Re: Draft "Unsafe fp optimizations" project description.

[Ross Smith <ross dot s at ihug dot co dot nz>]

dewar@gnat.com wrote:
> 
> <<I think what Toon meant was something like: if you throw all the
> possible distinct values for a given FP representation into a sack, and
> pick the operands at random from the sack, there's roughly a 50/50
> chance that B*C will overflow or underflow.
> >>
> 
> I agree that's what he meant, but that is entirely wrong, the proportion
> of numbers that overflow is far far smaller. Remember we are talking about
> floating-point values here, not real values. There are as many fpt
> numbers with an exponent of 1 as there are with an exponent of 100 :-)

On further consideration, I think we were all wrong :-) The probability
of an overflow or underflow is actually 25% give or take a smidgeon.
(Hint: The logarithms of FP numbers are approximately uniformly
distributed.)

-- 
Ross Smith <ross.s@ihug.co.nz> The Internet Group, Auckland, New Zealand
========================================================================
"Unix has always lurked provocatively in the background of the operating
system wars, like the Russian Army."                  -- Neal Stephenson