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Ingy döt Net 2026-02-01 16:33:20 -08:00
parent 5150844a7d
commit 4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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65
Task/Pells-equation/Ada/pells-equation.ada
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@ -1,65 +0,0 @@
with Ada.Text_Io;
with Ada.Numerics.Elementary_Functions;
with Ada.Numerics.Big_Numbers.Big_Integers;
procedure Pells_Equation is
use Ada.Numerics.Big_Numbers.Big_Integers;
type Pair is
record
V1, V2 : Big_Integer;
end record;
procedure Solve_Pell (N : Natural; X, Y : out Big_Integer) is
use Ada.Numerics.Elementary_Functions;
Big_N : constant Big_Integer := To_Big_Integer (N);
XX : constant Big_Integer := To_Big_Integer (Natural (Float'Floor (Sqrt (Float (N)))));
begin
if XX**2 = Big_N then
X := 1; Y := 0;
return;
end if;
declare
YY : Big_Integer := XX;
Z : Big_Integer := 1;
R : Big_Integer := 2 * XX;
E : Pair := Pair'(V1 => 1, V2 => 0);
F : Pair := Pair'(V1 => 0, V2 => 1);
begin
loop
YY := R * Z - YY;
Z := (Big_N - YY**2) / Z;
R := (XX + YY) / Z;
E := Pair'(V1 => E.V2, V2 => R * E.V2 + E.V1);
F := Pair'(V1 => F.V2, V2 => R * F.V2 + F.V1);
X := E.V2 + XX * F.V2;
Y := F.V2;
exit when X**2 - Big_N * Y**2 = 1;
end loop;
end;
end Solve_Pell;
procedure Test (N : Natural) is
package Natural_Io is new Ada.Text_Io.Integer_Io (Natural);
use Ada.Text_Io, Natural_Io;
X, Y : Big_Integer;
begin
Solve_Pell (N, X => X, Y => Y);
Put ("X**2 - ");
Put (N, Width => 3);
Put (" * Y**2 = 1 for X = ");
Put (To_String (X, Width => 22));
Put (" and Y = ");
Put (To_String (Y, Width => 20));
New_Line;
end Test;
begin
Test (61);
Test (109);
Test (181);
Test (277);
end Pells_Equation;