#11767: elliptic_logarithm of high precision points often hangs forever
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Reporter: was | Owner: cremona
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.7.2
Component: elliptic curves | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by zimmerma):
I have added a 2nd patch (to be applied after the first one) which solves
the typo, and
modifies the termination condition.
As far as I understand, the termination is when the (complex) variable
{{{r}}} becomes 1.
We compute the complex norm of {{{r}}}, subtract one from it, and compare
to {{{eps}}}
which is {{{2^(-prec2)}}}.
If {{{r}}} is near one, typically {{{r.abs()}}} will be 1, or one of the
floating-point numbers
near from 1, which are {{{1-2^(-prec2)}}} and {{{1+2^(1-prec2)}}}. The
subtraction of 1 is exact,
and the only case where the comparison {{{r.abs()-1 < eps}}} can be true
is when {{{r=1}}}.
What I've done is that I've changed the termination condition to also
check whether the
relative difference {{{r.abs()-1}}} does not change from one step to the
next one.
Since {{{r.abs()-1}}} converges to one, this should catch cases where it
stays at say
{{{1-2^(-prec2)}}} due to rounding errors. However it will not catch cases
where it oscillates
between two different values near from 1.
Paul
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11767#comment:7>
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