java.lang.Number
java.math.BigInteger
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java.lang.Object
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| Field Summary | |
|---|---|
static BigInteger |
ONE
The BigInteger constant one. |
static BigInteger |
TEN
The BigInteger constant ten. |
static BigInteger |
ZERO
The BigInteger constant zero. |
| Constructor Summary | |
|---|---|
BigInteger(byte[] val)
Translates a byte array containing the two's-complement binary representation of a BigInteger into a BigInteger. |
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BigInteger(int signum,
byte[] magnitude)
Translates the sign-magnitude representation of a BigInteger into a BigInteger. |
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BigInteger(int bitLength,
int certainty,
Random rnd)
Constructs a randomly generated positive BigInteger that is probably prime, with the specified bitLength. |
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BigInteger(int numBits,
Random rnd)
Constructs a randomly generated BigInteger, uniformly distributed over the range 0 to (2 numBits - 1), inclusive. |
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BigInteger(String val)
Translates the decimal String representation of a BigInteger into a BigInteger. |
|
BigInteger(String val,
int radix)
Translates the String representation of a BigInteger in the specified radix into a BigInteger. |
|
| Method Summary | |
|---|---|
BigInteger |
abs()
Returns a BigInteger whose value is the absolute value of this BigInteger. |
BigInteger |
add(BigInteger val)
Returns a BigInteger whose value is (this + val). |
BigInteger |
and(BigInteger val)
Returns a BigInteger whose value is (this & val). |
BigInteger |
andNot(BigInteger val)
Returns a BigInteger whose value is (this & ~val). |
int |
bitCount()
Returns the number of bits in the two's complement representation of this BigInteger that differ from its sign bit. |
int |
bitLength()
Returns the number of bits in the minimal two's-complement representation of this BigInteger, excluding a sign bit. |
BigInteger |
clearBit(int n)
Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit cleared. |
int |
compareTo(BigInteger val)
Compares this BigInteger with the specified BigInteger. |
BigInteger |
divide(BigInteger val)
Returns a BigInteger whose value is (this / val). |
BigInteger[] |
divideAndRemainder(BigInteger val)
Returns an array of two BigIntegers containing (this / val)
followed by (this % val). |
double |
doubleValue()
Converts this BigInteger to a double. |
boolean |
equals(Object x)
Compares this BigInteger with the specified Object for equality. |
BigInteger |
flipBit(int n)
Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit flipped. |
float |
floatValue()
Converts this BigInteger to a float. |
BigInteger |
gcd(BigInteger val)
Returns a BigInteger whose value is the greatest common divisor of abs(this) and abs(val). |
int |
getLowestSetBit()
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). |
int |
hashCode()
Returns the hash code for this BigInteger. |
int |
intValue()
Converts this BigInteger to an int. |
boolean |
isProbablePrime(int certainty)
Suppressed. Returns true if this BigInteger is probably prime,
false if it's definitely composite. |
long |
longValue()
Converts this BigInteger to a long. |
BigInteger |
max(BigInteger val)
Returns the maximum of this BigInteger and val. |
BigInteger |
min(BigInteger val)
Returns the minimum of this BigInteger and val. |
BigInteger |
mod(BigInteger m)
Returns a BigInteger whose value is (this mod m). |
BigInteger |
modInverse(BigInteger m)
Returns a BigInteger whose value is (this-1 mod m). |
BigInteger |
modPow(BigInteger exponent,
BigInteger m)
Returns a BigInteger whose value is (thisexponent mod m). |
BigInteger |
multiply(BigInteger val)
Returns a BigInteger whose value is (this * val). |
BigInteger |
negate()
Returns a BigInteger whose value is (-this). |
BigInteger |
nextProbablePrime()
Suppressed. Returns the first integer greater than this BigInteger that
is probably prime. |
BigInteger |
not()
Returns a BigInteger whose value is (~this). |
BigInteger |
or(BigInteger val)
Returns a BigInteger whose value is (this | val). |
BigInteger |
pow(int exponent)
Returns a BigInteger whose value is (thisexponent). |
static BigInteger |
probablePrime(int bitLength,
Random rnd)
Returns a positive BigInteger that is probably prime, with the specified bitLength. |
BigInteger |
remainder(BigInteger val)
Returns a BigInteger whose value is (this % val). |
BigInteger |
setBit(int n)
Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit set. |
BigInteger |
shiftLeft(int n)
Returns a BigInteger whose value is (this << n). |
BigInteger |
shiftRight(int n)
Returns a BigInteger whose value is (this >> n). |
int |
signum()
Returns the signum function of this BigInteger. |
BigInteger |
subtract(BigInteger val)
Returns a BigInteger whose value is (this - val). |
boolean |
testBit(int n)
Returns true if and only if the designated bit is set. |
byte[] |
toByteArray()
Returns a byte array containing the two's-complement representation of this BigInteger. |
String |
toString()
Returns the decimal String representation of this BigInteger. |
String |
toString(int radix)
Returns the String representation of this BigInteger in the given radix. |
static BigInteger |
valueOf(long val)
Returns a BigInteger whose value is equal to that of the specified long. |
BigInteger |
xor(BigInteger val)
Returns a BigInteger whose value is (this ^ val). |
| 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 |
|---|
public static final BigInteger ZERO
public static final BigInteger ONE
public static final BigInteger TEN
| Constructor Detail |
|---|
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)
Character.digit. The String may not contain any extraneous
characters (whitespace, for example).
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)
Character.digit.
The String may not contain any extraneous characters (whitespace, for
example).
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 - 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.
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()| Method Detail |
|---|
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.
bitLength bits that is probably prime
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)
(this + val).
val - value to be added to this BigInteger.
this + valpublic BigInteger subtract(BigInteger val)
(this - val).
val - value to be subtracted from this BigInteger.
this - valpublic BigInteger multiply(BigInteger val)
(this * val).
val - value to be multiplied by this BigInteger.
this * valpublic BigInteger divide(BigInteger val)
(this / val).
val - value by which this BigInteger is to be divided.
this / val
ArithmeticException - if val is zero.public BigInteger[] divideAndRemainder(BigInteger val)
(this / val)
followed by (this % val).
val - value by which this BigInteger is to be divided, and the
remainder computed.
(this / val)
is the initial element, and the remainder (this % val)
is the final element.
ArithmeticException - if val is zero.public BigInteger remainder(BigInteger val)
(this % val).
val - value by which this BigInteger is to be divided, and the
remainder computed.
this % val
ArithmeticException - if val is zero.public BigInteger pow(int exponent)
exponent is an integer rather than a BigInteger.
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)
abs(this) and abs(val). Returns 0 if
this==0 && val==0.
val - value with which the GCD is to be computed.
GCD(abs(this), abs(val))public BigInteger abs()
abs(this)public BigInteger negate()
(-this).
-thispublic int signum()
public BigInteger mod(BigInteger m)
(this mod m). This method
differs from remainder in that it always returns a
non-negative BigInteger.
m - the modulus.
this mod m
ArithmeticException - m ≤ 0remainder(java.math.BigInteger)
public BigInteger modPow(BigInteger exponent,
BigInteger m)
pow, this
method permits negative exponents.)
exponent - the exponent.m - the modulus.
ArithmeticException - m ≤ 0 or the exponent is
negative and this BigInteger is not relatively
prime to m.modInverse(java.math.BigInteger)public BigInteger modInverse(BigInteger m)
(this-1 mod m).
m - the modulus.
this-1 mod m.
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)
(this << n).
The shift distance, n, may be negative, in which case
this method performs a right shift.
(Computes floor(this * 2n).)
n - shift distance, in bits.
this << n
ArithmeticException - if the shift distance is Integer.MIN_VALUE.shiftRight(int)public BigInteger shiftRight(int n)
(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).)
n - shift distance, in bits.
this >> n
ArithmeticException - if the shift distance is Integer.MIN_VALUE.shiftLeft(int)public BigInteger and(BigInteger val)
(this & val). (This
method returns a negative BigInteger if and only if this and val are
both negative.)
val - value to be AND'ed with this BigInteger.
this & valpublic BigInteger or(BigInteger val)
(this | val). (This method
returns a negative BigInteger if and only if either this or val is
negative.)
val - value to be OR'ed with this BigInteger.
this | valpublic BigInteger xor(BigInteger val)
(this ^ val). (This method
returns a negative BigInteger if and only if exactly one of this and
val are negative.)
val - value to be XOR'ed with this BigInteger.
this ^ valpublic BigInteger not()
(~this). (This method
returns a negative value if and only if this BigInteger is
non-negative.)
~thispublic BigInteger andNot(BigInteger val)
(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.)
val - value to be complemented and AND'ed with this BigInteger.
this & ~valpublic boolean testBit(int n)
true if and only if the designated bit is set.
(Computes ((this & (1<<n)) != 0).)
n - index of bit to test.
true if and only if the designated bit is set.
ArithmeticException - n is negative.public BigInteger setBit(int n)
(this | (1<<n)).)
n - index of bit to set.
this | (1<<n)
ArithmeticException - n is negative.public BigInteger clearBit(int n)
(this & ~(1<<n)).)
n - index of bit to clear.
this & ~(1<<n)
ArithmeticException - n is negative.public BigInteger flipBit(int n)
(this ^ (1<<n)).)
n - index of bit to flip.
this ^ (1<<n)
ArithmeticException - n is negative.public int getLowestSetBit()
(this==0? -1 : log2(this & -this)).)
public int bitLength()
(ceil(log2(this < 0 ? -this : this+1))).)
public int bitCount()
public boolean isProbablePrime(int certainty)
true if this BigInteger is probably prime,
false if it's definitely composite. If
certainty is ≤ 0, true is
returned.
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.
true if this BigInteger is probably prime,
false if it's definitely composite.public int compareTo(BigInteger val)
(x.compareTo(y) <op> 0), where
<op> is one of the six comparison operators.
compareTo in interface Comparable<BigInteger>val - BigInteger to which this BigInteger is to be compared.
val.public boolean equals(Object x)
equals in class Objectx - Object to which this BigInteger is to be compared.
true if and only if the specified Object is a
BigInteger whose value is numerically equal to this BigInteger.Object.hashCode(),
HashMappublic BigInteger min(BigInteger val)
val.
val - value with which the minimum is to be computed.
val. If they are equal, either may be returned.public BigInteger max(BigInteger val)
val.
val - value with which the maximum is to be computed.
val. If they are equal, either may be returned.public int hashCode()
hashCode in class ObjectObject.equals(java.lang.Object),
System.identityHashCode(java.lang.Object)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()
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.)
toString in class ObjectCharacter.forDigit(int, int),
BigInteger(java.lang.String)public byte[] toByteArray()
(ceil((this.bitLength() +
1)/8)). (This representation is compatible with the
(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 Numberint.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 Numberlong.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 Numberfloat.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 Numberdouble.
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