R PNX(bessel_i0)(R x)
{
/* forward to GSL implementation */
return (R)gsl_sf_bessel_I0((double)x);
if (x < 0)
{
/* even function */
x = -x;
}
if (x < PNFFT_EPSILON)
return K(1.0);
if (x <= K(15.0))
{
/* x in (0, 15] */
// const R y = x*x/K(112.5) - K(1.0); /* use this if the Chebyshev approximation was computed on [0,225] */
const R y = x * x; /* use this if the Chebyshev approximation was computed on [-1,1] */
return evaluate_chebyshev(N1, P1, y) / evaluate_chebyshev(M1, Q1, y);
}
else
{
/* x in (15, \infty) */
const R y = (K(30.0) - x) / x; /* use this if the Chebyshev approximation was computed on [0,15] */
// const R y = K(1.0) / x; /* use this if the Chebyshev approximation was computed on [-1,1] */
return (pnfft_exp(x) / pnfft_sqrt(x)) * (evaluate_chebyshev(N2, P2, y) /
evaluate_chebyshev(M2, Q2, y));
}
}
fcs_float ifcs_p2nfft_gamma_ln(
fcs_float x
)
{
/* Use a Chebyshev approximation on the interval [0,1] to
* avoid numerical difficulties due to the opposite singularities
* of Gamma[0,x] and Log[x]. */
if(x<1)
return evaluate_chebyshev(N, P, x);
return
}
