[Bug fortran/33197] Fortran 2008: math functions

["burnus at gcc dot gnu dot org" <gcc-bugzilla at gcc dot gnu dot org>]

------- Comment #22 from burnus at gcc dot gnu dot org  2009-07-10 11:46 -------
For z a complex number: Patch for tan(z), sinh(z), cosh(z), tanh(z) - see at
http://gcc.gnu.org/ml/fortran/2009-07/msg00071.html

Remark: atan(z), asin(z) and acos(z) are also missing besides a{sin,cos,tan}h.

Additionally, I think the description for ATAN2 in the gfortran manual is
wrong:
  "ATAN2(Y, X) computes the arctangent of the complex number X + i Y"
while the standard has:
  "The result has a value equal ... to the principal value of the argument of
the complex number (X, Y), expressed in radians."
That is: atan2(y, x) = Pr arg(x+iy) = Arg(x+iy) =/= ATAN(X+i Y).

 * * *

Fallback implementations via complex logarithm: I have no idea about NaN, Inf
etc. nor about the precision (I do not know how precise the fall back needs to
be), but Abramowitz & Stegun has the following:

a{tan,sin,cos}: http://www.iopb.res.in/~somen/abramowitz_and_stegun/page_80.htm
and http://en.wikipedia.org/wiki/Arctangent#Logarithmic_forms

a{sin,tan,cos}h:
http://www.iopb.res.in/~somen/abramowitz_and_stegun/page_87.htm  However, the
equations might need to be slightly for complex arguments as written at
http://en.wikipedia.org/wiki/Inverse_hyperbolic_function#Logarithmic_representation


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http://gcc.gnu.org/bugzilla/show_bug.cgi?id=33197