Package com.google.common.math

Class BigIntegerMath

java.lang.Object

com.google.common.math.BigIntegerMath

public final class BigIntegerMath
extends java.lang.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

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
private static class	BigIntegerMath.BigIntegerToDoubleRounder

Field Summary

Fields

Modifier and Type	Field	Description
private static double	LN_10
private static double	LN_2
(package private) static int	SQRT2_PRECOMPUTE_THRESHOLD
(package private) static java.math.BigInteger	SQRT2_PRECOMPUTED_BITS

Constructor Summary

Constructors

Modifier	Constructor	Description
private	BigIntegerMath()

Method Summary

Modifier and Type	Method	Description
static java.math.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 java.math.BigInteger	ceilingPowerOfTwo(java.math.BigInteger x)	Returns the smallest power of two greater than or equal to x.
static java.math.BigInteger	divide(java.math.BigInteger p, java.math.BigInteger q, java.math.RoundingMode mode)	Returns the result of dividing p by q, rounding using the specified RoundingMode.
static java.math.BigInteger	factorial(int n)	Returns n!, that is, the product of the first n positive integers, or 1 if n == 0.
(package private) static boolean	fitsInLong(java.math.BigInteger x)
static java.math.BigInteger	floorPowerOfTwo(java.math.BigInteger x)	Returns the largest power of two less than or equal to x.
static boolean	isPowerOfTwo(java.math.BigInteger x)	Returns true if x represents a power of two.
(package private) static java.math.BigInteger	listProduct(java.util.List<java.math.BigInteger> nums)
(package private) static java.math.BigInteger	listProduct(java.util.List<java.math.BigInteger> nums, int start, int end)
static int	log10(java.math.BigInteger x, java.math.RoundingMode mode)	Returns the base-10 logarithm of x, rounded according to the specified rounding mode.
static int	log2(java.math.BigInteger x, java.math.RoundingMode mode)	Returns the base-2 logarithm of x, rounded according to the specified rounding mode.
static double	roundToDouble(java.math.BigInteger x, java.math.RoundingMode mode)	Returns x, rounded to a double with the specified rounding mode.
static java.math.BigInteger	sqrt(java.math.BigInteger x, java.math.RoundingMode mode)	Returns the square root of x, rounded with the specified rounding mode.
private static java.math.BigInteger	sqrtApproxWithDoubles(java.math.BigInteger x)
private static java.math.BigInteger	sqrtFloor(java.math.BigInteger x)

Methods inherited from class java.lang.Object

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

Field Detail

SQRT2_PRECOMPUTE_THRESHOLD

static final int SQRT2_PRECOMPUTE_THRESHOLD

See Also:

Constant Field Values

SQRT2_PRECOMPUTED_BITS

static final java.math.BigInteger SQRT2_PRECOMPUTED_BITS

LN_10

private static final double LN_10

LN_2

private static final double LN_2

Constructor Detail

BigIntegerMath

private BigIntegerMath()

Method Detail

ceilingPowerOfTwo

public static java.math.BigInteger ceilingPowerOfTwo(java.math.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:

java.lang.IllegalArgumentException - if x <= 0

Since:

20.0

floorPowerOfTwo

public static java.math.BigInteger floorPowerOfTwo(java.math.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:

java.lang.IllegalArgumentException - if x <= 0

Since:

20.0

isPowerOfTwo

public static boolean isPowerOfTwo(java.math.BigInteger x)

Returns true if x represents a power of two.

log2

public static int log2(java.math.BigInteger x,
                       java.math.RoundingMode mode)

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

Throws:

java.lang.IllegalArgumentException - if x <= 0

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

log10

public static int log10(java.math.BigInteger x,
                        java.math.RoundingMode mode)

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

Throws:

java.lang.IllegalArgumentException - if x <= 0

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

sqrt

public static java.math.BigInteger sqrt(java.math.BigInteger x,
                                        java.math.RoundingMode mode)

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

Throws:

java.lang.IllegalArgumentException - if x < 0

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

sqrtFloor

private static java.math.BigInteger sqrtFloor(java.math.BigInteger x)

sqrtApproxWithDoubles

private static java.math.BigInteger sqrtApproxWithDoubles(java.math.BigInteger x)

roundToDouble

public static double roundToDouble(java.math.BigInteger x,
                                   java.math.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:

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

Since:

30.0

divide

public static java.math.BigInteger divide(java.math.BigInteger p,
                                          java.math.BigInteger q,
                                          java.math.RoundingMode mode)

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

Throws:

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

factorial

public static java.math.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:

java.lang.IllegalArgumentException - if n < 0

listProduct

static java.math.BigInteger listProduct(java.util.List<java.math.BigInteger> nums)

listProduct

static java.math.BigInteger listProduct(java.util.List<java.math.BigInteger> nums,
                                        int start,
                                        int end)

binomial

public static java.math.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:

java.lang.IllegalArgumentException - if n < 0, k < 0, or k > n

fitsInLong

static boolean fitsInLong(java.math.BigInteger x)