[Bug-gsl] [bug #39292] possible error in gsl_sf_coulomb_wave_FG_e

[Patrick Alken]

URL:
  <http://savannah.gnu.org/bugs/?39292>

                 Summary: possible error in gsl_sf_coulomb_wave_FG_e
                 Project: GNU Scientific Library
            Submitted by: psa
            Submitted on: Wed 19 Jun 2013 04:37:38 PM GMT
                Category: Runtime error
                Severity: 3 - Normal
        Operating System: 
                  Status: None
             Assigned to: None
             Open/Closed: Open
                 Release: 
         Discussion Lock: Any

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Details:

>From Alexey A. Illarionov:

Accidentally found a bug in specfun/coulomb.c . Trivial error in
solution of quadratic equation. None of the current test cases are
influenced by this bug since the value of C (actually N) determines
only the condition of applicability of "continued fraction+recursion"
algorithm.

=== modified file 'specfunc/coulomb.c'
- --- specfunc/coulomb.c        2007-07-02 18:34:24 +0000
+++ specfunc/coulomb.c  2012-10-26 04:27:18 +0000
@@ -1121,7 +1121,7 @@
      *           we must go at least as low as lam_G
      */
     const double SMALL = GSL_SQRT_DBL_EPSILON;
- -    const double C = sqrt(1.0 + 4.0*x*(x-2.0*eta));
+    const double C = 0.5 * sqrt(1.0 + 4.0*x*(x-2.0*eta));
     const int N = ceil(lam_F - C + 0.5);
     const double lam_0   = lam_F - GSL_MAX(N, 0);
     const double lam_min = GSL_MIN(lam_0, lam_G);




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