c/numeric/complex/csinh

@1-3@ Computes the complex hyperbolic sine of. @4@ Type-generic macro: If has type,  is called. if has type,  is called, if  has type ,  is called. If is real or integer, then the macro invokes the corresponding real function. If is imaginary, then the macro invokes the corresponding real version of the function sin, implementing the formula $sinh(iy) = i sin(y)$, and the return type is imaginary.

Return value
If no errors occur, complex hyperbolic sine of is returned

Error handling and special values
Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,
 * If is, the result is
 * If is, the result is  (the sign of the real part is unspecified) and fe_invalid is raised
 * If is, the result is
 * If is  (for any positive finite x), the result is  and fe_invalid is raised
 * If is  (for any positive finite x), the result is  and fe_invalid may be raised
 * If is, the result is
 * If is  (for any positive finite y), the result is
 * If is, the result is  (the sign of the real part is  unspecified) and fe_invalid is raised
 * If is, the result is  (the sign of the real part is  unspecified)
 * If is, the result is
 * If is  (for any finite nonzero y), the result is  and fe_invalid may be raised
 * If is, the result is
 * If is  (for any finite nonzero y), the result is  and fe_invalid may be raised
 * If is, the result is

where $cis(y)$ is $cos(y) + i sin(y)$