[Bug libstdc++/51133] New: Incorrect implementation of std::tr1::hermite()

[dickphd at gmail dot com]

http://gcc.gnu.org/bugzilla/show_bug.cgi?id=51133

             Bug #: 51133
           Summary: Incorrect implementation of std::tr1::hermite()
    Classification: Unclassified
           Product: gcc
           Version: 4.6.1
            Status: UNCONFIRMED
          Severity: normal
          Priority: P3
         Component: libstdc++
        AssignedTo: unassigned@gcc.gnu.org
        ReportedBy: dickphd@gmail.com


Created attachment 25820
  --> http://gcc.gnu.org/bugzilla/attachment.cgi?id=25820
Patch fixing error in poly_hermite.tcc recursion relation

The hermite() function in std::tr1, defined in
libstdc++-v3/include/tr1/poly_hermite.tcc uses a recursion relation which has a
sign error.  The following line:

          __H_n = 2 * (__x * __H_nm1 + (__i - 1) * __H_nm2);

should be changed to:


          __H_n = 2 * (__x * __H_nm1 - (__i - 1) * __H_nm2);

I have attached a patch (generated inside poly_hermite.tcc's folder) which
makes this change.  This patch has been tested with gcc 4.6.1 by checking via
numerical integration that the resultant polynomial has the correct
orthogonality.  As implemented, the result of this numerical integration was
extremely accurate to at least 14 decimal places at up to n=84 for double
precision.