Kahan summation: Difference between revisions

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=={{header|Ada}}==

<lang Ada>with Ada.Text_Io; use Ada.Text_Io;

procedure Kahan is

type Kahan_Summer is

record

Sum : Float := 0.0;

C : Float := 0.0;

end record;

procedure Add (Acc : in out Kahan_Summer; Right : Float) is

Y : constant Float := Right - Acc.C;

T : constant Float := Acc.Sum + Y;

begin

Acc.C := (T - Acc.Sum) - Y;

acc.Sum := T;

end Add;

function Sum (Acc : Kahan_Summer) return Float

is (Acc.Sum);

function Epsilon return Float is

E : Float := 1.000;

begin

while 1.0 + E /= 1.0 loop

E := E / 2.0;

end loop;

return E;

end Epsilon;

A : constant Float := 1.000;

B : constant Float := Epsilon;

C : constant Float := -B;

D : constant Float := (A + B) + C;

K : Kahan_Summer;

package Float_Io is new Ada.Text_Io.Float_Io (Float);

use Float_Io;

begin

Add (K, A);

Add (K, B);

Add (K, C);

Default_Exp := 0;

Default_Aft := 12;

Put ("Epsilon : "); Put (B); New_Line;

Put ("(A + B) - C : "); Put (D); New_Line;

Put ("Kahan sum : "); Put (Sum (K)); New_Line;

end Kahan;</lang>

{{out}}

<pre>

Epsilon : 0.000000059605

(A + B) - C : 0.999999940395

Kahan sum : 1.000000000000