java.lang.Object
java.lang.Number
java.math.BigInteger
public class BigInteger
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.
BigDecimal, Serialized Form
BigInteger(byte[] val)
BigInteger(int signum, byte[] magnitude)
BigInteger(int bitLength, int certainty, Random rnd)
BigInteger(int numBits, Random rnd)
BigInteger(String val)
BigInteger(String val, int radix)
public static final BigInteger ZERO
public static final BigInteger ONE
public static final BigInteger TEN
public BigInteger(byte[] val)
val - big-endian two's-complement binary representation of BigInteger.
NumberFormatException - val is zero bytes long.
public BigInteger(int signum,
byte[] magnitude)
signum - signum of the number (-1 for negative, 0 for zero, 1 for positive).
magnitude - big-endian binary representation of the magnitude of the number.
NumberFormatException - 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)
val - String representation of BigInteger.
radix - radix to be used in interpreting val.
NumberFormatException - 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.
Character.digit(char, int)
public BigInteger(String val)
val - decimal String representation of BigInteger.
NumberFormatException - val is not a valid representation of a BigInteger.
Character.digit(char, int)
public BigInteger(int numBits,
Random rnd)
numBits - maximum bitLength of the new BigInteger.
rnd - source of randomness to be used in computing the new BigInteger.
IllegalArgumentException - numBits is negative.
bitLength
public BigInteger(int bitLength,
int certainty,
Random rnd)
It is recommended that the probablePrime method be used in preference to this constructor unless there is a compelling need to specify a certainty.
bitLength - bitLength of the returned BigInteger.
certainty - a 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.
rnd - source of random bits used to select candidates to be tested for primality.
ArithmeticException - bitLength < 2.
bitLength
public static BigInteger probablePrime(int bitLength,
Random rnd)
bitLength - bitLength of the returned BigInteger.
rnd - source of random bits used to select candidates to be tested for primality.
ArithmeticException - bitLength < 2.
bitLength
public BigInteger nextProbablePrime()
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.
BigInteger that is probably prime.
ArithmeticException - this < 0.
public static BigInteger valueOf(long val)
long. This "static factory method" is provided in preference to a (long) constructor because it allows for reuse of frequently used BigIntegers.
val - value of the BigInteger to return.
public BigInteger add(BigInteger val)
val - value to be added to this BigInteger.
public BigInteger subtract(BigInteger val)
val - value to be subtracted from this BigInteger.
public BigInteger multiply(BigInteger val)
val - value to be multiplied by this BigInteger.
public BigInteger divide(BigInteger val)
val - value by which this BigInteger is to be divided.
ArithmeticException - val==0
public BigInteger[] divideAndRemainder(BigInteger val)
val - value by which this BigInteger is to be divided, and the remainder computed.
ArithmeticException - val==0
public BigInteger remainder(BigInteger val)
val - value by which this BigInteger is to be divided, and the remainder computed.
ArithmeticException - val==0
public BigInteger pow(int exponent)
exponent - exponent to which this BigInteger is to be raised.
ArithmeticException - exponent is negative. (This would cause the operation to yield a non-integer value.)
public BigInteger gcd(BigInteger val)
val - value with which the GCD is to be computed.
public BigInteger abs()
public BigInteger negate()
public int signum()
public BigInteger mod(BigInteger m)
m - the modulus.
ArithmeticException - m <= 0
remainder(java.math.BigInteger)
public BigInteger modPow(BigInteger exponent,
BigInteger m)
exponent - the exponent.
m - the modulus.
ArithmeticException - m <= 0
modInverse(java.math.BigInteger)
public BigInteger modInverse(BigInteger m)
m - the modulus.
ArithmeticException - m <= 0, or this BigInteger has no multiplicative inverse mod m (that is, this BigInteger is not relatively prime to m).
public BigInteger shiftLeft(int n)
n - shift distance, in bits.
shiftRight(int)
public BigInteger shiftRight(int n)
n - shift distance, in bits.
shiftLeft(int)
public BigInteger and(BigInteger val)
val - value to be AND'ed with this BigInteger.
public BigInteger or(BigInteger val)
val - value to be OR'ed with this BigInteger.
public BigInteger xor(BigInteger val)
val - value to be XOR'ed with this BigInteger.
public BigInteger not()
public BigInteger andNot(BigInteger val)
val - value to be complemented and AND'ed with this BigInteger.
public boolean testBit(int n)
n - index of bit to test.
ArithmeticException - n is negative.
public BigInteger setBit(int n)
n - index of bit to set.
ArithmeticException - n is negative.
public BigInteger clearBit(int n)
n - index of bit to clear.
ArithmeticException - n is negative.
public BigInteger flipBit(int n)
n - index of bit to flip.
ArithmeticException - n is negative.
public int getLowestSetBit()
public int bitLength()
public int bitCount()
public boolean isProbablePrime(int certainty)
certainty - a 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.
public int compareTo(BigInteger val)
compareTo in interface Comparable<BigInteger>
val - BigInteger to which this BigInteger is to be compared.
public boolean equals(Object x)
equals in class Object
x - Object to which this BigInteger is to be compared.
Object.hashCode(), Hashtable
public BigInteger min(BigInteger val)
val - value with which the minimum is to be computed.
public BigInteger max(BigInteger val)
val - value with which the maximum is to be computed.
public int hashCode()
hashCode in class Object
Object.equals(java.lang.Object), Hashtable
public String toString(int radix)
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.)
radix - radix of the String representation.
Integer.toString(int, int), Character.forDigit(int, int), BigInteger(java.lang.String, int)
public String toString()
(String) constructor, and allows for String concatenation with Java's + operator.)
toString in class Object
Character.forDigit(int, int), BigInteger(java.lang.String)
public byte[] toByteArray()
(byte[]) constructor.)
BigInteger(byte[])
public int intValue()
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.
intValue in class Number
int.
public long longValue()
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.
longValue in class Number
long.
public float floatValue()
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.
floatValue in class Number
float.
public double doubleValue()
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.
doubleValue in class Number
double.
Copyright © 2004, 2010 Oracle and/or its affiliates. All rights reserved. Use is subject to license terms. Also see the documentation redistribution policy.
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