Package com.google.common.math

Class BigIntegerMath

java.lang.Object

com.google.common.math.BigIntegerMath

@GwtCompatible(emulated=true)
public final class BigIntegerMath
extends Object

A class for arithmetic on values of type BigInteger.

The implementations of many methods in this class are based on material from Henry S. Warren, Jr.'s Hacker's Delight, (Addison Wesley, 2002).

Similar functionality for int and for long can be found in IntMath and LongMath respectively.

Since:

11.0

Author:

Louis Wasserman

Method Summary

Modifier and Type	Method	Description
static BigInteger	binomial(int n, int k)	Returns n choose k, also known as the binomial coefficient of n and k, that is, n! / (k! (n - k)!).
static BigInteger	ceilingPowerOfTwo(BigInteger x)	Returns the smallest power of two greater than or equal to x.
static BigInteger	divide(BigInteger p, BigInteger q, RoundingMode mode)	Returns the result of dividing p by q, rounding using the specified RoundingMode.
static BigInteger	factorial(int n)	Returns n!, that is, the product of the first n positive integers, or 1 if n == 0.
static BigInteger	floorPowerOfTwo(BigInteger x)	Returns the largest power of two less than or equal to x.
static boolean	isPowerOfTwo(BigInteger x)	Returns true if x represents a power of two.
static int	log10(BigInteger x, RoundingMode mode)	Returns the base-10 logarithm of x, rounded according to the specified rounding mode.
static int	log2(BigInteger x, RoundingMode mode)	Returns the base-2 logarithm of x, rounded according to the specified rounding mode.
static double	roundToDouble(BigInteger x, RoundingMode mode)	Returns x, rounded to a double with the specified rounding mode.
static BigInteger	sqrt(BigInteger x, RoundingMode mode)	Returns the square root of x, rounded with the specified rounding mode.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

ceilingPowerOfTwo

@Beta
public static BigInteger ceilingPowerOfTwo(BigInteger x)

Returns the smallest power of two greater than or equal to x. This is equivalent to BigInteger.valueOf(2).pow(log2(x, CEILING)).

Throws:

IllegalArgumentException - if x <= 0

Since:

20.0

floorPowerOfTwo

@Beta
public static BigInteger floorPowerOfTwo(BigInteger x)

Returns the largest power of two less than or equal to x. This is equivalent to BigInteger.valueOf(2).pow(log2(x, FLOOR)).

Throws:

IllegalArgumentException - if x <= 0

Since:

20.0

isPowerOfTwo

public static boolean isPowerOfTwo(BigInteger x)

Returns true if x represents a power of two.

log2

public static int log2(BigInteger x,
                       RoundingMode mode)

Returns the base-2 logarithm of x, rounded according to the specified rounding mode.

Throws:

IllegalArgumentException - if x <= 0

ArithmeticException - if mode is RoundingMode.UNNECESSARY and x is not a power of two

log10

@GwtIncompatible
public static int log10(BigInteger x,
                        RoundingMode mode)

Returns the base-10 logarithm of x, rounded according to the specified rounding mode.

Throws:

IllegalArgumentException - if x <= 0

ArithmeticException - if mode is RoundingMode.UNNECESSARY and x is not a power of ten

sqrt

@GwtIncompatible
public static BigInteger sqrt(BigInteger x,
                              RoundingMode mode)

Returns the square root of x, rounded with the specified rounding mode.

Throws:

IllegalArgumentException - if x < 0

ArithmeticException - if mode is RoundingMode.UNNECESSARY and sqrt(x) is not an integer

roundToDouble

@GwtIncompatible
public static double roundToDouble(BigInteger x,
                                   RoundingMode mode)

Returns x, rounded to a double with the specified rounding mode. If x is precisely representable as a double, its double value will be returned; otherwise, the rounding will choose between the two nearest representable values with mode.

For the case of RoundingMode.HALF_DOWN, HALF_UP, and HALF_EVEN, infinite double values are considered infinitely far away. For example, 2^2000 is not representable as a double, but roundToDouble(BigInteger.valueOf(2).pow(2000), HALF_UP) will return Double.MAX_VALUE, not Double.POSITIVE_INFINITY.

For the case of RoundingMode.HALF_EVEN, this implementation uses the IEEE 754 default rounding mode: if the two nearest representable values are equally near, the one with the least significant bit zero is chosen. (In such cases, both of the nearest representable values are even integers; this method returns the one that is a multiple of a greater power of two.)

Throws:

ArithmeticException - if mode is RoundingMode.UNNECESSARY and x is not precisely representable as a double

Since:

30.0

divide

@GwtIncompatible
public static BigInteger divide(BigInteger p,
                                BigInteger q,
                                RoundingMode mode)

Returns the result of dividing p by q, rounding using the specified RoundingMode.

Throws:

ArithmeticException - if q == 0, or if mode == UNNECESSARY and a is not an integer multiple of b

factorial

public static BigInteger factorial(int n)

Returns n!, that is, the product of the first n positive integers, or 1 if n == 0.

Warning: the result takes O(n log n) space, so use cautiously.

This uses an efficient binary recursive algorithm to compute the factorial with balanced multiplies. It also removes all the 2s from the intermediate products (shifting them back in at the end).

Throws:

IllegalArgumentException - if n < 0

binomial

public static BigInteger binomial(int n,
                                  int k)

Returns n choose k, also known as the binomial coefficient of n and k, that is, n! / (k! (n - k)!).

Warning: the result can take as much as O(k log n) space.

Throws:

IllegalArgumentException - if n < 0, k < 0, or k > n