June 2018 Update

Task/Modular-inverse/Modula-2/modular-inverse.mod2

@@ -0,0 +1,43 @@
+MODULE ModularInverse;
+  FROM InOut IMPORT WriteString, WriteInt, WriteLn;
+
+  TYPE Data = RECORD x : INTEGER;
+                     y : INTEGER
+              END;
+
+  VAR c  : INTEGER;
+      ab : ARRAY [1..5] OF Data;
+
+PROCEDURE mi(VAR a, b : INTEGER): INTEGER;
+  VAR t, nt, r, nr, q, tmp : INTEGER;
+
+BEGIN
+  b := ABS(b);
+  IF a < 0 THEN a := b - (-a MOD b) END;
+  t := 0; nt := 1; r := b; nr := a MOD b;
+  WHILE (nr # 0) DO
+    q := r / nr;
+    tmp := nt; nt := t - q * nt; t := tmp;
+    tmp := nr; nr := r - q * nr; r := tmp;
+  END;
+  IF (r > 1) THEN RETURN -1 END;
+  IF (t < 0) THEN RETURN t + b END;
+  RETURN t;
+END mi;
+
+BEGIN
+  ab[1].x := 42;   ab[1].y := 2017;
+  ab[2].x := 40;   ab[2].y := 1;
+  ab[3].x := 52;   ab[3].y := -217;
+  ab[4].x := -486; ab[4].y := 217;
+  ab[5].x := 40;   ab[5].y := 2018;
+  WriteLn;
+  WriteString("Modular inverse");
+  WriteLn;
+  FOR c := 1 TO 5 DO
+    WriteInt(ab[c].x, 6); WriteString(", ");
+    WriteInt(ab[c].y, 6); WriteString(" = ");
+    WriteInt(mi(ab[c].x, ab[c].y),6);
+    WriteLn;
+  END;
+END ModularInverse.