In article <[EMAIL PROTECTED]>, "Hendrik van Rooyen" <[EMAIL PROTECTED]> writes: |> "Tim Peters" <[EMAIL PROTECTED]> wrote: |> |> > What you will still see stated is variations on Kahan's telegraphic |> > "binary is better than any other radix for error analysis (but not very |> > much)", listed as one of two techincal advantages for binary fp in: |> > |> > http://www.cs.berkeley.edu/~wkahan/MktgMath.pdf
Which I believe to be the final statement of the matter. It was a minority view 30 years ago, but I now know of little dissent. He has omitted that mid-point invariant as a third advantage of binary, but I agree that it could be phrased as "one or two extra mathematical invariants hold for binary (but not very important ones)". |> My basic error of thinking ( ? - more like gut feel ) was that the |> bigger bases somehow lose "more bits" at every round, |> forgetting that half a microvolt is still half a microvolt, whether |> it is rounded in binary, decimal, or hex... That is not an error, but only a mistake :-) Yes, you have hit the nail on the head. Some people claimed that some important algorithms did that, and that binary was consequently much better. If it were true, then the precision you would need would be pro rata to the case - so the decimal equivalent of 64-bit binary would need 160 bits. Experience failed to confirm their viewpoint, and the effect was seen in only artificial algorithms (sorry - I can no longer remember the examples and am reluctant to waste time trying to reinvent them). But it was ALSO found that the converse was not QUITE true, either, and the effective numerical precision is not FULLY independent of the base. So, at a wild guesstimate, 64-bit decimal will deliver a precision comparable to about 56-bit binary, and will cause significant numerical problems to a FEW applications. Hence people will have to convert to the much more expensive 128-bit decimal format for such work. Bloatware rules. All your bits are belong to us. Regards, Nick Maclaren. -- http://mail.python.org/mailman/listinfo/python-list
