pragma GCC optimize prevents inlining
Gabriel Ravier
gabravier@gmail.com
Sun Jan 7 18:36:07 GMT 2024
On 1/7/24 17:51, Segher Boessenkool wrote:
> 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.
That seems to be where the disagreement lies. Those that use -ffast-math
with full knowledge of what it does are presumably acting with the
intent that their program should indeed be treated as "some formulas 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
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