URL: <https://savannah.gnu.org/bugs/?67774>
Summary: Feature: arctan integral is also defined for
negative inputs
Group: GNU Scientific Library
Submitter: fermelelundi
Submitted: Fri 05 Dec 2025 11:36:25 AM UTC
Category: Accuracy problem
Severity: 3 - Normal
Priority: 5 - Normal
Operating System:
Status: None
Assigned to: None
Open/Closed: Open
Discussion Lock: Unlocked
Release: 2.8
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Follow-up Comments:
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Date: Fri 05 Dec 2025 11:36:25 AM UTC By: Fermé le Lundi <fermelelundi>
The arctangent integral is well defined for x < 0:
AtanInt(x) = \int_0^x dt \arctan(t)/t
and the following simple change to the function gsl_sf_atanint_e in
specfunc/atanint.c makes it well behaved, from:
result->err = x * result_c.err;
to:
result->err = ax * result_c.err;
Test cases for file specfunc/test_sf.c:
TEST_SF(s, gsl_sf_atanint_e, (-1.0, &r), -0.91596559417721901505, TEST_TOL0,
GSL_SUCCESS);
TEST_SF(s, gsl_sf_atanint_e, (-2.0, &r), -1.57601540344632342236, TEST_TOL0,
GSL_SUCCESS);
TEST_SF(s, gsl_sf_atanint_e, (0.0, &r), 0.0, TEST_TOL0, GSL_SUCCESS);
The latter special case is added to the test cases.
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