#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 | 17883e34f96f7f78f35f56bad527dcbaa728169d
Dependencies: | Stopgaps:
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Comment (by jdemeyer):
I think the `long double` is overkill and would revert to using `sqrt()`.
1. It decreases portability (`sqrtl()` is C99 so at least you need to
compile in C99 mode and not all systems have this function).
2. You will never want to call `two_squares` in this range (`2^53`)
anyway.
3. For `three_squares` and `four_squares`, there are many solutions, so it
doesn't matter if the square root is off by 1.
4. I have to check the details, but I think that `<unsigned long>
sqrt(<double> n)` is actually sufficiently precise that it computes the
exact integer square root.
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Ticket URL: <http://trac.sagemath.org/ticket/16374#comment:29>
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