# 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.

### 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 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 `+∞+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`
1. per DR471, this holds for non-zero x only. If `z` is `0+NaNi`, the result should be `NaN+iπ/2`