June 2018 Update

Task/Modular-inverse/C-sharp/modular-inverse.cs

@@ -0,0 +1,24 @@
+public class Program
+{
+    static void Main()
+    {
+        System.Console.WriteLine(42.ModInverse(2017));
+    }
+}
+
+public static class IntExtensions
+{
+    public static int ModInverse(this int a, int m)
+    {
+        if (m == 1) return 0;
+        int m0 = m;
+        (int x, int y) = (1, 0);
+
+        while (a > 1) {
+            int q = a / m;
+            (a, m) = (m, a % m);
+            (x, y) = (y, x - q * y);
+        }
+        return x < 0 ? x + m0 : x;
+    }
+}

Task/Modular-inverse/Factor/modular-inverse.factor

@@ -0,0 +1,2 @@
+USE: math.functions
+42 2017 mod-inv

Task/Modular-inverse/GW-BASIC/modular-inverse.gw-basic

@@ -0,0 +1,27 @@
+10 ' Modular inverse
+20 LET E% = 42
+30 LET T% = 2017
+40 GOSUB 1000
+50 PRINT MODINV%
+60 END
+
+990  ' increments e stp (step) times until bal is greater than t
+992  ' repeats until bal = 1 (mod = 1) and returns count
+994  ' bal will not be greater than t + e
+1000 LET D% = 0
+1010 IF E% >= T% THEN GOTO 1140
+1020  LET BAL% = E%
+1025  ' At least one iteration is necessary
+1030  LET STP% = ((T% - BAL%) \ E%) + 1
+1040  LET BAL% = BAL% + STP% * E%
+1050  LET COUNT% = 1 + STP%
+1060  LET BAL% = BAL% - T%
+1070  WHILE BAL% <> 1
+1080   LET STP% = ((T% - BAL%) \ E%) + 1
+1090   LET BAL% = BAL% + STP% * E%
+1100   LET COUNT% = COUNT% + STP%
+1110   LET BAL% = BAL% - T%
+1120  WEND
+1130  LET D% = COUNT%
+1140 LET MODINV% = D%
+1150 RETURN

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.

Task/Modular-inverse/PureBasic/modular-inverse.purebasic

@@ -0,0 +1,37 @@
+EnableExplicit
+Declare main()
+Declare.i mi(a.i, b.i)
+
+If OpenConsole("MODULAR-INVERSE")
+  main() : Input() : End
+EndIf
+
+Macro ModularInverse(a, b)
+  PrintN(~"\tMODULAR-INVERSE(" + RSet(Str(a),5) + "," +
+         RSet(Str(b),5)+") = " +
+         RSet(Str(mi(a, b)),5))
+EndMacro
+
+Procedure main()
+  ModularInverse(42, 2017)  ; = 1969
+  ModularInverse(40, 1)     ; = 0
+  ModularInverse(52, -217)  ; = 96
+  ModularInverse(-486, 217) ; = 121
+  ModularInverse(40, 2018)  ; = -1
+EndProcedure
+
+Procedure.i mi(a.i, b.i)
+  Define x.i = 1,
+         y.i = Int(Abs(b)),
+         r.i = 0
+  If y = 1 : ProcedureReturn 0 : EndIf
+  While x < y
+    r = (a * x) % b
+    If r = 1 Or (y + r) = 1
+      Break
+    EndIf
+    x + 1
+  Wend
+  If x > y - 1 : x = -1 : EndIf
+  ProcedureReturn x
+EndProcedure