From cppreference.com
template<classT>complex<T>tanh(constcomplex<T>&z);(since C++11)Computes complex hyperbolic tangent of a complex value z.
Parameters
z - complex value Return value
If no errors occur, complex hyperbolic tangent of z is returned.
Error handling and special values
Errors are reported consistent with
.
If the implementation supports IEEE floating-point arithmetic,
std::tanh(std::conj(z))==std::conj(std::tanh(z)).
std::tanh(-z)==-std::tanh(z).
If z is (+0,+0), the result is (+0,+0).
If z is (x,+∞) (for any
finite x), the result is (NaN,NaN) and
is raised.
If z is (x,NaN) (for any
finite x), the result is (NaN,NaN) and
may be raised.
If z is (+∞,y) (for any finite positive y), the result is (1,+0).
If z is (+∞,+∞), the result is (1,±0) (the sign of the imaginary part is unspecified).
If z is (+∞,NaN), the result is (1,±0) (the sign of the imaginary part is unspecified).
If z is (NaN,+0), the result is (NaN,+0).
If z is (NaN,y) (for any non-zero y), the result is (NaN,NaN) and
may be raised.
If z is (NaN,NaN), the result is (NaN,NaN).
per
, this only holds for non-zero x. If z is (0,∞), the result should be (0,NaN).
per
, this only holds for non-zero x. If z is (0,NaN), the result should be (0,NaN).
Notes
Mathematical definition of hyperbolic tangent is
tanh z = ez
-e-z
ez
+e-z
.
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 floating-point 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<cmath>#include<complex>#include<iostream>intmain(){std::cout<<std::fixed;std::complex<double>z(1.0,0.0);// behaves like real tanh along the real linestd::cout<<"tanh"<<z<<" = "<<std::tanh(z)<<" (tanh(1) = "<<std::tanh(1)<<")\n";std::complex<double>z2(0.0,1.0);// behaves like tangent along the imaginary linestd::cout<<"tanh"<<z2<<" = "<<std::tanh(z2)<<" ( tan(1) = "<<std::tan(1)<<")\n";}Output:
tanh(1.000000,0.000000) = (0.761594,0.000000) (tanh(1) = 0.761594) tanh(0.000000,1.000000) = (0.000000,1.557408) ( tan(1) = 1.557408) See also
computes hyperbolic sine of a complex number (sinh(z))
(function template)
computes hyperbolic cosine of a complex number (cosh(z))
(function template)
(C++11)
computes area hyperbolic tangent of a complex number (artanh(z))
(function template)
(C++11)(C++11)
computes hyperbolic tangent (tanh(x))
(function)
applies the function
to each element of valarray
(function template)
for ctanh