NAME    [Toc]    [Back]

       asinh, acosh, atanh - Compute inverse hyperbolic functions

SYNOPSIS    [Toc]    [Back]

       #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 );

LIBRARY    [Toc]    [Back]

       Math Library (libm)

STANDARDS    [Toc]    [Back]

       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    [Toc]    [Back]

       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:









       ----------------------------------------------------
       Function    Exceptional Argument   Routine Behavior
       ----------------------------------------------------
       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
       ----------------------------------------------------




                                                         asinh(3)