asinh, asinhf, asinhl

 

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Technical Specifications

 

Numerics

Common mathematical functions

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Complex number arithmetics

Random number generation

Type-generic math

 

Common mathematical functions

Functions
Basic operations
abslabsllabsimaxabs (C99) fabs divldivlldivimaxdiv (C99) fmod	remainder (C99) remquo (C99) fma (C99) fmax (C99) fmin (C99) fdim (C99) nannanfnanl (C99)(C99)(C99)
Exponential functions
exp exp2 (C99) expm1 (C99)	log log10 log1p (C99) log2 (C99)
Power functions
sqrt cbrt (C99)	hypot (C99) pow
Trigonometric and hyperbolic functions
sin cos tan asin acos atan atan2	sinh cosh tanh asinh (C99) acosh (C99) atanh (C99)
Error and gamma functions
erf (C99) erfc (C99)	lgamma (C99) tgamma (C99)
Nearest integer floating point operations
ceil floor roundlroundllround (C99)(C99)(C99)	trunc (C99) nearbyint (C99) rintlrintllrint (C99)(C99)(C99)
Floating point manipulation functions
ldexp scalbnscalbln (C99)(C99) ilogb (C99) logb (C99)	frexp modf nextafternexttoward (C99)(C99) copysign (C99)
Classification
fpclassify (C99) isfinite (C99) isinf (C99) isnan (C99) isnormal (C99) signbit (C99)	isgreater (C99) isgreaterequal (C99) isless (C99) islessequal (C99) islessgreater (C99) isunordered (C99)
Macro constants
HUGE_VALFHUGE_VALHUGE_VALL (C99)(C99)	FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C99)(C99)(C99)(C99)(C99)

 

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 <stdio.h>
#include <math.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

• 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

acoshacoshfacoshl (C99)(C99)(C99)	computes inverse hyperbolic cosine (arcosh(x)) (function)
atanhatanhfatanhl (C99)(C99)(C99)	computes inverse hyperbolic tangent (artanh(x)) (function)
sinhsinhfsinhl (C99)(C99)	computes hyperbolic sine (sh(x)) (function)
casinhcasinhfcasinhl (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.