Add Fibonacci example

examples/fibonacci/README.md

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+# fibonacci.aleo
+
+## Build Guide
+
+To compile this Aleo program, run:
+```bash
+aleo build
+```
+To run this program, run:
+```bash
+leo run fibonacci
+```
+
+## Overview
+This example shows how to calculate Fibonacci number using the fast-doubling method.
+
+It takes the input data from `inputs/fibonacci.in`

examples/fibonacci/inputs/fibonacci.in

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+// The program input for fibonacci/src/main.leo
+[main]
+public n: u128 = 63u128;

examples/fibonacci/program.json

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+{
+    "program": "fibonacci.aleo",
+    "version": "0.0.0",
+    "description": "",
+    "development": {
+        "private_key": "APrivateKey1zkpFebmqLzRHMbtdwensSVNUPDWV6WnYw5JcNsYVLDuu8ig",
+        "address": "aleo1l0l25evjzxac3j4r5xf7uwv3jfnqwll2g9h8j0g5vvk0grnnmq8qexra3d"
+    },
+    "license": "MIT"
+}

examples/fibonacci/src/main.leo

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+program fibonacci.aleo {
+    // This calculates the n-th fibonacci number (up to 64th)
+    transition fibonacci(public n: u128) -> u128 {
+        let f0: u128 = 0u128;
+        let f1: u128 = 1u128;
+        let c: u16 = 0u16;
+
+        let z: u128 = reverse_bits(n);
+
+        for i:u16 in 0u16..8u16 {
+            if n > 0u128 {
+                let f2i1: u128 = f1 * f1 + f0 * f0;
+                let f2i: u128 =  f0 * (2u128 * f1 - f0);
+                if z & 1u128.shl(c) == 0u128 {
+                    f0 = f2i;
+                    f1 = f2i1;
+                } else {
+                    f0 = f2i1;
+                    f1 = f2i + f2i1;
+                }
+                c = c + 1u16;
+                n = n >> 1u16;
+            }
+        }
+
+        return f0;
+    }
+
+    function reverse_bits(n: u128) -> u128 {
+        let reverse: u128 = 0u128;
+ 
+        for i:u128 in 0u128..128u128 {
+            if n > 0u128 {
+                reverse = reverse << 1u16;
+        
+                if n & 1u128 == 1u128 {
+                    reverse ^= 1u128;
+                }
+        
+                n = n >> 1u16;
+            }
+        }
+
+        return reverse;
+    }
+}