Steven D'Aprano wrote: > On Fri, 20 Jan 2006 04:25:01 +0000, Bengt Richter wrote: > > >>On Thu, 19 Jan 2006 12:16:22 +0100, =?ISO-8859-1?Q?Gerhard_H=E4ring?= <[EMAIL >>PROTECTED]> wrote: >>[...] >> >>>floating points are always imprecise, so you wouldn't want them as an >> >>Please, floating point is not "always imprecise." In a double there are >>64 bits, and most patterns represent exact rational values. Other than >>infinities and NaNs, you can't pick a bit pattern that doesn't have >>a precise, exact rational value. > > > Of course every float has a precise rational value. > 0.1000000000000000000001 has a precise rational value: > > 1000000000000000000001/10000000000000000000000 > > But that's hardly what people are referring to. The question isn't whether > every float is an (ugly) rational, but whether every (tidy) rational is a > float. And that is *not* the case, simple rationals like 1/10 cannot be > written precisely as floats no matter how many bits you use. > > >>You can't represent all arbitarily chosen reals exactly as floats, that's >>true, >>but that's not the same as saying that "floating points are always imprecise." > > > "Always" is too strong, since (for example) 1/2 can be represented > precisely as a float. But in general, for any "random" rational value N/M, > the odds are that it cannot be represented precisely as a float. And > that's what people mean when they say floats are imprecise. > > > And you thought Bengt didn't know that?
regards Steve -- Steve Holden +44 150 684 7255 +1 800 494 3119 Holden Web LLC www.holdenweb.com PyCon TX 2006 www.python.org/pycon/ -- http://mail.python.org/mailman/listinfo/python-list
