cosh, coshf, coshl

 

C

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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)

Bit manipulation(C23)

Checked integer arithmetic(C23)

 

Common mathematical functions

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) fmin (C99) fmaximum (C23) fminimum (C23) fmaximum_mag (C23)  fmaximum_num (C23) fminimum_mag (C23) fminimum_num (C23) fmaximum_mag_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)

Nearest integer floating-point ceil floor roundlroundllround (C99)(C99)(C99) roundeven (C23) trunc (C99) nearbyint (C99) rintlrintllrint (C99)(C99)(C99) fromfpfromfpxufromfpufromfpx (C23)(C23)(C23)(C23) Floating-point manipulation 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 quantizedN (C23) quantumdN (C23) samequantumdN (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)

Error and gamma functions erf (C99) erfc (C99) lgamma (C99) tgamma (C99) Types div_tldiv_tlldiv_timaxdiv_t (C99)(C99) float_tdouble_t (C99)(C99) _Decimal32_t_Decimal64_t (C23)(C23) Macro constants Special floating-point values HUGE_VALHUGE_VALFHUGE_VALLHUGE_VALDN (C99)(C99)(C23) INFINITYDEC_INFINITY (C99)(C23) NANDEC_NAN (C99)(C23) Arguments and return values FP_ILOGB0FP_ILOGBNAN (C99)(C99) FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C99)(C99)(C99)(C99)(C99) FP_LLOGB0FP_LLOGBNAN (C23)(C23) FP_INT_UPWARDFP_INT_DOWNWARDFP_INT_TOWARDZEROFP_INT_TONEARESTFROMZEROFP_INT_TONEAREST (C23)(C23)(C23)(C23)(C23) 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       coshf(float arg );	(1)	(since C99)
double      cosh(double arg );	(2)
longdouble coshl(longdouble arg );	(3)	(since C99)
Defined in header <tgmath.h>
#define cosh( arg )	(4)	(since C99)

1-3) Computes the hyperbolic cosine of arg.

4) Type-generic macro: If the argument has type longdouble, coshl is called. Otherwise, if the argument has integer type or the type double, cosh is called. Otherwise, coshf is called. If the argument is complex, then the macro invokes the corresponding complex function (ccoshf, ccosh, ccoshl).

Parameters

arg

-

floating-point value representing a hyperbolic angle

Return value

If no errors occur, the hyperbolic cosine of arg (cosh(arg), or

earg +e-arg

2

) is returned.

If a range error due to overflow occurs, +HUGE_VAL, +HUGE_VALF, or +HUGE_VALL 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, 1 is returned
• If the argument is ±∞, +∞ is returned
• if the argument is NaN, NaN is returned

Notes

For the IEEE-compatible type double, if |arg| > 710.5, then cosh(arg) overflows.

Example

Run this code

#include <errno.h>#include <fenv.h>#include <math.h>#include <stdio.h>   // #pragma STDC FENV_ACCESS ONint main(void){printf("cosh(1) = %f\ncosh(-1)= %f\n", cosh(1), cosh(-1));printf("log(sinh(1) + cosh(1))=%f\n", log(sinh(1)+ cosh(1)));// special valuesprintf("cosh(+0) = %f\ncosh(-0) = %f\n", cosh(0.0), cosh(-0.0));// error handlingerrno=0;feclearexcept(FE_ALL_EXCEPT);printf("cosh(710.5) = %f\n", cosh(710.5));if(errno==ERANGE)perror(" errno == ERANGE");if(fetestexcept(FE_OVERFLOW))puts(" FE_OVERFLOW raised");}

Possible output:

cosh(1) = 1.543081 cosh(-1)= 1.543081 log(sinh(1) + cosh(1))=1.000000 cosh(+0) = 1.000000 cosh(-0) = 1.000000 cosh(710.5) = inf errno == ERANGE: Numerical result out of range FE_OVERFLOW raised

References

• C23 standard (ISO/IEC 9899:2024):

• 7.12.5.4 The cosh functions (p: TBD)

• 7.25 Type-generic math <tgmath.h> (p: TBD)

• F.10.2.4 The cosh functions (p: TBD)

• C17 standard (ISO/IEC 9899:2018):

• 7.12.5.4 The cosh functions (p: 176)

• 7.25 Type-generic math <tgmath.h> (p: 272-273)

• F.10.2.4 The cosh functions (p: 379)

• C11 standard (ISO/IEC 9899:2011):

• 7.12.5.4 The cosh functions (p: 241)

• 7.25 Type-generic math <tgmath.h> (p: 373-375)

• F.10.2.4 The cosh functions (p: 520)

• C99 standard (ISO/IEC 9899:1999):

• 7.12.5.4 The cosh functions (p: 222)

• 7.22 Type-generic math <tgmath.h> (p: 335-337)

• F.9.2.4 The cosh functions (p: 457)

• C89/C90 standard (ISO/IEC 9899:1990):

• 4.5.3.1 The cosh function

See also

sinhsinhfsinhl (C99)(C99)	computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x)) (function)
tanhtanhftanhl (C99)(C99)	computes hyperbolic tangent (\({\small\tanh{x} }\)tanh(x)) (function)
acoshacoshfacoshl (C99)(C99)(C99)	computes inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x} }\)arcosh(x)) (function)
ccoshccoshfccoshl (C99)(C99)(C99)	computes the complex hyperbolic cosine (function)
C++ documentation for cosh