# casinhf, casinh, casinhl

< 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       casinhf( float complex z ); (1) (since C99) double complex      casinh( double complex z ); (2) (since C99) long double complex casinhl( long double complex z ); (3) (since C99) Defined in header `` #define asinh( z ) (4) (since C99)
1-3) Computes the complex arc hyperbolic sine of `z` with branch cuts outside the interval [−i; +i] along the imaginary axis.
4) Type-generic macro: If `z` has type long double complex, `casinhl` is called. if `z` has type double complex, `casinh` is called, if `z` has type float complex, `casinhf` is called. If `z` is real or integer, then the macro invokes the corresponding real function (asinhf, asinh, asinhl). If `z` is imaginary, then the macro invokes the corresponding real version of the function asin, implementing the formula asinh(iy) = i asin(y), and the return type is imaginary.

### Parameters

 z - complex argument

### Return value

If no errors occur, the complex arc hyperbolic sine of `z` is returned, in the range of a 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,

• casinh(conj(z)) == conj(casinh(z))
• casinh(-z) == -casinh(z)
• If `z` is `+0+0i`, the result is `+0+0i`
• If `z` is `x+∞i` (for any positive finite x), the result is `+∞+π/2`
• If `z` is `x+NaNi` (for any finite x), the result is `NaN+NaNi` and FE_INVALID may be raised
• If `z` is `+∞+yi` (for any positive finite y), the result is `+∞+0i`
• If `z` is `+∞+∞i`, the result is `+∞+iπ/4`
• If `z` is `+∞+NaNi`, the result is `+∞+NaNi`
• If `z` is `NaN+0i`, the result is `NaN+0i`
• If `z` is `NaN+yi` (for any finite nonzero y), the result is `NaN+NaNi` and FE_INVALID may be raised
• If `z` is `NaN+∞i`, the result is `±∞+NaNi` (the sign of the real part is unspecified)
• If `z` is `NaN+NaNi`, the result is `NaN+NaNi`