#include <Concepts/AlgebraicKernel_d_1--ApproximateRelative_1.h>

Definition

A model of AlgebraicKernel_d_1::ApproximateRelative_1 is an AdaptableBinaryFunction that computes an approximation of an AlgebraicKernel_d_1::Algebraic_real_1 value with respect to a given relative precision.

Refines:: AdaptableBinaryFunction

See also: AlgebraicKernel_d_1::ApproximateAbsolute_1

Types
typedef std::pair< AlgebraicKernel_d_1::Bound, AlgebraicKernel_d_1::Bound >	result_type

typedef AlgebraicKernel_d_1::Algebraic_real_1	first_argument_type

typedef int	second_argument_type

Operations
result_type	operator() (const first_argument_type &x, const second_argument_type &r)
	The function computes a pair \( p\) of `AlgebraicKernel_d_1::Bound`, where \( p.first\) represents the lower approximation and \( p.second\) represents the upper approximation. More...

Member Typedef Documentation

◆ first_argument_type

typedef AlgebraicKernel_d_1::Algebraic_real_1 AlgebraicKernel_d_1::ApproximateRelative_1::first_argument_type

◆ result_type

typedef std::pair<AlgebraicKernel_d_1::Bound, AlgebraicKernel_d_1::Bound> AlgebraicKernel_d_1::ApproximateRelative_1::result_type

◆ second_argument_type

typedef int AlgebraicKernel_d_1::ApproximateRelative_1::second_argument_type

Member Function Documentation

◆ operator()()

result_type AlgebraicKernel_d_1::ApproximateRelative_1::operator()	(	const first_argument_type &	x,
		const second_argument_type &	r
	)

The function computes a pair \( p\) of AlgebraicKernel_d_1::Bound, where \( p.first\) represents the lower approximation and \( p.second\) represents the upper approximation.

The pair \( p\) approximates the given value \( x\) with respect to the given relative precision \( r\).

Postcondition: \( p.first <= x \); \( x <= p.second \); \( (x - p.first) <= 2^{-r} *|x|\); \( (p.second - x) <= 2^{-r} *|x|\)