ctanhf, ctanh, ctanhl
Defined in header <complex.h>


(1)  (since C99)  
(2)  (since C99)  
(3)  (since C99)  
Defined in header <tgmath.h>


#define tanh( z ) 
(4)  (since C99) 
13) Computes the complex hyperbolic tangent of
z
.4) Typegeneric macro: If
z
has type long double complex, ctanhl
is called. if z
has type double complex, ctanh
is called, if z
has type float complex, ctanhf
is called. If z
is real or integer, then the macro invokes the corresponding real function (tanhf, tanh, tanhl). If z
is imaginary, then the macro invokes the corresponding real version of the function tan, implementing the formula tanh(iy) = i tan(y), and the return type is imaginary.Parameters
z    complex argument 
Return value
If no errors occur, complex hyperbolic tangent of z
is returned
Error handling and special values
Errors are reported consistent with math_errhandling
If the implementation supports IEEE floatingpoint arithmetic,
 ctanh(conj(z)) == conj(ctanh(z))
 ctanh(z) == ctanh(z)
 If
z
is+0+0i
, the result is+0+0i
 If
z
isx+∞i
(for any^{[1]} finite x), the result isNaN+NaNi
and FE_INVALID is raised  If
z
isx+NaN
(for any^{[2]} finite x), the result isNaN+NaNi
and FE_INVALID may be raised  If
z
is+∞+yi
(for any finite positive y), the result is1+0i
 If
z
is+∞+∞i
, the result is1±0i
(the sign of the imaginary part is unspecified)  If
z
is+∞+NaNi
, the result is1±0i
(the sign of the imaginary part is unspecified)  If
z
isNaN+0i
, the result isNaN+0i
 If
z
isNaN+yi
(for any nonzero y), the result isNaN+NaNi
and FE_INVALID may be raised  If
z
isNaN+NaNi
, the result isNaN+NaNi
 ↑ per DR471, this only holds for nonzero x. If
z
is0+∞i
, the result should be0+NaNi
 ↑ per DR471, this only holds for nonzero x. If
z
is0+NaNi
, the result should be0+NaNi
Notes
Mathematical definition of hyperbolic tangent is tanh z =ez ez 
ez +ez 
Hyperbolic tangent is an analytical function on the complex plane and has no branch cuts. It is periodic with respect to the imaginary component, with period πi, and has poles of the first order along the imaginary line, at coordinates (0, π(1/2 + n)). However no common floatingpoint representation is able to represent π/2 exactly, thus there is no value of the argument for which a pole error occurs.
Example
Run this code
#include <stdio.h> #include <math.h> #include <complex.h> int main(void) { double complex z = ctanh(1); // behaves like real tanh along the real line printf("tanh(1+0i) = %f%+fi (tanh(1)=%f)\n", creal(z), cimag(z), tanh(1)); double complex z2 = ctanh(I); // behaves like tangent along the imaginary line printf("tanh(0+1i) = %f%+fi ( tan(1)=%f)\n", creal(z2), cimag(z2), tan(1)); }
Output:
tanh(1+0i) = 0.761594+0.000000i (tanh(1)=0.761594) tanh(0+1i) = 0.000000+1.557408i ( tan(1)=1.557408)
References
 C11 standard (ISO/IEC 9899:2011):
 7.3.6.6 The ctanh functions (p: 194)
 7.25 Typegeneric math <tgmath.h> (p: 373375)
 G.6.2.6 The ctanh functions (p: 542)
 G.7 Typegeneric math <tgmath.h> (p: 545)
 C99 standard (ISO/IEC 9899:1999):
 7.3.6.6 The ctanh functions (p: 176)
 7.22 Typegeneric math <tgmath.h> (p: 335337)
 G.6.2.6 The ctanh functions (p: 477)
 G.7 Typegeneric math <tgmath.h> (p: 480)
See also
(C99)(C99)(C99) 
computes the complex hyperbolic sine (function) 
(C99)(C99)(C99) 
computes the complex hyperbolic cosine (function) 
(C99)(C99)(C99) 
computes the complex arc hyperbolic tangent (function) 
(C99)(C99) 
computes hyperbolic tangent (function) 