From: "John Herbster" <herb-sci@swbell.net>
Newsgroups: borland.public.delphi.objectpascal
References: <3C4747A3.5F295536@bellatlantic.net>
Subject: Re: sin(1E19) ?
Date: Thu, 17 Jan 2002 19:49:40 -0600
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"Ben Crain" <bcrain@bellatlantic.net> wrote
> D5's math unit correctly returns sin(1E18),
> but not sin(1E19) or above.  Why not?

The specs for the 387 FPU says that for the sine
function the magnitude of the input cannot exceed
2^63 which is about 9.22337E+18.  The 387 is
similar to the Pentium FPU and both are based
on specification IEEE-754.

Also of note is that the resolution of the numbers
out near 1e18 gets rather course.  While taking
the sin(1e18) gives about -0.99282, the
sin(1e18 - delta) where delta is the smallest
decrement possible on an extended type
number the size of 1e18 gives about -0.99835.
That means the radians are taking big steps
and the sine function is by no means continuous
out there.

So my advice is don't depend on the sine
of extreme numbers to be very useful.

Regards, JohnH