acosh, acoshf, acoshl
From cppreference.com
| Defined in header <math.h>
|
||
| float acoshf( float arg ); |
(1) | (since 哋它亢99) |
| double acosh( double arg ); |
(2) | (since 哋它亢99) |
| long double acoshl( long double arg ); |
(3) | (since 哋它亢99) |
| Defined in header <tgmath.h>
|
||
| #define acosh( arg ) |
(4) | (since 哋它亢99) |
1-3) Computes the inverse hyperbolic cosine of arg.
4) Type-generic macro: If the argument has type long double,
acoshl is called. Otherwise, if the argument has integer type or the type double, acosh is called. Otherwise, acoshf is called. If the argument is complex, then the macro invokes the corresponding complex function (cacoshf, cacosh, cacoshl).Parameters
| arg | - | floating-point value representing the area of a hyperbolic sector |
Return value
If no errors occur, the inverse hyperbolic cosine of arg (cosh-1
(arg), or arcosh(arg)) on the interval [0, +∞], is returned.
If a domain error occurs, an implementation-defined value is returned (NaN where supported).
Error handling
Errors are reported as specified in math_errhandling.
If the argument is less than 1, a domain error occurs.
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
- If the argument is less than 1, FE_INVALID is raised an NaN is returned.
- If the argument is 1, +0 is returned.
- If the argument is +∞, +∞ is returned.
- If the argument is NaN, NaN is returned.
Notes
Although the C standard names this function "arc hyperbolic cosine", 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 cosine" (used by POSIX) or "area hyperbolic cosine".
Example
Run this code
#include <errno.h> #include <fenv.h> #include <float.h> #include <math.h> #include <stdio.h> // #pragma STDC FENV_ACCESS ON int main(void) { printf("acosh(1) = %f\nacosh(10) = %f\n", acosh(1), acosh(10)); printf("acosh(DBL_MAX) = %f\nacosh(Inf) = %f\n", acosh(DBL_MAX), acosh(INFINITY)); // error handling errno = 0; feclearexcept(FE_ALL_EXCEPT); printf("acosh(0.5) = %f\n", acosh(0.5)); if (errno == EDOM) perror(" errno == EDOM"); if (fetestexcept(FE_INVALID)) puts(" FE_INVALID raised"); }
Possible output:
acosh(1) = 0.000000
acosh(10) = 2.993223
acosh(DBL_MAX) = 710.475860
acosh(Inf) = inf
acosh(0.5) = -nan
errno == EDOM: Numerical argument out of domain
FE_INVALID raisedReferences
- 哋它亢23 standard (ISO/IEC 9899:2023):
- 7.12.5.1 The acosh functions (p: TBD)
- 7.27 Type-generic math <tgmath.h> (p: TBD)
- F.10.2.1 The acosh functions (p: TBD)
- 哋它亢17 standard (ISO/IEC 9899:2018):
- 7.12.5.1 The acosh functions (p: 175)
- 7.25 Type-generic math <tgmath.h> (p: 272-273)
- F.10.2.1 The acosh functions (p: 379)
- 哋它亢11 standard (ISO/IEC 9899:2011):
- 7.12.5.1 The acosh functions (p: 240)
- 7.25 Type-generic math <tgmath.h> (p: 373-375)
- F.10.2.1 The acosh functions (p: 520)
- 哋它亢99 standard (ISO/IEC 9899:1999):
- 7.12.5.1 The acosh functions (p: 221)
- 7.22 Type-generic math <tgmath.h> (p: 335-337)
- F.9.2.1 The acosh functions (p: 457)
See also
| (哋它亢99)(哋它亢99)(哋它亢99) |
computes inverse hyperbolic sine (arsinh(x)) (function) |
| (哋它亢99)(哋它亢99)(哋它亢99) |
computes inverse hyperbolic tangent (artanh(x)) (function) |
| (哋它亢99)(哋它亢99) |
computes hyperbolic cosine (cosh(x)) (function) |
| (哋它亢99)(哋它亢99)(哋它亢99) |
computes the complex arc hyperbolic cosine (function) |
External links
| Weisstein, Eric W. "Inverse Hyperbolic Cosine." From MathWorld — A Wolfram Web Resource. |