Operator definitions for integers. More...

Namespaces
	plll
	Contains the `plll` library.

	plll::arithmetic
	Contains the arithmetic backend of `plll`.

	plll::arithmetic::expressions
	Expression templates.

Functions
Operators.
expressions::Expression < IntegerContext, expressions::Wrapper < IntegerContext > , expressions::NegOp >	plll::arithmetic::operator- (const Integer &a)
	Negates the integer. More...

expressions::Expression < IntegerContext, expressions::Wrapper < IntegerContext > , expressions::BitInvOp >	plll::arithmetic::operator~ (const Integer &a)
	Bitwise negates the integer. More...

expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::AddOp >	plll::arithmetic::operator+ (const Integer &a, const Integer &b)
	Adds the two integers and returns the result. More...

expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::SubOp >	plll::arithmetic::operator- (const Integer &a, const Integer &b)
	Subtracts the second from the first integer and returns the result. More...

expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::MulOp >	plll::arithmetic::operator* (const Integer &a, const Integer &b)
	Multiplies the two integers and returns the result. More...

expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::DivOp >	plll::arithmetic::operator/ (const Integer &a, const Integer &b)
	Divides the first by the second integer and returns the result. More...

expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::ModOp >	plll::arithmetic::operator% (const Integer &a, const Integer &b)
	Divides the first by the second integer and returns the remainder. More...

expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::AndOp >	plll::arithmetic::operator& (const Integer &a, const Integer &b)
	Computes the bitwise and of the two integers and returns the result. More...

expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::OrOp >	plll::arithmetic::operator\| (const Integer &a, const Integer &b)
	Computes the bitwise or of the two integers and returns the result. More...

expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::XOROp >	plll::arithmetic::operator^ (const Integer &a, const Integer &b)
	Computes the bitwise exclusive or of the two integers and returns the result. More...

expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::ShLOp >	plll::arithmetic::operator<< (const Integer &a, const Integer &b)
	Computes the bitwise left shift of the first integer by the number of bits given by the second integer, and returns the result. More...

expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::ShROp >	plll::arithmetic::operator>> (const Integer &a, const Integer &b)
	Computes the bitwise right shift of the first integer by the number of bits given by the second integer, and returns the result. More...

expressions::Expression < IntegerContext, expressions::Wrapper < IntegerContext > , expressions::ShiftCOp >	plll::arithmetic::operator<< (const Integer &a, signed long b)
	Computes the bitwise left shift of the first integer by the number of bits given by the second integer, and returns the result. More...

expressions::Expression < IntegerContext, expressions::Wrapper < IntegerContext > , expressions::ShiftCOp >	plll::arithmetic::operator>> (const Integer &a, signed long b)
	Computes the bitwise right shift of the first integer by the number of bits given by the second integer, and returns the result. More...

Integer	plll::arithmetic::operator++ (Integer &cur, int)
	Increments the integer by one and returns the previous value. More...

Integer	plll::arithmetic::operator-- (Integer &cur, int)
	Decrements the integer by one and returns the previous value. More...

Integer &	plll::arithmetic::operator++ (Integer &cur)
	Increments the integer by one and returns the new value. More...

Integer &	plll::arithmetic::operator-- (Integer &cur)
	Decreases the integer by one and returns the new value. More...

expressions::Expression < IntegerContext, expressions::Wrapper < IntegerContext > , expressions::AbsOp >	plll::arithmetic::abs (const Integer &i)
	Computes and returns the absolute value of `i`. More...

expressions::Expression < IntegerContext, expressions::Wrapper < IntegerContext > , expressions::SquareOp >	plll::arithmetic::square (const Integer &i)
	Computes and returns the square of `i`. More...

Assignment-operation operators.
template<class D >
Integer &	plll::arithmetic::operator-= (Integer &cur, const expressions::Expression< IntegerContext, D, expressions::MulOp > &E)
	Subtracts the multiplication expression `E` from `cur`. More...

Integer &	plll::arithmetic::operator-= (Integer &cur, const Integer &i)
	Subtracts the integer `i` from `cur`. More...

template<class D >
Integer &	plll::arithmetic::operator+= (Integer &cur, const expressions::Expression< IntegerContext, D, expressions::MulOp > &E)
	Adds the given multiplication expression to `cur`. More...

Integer &	plll::arithmetic::operator+= (Integer &cur, const Integer &i)
	Adds the integer `i` to `cur`. More...

Integer &	plll::arithmetic::operator*= (Integer &cur, const Integer &i)
	Multiplies the given integer `i` with `cur`. More...

Integer &	plll::arithmetic::operator/= (Integer &cur, const Integer &i)
	Divides `cur` by the given integer `i`. More...

Integer &	plll::arithmetic::operator%= (Integer &cur, const Integer &i)
	Divides `cur` by the given integer `i` and stores the remainder in `cur`. More...

Integer &	plll::arithmetic::operator\|= (Integer &cur, const Integer &i)
	Computes the bitwise or of `cur` with `i` and stores the result in `cur`. More...

Integer &	plll::arithmetic::operator&= (Integer &cur, const Integer &i)
	Computes the bitwise and of `cur` with `i` and stores the result in `cur`. More...

Integer &	plll::arithmetic::operator^= (Integer &cur, const Integer &i)
	Computes the bitwise exclusive or of `cur` with `i` and stores the result in `cur`. More...

Integer &	plll::arithmetic::operator<<= (Integer &cur, const Integer &i)
	Computes the bitwise left shift of `cur` by `i` bits, and stores the result in `cur`. More...

Integer &	plll::arithmetic::operator>>= (Integer &cur, const Integer &i)
	Computes the bitwise right shift of `cur` by `i` bits, and stores the result in `cur`. More...

Integer &	plll::arithmetic::operator<<= (Integer &cur, long i)
	Computes the bitwise left shift of `cur` by `i` bits, and stores the result in `cur`. More...

Integer &	plll::arithmetic::operator>>= (Integer &cur, long i)
	Computes the bitwise right shift of `cur` by `i` bits, and stores the result in `cur`. More...

Comparisons.
bool	plll::arithmetic::operator== (const Integer &a, const Integer &b)
	Compares the current integer with the given one for equality. More...

bool	plll::arithmetic::operator!= (const Integer &a, const Integer &b)
	Compares the current integer with the given one for inequality. More...

bool	plll::arithmetic::operator<= (const Integer &a, const Integer &b)
	Compares the current integer with the given one. More...

bool	plll::arithmetic::operator>= (const Integer &a, const Integer &b)
	Compares the current integer with the given one. More...

bool	plll::arithmetic::operator< (const Integer &a, const Integer &b)
	Compares the current integer with the given one. More...

bool	plll::arithmetic::operator> (const Integer &a, const Integer &b)
	Compares the current integer with the given one. More...

Integer approximation.
expressions::Expression < IntegerContext, expressions::Wrapper < IntegerContext > , expressions::SqrtCeilOp >	plll::arithmetic::sqrtCeil (const Integer &i)
	Computes and returns the ceil of the square root of `i`. More...

expressions::Expression < IntegerContext, expressions::Wrapper < IntegerContext > , expressions::SqrtFloorOp >	plll::arithmetic::sqrtFloor (const Integer &i)
	Computes and returns the floor of the square root of `i`. More...

expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::FloorDivOp >	plll::arithmetic::floorDiv (const Integer &a, const Integer &b)
	Computes and returns $\lfloor \tfrac{a}{b} \rfloor$ . More...

expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::CeilDivOp >	plll::arithmetic::ceilDiv (const Integer &a, const Integer &b)
	Computes and returns $\lceil \tfrac{a}{b} \rceil$ . More...

expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::RoundDivOp >	plll::arithmetic::roundDiv (const Integer &a, const Integer &b)
	Computes and returns $\lfloor \tfrac{a}{b} \rceil$ . More...

Euclidean ring functions.
expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::GCDOp >	plll::arithmetic::GCD (const Integer &a, const Integer &b)
	Computes and returns the non-negative Greatest Common Divisor of `a` and `b`. More...

expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::LCMOp >	plll::arithmetic::LCM (const Integer &a, const Integer &b)
	Computes and returns the non-negative Least Common Multiple of `a` and `b`. More...

Exponentiation.
expressions::Expression < IntegerContext, std::pair < expressions::Wrapper < IntegerContext > , expressions::Wrapper < IntegerContext > >, expressions::PowerOp >	plll::arithmetic::power (const Integer &a, const Integer &b)
	Computes and returns `a` raised to the power of `b`. More...

expressions::Expression < IntegerContext, expressions::Wrapper < IntegerContext > , expressions::PowerCOp < signed long >::impl >	plll::arithmetic::power (const Integer &a, signed long b)
	Computes and returns `a` raised to the power of `b`. More...

Detailed Description

Operator definitions for integers.

This header contains templates and instantiations to implement all operations on integers.

Definition in file arithmetic-gmp-iops.hpp.

Namespaces

Functions

Detailed Description