# 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.

## Contents

### 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