{"id":3492,"date":"2013-10-11T11:41:23","date_gmt":"2013-10-11T15:41:23","guid":{"rendered":"http:\/\/jdhitsolutions.com\/blog\/?p=3492"},"modified":"2013-10-10T15:43:53","modified_gmt":"2013-10-10T19:43:53","slug":"friday-fun-pi-romania","status":"publish","type":"post","link":"https:\/\/jdhitsolutions.com\/blog\/powershell\/3492\/friday-fun-pi-romania\/","title":{"rendered":"Friday Fun: Pi-romania"},"content":{"rendered":"

\"\"I was doing some benchmarks the other day, and one of the tests was a calculation of pi using a particular algorithm. I found that quite interesting and naturally this made me curious if I could do the same calculation in PowerShell. Of course, if all you need is the value of pi, that is easily obtained with the [Math] .NET class.<\/p>\n

PS C:\\> [math]::pi\r\n3.14159265358979<\/pre>\n
But this Friday Fun is as much about the journey as anything. I started with finding an algorithm I could use to calculate pi. I decided to use the Gauss-Legendre algorithm<\/a>. The general process is to iterate through a series of equations, each pass getting you closer to pi.<\/p>\n
\"\"<\/a>
The Gauss-Legendre Algorithm<\/figcaption><\/figure>\n
Pi is then calculated like this:<\/p>\n
\"\"
calculating pi with the Gauss-Legendre algorithm<\/figcaption><\/figure>\n
From my research, I knew what the starting values should be. For reasons that will become clear in a moment, I explicitly defined my variables as arrays.<\/p>\n
$a = @(1)\r\n$b = @(1\/[math]::Sqrt(2))\r\n$t = @(1\/4)\r\n$p = @(1)<\/pre>\n
As you can see, I still need to rely on the [Math] class for things like the square root of 2. Now the fun part. The algorithm loops and each subsequent value of a variable is based on a calculation of the current variable. My solution was to use a For loop and run the equations for each variable I also decided to evaluate for pi each time through the loop so I could see how close I was getting.<\/p>\n
for ($n=0;$n -lt 3;$n++) {\r\n#each time through the array add a new value to each array using the += operator\r\n$a+= ($a[$n]+$b[$n])\/2\r\n$b+= [math]::Sqrt(($a[$n]*$b[$n]))\r\n$t+= $t[$n] - ($p[$n] * ([math]::Pow(($a[$n] - $a[$n+1]),2)))\r\n$p+= 2*$p[$n]\r\n([math]::Pow($a[$n+1] +$b[$n+1],2))\/(4 *($t[$n+1]))\r\n}<\/pre>\n
This worked out nicely because $n can serve as the index number for each calculated variable so that I can get the correct ones for the final calculation. The for loop starts with $n=0 and loops while $n is less than or equal to 3. Each time through the loop, $n is incremented by 1 ($n++). You may be wondering why I'm only looping until 3. Well, here's what happens when I run my little script.<\/p>\n
\r\nPS C:\\> Get-Pi.ps1\r\n3.14057925052217\r\n3.14159264621354\r\n3.14159265358979<\/pre>\n
No matter how many more times I run the loop, I won't get a value any more precise than 3.14159265358979 which just happens to be the same value as [math]::pi. I thought there might be a way to force PowerShell or .NET to run the calculation to more decimal places but that's a bit beyond my .NET pay grade apparently. But I hoped you picked up something about the For construct or arrays. And don't ask me about the math.I can punch in the numbers but I have no idea what it all means. But I had fun and hope you do to.<\/p>\n","protected":false},"excerpt":{"rendered":"
I was doing some benchmarks the other day, and one of the tests was a calculation of pi using a particular algorithm. I found that quite interesting and naturally this made me curious if I could do the same calculation in PowerShell. 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Pipe something to Get-Member and you can discover all of the object's properties and methods (ie its members). Some objects, like strings, have many methods but very few properties. Some\u2026","rel":"","context":"In "Friday Fun"","block_context":{"text":"Friday Fun","link":"https:\/\/jdhitsolutions.com\/blog\/category\/friday-fun\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/jdhitsolutions.com\/blog\/wp-content\/uploads\/2011\/11\/gno-300x205.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":633,"url":"https:\/\/jdhitsolutions.com\/blog\/scripting\/633\/bool-vs-switch\/","url_meta":{"origin":3492,"position":4},"title":"Bool vs Switch","author":"Jeffery Hicks","date":"April 30, 2010","format":false,"excerpt":"I have to say I\u2019m generally impressed with the quality of submissions to this year\u2019s Scripting Games. But there is a recurring concept that some people are using and I think there\u2019s a better way. 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