public class java.math
BigInteger


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Java SE 6
  
Extends: Number
Implements: Comparable
Details
Immutable arbitrary-precision integers. All operations behave as if BigIntegers were represented in two's-complement notation (like Java's primitive integer types). BigInteger provides analogues to all of Java's primitive integer operators, and all relevant methods from java.lang.Math. Additionally, BigInteger provides operations for modular arithmetic, GCD calculation, primality testing, prime generation, bit manipulation, and a few other miscellaneous operations.

Semantics of arithmetic operations exactly mimic those of Java's integer arithmetic operators, as defined in The Java Language Specification. For example, division by zero throws an ArithmeticException, and division of a negative by a positive yields a negative (or zero) remainder. All of the details in the Spec concerning overflow are ignored, as BigIntegers are made as large as necessary to accommodate the results of an operation.

Semantics of shift operations extend those of Java's shift operators to allow for negative shift distances. A right-shift with a negative shift distance results in a left shift, and vice-versa. The unsigned right shift operator (>>>) is omitted, as this operation makes little sense in combination with the "infinite word size" abstraction provided by this class.

Semantics of bitwise logical operations exactly mimic those of Java's bitwise integer operators. The binary operators (and, or, xor) implicitly perform sign extension on the shorter of the two operands prior to performing the operation.

Comparison operations perform signed integer comparisons, analogous to those performed by Java's relational and equality operators.

Modular arithmetic operations are provided to compute residues, perform exponentiation, and compute multiplicative inverses. These methods always return a non-negative result, between 0 and (modulus - 1), inclusive.

Bit operations operate on a single bit of the two's-complement representation of their operand. If necessary, the operand is sign- extended so that it contains the designated bit. None of the single-bit operations can produce a BigInteger with a different sign from the BigInteger being operated on, as they affect only a single bit, and the "infinite word size" abstraction provided by this class ensures that there are infinitely many "virtual sign bits" preceding each BigInteger.

For the sake of brevity and clarity, pseudo-code is used throughout the descriptions of BigInteger methods. The pseudo-code expression (i + j) is shorthand for "a BigInteger whose value is that of the BigInteger i plus that of the BigInteger j." The pseudo-code expression (i == j) is shorthand for "true if and only if the BigInteger i represents the same value as the BigInteger j." Other pseudo-code expressions are interpreted similarly.

All methods and constructors in this class throw NullPointerException when passed a null object reference for any input parameter.
version1.75, 06/28/06
sinceJDK1.1
See also java.math.BigDecimal


Fields
final public static BigInteger ZERO Details
The BigInteger constant zero.
since1.2
final public static BigInteger ONE Details
The BigInteger constant one.
since1.2
final public static BigInteger TEN Details
The BigInteger constant ten.
since1.5

Constructors
public BigInteger(byte[] val) Details
Translates a byte array containing the two's-complement binary representation of a BigInteger into a BigInteger. The input array is assumed to be in big-endian byte-order: the most significant byte is in the zeroth element.
valbig-endian two's-complement binary representation of BigInteger.
ThrowsNumberFormatException: val is zero bytes long.
public BigInteger(int signum, byte[] magnitude) Details
Translates the sign-magnitude representation of a BigInteger into a BigInteger. The sign is represented as an integer signum value: -1 for negative, 0 for zero, or 1 for positive. The magnitude is a byte array in big-endian byte-order: the most significant byte is in the zeroth element. A zero-length magnitude array is permissible, and will result inin a BigInteger value of 0, whether signum is -1, 0 or 1.
signumsignum of the number (-1 for negative, 0 for zero, 1 for positive).
magnitudebig-endian binary representation of the magnitude of the number.
ThrowsNumberFormatException: signum is not one of the three legal values (-1, 0, and 1), or signum is 0 and magnitude contains one or more non-zero bytes.
public BigInteger(String val, int radix) Details
Translates the String representation of a BigInteger in the specified radix into a BigInteger. The String representation consists of an optional minus sign followed by a sequence of one or more digits in the specified radix. The character-to-digit mapping is provided by Character.digit. The String may not contain any extraneous characters (whitespace, for example).
valString representation of BigInteger.
radixradix to be used in interpreting val.
ThrowsNumberFormatException: val is not a valid representation of a BigInteger in the specified radix, or radix is outside the range from Character#MIN_RADIX to Character#MAX_RADIX, inclusive.
See also digit
public BigInteger(String val) Details
Translates the decimal String representation of a BigInteger into a BigInteger. The String representation consists of an optional minus sign followed by a sequence of one or more decimal digits. The character-to-digit mapping is provided by Character.digit. The String may not contain any extraneous characters (whitespace, for example).
valdecimal String representation of BigInteger.
ThrowsNumberFormatException: val is not a valid representation of a BigInteger.
See also digit
public BigInteger(int numBits, Random rnd) Details
Constructs a randomly generated BigInteger, uniformly distributed over the range 0 to (2numBits - 1), inclusive. The uniformity of the distribution assumes that a fair source of random bits is provided in rnd. Note that this constructor always constructs a non-negative BigInteger.
numBitsmaximum bitLength of the new BigInteger.
rndsource of randomness to be used in computing the new BigInteger.
ThrowsIllegalArgumentException: numBits is negative.
See also bitLength()
public BigInteger(int bitLength, int certainty, Random rnd) Details
Constructs a randomly generated positive BigInteger that is probably prime, with the specified bitLength.

It is recommended that the probablePrime method be used in preference to this constructor unless there is a compelling need to specify a certainty.
bitLengthbitLength of the returned BigInteger.
certaintya measure of the uncertainty that the caller is willing to tolerate. The probability that the new BigInteger represents a prime number will exceed (1 - 1/2certainty). The execution time of this constructor is proportional to the value of this parameter.
rndsource of random bits used to select candidates to be tested for primality.
ThrowsArithmeticException: bitLength < 2.
See also bitLength()


Methods
public BigInteger abs() Details
Returns a BigInteger whose value is the absolute value of this BigInteger.
returnabs(this)
public BigInteger add(BigInteger val) Details
Returns a BigInteger whose value is (this + val).
valvalue to be added to this BigInteger.
returnthis + val
public BigInteger and(BigInteger val) Details
Returns a BigInteger whose value is (this & val). (This method returns a negative BigInteger if and only if this and val are both negative.)
valvalue to be AND'ed with this BigInteger.
returnthis & val
public BigInteger andNot(BigInteger val) Details
Returns a BigInteger whose value is (this & ~val). This method, which is equivalent to and(val.not()), is provided as a convenience for masking operations. (This method returns a negative BigInteger if and only if this is negative and val is positive.)
valvalue to be complemented and AND'ed with this BigInteger.
returnthis & ~val
public int bitCount() Details
Returns the number of bits in the two's complement representation of this BigInteger that differ from its sign bit. This method is useful when implementing bit-vector style sets atop BigIntegers.
returnnumber of bits in the two's complement representation of this BigInteger that differ from its sign bit.
public int bitLength() Details
Returns the number of bits in the minimal two's-complement representation of this BigInteger, excluding a sign bit. For positive BigIntegers, this is equivalent to the number of bits in the ordinary binary representation. (Computes (ceil(log2(this < 0 ? -this : this+1))).)
returnnumber of bits in the minimal two's-complement representation of this BigInteger, excluding a sign bit.
public BigInteger clearBit(int n) Details
Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit cleared. (Computes (this & ~(1<<n)).)
nindex of bit to clear.
returnthis & ~(1<<n)
ThrowsArithmeticException: n is negative.
public int compareTo(BigInteger val) Details
Compares this BigInteger with the specified BigInteger. This method is provided in preference to individual methods for each of the six boolean comparison operators (<, ==, >, >=, !=, <=). The suggested idiom for performing these comparisons is: (x.compareTo(y) <op> 0), where <op> is one of the six comparison operators.
valBigInteger to which this BigInteger is to be compared.
return-1, 0 or 1 as this BigInteger is numerically less than, equal to, or greater than val.
public BigInteger divide(BigInteger val) Details
Returns a BigInteger whose value is (this / val).
valvalue by which this BigInteger is to be divided.
returnthis / val
ThrowsArithmeticException: val==0
public BigInteger[] divideAndRemainder(BigInteger val) Details
Returns an array of two BigIntegers containing (this / val) followed by (this % val).
valvalue by which this BigInteger is to be divided, and the remainder computed.
returnan array of two BigIntegers: the quotient (this / val) is the initial element, and the remainder (this % val) is the final element.
ThrowsArithmeticException: val==0
public double doubleValue() Details
Converts this BigInteger to a double. This conversion is similar to the narrowing primitive conversion from double to float defined in the Java Language Specification: if this BigInteger has too great a magnitude to represent as a double, it will be converted to Double#NEGATIVE_INFINITY or Double#POSITIVE_INFINITY as appropriate. Note that even when the return value is finite, this conversion can lose information about the precision of the BigInteger value.
returnthis BigInteger converted to a double.
public boolean equals(Object x) Details
Compares this BigInteger with the specified Object for equality.
xObject to which this BigInteger is to be compared.
returntrue if and only if the specified Object is a BigInteger whose value is numerically equal to this BigInteger.
public BigInteger flipBit(int n) Details
Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit flipped. (Computes (this ^ (1<<n)).)
nindex of bit to flip.
returnthis ^ (1<<n)
ThrowsArithmeticException: n is negative.
public float floatValue() Details
Converts this BigInteger to a float. This conversion is similar to the narrowing primitive conversion from double to float defined in the Java Language Specification: if this BigInteger has too great a magnitude to represent as a float, it will be converted to Float#NEGATIVE_INFINITY or Float#POSITIVE_INFINITY as appropriate. Note that even when the return value is finite, this conversion can lose information about the precision of the BigInteger value.
returnthis BigInteger converted to a float.
public BigInteger gcd(BigInteger val) Details
Returns a BigInteger whose value is the greatest common divisor of abs(this) and abs(val). Returns 0 if this==0 && val==0.
valvalue with which the GCD is to be computed.
returnGCD(abs(this), abs(val))
public int hashCode() Details
Returns the hash code for this BigInteger.
returnhash code for this BigInteger.
public int intValue() Details
Converts this BigInteger to an int. This conversion is analogous to a narrowing primitive conversion from long to int as defined in the Java Language Specification: if this BigInteger is too big to fit in an int, only the low-order 32 bits are returned. Note that this conversion can lose information about the overall magnitude of the BigInteger value as well as return a result with the opposite sign.
returnthis BigInteger converted to an int.
public long longValue() Details
Converts this BigInteger to a long. This conversion is analogous to a narrowing primitive conversion from long to int as defined in the Java Language Specification: if this BigInteger is too big to fit in a long, only the low-order 64 bits are returned. Note that this conversion can lose information about the overall magnitude of the BigInteger value as well as return a result with the opposite sign.
returnthis BigInteger converted to a long.
public BigInteger max(BigInteger val) Details
Returns the maximum of this BigInteger and val.
valvalue with which the maximum is to be computed.
returnthe BigInteger whose value is the greater of this and val. If they are equal, either may be returned.
public BigInteger min(BigInteger val) Details
Returns the minimum of this BigInteger and val.
valvalue with which the minimum is to be computed.
returnthe BigInteger whose value is the lesser of this BigInteger and val. If they are equal, either may be returned.
public BigInteger mod(BigInteger m) Details
Returns a BigInteger whose value is (this mod m). This method differs from remainder in that it always returns a non-negative BigInteger.
mthe modulus.
returnthis mod m
ThrowsArithmeticException: m <= 0
See also remainder
public BigInteger modInverse(BigInteger m) Details
Returns a BigInteger whose value is (this-1 mod m).
mthe modulus.
returnthis-1 mod m.
ThrowsArithmeticException: m <= 0, or this BigInteger has no multiplicative inverse mod m (that is, this BigInteger is not relatively prime to m).
public BigInteger modPow(BigInteger exponent, BigInteger m) Details
Returns a BigInteger whose value is (thisexponent mod m). (Unlike pow, this method permits negative exponents.)
exponentthe exponent.
mthe modulus.
returnthisexponent mod m
ThrowsArithmeticException: m <= 0
See also modInverse
public BigInteger multiply(BigInteger val) Details
Returns a BigInteger whose value is (this * val).
valvalue to be multiplied by this BigInteger.
returnthis * val
public BigInteger negate() Details
Returns a BigInteger whose value is (-this).
return-this
public BigInteger nextProbablePrime() Details
Returns the first integer greater than this BigInteger that is probably prime. The probability that the number returned by this method is composite does not exceed 2-100. This method will never skip over a prime when searching: if it returns p, there is no prime q such that this < q < p.
returnthe first integer greater than this BigInteger that is probably prime.
ThrowsArithmeticException: this < 0.
since1.5
public BigInteger not() Details
Returns a BigInteger whose value is (~this). (This method returns a negative value if and only if this BigInteger is non-negative.)
return~this
public BigInteger or(BigInteger val) Details
Returns a BigInteger whose value is (this | val). (This method returns a negative BigInteger if and only if either this or val is negative.)
valvalue to be OR'ed with this BigInteger.
returnthis | val
public BigInteger pow(int exponent) Details
Returns a BigInteger whose value is (thisexponent). Note that exponent is an integer rather than a BigInteger.
exponentexponent to which this BigInteger is to be raised.
returnthisexponent
ThrowsArithmeticException: exponent is negative. (This would cause the operation to yield a non-integer value.)
public static BigInteger probablePrime(int bitLength, Random rnd) Details
Returns a positive BigInteger that is probably prime, with the specified bitLength. The probability that a BigInteger returned by this method is composite does not exceed 2-100.
bitLengthbitLength of the returned BigInteger.
rndsource of random bits used to select candidates to be tested for primality.
returna BigInteger of bitLength bits that is probably prime
ThrowsArithmeticException: bitLength < 2.
since1.4
See also bitLength()
public BigInteger remainder(BigInteger val) Details
Returns a BigInteger whose value is (this % val).
valvalue by which this BigInteger is to be divided, and the remainder computed.
returnthis % val
ThrowsArithmeticException: val==0
public BigInteger shiftLeft(int n) Details
Returns a BigInteger whose value is (this << n). The shift distance, n, may be negative, in which case this method performs a right shift. (Computes floor(this * 2n).)
nshift distance, in bits.
returnthis << n
See also shiftRight
public BigInteger shiftRight(int n) Details
Returns a BigInteger whose value is (this >> n). Sign extension is performed. The shift distance, n, may be negative, in which case this method performs a left shift. (Computes floor(this / 2n).)
nshift distance, in bits.
returnthis >> n
See also shiftLeft
public int signum() Details
Returns the signum function of this BigInteger.
return-1, 0 or 1 as the value of this BigInteger is negative, zero or positive.
public BigInteger subtract(BigInteger val) Details
Returns a BigInteger whose value is (this - val).
valvalue to be subtracted from this BigInteger.
returnthis - val
public boolean testBit(int n) Details
Returns true if and only if the designated bit is set. (Computes ((this & (1<<n)) != 0).)
nindex of bit to test.
returntrue if and only if the designated bit is set.
ThrowsArithmeticException: n is negative.
public byte[] toByteArray() Details
Returns a byte array containing the two's-complement representation of this BigInteger. The byte array will be in big-endian byte-order: the most significant byte is in the zeroth element. The array will contain the minimum number of bytes required to represent this BigInteger, including at least one sign bit, which is (ceil((this.bitLength() + 1)/8)). (This representation is compatible with the (byte[]) constructor.)
returna byte array containing the two's-complement representation of this BigInteger.
See also BigInteger(byte[])
public String toString(int radix) Details
Returns the String representation of this BigInteger in the given radix. If the radix is outside the range from Character#MIN_RADIX to Character#MAX_RADIX inclusive, it will default to 10 (as is the case for Integer.toString). The digit-to-character mapping provided by Character.forDigit is used, and a minus sign is prepended if appropriate. (This representation is compatible with the (String, int) constructor.)
radixradix of the String representation.
returnString representation of this BigInteger in the given radix.
See also toString, forDigit, BigInteger(java.lang.String, int)
public String toString() Details
Returns the decimal String representation of this BigInteger. The digit-to-character mapping provided by Character.forDigit is used, and a minus sign is prepended if appropriate. (This representation is compatible with the (String) constructor, and allows for String concatenation with Java's + operator.)
returndecimal String representation of this BigInteger.
See also forDigit, BigInteger(java.lang.String)
public static BigInteger valueOf(long val) Details
Returns a BigInteger whose value is equal to that of the specified long. This "static factory method" is provided in preference to a (long) constructor because it allows for reuse of frequently used BigIntegers.
valvalue of the BigInteger to return.
returna BigInteger with the specified value.
public BigInteger xor(BigInteger val) Details
Returns a BigInteger whose value is (this ^ val). (This method returns a negative BigInteger if and only if exactly one of this and val are negative.)
valvalue to be XOR'ed with this BigInteger.
returnthis ^ val

Properties
public BigInteger setBit(int n) Details
Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit set. (Computes (this | (1<<n)).)
nindex of bit to set.
returnthis | (1<<n)
ThrowsArithmeticException: n is negative.
public int getLowestSetBit() Details
Returns the index of the rightmost (lowest-order) one bit in this BigInteger (the number of zero bits to the right of the rightmost one bit). Returns -1 if this BigInteger contains no one bits. (Computes (this==0? -1 : log2(this & -this)).)
returnindex of the rightmost one bit in this BigInteger.
public boolean isProbablePrime(int certainty) Details
Returns true if this BigInteger is probably prime, false if it's definitely composite. If certainty is <= 0, true is returned.
certaintya measure of the uncertainty that the caller is willing to tolerate: if the call returns true the probability that this BigInteger is prime exceeds (1 - 1/2certainty). The execution time of this method is proportional to the value of this parameter.
returntrue if this BigInteger is probably prime, false if it's definitely composite.
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