c------------------------------------------------------------------------------
c returns the positive branch    
      real function acosh(y)
*************************************variables*********************************
      implicit none
      real y
*******************************************************************************
      acosh=log(y+sqrt(y*y-1.0))
      return
      end
c------------------------------------------------------------------------------
c     
      real function atanh(y)
*************************************variables*********************************
      implicit none
      real y
*******************************************************************************
      atanh=0.5*log((1.0+y)/(1.0-y))
      return
      end
c------------------------------------------------------------------------------
c     
      real function asinh(y)
*************************************variables*********************************
      implicit none
      real y
*******************************************************************************
      asinh=log(y+sqrt(y*y+1.0))
      return
      end
c------------------------------------------------------------------------------