BigAl  2.4.0

Description:

In February 2001, I wanted to know the exact result of the factorial of one million. BigAl was born and both many CPU cycles and months later I  knew the exact result. Since the beginning, BigAl was able to handle numbers stored in files. Meanwhile a lot of functions has been added and a few of them got a much better performance. BigAl uses the Java classes called BigInteger and BigDecimal.

Here are some examples and a short description of the usage to demonstrate the program. BigAl can also be used to simulate a high load on your computer ;-)

Version:

Copyright:

Requirements:

Download:

Download BigAl (version 2.4.0, June 23, 2007) Filename:    bigal-2.4.0.zip Filesize:    116 KB MD5:         bf5f47a68d76609945f7ffb82ff6af22 SHA1:        4b379fcd57fc42dea4db6012d67e4c4818945f9e SHA256:      603a1a406cf88faf355d22b0fb74ee0f1ced7970eabf120eb2e7766dd2b67503 Download BigAl on Puppy Linux on VMware (BigAl 2.4.0 installed with JRE 6u1 on Puppy Linux 2.16.1 installed on a VMware image, June 30, 2007; useful if you want to perform stop-and-continue calculations and your host operating system is Linux or Windows) Filename:    bigal-2.4.0-on-puppy-linux-2.16.1.zip Filesize:    94 MB MD5:         9d8fc46533fc19cc99e03f67102ca26c SHA1:        d448156b8d33d36e1d048e3b579983e13e7bc994 SHA256:      b14d6e9990c791c2198f7734a7b27e126b7a1eb07e026089fd3a4dfb049f24eb Download BigAl on Puppy Linux in a VirtualBox (BigAl 2.4.0 installed with JRE 6u4 on Puppy Linux 3.01 installed in a VirtualBox image, February 23, 2008; useful if you want to perform stop-and-continue calculations and your host operating system is Linux, Windows, Mac OS X or OpenSolaris) Filename:    bigal-2.4.0-on-puppy-linux-3.01-in-virtualbox.zip Filesize:    118 MB MD5:         8464b55ef0afb5477f1252f0783b792c SHA1:        aba57d0f54feed4ac82466fb014efedd04760431 SHA256:      e23ae1a748a5502d9873138c6a9ec3a0ed3fe778695904524a596e5b86583a9d

Acknowledgement: Barry Kauler is the original developer and current maintainer of Puppy Linux (http://www.puppylinux.com).
Note: Install instructions on How to Install Puppy Linux on VMware und How to Install Puppy Linux in a Virtualbox are available.

To verify the MD5 and the SHA digests, you can use the free program called Jacksum.
Read the readme.txt, stored in the file zip file to get useful information how to install the program on your computer.

Contact:

Keep updated - the announcement-mail-alias:
Are you interested in hearing the latest from BigAl? If so, it is easy to stay informed. Just subscribe to the announcement alias. It's just only me who can post messages to the list. Expect a maximum of 12 email per year.

   To subscribe to the list, send a message to:  announce-subscribe@bigal.dev.java.net
   To remove your address from the list, send a message to: announce-unsubscribe@bigal.dev.java.net
   View the announcements list archive: https://bigal.dev.java.net/servlets/SummarizeList?listName=announce
 

Discuss with other users - the user-mail-alias:
If you have something for the wish list or if you have troulbe with BigAl, write to this mailing list. The mailing list is a good place to discuss new ideas, features and bugs.

   To subscribe to the list, send a message to:  users-subscribe@bigal.dev.java.net
   To remove your address from the list, send a message to: users-unsubscribe@bigal.dev.java.net
   To write to the list, send a message to:  users@bigal.dev.java.net

Trackers (Bug database, Support and Feature requests):
http://sourceforge.net/projects/bigal

Usage:

Put the parameter "help" and you get a full description how the program can be used:
 

% bigal help NAME     BigAl (Big Algorithms)   VERSION     2.4.0   SYNOPSIS     java -classpath bigal.jar BigAl [parameters]...     or     java -jar bigal.jar [parameters]...   DESCRIPTION     BigAl is both a free open source software and a platform independent     utility for computing really big numbers. BigAl is written entirely     in Java. A Java Runtime Environment (JRE) is required.     The following parameters are supported:     [help|-h] | <number|file|[std]in> <op> <number|file|[std]in> [?[?]]     help     this help     -h       this help     number   A and B are unlimited floating point variables respectively              unlimited integers (see also FUNCTIONS); a, b and c are limited              integers     file     ASCII file containing a number     op       operation, see also FUNCTIONS     stdin    read from the standard input device     in       read from the standard input device     ?        print the required duration of the function in ms     ??       print the required duration of the function in format              "d,h,m,s,ms"   FUNCTIONS      A and B are unlimited decimal variables     ---------------------------------------     number  operation      number  description     ---------------------------------------------------------------------------     A       add|+          B       addition     A       sub|-          B       subtraction     A       mul|*|x        B       multiplication     A       div|/|:        B       division (exact, as fraction)     A       divide|//|::   B       division (exact, period is marked by ~),     A       divide|//|::   B x     division (rounded, x digits after the point)     A       eq             B       equals?     A       gt             B       greater than?     A       ge             B       greater or equals?     A       lt             B       less than?     A       le             B       less or equals?     A       abs|absolute           returns |A|     A       neg|negate             returns -A     A       nop                    returns A, standard format (no operation)     A       round          x       rounded A, x digits after the dec. point     A       sgn|signum             returns the signum of A     A       sci            [x]     returns A, scientific formatting (exact),                                    with x significant figures (optional)     A       pow|^          N       power(A,N)     A       rt|root        n x     n.th root of A, x digits after the point     A       sqrt           x       squareroot of A, x digits after the point       A and B are unlimited integer variables     ---------------------------------------     number  operation      number  description     ---------------------------------------------------------------------------     A       base           b       A in a base b numeral system     A       tobase         b       A to a base b numeral system     a       ack            B       ack(a,B) [Ackermann function]     A      even                   is A an even number?     A       fac|!          [B C]   factorial(A) [predefined factorial(B):=C]     A       factorize              factorize A by using the Pollard-Rho method     A       fib|fibonacci  [b c]   fibonacci(A) [with different init values]     A       gcd|ggt        B       greatest common divisor     A       len|length             number of digits of A      A       lcm|kgv        B       least common multiple     A       luc|lucas              lucas(A)     A       mod|%          B       modulo     A       nk|choose      B       A choose B (binomial coefficient)     A       odd                    is A an odd number?     A       random         B [n]   n positive random numbers in [A..B]     a       randdigits     b [n]   n positive random number with [a..b] digits     A       sod                    sum of the digits       Bit oriented, A and B are unlimited integer variables     -----------------------------------------------------     number  operation      number  description     ---------------------------------------------------------------------------     A       gbit|getbit    b       returns the bit at pos b, pos 0 is right     A       sbit|setbit    b       sets the bit at pos b, pos 0 is right     A       fbit|flipbit   b       flips the bit at position b     A       cbit|clearbit  b       sets the bit at position b to 0     A       and            B       bit oriented AND     A       or             B       bit oriented OR     A       xor            B       bit oriented XOR     A       not                    bit oriented NOT     A       bcnt|bitcount          number of bits that differ from its sign bit     A       blen|bitlength         number of bits excluding a sign bit    EXAMPLES     Program arguments              description      ---------------------------------------------------------------------------     1 + 9999999999999999999999999  simple addition     VeryBigNumber.txt sub 6        subtraction with file-content     in mul 5                       multiplication by using 'standard in'     1.23456e3 nop                  returns 1234.56     1234.56 sci                    returns 1.23456e3     1234.56 eq 1.23456e3           returns true     1 / 1234.56                    result of division (exakt) as fraction     1 // 1234.56                   result of division (exakt) with period     1 divide 1234.56               result of division (exakt) with period     1 divide 1234.56 10            result of division (rounded), scale 10     2 sqrt 100                     square root of 2, scale 100     1.728 root 3 12                3rd root of 1.728, scale 12     77 pow 10000 "?"               power-function, duration as ms     in fac                         factorial of n by entering n     10000 fac 4 24                 factorial of 10000, use 4!:=24     100 fac | java BigAl in pow 6  working with 'in', (100!)^6     123 fib                        123th number in Fibonacci-sequence     123 fib "??"                   fibonacci, duration as d, h, m, s, ms     123 fib 2 1                    different seed 2 and 1 => Lucas-sequence     123 luc                        123th number in Lucas-sequence     282361 factorize               factorize the number 282361     big.txt length                 length of number in big.txt     1234567890 mod 12345           modulo     60 gcd 24                      greatest common divisor     1820 lcm 6825                  least common multiplier     0123456789 sod                 sum of the digits     number.txt getbit 0            odd or even number?     49 nk 6                        binomial coefficient (49 choose 6)     3 ack 5                        ackermann function ack(3,5)     1 random 6 10                  10 random numbers from 1 to 6     2 randdigits 6 1000            1000 random numbers, each with 2 to 6 digits     42 tobase 2                    convert 42 to base 2     101010 base 2                  101010 in base 2     help | more                    prints the english help   AUTHOR     Copyright (C) 2001-2007, Dipl.-Inf. (FH) Johann N. Loefflmann     mailto:jonelo@jonelo.de, http://www.jonelo.de/java/bigal/index.html   LICENSE     This program is free software; you can redistribute it and/or modify     it under the terms of the GNU General Public License as published by     the Free Software Foundation; either version 2 of the License, or any     later version.     This program is distributed in the hope that it will be useful,     but WITHOUT ANY WARRANTY; without even the implied warranty of     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the     GNU General Public License for more details.     You should have received a copy of the GNU General Public License     along with this program; if not, write to the Free Software     Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA

FAQ:

A:  It is a standard Unix convention to use % to represent the Unix command prompt (as known as "shell"). If you see that sign, type everything behind it. It's also a standard Windows convention to use C:\> to represent the Windows command prompt. When you see a "prompt", type everything behind it.

A: Usually, shells expands special characters like * to a filelist. Use the text operators (e. g. "mul") or mark it as a special character:

% bigal 3 \* 4
% bigal 3 "*" 4
C:\> java BigAl 3 "*" 4
C:\> java BigAl 3 mul 4
C:\> java BigAl 3 x 4

A: Yes, you can. Use the operation "div" alias "/".
 

% bigal 15 / 145 3/29

A: Yes, but you need to generate a normal decimal number rather than a fraction.
 

bigal 15 // 145 10 0.1034482759

______
Q: Is there a graphical user interface for BigAl ?

A: No. BigAl's purpose is to calculate with absolutely accuracy and it prefers to calculate with really big numbers. Those tasks are often very time consuming and it's possible that you don't get the result in a few minutes. It can take hours, days, weeks, month or even years until BigAl returns the result. Therefore, the commandline interface is the primary interface for BigAl. Let BigAl working in the background, redirect the output to files and do further processing with numbers stored in files.

Well, of course BigAl will help you also by solving simple tasks, but right now, also only at the command line.

A: The VMware Player respectively the VirtualBox are able to save the state of a Virtual Machine (VM). For the VMware Player select "Player -> Exit". For the VirtualBox select "Machine -> Close... -> Save the machine state". In order to restore the VM simply start the VM again.

As soon as the VM state has been restored, BigAl continues with the calculation. BigAl won't even recognize that there was a pause. Repeat the procedure as often as needed.

With this trick you can perform calculation tasks which take longer than only a few seconds or minutes. You can perform calculations which could take hours, days, months or even years if required, because you can interrupt a calculation at any time and you can continue a calculation whenever you want. You can even continue a calculation on a different computer!

Detailled descriptions can be found in the readme files which are included in the .zip file. Go to the download section. Do you want to see a screenshot?

A: No. Basically, only the simple expression <number> <operation> <number> is supported. But you can process the output of BigAl further with standard-input, pipes and files.

A: Your shell (or your command line interpreter) does not allow to do write to a file while you want to read from it. In other words, you cannot use the a file as output if it is part of one of the operators. What you can do is this:

A: Your shell (or your command line interpreter) has a limit in accepting long strings, use a different shell (I recommend the bash on Linux/Unix) or store numbers in files. Numbers in files can be handled very well by BigAl.

A: The calculation you would like to perform requires more memory. You can increase the maximum heap space for the Java process with the option -Xmx. Example:

java -Xmx128m -jar bigal.jar
 

Examples:

If you would like to know how this number is called in words, use the NumericalChameleon.

Task: 123456789.987654321 * 987654321.123456789
 

% bigal 123456789.987654321 * 987654321.123456789 = 121932632103337905.662094193112635269

Task: 4261655511456885005249781170177
                      34
 

% bigal 4261655511456885005249781170177 div 34 125342809160496617801464152064, 1/34

To evaluate also the rest (1/34), use the operators called "division" or "//" rather than "div" or "/":
 

% bigal 4261655511456885005249781170177 division 34 125342809160496617801464152064.0~2941176470588235

The "~" marks the beginning of the period. That means, the result is exactly:
                                ________________
125342809160496617801464152064.02941176470588235

Task: What is the scientific representation of 12345.6789 ?
 

% bigal 12345.6789 sci 1.23456789e4

=> the "scientific function" (sci) formats a normal number (12345.6789) to a scientific representation (1.23456789 * 10⁴)

Task: What does the representation -12.34e-4 mean?
 

% bigal -12.34e-4 nop -0.001234

=> the "no operation" (nop) formats a scientific representation (-12.34 * 10^-4)  to a normal number representation (-0.001234).

Task: fibonacci(100)
 

% bigal 100 fib 354224848179261915075

Task: 100!
 

% bigal 100 fac 93326215443944152681699238856266700490715968264381621468592963895217599993229915 608941463976156518286253697920827223758251185210916864000000000000000000000000

Note: the line break above (actually the number hasn't any line breaks) has been inserted by the terminal output.

Task: How long does it take to calculate 10000!

In this case, the result is unimportant, we redirect the output to "/dev/null" (use "nul" on Windows). It's saver to quote the question mark to avoid any replacements by your shell.
 

% bigal 10000 fac "?" > /dev/null 13450

The duration of the operation above was 13450 milliseconds. If you want it in format "day, hours, minutes, seconds, milliseconds" use "??" rather than "?".
 

C:\> bigal 10000 fac "??" > nul 0 d, 0 h, 0 m, 13 s, 589 ms

Task: (100!)⁶

"in" or "stdin" are the names for BigAl's standard input channel. Use it with pipes ...
 

% bigal 100 fac | java BigAl in pow 6

... or use numbers stored in files ...
 

% bigal 100 fac > result.txt % bigal result.txt pow 6 > endresult.txt

The result of the task above is:
 

66072680842782571700144839317101301840126585582826215148182176376029419461561540 30965460940939195302947971311708312011730742707341761732940037569795738901145841 02473269764347820044961963433409159401386526300292515277729398331732374219968976 99619834464113022611312719240875831865184564835775630706232444860433123623379812 46320521788189559706361843657615135829382676759234804035064801643503656481020612 21954927504951861542739963712581629078497934366978856354573867875864286273108108 56212491608660094570046363549762087879009868883927677818940596991238387787187461 67935477457578759626212444254353125120437311719888665936989596855580234713843881 73909093242149941049935868447701664879408027118356453839078411480484971625514580 20383207512507640293499758197908132405790921327188236292549905069502719116940253 59360000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000

How many digits does the number have? Use the operation called "length" to get this info.
 

% bigal endresult.txt length 948

The example (100!)⁶ results in a number having 948 digits.

That is the same as 2^8 and not 4^3. You must first calcualte the exponent and pass the result as being the next exponent. Use a pipe to pass the result to the next function.

Task: Factorize the number 44343535354351600000003434353
 

% bigal 44343535354351600000003434353 factorize 149 329569479697 903019357561501

=> 149 * 329569479697 * 903019357561501 = 44343535354351600000003434353
All three numbers are primes.

Task: x * y by entering x and y interactively
 

% bigal in mul in 3 4 12

Task: Is 98 an odd or an even number?
 

% bigal 98 getbit 0 0

Find out what bit 0 is (bit 0 is the least significant bit). The result 0 means that the number 98 is even.
 

% bigal 98 even true

Also the operator called "even", tells you that 98 is even.

Task: Get the parity of a number
 

% bigal 98 bitcount | bigal stdin getbit 0 1

3 bits are set in 98 (1100010) and 3 is an odd number. Therefore the result is 1.
 

Factorial:

Here are the results from the factorial-function:
 

n	factorial (n)
10	3.6288 *106 (most human brains give up here,  try it: 1*2*3*4*5*6*7*8*9*10 = 3628800)
70	1.197857166... * 10100 (most calculators fail here already)
100	9.332621544... * 10157 (this is already more than one gogool)
171	1.241018070... * 10309 (a few Javascript based Online-Programs give up at this stage)
1000	4.023872600... * 102567
10000	2.846259680... *1035659
100000	2.824229407... *10456573
200000	1.420225345... *10973350
300000	1.477391531... *101512851
400000	2.534486046... *102067109
500000	1.022801584... *102632341
550000	6.073602851... *102918340
600000	2.234878177... *103206317
650000	3.750830256... *103496105
700000	6.491076229... *103787565
750000	2.646896442... *104080578
800000	5.684678740... *104375039
850000	1.383690070... *104670859
900000	3.990191093... *104967956
1000000	8.263931688... *105565708 (a really nice large number - you need more than 5.5 million digits to write the number down)
2000000	3.776821057... * 1011733474 (it's bigger, 11 million digits, 11 MB are required to store the number uncompressed)
3000000	9.038571657.... * 1018128483
...	...
1000000!	BigAl is still calculating ...

History:

Version 2.3.1 (Jan 29, 2006):
- bugs fixed:
  o since JRE 5.0 BigAl prints out scientific format in some cases, even if
    we don't want sci format. This change in BigDecimal's toString() method
    has been introduced by JSR 13. BigAl works around the documented
    incompatibility to keep compatibility with older JVMs.
  o ant script print warnings about non UTF-8 comments in sourcecode
    while compiling on Linux with UTF-8 locale
- performance improvement for ackermann({0-4},n)
- BigAl 2.3.1 has been successfully tested with the Java Runtime Environments
  gij 4.0.2, J2SE 1.3.1, J2SE 1.4.2, J2SE 5.0 and Java SE 6.0-rc-b69

Version 2.3.0 (30-Apr-2005):
- BigAl has been successfully tested with the Java Runtime Environments
  Kaffe 1.1.4, gij 3.2.2, J2SE 1.3.1, J2SE 1.4.2, J2SE 5.0 and J2SE 6.0-ea-b29
- bug fixed:
  o information about the time needed for an operation is wrong
    if the operation takes more than 24 hours. Thanks to
    Stéphane Ecochard, France for both the bug report and the fix
  o function divide throws OutOfMemoryException if dividend is negative
  o function divide drops all digits after the comma if divisor is negative
  o functions sod and len retrun wrong result if value is negative
- improved operations:
  o Much faster Fibonacci function, provided by Tobias Wahl, Germany
  o Floating point support for operations abs, add, div, divide, eq,
    gt, ge, lt, le, mul, negate, nop, round, sci, signum, sub
- new operations:
  o Factorize function (Pollard-Rho) from the Princeton University
  o Ackermann function provided by Tobias Braun, Germany
  o Random function to generate random numbers
  o Round function for rounding numbers
  o Sci function for formatting numbers in the scientific format
  o Signum and Negate function
  o Comparison functions eq, gt, ge, lt, le, odd and even
- Unix/Linux-script and Windows-batch for being able to start BigAl easier
- System.exit() has been avoided, so BigAl can be used in other projects easier
- documentation updated
- with Ant build.xml file for developers

Version 2.2.0 (23-Feb-2002):
- improved fibonacci
  (fixed an index problem, it is faster and can use different init values
  for the lucas sequence for example)
- the factorial function gives now also a result for 0!
- new operations: abs, nk (very fast binomial coefficient algorithm),
  luc (lucas sequence)
- language support for english and german
- improved timer
- using J2SDK 1.3.1
- jar package, all you need is one jar file

Version 2.1.0a (08-Nov-2001):
- fixed some typos in the HTML
- still 2.1.0

Version 2.1.0 (25-Mar-2001):
- updated documentation
- new operations: length, getbit, setbit, flipbit, clearbit,
  and, or, xor, not, bitcount, bitlength

Version 2.0.0 (11-Mar-2001):
- new operaion: nop (no operation)
- read values from standard input and from files
- duration of operations in ms and in d,h,m,s,ms on demand
- length of an operand on demand
- you can continue calculating factorial from a given value
- you can evaluate fractions with detailed period

Version 1.0.0 (25-Feb-2001):
- simple expression evaluation with unlimited numbers
- operations available: add, sub, mul, div, divide, mod, fib,
  fac, pow, gcd, lcm, sod
 

Links where you can reach BigAl:

• http://dmoz.org
• http://www.codearchive.com
• http://www.codebeach.com
• http://www.freeware.de
• http://www.freewarepage.de
• http://www.heise.de/ct
• http://www.javashareware.com
• http://www.scriptsearch.com
• http://www.shareware.de