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asinh, acosh, atanh - Compute inverse hyperbolic functions
#include <math.h>
double asinh (double x); float asinhf (float x); double acosh (double x); float acoshf (float x); double atanh (double x); float atanhf (float x);
Interfaces documented on this reference page conform to industry standards as follows:
asinh(): XPG4-UNIX
acosh(): XPG4-UNIX
atanh(): XPG4-UNIX
Refer to the standards(5) reference page for more information about industry standards and associated tags.
The asinh() and asinhf() functions return the hyperbolic arc sine of x, in the range [-infinity, +infinity] where asinh(x) = ln(x + sqrt(x**2 + 1)). The asinh() function is the reverse function of sinh() where asinh(sinh(x)) = x.
The acosh() and acoshf() functions return the hyperbolic arc cosine of x, in the range [1, +infinity] where acosh(x) = ln(x + sqrt(x**2 - 1)). The acosh() function is the reverse function of cosh() where acosh(cosh(x)) = x.
The atanh() and atanhf() functions return the hyperbolic arc tangent of x, in the range (-1, 1). The atanh() function is the reverse function of tanh() where atanh(tanh(x)) = x.
The following table describes function behavior in response to exceptional arguments:
Function | Exceptional Argument | Routine Behavior |
asinh() | None | N/A |
asinhf() | None | N/A |
acosh() | x<1 | Invalid argument |
acoshf() | x<1 | Invalid argument |
atanh() | x>1 or x=1 | Invalid argument |
atanhf() | x>1 or x=1 | Invalid argument |