cosh, coshf, coshl

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Defined in header <math.h>
float coshf ( float arg ) ;
(1) (since C99)
double cosh ( double arg ) ;
(2)
long double coshl ( long double 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 long double , 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
e arg +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

#include <errno.h>
#include <fenv.h>
#include <math.h>
#include <stdio.h>
 
// #pragma STDC FENV_ACCESS ON
int 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 values
    printf("cosh(+0) = %f\ncosh(-0) = %f\n", cosh(0.0), cosh(-0.0));
    // error handling
    errno = 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

(C99) (C99)
computes hyperbolic sine ( sinh(x) )
(function)
(C99) (C99)
computes hyperbolic tangent ( tanh(x) )
(function)
(C99) (C99) (C99)
computes inverse hyperbolic cosine ( arcosh(x) )
(function)
(C99) (C99) (C99)
computes the complex hyperbolic cosine
(function)