Initial data commit

Task/Modular-arithmetic/Go/modular-arithmetic.go

@@ -0,0 +1,63 @@
+package main
+
+import "fmt"
+
+// Define enough of a ring to meet the needs of the task.  Addition and
+// multiplication are mentioned in the task; multiplicative identity is not
+// mentioned but is useful for the power function.
+
+type ring interface {
+    add(ringElement, ringElement) ringElement
+    mul(ringElement, ringElement) ringElement
+    mulIdent() ringElement
+}
+
+type ringElement interface{}
+
+// Define a power function that works for any ring.
+
+func ringPow(r ring, a ringElement, p uint) (pow ringElement) {
+    for pow = r.mulIdent(); p > 0; p-- {
+        pow = r.mul(pow, a)
+    }
+    return
+}
+
+// The task function f has that constant 1 in it.
+// Define a special kind of ring that has this element.
+
+type oneRing interface {
+    ring
+    one() ringElement // return ring element corresponding to '1'
+}
+
+// Now define the required function f.
+// It works for any ring (that has a "one.")
+
+func f(r oneRing, x ringElement) ringElement {
+    return r.add(r.add(ringPow(r, x, 100), x), r.one())
+}
+
+// With rings and the function f defined in a general way, now define
+// the specific ring of integers modulo n.
+
+type modRing uint // value is congruence modulus n
+
+func (m modRing) add(a, b ringElement) ringElement {
+    return (a.(uint) + b.(uint)) % uint(m)
+}
+
+func (m modRing) mul(a, b ringElement) ringElement {
+    return (a.(uint) * b.(uint)) % uint(m)
+}
+
+func (modRing) mulIdent() ringElement { return uint(1) }
+
+func (modRing) one() ringElement { return uint(1) }
+
+// Demonstrate the general function f on the specific ring with the
+// specific values.
+
+func main() {
+    fmt.Println(f(modRing(13), uint(10)))
+}