rational.hpp File Reference

Header for rational number arithmetic. More...

#include <plll/arithmetic.hpp>
#include "helper.hpp"
#include <sstream>
#include <cassert>
#include <cmath>
#include "rational-ops.hpp"
#include "rational-conv.hpp"

Go to the source code of this file.

Classes
class	plll::arithmetic::Rational
	Represents a rational number as a quotient of two arbitrary precision integers. More...
class	plll::arithmetic::RationalContext
	Represents an arithmetic context for rational numbers. More...

Namespaces
	plll
	Contains the plll library.
	plll::arithmetic
	Contains the arithmetic backend of plll.

Functions
Predicates.
bool	plll::arithmetic::isZero (const Rational &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given rational number for being zero. More...
bool	plll::arithmetic::isOne (const Rational &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given plll::arithmetic::Real object for being zero. More...
bool	plll::arithmetic::isPositive (const Rational &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given rational number for being strictly positive. More...
bool	plll::arithmetic::isNonNegative (const Rational &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given rational number for being positive or zero. More...
bool	plll::arithmetic::isNegative (const Rational &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given rational number for being strictly negative. More...
bool	plll::arithmetic::isNonPositive (const Rational &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given rational number for being negative or zero. More...
Functional versions of operators.
void	plll::arithmetic::add (Rational &r, const Rational &a, const Rational &b)
	Adds a and b and stores the result in r. More...
void	plll::arithmetic::sub (Rational &r, const Rational &a, const Rational &b)
	Subtracts b from a and stores the result in r. More...
void	plll::arithmetic::addmul (Rational &r, const Rational &a, const Rational &b)
	Multiplies a and b and adds the result to r. More...
void	plll::arithmetic::submul (Rational &r, const Rational &a, const Rational &b)
	Multiplies a and b and subtracts the result from r. More...
void	plll::arithmetic::mul (Rational &r, const Rational &a, const Rational &b)
	Multiplies a with b and stores the result in r. More...
void	plll::arithmetic::div (Rational &r, const Rational &a, const Rational &b)
	Divides a by b and stores the result in r. More...
void	plll::arithmetic::mod (Rational &r, const Rational &a, const Rational &b)
	Takes the remainder of the division of a by b and stores it in r. More...
void	plll::arithmetic::shl (Rational &r, const Rational &a, long b)
	Multiplies a by and stores the result in r. More...
void	plll::arithmetic::shr (Rational &r, const Rational &a, long b)
	Multiplies a by and stores the result in r. More...
void	plll::arithmetic::increment (Rational &r, const Rational &a)
	Increments a by one and stores the result in r. More...
void	plll::arithmetic::decrement (Rational &r, const Rational &a)
	Negates a and stores the result in r. More...
void	plll::arithmetic::neg (Rational &r, const Rational &a)
	Negates a and stores the result in r. More...
void	plll::arithmetic::abs (Rational &r, const Rational &a)
	Takes the absolute value of a and stores the result in r. More...
void	plll::arithmetic::square (Rational &r, const Rational &a)
	Computes the square of a and stores the result in r. More...
Sign querying/modification.
void	plll::arithmetic::makeAbs (Rational &a) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Makes the operand non-negative. More...
int	plll::arithmetic::sign (const Rational &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Returns the sign of the given rational number. More...
Stream input/output.
std::ostream &	plll::arithmetic::operator<< (std::ostream &s, const Rational &r)
	Outputs the rational number on the given output stream.
std::istream &	plll::arithmetic::operator>> (std::istream &s, Rational &r)
	Reads the rational number from the given input stream.
Setting to specific constants.
void	plll::arithmetic::setZero (Rational &r, bool sign=true)
	Sets the given rational number to . More...
void	plll::arithmetic::setOne (Rational &r)
	Sets the given rational number to one. More...
Comparisons.
int	plll::arithmetic::compare (const Rational &a, const Rational &b)
	Compares the two rational numbers. More...
int	plll::arithmetic::compareAbsValues (const Rational &a, const Rational &b)
	Compares the two rational numbers in absolute value. More...
Exponentiation.
void	plll::arithmetic::power (Rational &r, const Rational &a, signed long e)
	Raises a to the power e and stores the result in r. More...
void	plll::arithmetic::power (Rational &r, const Rational &a, unsigned long e)
	Raises a to the power e and stores the result in r. More...
void	plll::arithmetic::power (Rational &r, const Rational &a, const Integer &e)
	Raises a to the power e and stores the result in r. More...
Swap functions.
void	plll::arithmetic::swap (Rational &, Rational &) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Swaps two plll::arithmetic::Rational objects.

Detailed Description

Header for rational number arithmetic.

This header provides rational number arithmetic for plll. It provides plll::arithmetic::RationalContext, an arithmetic context as described in Arithmetic Contexts. Concrete rational numbers are represented by plll::arithmetic::Rational objects, which essentially consist of two plll::arithmetic::Integer objects, and expressions are represented by plll::arithmetic::expressions::expression<> templates.

Definition in file rational.hpp.