Represents a native integer. More...

#include <arithmetic-nint.hpp>

Public Types
typedef NIntContext< Type >	Context
	The context type.

Public Member Functions
	NInt () PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Creates a new integer. Default value is zero.

	NInt (const NIntContext< Type > &c) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Creates a new integer. Default value is zero. More...

	NInt (const NInt &i) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Creates a copy of the given integer. More...

template<typename T >
	NInt (const NInt< T > &i) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Creates a copy of the given integer (of another native type). More...

	NInt (const NInt &i, const NIntContext< Type > &ic) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Creates a copy of the given integer. More...

template<typename T >
	NInt (const NInt< T > &i, const NIntContext< Type > &ic) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Creates a copy of the given integer (of another native type). More...

	NInt (double d) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Creates a native CPU integer from the given native floating point number. More...

	NInt (long double d) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Creates a native CPU integer from the given native floating point number. More...

	NInt (long i) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Creates a native CPU integer from the given native integer. More...

	NInt (unsigned long i) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Creates a native CPU integer from the given native integer. More...

	NInt (const Integer &i)
	Creates a native CPU integer from the given arbitrary precision integer. More...

NInt &	operator= (const NInt &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Copies the given integer into this one. More...

Static Public Member Functions
static void	setContext (const NIntContext< Type > &c) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Sets the integer context `c`. More...

Friends
void	abs (NInt< Type > &r, const NInt< Type > &a) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Takes the absolute value of `a` and stores the result in `r`. More...

NInt< Type >	abs (const NInt< Type > &i) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes and returns the absolute value of `i`. More...

void	add (NInt< Type > &r, const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Adds `a` and `b` and stores the result in `r`. More...

long	approxLog2 (const NInt< Type > &x) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Quickly approximates $\log_2 \|x\|$ and returns the approximation. More...

int	bit (const NInt< Type > &, long n) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Returns the `n` bit of in the usual binary representation. More...

long	bitLength (const NInt< Type > &x) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes and returns `n` such that $2^{n-1} \le \|x\| < 2^n$ . More...

void	ceilDiv (NInt< Type > &r, const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes $\lceil \tfrac{a}{b} \rceil$ and stores the result in `r`. More...

NInt< Type >	ceilDiv (const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes and returns $\lceil \tfrac{a}{b} \rceil$ . More...

long	ceilOfLog2 (const NInt< Type > &x) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes and returns $\lceil \log_2 \|x\| \rceil$ . More...

int	compare (const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Compares the two integers. More...

int	compareAbsValues (const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Compares the two integers in absolute value. More...

void	decrement (NInt< Type > &r, const NInt< Type > &a) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Decrements `a` by one and stores the result in `r`. More...

void	div (NInt< Type > &r, const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Divides `a` by `b` and stores the result in `r`. More...

void	euclideanDivision (NInt< Type > &q, NInt< Type > &r, const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes an Euclidean Division of `a` by `b`. More...

void	euclideanDivisionPos (NInt< Type > &q, NInt< Type > &r, const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes an Euclidean Division of `a` by `b`. More...

void	floorDiv (NInt< Type > &r, const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes $\lfloor \tfrac{a}{b} \rfloor$ and stores the result in `r`. More...

NInt< Type >	floorDiv (const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes and returns $\lfloor \tfrac{a}{b} \rfloor$ . More...

long	floorOfLog2 (const NInt< Type > &x) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes and returns $\lfloor \log_2 \|x\| \rfloor$ . More...

void	GCD (NInt< Type > &r, const NInt< Type > &x, const NInt< Type > &y) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes the non-negative Greatest Common Divisior `r` of `x` and `y`. More...

NInt< Type >	GCD (const NInt< Type > &x, const NInt< Type > &y) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes and returns the non-negative Greatest Common Divisior of `x` and `y`. More...

void	increment (NInt< Type > &r, const NInt< Type > &a) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Increments `a` by one and stores the result in `r`. More...

bool	isNegative (const NInt< Type > &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given `plll::arithmetic::Integer` object for being strictly negative. More...

bool	isNonNegative (const NInt< Type > &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given `plll::arithmetic::Integer` object for being positive or zero. More...

bool	isNonPositive (const NInt< Type > &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given `plll::arithmetic::Integer` object for being negative or zero. More...

bool	isOne (const NInt< Type > &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given `plll::arithmetic::Integer` object for being one. More...

bool	isPMOne (const NInt< Type > &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given `plll::arithmetic::Integer` object for being one or minus one. More...

bool	isPMTwo (const NInt< Type > &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given `plll::arithmetic::Integer` object for being two or minus two. More...

bool	isPositive (const NInt< Type > &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given `plll::arithmetic::Integer` object for being strictly positive. More...

bool	isZero (const NInt< Type > &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given `plll::arithmetic::Integer` object for being zero. More...

void	LCM (NInt< Type > &r, const NInt< Type > &x, const NInt< Type > &y) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes the non-negative Least Common Multiple `r` of `x` and `y`. More...

NInt< Type >	LCM (const NInt< Type > &x, const NInt< Type > &y) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes and returns the non-negative Least Common Multiple of `x` and `y`. More...

void	makeAbs (NInt< Type > &a) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Makes the operand non-negative. More...

void	mod (NInt< Type > &r, const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Takes the remainder of the division of `a` by `b` and stores it in `r`. More...

void	mul (NInt< Type > &r, const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Multiplies `a` with `b` and stores the result in `r`. More...

void	neg (NInt< Type > &r, const NInt< Type > &a) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Negates `a` and stores the result in `r`. More...

bool	operator!= (const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Compares the current integer with the given one for inequality. More...

NInt< Type >	operator% (const NInt< Type > &, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Divides the first by the second integer and returns the remainder. More...

NInt< Type > &	operator%= (NInt< Type > &, const NInt< Type > &i) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Divides `cur` by the given integer `i` and stores the remainder in `cur`. More...

NInt< Type >	operator* (const NInt< Type > &, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Multiplies the two integers and returns the result. More...

NInt< Type > &	operator*= (NInt< Type > &, const NInt< Type > &i) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Multiplies the given integer `i` with `cur`. More...

NInt< Type >	operator+ (const NInt< Type > &, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Adds the two integers and returns the result. More...

NInt< Type >	operator++ (NInt< Type > &, int) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Increments the integer by one and returns the previous value. More...

NInt< Type > &	operator++ (NInt< Type > &) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Increments the integer by one and returns the new value. More...

NInt< Type > &	operator+= (NInt< Type > &, const NInt< Type > &i) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Adds the integer `i` to `cur`. More...

NInt< Type >	operator- (const NInt< Type > &) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Negates the integer. More...

NInt< Type >	operator- (const NInt< Type > &, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Subtracts the second from the first integer and returns the result. More...

NInt< Type >	operator-- (NInt< Type > &, int) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Decrements the integer by one and returns the previous value. More...

NInt< Type > &	operator-- (NInt< Type > &) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Decreases the integer by one and returns the new value. More...

NInt< Type > &	operator-= (NInt< Type > &, const NInt< Type > &i) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Subtracts the integer `i` from `cur`. More...

NInt< Type >	operator/ (const NInt< Type > &, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Divides the first by the second integer and returns the result. More...

NInt< Type > &	operator/= (NInt< Type > &, const NInt< Type > &i) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Divides `cur` by the given integer `i`. More...

bool	operator< (const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Compares the current integer with the given one. More...

NInt< Type >	operator<< (const NInt< Type > &a, long b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes the bitwise left shift of the first integer by the number of bits given by the second integer, and returns the result. More...

NInt< Type >	operator<< (const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes the bitwise left shift of the first integer by the number of bits given by the second integer, and returns the result. More...

std::ostream &	operator<< (std::ostream &s, const NInt< Type > &r)
	Outputs the integer on the given output stream.

bool	operator<= (const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Compares the current integer with the given one. More...

bool	operator== (const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Compares the current integer with the given one for equality. More...

bool	operator> (const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Compares the current integer with the given one. More...

bool	operator>= (const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Compares the current integer with the given one. More...

NInt< Type >	operator>> (const NInt< Type > &a, long b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes the bitwise right shift of the first integer by the number of bits given by the second integer, and returns the result. More...

NInt< Type >	operator>> (const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes the bitwise right shift of the first integer by the number of bits given by the second integer, and returns the result. More...

std::istream &	operator>> (std::istream &s, NInt< Type > &r)
	Reads the integer from the given input stream.

NInt< Type >	power (const NInt< Type > &, long) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes and returns `a` raised to the power of `b`. More...

void	power (NInt< Type > &, const NInt< Type > &, long) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Raises `a` to the power `b` and stores the result in `r`. More...

NInt< Type >	power (const NInt< Type > &, const NInt< Type > &) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes and returns `a` raised to the power of `b`. More...

void	power (NInt< Type > &, const NInt< Type > &, const NInt< Type > &) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Raises `a` to the power `b` and stores the result in `r`. More...

void	roundDiv (NInt< Type > &r, const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes $\lfloor \tfrac{a}{b} \rceil$ (rounding to the next integer) and stores the result in `r`. More...

NInt< Type >	roundDiv (const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes and returns $\lfloor \tfrac{a}{b} \rceil$ (rounding to the next integer). More...

void	setOne (NInt< Type > &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Sets the given integer to one.

void	setZero (NInt< Type > &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Sets the given integer to zero.

void	shl (NInt< Type > &r, const NInt< Type > &a, long b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Shifts `a` by `b` bits to the left and stores the result in `r`. More...

void	shl (NInt< Type > &r, const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Shifts `a` by `b` bits to the left and stores the result in `r`. More...

void	shr (NInt< Type > &r, const NInt< Type > &a, long b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Shifts `a` by `b` bits to the left and stores the result in `r`. More...

void	shr (NInt< Type > &r, const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Shifts `a` by `b` bits to the left and stores the result in `r`. More...

int	sign (const NInt< Type > &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Returns the sign of the given integer. More...

void	sqrtCeil (NInt< Type > &, const NInt< Type > &) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes $\lceil\sqrt{a}\rceil$ and stores the result in `r`. More...

void	sqrtFloor (NInt< Type > &, const NInt< Type > &) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes $\lfloor\sqrt{a}\rfloor$ and stores the result in `r`. More...

NInt< Type >	square (const NInt< Type > &i) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes and returns the square of `i`. More...

void	square (NInt< Type > &r, const NInt< Type > &a) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes the square of `a` and stores the result in `r`. More...

void	sub (NInt< Type > &r, const NInt< Type > &a, const NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Subtracts `b` from `a` and stores the result in `r`. More...

void	swap (NInt< Type > &a, NInt< Type > &b) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Swaps two `plll::arithmetic::NInt<>` objects.

void	XGCD (NInt< Type > &r, NInt< Type > &a, NInt< Type > &b, const NInt< Type > &x, const NInt< Type > &y) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Computes the non-negative extended Greatest Common Divisior `r` of `x` and `y`. More...

Detailed Description

template<typename Type>
class plll::arithmetic::NInt< Type >

Represents a native integer.

Template Parameters

Type	A native signed integer type, such as `int`, `long int` and `long long`.

Definition at line 48 of file arithmetic-nint.hpp.

Constructor & Destructor Documentation

template<typename Type>

plll::arithmetic::NInt< Type >::NInt ( const NIntContext< Type > & c )

inline

Creates a new integer. Default value is zero.

Parameters

c	A native CPU integer context.

Definition at line 1168 of file arithmetic-nint.hpp.

template<typename Type>

plll::arithmetic::NInt< Type >::NInt ( const NInt< Type > & i )

inline

Creates a copy of the given integer.

Parameters

i	The integer to be copied.

Definition at line 1178 of file arithmetic-nint.hpp.

template<typename Type>

template<typename T >

plll::arithmetic::NInt< Type >::NInt ( const NInt< T > & i )

inline

Creates a copy of the given integer (of another native type).

Parameters

i	The integer to be copied.

Definition at line 1189 of file arithmetic-nint.hpp.

template<typename Type>

plll::arithmetic::NInt< Type >::NInt	(	const NInt< Type > &	i,
		const NIntContext< Type > &	ic
	)

inline

Creates a copy of the given integer.

Parameters

i	The integer to be copied.
ic	An integer context.

Definition at line 1200 of file arithmetic-nint.hpp.

template<typename Type>

template<typename T >

plll::arithmetic::NInt< Type >::NInt	(	const NInt< T > &	i,
		const NIntContext< Type > &	ic
	)

inline

Creates a copy of the given integer (of another native type).

Parameters

i	The integer to be copied.
ic	An integer context.

Definition at line 1212 of file arithmetic-nint.hpp.

template<typename Type>

plll::arithmetic::NInt< Type >::NInt ( double d )

inlineexplicit

Creates a native CPU integer from the given native floating point number.

Parameters

d	The native floating point number.

Definition at line 1231 of file arithmetic-nint.hpp.

template<typename Type>

plll::arithmetic::NInt< Type >::NInt ( long double d )

inlineexplicit

Creates a native CPU integer from the given native floating point number.

Parameters

d	The native floating point number.

Definition at line 1241 of file arithmetic-nint.hpp.

template<typename Type>

plll::arithmetic::NInt< Type >::NInt ( long i )

inlineexplicit

Creates a native CPU integer from the given native integer.

Parameters

i	The native integer.

Definition at line 1251 of file arithmetic-nint.hpp.

template<typename Type>

plll::arithmetic::NInt< Type >::NInt ( unsigned long i )

inlineexplicit

Creates a native CPU integer from the given native integer.

Parameters

i	The native integer.

Definition at line 1261 of file arithmetic-nint.hpp.

template<typename Type>

plll::arithmetic::NInt< Type >::NInt ( const Integer & i )

inlineexplicit

Creates a native CPU integer from the given arbitrary precision integer.

Parameters

i	The native integer.

Definition at line 1271 of file arithmetic-nint.hpp.

Member Function Documentation

template<typename Type>

NInt& plll::arithmetic::NInt< Type >::operator= ( const NInt< Type > & r )

inline

Copies the given integer into this one.

Parameters

r	A integer to be moved into this one.

Definition at line 1281 of file arithmetic-nint.hpp.

template<typename Type>

static void plll::arithmetic::NInt< Type >::setContext ( const NIntContext< Type > & c )

inlinestatic

Sets the integer context c.

Parameters

c	The integer context.

Definition at line 1222 of file arithmetic-nint.hpp.

Friends And Related Function Documentation

template<typename Type>

void abs	(	NInt< Type > &	r,
		const NInt< Type > &	a
	)

friend

Takes the absolute value of a and stores the result in r.

Parameters

r	The result.
a	The operand.

Definition at line 1752 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> abs ( const NInt< Type > & i )

friend

Computes and returns the absolute value of i.

Parameters

i	The operand.

Returns: The result.

Definition at line 1758 of file arithmetic-nint.hpp.

template<typename Type>

void add	(	NInt< Type > &	r,
		const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Adds a and b and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 1631 of file arithmetic-nint.hpp.

template<typename Type>

long approxLog2 ( const NInt< Type > & x )

friend

Quickly approximates $\log_2 |x|$ and returns the approximation.

Parameters

x	A non-zero integer.

Returns: $\approx \log_2 |x|$ .

Definition at line 2161 of file arithmetic-nint.hpp.

template<typename Type>

int bit	(	const NInt< Type > &	x,
		long	n
	)

friend

Returns the n bit of $|x|$ in the usual binary representation.

Parameters

x	The integer whose bit to query.
n	The index of the bit to query.

Definition at line 1846 of file arithmetic-nint.hpp.

template<typename Type>

long bitLength ( const NInt< Type > & x )

friend

Computes and returns n such that $2^{n-1} \le |x| < 2^n$ .

Parameters

x	A non-zero integer.

Returns: $n \in \mathbb{N}$ such that ` $2^{n-1} \le |x| < 2^n$ .

See also: Integer Functions

Definition at line 2168 of file arithmetic-nint.hpp.

template<typename Type>

void ceilDiv	(	NInt< Type > &	r,
		const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Computes $\lceil \tfrac{a}{b} \rceil$ and stores the result in r.

Parameters

r	The result.
a	The divident.
b	The divisor.

See also: Integer Functions

Definition at line 2196 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> ceilDiv	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Computes and returns $\lceil \tfrac{a}{b} \rceil$ .

Returns: The result.

Parameters

a	The divident.
b	The divisor.

See also: Integer Functions

Definition at line 2209 of file arithmetic-nint.hpp.

template<typename Type>

long ceilOfLog2 ( const NInt< Type > & x )

friend

Computes and returns $\lceil \log_2 |x| \rceil$ .

Parameters

x	A non-zero integer.

Returns: $n \in \mathbb{N}$ such that ` $2^{n-1} < |x| \le 2^n$ .

See also: Integer Functions

Definition at line 1965 of file arithmetic-nint.hpp.

template<typename Type>

int compare	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Compares the two integers.

Parameters

a	The first operand.
b	The second operand.

Returns: Returns a negative number if , zero if and a positive number if .

Definition at line 1799 of file arithmetic-nint.hpp.

template<typename Type>

int compareAbsValues	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Compares the two integers in absolute value.

Parameters

a	The first operand.
b	The second operand.

Returns: Returns a negative number if , zero if and a positive number if .

Definition at line 1806 of file arithmetic-nint.hpp.

template<typename Type>

void decrement	(	NInt< Type > &	r,
		const NInt< Type > &	a
	)

friend

Decrements a by one and stores the result in r.

Parameters

r	The result.
a	The operand.

Definition at line 1740 of file arithmetic-nint.hpp.

template<typename Type>

void div	(	NInt< Type > &	r,
		const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Divides a by b and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 1661 of file arithmetic-nint.hpp.

template<typename Type>

void euclideanDivision	(	NInt< Type > &	q,
		NInt< Type > &	r,
		const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Computes an Euclidean Division of a by b.

Parameters

q	The quotient of `a` divided by `b`.
r	The remainder of `a` divided by `b`, i.e. `a` modulo `b`.
a	The first operand.
b	The second operand. Must be non-zero.

Computes q and r such that a == q * b + r and that $0 \le |r| \le |b|$ and $b \cdot r \ge 0$ .

Definition at line 2238 of file arithmetic-nint.hpp.

template<typename Type>

void euclideanDivisionPos	(	NInt< Type > &	q,
		NInt< Type > &	r,
		const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Computes an Euclidean Division of a by b.

Parameters

q	The quotient of `a` divided by `b`.
r	The remainder of `a` divided by `b`, i.e. `a` modulo `b`.
a	The first operand.
b	The second operand. Must be non-zero.

Computes q and r such that a == q * b + r and that $0 \le r \le |b|$ .

Definition at line 2246 of file arithmetic-nint.hpp.

template<typename Type>

void floorDiv	(	NInt< Type > &	r,
		const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Computes $\lfloor \tfrac{a}{b} \rfloor$ and stores the result in r.

Parameters

r	The result.
a	The divident.
b	The divisor.

See also: Integer Functions

Definition at line 2175 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> floorDiv	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Computes and returns $\lfloor \tfrac{a}{b} \rfloor$ .

Returns: The result.

Parameters

a	The divident.
b	The divisor.

See also: Integer Functions

Definition at line 2188 of file arithmetic-nint.hpp.

template<typename Type>

long floorOfLog2 ( const NInt< Type > & x )

friend

Computes and returns $\lfloor \log_2 |x| \rfloor$ .

Parameters

x	A non-zero integer.

Returns: $n \in \mathbb{N}$ such that ` $2^n \le |x| < 2^{n+1}$ .

See also: Integer Functions

Definition at line 1982 of file arithmetic-nint.hpp.

template<typename Type>

void GCD	(	NInt< Type > &	r,
		const NInt< Type > &	x,
		const NInt< Type > &	y
	)

friend

Computes the non-negative Greatest Common Divisior r of x and y.

Parameters

r	The result is stored in here.
x	The first operand.
y	The first operand.

See also: Integer Functions

Definition at line 2260 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> GCD	(	const NInt< Type > &	x,
		const NInt< Type > &	y
	)

friend

Computes and returns the non-negative Greatest Common Divisior of x and y.

Returns: The GCD of x and y.

Parameters

x	The first operand.
y	The first operand.

See also: Integer Functions

Definition at line 2278 of file arithmetic-nint.hpp.

template<typename Type>

void increment	(	NInt< Type > &	r,
		const NInt< Type > &	a
	)

friend

Increments a by one and stores the result in r.

Parameters

r	The result.
a	The operand.

See also: Integer Functions

Definition at line 1734 of file arithmetic-nint.hpp.

template<typename Type>

bool isNegative ( const NInt< Type > & r )

friend

Tests the given plll::arithmetic::Integer object for being strictly negative.

Returns: Returns true if and only if the argument is strictly negative.

See also: Predicates

Definition at line 1617 of file arithmetic-nint.hpp.

template<typename Type>

bool isNonNegative ( const NInt< Type > & r )

friend

Tests the given plll::arithmetic::Integer object for being positive or zero.

Returns: Returns true if and only if the argument is positive or zero.

See also: Predicates

Definition at line 1610 of file arithmetic-nint.hpp.

template<typename Type>

bool isNonPositive ( const NInt< Type > & r )

friend

Tests the given plll::arithmetic::Integer object for being negative or zero.

Returns: Returns true if and only if the argument is negative or zero.

See also: Predicates

Definition at line 1624 of file arithmetic-nint.hpp.

template<typename Type>

bool isOne ( const NInt< Type > & r )

friend

Tests the given plll::arithmetic::Integer object for being one.

Returns: Returns true if and only if the argument is one.

See also: Predicates

Definition at line 1582 of file arithmetic-nint.hpp.

template<typename Type>

bool isPMOne ( const NInt< Type > & r )

friend

Tests the given plll::arithmetic::Integer object for being one or minus one.

Returns: Returns true if and only if the argument is $\pm 1$ .

See also: Predicates

Definition at line 1589 of file arithmetic-nint.hpp.

template<typename Type>

bool isPMTwo ( const NInt< Type > & r )

friend

Tests the given plll::arithmetic::Integer object for being two or minus two.

Returns: Returns true if and only if the argument is $\pm 2$ .

See also: Predicates

Definition at line 1596 of file arithmetic-nint.hpp.

template<typename Type>

bool isPositive ( const NInt< Type > & r )

friend

Tests the given plll::arithmetic::Integer object for being strictly positive.

Returns: Returns true if and only if the argument is strictly positive.

See also: Predicates

Definition at line 1603 of file arithmetic-nint.hpp.

template<typename Type>

bool isZero ( const NInt< Type > & r )

friend

Tests the given plll::arithmetic::Integer object for being zero.

Returns: Returns true if and only if the argument is zero.

See also: Predicates

Definition at line 1575 of file arithmetic-nint.hpp.

template<typename Type>

void LCM	(	NInt< Type > &	r,
		const NInt< Type > &	x,
		const NInt< Type > &	y
	)

friend

Computes the non-negative Least Common Multiple r of x and y.

Parameters

r	The result is stored in here.
x	The first operand.
y	The first operand.

See also: Integer Functions

Definition at line 2330 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> LCM	(	const NInt< Type > &	x,
		const NInt< Type > &	y
	)

friend

Computes and returns the non-negative Least Common Multiple of x and y.

Returns: The LCM of x and y.

Parameters

x	The first operand.
y	The first operand.

See also: Integer Functions

Definition at line 2337 of file arithmetic-nint.hpp.

template<typename Type>

void makeAbs ( NInt< Type > & a )

friend

Makes the operand non-negative.

Parameters

a	The operand.

Definition at line 1764 of file arithmetic-nint.hpp.

template<typename Type>

void mod	(	NInt< Type > &	r,
		const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Takes the remainder of the division of a by b and stores it in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 1667 of file arithmetic-nint.hpp.

template<typename Type>

void mul	(	NInt< Type > &	r,
		const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Multiplies a with b and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 1655 of file arithmetic-nint.hpp.

template<typename Type>

void neg	(	NInt< Type > &	r,
		const NInt< Type > &	a
	)

friend

Negates a and stores the result in r.

Parameters

r	The result.
a	The operand.

Definition at line 1746 of file arithmetic-nint.hpp.

template<typename Type>

bool operator!=	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Compares the current integer with the given one for inequality.

Parameters

a	The first operand.
b	The second operand.

Returns: true if a does not equal b.

Definition at line 1545 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> operator%	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Divides the first by the second integer and returns the remainder.

Parameters

a	The first operand.
b	The second operand.

Returns: The result.

Definition at line 1412 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type>& operator%=	(	NInt< Type > &	cur,
		const NInt< Type > &	i
	)

friend

Divides cur by the given integer i and stores the remainder in cur.

Parameters

cur	The integer to operate on.
i	The integer to divide by.

Returns: A reference to cur containing the result.

Definition at line 1446 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> operator*	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Multiplies the two integers and returns the result.

Parameters

a	The first operand.
b	The second operand.

Returns: The result.

Definition at line 1400 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type>& operator*=	(	NInt< Type > &	cur,
		const NInt< Type > &	i
	)

friend

Multiplies the given integer i with cur.

Parameters

cur	The integer to operate on.
i	The integer to multiply to `cur`.

Returns: A reference to cur containing the result.

Definition at line 1432 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> operator+	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Adds the two integers and returns the result.

Parameters

a	The first operand.
b	The second operand.

Returns: The result.

Definition at line 1388 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> operator++	(	NInt< Type > &	cur,
		int
	)

friend

Increments the integer by one and returns the previous value.

Parameters

cur	The integer to work on.

Returns: The previous value.

Definition at line 1481 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type>& operator++ ( NInt< Type > & cur )

friend

Increments the integer by one and returns the new value.

Parameters

cur	The integer to work on.

Returns: The new value (a reference to cur).

Definition at line 1493 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type>& operator+=	(	NInt< Type > &	cur,
		const NInt< Type > &	i
	)

friend

Adds the integer i to cur.

Parameters

cur	The integer to operate on.
i	The integer to add to `cur`.

Returns: A reference to cur containing the result.

Definition at line 1425 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> operator- ( const NInt< Type > & a )

friend

Negates the integer.

Parameters

a	The integer.

Returns: The result.

Definition at line 1382 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> operator-	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Subtracts the second from the first integer and returns the result.

Parameters

a	The first operand.
b	The second operand.

Returns: The result.

Definition at line 1394 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> operator--	(	NInt< Type > &	cur,
		int
	)

friend

Decrements the integer by one and returns the previous value.

Parameters

cur	The integer to work on.

Returns: The previous value.

Definition at line 1487 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type>& operator-- ( NInt< Type > & cur )

friend

Decreases the integer by one and returns the new value.

Parameters

cur	The integer to work on.

Returns: The new value (a reference to cur).

Definition at line 1500 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type>& operator-=	(	NInt< Type > &	cur,
		const NInt< Type > &	i
	)

friend

Subtracts the integer i from cur.

Parameters

cur	The integer to operate on.
i	The integer to subtract from `cur`.

Returns: A reference to cur containing the result.

Definition at line 1418 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> operator/	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Divides the first by the second integer and returns the result.

Parameters

a	The first operand.
b	The second operand.

Returns: The result.

Definition at line 1406 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type>& operator/=	(	NInt< Type > &	cur,
		const NInt< Type > &	i
	)

friend

Divides cur by the given integer i.

Parameters

cur	The integer to operate on.
i	The integer to divide by.

Returns: A reference to cur containing the result.

Definition at line 1439 of file arithmetic-nint.hpp.

template<typename Type>

bool operator<	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Compares the current integer with the given one.

Parameters

a	The first operand.
b	The second operand.

Returns: true if a is less than b.

Definition at line 1563 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> operator<<	(	const NInt< Type > &	a,
		long	b
	)

friend

Computes the bitwise left shift of the first integer by the number of bits given by the second integer, and returns the result.

This effectively multiplies the first integer by 2 to the power of the second integer.

Parameters

a	The first operand.
b	The second operand.

Returns: The result.

Definition at line 1507 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> operator<<	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Computes the bitwise left shift of the first integer by the number of bits given by the second integer, and returns the result.

This effectively multiplies the first integer by 2 to the power of the second integer.

Parameters

a	The first operand.
b	The second operand.

Returns: The result.

Definition at line 1523 of file arithmetic-nint.hpp.

template<typename Type>

bool operator<=	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Compares the current integer with the given one.

Parameters

a	The first operand.
b	The second operand.

Returns: true if a is less than or equal to b.

Definition at line 1551 of file arithmetic-nint.hpp.

template<typename Type>

bool operator==	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Compares the current integer with the given one for equality.

Parameters

a	The first operand.
b	The second operand.

Returns: true if a equals b.

Definition at line 1539 of file arithmetic-nint.hpp.

template<typename Type>

bool operator>	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Compares the current integer with the given one.

Parameters

a	The first operand.
b	The second operand.

Returns: true if a is greater than b.

Definition at line 1569 of file arithmetic-nint.hpp.

template<typename Type>

bool operator>=	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Compares the current integer with the given one.

Parameters

a	The first operand.
b	The second operand.

Returns: true if a is greater than or equal to b.

Definition at line 1557 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> operator>>	(	const NInt< Type > &	a,
		long	b
	)

friend

Computes the bitwise right shift of the first integer by the number of bits given by the second integer, and returns the result.

This effectively divides the first integer by 2 to the power of the second integer, and rounds towards zero.

Parameters

a	The first operand.
b	The second operand.

Returns: The result.

Definition at line 1515 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> operator>>	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Computes the bitwise right shift of the first integer by the number of bits given by the second integer, and returns the result.

This effectively divides the first integer by 2 to the power of the second integer, and rounds towards zero.

Parameters

a	The first operand.
b	The second operand.

Returns: The result.

Definition at line 1531 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> power	(	const NInt< Type > &	a,
		long	b
	)

friend

Computes and returns a raised to the power of b.

Parameters

a	The first operand.
b	The second operand.

Returns: The result.

Definition at line 1899 of file arithmetic-nint.hpp.

template<typename Type>

void power	(	NInt< Type > &	r,
		const NInt< Type > &	a,
		long	b
	)

friend

Raises a to the power b and stores the result in r.

Parameters

r	The result.
a	The base.
b	The exponent.

Definition at line 1893 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> power	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Computes and returns a raised to the power of b.

Parameters

a	The first operand.
b	The second operand.

Returns: The result.

Definition at line 1911 of file arithmetic-nint.hpp.

template<typename Type>

void power	(	NInt< Type > &	r,
		const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Raises a to the power b and stores the result in r.

Parameters

r	The result.
a	The base.
b	The exponent.

Definition at line 1905 of file arithmetic-nint.hpp.

template<typename Type>

void roundDiv	(	NInt< Type > &	r,
		const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Computes $\lfloor \tfrac{a}{b} \rceil$ (rounding to the next integer) and stores the result in r.

Parameters

r	The result.
a	The divident.
b	The divisor.

See also: Integer Functions

Definition at line 2217 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> roundDiv	(	const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Computes and returns $\lfloor \tfrac{a}{b} \rceil$ (rounding to the next integer).

Returns: The result.

Parameters

a	The divident.
b	The divisor.

See also: Integer Functions

Definition at line 2230 of file arithmetic-nint.hpp.

template<typename Type>

void shl	(	NInt< Type > &	r,
		const NInt< Type > &	a,
		long	b
	)

friend

Shifts a by b bits to the left and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 1681 of file arithmetic-nint.hpp.

template<typename Type>

void shl	(	NInt< Type > &	r,
		const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Shifts a by b bits to the left and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 1719 of file arithmetic-nint.hpp.

template<typename Type>

void shr	(	NInt< Type > &	r,
		const NInt< Type > &	a,
		long	b
	)

friend

Shifts a by b bits to the left and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 1700 of file arithmetic-nint.hpp.

template<typename Type>

void shr	(	NInt< Type > &	r,
		const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Shifts a by b bits to the left and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 1725 of file arithmetic-nint.hpp.

template<typename Type>

int sign ( const NInt< Type > & r )

friend

Returns the sign of the given integer.

Returns: Returns a negative value if the value is negative, 0 if it is zero, and a positive value if it is positive.

Definition at line 1815 of file arithmetic-nint.hpp.

template<typename Type>

void sqrtCeil	(	NInt< Type > &	r,
		const NInt< Type > &	a
	)

friend

Computes $\lceil\sqrt{a}\rceil$ and stores the result in r.

Parameters

r	The result.
a	The operand.

Definition at line 1917 of file arithmetic-nint.hpp.

template<typename Type>

void sqrtFloor	(	NInt< Type > &	r,
		const NInt< Type > &	a
	)

friend

Computes $\lfloor\sqrt{a}\rfloor$ and stores the result in r.

Parameters

r	The result.
a	The operand.

Definition at line 1941 of file arithmetic-nint.hpp.

template<typename Type>

NInt<Type> square ( const NInt< Type > & i )

friend

Computes and returns the square of i.

Parameters

i	The operand.

Returns: The result.

Definition at line 1865 of file arithmetic-nint.hpp.

template<typename Type>

void square	(	NInt< Type > &	r,
		const NInt< Type > &	a
	)

friend

Computes the square of a and stores the result in r.

Parameters

r	The result.
a	The operand.

Definition at line 1871 of file arithmetic-nint.hpp.

template<typename Type>

void sub	(	NInt< Type > &	r,
		const NInt< Type > &	a,
		const NInt< Type > &	b
	)

friend

Subtracts b from a and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 1637 of file arithmetic-nint.hpp.

template<typename Type>

void XGCD	(	NInt< Type > &	r,
		NInt< Type > &	a,
		NInt< Type > &	b,
		const NInt< Type > &	x,
		const NInt< Type > &	y
	)

friend

Computes the non-negative extended Greatest Common Divisior r of x and y.

Parameters

r	The result is stored in here.
a	The Bezout coefficient of `x`.
b	The Bezout coefficient of `y`.
x	The first operand.
y	The first operand.

Afterwards, the variables r, a and b satisfy r == a * x + b * y.

See also: Integer Functions

Definition at line 2286 of file arithmetic-nint.hpp.

The documentation for this class was generated from the following file:

/home/felix/projects/code/plll/plll/plll/include/plll/arithmetic-nint.hpp

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

template<typename Type> class plll::arithmetic::NInt< Type >

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

template<typename Type>
class plll::arithmetic::NInt< Type >