Java Big Integers
From Compsci.ca Wiki
What Are They?
(From sun.com) "Immutable arbitrary-precision integers." (From Answers.com) Immutatble: "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 value of -1 (Less Than), 0 (Equal), 1 (Greater Then), in this case, it will be -1 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
Youll 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 initiallized 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) == true){
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
Im A 'Bit' Hungry, Lets 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 recomend 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 its unadvisable as it will be extremly 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")) == -1; 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 Recommmend 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
