> But, you are using a number in the range of 2^90, only
> have 64 bits for storing the floating point representation, and
> some of that is needed for the exponent.
> 2^90 would require 91 bits for the base alone (as an integer
> value), plus a couple more for the '*PI' portion, and then
> more for the exponent. And that wouldn't include anything
> past the decimal point.
> You are more than 30 bits short of getting a crappy result.
This is not right.
Floating point variables are perfectly capable of holding _some_ rather large
floating point numbers completely accurately. The integer 2^90 is one of them
(on a standard base-2 machine).
It is true that its nearest neighbours are about 2^30 away, but that is not
relevant for the accuracy of 2^90. pow(2.0,90.0) generates that value
with no error.
Therefore sin(2^90) is a well defined number somewhere between -1 and 1
and the C fragment
sin(pow(2.0,90.0))
should calculate it with at most one wrong bit at the end. (You get a one-bit
allowance since "sin" is trancendental.)
Morten
(who wouldn't be too surprised if some "sin" implementations failed to do that)
