/*!
* Modified Bessel function of the first kind
* This function wraps the following order-specific functions
*/
double besselI(size_t order, double x)
{
switch (order)
{
case 0:
return besselIOrderZero(x);
case 1:
return besselIOrderOne(x);
default:
return besselIOrderN(order, x);
}
}
/*!
* Modified Bessel function of the first kind, order n > 1
*/
double besselIOrderN(size_t order, double x)
{
const double ACC = 200;
const int IEXP = std::numeric_limits<double>::max_exponent / 2;
int k;
double bm, dum;
if (x * x <= 8.0 * std::numeric_limits<double>::min())
{
return 0;
}
double tox = 2.0 / std::abs(x);
double bip = 0;
double ans = 0;
double bi = 1.0;
//Downward recurrence from even n
for (size_t jj = 2 * (order + int(std::sqrt(ACC * order))); jj > 0; jj--)
{
double bim = bip + (jj * tox * bi);
bip = bi;
bi = bim;
dum = std::frexp(bi, &k);
//Renormalize to prevent overflow
if (k > IEXP)
{
ans = std::ldexp(ans, -IEXP);
bi = std::ldexp(bi, -IEXP);
bip = std::ldexp(bip, -IEXP);
}
if (jj == order)
{
ans = bip;
}
}
//Normalize
ans *= besselIOrderZero(x) / bi;
return x < 0 && (order & 1) ? -ans : ans;
}
