Bill Hart wrote:
That's actually a very interesting paper. I've recently been playing
with Forth, which is a kind of "Lisp type language" (yeah I know you
won't agree with that), based on a data stack. I also worked through a
book on Lisp up to the point where macros were defined, as I wanted to
understand how that was handled in Lisp. I actually "get" Lisp now,
but it was a round about way that I got there. It's clearly not for
everyone.
I've also been experimenting with how short programs can be that still
give reasonable performance. The answer is, amazingly short, if one
spends a lot of time thinking about it before coding.
Another thing I've been enjoying lately is literate programming.
Amazingly it turns out to be faster to write a literate program than
an ordinary program because debugging takes almost no time.
Can I quote you on that in the Axiom system (which is moving toward
being fully literate)?
Anyhow, I'm going to read this paper of yours now.
Bill.
On May 3, 3:37 pm, rjf <fate...@gmail.com> wrote:
If you are not doing floating point arithmetic with machine
arithmetic, but using MPFR, then you are sacrificing a huge amount of
time. You might as well be using rational arithmetic, or the kind of
arithmetic that Collins once proposed, where the denominator is a
power of 2. Makes reducing to lowest terms relatively fast because
the
GCD is trivial. Compare that to boosting the overall precision in
MPFR to "big enough".
If you want to read more about multiplying polynomials, you can read
the (unpublished, unfinished, too-long) paper here:
www.cs.berkeley.edu/~fateman/papers/shortprog.tex
RJF
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