approximate ( x epsilon -- y )

Vocabulary

math.approx

Inputs

x	a ratio
epsilon	a ratio

Outputs

y

a ratio

Word description

Applied to two fractional numbers "x" and "epsilon", returns the simplest rational number within "epsilon" of "x".

A rational number "y" is said to be simpler than another "y'" if abs numerator y <= abs numerator y', and denominator y <= denominator y'

Any real interval contains a unique simplest rational; in particular note that 0/1 is the simplest rational of all.

Definition

USING: kernel math math.approx.private ;

IN: math.approx

: approximate ( x epsilon -- y )
    [ check-float ] bi@ [ - ] [ + ] 2bi simplest ;