This funcion evaluates the cube root.
Function Return Value
CBRT — Function value. (Output)
Required Arguments
X — Argument for which the cube root is desired. (Input)
FORTRAN 90 Interface
Generic: CBRT (X)
Specific: The specific interface names are S_CBRT, D_CBRT, C_CBRT, and Z_CBRT.
FORTRAN 77 Interface
Single: CBRT (X)
Double: The double precision name is DCBRT.
Complex: The complex precision name is CCBRT.
Double Complex: The double complex precision name is ZCBRT.
Description
The function CBRT(X) evaluates x1/3. All arguments are legal. For complex argument, x, the value of |x| must not overflow.
Comments
For complex arguments, the branch cut for the cube root is taken along the negative real axis. The argument of the result, therefore, is greater than –π/3 and less than or equal to π/3. The other two roots are obtained by rotating the principal root by 3 π/3 and π/3.
Example 1
In this example, the cube root of 3.45 is computed and printed.
USE CBRT_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
REAL VALUE, X
! Compute
X = 3.45
VALUE = CBRT(X)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) X, VALUE
99999 FORMAT (' CBRT(', F6.3, ') = ', F6.3)
END
Output
CBRT( 3.450) = 1.511
Additional Example
Example 2
In this example, the cube root of –3 + 0.0076i is computed and printed.
IMPLICIT NONE
!
Declare variables
INTEGER NOUT
COMPLEX VALUE, Z
! Compute
Z = (-3.0, 0.0076)
VALUE = CBRT(Z)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) Z, VALUE
99999 FORMAT (' CBRT((', F7.4, ',', F7.4, ')) = (', &
F6.3, ',', F6.3, ')')
END
Output
CBRT((-3.0000, 0.0076)) = ( 0.722, 1.248)
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