T cyl_bessel_j_imp(T v, T x, const bessel_no_int_tag& t, const Policy& pol)
{
BOOST_MATH_STD_USING
static const char* function = "boost::math::bessel_j<%1%>(%1%,%1%)";
if(x < 0)
{
// better have integer v:
if(floor(v) == v)
{
T r = cyl_bessel_j_imp(v, T(-x), t, pol);
if(iround(v, pol) & 1)
r = -r;
return r;
}
else
return policies::raise_domain_error<T>(
function,
"Got x = %1%, but we need x >= 0", x, pol);
}
if(x == 0)
return (v == 0) ? 1 : (v > 0) ? 0 :
policies::raise_domain_error<T>(
function,
"Got v = %1%, but require v >= 0 or a negative integer: the result would be complex.", v, pol);
if((v >= 0) && ((x < 1) || (v > x * x / 4)))
{
return bessel_j_small_z_series(v, x, pol);
}
T j, y;
bessel_jy(v, x, &j, &y, need_j, pol);
return j;
}
inline T cyl_bessel_j_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& pol)
{
BOOST_MATH_STD_USING // ADL of std names.
int ival = detail::iconv(v, pol);
if((abs(ival) < 200) && (0 == v - ival))
{
return bessel_jn(ival/*iround(v, pol)*/, x, pol);
}
return cyl_bessel_j_imp(v, x, bessel_no_int_tag(), pol);
}
inline T cyl_bessel_j_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& pol)
{
BOOST_MATH_STD_USING // ADL of std names.
int ival = detail::iconv(v, pol);
// If v is an integer, use the integer recursion
// method, both that and Steeds method are O(v):
if((0 == v - ival))
{
return bessel_jn(ival, x, pol);
}
return cyl_bessel_j_imp(v, x, bessel_no_int_tag(), pol);
}
inline T cyl_bessel_j_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& pol)
{
BOOST_MATH_STD_USING // ADL of std names.
typedef typename bessel_asymptotic_tag<T, Policy>::type tag_type;
if((fabs(v) < 200) && (floor(v) == v))
{
if(fabs(x) > asymptotic_bessel_j_limit<T>(v, tag_type()))
return asymptotic_bessel_j_large_x_2(v, x);
else
return bessel_jn(iround(v, pol), x, pol);
}
return cyl_bessel_j_imp(v, x, bessel_no_int_tag(), pol);
}
T cyl_bessel_j_imp(T v, T x, const bessel_no_int_tag& t, const Policy& pol)
{
BOOST_MATH_STD_USING
static const char* function = "boost::math::bessel_j<%1%>(%1%,%1%)";
if(x < 0)
{
// better have integer v:
if(floor(v) == v)
{
T r = cyl_bessel_j_imp(v, T(-x), t, pol);
if(iround(v, pol) & 1)
r = -r;
return r;
}
else
return policies::raise_domain_error<T>(
function,
"Got x = %1%, but we need x >= 0", x, pol);
}
if(x == 0)
return (v == 0) ? 1 : (v > 0) ? 0 :
policies::raise_domain_error<T>(
function,
"Got v = %1%, but require v >= 0 or a negative integer: the result would be complex.", v, pol);
if((v >= 0) && ((x < 1) || (v > x * x / 4) || (x < 5)))
{
//
// This series will actually converge rapidly for all small
// x - say up to x < 20 - but the first few terms are large
// and divergent which leads to large errors :-(
//
return bessel_j_small_z_series(v, x, pol);
}
T j, y;
bessel_jy(v, x, &j, &y, need_j, pol);
return j;
}
T cyl_bessel_j_imp(T v, T x, const bessel_no_int_tag& t, const Policy& pol)
{
BOOST_MATH_STD_USING
static const char* function = "boost::math::bessel_j<%1%>(%1%,%1%)";
if(x < 0)
{
// better have integer v:
if(floor(v) == v)
{
T r = cyl_bessel_j_imp(v, T(-x), t, pol);
if(iround(v, pol) & 1)
r = -r;
return r;
}
else
return policies::raise_domain_error<T>(
function,
"Got x = %1%, but we need x >= 0", x, pol);
}
T j, y;
bessel_jy(v, x, &j, &y, need_j, pol);
return j;
}