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.
It is recommended that the probablePrime method be used in preference to this constructor unless there is a compelling need to specify a certainty.
byte.
This may involve rounding or truncation.In the foregoing description, the notation sgn(expression) designates the mathematical signum function, which is defined to return one of -1, 0, or 1 according to whether the value of expression is negative, zero or positive. The implementor must ensure sgn(x.compareTo(y)) == -sgn(y.compareTo(x)) for all x and y. (This implies that x.compareTo(y) must throw an exception iff y.compareTo(x) throws an exception.)
The implementor must also ensure that the relation is transitive: (x.compareTo(y)>0 && y.compareTo(z)>0) implies x.compareTo(z)>0.
Finally, the implementer must ensure that x.compareTo(y)==0 implies that sgn(x.compareTo(z)) == sgn(y.compareTo(z)), for all z.
It is strongly recommended, but not strictly required that (x.compareTo(y)==0) == (x.equals(y)). Generally speaking, any class that implements the Comparable interface and violates this condition should clearly indicate this fact. The recommended language is "Note: this class has a natural ordering that is inconsistent with equals."
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.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.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.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.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.wait methods.
The awakened thread will not be able to proceed until the current thread relinquishes the lock on this object. The awakened thread will compete in the usual manner with any other threads that might be actively competing to synchronize on this object; for example, the awakened thread enjoys no reliable privilege or disadvantage in being the next thread to lock this object.
This method should only be called by a thread that is the owner of this object's monitor. A thread becomes the owner of the object's monitor in one of three ways:
synchronized statement
that synchronizes on the object.
Class, by executing a
synchronized static method of that class.
Only one thread at a time can own an object's monitor.
wait methods.
The awakened threads will not be able to proceed until the current thread relinquishes the lock on this object. The awakened threads will compete in the usual manner with any other threads that might be actively competing to synchronize on this object; for example, the awakened threads enjoy no reliable privilege or disadvantage in being the next thread to lock this object.
This method should only be called by a thread that is the owner
of this object's monitor. See the notify method for a
description of the ways in which a thread can become the owner of
a monitor.
short.
This may involve rounding or truncation.int)
constructor.)long. This "static factory method" is
provided in preference to a (long) constructor
because it allows for reuse of frequently used BigIntegers.
The current thread must own this object's monitor. The thread
releases ownership of this monitor and waits until another thread
notifies threads waiting on this object's monitor to wake up
either through a call to the notify method or the
notifyAll method. The thread then waits until it can
re-obtain ownership of the monitor and resumes execution.
As in the one argument version, interrupts and spurious wakeups are possible, and this method should always be used in a loop:
synchronized (obj) {
while (<condition does not hold>)
obj.wait();
... // Perform action appropriate to condition
}
This method should only be called by a thread that is the owner
of this object's monitor. See the notify method for a
description of the ways in which a thread can become the owner of
a monitor.The current thread must own this object's monitor.
This method causes the current thread (call it T) to place itself in the wait set for this object and then to relinquish any and all synchronization claims on this object. Thread T becomes disabled for thread scheduling purposes and lies dormant until one of four things happens:
A thread can also wake up without being notified, interrupted, or timing out, a so-called spurious wakeup. While this will rarely occur in practice, applications must guard against it by testing for the condition that should have caused the thread to be awakened, and continuing to wait if the condition is not satisfied. In other words, waits should always occur in loops, like this one:
synchronized (obj) {
while (<condition does not hold>)
obj.wait(timeout);
... // Perform action appropriate to condition
}
(For more information on this topic, see Section 3.2.3 in Doug Lea's
"Concurrent Programming in Java (Second Edition)" (Addison-Wesley,
2000), or Item 50 in Joshua Bloch's "Effective Java Programming
Language Guide" (Addison-Wesley, 2001).
If the current thread is interrupted by another thread while it is waiting, then an InterruptedException is thrown. This exception is not thrown until the lock status of this object has been restored as described above.
Note that the wait method, as it places the current thread into the wait set for this object, unlocks only this object; any other objects on which the current thread may be synchronized remain locked while the thread waits.
This method should only be called by a thread that is the owner
of this object's monitor. See the notify method for a
description of the ways in which a thread can become the owner of
a monitor.
This method is similar to the wait method of one
argument, but it allows finer control over the amount of time to
wait for a notification before giving up. The amount of real time,
measured in nanoseconds, is given by:
1000000*timeout+nanos
In all other respects, this method does the same thing as the method of one argument. In particular, wait(0, 0) means the same thing as wait(0).
The current thread must own this object's monitor. The thread releases ownership of this monitor and waits until either of the following two conditions has occurred:
notify method
or the notifyAll method.
timeout
milliseconds plus nanos nanoseconds arguments, has
elapsed.
The thread then waits until it can re-obtain ownership of the monitor and resumes execution.
As in the one argument version, interrupts and spurious wakeups are possible, and this method should always be used in a loop:
synchronized (obj) {
while (<condition does not hold>)
obj.wait(timeout, nanos);
... // Perform action appropriate to condition
}
This method should only be called by a thread that is the owner
of this object's monitor. See the notify method for a
description of the ways in which a thread can become the owner of
a monitor.