/C

# asinh, asinhf, asinhl

Defined in header `<math.h>`
`float       asinhf( float arg );`
(1) (since C99)
`double      asinh( double arg );`
(2) (since C99)
`long double asinhl( long double arg );`
(3) (since C99)
Defined in header `<tgmath.h>`
`#define asinh( arg )`
(4) (since C99)
1-3) Computes the inverse hyperbolic sine of `arg`.
4) Type-generic macro: If the argument has type `long double`, `asinhl` is called. Otherwise, if the argument has integer type or the type `double`, `asinh` is called. Otherwise, `asinhf` is called. If the argument is complex, then the macro invokes the corresponding complex function (`casinhf`, `casinh`, `casinhl`).

### Parameters

 arg - floating point value representing the area of a hyperbolic sector

### Return value

If no errors occur, the inverse hyperbolic sine of `arg` (sinh-1
(arg), or arsinh(arg)), is returned.

If a range error occurs due to underflow, the correct result (after rounding) is returned.

### Error handling

Errors are reported as specified in math_errhandling.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

• if the argument is ±0 or ±∞, it is returned unmodified
• if the argument is NaN, NaN is returned

Although the C standard names this function "arc hyperbolic sine", the inverse functions of the hyperbolic functions are the area functions. Their argument is the area of a hyperbolic sector, not an arc. The correct name is "inverse hyperbolic sine" (used by POSIX) or "area hyperbolic sine".

### Example

```#include <stdio.h>
#include <math.h>

int main(void)
{
printf("asinh(1) = %f\nasinh(-1) = %f\n", asinh(1), asinh(-1));
// special values
printf("asinh(+0) = %f\nasinh(-0) = %f\n", asinh(0.0), asinh(-0.0));
}```

Output:

```asinh(1) = 0.881374
asinh(-1) = -0.881374
asinh(+0) = 0.000000
asinh(-0) = -0.000000```
• C11 standard (ISO/IEC 9899:2011):
• 7.12.5.2 The asinh functions (p: 240-241)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• F.10.2.2 The asinh functions (p: 520)
• C99 standard (ISO/IEC 9899:1999):
• 7.12.5.2 The asinh functions (p: 221)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• F.9.2.2 The asinh functions (p: 457)

 acoshacoshfacoshl (C99)(C99)(C99) computes inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x} }\)arcosh(x)) (function) atanhatanhfatanhl (C99)(C99)(C99) computes inverse hyperbolic tangent (\({\small\operatorname{artanh}{x} }\)artanh(x)) (function) sinhsinhfsinhl (C99)(C99) computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x)) (function) casinhcasinhfcasinhl (C99)(C99)(C99) computes the complex arc hyperbolic sine (function) C++ documentation for `asinh`