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

Required Arguments

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.

FORTRAN 90 Interface

Generic:                              CALL ALGAMS (X, ALGM, S)

Specific:                             The specific interface names are S_ALGAMS and D_ALGAMS.

FORTRAN 77 Interface

Single:                                CALL ALGAMS (X, ALGM, S)

Double:                              The double precision function name is DLGAMS.

Description

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.

Comments

Informational error

Type Code

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

Example

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

Output

 

Log Abs(Gamma( 1.850)) = -0.056

 Sign(Gamma( 1.850)) =   1.00

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