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Java Source Code / Java Documentation » Science » jscience 4.3.1 » org.jscience.mathematics.number

Source Cross Reference Class Diagram Java Document (Java Doc)

org.jscience.mathematics.number .LargeInteger

LargeInteger

final public class LargeInteger extends Number (Code)

This class represents an immutable integer number of arbitrary size.

It has the following advantages over the java.math.BigInteger class:

Optimized for 64 bits architectures. But still runs significantly faster on 32 bits processors.
Real-time compliant for improved performance and predictability (no garbage generated when executing in javolution.context.StackContext StackContext ).
Improved algorithms (e.g. Concurrent Karabutsa multiplication in O(n^Log3) instead of O(n²).

Note: This class uses ConcurrentContext ConcurrentContext to accelerate calculations on multi-cores systems.

author:
   Jean-Marie Dautelle
version:
   3.3, January 14, 2007
See Also:    * Wikipedia: Arbitrary-precision Arithmetic

Field Summary
final static TextFormat<LargeInteger>	DECIMAL_FORMAT Holds the format for large integers (decimal representation by default).
final static LargeInteger	FIVE Holds five.
final static LargeInteger	LONG_MIN_VALUE
final public static LargeInteger	ONE The large integer representing the multiplicative identity.
final public static Configurable<Integer>	PRIME_CERTAINTY Holds the certainty required when testing for primality (default `100`, the probability for a composite to pass the primality test is less than `2^-100`).
final static XMLFormat<LargeInteger>	XML Holds the default XML representation for large integers.
final public static LargeInteger	ZERO The large integer representing the additive identity.

Method Summary
public LargeInteger	abs() Returns the absolute value of this large integer.
public int	bitLength() Returns the minimal number of bits to represent this large integer in the minimal two's-complement (sign excluded).
public int	compareTo(LargeInteger that) Compares two large integers numerically. Parameters: that - the integer to compare with.
public int	compareTo(long value) Compares this large integer to the specified `long` value. Parameters: value - the `long` value to compare with.
public LargeInteger	copy()
public int	digitLength() Returns the minimal number of decimal digits necessary to represent this large integer (sign excluded).
public LargeInteger	divide(LargeInteger that) Returns this large integer divided by the one specified (integer division).
public LargeInteger	divide(int divisor) Returns this large integer divided by the specified `int` divisor.
public double	doubleValue() Returns the value of this large integer as a `double`.
public boolean	equals(Object that) Compares this large integer against the specified object. Parameters: that - the object to compare with.
public boolean	equals(long value) Compares this large integer against the specified `long` value. Parameters: value - `long` value to compare with.
public static Appendable	format(LargeInteger li, int radix, Appendable out) Formats the specified large integer in the specified radix and into the specified `Appendable` argument. Parameters: li - the large integer to format. Parameters: radix - the radix. Parameters: out - the `Appendable` to append.
public LargeInteger	gcd(LargeInteger that) Returns the greatest common divisor of this large integer and the one specified. Parameters: that - the other number to compute the GCD with.
public int	getLowestSetBit() Returns the index of the lowest-order one bit in this large integer or `-1` if `this.equals(ZERO)`.
public LargeInteger	getRemainder() Returns the final undivided part after division that is less or of lower degree than the divisor.
public int	hashCode() Returns the hash code for this large integer number.
public LargeInteger	inverseScaled(int precision) Returns a scaled approximation of `1 / this`. Parameters: precision - the requested precision (reciprocal error being ± 1).
public boolean	isEven() Indicates if this large integer is an even number.
public boolean	isLargerThan(LargeInteger that) Indicates if this large integer is larger than the one specified in absolute value. Parameters: that - the integer to be compared with.
public boolean	isNegative() Indicates if this large integer is less than LargeInteger.ZERO .
public boolean	isOdd() Indicates if this large integer is an odd number.
public boolean	isPositive() Indicates if this large integer is greater than LargeInteger.ZERO ( LargeInteger.ZERO is not included).
public boolean	isPowerOfTwo() Indicates if this number is a power of two (equals to 2^{( LargeInteger.bitLength bitLength() - 1)}).
public boolean	isProbablyPrime() Indicates if this large integer is probably prime.
public boolean	isZero() Indicates if this large integer is equal to LargeInteger.ZERO .
public long	longValue() Returns the low order bits of this large integer as a `long`.
public LargeInteger	minus(LargeInteger that) Returns the difference between this large integer and the one specified. Parameters: that - the integer to be subtracted.
public LargeInteger	minus(long value) Returns the difference between this large integer and the specified value Parameters: value - the value to be subtracted.
public LargeInteger	mod(LargeInteger m) Returns this large integer modulo the specified large integer.
public LargeInteger	modInverse(LargeInteger m) Returns the large integer whose value is `(this^-1 mod m)`. Parameters: m - the modulus.
public LargeInteger	modPow(LargeInteger exp, LargeInteger m) Returns this large integer raised at the specified exponent modulo the specified modulus. Parameters: exp - the exponent. Parameters: m - the modulus.
public LargeInteger	opposite() Returns the opposite of this large integer.
public static LargeInteger	parse(CharSequence csq, int radix, Cursor cursor) Parses the specified character sequence from the specified position as a large integer in the specified radix. Parameters: csq - the character sequence to parse. Parameters: radix - the radix to be used while parsing. Parameters: cursor - the current cursor position (being maintained).
public LargeInteger	plus(long value) Returns the sum of this large integer with the specified `long` integer (convenience method) Parameters: value - the `long` integer being added.
public LargeInteger	plus(LargeInteger that) Returns the sum of this large integer with the one specified. Parameters: that - the integer to be added.
public LargeInteger	remainder(LargeInteger that) Returns the remainder of the division of this large integer with the one specified (convenience method equivalent to `this.divide(that).getRemainder()`). Parameters: that - the value by which this integer is to be divided, and theremainder returned.
public LargeInteger	shiftLeft(int n) Returns the value of this large integer after performing a binary shift to left.
public LargeInteger	shiftRight(int n) Returns the value of this large integer after performing a binary shift to right with sign extension `(-1 >> 1 == -1)`. The shift distance, `n`, may be negative, in which case this method performs a LargeInteger.shiftLeft(int) . Parameters: n - the shift distance, in bits.
public LargeInteger	sqrt() Returns the integer square root of this integer.
public LargeInteger	times(LargeInteger that) Returns the product of this large integer with the one specified. Parameters: that - the large integer multiplier.
public LargeInteger	times(long multiplier) Returns the product of this large integer with the specified `long` multiplier. Parameters: multiplier - the `long` multiplier.
public LargeInteger	times10pow(int n) Returns the value of this large integer after multiplication by a power of ten.
public LargeInteger	times2pow(int n) Returns the value of this large integer after multiplication by a power of two.
public int	toByteArray(byte[] bytes, int offset) Returns the two's-complement binary representation of this large integer.
public Text	toText() Returns the text representation of this number using the current TextFormat.getInstance(Class) format .
public Text	toText(int radix) Returns the text representation of this number in the specified radix. Parameters: radix - the radix of the representation.
public static LargeInteger	valueOf(long value) Returns the large integer of specified `long` value. Parameters: value - the `long` value.
public static LargeInteger	valueOf(byte[] bytes, int offset, int length) Returns the large integer of specified two's-complement binary representation.
public static LargeInteger	valueOf(CharSequence csq) Returns the large integer for the specified character sequence using the current TextFormat.getInstance(Class) format . Parameters: csq - the character sequence to parse.
public static LargeInteger	valueOf(CharSequence csq, int radix) Returns the large integer for the specified character sequence in the specified radix. Parameters: csq - the character sequence to parse. Parameters: radix - the radix of the representation.
public static LargeInteger	valueOf(java.math.BigInteger bigInteger) Returns the large integer corresponding to the specified `java.math.BigInteger` instance. Parameters: bigInteger - the big integer instance.

Field Detail

DECIMAL_FORMAT
final static TextFormat<LargeInteger> DECIMAL_FORMAT(Code)
	Holds the format for large integers (decimal representation by default). See Also: LargeInteger.parse(CharSequence,int,TextFormat.Cursor) See Also: LargeInteger.format(LargeInteger,int,Appendable)

FIVE
final static LargeInteger FIVE(Code)
	Holds five.

LONG_MIN_VALUE
final static LargeInteger LONG_MIN_VALUE(Code)
	Holds Long.MIN_VALUE

ONE
final public static LargeInteger ONE(Code)
	The large integer representing the multiplicative identity.

PRIME_CERTAINTY
final public static Configurable<Integer> PRIME_CERTAINTY(Code)
	Holds the certainty required when testing for primality (default `100`, the probability for a composite to pass the primality test is less than `2^-100`).

XML
final static XMLFormat<LargeInteger> XML(Code)
	Holds the default XML representation for large integers. This representation consists of a simple `value` attribute holding the LargeInteger.toText() textual representation.

ZERO
final public static LargeInteger ZERO(Code)
	The large integer representing the additive identity.

Method Detail

abs
public LargeInteger abs()(Code)
	Returns the absolute value of this large integer. `\|this\|`.

bitLength
public int bitLength()(Code)
	Returns the minimal number of bits to represent this large integer in the minimal two's-complement (sign excluded). the length of this integer in bits (sign excluded).

compareTo
public int compareTo(LargeInteger that)(Code)
	Compares two large integers numerically. Parameters: that - the integer to compare with. -1, 0 or 1 as this integer is numerically less than, equal to,or greater than `that`. throws: ClassCastException - `that` is not a large integer.

compareTo
public int compareTo(long value)(Code)
	Compares this large integer to the specified `long` value. Parameters: value - the `long` value to compare with. -1, 0 or 1 as this integer is numerically less than, equal to,or greater than the specified value.

copy
public LargeInteger copy()(Code)

digitLength
public int digitLength()(Code)
	Returns the minimal number of decimal digits necessary to represent this large integer (sign excluded). the maximum number of digits.

divide
public LargeInteger divide(LargeInteger that)(Code)
	Returns this large integer divided by the one specified (integer division). The remainder of this division is accessible using LargeInteger.getRemainder . Parameters: that - the integer divisor. `this / that` and `this % that` (LargeInteger.getRemainder) throws: ArithmeticException - if `that.equals(ZERO)`

divide
public LargeInteger divide(int divisor)(Code)
	Returns this large integer divided by the specified `int` divisor. The remainder of this division is accessible using LargeInteger.getRemainder . Parameters: divisor - the `int` divisor. `this / divisor` and `this % divisor`(LargeInteger.getRemainder) throws: ArithmeticException - if `divisor == 0`

doubleValue
public double doubleValue()(Code)
	Returns the value of this large integer as a `double`. the numeric value represented by this integer after conversionto type `double`.

equals
public boolean equals(Object that)(Code)
	Compares this large integer against the specified object. Parameters: that - the object to compare with. `true` if the objects are the same; `false`otherwise.

equals
public boolean equals(long value)(Code)
	Compares this large integer against the specified `long` value. Parameters: value - `long` value to compare with. `true` if this large integer has the specified value;`false` otherwise.

format
public static Appendable format(LargeInteger li, int radix, Appendable out) throws IOException(Code)
	Formats the specified large integer in the specified radix and into the specified `Appendable` argument. Parameters: li - the large integer to format. Parameters: radix - the radix. Parameters: out - the `Appendable` to append. the specified `Appendable` object. throws: IllegalArgumentException - if radix is not in [2 .. 36] range. throws: IOException - if an I/O exception occurs.

gcd
public LargeInteger gcd(LargeInteger that)(Code)
	Returns the greatest common divisor of this large integer and the one specified. Parameters: that - the other number to compute the GCD with. a positive number or LargeInteger.ZERO if`(this.isZero() && that.isZero())`.

getLowestSetBit
public int getLowestSetBit()(Code)
	Returns the index of the lowest-order one bit in this large integer or `-1` if `this.equals(ZERO)`. the index of the rightmost bit set or `-1`

getRemainder
public LargeInteger getRemainder()(Code)
	Returns the final undivided part after division that is less or of lower degree than the divisor. This value is only set by the LargeInteger.divide operation and is not considered as part of this large integer (ignored by all methods). the remainder of the division for which this large integeris the quotient.

hashCode
public int hashCode()(Code)
	Returns the hash code for this large integer number. the hash code value.

inverseScaled
public LargeInteger inverseScaled(int precision)(Code)
	Returns a scaled approximation of `1 / this`. Parameters: precision - the requested precision (reciprocal error being ± 1). `2^{(precision + this.bitLength())} / this` throws: ArithmeticException - if `this.isZero()`

isEven
public boolean isEven()(Code)
	Indicates if this large integer is an even number. `(this & 1) == ZERO`

isLargerThan
public boolean isLargerThan(LargeInteger that)(Code)
	Indicates if this large integer is larger than the one specified in absolute value. Parameters: that - the integer to be compared with. `this.abs().compareTo(that.abs()) > 0`.

isNegative
public boolean isNegative()(Code)
	Indicates if this large integer is less than LargeInteger.ZERO . `this < ZERO`

isOdd
public boolean isOdd()(Code)
	Indicates if this large integer is an odd number. `(this & 1) != ZERO`

isPositive
public boolean isPositive()(Code)
	Indicates if this large integer is greater than LargeInteger.ZERO ( LargeInteger.ZERO is not included). `this > ZERO`

isPowerOfTwo
public boolean isPowerOfTwo()(Code)
	Indicates if this number is a power of two (equals to 2^{( LargeInteger.bitLength bitLength() - 1)}). `true` if this number is a power of two; `false` otherwise.

isProbablyPrime
public boolean isProbablyPrime()(Code)
	Indicates if this large integer is probably prime. `true` if this large integer is probable prime;`false` otherwise.

isZero
public boolean isZero()(Code)
	Indicates if this large integer is equal to LargeInteger.ZERO . `this == ZERO`

longValue
public long longValue()(Code)
	Returns the low order bits of this large integer as a `long`. Note: This conversion can lose information about the overall magnitude of the integer value and may return a result with the opposite sign. the numeric value represented by this integer after conversionto type `long`.

minus
public LargeInteger minus(LargeInteger that)(Code)
	Returns the difference between this large integer and the one specified. Parameters: that - the integer to be subtracted. `this - that`.

minus
public LargeInteger minus(long value)(Code)
	Returns the difference between this large integer and the specified value Parameters: value - the value to be subtracted. `this - value`.

mod
public LargeInteger mod(LargeInteger m)(Code)
	Returns this large integer modulo the specified large integer. Note: The result as the same sign as the divisor unlike the Java remainder (%) operator (which as the same sign as the dividend). Parameters: m - the modulus. `this mod m` See Also: LargeInteger.getRemainder()

modInverse
public LargeInteger modInverse(LargeInteger m)(Code)
	Returns the large integer whose value is `(this^-1 mod m)`. Parameters: m - the modulus. `this^-1 mod m`. throws: ArithmeticException - `m <= 0`, or this integerhas no multiplicative inverse mod m (that is, this integeris not relatively prime to m).

modPow
public LargeInteger modPow(LargeInteger exp, LargeInteger m)(Code)
	Returns this large integer raised at the specified exponent modulo the specified modulus. Parameters: exp - the exponent. Parameters: m - the modulus. `this^exp mod m` throws: ArithmeticException - `m <= 0` See Also: LargeInteger.modInverse

opposite
public LargeInteger opposite()(Code)
	Returns the opposite of this large integer. `-this`.

parse
public static LargeInteger parse(CharSequence csq, int radix, Cursor cursor)(Code)
	Parses the specified character sequence from the specified position as a large integer in the specified radix. Parameters: csq - the character sequence to parse. Parameters: radix - the radix to be used while parsing. Parameters: cursor - the current cursor position (being maintained). the corresponding large integer. throws: NumberFormatException - if error when parsing.

plus
public LargeInteger plus(long value)(Code)
	Returns the sum of this large integer with the specified `long` integer (convenience method) Parameters: value - the `long` integer being added. `this + value`.

plus
public LargeInteger plus(LargeInteger that)(Code)
	Returns the sum of this large integer with the one specified. Parameters: that - the integer to be added. `this + that`.

remainder
public LargeInteger remainder(LargeInteger that)(Code)
	Returns the remainder of the division of this large integer with the one specified (convenience method equivalent to `this.divide(that).getRemainder()`). Parameters: that - the value by which this integer is to be divided, and theremainder returned. `this % that` throws: ArithmeticException - if `that.equals(ZERO)` See Also: LargeInteger.divide(LargeInteger)

shiftLeft
public LargeInteger shiftLeft(int n)(Code)
	Returns the value of this large integer after performing a binary shift to left. The shift distance, `n`, may be negative, in which case this method performs a right shift. Parameters: n - the shift distance, in bits. `this << n`. See Also: LargeInteger.shiftRight

shiftRight
public LargeInteger shiftRight(int n)(Code)
	Returns the value of this large integer after performing a binary shift to right with sign extension `(-1 >> 1 == -1)`. The shift distance, `n`, may be negative, in which case this method performs a LargeInteger.shiftLeft(int) . Parameters: n - the shift distance, in bits. `this >> n`.

sqrt
public LargeInteger sqrt()(Code)
	Returns the integer square root of this integer. `k such as k^2 <= this < (k + 1)^2 throws: ArithmeticException - if this integer is negative.`

times
public LargeInteger times(LargeInteger that)(Code)
	Returns the product of this large integer with the one specified. Parameters: that - the large integer multiplier. `this · that`.

times
public LargeInteger times(long multiplier)(Code)
	Returns the product of this large integer with the specified `long` multiplier. Parameters: multiplier - the `long` multiplier. `this · multiplier`.

times10pow
public LargeInteger times10pow(int n)(Code)
	Returns the value of this large integer after multiplication by a power of ten. For example:[code] LargeInteger billion = LargeInteger.ONE.times10pow(9); // 1E9 LargeInteger million = billion.times10pow(-3);[/code] Parameters: n - the decimal exponent. `this · 10ⁿ`

times2pow
public LargeInteger times2pow(int n)(Code)
	Returns the value of this large integer after multiplication by a power of two. This method is equivalent to LargeInteger.shiftLeft(int) for positive `n`; but is different from LargeInteger.shiftRight(int) for negative `n` as no sign extension is performed (`-1 >>> 1 == 0`). Parameters: n - the power of 2 exponent. `this · 2ⁿ`.

toByteArray
public int toByteArray(byte[] bytes, int offset)(Code)
	Returns the two's-complement binary representation of this large integer. The output array is in big-endian byte-order: the most significant byte is at the offset position. Parameters: bytes - the bytes to hold the binary representation (two's-complement) of this large integer. Parameters: offset - the offset at which to start writing the bytes. the number of bytes written. throws: IndexOutOfBoundsException - if `bytes.length < (bitLength() >> 3) + 1` See Also: LargeInteger.valueOf(byte[],int,int) See Also: LargeInteger.bitLength

toText
public Text toText()(Code)
	Returns the text representation of this number using the current TextFormat.getInstance(Class) format . `TextFormat.getInstance(LargeInteger.class).format(this)`

toText
public Text toText(int radix)(Code)
	Returns the text representation of this number in the specified radix. Parameters: radix - the radix of the representation. the text representation of this number in the specified radix.

valueOf
public static LargeInteger valueOf(long value)(Code)
	Returns the large integer of specified `long` value. Parameters: value - the `long` value. the corresponding large integer number.

valueOf
public static LargeInteger valueOf(byte[] bytes, int offset, int length)(Code)
	Returns the large integer of specified two's-complement binary representation. The input array is assumed to be in big-endian byte-order: the most significant byte is at the offset position. Parameters: bytes - the binary representation (two's-complement). Parameters: offset - the offset at which to start reading the bytes. Parameters: length - the maximum number of bytes to read. the corresponding large integer number. throws: IndexOutOfBoundsException - if `offset + length > bytes.length` See Also: LargeInteger.toByteArray

valueOf
public static LargeInteger valueOf(CharSequence csq)(Code)
	Returns the large integer for the specified character sequence using the current TextFormat.getInstance(Class) format . Parameters: csq - the character sequence to parse. `TextFormat.getInstance(LargeInteger.class).parse(csq)` throws: NumberFormatException - if error when parsing.

valueOf
public static LargeInteger valueOf(CharSequence csq, int radix)(Code)
	Returns the large integer for the specified character sequence in the specified radix. Parameters: csq - the character sequence to parse. Parameters: radix - the radix of the representation. `LargeInteger.parse(csq, radix, cursor)` throws: NumberFormatException - if error when parsing.

valueOf
public static LargeInteger valueOf(java.math.BigInteger bigInteger)(Code)
	Returns the large integer corresponding to the specified `java.math.BigInteger` instance. Parameters: bigInteger - the big integer instance. the large integer having the same value.

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