Merge pull request #40 from DanexCodr/copilot/add-linear-recurrence-closed-form

Make linear-recurrence array access O(1) / amortized O(1)

Author: DanexCodr

src/main/cod/src/main/test/LinearRecurrenceOptimization.cod

@@ -0,0 +1,37 @@
+unit test
+
+share main() {
+    out("=== Linear recurrence optimization ===")
+    start := timer()
+
+    fib := [0 to 2000]
+    fib[0] = 0
+    fib[1] = 1
+    for i of [2 to 2000] {
+        fib[i] = fib[i-1] + fib[i-2]
+    }
+    out("fib-metadata=" + fib)
+    out("fib[10]=" + fib[10] + " expected=55")
+    out("fib[20]=" + fib[20] + " expected=6765")
+    out("fib[30]=" + fib[30] + " expected=832040")
+
+    jac := [0 to 2000]
+    jac[0] = 0
+    jac[1] = 1
+    for i of [2 to 2000] {
+        jac[i] = jac[i-1] + 2 * jac[i-2]
+    }
+    out("jac[10]=" + jac[10] + " expected=341")
+    out("jac[20]=" + jac[20] + " expected=349525")
+
+    shift := [0 to 2000]
+    shift[0] = 0
+    shift[1] = 1
+    for i of [2 to 2000] {
+        shift[i] = shift[i-1] + shift[i-2] + 5
+    }
+    out("shift[2]=" + shift[2] + " expected=6")
+    out("shift[3]=" + shift[3] + " expected=12")
+    out("shift[10]=" + shift[10] + " expected=495")
+    out("elapsed_ms=" + (timer() - start))
+}