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TextFile

separate (Generic_Elementary_Functions)

function Arccosh (X : Float_Type) return Float_Type is

-- On input, X is a floating-point value in Float_Type;
-- On output, the value of Arccosh(X) (the inverse hyperbolic cos of X)
--            is returned.

-- The definition of Arccosh(Y) is log( Y + sqrt(Y*Y - 1) ), Y >= 1.
-- To obtain good accuracy, we consider several cases:
-- 1) Y = 1, simply return 0.
-- 2) 1 < Y <= sqrt(2)
--    Y + sqrt(Y*Y-1) = Y + sqrt( (Y-1)*(Y+1) )
-- 3) sqrt(2) < Y < 10/epsilon,
--    Y + sqrt(Y*Y-1) = 2( Y  -  0.5/[ sqrt(Y*Y-1) + Y ] ).
-- 4) 10/epsilon <= Y, then
--    Y + sqrt(Y*Y-1) = 2Y for practical purposes.
-- Note that (3) and (4) are suited for invoking the kernel procedure
-- KP_Log(Input) which returns M, Z1, and Z2 where
--    log(Input) = M * log(2)   +   Z1   +   Z2.
--

   Y1, Y, M, Z1, Z2, Result : Common_Float;

   Zero  : constant := 0.0;
   One   : constant := 1.0;
   Half  : constant := 0.5;
   Root2 : constant := 1.41421_35623_73095_04880_16887_24209_69807;

   Large_Threshold : constant Common_Float := 10.0 / Common_Float'Base'Epsilon;
   Log2_Lead       : constant Common_Float := 16#0.B17#;
   Log2_Trail      : constant Common_Float :=
      16#0.000217F7D1CF79ABC9E3B39803F2F6AF40#;

begin


   Y := Common_Float (X);
   if (Y < One) then
      raise Argument_Error;
   end if;

   if (Y <= Root2) then

      if (Y = One) then
         return (Float_Type (Zero));
      else
         Y1 := Y - One;
         Y  := Y1 + Kf_Sqrt (Y1 * (Y + One));
         return (Float_Type (Kf_L1p (Y)));
      end if;

   else

      if (Y < Large_Threshold) then
         Y := Y - Half / (Y + Kf_Sqrt ((Y - One) * (Y + One)));
      end if;
      Kp_Log (Y, M, Z1, Z2);
      M := M + One;

   end if;

   Result := M * Log2_Lead + (Z1 + (Z2 + M * Log2_Trail));


   return (Float_Type (Result));

end Arccosh;