#16374: better two_squares, three_squares, four_squares for small input
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_work
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):
Replying to [comment:32 leif]:
> While there are (very few) platforms where the math library at least
used to lack some long double functions, I really wouldn't care here.
Yes indeed, I was referring to the math library part of C99.
> > 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.
>
> `(unsigned long)sqrt((double)(N*N)) == N` (for all N < 2^26^, say)?
I meant this, which is true even for much larger values of `N` (as long as
`N` is representable in a `double`). But we actually require
`sqrt((double) n)**2 <= n` for all inputs `n`, which is not true with my
formula.
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Ticket URL: <http://trac.sagemath.org/ticket/16374#comment:33>
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