Le 02/02/2021 à 13:40, Martin Simmons a écrit :
On Mon, 1 Feb 2021 20:12:48 +0100, Pascal Bourguignon said:
Le 01/02/2021 à 19:51, Marco Antoniotti a écrit :
Duh again!
What?
Note that the naive version is not necessarily worse than the "smart"
one, on bignums. On numbers like (+ (expt 2 1000) (expt 2 10)),
logand, lognot and even 1+ will have to process the whole bignum, with a
lot of memory accesses, while the naive loop would access only one word.
Really?
The naive version below repeatedly does (setf n (ash n -1)), which most likely
accesses the whole bignum and allocates a new one each time. A better naive
version would use logbitp instead of evenp and not modify n.
Yes, that's what I meant. Sorry for the confusion.
I think this definition does reasonably well too:
(defun ffs (x)
(1- (integer-length (logand x (- x)))))
I would avoid using log because it may get floating-point overflow for large
values.
Indeed.
Note: if we have access to the implementation of bignum (eg. if we patch
the implementation to provide ffs "natively"), we can optimize even more
by merging the two solutions.
(- x) would process the whole bignum, as would (logand x (- x)), but
after this operation, we have only 0s on the left of the bignum.
Instead, we can process the bignum word by word (starting with the least
significant word), computing:
(+ (lognot (bignum-word-ref bignum i)) carry) -> i+1, new-carry
and (logand (bignum-word-ref bignum i)
(+ (lognot (bignum-word-ref bignum i)) carry))
while we get 0.
Once we get a value ≠ 0, it has a single bit set which we can identify
with integer-length or looping etc (we process a single word here),
and stop processing now, because all the other words will give 0 as result.
--
__Pascal Bourguignon__