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From: Jan Burse <janburse@fastmail.fm>
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Subject: Re: higher precision doubles
Date: Sun, 11 Sep 2011 13:29:58 +0200
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Lew schrieb:
> Since Mathematica runs on *floating point hardware*, create by humans,

This is not quite true what your are saying
here. Mathematica has actually 3 modes in
dealing with sin. The modes are as follows:

   - Symbolic
   - Machine Precision
   - High Precision

What the poster showed, sin[2 Pi] = 0, was an
implicit FunctionExpand of sin, so a symbolic
manoeuvre. If he would force mathematica to
use machine precision or high precision he
would get another result. Here is an example:

    N[pi,18] = 3.14159265358979324.

    N[sin[3.14159265358979324],18] =

	-1.53735661672049712×10^-18

Whether the machine precision uses the floating
point hardware is unspecified. Most likely, but
it could also use some software emulation. So as
to prevent differences from platform to platform,
like the strictfp modifier. Would need to further
dig into the Mathematica documentation for this
question.

For more details and many example uses
of the modes see for example here:
http://reference.wolfram.com/mathematica/ref/Sin.html
For a first intro into the modes see the "Scope" section.

Bye