Computes complex hyperbolic tangent of a complex valuez.

[edit]Parameters

[edit]Return value

If no errors occur, complex hyperbolic tangent ofz is returned.

[edit]Error handling and special values

Errors are reported consistent withmath_errhandling.

If the implementation supports IEEE floating-point arithmetic,

• std::tanh(std::conj(z))==std::conj(std::tanh(z)).
• std::tanh(-z)==-std::tanh(z).
• Ifz is(+0,+0), the result is(+0,+0).
• Ifz is(x,+∞) (for any^[1] finite x), the result is(NaN,NaN) andFE_INVALID is raised.
• Ifz is(x,NaN) (for any^[2] finite x), the result is(NaN,NaN) andFE_INVALID may be raised.
• Ifz is(+∞,y) (for any finite positive y), the result is(1,+0).
• Ifz is(+∞,+∞), the result is(1,±0) (the sign of the imaginary part is unspecified).
• Ifz is(+∞,NaN), the result is(1,±0) (the sign of the imaginary part is unspecified).
• Ifz is(NaN,+0), the result is(NaN,+0).
• Ifz is(NaN,y) (for any non-zero y), the result is(NaN,NaN) andFE_INVALID may be raised.
• Ifz is(NaN,NaN), the result is(NaN,NaN).

1. ↑perC11 DR471, this only holds for non-zero x. Ifz is(0,∞), the result should be(0,NaN).
2. ↑perC11 DR471, this only holds for non-zero x. Ifz is(0,NaN), the result should be(0,NaN).

[edit]Notes

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 representπ/2 exactly, thus there is no value of the argument for which a pole error occurs.

[edit]Example

#include <cmath>#include <complex>#include <iostream> int main(){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";}

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)

[edit]See also

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