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std::asinh, std::asinhf, std::asinhl

Defined in header <cmath>
(1) 
float       asinh ( float num );
double      asinh ( double num );
long double asinh ( long double num );
 (until C++23) 
/* floating-point-type */
            asinh ( /* floating-point-type */ num );
 (since C++23)
(constexpr since C++26) 
float       asinhf( float num );
 (2) (since C++11)
(constexpr since C++26) 
long double asinhl( long double num );
 (3) (since C++11)
(constexpr since C++26)
Additional overloads (since C++11)
Defined in header <cmath> 
template< class Integer >
double      asinh ( Integer num );
 (A) (constexpr since C++26)
1-3) Computes the inverse hyperbolic sine of num. The library provides overloads of std::asinh for all cv-unqualified floating-point types as the type of the parameter. (since C++23) 
double
 (since C++11)

Parameters

num - floating-point or integer value

Return value

If no errors occur, the inverse hyperbolic sine of num (sinh-1
(num), or arsinh(num)), 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 (to which C++ refers for this function) 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".

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::asinh(num) has the same effect as std::asinh(static_cast<double>(num)).

Examples

#include <cmath>
#include <iostream>
 
int main()
{
    std::cout << "asinh(1) = " << std::asinh(1) << '\n'
              << "asinh(-1) = " << std::asinh(-1) << '\n';
 
    // special values
    std::cout << "asinh(+0) = " << std::asinh(+0.0) << '\n'
              << "asinh(-0) = " <<  std::asinh(-0.0) << '\n';
}

Output:

asinh(1) = 0.881374
asinh(-1) = -0.881374
asinh(+0) = 0
asinh(-0) = -0

See also

(C++11)(C++11)(C++11)
 computes the inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x} }\)arcosh(x))
(function)
(C++11)(C++11)(C++11)
 computes the inverse hyperbolic tangent (\({\small\operatorname{artanh}{x} }\)artanh(x))
(function)
(C++11)(C++11)
 computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x))
(function)
(C++11)
 computes area hyperbolic sine of a complex number (\({\small\operatorname{arsinh}{z} }\)arsinh(z))
(function template)
C documentation for asinh
Weisstein, Eric W. "Inverse Hyperbolic Sine." From MathWorld — A Wolfram Web Resource.

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