[Maxima] computing expontential as repeated multiplication for small integer exponent
robert.dodier at gmail.com
Mon Jul 30 10:35:41 CDT 2007
On 7/30/07, Raymond Toy <raymond.toy at ericsson.com> wrote:
> Your example of 1.2345678901234567d0^3 just illustrates that expt and
> multiplication are different. As best as I can tell, (expt x 3) from
> cmucl (and sbcl?) is more accurate than repeated multiplication.
At this point, I think it is more important to get various Lisp
implementations to agree, rather than getting maximally-accurate
results for some implementations. I say this after having crunched
more than a few numbers in various contexts.
That said, I would be equally happy with an implementation of
EXPTB which didn't treat small integer exponents as repeated
multiplication. All I want is for different Lisps to get the same result.
> I think rtest8 #69 shouldn't expect exactly the same result. We should
> add a fuzz factor, like in some of the other tests for approximately equal.
Well, this fuzz factor business is problematic. There is already
a fuzz factor; it is 8 * (64 bit float epsilon). Test #69 comes out
with a greater error because it is the result of an iterative algorithm
(namely find_root); a small discrepancy in EXPTB causes find_root
to take a different number of steps for different Lisps.
In general it is difficult to gauge an acceptable discrepancy.
For one of the test cases for lsquares which I was recently working
on, different Lisps agree to only 3 decimal places.
When floating point operations aren't guaranteed to come
out the same, we can't find a suitable fuzz factor without
considering each case, which is tedious.
More information about the Maxima