YAPC::EU 2018 Glasgow Update!

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

@@ -5,7 +5,8 @@ procedure modular_inverse is
   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));
+    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;

Task/Modular-inverse/FreeBASIC/modular-inverse.freebasic

@@ -0,0 +1,75 @@
+' version 10-07-2018
+' compile with: fbc -s console
+
+Type ext_euclid
+    Dim As Integer a, b
+End Type
+
+' "Table method" aka "The Magic Box"
+Function magic_box(x As Integer, y As Integer) As ext_euclid
+
+    Dim As Integer a(1 To 128), b(1 To 128), d(1 To 128), k(1 To 128)
+
+    a(1) = 1 : b(1) = 0 : d(1) = x
+    a(2) = 0 : b(2) = 1 : d(2) = y : k(2) = x \ y
+
+    Dim As Integer i = 2
+
+    While Abs(d(i)) <> 1
+        i += 1
+        a(i) = a(i -2) - k(i -1) * a(i -1)
+        b(i) = b(i -2) - k(i -1) * b(i -1)
+        d(i) = d(i -2) Mod d(i -1)
+        k(i) = d(i -1) \ d(i)
+        'Print a(i),b(i),d(i),k(i)
+        If d(i -1) Mod d(i) = 0 Then Exit While
+    Wend
+
+    If d(i) = -1 Then '  -1 * (ab + by) = -1 * -1 ==> -ab -by = 1
+        a(i) = -a(i)
+        b(i) = -b(i)
+    End If
+
+    Function = Type( a(i), b(i) )
+
+End Function
+' ------=< MAIN >=------
+
+Dim As Integer x, y, gcd
+Dim As ext_euclid result
+
+Do
+    Read x, y
+    If x = 0 AndAlso y = 0 Then Exit Do
+    result = magic_box(x, y)
+    With result
+        gcd = .a * x + .b * y
+        Print "a * "; Str(x); " + b * "; Str(y);
+        Print " = GCD("; Str(x); ", "; Str(y); ") ="; gcd
+        If gcd > 1 Then
+            Print "No solution, numbers are not coprime"
+        Else
+            Print "a = "; .a; ", b = ";.b
+            Print "The Modular inverse of "; x; " modulo "; y; " = ";
+            While .a < 0 : .a += IIf(y > 0, y, -y) : Wend
+            Print .a
+            'Print "The Modular inverse of "; y; " modulo "; x; " = ";
+            'While .b < 0 : .b += IIf(x > 0, x, -x) : Wend
+            'Print .b
+        End if
+    End With
+    Print
+Loop
+
+Data 42, 2017
+Data 40, 1
+Data 52, -217
+Data -486, 217
+Data 40, 2018
+Data 0, 0
+
+' empty keyboard buffer
+While Inkey <> "" : Wend
+Print : Print "hit any key to end program"
+Sleep
+End