EXPRL

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.

Examples

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

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)