I think Knuth (Section 4.2.2 of Seminumerical Algorithms (3rd edition)) has
an
algorithm for floating point comparison. Next time I visit the library,
I'll
look it up.
Barton
-----maxima-bounces at math.utexas.edu wrote: -----
>On?8/7/09,?Barton?Willis?<willisb at unk.edu>?wrote:
>
>>?;;?Return?true?if?$float?converts?both?a?and?b?to?floats?and
>>?;;?|a?-?b|?<=?float_approx_equal_tolerance?*?min(|a|,?|b|).
>>?;;?In?all?other?cases,?return?false.
>
>Incidentally?this?definition?is,?I?believe,?unnecessarily?strict?for
>quantities?near?zero.?There?are?some?tests?which?fail?for?some
>Lisp?implementations?because?e.g.?1e-16?isn't?close?enough?to
>1.1e-16?where?these?numbers?are?residual?errors?of?some?kind
>(i.e.?computed?by?subtracting?much?larger?numbers?which?are
>nearly?equal).
>
>FWIW
>
>Robert?Dodier
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