Re: [Boost-users] Boost_1_54_0: boost::math::sph_bessel(n, x) crash at x=0 n>0

Subject: Re: [Boost-users] Boost_1_54_0: boost::math::sph_bessel(n, x) crash at x=0 n>0
From: John Maddock (john_at_[hidden])
Date: 2013-10-17 14:20:18

> I'am running Boost 1_54_0 on Scientific Linux  slc-6.1,  gcc-4.4.5, 64 
> bits machine.
>
> I face a problem with computation of spherical bessel function, although 
> the problem seems well known here
> is a test program

Not well known to me - there are a number of fixes to the (cyclic) Bessel 
functions due out with 1.55, but I'm afraid this isn't one of them.  BTW the 
issue effects all x < 1, not just x == 0.

Here's the patch I'm about to commit to SVN:

Index: boost/math/special_functions/bessel.hpp
===================================================================
--- boost/math/special_functions/bessel.hpp (revision 86329)
+++ boost/math/special_functions/bessel.hpp (working copy)
@@ -48,7 +48,16 @@
    {
       BOOST_MATH_STD_USING
       mult = x / 2;
-      term = pow(mult, T(v)) / boost::math::tgamma(v+1+T(0.5f), Policy());
+      if(v + 3 > max_factorial<T>::value)
+      {
+         // term = v * log(mult) - boost::math::lgamma(v+1+T(0.5f), 
Policy());
+         // term = exp(term);
+         // Denominator increases faster than numerator each time v 
increases by one,
+         // so if tgamma would overflow then the result is neceesarily 
zero.
+         term = 0;
+      }
+      else
+         term = pow(mult, T(v)) / boost::math::tgamma(v+1+T(0.5f), 
Policy());
       mult *= -mult;
    }
    T operator()()
@@ -142,6 +151,11 @@
    if(n == 0)
       return boost::math::sinc_pi(x, pol);
    //
+   // Special case for x == 0:
+   //
+   if(x == 0)
+      return 0;
+   //
    // When x is small we may end up with 0/0, use series evaluation
    // instead, especially as it converges rapidly:
    //
Index: libs/math/test/test_bessel_j.hpp
===================================================================
--- libs/math/test/test_bessel_j.hpp (revision 86329)
+++ libs/math/test/test_bessel_j.hpp (working copy)
@@ -262,6 +262,13 @@
     do_test_sph_bessel_j<T>(sph_bessel_data, name, "Bessel j: Random 
Data");

     //
+    // Some special cases:
+    //
+    BOOST_CHECK_EQUAL(boost::math::sph_bessel(0, T(0)), T(1));
+    BOOST_CHECK_EQUAL(boost::math::sph_bessel(1, T(0)), T(0));
+    BOOST_CHECK_EQUAL(boost::math::sph_bessel(100000, T(0)), T(0));
+
+    //
     // Special cases that are errors:
     //
     BOOST_CHECK_THROW(boost::math::cyl_bessel_j(T(-2.5), T(0)), 
std::domain_error);

HTH, John.