asinh, asinhf, asinhl

 

C

Compiler support

Language

Headers

Type support

Program utilities

Variadic function support

Error handling

Dynamic memory management

Strings library

Algorithms

Numerics

Date and time utilities

Input/output support

Localization support

Concurrency support (C11)

Technical Specifications

Symbol index

 

Numerics

Common mathematical functions

Floating-point environment (C99)

Pseudo-random number generation

Complex number arithmetic (C99)

Type-generic math (C99)

 

Common mathematical functions

Types
div_tldiv_tlldiv_timaxdiv_t (C99)(C99)     float_tdouble_t (C99)(C99)     _Decimal32_t_Decimal64_t (C23)(C23)
Functions
Basic operations abslabsllabsimaxabs (C99)(C99) fabs divldivlldivimaxdiv (C99)(C99) fmod remainder (C99) remquo (C99) fma (C99) fdim (C99) nannanfnanlnandN (C99)(C99)(C99)(C23) Maximum/minimum operations fmax (C99) fmaximum (C23) fmaximum_mag (C23) fmaximum_num (C23) fmaximum_mag_num (C23)     fmin (C99) fminimum (C23) fminimum_mag (C23) fminimum_num (C23) fminimum_mag_num (C23) Exponential functions exp exp10 (C23) exp2 (C99) expm1 (C99) exp10m1 (C23) exp2m1 (C23) log log10 log2 (C99) log1plogp1 (C99)(C23) log10p1 (C23) log2p1 (C23) Power functions sqrt cbrt (C99) rootn (C23) rsqrt (C23) hypot (C99) compound (C23) pow pown (C23) powr (C23) Trigonometric and hyperbolic functions sin cos tan asin acos atan atan2 sinpi (C23) cospi (C23) tanpi (C23) asinpi (C23) acospi (C23) atanpi (C23) atan2pi (C23) 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) roundeven (C23) trunc (C99) nearbyint (C99) rintlrintllrint (C99)(C99)(C99) fromfpfromfpxufromfpufromfpx (C23)(C23)(C23)(C23) Floating-point manipulation functions ldexp frexp scalbnscalbln (C99)(C99) ilogbllogb (C99)(C23) logb (C99) modf nextafternexttoward (C99)(C99) nextupnextdown (C23)(C23) copysign (C99) canonicalize (C23) Narrowing operations fadd (C23) fsub (C23) fmul (C23) fdiv (C23) ffma (C23) fsqrt (C23) Quantum and quantum exponent functions quantizedN (C23) samequantumdN (C23) quantumdN (C23) llquantexpdN (C23) Decimal re-encoding functions encodedecdN (C23) decodedecdN (C23) encodebindN (C23) decodebindN (C23) Total order and payload functions totalorder (C23) getpayload (C23) setpayload (C23) setpayloadsig (C23) Classification fpclassify (C99) iscanonical (C23) isfinite (C99) isinf (C99) isnan (C99) isnormal (C99) signbit (C99) issubnormal (C23) iszero (C23) isgreater (C99) isgreaterequal (C99) isless (C99) islessequal (C99) islessgreater (C99) isunordered (C99) issignaling (C23) iseqsig (C23)
Macro constants
Special floating-point values HUGE_VALFHUGE_VALHUGE_VALLHUGE_VALDN (C99)(C99)(C23) INFINITYDEC_INFINITY (C99)(C23) NANDEC_NAN (C99)(C23) Arguments and return values FP_ILOGB0FP_ILOGBNAN (C99)(C99) FP_INT_UPWARDFP_INT_DOWNWARDFP_INT_TOWARDZEROFP_INT_TONEARESTFROMZEROFP_INT_TONEAREST (C23)(C23)(C23)(C23)(C23)     FP_LLOGB0FP_LLOGBNAN (C23)(C23) FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C99)(C99)(C99)(C99)(C99)     Error handling MATH_ERRNOMATH_ERRNOEXCEPT (C99)(C99) math_errhandling (C99)	Fast operation indicators FP_FAST_FMAFFP_FAST_FMA (C99)(C99) FP_FAST_FADDFP_FAST_FADDLFP_FAST_DADDLFP_FAST_DMADDDN (C23)(C23)(C23)(C23)     FP_FAST_FMULFP_FAST_FMULLFP_FAST_DMULLFP_FAST_DMMULDN (C23)(C23)(C23)(C23) FP_FAST_FFMAFP_FAST_FFMALFP_FAST_DFMALFP_FAST_DMFMADN (C23)(C23)(C23)(C23) FP_FAST_FMALFP_FAST_FMADN (C99)(C23) FP_FAST_FSUBFP_FAST_FSUBLFP_FAST_DSUBLFP_FAST_DMSUBDN (C23)(C23)(C23)(C23) FP_FAST_FDIVFP_FAST_FDIVLFP_FAST_DDIVLFP_FAST_DMDIVDN (C23)(C23)(C23)(C23) FP_FAST_FSQRTFP_FAST_FSQRTLFP_FAST_DSQRTLFP_FAST_DMSQRTDN (C23)(C23)(C23)(C23)

 

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

acoshacoshfacoshl (C99)(C99)(C99)	computes inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x} }\)arcosh(x)) (function)
atanhatanhfatanhl (C99)(C99)(C99)	computes inverse hyperbolic tangent (\({\small\operatorname{artanh}{x} }\)artanh(x)) (function)
sinhsinhfsinhl (C99)(C99)	computes hyperbolic sine (\({\small\sinh{x} }\)sinh(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.