asinh(3) Library Functions Manual asinh(3)
NAME
asinh, acosh, atanh - Compute inverse hyperbolic functions
LIBRARY
Math Library (libm.a)
SYNOPSIS
#include <math.h>
double asinh (double x); float asinhf (float x); long double asinhl (long double x); double acosh (double x); float acoshf (float
x); long double acoshl (long double x); double atanh (double x); float atanhf (float x); long double atanhl (long double x);
STANDARDS
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.
DESCRIPTION
The asinh(), asinhf(), and asinhl() 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 inverse function of sinh() where asinh(sinh(x)) = x.
The acosh(), acoshf(), and acoshl() 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 inverse function of cosh() where acosh(cosh(x)) = |x|.
The atanh(), atanhf() and atanhl() functions return the hyperbolic arc tangent of x, in the range (-1, 1). The atanh() function is the
inverse function of tanh() where atanh(tanh(x)) = x.
The following table describes function behavior in response to exceptional arguments:
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Function Exceptional Argument Routine Behavior
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asinh() None N/A
asinhf() None N/A
asinhl() None N/A
acosh() x<1 Invalid argument
acoshf() x<1 Invalid argument
acoshl() x<1 Invalid argument
atanh() x>1 or x=1 Invalid argument
atanhf() x>1 or x=1 Invalid argument
atanhl() x>1 or x=1 Invalid argument
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asinh(3)