NAME¶

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

Synopsis¶

Defined in header <cmath>
float asinh ( float num );

double asinh ( double num ); (until C++23)

long double asinh ( long double num );
/* floating-point-type */ (since C++23)
asinh ( /* floating-point-type */ num ); (constexpr since C++26)
float asinhf( float num ); (1) (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 > (A) (constexpr since C++26)
double asinh ( Integer num );

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)

A) Additional overloads are provided for all integer types, which are (since C++11)
treated as double.

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¶

// Run this code

#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¶

acosh
acoshf computes the inverse hyperbolic cosine
acoshl (\({\small\operatorname{arcosh}{x}}\)arcosh(x))
(C++11) (function)
(C++11)
(C++11)
atanh
atanhf computes the inverse hyperbolic tangent
atanhl (\({\small\operatorname{artanh}{x}}\)artanh(x))
(C++11) (function)
(C++11)
(C++11)
sinh
sinhf computes hyperbolic sine (\({\small\sinh{x}}\)sinh(x))
sinhl (function)
(C++11)
(C++11)
asinh(std::complex) computes area hyperbolic sine of a complex number
(C++11) (\({\small\operatorname{arsinh}{z}}\)arsinh(z))
(function template)
C documentation for
asinh

External links¶

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