Namespace for factorization using QUBO++ library. More...

Classes
class	SolHolder
	Solution holder to store the best solution of factorization. More...

class	ABS2Callback
	Class to define ABS2 callback function for factorization. More...

class	GRB_Callback
	Class to define Gurobi callback function for factorization. More...

Functions
Expr	and_gate (const Expr &a, const Expr &b, Var x, MapList &opt_sol)
	Function to generate a QUBO expression Expr object for the AND gate. More...

Expr	half_adder (const Expr &x, const Expr &y, Var s, Var c, MapList &opt_sol)
	Function to generates a QUBO expression Expr object for the Half Adder. More...

Expr	full_adder (const Expr &x, const Expr &y, const Expr &z, Var s, Var c, MapList &opt_sol)
	Function to generate a QUBO expression Expr object for the Full Adder. More...

template<typename T , typename U >
Expr	adder (const qbpp::Vector< T > &x, const qbpp::Vector< U > &y, const qbpp::Vector< Var > &s, const qbpp::Vector< Var > &c, MapList &opt_sol)
	function to generate QUBO expression for n-bit adder More...

template<typename T , typename U >
Expr	multiplier (const qbpp::Vector< T > &x, const qbpp::Vector< U > &y, const qbpp::Vector< Var > &z, MapList &opt_sol)
	Function to generate QUBO expression for multiplier. More...

std::string	toBinaryString (uint64_t num)
	Converts a number to a binary string. More...

uint64_t	as_uint64 (const qbpp::Sol &sol, const qbpp::Vector< qbpp::Var > &var, bool fix_lsb)
	Converts a vector of Var in a solution to a 64-bit unsigned integer. More...

uint64_t	as_uint64 (const qbpp::SolHolder &sol_holder, const qbpp::Vector< qbpp::Var > &var, bool fix_lsb)
	Converts a vector of Var in a solution holder to a 64-bit unsigned integer. More...

bool	is_prime (uint32_t num)

uint32_t	rand_prime (int size)
	Generates a random prime number of the specified size. More...

Detailed Description

Namespace for factorization using QUBO++ library.

Function Documentation

◆ and_gate()

Expr qbpp::factorization::and_gate	(	const Expr &	a,
		const Expr &	b,
		Var	x,
		MapList &	opt_sol
	)

inline

Function to generate a QUBO expression Expr object for the AND gate.

Parameters

a	The Expr object of the input.
b	The Expr object of the input.
x	The Var object of the output.
opt_sol	The MapList object of the optimal solution.

Returns: Expr satisfying x = a & b

Expr is a binary expression taking the minimum value 0 if x = a & b

Note: opt_sol[x] is determined by opt_sol[a] and opt_sol[b]

Definition at line 26 of file qbpp_multiplier.hpp.

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◆ half_adder()

Expr qbpp::factorization::half_adder	(	const Expr &	x,
		const Expr &	y,
		Var	s,
		Var	c,
		MapList &	opt_sol
	)

inline

Function to generates a QUBO expression Expr object for the Half Adder.

Parameters

x	The Expr object of the input.
y	The Expr object of the input.
s	The Var object of the sum output.
c	The Var object of the carry output.
opt_sol	The MapList object of the optimal solution.

Returns: Expr satisfying s = x ^ y and c = x & y

Expr is a binary expression taking the minimum value 0 if x, y, s, c satisfy s = x ^ y and c = x & y

Note: opt_sol[s] and opt_sol[c] are determined by opt_sol[x] and opt_sol[y]

Definition at line 43 of file qbpp_multiplier.hpp.

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◆ full_adder()

Expr qbpp::factorization::full_adder	(	const Expr &	x,
		const Expr &	y,
		const Expr &	z,
		Var	s,
		Var	c,
		MapList &	opt_sol
	)

inline

Function to generate a QUBO expression Expr object for the Full Adder.

Parameters

x	The Expr object of the input.
y	The Expr object of the input.
z	The Expr object of the input.
s	The Var object of the sum output.
c	The Var object of the carry output.
opt_sol	optimal solution of the QUBO expression to be updated

Returns: Expr satisfying s = x ^ y ^ z and c = x & y + y & z + z & x

Expr is a binary expression taking the minimum value 0 if x, y, z, s, satisfy s = x ^ y ^ z and c = x & y + y & z + z & x

Note: opt_sol[s] and opt_sol[c] are determined by opt_sol[x], opt_sol[y] and opt_sol[z]

Definition at line 66 of file qbpp_multiplier.hpp.

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◆ adder()

template<typename T , typename U >

Expr qbpp::factorization::adder	(	const qbpp::Vector< T > &	x,
		const qbpp::Vector< U > &	y,
		const qbpp::Vector< Var > &	s,
		const qbpp::Vector< Var > &	c,
		MapList &	opt_sol
	)

function to generate QUBO expression for n-bit adder

Template Parameters

T	input type of x: Var or Expr.
U	input type of y: Var or Expr.

Parameters

x	The input vector of T object.
y	The input vector of U object.
s	The output vector of Var object.
c	The carry vector of Var object.
opt_sol	optimal solution of the QUBO expression to be updated.

Returns: Expr satisfying s = x + y and c are carry bits

Expr is a binary expression taking the minimum value 0 if x, y, s, c satisfy s = x + y and c are carry bits

Note: opt_sol[s] and opt_sol[c] are determined by opt_sol[x] and opt_sol[y]. The QUBO expression is generated by the following function calls: full_adder(x[0],y[0],0,s[0],c[0]), full_adder(x[1],y[1],c[0],s[1],c[1]),..., full_adder(x[n-1],y[n-1],c[n-2],s[n-1],c[n-1])

Definition at line 95 of file qbpp_multiplier.hpp.

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◆ multiplier()

template<typename T , typename U >

Expr qbpp::factorization::multiplier	(	const qbpp::Vector< T > &	x,
		const qbpp::Vector< U > &	y,
		const qbpp::Vector< Var > &	z,
		MapList &	opt_sol
	)

Function to generate QUBO expression for multiplier.

Template Parameters

T	input type of input vector x: Var or Expr
U	input type of input vector y: Var or Expr

Parameters

x	input vector of T
y	input vector of U
z	input vector of Var
opt_sol	optimal solution of the QUBO expression to be updated

Returns: Expr taking minimum value of 0 if z = x * y

Expr is a binary expression taking the minimum value 0 if z = x * y

Note: opt_sol[z] is determined by opt_sol[x] and opt_sol[y]

Definition at line 122 of file qbpp_multiplier.hpp.

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◆ toBinaryString()

std::string qbpp::factorization::toBinaryString ( uint64_t num )

Converts a number to a binary string.

Parameters

num	The number to be easyerted.

Returns: std::string The binary string.

Definition at line 40 of file factorization.cpp.

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◆ as_uint64() [1/2]

uint64_t qbpp::factorization::as_uint64	(	const qbpp::Sol &	sol,
		const qbpp::Vector< qbpp::Var > &	var,
		bool	fix_lsb
	)

Converts a vector of Var in a solution to a 64-bit unsigned integer.

Parameters

sol	The solution.
var	The vector of Var.
fix_lsb	True if the LSBs of x, y, and z are fixed to 1.

Returns: uint64_t The 64-bit unsigned integer.

Definition at line 55 of file factorization.cpp.

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◆ as_uint64() [2/2]

uint64_t qbpp::factorization::as_uint64	(	const qbpp::SolHolder &	sol_holder,
		const qbpp::Vector< qbpp::Var > &	var,
		bool	fix_lsb
	)

Converts a vector of Var in a solution holder to a 64-bit unsigned integer.

Parameters

sol_holder	The solution holder.
var	The vector of Var.
fix_lsb	True if the LSBs of x, y, and z are fixed to 1.

Returns: uint64_t The 64-bit unsigned integer.

Definition at line 75 of file factorization.cpp.

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◆ is_prime()

bool qbpp::factorization::is_prime ( uint32_t num )

Definition at line 80 of file factorization.cpp.

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◆ rand_prime()

uint32_t qbpp::factorization::rand_prime ( int size )

Generates a random prime number of the specified size.

Parameters

size	The number of bits of the prime number.

Returns: uint32_t Random prime number. The MSB is 1.

Note: The prime number is generated by the Miller-Rabin primality test.

Definition at line 89 of file factorization.cpp.

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Classes

Functions

Detailed Description

Function Documentation

◆ and_gate()

◆ half_adder()

◆ full_adder()

◆ adder()

◆ multiplier()

◆ toBinaryString()

◆ as_uint64() [1/2]

◆ as_uint64() [2/2]

◆ is_prime()

◆ rand_prime()