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

$p.first <= x$

$x <= p.second$

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

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