round() ignores the innate precision of a real number

[jonhanke]

The function round() seems to ignore precision information slightly beyond the default 53 bits for a real number. This leads to some incorrect rounding results for close calls.

sage: a = 5.499999999999999 
sage: a.prec()
56
sage: round(a)  ## This is ok
5.0

sage: b = 5.4999999999999999
sage: b.prec()
59
sage: round(b)  ## This isn't ok 
6.0

Component: algebraic geometry

Keywords: round, real, precision, arithmetic

Issue created by migration from https://trac.sagemath.org/ticket/392

[jonhanke]

Changed keywords from round, real, arithmetic to round, real, precision, arithmetic