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⟦98592f6df⟧ Ada Source

    Length: 4096 (0x1000)
    Types: Ada Source
    Notes: 03_class, FILE, R1k_Segment, e3_tag, function Arcsinh, seg_0130c0, separate Generic_Elementary_Functions

Derivation

└─⟦8527c1e9b⟧ Bits:30000544 8mm tape, Rational 1000, Arrival backup of disks in PAM's R1000
    └─ ⟦5a81ac88f⟧ »Space Info Vol 1« 
        └─⟦this⟧ 

separate (Generic_Elementary_Functions)

function Arcsinh (X : Float_Type) return Float_Type is

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

-- The definition of Arcsinh(Y) is log( Y + sqrt(Y*Y + 1) )
-- For symmetry, we return sign(Y)*Arcsinh(|Y|). The discussions below
-- therefore assume Y >= 0.
-- To obtain good accuracy, we consider several cases:
-- 1) Y <= epsilon, simply return Y.
-- 2) epsilon < Y <= 0.5,
--    Y + sqrt(Y*Y+1) = 1 + ( Y  +  Y*Y/[1 + sqrt(Y*Y+1)] )
--                    = 1 + ( Y  +  Y / [ (1/Y) + sqrt(1 + [1/Y*Y]) ] )
--    A formula best suited for the kernel function L1p.
-- 3) 0.5 < 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.
--

   Y, Sign_X, V, M, Z1, Z2, Result : Common_Float;

   One  : constant := 1.0;
   Half : constant := 0.5;

   Small_Threshold : constant Common_Float := Common_Float'Base'Epsilon;
   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);
   Sign_X := Copy_Sign (One, Y);
   Y      := abs (Y);

   if (Y <= Half) then

      if (Y < Small_Threshold) then
         return (Float_Type (Copy_Sign (Y, Sign_X)));
      else
         V      := Y + Y / ((One / Y) + Kf_Sqrt (One + (One / (Y * Y))));
         Result := Kf_L1p (V);
      end if;

   else

      if (Y < Large_Threshold) then
         Y := Y + Half / (Y + Kf_Sqrt (One + Y * Y));
      end if;
      Kp_Log (Y, M, Z1, Z2);
      M      := M + One;
      Result := M * Log2_Lead + (Z1 + (Z2 + M * Log2_Trail));

   end if;

   return (Float_Type (Copy_Sign (Result, Sign_X)));

end Arcsinh;

    nblk1=3
    nid=0
    hdr6=6
        [0x00] rec0=18 rec1=00 rec2=01 rec3=01c
        [0x01] rec0=24 rec1=00 rec2=02 rec3=01a
        [0x02] rec0=0a rec1=00 rec2=03 rec3=000
    tail 0x2150db4e282b1516dcfb9 0x42a00066462061e03