#16374: better two_squares, three_squares, four_squares for small input
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.3
Component: number theory | Resolution:
Keywords: | Merged in:
Authors: Vincent Delecroix | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vdelecroix/16374 | f1354e68519feecd5de198c10a532b89ee938a7b
Dependencies: #16308 | Stopgaps:
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Comment (by vdelecroix):
Hi Nathann,
Thanks for reading it.
> I added a commit in u/ncohen/16374 which contains some tests and
comments.
Great. I also have something important to modify in `three_squares_pyx`
and `four_squares_pyx`. It is '''much''' faster to first remove a huge
square and then try to decompose the rest into a sum of less squares. The
result is not the smallest for lexicographical order but the timings are
x4 better.
It seems that you like C function declaration of the form {{{int f(int
res[3])}}}. It makes the specifications clearer but at compilation the
results are strictly equivalent.
> I have two questions to ask though :
>
> - Why {{{ii <= n/2}}} and not {{{ii<=jj}}} ?
Right.
> - Why a "while" instead of a "if" in the following code ?
> {{{
> j = (<unsigned int> sqrt(<double> n)) + 1 # (rounding is toward
zero)
> while j*j > n:
> j -= 1
> }}}
I am not sure of the specification (if any) of `sqrt` which deals with
double... I will try to improve it.
> Besides, there is a way to avoid many multiplications, and **perhaps**
it can improve the code a bit (no idea, profiling is the only way `:-P`)
I thought about it. I am not sure that {{{ii += 2*i + 1}}} is cheaper than
{{{ii = i*i}}} ? Will have a look.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16374#comment:5>
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