From 7d26a7e762eb82c3c9f0daa169d58f6c5381c4b1 Mon Sep 17 00:00:00 2001
From: amosgarner <aagarner.7@gmail.com>
Date: Mon, 29 Oct 2018 23:16:11 -0400
Subject: [PATCH] Implement PHP Fizzbuzz W/ Bitwise Ops.

---
 php/fizzbuzzImproved.php | 73 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 73 insertions(+)
 create mode 100644 php/fizzbuzzImproved.php

diff --git a/php/fizzbuzzImproved.php b/php/fizzbuzzImproved.php
new file mode 100644
index 0000000..db476e0
--- /dev/null
+++ b/php/fizzbuzzImproved.php
@@ -0,0 +1,73 @@
+<?php
+/*
+    Fizzbuzz is cyclical, we can prove this with the equations:
+        n % 3 = (n + 15) % 3
+        n % 5 = (n + 15) % 5
+    This basically says that any number modulas 3 or 5 
+    will be the same value when you add 15.
+
+    So we know that 15 is the max number here so we can create a bit queue
+    from the number of 0 - 15.
+        15 14 13 12 11 10 09 08 07 06 05 04 03 02 01
+        00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
+    if that number is divisible by:
+        neither = 00, 3 = 01, 5 = 10, both = 11
+    so the queue above will become
+        15 14 13 12 11 10 09 08 07 06 05 04 03 02 01
+        11 00 00 01 00 10 01 00 00 01 10 00 01 00 00
+    Do you see a pattern? This binary number equals 810092048 in decimal 
+    and that will be our queue.
+    
+    Now that we have this queue system we can check the queue as a whole using bitwise ops
+    against the value of 3. If the result of that check is 0 then we display a counter, 
+    else we display the proper message from the messages array. 
+    You will see that the index of those values map to the values
+    returned when doing a bitwise comparison for 3 and 5.
+
+    To use the queue we will shift the queue value to the right by two bits.
+    Then we will add the value of the queue after the bitwise and check
+    to the end of the queue by doing an or operation on the queue 
+    and shifting by 28 digits. (30 - 2 = 28)
+
+    EX 1:
+    15 14 13 12 11 10 09 08 07 06 05 04 03 02 01
+    11 00 00 01 00 10 01 00 00 01 10 00 01 00 00
+&
+    00 00 00 00 00 00 00 00 00 00 00 00 00 00 11
+    --------------------------------------------
+                                            [00]
+    EX 2:
+    15 14 13 12 11 10 09 08 07 06 05 04 03 02 01
+    00 00 11 00 00 01 00 10 01 00 00 01 10 00 01 
+&
+    00 00 00 00 00 00 00 00 00 00 00 00 00 00 11
+    --------------------------------------------
+                                            [01]
+    EX 3:
+    15 14 13 12 11 10 09 08 07 06 05 04 03 02 01
+    00 01 00 00 11 00 00 01 00 10 01 00 00 01 10
+&
+    00 00 00 00 00 00 00 00 00 00 00 00 00 00 11
+    --------------------------------------------
+                                            [10]
+*/
+
+function fizzbuzz($counter){
+    $messages = array(null, "Fizz", "Buzz", "FizzBuzz");
+    $queueMask = 810092048;
+    for($i = 1; $i <= $counter; $i++){
+        $value = $queueMask & 3;
+        if($value > 0){
+            print($messages[$value]."\n");
+        }else{
+            print($i."\n");
+        }
+        $queueMask = $queueMask >> 2 | $value << 28;
+    }
+}
+fizzbuzz(100);
+
+/*
+TBA: This solution is difficult to grok and only serves one purpose...
+to confuse the hell out of any one giving you a programming test.
+*/
\ No newline at end of file