`atanh`, `atanhf`, `atanhl`

Article
2022-12-02

Calculates the inverse hyperbolic tangent.

Syntax

double atanh( double x );
float atanhf( float x );
long double atanhl( long double x );
#define atanh(X) // Requires C11 or higher

float atanh( float x );  // C++ only
long double atanh( long double x );  // C++ only

Parameters

x
Floating-point value.

Return value

The atanh functions return the inverse hyperbolic tangent (arc hyperbolic tangent) of x. If x is greater than 1, or less than -1, errno is set to EDOM and the result is a quiet NaN. If x is equal to 1 or -1, a positive or negative infinity is returned, respectively, and errno is set to ERANGE.

Input	SEH exception	`_matherr` exception
± QNaN, IND	none	none
`X` ≥ 1; `x` ≤ -1	none	none

Remarks

Because C++ allows overloading, you can call overloads of atanh that take and return float or long double values. In a C program, unless you're using the <tgmath.h> macro to call this function, atanh always takes and returns double.

If you use the <tgmath.h> atanh() macro, the type of the argument determines which version of the function is selected. See Type-generic math for details.

By default, this function's global state is scoped to the application. To change this behavior, see Global state in the CRT.

Requirements

Function	C header	C++ header
`atanh`, `atanhf`, `atanhl`	<math.h>	<cmath> or <math.h>
`atanh` macro	<tgmath.h>

For more compatibility information, see Compatibility.

Example

// crt_atanh.c
// This program displays the hyperbolic tangent of pi / 4
// and the arc hyperbolic tangent of the result.
//

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

int main( void )
{
   double pi = 3.1415926535;
   double x, y;

   x = tanh( pi / 4 );
   y = atanh( x );
   printf( "tanh( %f ) = %f\n", pi/4, x );
   printf( "atanh( %f ) = %f\n", x, y );
}

tanh( 0.785398 ) = 0.655794
atanh( 0.655794 ) = 0.785398

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atanh, atanhf, atanhl