# cacoshf, cacosh, cacoshl

< 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       cacoshf( float complex z ); (1) (since C99) double complex      cacosh( double complex z ); (2) (since C99) long double complex cacoshl( long double complex z ); (3) (since C99) Defined in header  #define acosh( z ) (4) (since C99)
1-3) Computes complex arc hyperbolic cosine of a complex value z with branch cut at values less than 1 along the real axis.
4) Type-generic macro: If z has type long double complex, cacoshl is called. if z has type double complex, cacosh is called, if z has type float complex, cacoshf is called. If z is real or integer, then the macro invokes the corresponding real function (acoshf, acosh, acoshl). If z is imaginary, then the macro invokes the corresponding complex number version and the return type is complex.

## Contents

### Parameters

 z - complex argument

### Return value

The complex arc hyperbolic cosine of z in the interval [0; ∞) along the real axis and in the interval [−iπ; +iπ] along the imaginary axis.

### Error handling and special values

Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,

• cacosh(conj(z)) == conj(cacosh(z))
• If z is ±0+0i, the result is +0+iπ/2
• If z is +x+∞i (for any finite x), the result is +∞+iπ/2
• If z is +x+NaNi (for non-zero finite x), the result is NaN+NaNi and FE_INVALID may be raised.
• If z is 0+NaNi, the result is NaN±iπ/2, where the sign of the imaginary part is unspecified
• If z is -∞+yi (for any positive finite y), the result is +∞+iπ
• If z is +∞+yi (for any positive finite y), the result is +∞+0i
• If z is -∞+∞i, the result is +∞+3iπ/4
• If z is ±∞+NaNi, the result is +∞+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 +∞+NaNi
• If z is NaN+NaNi, the result is NaN+NaNi