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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