A-M baby

Task/Modular-inverse/Ada/modular-inverse.ada

@@ -0,0 +1,42 @@
+with Ada.Text_IO;
+
+procedure Mod_Inv is
+
+   procedure X_GCD(A, B: in Natural; D, X, Y: out Integer) is
+      -- the Extended Euclidean Algorithm
+      -- finds (D, X, Y) with D = GCD(A, B) = A*X + B*Y
+      R: Natural := A mod B;
+   begin
+      if R=0 then
+         D := B;
+         X := 0;
+         Y := 1;
+      else
+         X_GCD(B, R, D, Y, X);
+         Y := Y - (A/B)*X;
+      end if;
+   end X_GCD;
+
+   function Inverse(A, M: Integer) return Integer is
+      -- computes the multiplicative inverse of A mod M, using X_GCD
+      Result, GCD, Dummy: Integer;
+   begin
+      X_GCD(A, M, GCD, Result, Dummy);
+      if GCD /= 1 then -- inverse does not exist!
+         raise Constraint_Error with
+           "GCD (" & Integer'Image(A) & "," & Integer'Image(M) & " ) =" &
+           Integer'Image(GCD) & " /= 1";
+      else -- make sure Result is in {0, ..., M-1}
+         if Result < 0 then
+            return Result+M;
+         else
+            return Result;
+         end if;
+      end if;
+   end Inverse;
+
+begin
+   Ada.Text_IO.Put_Line(Natural'Image(Inverse(42, 2017)));
+   -- Ada.Text_IO.Put_Line(Natural'Image(Inverse(154, 3311)));
+   -- The above would raise CONSTRAINT_ERROR : GCD ( 154, 3311 ) = 77 /= 1
+end Mod_Inv;