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Difference between revisions of "cpp/numeric/math/asinh"

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{{cpp/title|asinh}}
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{{cpp/title|asinh|asinhf|asinhl}}
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{{cpp/numeric/math/sidebar}}
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{{cpp/numeric/math/navbar}}
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{{ddcl list begin}}
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{{cpp/numeric/math/declarations
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{{ddcl list header | cmath}}
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|family=asinh
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{{ddcl list item | notes={{mark c++11 feature}} |
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|param1=num
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float      asinh( float arg );
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|constexpr_since=26
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|desc=Computes the inverse hyperbolic sine of {{c|num}}.
 
}}
 
}}
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{{ddcl list item | notes={{mark c++11 feature}} |
 
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double      asinh( double arg );
 
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}}
 
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{{ddcl list item | notes={{mark c++11 feature}} |
 
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long double asinh( long double arg );
 
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}}
 
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{{ddcl list end}}
 
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Computes hyperbolic arc sine of {{tt|arg}}
 
  
 
===Parameters===
 
===Parameters===
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{{param list begin}}
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{{par begin}}
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{{param list item | arg | floating point value}}
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{{par|num|floating-point or integer value}}
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{{param list end}}
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{{par end}}
  
 
===Return value===
 
===Return value===
 +
If no errors occur, the inverse hyperbolic sine of {{c|num}} ({{math|sinh{{su|p=-1}}(num)}}, or {{math|arsinh(num)}}), is returned.
  
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inverse hyperbolic sine of {{tt|arg}}
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If a range error occurs due to underflow, the correct result (after rounding) is returned.
  
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===See also===
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===Error handling===
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Errors are reported as specified in {{lc|math_errhandling}}.
  
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{{dcl list begin}}
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If the implementation supports IEEE floating-point arithmetic (IEC 60559),
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{{dcl list template | cpp/numeric/math/dcl list acosh}}
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* if the argument is ±0 or ±∞, it is returned unmodified.
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{{dcl list template | cpp/numeric/math/dcl list atanh}}
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* if the argument is NaN, NaN is returned.
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{{dcl list template | cpp/numeric/math/dcl list sinh}}
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{{dcl list end}}
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===Notes===
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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".
 +
 
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{{cpp/numeric/math/additional integer overload note|asinh}}
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 +
===Examples===
 +
{{example
 +
|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'
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              << "asinh(-0) = " <<  std::asinh(-0.0) << '\n';
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}
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|output=
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asinh(1) = 0.881374
 +
asinh(-1) = -0.881374
 +
asinh(+0) = 0
 +
asinh(-0) = -0
 +
}}
 +
 
 +
===See also===
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{{dsc begin}}
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{{dsc inc|cpp/numeric/math/dsc acosh}}
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{{dsc inc|cpp/numeric/math/dsc atanh}}
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{{dsc inc|cpp/numeric/math/dsc sinh}}
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{{dsc inc|cpp/numeric/complex/dsc asinh}}
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{{dsc see c|c/numeric/math/asinh}}
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{{dsc end}}
  
 
===External links===
 
===External links===
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[http://mathworld.wolfram.com/InverseHyperbolicSine.html Weisstein, Eric W. "Inverse Hyperbolic Sine."] From MathWorld--A Wolfram Web Resource.
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{{eli|[https://mathworld.wolfram.com/InverseHyperbolicSine.html Weisstein, Eric W. "Inverse Hyperbolic Sine."] From MathWorld &mdash; A Wolfram Web Resource.}}
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{{langlinks|de|es|fr|it|ja|pt|ru|zh}}

Latest revision as of 08:00, 14 September 2023

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

Contents

[edit] Parameters

num - floating-point or integer value

[edit] 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.

[edit] 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.

[edit] 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)).

[edit] 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

[edit] See also

(C++11)(C++11)(C++11)
 computes the inverse hyperbolic cosine (arcosh(x))
(function) [edit]
(C++11)(C++11)(C++11)
 computes the inverse hyperbolic tangent (artanh(x))
(function) [edit]
(C++11)(C++11)
 computes hyperbolic sine (sinh(x))
(function) [edit]
(C++11)
 computes area hyperbolic sine of a complex number (arsinh(z))
(function template) [edit]
C documentation for asinh

[edit] External links

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