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Re: inexactness vs. exactness



> From: Aubrey Jaffer <agj@xxxxxxxxxxxx>
> Each exact number corresponds to a single mathematical number.  For
> exact numbers, it is the programmer's responsibility to avoid using
> numbers with magnitude or precision too large to be represented in the
> implementation.
> 
> Inexact numbers are approximate.  Every mathematical number within the
> (convex) range of inexacts supported by an implementation will round
> to an inexact number on input or as a result of computation.  The
> neighborhood of mathematical numbers rounding to a particular inexact
> number must be simply connected.
> 
> Because real infinities are mandated (in implementations supporting
> inexacts), all mathematical real numbers map to inexact numbers.  For
> non-real complex numbers, it is the programmer's responsibility to
> avoid using numbers with magnitude too large to be represented in the
> implementation.

I pre-apologize if this is a dumb question, but as it seems that exact
values are only interesting for integer ratios, which correspondingly seem
reasonable to expect to have some practical limited representational
precision, therefore also imply the necessity to depict an over/underflowed
value (i.e. +/- infinity and reciprocals); why is it perceived as necessary
and/or appropriate to presume it's the responsibility of the programmer to
limit computed values to reasonable precision rational values as opposed to
possibly more simply defining that exacts are merely only more exact than
inexacts to some definable precision?  As beyond academic definition of
exact, pretending that an arbitrary exact implementation supports infinitely
exact computations seems both naive and impractical?