Java Big Integers

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Latest revision as of 09:39, 22 February 2010

What Are They?

(From sun.com) "Immutable arbitrary-precision integers." (From Answers.com) Immutable: "Incapable of changing or being modified", meaning the precision cannot be changed (any one else have a better.. desc?)

In 'Laymans' terms, they are very large 'integer' type variables, with the capacity to hold as many digits as your RAM will fit.

When Should You Use Them?

They should be used whenever you need to handle very large numbers, anything larger then 'long' variables. Long's have a max a max value of 9223372036854775807. As well, BigInteger provides some useful functions for bit manipulation, GCD, random number, and primality testing and generation.

Do I Need To Import Anything?

Yes, add this import line at the top of your java file Java:

import java.math.*;

Declaring A BigInteger Variable (4 Examples)

Java:

BigInteger bigInt0 = BigInteger.ZERO;
BigInteger bigInt1 = BigInteger.ONE;
BigInteger bigInt3 = new BigInteger ("3");
BigInteger bigInt5 = BigInteger.valueOf(5);

Note: You cannot pass an int/long into a BigInteger directly, the easiest way to do this it to pass it as a static BigInteger using valueOf, Thank You "OneOffDriveByPoster" for that method.

Java:

long num = 9876543210;
BigInteger bigInt123 = BigInteger.valueOf (num);

So, How Do I Use Them?

Well, BigIntegers contain all the regular math functions, plus more, the main difference is, it does not use symbols such as '*', '+','=','>' etc. rather it uses words (multiply,add,equals,compareTo). Examples;

To Multiply: Java:

bigInt1.multiply(bigInt3);

Returns: A Big Integer With Value 3 (1*3) Whereas, bigInt1 and bigInt3 are both BigInteger's

To Subtract: Java:

bigInt1.subtract(bigInt3);

Returns: A BigInteger with value -2 (3-1) Whereas, bigInt1 and bigInt3 are both BigInteger's

To Compare: Java:

bigInt1.compareTo(bigInt3);

Returns: An Integer with a negative value (Less Than), 0 (Equal), positive value (Greater Than), in this case, it will be negative since 1 is less then 3. Whereas, bigInt1 and bigInt3 are both BigInteger's

To Check If Equal: Java:

bigInt1.equals(bigInt3);

Returns: A boolean with a value of false since 1 != 3 Whereas, bigInt1 and bigInt3 are both BigInteger's

You'll notice, its just like dealing with strings (equals, compareTo)...

As well, you can create a new BigInteger inline (outputs 8) Java:

System.out.println ("2**3 = "+new BigInteger("2").pow(3));

Note: I Used this as a special example, 'pow', raises the BigInteger '2' to the power of a regular integer '3'. Most of the math methods need BigIntegers as the initial and secondary values but this is a worthy exception to point out.

Can I Make An Array?

Sure, why not, arrays can be made of any object/class. Both arrays have a length of 10, both have been initialized to value '1' Java:

//------Example One-------//
BigInteger i = BigInteger.ONE;
BigInteger [] biggg = {i,i,i,i,i,i,i,i,i,i};

//------Example Two-------//
BigInteger [] biggg = new BigInteger [10];
for (int c = 0; c < biggg.length; c ++){
    biggg [c] = BigInteger.ONE;
}

Primality Testing

You Mentioned Primality Testing...

Checking if a number is prime is easy with BigIntegers, Java:

if (new BigInteger("17").isProbablePrime(5)){
        System.out.println("17 Is Prime!");
}

Note: The 5 is the certainty that the number is prime, this value reflects how long it takes to complete, for small primes, a value of 1-5 works, but bigger numbers may return false positives unless certainty is >= 5.

Bit Manipulation

I'm A 'Bit' Hungry, Let's Do Bit Manipulation!

One of the most used is XOR, in encryption methods. Eg: 65 XOR 42 = 107, and 107 XOR 42 = 65. The work behind this is, it converts the numbers to binary (1's, 0's), and compares the bits in each position, if they are different, bit = 1, if they are the same, bit = 0 Kevin wrote:

65: 1000001_______107: 1101011
XOR______________XOR
42: 0101010_______42: 0101010
=________________=
107: 1101011______65: 1000001

Java:

System.out.println ("65 XOR 42 = "+new BigInteger("65").xor(new BigInteger("42"));

Constant Recomendations

Seeing how it takes quite a bit of typing to make a new BigInteger every time you say want to multiply something by two... bigInt.multiply (new BigInteger("2");.. etc.. I recommend making some constants at the top of your program for the most common numbers as follows:

Java:

BigInteger TWO = new BigInteger ("2");
BigInteger THREE = new BigInteger ("3");
BigInteger FIVE = new BigInteger ("5");
BigInteger TEN = new BigInteger ("10");
...
System.out.println ("2 * 10 = "+TWO.multiply(TEN));

For Loops

What About For Loops, Can BigIntegers Be Used?[b]

They can be, but it's inadvisable as it will be extremely slow, unless incrementing by say 100 or 1000... (bellow I used 1 for increment)...

Java:

for (BigInteger bigCount = BigInteger.ZERO; bigCount.compareTo(new BigInteger ("99999999999999999")) < 0; bigCount = bigCount.add(BigInteger.ONE)){
     System.out.println ("Big:"+bigCount);
}

Example Program

Can I See A Full Program Using BigIntegers?

Sure...A Method To Evaluate Factorials! I used BigInteger for the result, because even 25! uses 26 digits, far larger then the max 'long' capacity.

Java:

public static BigInteger factorial(int n){
    /* n must be >= 0, 0! = 1, eg: n=5 returns (5x4x3x2x1) */

    /* Holds the value of the factorial, in BigInteger form */
    BigInteger product = BigInteger.ONE;
       
    /* Inform User that n was erroneous parameter */
    if (n < 0){
        System.out.println ("Factorial Error! n = "+n);
        return new BigInteger ("-1");
    }   
       
    /* Chain Multiply from 'n' to '1' */
    for (int c = n; c > 0; c --){
        product = product.multiply(BigInteger.valueOf(c));
    }
                       
    System.out.println ("Factorial "+n+"! = "+product);
       
    /* Return a BigInteger with the product from n! */
    return product;
}// end factorial

For More Information

For More Information & Complete Method List

Check Out Sun's Java Docs On BigInteger. BigInteger @ Sun.com (I Highly Recommend You Read Through The Whole Method Summary Section)

As well, for the decimal equivalent, check out 'BigDecimal' BigDecimal @ Sun.com BigDecimal's use the same concepts as BigInteger, so I wont go into much detail, but if you have questions about BigDecimals, ask away.

If you have any questions, comments, or things to add, feel free to leave a message, or pm me. -Kevin

Credits

Author: the_short1

Added to Wiki by: TheFerret