TANH
This function extends FORTRAN’s generic function TANH to evaluate the complex hyperbolic tangent.
Function Return Value
TANH — Complex function value. (Output)
Required Arguments
Z — Complex number representing the angle in radians for which the hyperbolic tangent is desired. (Input)
FORTRAN 90 Interface
Generic: TANH (Z)
Specific: The specific interface names are CTANH and ZTANH.
FORTRAN 77 Interface
Complex: CTANH (Z)
Double complex:  The double complex function name is ZTANH.
Description
Let z = x + iy. If cosh z2 is very small, that is, if y mod π is very close to π/2 or 3π/2 and if x is small, then tanh z is nearly singular; a fatal error condition is reported. If cosh z2 is somewhat larger but still small, then the result will be less accurate than half precision. When 2y (z = x + iy) is so large that sin 2y cannot be evaluated accurately to even zero precision, the following situation results. If x < 3/2, then TANH cannot be evaluated accurately to better than one significant figure. If 3/2 ≤∣y < –1/2 ln (ɛ/2), then TANH can be evaluated by ignoring the imaginary part of the argument; however, the answer will be less accurate than half precision. Here, ɛ = AMACH(4) is the machine precision.
Example
In this example, tanh(1 + i) is computed and printed.
 
USE TANH_INT
USE UMACH_INT
 
IMPLICIT NONE
! Declare variables
INTEGER NOUT
COMPLEX VALUE, Z
! Compute
Z = (1.0, 1.0)
VALUE = TANH(Z)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) Z, VALUE
99999 FORMAT (' TANH((', F6.3, ',', F6.3, ')) = (',&
F6.3, ',', F6.3, ')')
END
Output
 
TANH(( 1.000, 1.000)) = ( 1.084, 0.272)