This function evaluates the factorial of the argument.

Function Return Value

FAC — Function value.   (Output)
See Comment 1.

Required Arguments

N — Argument for which the factorial is desired.   (Input)

FORTRAN 90 Interface

Generic:                              FAC (N)

Specific:                             The specific interface names are S_FAC and D_FAC.

FORTRAN 77 Interface

Single:                                FAC (N)

Double:                              The double precision function name is DFAC.

Description

The factorial is computed using the relation n! = G(n + 1). The function G(x) is defined in GAMMA. The argument n must be greater than or equal to zero, and it must not be so large that n! overflows. Approximately, n! overflows when nne−n overflows.

Comments

If the generic version of this function is used, the immediate result must be stored in a variable before use in an expression. For example:

X = FAC(6)
Y = SQRT(X)

must be used rather than

Y = SQRT(FAC(6)).

If this is too much of a restriction on the programmer, then the specific name can be used without this restriction.

To evaluate the factorial for nonintegral values of the argument, the gamma function should be used. For large values of the argument, the log gamma function should be used.

Example

In this example, 6! is computed and printed.

 

      USE FAC_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    N, NOUT

      REAL       VALUE

!                                 Compute

      N     = 6

      VALUE = FAC(N)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) N, VALUE

99999 FORMAT (' FAC(', I1, ') = ', F6.2)

      END

Output

 

FAC(6) = 720.00

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