org.josef.science.math

Class CBigInteger

java.lang.Object

java.lang.Number

java.math.BigInteger

org.josef.science.math.CBigInteger

All Implemented Interfaces:

Serializable, Comparable<BigInteger>

@Status(stage=PRODUCTION,
        unitTests=COMPLETE)
 @Review(by="Kees Schotanus",
        at="2009-09-28")
 @ThreadSafety(level=IMMUTABLE)
public class CBigInteger
extends BigInteger

Collection of mathematical methods that operate on integers (of unlimited size).
Keep in mind that using methods of this class could involve the creation of a lot of large objects.

Version:

2.0 $Revision: 6488 $

Author:

Kees Schotanus

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	CBigInteger.FibonacciIterator Iterator suitable for iterating over all the Fibonacci numbers in sequence.

Field Summary

Fields

Modifier and Type	Field and Description
static BigInteger	FIVE The constant value 5.
static BigInteger	FOUR The constant value 4.
static BigInteger	THREE The constant value 3.
static BigInteger	TWO The constant value 2.

Fields inherited from class java.math.BigInteger

ONE, TEN, ZERO

Constructor Summary

Constructors

Constructor and Description
CBigInteger(BigInteger value) Constructs a new CBigInteger from the supplied BigInteger value.
CBigInteger(String value) Constructs a new CBigInteger from the supplied String value.

Method Summary

Modifier and Type	Method and Description
static List<BigInteger>	computeCollatzConjecture(BigInteger number) Computes Collatz Conjecture.
BigInteger	factorial() Computes the factorial of this CBigInteger.
static BigInteger	fibonacci(int x) Computes Fibonacci number x.
static CBigInteger.FibonacciIterator	fibonacciIterator() Creates a Fibonacci Iterator that allows you to iterate over all the Fibonacci numbers in sequence.
boolean	isFibonacci() Determines whether this CBigInteger represents a number that occurs in the row of Fibonacci numbers.
boolean	isPrime() Determines whether this CBigInteger is a prime.
BigInteger	squareRoot() Computes the square root of this CBigInteger.

Methods inherited from class java.math.BigInteger

abs, add, and, andNot, bitCount, bitLength, byteValueExact, clearBit, compareTo, divide, divideAndRemainder, doubleValue, equals, flipBit, floatValue, gcd, getLowestSetBit, hashCode, intValue, intValueExact, isProbablePrime, longValue, longValueExact, max, min, mod, modInverse, modPow, multiply, negate, nextProbablePrime, not, or, pow, probablePrime, remainder, setBit, shiftLeft, shiftRight, shortValueExact, signum, subtract, testBit, toByteArray, toString, toString, valueOf, xor

Methods inherited from class java.lang.Number

byteValue, shortValue

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

TWO

public static final BigInteger TWO

The constant value 2.

THREE

public static final BigInteger THREE

The constant value 3.

FOUR

public static final BigInteger FOUR

The constant value 4.

FIVE

public static final BigInteger FIVE

The constant value 5.

Constructor Detail

CBigInteger

public CBigInteger(String value)

Constructs a new CBigInteger from the supplied String value.

Parameters:

value - Value to convert to a CBigInteger.

Throws:

NumberFormatException - When the supplied value is not a valid integer.

CBigInteger

public CBigInteger(BigInteger value)

Constructs a new CBigInteger from the supplied BigInteger value.

Parameters:

value - The BigInteger to convert to a CBigInteger.

Method Detail

isPrime

public boolean isPrime()

Determines whether this CBigInteger is a prime.
A number is a prime if the number is only divisible by 1 and by itself. By definition 0 and 1 are not primes.
You can check whether a number is a prime by dividing the number by all values from 2 up to and including the square root of the number. If none of these divisions result in an integer the number is a prime.
The only optimization made here is that the number is only divided by odd numbers from 3 up. In theory this would be twice as fast compared to having no optimization at all but still this method is quite slow for large values!
Did you know that for every n >= 2 at least one prime exists between n and 2 times n?
Since instances are immutable this method is quite slow and involves the creation of a lot of objects!

Returns:

True when this big integer is a prime, false otherwise.

factorial

public BigInteger factorial()

Computes the factorial of this CBigInteger.
The factorial of 0 is 1 and for all other positive numbers n it is defined as: 1x2x3x...n
Precondition: Value >= 0. No check however is made in this method, just returns 1.
Note: Calculating the factorial of large numbers takes considerable time since a lot of new BigIntegers are created in the process.

Returns:

Factorial of this CBigInteger or 1 when the pre condition is not met.

See Also:

CLong.factorial(int)

squareRoot

public BigInteger squareRoot()

Computes the square root of this CBigInteger.
This method uses the Babylonian method. This method can be derived from Newton's method but the Babylonian method is older.
Mathematically it works like this:
Assume the root of S needs to be calculated.
Start with an arbitrary positive as close to the root of S as possible.
Let x_n + 1 be the average of x_n and S / x_n.
The information above is from: Methods of computing square roots on WikiPedia.
This Babylonian method has been changed to work with BigInteger values without resorting to the usage of BigDecimal objects.

Returns:

Approximate root of this big integer.
The returned value is guaranteed to be the closest integer root.

Throws:

ArithmeticException - When this object has a negative value.

computeCollatzConjecture

public static List<BigInteger> computeCollatzConjecture(BigInteger number)

Computes Collatz Conjecture.
For details see: WikiPedia
The simple rules are that while the number is not 1 If the number is even, divide it by two, else multiply with 3 and add 1.

Parameters:

number - The number to compute Collatz Conjecture for.

Returns:

The list of all the numbers in Collatz Conjecture.
The returned list starts with the supplied number and ends with the number 1. That is if Collatz is right. When Collatz is not right, the list will grow until you are out of memory. Unfortunately Collatz can still be right when you run out of memory. Maybe you just have to increase the available memory.

fibonacci

public static BigInteger fibonacci(int x)

Computes Fibonacci number x.
The sequence of Fibonacci numbers goes like this:

 #0:  0 By definition
 #1:  1 By definition
 #2:  1 For all others it is the sum of the previous two numbers.
 #3:  2
 #4:  3
 #5:  5
 #6:  8
 #7: 13
 #8: 21
 #9: 34
 

This method calculates the Fibonacci numbers in sequence and can be expensive for large values of x.

Parameters:

x - The Fibonacci number to compute.

Returns:

Fibonacci number x.

Throws:

IllegalArgumentException - When the supplied x value is < 0.

fibonacciIterator

public static CBigInteger.FibonacciIterator fibonacciIterator()

Creates a Fibonacci Iterator that allows you to iterate over all the Fibonacci numbers in sequence.

Returns:

A Fibonacci Iterator.

isFibonacci

public boolean isFibonacci()

Determines whether this CBigInteger represents a number that occurs in the row of Fibonacci numbers.
This method uses a test formulated by Ira Gessel:
The number n occurs in the row of Fibonacci numbers when 5n² + 4 or 5n² - 4 is a perfect square.

Returns:

True when this CBigInteger represents a number that occurs in the row of Fibonacci numbers.