Calculate Pi

Programs for Calculating
On Your Own Computer

Super_Pi by Yasumasa Kanada. [ Windows binary available. ]

Pi-AGM by Carey Bloodworth

pi_fft5 by Takuya Ooura.

PiFast33 by Xavier Gourdon.

Quick Pi by Steve Pagliarulo. [ Win 32 binary available. ]

The following programs are generally listed according to the speed at which they compute values of Pi. (The last one listed here being the fastest program!)
Since I'm running Windows 95/DOS 7 on a PC, each program listed here is at least available in an x86 (PC) DOS (or Win32) binary form. Executables for a particular program on another platform may exist, since some of them come with their own open source code! (Consult the program homepages and links listed below.)

1) The easy to run Super_Pi (for MS-Windows™) by Yasumasa Kanada

Download Super_Pi now (in a 72 kb .zip file) and Calculate up to 32 Million digits of Pi. There are twelve different digit-lengths to choose from (see below). Simply extract the files (Super_pi.exe, Super_pi.hlp and Super_pi.txt) into any directory and run the program. The program creates the file pi_rec.txt to keep track of which sizes you've calculated, and the digits are placed into a file called "pi_data.txt" (CAUTION: Each time you calculate a different length of Pi, this file will be overwritten! So rename the file if you want to keep those digits.)

When the program starts, you'll see a window like this:

Click on 'Calculate' and choose one of the twelve sizes (K=1,024 bytes and M=1,048,576 bytes) in the next window. After clicking OK in that window, a 'confirmation' box will pop up.

When you begin a calculation, a " Stop (S) " item will appear on the Menu so you can abort any runs you accidentally started or that are taking too long.

The following pic shows a full run to calculate just 32,768 digits ( the 32K choice) on a 100MHz PC. Time shown: 32 seconds; that's exactly 1024 digits/sec (not very fast). Calculating 512K, took 11m 06s, so the speed went down to only about 787 digits/sec; even worse! You could probably D/L large files of Pi from the Net faster than trying to calculate them on an old computer (less than 300 MHz CPU) with this program; especially if you download those files with over 50% .zip compression.

After reading Carey Bloodworth's comments about Windows 95/98 for calculating Pi, I found out why very few Pi programmers ever bother using the Windows OS (with API functions to draw windows, etc.): It usually causes serious losses in the performance (speed) of your program! Especially if you have an older CPU and not much memory!
On the other hand, most would agree that it's one of the simplest Pi programs for a user to run; so perhaps it should be called 'Easy_Pi' instead.

2) pi-AGM (Arithmetic Geometric Mean Program) by Carey Bloodworth

Check out Carey's Home Page and detailed math descriptions of subroutines that help you build a fast Pi program here:
http://www.bloodworth.org/.

3) pi_fft5 (pi_css5) by Takuya Ooura

4) PiFast33 by Xavier Gourdon

5) QPI-Quick Pi by Steve Pagliarulo

Download: qpi10.zip (only 44kb) Read: QuickPi.txt
A Win 32 console program for i386 or above (PC) computers.

Steve's program is somewhat faster than Xavier Gourdon's; if you keep the number of digits under 8 million (this crossover point may vary a bit for different machines), and eight (8) times faster than that of Kanada's Super_Pi for a 512Kb run!

Besides computing Pi, by adding either the parameter -2 or -e to the command line, this program can also carry out the square-root of 2 (using Newton's iteration method) or compute e (using the series SUM of 1/n!).
For Pi itself, the program can use the following formulas: one from the Chudnovsky brothers [default], a Gauss-Legendre AGM [-a], the Brent-Salamin AGM [-s], or a quartic from the Borwein brothers [-b].

Program usage: qpi [digits] [-2|-e|-a|-s|-b]

Steve included the other Pi methods for verification or comparison purposes, the default (Chudnovsky) is always the fastest of the four! On my old 100MHz machine, I got the following times when calculating 524,288 digits of Pi:

default (Chudnovsky brother's Equ.) =  83.29 seconds
  -a        (Gauss-Legendre AGM) = 170.61 seconds
  -s         (Brent-Salamin AGM) = 209.32 seconds
  -b    (Borwein brother's Quartic) = 257.95 seconds

  Note: For the calculations above...
        The Default method -> Has to compute only:   524,295 Digits
   But, the Gauss-Legendre AGM ->  Has to compute:   715,319 Digits
        using 18 Iterations,
        the Brent-Salamin AGM  ->  Has to compute: 1,011,616 Digits
        using 19 Iterations and
        the Borweins' Quartic  ->  Has to compute:   715,319 Digits
        using  9 Iterations.
   However,
     These other methods must not be actually calculating Pi out to
     these other digit lengths fully as you might surmise, because:
     Although asking qpi to calculate  1,011,600 digits  using  -s
     (the Brent-Salmin AGM) does reveal that it will be computing 
     only 1,011,616 digits to do so, it still took 413.04 seconds
     to complete the the calculations. Whereas, the Default method
     (Chudnovskys' formula), which computed 1,011,605 digits took
     only 182.21 seconds!

As you can see, Steve listed the other methods in his usage statement in the order of their speeds (-a, -s, -b).

qpi.exe defaults to "Chudnovskys' formula" for Pi when you enter only "digits" values. You must redirect the output (using ">") if you want to save it to a file, for example:

C:\thestarman3\math\pi\QuickPi>qpi > pi.txt

will create the following lines in pi.txt:

QPI-Quick Pi v1.0, (c) 2000 S. Pagliarulo
Address comments to: s_pagliarulo@hotmail.com

usage: qpi [digits] [-2|-e|-a|-s|-b]

400 digits of pi using Chudnovskys' formula
Series size : 29  (411 Digits)
Series computation time : 0.01
Final value computation time : 0.01
Total time : 0.05 seconds

Pi = 3.
1415926535 8979323846 2643383279 5028841971 6939937510  : 50
5820974944 5923078164 0628620899 8628034825 3421170679  : 100
8214808651 3282306647 0938446095 5058223172 5359408128  : 150
4811174502 8410270193 8521105559 6446229489 5493038196  : 200
4428810975 6659334461 2847564823 3786783165 2712019091  : 250
4564856692 3460348610 4543266482 1339360726 0249141273  : 300
7245870066 0631558817 4881520920 9628292540 9171536436  : 350
7892590360 0113305305 4882046652 1384146951 9415116094  : 400

You always get a layout of 50 digits per line in 10-digit groups with a " : sum" at the end of each line giving the total digits of Pi up to the last digit in that line. There's no way to change the layout as you can with Gourdon's PiFast program.

This page is still under construction... I plan on adding descriptions and displays of sample runs for each of these Pi programs and other unique ones as I discover them!

The Starman's Pi Files