#16374: better two_squares, three_squares, four_squares for small input
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_review
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 | 352e255834a35c951f8bf22a6161df8cef56e51a
Dependencies: | Stopgaps:
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Changes (by vdelecroix):
* status: needs_work => needs_review
Comment:
Hi,
The file is now `sum_of_squares.pyx`.
I changed the `unsigned int` to `unsigned long` as Jeroen suggested. The
loss in terms of timing seems to be around 1% (see below). Nevertheless,
the function makes no sense for very large input as it is much faster to
called the Python function from `arith` (see also below).
For the rounding issue with `sqrt`, it uses now `<unsigned long>
sqrt(<double> n)` and there is an exhaustive test in the doc of the
function `two_squares_pyx`.
unsigned int
{{{
sage: from sage.rings.sum_of_squares import four_squares_pyx
sage: timeit("for n in xrange(10000,50000): x = four_squares_pyx(n)")
25 loops, best of 3: 11 ms per loop
}}}
unsigned long
{{{
sage: from sage.rings.sum_of_squares import four_squares_pyx
sage: timeit("for n in xrange(10000,50000): x = four_squares_pyx(n)")
25 loops, best of 3: 11.3 ms per loop
}}}
Very large input
{{{
sage: from sage.rings.sum_of_squares import two_squares_pyx
sage: %timeit two_squares_pyx(2**51+21)
10 loops, best of 3: 88.1 ms per loop
sage: %timeit two_squares(2**51+21)
1000 loops, best of 3: 1.04 ms per loop
}}}
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16374#comment:19>
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