This function extends FORTRAN’s generic function TANH to evaluate the complex hyperbolic tangent.

Let z = x + iy. If ∣cosh z∣2 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 z∣2 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.

In this example, tanh(1 + i) is computed and printed.