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java.math
Class BigInteger
java.lang.Object
java.lang.Number
java.math.BigInteger

All Implemented Interfaces:

Comparable
,
Serializable

public class
BigInteger

extends
Number

implements
Comparable
<
BigInteger
>
Immutable arbitraryprecision integers. All operations behave as if BigIntegers were represented in two'scomplement 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 rightshift with a negative shift distance results in a left shift, and viceversa. 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 nonnegative result, between
0
and
(modulus  1)
, inclusive.
Bit operations operate on a single bit of the two'scomplement representation of their operand. If necessary, the operand is sign extended so that it contains the designated bit. None of the singlebit 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, pseudocode is used throughout the descriptions of BigInteger methods. The pseudocode expression
(i + j)
is shorthand for "a BigInteger whose value is that of the BigInteger
i
plus that of the BigInteger
j
." The pseudocode expression
(i == j)
is shorthand for "
true
if and only if the BigInteger
i
represents the same value as the the BigInteger
j
." Other pseudocode expressions are interpreted similarly.
All methods and constructors in this class throw NullPointerException when passed a null object reference for any input parameter.

Since:

JDK1.1

See Also:

BigDecimal
,
Serialized Form
Constructor Summary

BigInteger
(byte[] val)
Translates a byte array containing the two'scomplement binary representation of a BigInteger into a BigInteger. 
BigInteger
(int signum, byte[] magnitude)
Translates the signmagnitude representation of a BigInteger into a BigInteger. 
BigInteger
(int bitLength, int certainty,
Random
rnd)
Constructs a randomly generated positive BigInteger that is probably prime, with the specified bitLength. 
BigInteger
(int numBits,
Random
rnd)
Constructs a randomly generated BigInteger, uniformly distributed over the range
0
to
(2^{
numBits}
 1)
, inclusive. 
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'scomplement 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. 
int

compareTo
(
Object
Compares this BigInteger with the specified Object.

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 (lowestorder) 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)
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
(this^{
exponent}
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
()
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
(this^{
exponent}
)
. 
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'scomplement 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

ZERO
public static final BigInteger ZERO

The BigInteger constant zero.

Since:

1.2
ONE
public static final BigInteger ONE

The BigInteger constant one.

Since:

1.2
TEN
public static final BigIntegerTEN

The BigInteger constant ten.

Since:

1.5
BigInteger
public BigInteger(byte[] val)

Translates a byte array containing the two'scomplement binary representation of a BigInteger into a BigInteger. The input array is assumed to be in
bigendian
byteorder: the most significant byte is in the zeroth element.

Parameters:

val  bigendian two'scomplement binary representation of BigInteger.

Throws:

NumberFormatException

val
is zero bytes long.
BigInteger
public BigInteger(int signum,
byte[] magnitude)

Translates the signmagnitude 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
bigendian
byteorder: the most significant byte is in the zeroth element. A zerolength magnitude array is permissible, and will result in in a BigInteger value of 0, whether signum is 1, 0 or 1.

Parameters:

signum  signum of the number (1 for negative, 0 for zero, 1 for positive).

magnitude  bigendian binary representation of the magnitude of the number.

Throws:

NumberFormatException

signum
is not one of the three legal values (1, 0, and 1), or
signum
is 0 and
magnitude
contains one or more nonzero bytes.
BigInteger
public BigInteger(String val,
int radix)

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 charactertodigit mapping is provided by
Character.digit
. The String may not contain any extraneous characters (whitespace, for example).

Parameters:

val  String representation of BigInteger.

radix  radix to be used in interpreting
val
.

Throws:

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.

See Also:

Character.digit(char, int)
BigInteger
public BigInteger(String val)

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 charactertodigit mapping is provided by
Character.digit
. The String may not contain any extraneous characters (whitespace, for example).

Parameters:

val  decimal String representation of BigInteger.

Throws:

NumberFormatException

val
is not a valid representation of a BigInteger.

See Also:

Character.digit(char, int)
BigInteger
public BigInteger(int numBits,
Random rnd)

Constructs a randomly generated BigInteger, uniformly distributed over the range
0
to
(2^{
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 nonnegative BigInteger.

Parameters:

numBits  maximum bitLength of the new BigInteger.

rnd  source of randomness to be used in computing the new BigInteger.

Throws:

IllegalArgumentException

numBits
is negative.

See Also:

bitLength()
BigInteger
public BigInteger(int bitLength,
int certainty,
Random rnd)

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.

Parameters:

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.

Throws:

ArithmeticException

bitLength < 2
.

See Also:

bitLength()
probablePrime
public static BigInteger probablePrime(int bitLength,
Random rnd)

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}
.



Parameters:

bitLength  bitLength of the returned BigInteger.

rnd  source of random bits used to select candidates to be tested for primality.

Returns:

a BigInteger of
bitLength
bits that is probably prime

Throws:

ArithmeticException

bitLength < 2
.

See Also:

bitLength()
nextProbablePrime
valueOf
public static BigIntegernextProbablePrime valueOf () (long val)

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
.
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.



Returns:
Parameters:

the first integer greater than this BigInteger that is probably prime.
val  value of the BigInteger to return.

Throws:
Returns:

ArithmeticException

this < 0
.

Since:

1.5
a BigInteger with the specified value.
valueOf
add
public static BigIntegervalueOf add (long val) ( BigInteger val)

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.
Returns a BigInteger whose value is
(this + val)
.



Parameters:

val  value of the BigInteger to return.
val  value to be added to this BigInteger.

Returns:

a BigInteger with the specified value.
this + val
add
subtract
public BigIntegeradd subtract (BigInteger val)

Returns a BigInteger whose value is
(this
+

val)
.



Parameters:

val  value to be
added to
subtracted from
this BigInteger. 
Returns:

this
+

val
subtract
multiply
public BigIntegersubtract multiply (BigInteger val)

Returns a BigInteger whose value is
(this

*
val)
.



Parameters:

val  value to be
subtracted from
multiplied by
this BigInteger. 
Returns:

this

*
val
multiply
divide
public BigIntegermultiply divide (BigInteger val)

Returns a BigInteger whose value is
(this
*
/
val)
.



Parameters:

val  value
by which this BigInteger is
to be
multiplied by this BigInteger.
divided.

Returns:

this
*
/
val

Throws:

ArithmeticException

val==0
divide
divideAndRemainder
public BigInteger[] divide divideAndRemainder (BigInteger val)

Returns a BigInteger whose value is
Returns an array of two BigIntegers containing
(this / val)
followed by
(this % val)
.



Parameters:

val  value by which this BigInteger is to be
divided.
divided, and the remainder computed.

Returns:

an array of two BigIntegers: the quotient
this / val
(this / val)
is the initial element, and the remainder
(this % val)
is the final element.

Throws:

ArithmeticException

val==0
divideAndRemainder
remainder
public BigInteger[] divideAndRemainder remainder (BigInteger val)

Returns an array of two BigIntegers containing
Returns a BigInteger whose value is
(this / val)
followed by
(this % val)
.



Parameters:

val  value by which this BigInteger is to be divided, and the remainder computed.

Returns:

an array of two BigIntegers: the quotient
(this / val)
this % val
is the initial element, and the remainder
(this % val)
is the final element.

Throws:

ArithmeticException

val==0
remainder
pow
public BigIntegerremainder pow ( BigInteger val) (int exponent)

Returns a BigInteger whose value is
(this % val)
(this
^{
exponent
}
)
.
Note that
exponent
is an integer rather than a BigInteger.



Parameters:

val
exponent

value by
exponent to
which this BigInteger is to be
divided, and the remainder computed.
raised.

Returns:

this % val
this
^{
exponent
}

Throws:

ArithmeticException

val==0
exponent
is negative. (This would cause the operation to yield a noninteger value.)
pow
gcd
public BigIntegerpow gcd (int exponent) ( BigInteger val)

Returns a BigInteger whose value is
the greatest common divisor of
(this
^{
exponent
}
)
abs(this)
and
abs(val)
.
Note that
Returns 0 if
exponent
this==0 && val==0
is an integer rather than a BigInteger.
.



Parameters:

exponent  exponent to which this BigInteger is to be raised.
val  value with with the GCD is to be computed.

Returns:

this
^{
exponent
}
GCD(abs(this), abs(val))

Throws:

ArithmeticException

exponent
is negative. (This would cause the operation to yield a noninteger value.)
gcd
abs
public BigIntegergcd abs ( BigInteger val) ()

Returns a BigInteger whose value is the greatest common divisor of
abs(this)
and
abs(val)
. Returns 0 if
this==0 && val==0
.
Returns a BigInteger whose value is the absolute value of this BigInteger.



Parameters:

val  value with with the GCD is to be computed.

Returns:

GCD(abs(this), abs(val))
abs(this)
abs
negate
public BigIntegerabs negate ()

Returns a BigInteger whose value is
the absolute value of this BigInteger.
(this)
.



Returns:

abs(this)
this
negate
signum
public BigInteger
public int negate signum ()

Returns a BigInteger whose value is
(this)
.
Returns the signum function of this BigInteger.



Returns:

this
1, 0 or 1 as the value of this BigInteger is negative, zero or positive.
signum
mod
public int
public BigIntegersignum mod () ( BigInteger m)

Returns the signum function of this BigInteger.
Returns a BigInteger whose value is
(this mod m
). This method differs from
remainder
in that it always returns a
nonnegative
BigInteger.



Parameters:

m  the modulus.

Returns:

1, 0 or 1 as the value of this BigInteger is negative, zero or positive.
this mod m

Throws:

ArithmeticException

m <= 0

See Also:

remainder(java.math.BigInteger)
mod
modPow
public BigIntegermod modPow (BigInteger exponent,
BigInteger m)

Returns a BigInteger whose value is
(this mod m
(this
^{
exponent
}
mod m)
). This method differs from
. (Unlike
remainder
pow
in that it always returns a
nonnegative
BigInteger.
, this method permits negative exponents.)



Parameters:

exponent  the exponent.

m  the modulus.

Returns:

this ^{
exponent
}
mod m

Throws:

ArithmeticException

m <= 0

See Also:

remainder(java.math.BigInteger)
modInverse(java.math.BigInteger)
modPow
modInverse
public BigIntegermodPow modInverse (BigInteger exponent,
BigInteger m)

Returns a BigInteger whose value is
(this^{
exponent
1
}
mod m)
.
(Unlike
pow
, this method permits negative exponents.)



Parameters:

exponent  the exponent.

m  the modulus.

Returns:

this^{
exponent
1
}
mod m
.

Throws:

ArithmeticException

m <= 0

See Also:

modInverse(java.math.BigInteger)
, or this BigInteger has no multiplicative inverse mod m (that is, this BigInteger is not
relatively prime
to m).
modInverse
shiftLeft
public BigIntegermodInverse shiftLeft ( BigInteger m) (int n)

Returns a BigInteger whose value is
(this
(this << n)
. The shift distance,
n
, may be negative, in which case this method performs a right shift. (Computes
floor(this * 2
^{
1
n
}
mod m)
)
.
.)



Parameters:

m  the modulus.
n  shift distance, in bits.

Returns:

this
^{
1
}
mod m
this << n
.

Throws:
See Also:

ArithmeticException
shiftRight(int)

m <= 0
, or this BigInteger has no multiplicative inverse mod m (that is, this BigInteger is not
relatively prime
to m).
shiftLeft
shiftRight
public BigIntegershiftLeft shiftRight (int n)

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
right
left
shift. (Computes
floor(this
*
/
2 ^{
n}
)
.)



Parameters:

n  shift distance, in bits.

Returns:

this
<<
>>
n

See Also:

shiftRight(int)
shiftLeft(int)
shiftRight
and
public BigIntegershiftRight and (int n) ( BigInteger val)

Returns a BigInteger whose value is
(this >> n)
(this & val)
.
Sign extension is performed. The shift distance,
n
, may be negative, in which case this method performs a left shift. (Computes
floor(this / 2
^{
n
}
)
.)
(This method returns a negative BigInteger if and only if this and val are both negative.)



Parameters:

n  shift distance, in bits.
val  value to be AND'ed with this BigInteger.

Returns:

this >> n
this & val

See Also:

shiftLeft(int)
and
or
public BigIntegerand or (BigInteger val)

Returns a BigInteger whose value is
(this
&

val)
. (This method returns a negative BigInteger if and only if
either
this
and
or
val
are both
is
negative.)



Parameters:

val  value to be
AND'ed
OR'ed
with this BigInteger. 
Returns:

this
&

val
or
xor
public BigIntegeror xor (BigInteger val)

Returns a BigInteger whose value is
(this

^
val)
. (This method returns a negative BigInteger if and only if
either
exactly one of
this
or
and
val
is
are
negative.)



Parameters:

val  value to be
OR'ed
XOR'ed
with this BigInteger. 
Returns:

this

^
val
xor
not
public BigIntegerxor not ( BigInteger val) ()

Returns a BigInteger whose value is
(this ^ val)
(~this)
. (This method returns a negative
BigInteger
value
if and only if
exactly one of
this
and val are negative.)
BigInteger is nonnegative.)



Parameters:

val  value to be XOR'ed with this BigInteger.

Returns:

this ^ val
~this
not
andNot
public BigIntegernot andNot () ( BigInteger val)

Returns a BigInteger whose value is
(~this)
(this & ~val)
.
(This method returns a negative value if and only if this BigInteger is nonnegative.)
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.)



Parameters:

val  value to be complemented and AND'ed with this BigInteger.

Returns:

~this
this & ~val
andNot
testBit
public BigInteger
public boolean andNot testBit ( BigInteger val) (int n)

Returns a BigInteger whose value is
Returns
(this & ~val)
true
. This method, which is equivalent to
if and only if the designated bit is set. (Computes
and(val.not())
((this & (1<<n)) != 0)
, 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.)
.)



Parameters:

val  value to be complemented and AND'ed with this BigInteger.
n  index of bit to test.

Returns:

this & ~val
true
if and only if the designated bit is set.

Throws:

ArithmeticException

n
is negative.
testBit
setBit
public boolean
public BigIntegertestBit setBit (int n)

Returns
true
if and only if the designated bit is set.
Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit set.
(Computes
((this & (1<<n)) != 0)
(this  (1<<n))
.)



Parameters:

n  index of bit to
test.
set.

Returns:

true
this  (1<<n)
if and only if the designated bit is set.

Throws:

ArithmeticException

n
is negative.
setBit
clearBit
public BigIntegersetBit clearBit (int n)

Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit
set.
cleared.
(Computes
(this  (1<<n))
(this & ~(1<<n))
.)



Parameters:

n  index of bit to
set.
clear.

Returns:

this  (1<<n)
this & ~(1<<n)

Throws:

ArithmeticException

n
is negative.
clearBit
flipBit
public BigIntegerclearBit flipBit (int n)

Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit
cleared.
flipped.
(Computes
(this & ~(1<<n))
(this ^ (1<<n))
.)



Parameters:

n  index of bit to
clear.
flip.

Returns:

this & ~(1<<n)
this ^ (1<<n)

Throws:

ArithmeticException

n
is negative.
flipBit
getLowestSetBit
public BigInteger
public int flipBit getLowestSetBit (int n) ()

Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit flipped.
Returns the index of the rightmost (lowestorder) 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 ^ (1<<n))
(this==0? 1 : log
_{
2
}
(this & this))
.)



Parameters:

n  index of bit to flip.

Returns:

this ^ (1<<n)

Throws:

ArithmeticException

n
is negative.
index of the rightmost one bit in this BigInteger.
getLowestSetBit
bitLength
public int getLowestSetBit bitLength ()

Returns the index of the rightmost (lowestorder) 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.
Returns the number of bits in the minimal two'scomplement 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
(this==0? 1 : log
(ceil(log
_{
2}
(this & this))
(this < 0 ? this : this+1)))
.)



Returns:

index of the rightmost one bit in this BigInteger.
number of bits in the minimal two'scomplement representation of this BigInteger,
excluding
a sign bit.
bitLength
bitCount
public int bitLength bitCount ()

Returns the number of bits in the minimal two'scomplement 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(log
_{
2
}
(this < 0 ? this : this+1)))
.)
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 bitvector style sets atop BigIntegers.



Returns:

number of bits in the
minimal two'scomplement
two's complement
representation of this
BigInteger,
excluding
a
BigInteger that differ from its
sign bit.
bitCount
isProbablePrime
public int boolean bitCount isProbablePrime () (int certainty)

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 bitvector style sets atop BigIntegers.
Returns
true
if this BigInteger is probably prime,
false
if it's definitely composite. If
certainty
is
<= 0
,
true
is returned.



Parameters:

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.

Returns:

number of bits in the two's complement representation of this BigInteger that differ from its sign bit.
true
if this BigInteger is probably prime,
false
if it's definitely composite.
isProbablePrime
compareTo
public boolean int isProbablePrime compareTo (int certainty) ( BigInteger val)

Returns
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:
true
(x.compareTo(y)
if this BigInteger is probably prime,
<
op
>
false
0)
if it's definitely composite. If
certainty
is
<= 0
,
true
is returned.
, where <
op
> is one of the six comparison operators.



Parameters:

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.
val  BigInteger to which this BigInteger is to be compared.

Returns:

1, 0 or 1 as this BigInteger is numerically less than, equal to, or greater than
true
val
if this BigInteger is probably prime,
false
if it's definitely composite.
.
compareTo
public int compareTo( BigIntegerObject val) o)

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:
Compares this BigInteger with the specified Object. If the Object is a BigInteger, this method behaves like
(x.compareTo(y)
compareTo(BigInteger)
<
op
>
. Otherwise, it throws a
0)
ClassCastException
, where <
op
> is one of the six comparison operators.
(as BigIntegers are comparable only to other BigIntegers).


Specified by:

compareTo
in interface
Comparable


Parameters:

val
o

BigInteger
Object
to which this BigInteger is to be compared. 
Returns:

1, 0
a negative number, zero,
or
1
a positive number
as
this BigInteger
this BigInteger
is numerically less than, equal to, or
greater than
greater than
val
o
.
, which must be a BigInteger.

Throws:

ClassCastException

o
is not a BigInteger.

Since:

1.2

See Also:

compareTo(java.math.BigInteger)
,
Comparable
equals
public boolean equals(Object x)

Compares this BigInteger with the specified Object for equality.


Overrides:

equals
in class
Object


Parameters:

x  Object to which this BigInteger is to be compared.

Returns:

true
if and only if the specified Object is a BigInteger whose value is numerically equal to this BigInteger.

See Also:

Object.hashCode()
,
Hashtable
min
public BigInteger min(BigInteger val)

Returns the minimum of this BigInteger and
val
.



Parameters:

val  value with with the minimum is to be computed.

Returns:

the BigInteger whose value is the lesser of this BigInteger and
val
. If they are equal, either may be returned.
max
public BigInteger max(BigInteger val)

Returns the maximum of this BigInteger and
val
.



Parameters:

val  value with with the maximum is to be computed.

Returns:

the BigInteger whose value is the greater of this and
val
. If they are equal, either may be returned.
hashCode
public int hashCode()

Returns the hash code for this BigInteger.


Overrides:

hashCode
in class
Object


Returns:

hash code for this BigInteger.

See Also:

Object.equals(java.lang.Object)
,
Hashtable
toString
public String toString(int radix)

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 digittocharacter mapping provided by
Character.forDigit
is used, and a minus sign is prepended if appropriate. (This representation is compatible with the
(String, int)
constructor.)



Parameters:

radix  radix of the String representation.

Returns:

String representation of this BigInteger in the given radix.

See Also:

Integer.toString(int, int)
,
Character.forDigit(int, int)
,
BigInteger(java.lang.String, int)
toString
public String toString()

Returns the decimal String representation of this BigInteger. The digittocharacter 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.)


Overrides:

toString
in class
Object


Returns:

decimal String representation of this BigInteger.

See Also:

Character.forDigit(int, int)
,
BigInteger(java.lang.String)
toByteArray
public byte[] toByteArray()

Returns a byte array containing the two'scomplement representation of this BigInteger. The byte array will be in
bigendian
byteorder: 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.)



Returns:

a byte array containing the two'scomplement representation of this BigInteger.

See Also:

BigInteger(byte[])
intValue
public int intValue()

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 loworder 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.


Specified by:

intValue
in class
Number


Returns:

this BigInteger converted to an int.
longValue
public long longValue()

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 loworder 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.


Specified by:

longValue
in class
Number


Returns:

this BigInteger converted to a long.
floatValue
public float floatValue()

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.


Specified by:

floatValue
in class
Number


Returns:

this BigInteger converted to a float.
doubleValue
public double doubleValue()

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.


Specified by:

doubleValue
in class
Number


Returns:

this BigInteger converted to a double.