# catanhf, catanh, catanhl

< c‎ | numeric‎ | complex

C
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Complex number arithmetic
Types and the imaginary constant
Manipulation
Power and exponential functions
Trigonometric functions
Hyperbolic functions
 cacosh casinh catanh

 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.

### 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`