asinh, asinhf, asinhl

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Defined in header <math.h>
float asinhf ( float arg ) ;
(1) (since C99)
double asinh ( double arg ) ;
(2) (since C99)
long double asinhl ( long double arg ) ;
(3) (since C99)
Defined in header <tgmath.h>
#define asinh( arg )
(4) (since C99)
1-3) Computes the inverse hyperbolic sine of arg .
4) Type-generic macro: If the argument has type long double , asinhl is called. Otherwise, if the argument has integer type or the type double , asinh is called. Otherwise, asinhf is called. If the argument is complex, then the macro invokes the corresponding complex function ( casinhf , casinh , casinhl ).

Parameters

arg - floating-point value representing the area of a hyperbolic sector

Return value

If no errors occur, the inverse hyperbolic sine of arg ( sinh -1 (arg) , or arsinh(arg) ), 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 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".

Example

Run this code 
#include <math.h>
#include <stdio.h>
 
int main(void)
{
    printf("asinh(1) = %f\nasinh(-1) = %f\n", asinh(1), asinh(-1));
    // special values
    printf("asinh(+0) = %f\nasinh(-0) = %f\n", asinh(0.0), asinh(-0.0));
}

Output: 

asinh(1) = 0.881374
asinh(-1) = -0.881374
asinh(+0) = 0.000000
asinh(-0) = -0.000000

References

  • C23 standard (ISO/IEC 9899:2024):
  • 7.12.5.2 The asinh functions (p: 240-241)
  • 7.25 Type-generic math <tgmath.h> (p: 373-375)
  • F.10.2.2 The asinh functions (p: 520)
  • C17 standard (ISO/IEC 9899:2018):
  • 7.12.5.2 The asinh functions (p: 240-241)
  • 7.25 Type-generic math <tgmath.h> (p: 373-375)
  • F.10.2.2 The asinh functions (p: 520)
  • C11 standard (ISO/IEC 9899:2011):
  • 7.12.5.2 The asinh functions (p: 240-241)
  • 7.25 Type-generic math <tgmath.h> (p: 373-375)
  • F.10.2.2 The asinh functions (p: 520)
  • C99 standard (ISO/IEC 9899:1999):
  • 7.12.5.2 The asinh functions (p: 221)
  • 7.22 Type-generic math <tgmath.h> (p: 335-337)
  • F.9.2.2 The asinh functions (p: 457)

See also

(C99) (C99) (C99)
computes inverse hyperbolic cosine ( arcosh(x) )
(function)
(C99) (C99) (C99)
computes inverse hyperbolic tangent ( artanh(x) )
(function)
(C99) (C99)
computes hyperbolic sine ( sinh(x) )
(function)
(C99) (C99) (C99)
computes the complex arc hyperbolic sine
(function)
C++ documentation for asinh

External links

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