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TextFile

separate (Generic_Elementary_Functions)

function Sinh (X : Float_Type) return Float_Type is

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

-- The definition of sinh(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, Sign_Y : Common_Float;

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

   One : constant Common_Float := 1.0;

   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;


begin

-- Filter out exceptional cases.

   if (X = 0.0) then
      return (X);
   end if;

   Y := Common_Float (X);
   if (Y > 0.0) then
      Sign_Y := One;
   else
      Sign_Y := -One;
   end if;

   Abs_Y := abs (Y);


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

   Cond := Base_Digits * Log2;
   if (Abs_Y >= Cond) then
--    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;

      Z := Sign_Y * Scale (Y, M);

--    Now,  Z = sign(X) * 1/2 * exp( abs(X) ).
--    When abs(Y) gets so big, subtracting (1/4)/Z will not make
--    a difference in the outcome of the sinh(X).

      return (Float_Type (Z));

   else

      Z := Kf_Em1 (Abs_Y);
      return (Float_Type (Sign_Y * 0.5 * (Z + (Z / (Z + 1.0)))));

   end if;

end Sinh;