Defined in header <complex.h> | ||
---|---|---|
float complex ctanhf( float complex z ); | (1) | (since C99) |
double complex ctanh( double complex z ); | (2) | (since C99) |
long double complex ctanhl( long double complex z ); | (3) | (since C99) |
Defined in header <tgmath.h> | ||
#define tanh( z ) | (4) | (since C99) |
z
.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.z | - | complex argument |
If no errors occur, complex hyperbolic tangent of z
is returned.
Errors are reported consistent with math_errhandling.
If the implementation supports IEEE floating-point arithmetic,
ctanh(conj(z)) == conj(ctanh(z))
ctanh(-z) == -ctanh(z)
z
is +0+0i
, the result is +0+0i
z
is x+∞i
(for any^{[1]} finite x), the result is NaN+NaNi
and FE_INVALID
is raised z
is x+NaN
(for any^{[2]} finite x), the result is NaN+NaNi
and FE_INVALID
may be raised z
is +∞+yi
(for any finite positive y), the result is 1+0i
z
is +∞+∞i
, the result is 1±0i
(the sign of the imaginary part is unspecified) z
is +∞+NaNi
, the result is 1±0i
(the sign of the imaginary part is unspecified) z
is NaN+0i
, the result is NaN+0i
z
is NaN+yi
(for any non-zero y), the result is NaN+NaNi
and FE_INVALID
may be raised z
is NaN+NaNi
, the result is NaN+NaNi
z
is 0+∞i
, the result should be 0+NaNi
z
is 0+NaNi
, the result should be 0+NaNi
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.
#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)
(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) |
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