java.lang.Object
- com.google.common.math.BigIntegerMath

```
@GwtCompatible(emulated=true)
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

Author:

Louis Wasserman

Method Summary

All Methods Static Methods Concrete Methods
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`.
`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.
`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.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- 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
```
@GwtIncompatible
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
```
@GwtIncompatible
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
  - roundToDouble
```
@GwtIncompatible
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
```
@GwtIncompatible
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
  - 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

Class BigIntegerMath

Method Summary

Methods inherited from class java.lang.Object

Method Detail

ceilingPowerOfTwo

floorPowerOfTwo

isPowerOfTwo

log2

log10

sqrt

roundToDouble

divide

factorial

binomial