| Pré. | Proc. |
rgamma
Reciprocal gamma function.SYNOPSIS:
double x, y, rgamma();
y = rgamma(x);
DESCRIPTION:
Returns one divided by the gamma function of the argument.
The function is approximated by a Chebyshev expansion in the interval [0,1]. Range reduction is by recurrence for arguments between -34.034 and +34.84425627277176174. 1/MAXNUM is returned for positive arguments outside this range. For arguments less than -34.034 the cosecant reflection formula is applied; logarithms are employed to avoid unnecessary overflow.
The reciprocal gamma function has no singularities, but overflow and underflow could occur for large arguments. These conditions return either MAXNUM or 1/MAXNUM with the appropriate sign.
ACCURACY:
Relative error:
arithmetic domain # trials peak rms
DEC -30,+30 4000 1.2e-16 1.8e-17
IEEE -30,+30 30000 1.1e-15 2.0e-16
For arguments less than -34.034 the peak error is in the order of 5e-15 (DEC), excepting overflow or underflow.