Data update

Task/Modular-arithmetic/00-TASK.txt

@@ -19,4 +19,6 @@ You will use <math>13</math> as the congruence modulus and you will compute <mat
 It is important that the function <math>f</math> is agnostic about whether or not its argument is modular; it should behave the same way with normal and modular integers.  
 In other words, the function is an algebraic expression that could be used with any ring, not just integers.
 <br><br>
-
+;Related tasks:
+[[Modular exponentiation]]
+<br><br>

Task/Modular-arithmetic/FreeBASIC/modular-arithmetic.basic

@@ -0,0 +1,50 @@
+Type ModInt
+    As Ulongint Value
+    As Ulongint Modulo
+End Type
+
+Function Add_(lhs As ModInt, rhs As ModInt) As ModInt
+    If lhs.Modulo <> rhs.Modulo Then Print "Cannot add rings with different modulus": End
+    Dim res As ModInt
+    res.Value = (lhs.Value + rhs.Value) Mod lhs.Modulo
+    res.Modulo = lhs.Modulo
+    Return res
+End Function
+
+Function Multiply(lhs As ModInt, rhs As ModInt) As ModInt
+    If lhs.Modulo <> rhs.Modulo Then Print "Cannot multiply rings with different modulus": End
+    Dim res As ModInt
+    res.Value = (lhs.Value * rhs.Value) Mod lhs.Modulo
+    res.Modulo = lhs.Modulo
+    Return res
+End Function
+
+Function One(self As ModInt) As ModInt
+    Dim res As ModInt
+    res.Value = 1
+    res.Modulo = self.Modulo
+    Return res
+End Function
+
+Function Power(self As ModInt, p As Ulongint) As ModInt
+    If p < 0 Then Print "p must be zero or greater": End
+    Dim pp As Ulongint = p
+    Dim pwr As ModInt = One(self)
+    While pp > 0
+        pp -= 1
+        pwr = Multiply(pwr, self)
+    Wend
+    Return pwr
+End Function
+
+Function F(x As ModInt) As ModInt
+    Return Add_(Power(x, 100), Add_(x, One(x)))
+End Function
+
+Dim x As ModInt
+x.Value = 10
+x.Modulo = 13
+Dim y As ModInt = F(x)
+Print Using "x ^ 100 + x + 1 for x = ModInt(&, &) is ModInt(&, &)"; x.Value; x.Modulo; y.Value; y.Modulo
+
+Sleep