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TextFile

separate (Generic_Elementary_Functions)

function Cosh (X : Float_Type) return Float_Type is

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

-- The definition of cosh(Y) is (exp(Y) + exp(-Y))/2, therefore
-- the bulk of the computations are performed by the procedure
-- KP_Exp (Y, M, Z1, Z2) which returns exp(Y) in M, Z1, and Z2
-- where
--              exp(Y) = 2**M * ( Z1 + Z2 )
-- M of integer value, and Z1 only has at most 12 significant bits.

   Z : Common_Float;

   Y, Abs_Y, Z1, Z2 : Common_Float;
   M, J             : Common_Int;

   Log2 : constant Common_Float := 16#0.B17217F7D1CF79ABC9E3B39803F2F6AF40#;

   Base_Digits : constant Common_Float :=
      Common_Float (6 * Float_Type'Base'Digits);

   Two_To : constant array (Common_Int range -3 .. 3) of Common_Float :=
      (0.125, 0.25, 0.5, 1.0, 2.0, 4.0, 8.0);

   Large_Threshold : constant Common_Float :=
      8.0 * Common_Float (Float_Type'Safe_Emax) * 0.6931471806;

   Cond : constant Common_Float := Base_Digits * Log2;

begin

-- Filter out exceptional cases.

   Y     := Common_Float (X);
   Abs_Y := abs (Y);

   if Abs_Y >= Large_Threshold then
      -- Y := Common_Float (Common_Float'Machine_Radix **
      --                    Common_Float'Machine_Emax);
      -- return (Float_Type (Y * Y * Y));
      raise Constraint_Error; --pbk
   end if;

-- Get the values of M, Z1, and Z2  so that the natural exponential of Y
-- can be calculated by  Exp(Y) = 2**M * (Z1 + Z2)

   Kp_Exp (Abs_Y, M, Z1, Z2);

   M := M - 1;

   case Radix is
      when 2 =>
         Y := Z1 + Z2;
      when others =>
         J  := M rem 4;
         M  := (M - J) / 4;
         Z1 := Z1 * Two_To (J);
         Z2 := Z2 * Two_To (J);
         Y  := Z1 + Z2;
   end case;

-- Now,  Z = 1/2 * exp( abs(X) ).

   Z := Scale (Y, M);


   if (Abs_Y >= Cond) then
-- When abs(Y) gets so big, adding (1/4)/Z will not make a difference in the
-- outcome of cosh(X).
      return (Float_Type (Z));
   else
      return (Float_Type (Z + 0.25 / Z));
   end if;

end Cosh;