March 2014 update

Task/Fibonacci-sequence/D/fibonacci-sequence-2.d

@@ -1,4 +1,4 @@
-import std.stdio, std.bigint;
+import std.bigint;
 
 T fibonacciMatrix(T=BigInt)(size_t n) {
     int[size_t.sizeof * 8] binDigits;
@@ -26,5 +26,5 @@ T fibonacciMatrix(T=BigInt)(size_t n) {
 }
 
 void main() {
-    writeln(fibonacciMatrix(1_000_000));
+    10_000_000.fibonacciMatrix;
 }

Task/Fibonacci-sequence/D/fibonacci-sequence-3.d

@@ -0,0 +1,44 @@
+import std.bigint, std.math;
+
+// Algorithm from: Takahashi, Daisuke,
+// "A fast algorithm for computing large Fibonacci numbers".
+// Information Processing Letters 75.6 (30 November 2000): 243-246.
+// Implementation from:
+// pythonista.wordpress.com/2008/07/03/pure-python-fibonacci-numbers
+BigInt fibonacci(in ulong n)
+in {
+    assert(n > 0, "fibonacci(n): n must be > 0.");
+} body {
+    if (n <= 2)
+        return 1.BigInt;
+    BigInt F = 1;
+    BigInt L = 1;
+    int sign = -1;
+    immutable uint n2 = cast(uint)n.log2.floor;
+    auto mask = 2.BigInt ^^ (n2 - 1);
+    foreach (immutable i; 1 .. n2) {
+        auto temp = F ^^ 2;
+        F = (F + L) / 2;
+        F = 2 * F ^^ 2 - 3 * temp - 2 * sign;
+        L = 5 * temp + 2 * sign;
+        sign = 1;
+        if (n & mask) {
+            temp = F;
+            F = (F + L) / 2;
+            L = F + 2 * temp;
+            sign = -1;
+        }
+        mask /= 2;
+    }
+    if ((n & mask) == 0) {
+        F *= L;
+    } else {
+        F = (F + L) / 2;
+        F = F * L - sign;
+    }
+    return F;
+}
+
+void main() {
+    10_000_000.fibonacci;
+}