# catanhf, catanh, catanhl

< c‎ | numeric‎ | complex

C
 Language Headers Type support Program utilities Variadic function support Error handling Dynamic memory management Date and time utilities Strings library Algorithms Numerics Input/output support Localization support Atomic operations (C11) Thread support (C11) Technical Specifications

Complex number arithmetic
Types and the imaginary constant
 complex(C99) _Complex_I(C99) CMPLX(C11)
 imaginary(C99) _Imaginary_I(C99) I(C99)
Manipulation
 cimag(C99) creal(C99) carg(C99)
 cabs(C99) conj(C99) cproj(C99)
Power and exponential functions
 cexp(C99) clog(C99)
 cpow(C99) csqrt(C99)
Trigonometric functions
 ccos(C99) csin(C99) ctan(C99)
 cacos(C99) casin(C99) catan(C99)
Hyperbolic functions
 ccosh(C99) csinh(C99) ctanh(C99)
 cacosh(C99) casinh(C99) catanh(C99)

 Defined in header  float complex       catanhf( float complex z ); (1) (since C99) double complex      catanh( double complex z ); (2) (since C99) long double complex catanhl( long double complex z ); (3) (since C99) Defined in header  #define atanh( z ) (4) (since C99)
1-3) Computes the complex arc hyperbolic tangent of z with branch cuts outside the interval [−1; +1] along the real axis.
4) Type-generic macro: If z has type long double complex, catanhl is called. if z has type double complex, catanh is called, if z has type float complex, catanhf is called. If z is real or integer, then the macro invokes the corresponding real function (atanhf, atanh, atanhl). If z is imaginary, then the macro invokes the corresponding real version of atan, implementing the formula atanh(iy) = i atan(y), and the return type is imaginary.

## Contents

### Parameters

 z - complex argument

### Return value

If no errors occur, the complex arc hyperbolic tangent of z is returned, in the range of a half-strip mathematically unbounded along the real axis and in the interval [−iπ/2; +iπ/2] along the imaginary axis.

### Error handling and special values

Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,

• catanh(conj(z)) == conj(catanh(z))
• catanh(-z) == -catanh(z)
• If z is +0+0i, the result is +0+0i
• If z is +0+NaNi, the result is +0+NaNi
• If z is +1+0i, the result is +∞+0i and FE_DIVBYZERO is raised
• If z is x+∞i (for any finite positive x), the result is +0+iπ/2
• If z is x+NaNi (for any finite nonzero x), the result is NaN+NaNi and FE_INVALID may be raised
• If z is +∞+yi (for any finite positive y), the result is +0+iπ/2
• If z is +∞+∞i, the result is +0+iπ/2
• If z is +∞+NaNi, the result is +0+NaNi
• If z is NaN+yi (for any finite y), the result is NaN+NaNi and FE_INVALID may be raised
• If z is NaN+∞i, the result is ±0+iπ/2 (the sign of the real part is unspecified)
• If z is NaN+NaNi, the result is NaN+NaNi