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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); double acosh (dou- ble x); float acoshf (float x); double atanh (double x); float atanhf (float x); STANDARDS Interfaces documented on this reference page conform to industry stan- dards as follows: asinh(): XPG4-UNIX acosh(): XPG4-UNIX atanh(): XPG4-UNIX Refer to the standards(5) reference page for more information about in- dustry standards and associated tags. DESCRIPTION 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 as- inh(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 excep- tional arguments: tab(@); lfHB lfHB lfHB l l l . _ 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 _ delim off asinh(3)