[Boost-bugs] [Boost C++ Libraries] #12191: Unable to produce proper multiprecision output from sph_neumann() function

Subject: [Boost-bugs] [Boost C++ Libraries] #12191: Unable to produce proper multiprecision output from sph_neumann() function
From: Boost C++ Libraries (noreply_at_[hidden])
Date: 2016-05-11 22:24:32

#12191: Unable to produce proper multiprecision output from sph_neumann() function
---------------------------+------------------------------
 Reporter:  James_Booth@…  |       Type:  Bugs
   Status:  new            |  Milestone:  To Be Determined
Component:  None           |    Version:  Boost 1.61.0
 Severity:  Problem        |   Keywords:
---------------------------+------------------------------
 I am trying to use the boost c++ libraries to compute a multiprecision
 value for the spherical bessel functions and spherical neumann functions.
 To test the boost package I am using the relationships:

 pi/6*Spherical_Bessel(0,pi/6) = sin(pi/6) = 0.5

 -pi/6*Spherical_Neumann(0,pi/6) = cos(pi/6) = sqrt(3)/2 = 0.866....
 My test code is:

     #include <boost/multiprecision/mpfr.hpp>

     #include <boost/math/special_functions/bessel.hpp>

     #include <boost/math/constants/constants.hpp>

     #include <boost/multiprecision/number.hpp>

     #define PRECISION 40 // Can be set to any number desired.

     using namespace std;
     using namespace boost::multiprecision;
     using namespace boost;

     mpfr_float::default_precision(PRECISION);

     mpfr_float z, my_pi;

     my_pi =
 boost::multiprecision::atan(mpfr_float("1.0"))*mpfr_float("4.0");     //
 Define pi as a multiprecision value to precision = PRECISION.

     z = my_pi/mpfr_float("6.0");


     cout << z*mpfr_float(boost::math::sph_bessel(0,z)) << endl;

     cout << mpfr_float("-1.0")*z*mpfr_float(boost::math::sph_neumann(0,z))
 << endl;

 ========================================================================

     The value of my_pi agrees with the value computed by Wolfram (to at
 least 100 decimal places).
     The value of z also agrees with the value from Wolfram.
     The output for the z*sph_bessel(0,z) function is correct:
 0.5000000000....
     The output for the -z*sph_neumann(0,z) function is incorrect:
 0.86602540378443864***30***... instead of 0.86602540378443864***67***....
 Which looks like the answer is not multiprecision but a float.

 Can you please help with this bug?
 Thanks.

-- 
Ticket URL: <https://svn.boost.org/trac/boost/ticket/12191>
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