On Fri, 2011-02-25 at 00:33 +0000, Steven D'Aprano 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
Maybe I'm wrong, but wouldn't compiling Python with a compiler that supports extended precision for intermediates allow Python to use extended precision for its immediates? Or does Python use its own floating-point math? -- http://mail.python.org/mailman/listinfo/python-list
