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From: ldo@peace.waikato.ac.nz (Lawrence D'Oliveiro)
Newsgroups: comp.sys.mac
Subject: Re: Mac of the 90's: FLOPS, MegaFLOPS?
Summary: One of your wishes you don't want
Keywords: IEEE 754, numeric precision
Message-ID: <1990Jan22.060142.25577@peace.waikato.ac.nz>
Date: 22 Jan 90 06:01:42 GMT
References: <5338.25af60d1@jane.uh.edu>
Organization: University of Waikato, Hamilton, New Zealand
Lines: 18

In <5338.25af60d1@jane.uh.edu>, math1h3@jane.uh.edu (David Wagner),
in a list of wishes for the numeric capabilities of future Macintoshes,
asks for "support for single-precision and double precision arithmetic
and transcendental functions in whatever coprocessor is used. It seems
terribly wasteful to always do extended precision arithmetic and
transcendental functions when the user/programmer might only want or
need single precision."

That's as may be, but if you don't compute the intermediate results
to the maximum precision available, the final answers you get will be
even less accurate than you're used to.

The IEEE 754 standard demands that all arithmetic be carried out to
extended precision. Both the numeric coprocessor families for which I
have information (68881/68882, 80x87) work this way. Because of this,
it's actually *faster* to all the arithmetic in your program in
extended precision, and only convert to/from external formats when
inputting values, or outputting results.