#15299: Incorrect results for analytic Sha due to low precision
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Reporter: jdemeyer | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.13
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by jdemeyer):
Corrected the error computation for `at1()`. I believe this is rigorous
now:
{{{
for n in xrange(1,k+1):
term = (zpow * an[n])/n
zpow *= z
L += term
# 8n+1 is the relative error in half-ulps to compute term.
# For addition, multiplication, division, sqrt, this is
# bounded by the number of operations. exp(x) multiplies the
# relative error by abs(x) and adds 1 half-ulp. The relative
# error for -2*pi/sqrtN is 3 half-ulps. Assuming that
# 2*pi/sqrtN <= 2, the relative error for z is 7 half-ulps.
# This implies a relative error of 8n-1 half-ulps for zpow.
# Adding 2 for the computation of term gives:
error += term.ulp()*(8*n+1) + L.ulp()
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/15299#comment:10>
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