This function evaluates the exponential function factored from first order, (EXP(X) – 1.0)/X.

Function Return Value

EXPRL — Function value.   (Output)

Required Arguments

X — Argument for which the function value is desired.   (Input)

FORTRAN 90 Interface

Generic:                              EXPRL (X)

Specific:                             The specific interface names are S_EXPRL, D_EXPRL, and C_EXPRL.

FORTRAN 77 Interface

Single:                                EXPRL (X)

Double:                              The double precision function name is DEXPRL.

Complex:                            The complex name is CEXPRL.

Description

The function EXPRL(X) evaluates (ex – 1)/x. It will overflow if ex overflows.  For complex arguments, z, the argument z must not be so close to a multiple of 2 πi that substantial significance is lost due to cancellation. Also, the result must not overflow and |ℑz| must not be so large that the trigonometric functions are inaccurate.

Example 1

In this example, EXPRL(0.184) is computed and printed.

 

      USE EXPRL_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    NOUT

      REAL       VALUE, X

!                                 Compute

      X     = 0.184

      VALUE = EXPRL(X)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' EXPRL(', F6.3, ') = ', F6.3)

      END

Output

 

EXPRL( 0.184) =  1.098

Additional Example

Example 2

In this example, EXPRL(0.0076i) is computed and printed.

 

      USE EXPRL_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    NOUT

      COMPLEX    VALUE, Z

!                                 Compute

      Z     = (0.0, 0.0076)

      VALUE = EXPRL(Z)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) Z, VALUE

99999 FORMAT (' EXPRL((', F7.4, ',', F7.4, ')) = (', &

          F6.3, ',' F6.3, ')')

      END

Output

 

EXPRL(( 0.0000, 0.0076)) = ( 1.000, 0.004)

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