# asinh, asinhf, asinhl

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< c‎ | numeric‎ | math

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

### Notes

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

Run this code

    #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

### References

- 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)

### See also

acosh acoshf acoshl (C99)(C99)(C99) | computes inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x} }\)arcosh(x)) (function)
atanh atanhf atanhl (C99)(C99)(C99) | computes inverse hyperbolic tangent (\({\small\operatorname{artanh}{x} }\)artanh(x)) (function)
sinh sinhf sinhl (C99)(C99) | computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x)) (function)
casinh casinhf casinhl (C99)(C99)(C99) | computes the complex arc hyperbolic sine (function)

### External links

Weisstein, Eric W. "Inverse Hyperbolic Sine." From MathWorld — A Wolfram Web Resource.

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