AlgebraicKernel_d_1::ApproximateRelative_1 Concept Reference

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 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

\( p.first <= x \)

\( x <= p.second \)

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

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