Re: Sine and Cosine Accuracy

[Paul Koning <pkoning@equallogic.com>]

After some off-line exchanges with Dave Korn, it seems to me that part
of the problem is that the documentation for
-funsafe-math-optimizations is so vague as to have no discernable
meaning. 

For example, does the wording of the documentation convey the
limitation that one should only invoke math functions with a small
range of arguments (say, -pi to +pi)?  I cannot see anything remotely
resembling that limitation, but others can.

Given that, I wonder how we can tell whether a particular proposed
optimization governed by that flag is permissible.  Consider:

`-funsafe-math-optimizations'
     Allow optimizations for floating-point arithmetic that (a) assume
     that arguments and results are valid and (b) may violate IEEE or
     ANSI standards.  

What does (b) mean?  What if anything are its limitations?  Is
returning 1.2e27 as the result for a sin() call authorized by (b)?  I
would not have expected that, but I can't defend that expectation
based on a literal reading of the text...

      paul