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From: Jan Burse <janburse@fastmail.fm>
Newsgroups: comp.lang.java.programmer
Subject: Re: higher precision doubles
Date: Sun, 07 Aug 2011 01:34:11 +0200
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Patricia Shanahan schrieb:
> What is your general strategy for dealing with rounding error in your

The same strategy like ISO LIA is following. You have
the mathematical definition of sin, pi, etc.. And then
you have the machine objects SIN, PI, etc..

And then you have some requirements between these two
things. So each machine real x maps directly to a
mathematical real, but a mathematical real maps to
its nearest machine real if one exists, or if there
are two such machine reals, i.e. if the mathematical
real is exactly between two machine reals, then further
rules might be postulated.

So SIN, the machine function should ideally work as the
mathematical sin, and then before returning its result
pick a machine real as described above. Thats all I
expect from any trigonometric package. And it is
demonstrable (I guess, I didn't verify) that the ideal
can be turned into a practice. Modern FPUs exactly need
to do this in case they comply with some ISO
LIA standard.

So the requirements for sin are very high. One cannot
go on an just set SIN(PI)=0. Would not pass any LIA
ISO compliance test.