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. -- Steven. -- http://mail.python.org/mailman/listinfo/python-list
