Data commit

Task/Modular-inverse/ALGOL-68/modular-inverse.alg

@@ -0,0 +1,35 @@
+BEGIN
+   PROC modular inverse = (INT a, m) INT :
+   BEGIN
+      PROC extended gcd = (INT x, y) []INT :
+CO
+   Algol 68 allows us to return three INTs in several ways.  A [3]INT
+   is used here but it could just as well be a STRUCT.
+CO
+      BEGIN
+	 INT v := 1, a := 1, u := 0, b := 0, g := x, w := y;
+	 WHILE w>0
+	 DO
+	    INT q := g % w, t := a - q * u;
+	    a := u; u := t;
+	    t := b - q * v;
+	    b := v; v := t;
+	    t := g - q * w;
+	    g := w; w := t
+	 OD;
+	 a PLUSAB (a < 0 | u | 0);
+	 (a, b, g)
+      END;
+      [] INT egcd = extended gcd (a, m);
+      (egcd[3] > 1 | 0 | egcd[1] MOD m)
+   END;
+   printf (($"42 ^ -1 (mod 2017) = ", g(0)$, modular inverse (42, 2017)))
+CO
+   Note that if ϕ(m) is known, then a^-1 = a^(ϕ(m)-1) mod m which
+   allows an alternative implementation in terms of modular
+   exponentiation but, in general, this requires the factorization of
+   m.  If m is prime the factorization is trivial and ϕ(m) = m-1.
+   2017 is prime which may, or may not, be ironic within the context
+   of the Rosetta Code conditions.
+CO
+END