On Feb 25, 11:34 am, casevh <[EMAIL PROTECTED]> wrote: > On Feb 24, 7:56 pm, Mensanator <[EMAIL PROTECTED]> wrote: > > > But that doesn't mean they become less manageable than > > other unlimited precision usages. Did you see my example > > of the polynomial finder using Newton's Forward Differences > > Method? The denominator's certainly don't settle out, neither > > do they become unmanageable. And that's general mathematics. > > Since you are expecting to work with unlimited (or at least, very > high) precision, then the behavior of rationals is not a surprise. But > a naive user may be surprised when the running time for a calculation > varies greatly based on the values of the numbers. In contrast, the > running time for standard binary floating point operations are fairly > constant. > > > > > If the point was as SDA suggested, where things like 16/16 > > are possible, I see that point. As gmpy demonstrates thouigh, > > such concerns are moot as that doesn't happen. There's no > > reason to suppose a Python native rational type would be > > implemented stupidly, is there? > > In the current version of GMP, the running time for the calculation of > the greatest common divisor is O(n^2). If you include reduction to > lowest terms, the running time for a rational add is now O(n^2) > instead of O(n) for a high-precision floating point addition or O(1) > for a standard floating point addition. If you need an exact rational > answer, then the change in running time is fine. But you can't just > use rationals and expect a constant running time. > > There are trade-offs between IEEE-754 binary, Decimal, and Rational > arithmetic. They all have there appropriate problem domains.
I very agree with this statement. Fractionals do have its weakness, and so do Decimal and Hardware Floating Point. And they have their own usage, their own scenarios where they're appropriate. If you needed full-speed calculation, it is clear that floating point wins all over the place, OTOH, if you need to manage your precision carefully Fractional and Decimal both have their own plus and mins -- http://mail.python.org/mailman/listinfo/python-list
