`acosh`, `acoshf`, `acoshl`

Article
2022-12-02

Calculates the inverse hyperbolic cosine.

Syntax

double acosh( double x );
float acoshf( float x );
long double acoshl( long double x );
#define acosh(X) // Requires C11 or higher

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

Parameters

x
Floating-point value.

Return value

The acosh functions return the inverse hyperbolic cosine (arc hyperbolic cosine) of x. These functions are valid over the domain x ≥ 1. If x is less than 1, errno is set to EDOM, and the result is a quiet NaN. If x is a quiet NaN, indefinite, or infinity, the same value is returned.

Input	SEH exception	`_matherr` exception
± QNaN, IND, INF	none	none
`x` < 1	none	none

Remarks

When you use C++, you can call overloads of acosh 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, acosh always takes and returns double.

If you use the <tgmath.h> acosh() 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
`acosh`, `acoshf`, `acoshl`	<math.h>	<cmath>
`acosh` macro	<tgmath.h>

For more compatibility information, see Compatibility.

Example

// crt_acosh.c
// Compile by using: cl /W4 crt_acosh.c
// This program displays the hyperbolic cosine of pi / 4
// and the arc hyperbolic cosine of the result.

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

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

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

cosh( 0.785398 ) = 1.324609
acosh( 1.324609 ) = 0.785398

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acosh, acoshf, acoshl