On Sat, Jan 06, 2024 at 06:02:45PM +0100, David Brown wrote:
> On 05/01/2024 19:19, Segher Boessenkool wrote:
> >That's not the point. A program can be perfectly fine, with bounded
> >errors and all, and then -ffast-math will typically completely destroy
> >all that, and replace all arithmetic by the equivalent of a dice roll.
>
> The only difference between IEEE calculations and -ffast-math
> calculations is that with IEEE, the ordering and rounding is controlled
> and consistent.
No, that is not the only difference.
'-ffast-math'
Sets the options '-fno-math-errno', '-funsafe-math-optimizations',
'-ffinite-math-only', '-fno-rounding-math', '-fno-signaling-nans',
'-fcx-limited-range' and '-fexcess-precision=fast'.
Many of those do much more than what you say, can result in the compiler
generating completely different code.
> For any given /single/ arithmetic operation that is
> performed, each can have the same amount of rounding error or error due
> to the limited length of the mantissa. Agreed?
I don't understand what you mean to say even.
> >>The rounding errors in -ffast-math will be very similar to those in IEEE
> >>mode, for normal numbers.
> >
> >No, not at all. Look at what -fassociative-math does, for example.
> >This can **and does** cause the loss of **all** bits of precision in
> >certain programs. This is not theoretical. This is real.
>
> a = 1e120;
> b = 2;
>
> x = (a + b) - a;
>
> IEEE rules will give "x" equal to 1e120 - mathematically /completely/
> wrong. -ffast-math will give "x" equal to 2, which is mathematically
> precisely correct.
The IEEE result is 0. Which is the **exactly correct** result. This is
a computer program, not some formulas that you can manipulate at will.
> >The -ffast-math flag can only reasonably be used with programs that did
> >not want any specific results anyway. It would be even faster (and just
> >as correct!) to always return 0.
>
> That is simply wrong.
It is an exaggeration for dramatic effect, but it is fundamentally
correct.
Segher
