public class BigInteger extends Numberimplements Comparable <BigInteger >
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. BigInteger must support values in the range -2Integer.MAX_VALUE
(exclusive) to +2Integer.MAX_VALUE
(exclusive) and may support values outside of that range. The range of probable prime values is limited and may be less than the full supported positive range of BigInteger
. The range must be at least 1 to 2500000000.
BigDecimal
,
Serialized Form
Modifier and Type | Field and Description |
---|---|
static BigInteger |
ONE
The BigInteger constant one.
|
static BigInteger |
TEN
The BigInteger constant ten.
|
static BigInteger |
ZERO
The BigInteger constant zero.
|
Constructor and Description |
---|
BigInteger(byte[] val)
Translates a byte array containing the two's-complement binary representation of a BigInteger into a BigInteger.
|
BigInteger(int signum, byte[] magnitude)
Translates the sign-magnitude representation of a BigInteger into a BigInteger.
|
BigInteger(int bitLength, int certainty, Random
Constructs a randomly generated positive BigInteger that is probably prime, with the specified bitLength.
|
BigInteger(int numBits, Random
Constructs a randomly generated BigInteger, uniformly distributed over the range 0 to (2
numBits - 1), inclusive.
|
BigInteger(String
Translates the decimal String representation of a BigInteger into a BigInteger.
|
BigInteger(String
Translates the String representation of a BigInteger in the specified radix into a BigInteger.
|
Modifier and Type | Method and Description |
---|---|
BigInteger |
abs()
Returns a BigInteger whose value is the absolute value of this BigInteger.
|
BigInteger |
add(BigInteger
Returns a BigInteger whose value is
(this + val) .
|
BigInteger |
and(BigInteger
Returns a BigInteger whose value is
(this & val) .
|
BigInteger |
andNot(BigInteger
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.
|
byte |
byteValueExact()
Converts this
BigInteger to a
byte , checking for lost information.
|
BigInteger |
clearBit(int n)
Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit cleared.
|
int |
compareTo(BigInteger
Compares this BigInteger with the specified BigInteger.
|
BigInteger |
divide(BigInteger
Returns a BigInteger whose value is
(this / val) .
|
BigInteger |
divideAndRemainder(BigInteger
Returns an array of two BigIntegers containing
(this / val) followed by
(this % val) .
|
double |
doubleValue()
Converts this BigInteger to a
double .
|
boolean |
equals(Object
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
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 .
|
int |
intValueExact()
Converts this
BigInteger to an
int , checking for lost information.
|
boolean |
isProbablePrime(int certainty)
Returns
true if this BigInteger is probably prime,
false if it's definitely composite.
|
long |
longValue()
Converts this BigInteger to a
long .
|
long |
longValueExact()
Converts this
BigInteger to a
long , checking for lost information.
|
BigInteger |
max(BigInteger
Returns the maximum of this BigInteger and
val .
|
BigInteger |
min(BigInteger
Returns the minimum of this BigInteger and
val .
|
BigInteger |
mod(BigInteger
Returns a BigInteger whose value is
(this mod m ).
|
BigInteger |
modInverse(BigInteger
Returns a BigInteger whose value is
(this
-1
mod m) .
|
BigInteger |
modPow(BigInteger
Returns a BigInteger whose value is
(thisexponent mod m).
|
BigInteger |
multiply(BigInteger
Returns a BigInteger whose value is
(this * val) .
|
BigInteger |
negate()
Returns a BigInteger whose value is
(-this) .
|
BigInteger |
nextProbablePrime()
Returns the first integer greater than this
BigInteger that is probably prime.
|
BigInteger |
not()
Returns a BigInteger whose value is
(~this) .
|
BigInteger |
or(BigInteger
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
Returns a positive BigInteger that is probably prime, with the specified bitLength.
|
BigInteger |
remainder(BigInteger
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) .
|
short |
shortValueExact()
Converts this
BigInteger to a
short , checking for lost information.
|
int |
signum()
Returns the signum function of this BigInteger.
|
BigInteger |
subtract(BigInteger
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
Returns a BigInteger whose value is
(this ^ val) .
|
byteValue, shortValue
public static final BigIntegerZERO
public static final BigIntegerONE
public static final BigIntegerTEN
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(Stringval, 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(Stringval)
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, Randomrnd)
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, Randomrnd)
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 - 1/2
certainty
). 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
or
bitLength
is too large.
bitLength()
public static BigIntegerprobablePrime(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
or
bitLength
is too large.
bitLength()
public BigIntegernextProbablePrime()
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
or
this
is too large.
public static BigIntegervalueOf(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 BigIntegeradd(BigInteger val)
(this + val)
.
val
- value to be added to this BigInteger.
this + val
public BigIntegersubtract(BigInteger val)
(this - val)
.
val
- value to be subtracted from this BigInteger.
this - val
public BigIntegermultiply(BigInteger val)
(this * val)
.
val
- value to be multiplied by this BigInteger.
this * val
public BigIntegerdivide(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 BigIntegerremainder(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 BigIntegerpow(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 BigIntegergcd(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 BigIntegerabs()
abs(this)
public BigIntegernegate()
(-this)
.
-this
public int signum()
public BigIntegermod(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
≤ 0
remainder(java.math.BigInteger)
public BigIntegermodPow(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 BigIntegermodInverse(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 BigIntegershiftLeft(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
shiftRight(int)
public BigIntegershiftRight(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
shiftLeft(int)
public BigIntegerand(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 & val
public BigIntegeror(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 | val
public BigIntegerxor(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 ^ val
public BigIntegernot()
(~this)
. (This method returns a negative value if and only if this BigInteger is non-negative.)
~this
public BigIntegerandNot(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 & ~val
public 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 BigIntegersetBit(int n)
(this | (1<<n))
.)
n
- index of bit to set.
this | (1<<n)
ArithmeticException
-
n
is negative.
public BigIntegerclearBit(int n)
(this & ~(1<<n))
.)
n
- index of bit to clear.
this & ~(1<<n)
ArithmeticException
-
n
is negative.
public BigIntegerflipBit(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 - 1/2
certainty
). 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(BigIntegerval)
(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(Objectx)
equals
in class
Object
x
- 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()
,
HashMap
public BigIntegermin(BigInteger val)
val
.
val
- value with which the minimum is to be computed.
val
. If they are equal, either may be returned.
public BigIntegermax(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
Object
Object.equals(java.lang.Object)
,
System.identityHashCode(java.lang.Object)
public StringtoString(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 StringtoString()
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
Object
Character.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 section 5.1.3 of
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
.
intValueExact()
public long longValue()
long
. This conversion is analogous to a
narrowing primitive conversion from
long
to
int
as defined in section 5.1.3 of
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
.
longValueExact()
public float floatValue()
float
. This conversion is similar to the
narrowing primitive conversion from
double
to
float
as defined in section 5.1.3 of
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
as defined in section 5.1.3 of
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
.
public long longValueExact()
BigInteger
to a
long
, checking for lost information. If the value of this
BigInteger
is out of the range of the
long
type, then an
ArithmeticException
is thrown.
BigInteger
converted to a
long
.
ArithmeticException
- if the value of
this
will not exactly fit in a
long
.
longValue()
public int intValueExact()
BigInteger
to an
int
, checking for lost information. If the value of this
BigInteger
is out of the range of the
int
type, then an
ArithmeticException
is thrown.
BigInteger
converted to an
int
.
ArithmeticException
- if the value of
this
will not exactly fit in a
int
.
intValue()
public short shortValueExact()
BigInteger
to a
short
, checking for lost information. If the value of this
BigInteger
is out of the range of the
short
type, then an
ArithmeticException
is thrown.
BigInteger
converted to a
short
.
ArithmeticException
- if the value of
this
will not exactly fit in a
short
.
Number.shortValue()
public byte byteValueExact()
BigInteger
to a
byte
, checking for lost information. If the value of this
BigInteger
is out of the range of the
byte
type, then an
ArithmeticException
is thrown.
BigInteger
converted to a
byte
.
ArithmeticException
- if the value of
this
will not exactly fit in a
byte
.
Number.byteValue()