Re: FP negation optimization

[Geoff Keating <geoffk at geoffk dot org>]

Chris Lattner <sabre@nondot.org> writes:

> On Sun, 1 Feb 2004, Richard Henderson wrote:
> 
> > On Sun, Feb 01, 2004 at 02:50:31AM -0600, Chris Lattner wrote:
> > > Is '-0.0 - X' always guaranteed to be the same as '-X' with IEEE math?
> >
> > No.  X == +0.0 differs.
> 
> Are you sure?  It seems to work for me, at least on X86:
> 
> void test(double X) {
>   printf("%f %f\n", -0.0 - X, -X);
> }
> int main() {
>   test(+0.0);
>   test(-0.0);
> }

I looked this up.  '-0.0 - X' is the same as '-0.0 + (-X)'.  When -X
!= 0.0, the result will be -X, so that's OK.  Suppose X is +/- 0.0.
Then the following rules apply:

- If both operands have the same sign, the sign of the result is the
  same as the sign of the operands.  So if X is +0.0, you'll get -0.0,
  the same as -X.

- If the sum of two operands with opposite sign is exactly zero, the
  sign is positive in all rounding modes except round towards -Inf, in
  which case the sign is negative.  So, if X is -0.0, you'll get
  +0.0, the same as -X, *unless* we're rounding towards -Inf.

Thus, the answer to your question is "no".  The case that differs is
when X is -0.0 and the rounding mode is towards -Inf.

-- 
- Geoffrey Keating <geoffk@geoffk.org>