Correct interpretation of the Pentium non-bug

Correct interpretation of the Pentium non-bug

[David McClain]

Something Xavier showed got me thinking and I ran some more tests this
morning. It turns out that the problem previously reported actually has
nothing to do with FCHS vs FSUB. Rather, it has to do with how one adds a
real value to a complex value, especially when the complex value has a
IEEE(-0.0) imaginary component.

Adding a real to a complex number:

    a + (bre, bim)   !=  (a+bre, bim)

rather

    a + (bre, bim) == (a + bre, (+0.0) + bim)

This matters only when bim is (-0.0) because,

    FPADD (+0.0) (+0.0) = +0.0
    FPADD (+0.0) (-0.0)  = +0.0     (!!!)
    FAPDD (+0.0) x         =  x          (for all other x)

When this is properly handled, the routines all give the correct branch cut
behavior. It turns out that, indeed, I*(are, aim) = (- aim, are)  where the
negative sign is FCHS, instead of (0.0 - aim, are).  The second form is
incorrect.

While all very esoteric and nit-picking, it does show the importance in
compiler writing of being very careful during constant-folding and
strength-reduction phases of optimization. I am probably guilty, years ago,
of assuming that 0.0 + anything => anything, in my old C compilers. This
subtle fact simply isn't true in IEEE FP.

- DM