ALGAMS

Returns the logarithm of the absolute value of the gamma function and the sign of gamma.

X — Argument for which the logarithm of the absolute value of the gamma function is desired. (Input)

ALGM — Result of the calculation. (Output)

S — Sign of gamma(X). (Output)
If gamma(X) is greater than or equal to zero, S = 1.0. If gamma(X) is less than zero, S = ‑1.0.

Generic: CALL ALGAMS (X, ALGM, S)

Specific: The specific interface names are S_ALGAMS and D_ALGAMS.

Single: CALL ALGAMS (X, ALGM, S)

Double: The double precision function name is DLGAMS.

The function ALGAMS computes ln ∣Γ(x)∣ and the sign of Γ(x). See GAMMA for the definition of Γ(x).

The result overflows if ∣x∣ is too large. The accuracy is worse than half precision if x is too close to a negative integer.

Informational Error

Type	Code	Description
3	2	Result of ALGAMS is accurate to less than one‑half precision because X is too near a negative integer.

In this example, ln ∣Γ(1.85)∣ and the sign of Γ(1.85) are computed and printed.

USE ALGAMS_INT

USE UMACH_INT

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL VALUE, S, X

! Compute

X = 1.85

CALL ALGAMS(X, VALUE, S)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99998) X, VALUE

99998 FORMAT (' Log Abs(Gamma(', F6.3, ')) = ', F6.3)

WRITE (NOUT,99999) X, S

99999 FORMAT (' Sign(Gamma(', F6.3, ')) = ', F6.2)

END

Log Abs(Gamma( 1.850)) = -0.056

Sign(Gamma( 1.850)) = 1.00