std::acosh, std::acoshf, std::acoshl
Defined in header <cmath>
|
||
float acosh ( float arg ); float acoshf( float arg ); |
(1) | (since C++11) |
double acosh ( double arg ); |
(2) | (since C++11) |
long double acosh ( long double arg ); long double acoshl( long double arg ); |
(3) | (since C++11) |
double acosh ( IntegralType arg ); |
(4) | (since C++11) |
arg
.Parameters
arg | - | value of a floating-point or Integral type |
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 (to which C++ refers for this function) 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".
Examples
#include <iostream> #include <cmath> #include <cfloat> #include <cerrno> #include <cfenv> #include <cstring> #pragma STDC FENV_ACCESS ON int main() { std::cout << "acosh(1) = " << std::acosh(1) << '\n' << "acosh(10) = " << std::acosh(10) << '\n' << "acosh(DBL_MAX) = " << std::acosh(DBL_MAX) << '\n' << "acosh(Inf) = " << std::acosh(INFINITY) << '\n'; // error handling errno = 0; std::feclearexcept(FE_ALL_EXCEPT); std::cout << "acosh(0.5) = " << std::acosh(0.5) << '\n'; if (errno == EDOM) std::cout << " errno == EDOM: " << std::strerror(errno) << '\n'; if (std::fetestexcept(FE_INVALID)) std::cout << " FE_INVALID raised\n"; }
Possible output:
acosh(1) = 0 acosh(10) = 2.99322 acosh(DBL_MAX) = 710.476 acosh(Inf) = inf acosh(0.5) = -nan errno == EDOM: Numerical argument out of domain FE_INVALID raised
See also
(C++11)(C++11)(C++11) |
computes the inverse hyperbolic sine (arsinh(x)) (function) |
(C++11)(C++11)(C++11) |
computes the inverse hyperbolic tangent (artanh(x)) (function) |
(C++11)(C++11) |
computes hyperbolic cosine (ch(x)) (function) |
(C++11) |
computes area hyperbolic cosine of a complex number (function template) |
External links
Weisstein, Eric W. "Inverse Hyperbolic Cosine." From MathWorld--A Wolfram Web Resource.