#12557: RDF(1e-17).log() gives NaN
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Reporter: mariah | Owner: AlexGhitza
Type: defect | Status: new
Priority: minor | Milestone: sage-5.0
Component: basic arithmetic | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by dsm):
The problem is this branch:
{{{
if self._value < 2:
if self._value == 0:
return RDF(-1)/RDF(0)
if self._value < 0:
return RDF(0)/RDF(0)
sig_on()
a = self._new_c(gsl_sf_log_1plusx(self._value - 1) / log_of_base)
sig_off()
return a
}}}
When self._value is small enough, self._value-1 becomes -1 and we get the
log of 0. Frankly, even before this happens we lose precision
unnecessarily:
{{{
sage: [(log(x.n(1000))-RDF(x).log().n()).n(53) for x in [1/10**i for i in
[0..17]]]
[0.000000000000000, 0.000000000000000, -8.88178419700125e-16,
-8.88178419700125e-16,
1.10134124042816e-13, 4.55102622254344e-12, -2.87556645162113e-11,
5.26355847796367e-10,
-5.02475927532942e-9, 2.82819314634253e-8, -8.27403674463767e-8,
-8.27403674463767e-8,
0.0000221219648111060, -0.000310896853829234, 0.000799597430194865,
0.000799597430194865,
-0.104560918227634, NaN]
}}}
Probably the simplest fix is to use the 1+x trick only when the argument
is actually close to 1. Simply changing the condition to
if 0.5 <= self._value < 2:
will change the above results to the less exciting but more useful
{{{
[0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000, 0.000000000000000,
0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000, 0.000000000000000,
0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000, 0.000000000000000,
.000000000000000, 0.000000000000000, 0.000000000000000]
}}}
Any objections? Performance seems similar for values which previously
would have used gsl_sf_log_1plusx but now simply use gsl_sf_log.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12557#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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