Python fails on math

[Ben]

On Feb 25, 12:33 am, Steven D'Aprano <steve
+comp.lang.pyt... at pearwood.info> wrote:
> On Thu, 24 Feb 2011 10:40:45 -0600, Robert Kern wrote:
> > On 2/24/11 5:55 AM, Steven D'Aprano wrote:
> >> On Wed, 23 Feb 2011 13:26:05 -0800, John Nagle wrote:
>
> >>> The IEEE 754 compliant FPU on most machines today, though, has an
> >>> 80-bit internal representation.  If you do a sequence of operations
> >>> that retain all the intermediate results in the FPU registers, you get
> >>> 16 more bits of precision than if you store after each operation.
>
> >> That's a big if though. Which languages support such a thing? C doubles
> >> are 64 bit, same as Python.
>
> > C double *variables* are, but as John suggests, C compilers are allowed
> > (to my knowledge) to keep intermediate results of an expression in the
> > larger-precision FPU registers. The final result does get shoved back
> > into a 64-bit double when it is at last assigned back to a variable or
> > passed to a function that takes a double.
>
> So...
>
> (1) you can't rely on it, because it's only "allowed" and not mandatory;
>
> (2) you may or may not have any control over whether or not it happens;
>
> (3) it only works for calculations that are simple enough to fit in a
> single expression; and
>
> (4) we could say the same thing about Python -- there's no prohibition on
> Python using extended precision when performing intermediate results, so
> it too could be said to be "allowed".
>
> It seems rather unfair to me to single Python out as somehow lacking
> (compared to which other languages?) and to gloss over the difficulties
> in "If you do a sequence of operations that retain all the intermediate
> results..." Yes, *if* you do so, you get more precision, but *how* do you
> do so? Such a thing will be language or even implementation dependent,
> and the implication that it just automatically happens without any effort
> seems dubious to me.
>
> But I could be wrong, of course. It may be that Python, alone of all
> modern high-level languages, fails to take advantage of 80-bit registers
> in FPUs *wink*
>
> --
> Steven

And note that x64 machines use SSE for all their floating point maths,
which is 64bit max precision anyway

Ben