Tanh<complex> Returns Incorrect Value

["Thomas D. Dean" <tomdean at speakeasy dot org>]

tanh(complex) returns incorrect value.  See the code at the bottom.

limit(tanh(n*(1+I)),n=infinity) is 1.

Build the application with: g++ trig.cc -o trig

>g++ --version
g++ (GCC) 4.4.1

>./trig 5678 ## returns correct value of tanh(5678 + 5678I)
libc version 2.10.1
arg       (5678,5678)
sinh(arg) (-1.74513e+2465,-3.81804e+2465)
cosh(arg) (-1.74513e+2465,-3.81804e+2465)
s/c       (1,-0)
tanh(arg) (1,2.14543e-4932) 
>./trig 5679 ## returns incorrect value.
libc version 2.10.1
arg       (5679,5679)
sinh(arg) (6.17015e+2465,-9.59925e+2465)
cosh(arg) (6.17015e+2465,-9.59925e+2465)
s/c       (1,-0)
tanh(arg) (nan,-0)
Note:  s/c is still correct, but, tanh is not.

As arg increases, s/c is incorrect and tanh remains incorrect.

>more trig.cc
// trig.cc - test hyperbolic trig functions
//
// 20100417 tomdean - initial version
//
// copyright 2010 Thomas D. Dean tomdean@speakeasy.org
// This code is GPL
#include <iostream>
#include <complex>
#include <gnu/libc-version.h>
#include <stdlib.h> // atol
using namespace std;
int main(int argc, char **argv) {
  long mult;
  if (argc == 2) {
        mult = atol(argv[1]);
  } else {
        mult = 50000L;
  }
  complex<long double> arg(1,1);
  arg *= mult;
  complex<long double> s,c,r,t;
  s=sinh(arg);
  c=cosh(arg);
  r=s/c;
  t=tanh(arg); 
  cout << "libc version " << gnu_get_libc_version() << endl;
  cout << "arg       " << arg << endl;
  cout << "sinh(arg) " << s << endl;
  cout << "cosh(arg) " << c << endl;
  cout << "s/c       " << r << endl;
  cout << "tanh(arg) " << t << endl;
  return 0;
}