September 2017 Update

Task/Modular-inverse/Ada/modular-inverse-1.ada

@@ -1,11 +0,0 @@
-package Mod_Inv is
-
-   procedure X_GCD(A, B: in Natural; D, X, Y: out Integer);
-      -- the Extended Euclidean Algorithm
-      -- finds (D, X, Y) with D = GCD(A, B) = A*X + B*Y
-
-   function Inverse(A, M: Integer) return Integer;
-      -- computes the multiplicative inverse Inv_A of A mod M, using X_GCD
-      -- raises Constraint_Error if Inv_A does not exist
-
-end Mod_Inv;

Task/Modular-inverse/Ada/modular-inverse-2.ada

@@ -1,36 +0,0 @@
-package body 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;
-
-end Mod_Inv;

Task/Modular-inverse/Ada/modular-inverse-3.ada

@@ -1,9 +0,0 @@
-with Ada.Text_IO; with Mod_Inv; use Mod_Inv, Ada.text_IO;
-
-procedure Mod_Inv_Test is
-begin
-   -- Put_Line(Natural'Image(Inverse(154, 3311)));
-   -- The above would raise CONSTRAINT_ERROR : GCD ( 154, 3311 ) = 77 /= 1
-
-   Put_Line(Natural'Image(Inverse(42, 2017)));
-end Mod_Inv_Test;

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

@@ -0,0 +1,18 @@
+with Ada.Text_IO;use Ada.Text_IO;
+procedure modular_inverse is
+  -- inv_mod calculates the inverse of a mod n. We should have n>0 and, at the end, the contract is a*Result=1 mod n
+  -- If this is false then we raise an exception (don't forget the -gnata option when you compile
+  function inv_mod (a : Integer; n : Positive) return Integer with post=> (a * inv_mod'Result) mod n = 1 is
+    -- To calculate the inverse we do as if we would calculate the GCD with the Euclid extended algorithm
+    -- (but we just keep the coefficient on a)
+    function inverse (a, b, u, v : Integer) return Integer is (if b=0 then u else inverse (b, a mod b, v, u-(v*a)/b));
+  begin
+    return inverse (a, n, 1, 0);
+  end inv_mod;
+begin
+  -- This will output -48 (which is correct)
+  Put_Line (inv_mod (42,2017)'img);
+  -- The further line will raise an exception since the GCD will not be 1
+  Put_Line (inv_mod (42,77)'img);
+  exception when others => Put_Line ("The inverse doesn't exist.");
+end bitmap;

Task/Modular-inverse/Kotlin/modular-inverse.kotlin

@@ -0,0 +1,9 @@
+// version 1.0.6
+
+import java.math.BigInteger
+
+fun main(args: Array<String>) {
+    val a = BigInteger.valueOf(42)
+    val m = BigInteger.valueOf(2017)
+    println(a.modInverse(m))
+}

Task/Modular-inverse/Zkl/modular-inverse.zkl

@@ -0,0 +1,5 @@
+fcn gcdExt(a,b){
+   if(b==0) return(1,0,a);
+   q,r:=a.divr(b); s,t,g:=gcdExt(b,r); return(t,s-q*t,g);
+}
+fcn modInv(a,m){i,_,g:=gcdExt(a,m); if(g==1) {if(i<0)i+m} else Void}