Boost Users :

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