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gamma
Gamma function.SYNOPSIS:
double x, y, gamma();
y = gamma(x);
DESCRIPTION:
Returns the gamma function of the argument. The result is correctly signed, and the sign (+1 or -1) is also returned in a global (extern) variable named sgngam. This variable is also filled in by the logarithmic gamma function lgam().
Arguments |x| <= 34 are reduced by recurrence and the function approximated by a rational function of degree 6/7 in the interval (2,3). Large arguments are handled by Stirling's formula. Large negative arguments are made positive using a reflection formula.
ACCURACY:
Relative error:
arithmetic domain # trials peak rms
DEC -34, 34 10000 1.3e-16 2.5e-17
IEEE -170,-33 20000 2.3e-15 3.3e-16
IEEE -33, 33 20000 9.4e-16 2.2e-16
IEEE 33, 171.6 20000 2.3e-15 3.2e-16
Error for arguments outside the test range will be larger owing to error amplification by the exponential function.