September 2017 Update

Task/Fibonacci-sequence/Python/fibonacci-sequence-9.py

@@ -1,7 +1,30 @@
-def fib(n, c={0:1, 1:1}):
-    if n not in c:
-        x = n // 2
-        c[n] = fib(x-1) * fib(n-x-1) + fib(x) * fib(n - x)
-    return c[n]
+def prevPowTwo(n):
+    'Gets the power of two that is less than or equal to the given input'
+    if ((n & -n) == n):
+        return n
+    else:
+        n -= 1
+        n |= n >> 1
+        n |= n >> 2
+        n |= n >> 4
+        n |= n >> 8
+        n |= n >> 16
+        n += 1
+        return (n/2)
 
-fib(10000000)  # calculating it takes a few seconds, printing it takes eons
+def crazyFib(n):
+    'Crazy fast fibonacci number calculation'
+    powTwo = prevPowTwo(n)
+
+    q = r = i = 1
+    s = 0
+
+    while(i < powTwo):
+        i *= 2
+        q, r, s = q*q + r*r, r * (q + s), (r*r + s*s)
+
+    while(i < n):
+        i += 1
+        q, r, s = q+r, q, r
+
+    return q