Data commit

Task/Fibonacci-sequence/C-sharp/fibonacci-sequence-1.cs

@@ -0,0 +1,3 @@
+public static ulong Fib(uint n) {
+    return (n < 2)? n : Fib(n - 1) + Fib(n - 2);
+}

Task/Fibonacci-sequence/C-sharp/fibonacci-sequence-10.cs

@@ -0,0 +1,6 @@
+public static ulong Fib(uint n) {
+    var M = new Matrix(1,0,0,1);
+    var N = new Matrix(1,1,1,0);
+    for (uint i = 1; i < n; i++) M *= N;
+    return (ulong)M[0][0];
+}

Task/Fibonacci-sequence/C-sharp/fibonacci-sequence-11.cs

@@ -0,0 +1,16 @@
+private static Matrix M;
+private static readonly Matrix N = new Matrix(1,1,1,0);
+
+public static ulong Fib(uint n) {
+    M = new Matrix(1,0,0,1);
+    MatrixPow(n-1);
+    return (ulong)M[0][0];
+}
+
+private static void MatrixPow(double n){
+    if (n > 1) {
+        MatrixPow(n/2);
+        M *= M;
+    }
+    if (n % 2 == 0) M *= N;
+}

Task/Fibonacci-sequence/C-sharp/fibonacci-sequence-12.cs

@@ -0,0 +1,17 @@
+private static int[] fibs = new int[]{ -1836311903, 1134903170,
+  -701408733, 433494437, -267914296, 165580141, -102334155,
+  63245986, -39088169, 24157817, -14930352, 9227465, -5702887,
+  3524578, -2178309, 1346269, -832040, 514229, -317811, 196418,
+  -121393, 75025, -46368, 28657, -17711, 10946, -6765, 4181,
+  -2584, 1597, -987, 610, -377, 233, -144, 89, -55, 34, -21, 13,
+  -8, 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,
+  144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711,
+  28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040,
+  1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817,
+  39088169, 63245986, 102334155, 165580141, 267914296, 433494437,
+  701408733, 1134903170, 1836311903};
+
+public static int Fib(int n) {
+    if(n < -46 || n > 46) throw new ArgumentOutOfRangeException("n", n, "Has to be between -46 and 47.")
+    return fibs[n+46];
+}

Task/Fibonacci-sequence/C-sharp/fibonacci-sequence-13.cs

@@ -0,0 +1,44 @@
+using System;
+using System.Collections.Generic;
+using BI = System.Numerics.BigInteger;
+
+class Program
+{
+    // A sparse array of values calculated along the way
+    static SortedList<int, BI> sl = new SortedList<int, BI>();
+
+    // This routine is semi-recursive, but doesn't need to evaluate every number up to n.
+    // Algorithm from here: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibFormula.html#section3
+    static BI Fsl(int n)
+    {
+        if (n < 2) return n;
+        int n2 = n >> 1, pm = n2 + ((n & 1) << 1) - 1; IfNec(n2); IfNec(pm);
+        return n2 > pm ? (2 * sl[pm] + sl[n2]) * sl[n2] : sqr(sl[n2]) + sqr(sl[pm]);
+        // Helper routine for Fsl(). It adds an entry to the sorted list when necessary
+        void IfNec(int x) { if (!sl.ContainsKey(x)) sl.Add(x, Fsl(x)); }
+        // Helper function to square a BigInteger
+        BI sqr(BI x) { return x * x; }
+    }
+
+    // Conventional iteration method (not used here)
+    public static BI Fm(BI n)
+    {
+        if (n < 2) return n; BI cur = 0, pre = 1;
+        for (int i = 0; i <= n - 1; i++) { BI sum = cur + pre; pre = cur; cur = sum; }
+        return cur;
+    }
+
+    public static void Main()
+    {
+        int num = 2_000_000, digs = 35, vlen;
+        var sw = System.Diagnostics.Stopwatch.StartNew(); var v = Fsl(num); sw.Stop();
+        Console.Write("{0:n3} ms to calculate the {1:n0}th Fibonacci number, ",
+          sw.Elapsed.TotalMilliseconds, num);
+        Console.WriteLine("number of digits is {0}", vlen = (int)Math.Ceiling(BI.Log10(v)));
+        if (vlen < 10000) {
+            sw.Restart(); Console.WriteLine(v); sw.Stop();
+            Console.WriteLine("{0:n3} ms to write it to the console.", sw.Elapsed.TotalMilliseconds);
+        } else
+            Console.Write("partial: {0}...{1}", v / BI.Pow(10, vlen - digs), v % BI.Pow(10, digs));
+    }
+}

Task/Fibonacci-sequence/C-sharp/fibonacci-sequence-14.cs

@@ -0,0 +1,29 @@
+using System;
+using BI = System.Numerics.BigInteger;
+
+class Program {
+
+  // returns the nth Fibonacci number without calculating 0..n-1
+  static BI oneFib(int n) {
+    BI z = (BI)1 << ++n;
+    return BI.ModPow(z, n, (z << n) - z - 1) % z;
+  }
+
+  // returns an array of Fibonacci numbers from the 0th to the nth
+  static BI[] fibTab(int n) {
+    var res = new BI[++n];
+    BI z = (BI)1 << 1, zz = z << 1;
+    for (int i = 0; i < n; ) {
+      res[i] = BI.ModPow(z, ++i, zz - z - 1) % z;
+      z <<= 1; zz <<= 2;
+    }
+    return res;
+  }
+
+  static void Main(string[] args) {
+    int n = 20;
+    Console.WriteLine("Fibonacci numbers 0..{0}: {1}", n, string.Join(" ",fibTab(n)));
+    n = 1000;
+    Console.WriteLine("Fibonacci({0}): {1}", n, oneFib(n));
+  }
+}

Task/Fibonacci-sequence/C-sharp/fibonacci-sequence-2.cs

@@ -0,0 +1,7 @@
+public static ulong Fib(uint n) {
+    return Fib(0, 1, n);
+}
+
+private static ulong Fib(ulong a, ulong b, uint n) {
+    return (n < 1)? a :(n == 1)?  b : Fib(b, a + b, n - 1);
+}

Task/Fibonacci-sequence/C-sharp/fibonacci-sequence-3.cs

@@ -0,0 +1,13 @@
+public static ulong Fib(uint x) {
+    if (x == 0) return 0;
+
+    ulong prev = 0;
+    ulong next = 1;
+    for (int i = 1; i < x; i++)
+    {
+        ulong sum = prev + next;
+        prev = next;
+        next = sum;
+    }
+    return next;
+}

Task/Fibonacci-sequence/C-sharp/fibonacci-sequence-4.cs

@@ -0,0 +1,11 @@
+using System; using System.Text; // FIBRUS.cs Russia
+namespace Fibrus { class Program { static void Main()
+{ long fi1=1; long fi2=1; long fi3=1; int da; int i; int d;
+for (da=1; da<=78; da++) // rextester.com/MNGUV70257
+    { d = 20-Convert.ToInt32((Convert.ToString(fi3)).Length);
+    for (i=1; i<d; i++) Console.Write(".");
+Console.Write(fi3); Console.Write(" "); Console.WriteLine(da);
+    fi3 = fi2 + fi1;
+    fi1 = fi2;
+    fi2 = fi3;
+}}}}

Task/Fibonacci-sequence/C-sharp/fibonacci-sequence-5.cs

@@ -0,0 +1,14 @@
+public static IEnumerable<long> Fibs(uint x) {
+    IList<ulong> fibs = new List<ulong>();
+
+    ulong prev = -1;
+    ulong next = 1;
+    for (int i = 0; i < x; i++)
+    {
+     long sum = prev + next;
+        prev = next;
+        next = sum;
+        fibs.Add(sum);
+    }
+    return fibs;
+}

Task/Fibonacci-sequence/C-sharp/fibonacci-sequence-6.cs

@@ -0,0 +1,10 @@
+public static IEnumerable<ulong> Fibs(uint x) {
+    ulong prev = -1;
+    ulong next = 1;
+    for (uint i = 0; i < x; i++) {
+        ulong sum = prev + next;
+        prev = next;
+        next = sum;
+        yield return sum;
+    }
+}

Task/Fibonacci-sequence/C-sharp/fibonacci-sequence-7.cs

@@ -0,0 +1,6 @@
+static double r5 = Math.Sqrt(5.0), Phi = (r5 + 1.0) / 2.0;
+
+static ulong fib(uint n) {
+    if (n > 71) throw new ArgumentOutOfRangeException("n", n, "Needs to be smaller than 72.");
+    double r = Math.Pow(Phi, n) / r5;
+    return (ulong)(n < 64 ? Math.Round(r) : Math.Floor(r)); }

Task/Fibonacci-sequence/C-sharp/fibonacci-sequence-8.cs

@@ -0,0 +1,16 @@
+static decimal Sqrt_dec(decimal x, decimal g) { decimal t, lg;
+    do { t = x / g; lg = g; g = (t + g) / 2M; } while (lg != g);
+    return g; }
+
+static decimal Pow_dec (decimal bas, uint exp) {
+    if (exp == 0) return 1M;
+    decimal tmp = Pow_dec(bas, exp >> 1); tmp *= tmp;
+    if ((exp & 1) == 1) tmp *= bas; return tmp; }
+
+static decimal r5 = Sqrt_dec(5.0M, (decimal)Math.Sqrt(5.0)),
+               Phi = (r5 + 1.0M) / 2.0M;
+
+static ulong fib(uint n) {
+    if (n > 93) throw new ArgumentOutOfRangeException("n", n, "Needs to be smaller than 94.");
+    decimal r = Pow_dec(Phi, n) / r5;
+    return (ulong)(n < 64 ? Math.Round(r) : Math.Floor(r)); }

Task/Fibonacci-sequence/C-sharp/fibonacci-sequence-9.cs

@@ -0,0 +1,16 @@
+static decimal Sqrt_dec(decimal x, decimal g) { decimal t, lg;
+    do { t = x / g; lg = g; g = (t + g) / 2M; } while (lg != g);
+    return g; }
+
+static decimal Pow_dec (decimal bas, uint exp) {
+    if (exp == 0) return 1M;
+    decimal tmp = Pow_dec(bas, exp >> 1); tmp *= tmp;
+    if ((exp & 1) == 1) tmp *= bas; return tmp; }
+
+static decimal r5 = Sqrt_dec(5.0M, (decimal)Math.Sqrt(5.0)),
+               Phi = (r5 + 1.0M) / 2.0M;
+
+static decimal fib(uint n) {
+    if (n > 128) throw new ArgumentOutOfRangeException("n", n, "Needs to be smaller than 129.");
+    decimal r = Pow_dec(Phi, n) / r5;
+    return n < 64 ? Math.Round(r) : Math.Floor(r); }