lucas_sequence.cpp File Reference

Primary module interface unit for modlue lucas_sequence. More...

#include <cassert>
#include <utility>
import modulo;
import matrix;
import base;

Include dependency graph for lucas_sequence.cpp:

Functions
template<Integer N, Integer S>
constexpr std::pair< S, S >	ntlib::lucas_nth_term (N n, S P, S Q)
	Compute the \(n\)-th term of the Lucas sequences of the first and second kind.
template<Integer N, Integer S>
constexpr std::pair< S, S >	ntlib::mod_lucas_nth_term (N n, S P, S Q, S m)
	Compute the \(n\)-th term of the Lucas sequences of the first and second kind modulo some number.

Detailed Description

Primary module interface unit for modlue lucas_sequence.

Function Documentation

lucas_nth_term()

template<Integer N, Integer S>

std::pair< S, S > ntlib::lucas_nth_term ( N n, S P, S Q )

nodiscardconstexprexport

Compute the \(n\)-th term of the Lucas sequences of the first and second kind.

Runtime: \(O(\log(n))\)

Template Parameters

N	An integer-like type.
S	A signed integer-like type.

Parameters

n	Which term to compute.
P	Parameter \(P\).
Q	Parameter \(Q\).

Returns

A std::pair<S,S> containing \(U_n(P,Q)\) as its first element and \(V_n(P,Q)\) as its second element.

mod_lucas_nth_term()

template<Integer N, Integer S>

std::pair< S, S > ntlib::mod_lucas_nth_term ( N n, S P, S Q, S m )

nodiscardconstexprexport

Compute the \(n\)-th term of the Lucas sequences of the first and second kind modulo some number.

Runtime: \(O(\log(n))\)

Template Parameters

N	An integer-like type.
S	A signed integer-like type.

Parameters

n	Which term to compute.
P	Parameter \(P\).
Q	Parameter \(Q\).
m	The modulus.

Returns

A std::pair<T,T> containing \(U_n(P,Q) \mod m\) as its first element and \(V_n(P,Q) \mod m\) as its second element.