 of file intalg.hpp.

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