erroneous NaN from tanh if complex argument

[John W. Eaton]

On  1-Dec-2007, danny.johnson.vmail at verizon.net wrote:

| --------
| Bug report for Octave 2.9.16 configured for i686-pc-msdosmsvc
| 
| Description:
| -----------
| 
| Octave erroneously declares NaN when encountering exponent underflow in tanh with argument having high real absolute value and any reasonable complex part (answer should simply be +/- 1.0 real).  The size of the complex part does not matter greatly; simply being non-zero causes NaN when abs{real{argument}} > about 355.5 (i.e. when the imaginary part in the result would have an exponent underflow).
| 
| Note: the configuration data below may be confusing--I am running the Windows version from sourceforge.net but I brought up Cygwin in order to run this bug script. Running on AMD Athlon X2, Windows Vista Home Premium, 2GB RAM.
| 
| Repeat-By:
| ---------
| 
| octave.exe:34> tanh(355.5 + .1i)
| ans = 1.0000e+000 + 6.5431e-310i
| 
| octave.exe:35> tanh(355.6 + .1i)
| ans = NaN

Octave calls std::tanh to perform this calculation, so I guess the bug
is actually in the std::complex class, not Octave.

GNU libstdc++ appears to also have this problem, where the definition
in the <complex> header is:

  template<typename _Tp>
    inline complex<_Tp>
    __complex_tanh(const complex<_Tp>& __z)
    { return std::sinh(__z) / std::cosh(__z); }

jwe