/C

# atanh, atanhf, atanhl

Defined in header `<math.h>`
`float       atanhf( float arg );`
(1) (since C99)
`double      atanh( double arg );`
(2) (since C99)
`long double atanhl( long double arg );`
(3) (since C99)
Defined in header `<tgmath.h>`
`#define atanh( arg )`
(4) (since C99)
1-3) Computes the inverse hyperbolic tangent of `arg`.
4) Type-generic macro: If the argument has type `long double`, `atanhl` is called. Otherwise, if the argument has integer type or the type `double`, `atanh` is called. Otherwise, `atanhf` is called. If the argument is complex, then the macro invokes the corresponding complex function (`catanhf`, `catanh`, `catanhl`).

### Parameters

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

### Return value

If no errors occur, the inverse hyperbolic tangent of `arg` (tanh-1
(arg), or artanh(arg)), is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a pole error occurs, `±HUGE_VAL`, `±HUGE_VALF`, or `±HUGE_VALL` is returned (with the correct sign).

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 argument is not on the interval [-1, +1], a range error occurs.

If the argument is ±1, a pole error occurs.

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

• if the argument is ±0, it is returned unmodified
• if the argument is ±1, ±∞ is returned and `FE_DIVBYZERO` is raised.
• if |arg|>1, NaN is returned and `FE_INVALID` is raised.
• if the argument is NaN, NaN is returned

### Notes

Although the C standard names this function "arc hyperbolic tangent", 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 tangent" (used by POSIX) or "area hyperbolic tangent".

POSIX specifies that in case of underflow, `arg` is returned unmodified, and if that is not supported, an implementation-defined value no greater than DBL_MIN, FLT_MIN, and LDBL_MIN is returned.

### Example

```#include <stdio.h>
#include <math.h>
#include <float.h>
#include <errno.h>
#include <fenv.h>
#pragma STDC FENV_ACCESS ON
int main(void)
{
printf("atanh(0) = %f\natanh(-0) = %f\n", atanh(0), atanh(-0.0));
printf("atanh(0.9) = %f\n", atanh(0.9));
//error handling
errno = 0; feclearexcept(FE_ALL_EXCEPT);
printf("atanh(-1) = %f\n", atanh(-1));
if(errno == ERANGE) perror("    errno == ERANGE");
if(fetestexcept(FE_DIVBYZERO)) puts("    FE_DIVBYZERO raised");
}```

Possible output:

```atanh(0) = 0.000000
atanh(-0) = -0.000000
atanh(0.9) = 1.472219
atanh(-1) = -inf
errno == ERANGE: Numerical result out of range
FE_DIVBYZERO raised```

### References

• C11 standard (ISO/IEC 9899:2011):
• 7.12.5.3 The atanh functions (p: 241)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• F.10.2.3 The atanh functions (p: 520)
• C99 standard (ISO/IEC 9899:1999):
• 7.12.5.3 The atanh functions (p: 221-222)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• F.9.2.3 The atanh functions (p: 457)

 asinhasinhfasinhl (C99)(C99)(C99) computes inverse hyperbolic sine (\({\small\operatorname{arsinh}{x} }\)arsinh(x)) (function) acoshacoshfacoshl (C99)(C99)(C99) computes inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x} }\)arcosh(x)) (function) tanhtanhftanhl (C99)(C99) computes hyperbolic tangent (\({\small\tanh{x} }\)tanh(x)) (function) catanhcatanhfcatanhl (C99)(C99)(C99) computes the complex arc hyperbolic tangent (function) C++ documentation for `atanh`