NTL Namespace Reference

These functions are in the NTL namespace. More...

Functions
double	LLL_FP64 (NTL::Mat< long > &B, const double delta=0.99, long r=0, long c=0, NTL::Vec< double > *sqlen=0)
	This function is similar to LLL_FP in NTL, but only the first r rows and first c columns of the matrix B are considered, and a basis is built for the lattice generated by these (partial) rows.
double	BKZ_FP64 (NTL::Mat< long > &BB, const double delta=0.99, long blocksize=10, long prune=0, long r=0, long c=0, NTL::Vec< double > *sqlen=0)
	This function is similar to BKZ_FP in NTL, with the same modifications as in LLL_FP64 above.
double	LLL_FP_lt (mat_ZZ &B, double delta=0.99, long r=0, long c=0, vec_double *sqlen=0)
	This function is similar to LLL_FP in NTL, but only the first r rows and first c columns of the matrix B are considered, a basis is built for the lattice generated by these (partial) rows, and the square lengths of the returned basis vectors are returned in sqlen.
double	BKZ_FP_lt (mat_ZZ &BB, double delta=0.99, long blocksize=10, long prune=0, long r=0, long c=0, vec_double *sqlen=0)
	This function is similar to BKZ_FP in NTL, with the same modifications as in LLL_FPInt above.
xdouble	LLL_XD_lt (mat_ZZ &B, double delta=0.99, long r=0, long c=0, vec_xdouble *sqlen=0)
xdouble	BKZ_XD_lt (mat_ZZ &BB, double delta=0.99, long blocksize=10, long prune=0, long r=0, long c=0, vec_xdouble *sqlen=0)
	This function is similar to BKZ_XD in NTL, with the same modifications as in LLL_FPInt above.
quad_float	LLL_QP_lt (mat_ZZ &B, double delta=0.99, long r=0, long c=0, vec_quad_float *sqlen=0)
quad_float	BKZ_QP_lt (mat_ZZ &BB, double delta=0.99, long blocksize=10, long prune=0, long r=0, long c=0, vec_quad_float *sqlen=0)
	This function is similar to BKZ_FP in NTL, with the same modifications as in LLL_FPInt above.
RR	LLL_RR_lt (mat_ZZ &B, double delta=0.99, long r=0, long c=0, vec_RR *sqlen=0)
RR	BKZ_RR_lt (mat_ZZ &B, double delta=0.99, long blocksize=10, long prune=0, long r=0, long c=0, vec_RR *sqlen=0)
	These two functions are wrappers of BKZ_RR in NTL, with the same modifications as in LLL_RR_lt above.
Conversion functions for compatibility with NTL.
These functions perform conversions between different types. Most of them do not really need explanations, but sometimes a specific logic is used when doing the conversion.
void	conv (std::int64_t &l, const char *c)
	Converts the array of characters (string) c into an std::int64_t l using the strtol() function of cstdlib.h.
void	conv (double &r, const char *c)
	Converts the array of characters (string) c into a double r using the strtod() function of cstdlib.h.
bool	IsZero (const std::int64_t &x)
	Returns the bool resulting of the statement x == 0.
void	clear (double &x)
	Sets x to 0.
void	clear (std::int64_t &x)
	Sets x to 0.
std::int64_t	IsOdd (const std::int64_t &x)
	Tests if x is odd.
void	set (std::int64_t &x)
	Sets x to 1.
Mathematical functions
These are complementary overloads to NTL power functions.
std::int64_t	power (std::int64_t p, std::int64_t i)
	Returns \(p^i\).
void	power2 (std::int64_t &z, std::int64_t i)
	Sets \(z = 2^i\).
void	power2 (NTL::ZZ &z, std::int64_t i)
	Sets \(z = 2^i\).
Inline functions for certain operators, again for compatibility with NTL.
static void	add (int64_t &x, const int64_t a, const int64_t b)
static void	sub (int64_t &x, const int64_t a, const int64_t b)
static void	SubPos (int64_t &x, const int64_t a, const int64_t b)
static void	negate (int64_t &x, const int64_t a)
static void	mul (int64_t &x, const int64_t a, const int64_t b)
static void	div (int64_t &x, const int64_t a, const int64_t b)
static void	rem (int64_t &x, const int64_t a, const int64_t b)
static void	sqr (int64_t &x, const int64_t a)
static void	MulAddTo (int64_t &x, const int64_t a, const int64_t b)
static void	MulSubFrom (int64_t &x, int64_t a, int64_t b)
static void	LeftShift (int64_t &x, const int64_t a, int64_t k)
static void	RightShift (int64_t &x, const int64_t a, int64_t k)

Detailed Description

These functions are in the NTL namespace.

Function Documentation

LLL_FP64()

double NTL::LLL_FP64	(	NTL::Mat< long > &	B,
		const double	delta = 0.99,
		long	r = 0,
		long	c = 0,
		NTL::Vec< double > *	sqlen = 0 )

This function is similar to LLL_FP in NTL, but only the first r rows and first c columns of the matrix B are considered, and a basis is built for the lattice generated by these (partial) rows.

The other elements of B are ignored. The basis is returned in the upper left corner of B, with the shortest basis vector always in the first row. If r=0, then all the rows of the IntMat object are taken. If c=0, then all the columns are taken. The square lengths of the returned basis vectors are also returned in the double vector sqlen, in sqlen[0],..., sqlen[d-1], if this vector given. The indices of B and sqlen start at 0. The function returns the dimension of the computed basis (the number of independent rows).

BKZ_FP64()

double NTL::BKZ_FP64	(	NTL::Mat< long > &	BB,
		const double	delta = 0.99,
		long	blocksize = 10,
		long	prune = 0,
		long	r = 0,
		long	c = 0,
		NTL::Vec< double > *	sqlen = 0 )

This function is similar to BKZ_FP in NTL, with the same modifications as in LLL_FP64 above.

LLL_FP_lt()

double NTL::LLL_FP_lt	(	mat_ZZ &	B,
		double	delta = 0.99,
		long	r = 0,
		long	c = 0,
		vec_double *	sqlen = 0 )

This function is similar to LLL_FP in NTL, but only the first r rows and first c columns of the matrix B are considered, a basis is built for the lattice generated by these (partial) rows, and the square lengths of the returned basis vectors are returned in sqlen.

BKZ_FP_lt()

double NTL::BKZ_FP_lt	(	mat_ZZ &	BB,
		double	delta = 0.99,
		long	blocksize = 10,
		long	prune = 0,
		long	r = 0,
		long	c = 0,
		vec_double *	sqlen = 0 )

This function is similar to BKZ_FP in NTL, with the same modifications as in LLL_FPInt above.

LLL_XD_lt()

xdouble NTL::LLL_XD_lt	(	mat_ZZ &	B,
		double	delta = 0.99,
		long	r = 0,
		long	c = 0,
		vec_xdouble *	sqlen = 0 )

BKZ_XD_lt()

xdouble NTL::BKZ_XD_lt	(	mat_ZZ &	BB,
		double	delta = 0.99,
		long	blocksize = 10,
		long	prune = 0,
		long	r = 0,
		long	c = 0,
		vec_xdouble *	sqlen = 0 )

This function is similar to BKZ_XD in NTL, with the same modifications as in LLL_FPInt above.

LLL_QP_lt()

quad_float NTL::LLL_QP_lt	(	mat_ZZ &	B,
		double	delta = 0.99,
		long	r = 0,
		long	c = 0,
		vec_quad_float *	sqlen = 0 )

BKZ_QP_lt()

quad_float NTL::BKZ_QP_lt	(	mat_ZZ &	BB,
		double	delta = 0.99,
		long	blocksize = 10,
		long	prune = 0,
		long	r = 0,
		long	c = 0,
		vec_quad_float *	sqlen = 0 )

This function is similar to BKZ_FP in NTL, with the same modifications as in LLL_FPInt above.

LLL_RR_lt()

RR NTL::LLL_RR_lt	(	mat_ZZ &	B,
		double	delta = 0.99,
		long	r = 0,
		long	c = 0,
		vec_RR *	sqlen = 0 )

BKZ_RR_lt()

RR NTL::BKZ_RR_lt	(	mat_ZZ &	B,
		double	delta = 0.99,
		long	blocksize = 10,
		long	prune = 0,
		long	r = 0,
		long	c = 0,
		vec_RR *	sqlen = 0 )

These two functions are wrappers of BKZ_RR in NTL, with the same modifications as in LLL_RR_lt above.

conv() [1/2]

void NTL::conv ( std::int64_t & l, const char * c )

inline

Converts the array of characters (string) c into an std::int64_t l using the strtol() function of cstdlib.h.

conv() [2/2]

void NTL::conv ( double & r, const char * c )

inline

Converts the array of characters (string) c into a double r using the strtod() function of cstdlib.h.

IsZero()

bool NTL::IsZero ( const std::int64_t & x )

inline

Returns the bool resulting of the statement x == 0.

IsZero is already defined for the type NTL::ZZ in NTL, but not for std::int64_t.

clear() [1/2]

void NTL::clear ( double & x )

inline

Sets x to 0.

clear() [2/2]

void NTL::clear ( std::int64_t & x )

inline

Sets x to 0.

IsOdd()

std::int64_t NTL::IsOdd ( const std::int64_t & x )

inline

Tests if x is odd.

Returns 1 if it is odd, and 0 if it is even.

set()

void NTL::set ( std::int64_t & x )

inline

Sets x to 1.

power()

std::int64_t NTL::power ( std::int64_t p, std::int64_t i )

inline

Returns \(p^i\).

power2() [1/2]

void NTL::power2 ( std::int64_t & z, std::int64_t i )

inline

Sets \(z = 2^i\).

power2() [2/2]

void NTL::power2 ( NTL::ZZ & z, std::int64_t i )

inline

Sets \(z = 2^i\).

add()

void NTL::add ( int64_t & x, const int64_t a, const int64_t b )

inlinestatic

sub()

void NTL::sub ( int64_t & x, const int64_t a, const int64_t b )

inlinestatic

SubPos()

void NTL::SubPos ( int64_t & x, const int64_t a, const int64_t b )

inlinestatic

negate()

void NTL::negate ( int64_t & x, const int64_t a )

inlinestatic

mul()

void NTL::mul ( int64_t & x, const int64_t a, const int64_t b )

inlinestatic

div()

void NTL::div ( int64_t & x, const int64_t a, const int64_t b )

inlinestatic

rem()

void NTL::rem ( int64_t & x, const int64_t a, const int64_t b )

inlinestatic

sqr()

void NTL::sqr ( int64_t & x, const int64_t a )

inlinestatic

MulAddTo()

void NTL::MulAddTo ( int64_t & x, const int64_t a, const int64_t b )

inlinestatic

MulSubFrom()

void NTL::MulSubFrom ( int64_t & x, int64_t a, int64_t b )

inlinestatic

LeftShift()

void NTL::LeftShift ( int64_t & x, const int64_t a, int64_t k )

inlinestatic

RightShift()

void NTL::RightShift ( int64_t & x, const int64_t a, int64_t k )

inlinestatic