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

```
@GwtCompatible(emulated=true)
public final class LongMath
extends java.lang.Object
```
A class for arithmetic on values of type long. Where possible, methods are defined and named analogously to their BigInteger counterparts.
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 BigInteger can be found in IntMath and BigIntegerMath respectively. For other common operations on long values, see Longs.

Since:

11.0

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method	Description
`static long`	`binomial(int n, int k)`	Returns `n` choose `k`, also known as the binomial coefficient of `n` and `k`, or `Long.MAX_VALUE` if the result does not fit in a `long`.
`static long`	`checkedAdd(long a, long b)`	Returns the sum of `a` and `b`, provided it does not overflow.
`static long`	`checkedMultiply(long a, long b)`	Returns the product of `a` and `b`, provided it does not overflow.
`static long`	`checkedPow(long b, int k)`	Returns the `b` to the `k`th power, provided it does not overflow.
`static long`	`checkedSubtract(long a, long b)`	Returns the difference of `a` and `b`, provided it does not overflow.
`static long`	`divide(long p, long q, java.math.RoundingMode mode)`	Returns the result of dividing `p` by `q`, rounding using the specified `RoundingMode`.
`static long`	`factorial(int n)`	Returns `n!`, that is, the product of the first `n` positive integers, `1` if `n == 0`, or `Long.MAX_VALUE` if the result does not fit in a `long`.
`static long`	`gcd(long a, long b)`	Returns the greatest common divisor of `a, b`.
`static boolean`	`isPowerOfTwo(long x)`	Returns `true` if `x` represents a power of two.
`static int`	`log10(long x, java.math.RoundingMode mode)`	Returns the base-10 logarithm of `x`, rounded according to the specified rounding mode.
`static int`	`log2(long x, java.math.RoundingMode mode)`	Returns the base-2 logarithm of `x`, rounded according to the specified rounding mode.
`static long`	`mean(long x, long y)`	Returns the arithmetic mean of `x` and `y`, rounded toward negative infinity.
`static int`	`mod(long x, int m)`	Returns `x mod m`, a non-negative value less than `m`.
`static long`	`mod(long x, long m)`	Returns `x mod m`, a non-negative value less than `m`.
`static long`	`pow(long b, int k)`	Returns `b` to the `k`th power.
`static long`	`sqrt(long 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
  - isPowerOfTwo
```
public static boolean isPowerOfTwo(long x)
```
    Returns true if x represents a power of two.
    This differs from Long.bitCount(x) == 1, because Long.bitCount(Long.MIN_VALUE) == 1, but Long.MIN_VALUE is not a power of two.
  - log2
```
public static int log2(long 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("TODO")
public static int log10(long 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
  - pow
```
@GwtIncompatible("TODO")
public static long pow(long b,
                       int k)
```
    Returns b to the kth power. Even if the result overflows, it will be equal to BigInteger.valueOf(b).pow(k).longValue(). This implementation runs in O(log k) time.
    
    Throws:
    
    java.lang.IllegalArgumentException - if k < 0
  - sqrt
```
@GwtIncompatible("TODO")
public static long sqrt(long 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
  - divide
```
@GwtIncompatible("TODO")
public static long divide(long p,
                          long 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
  - mod
```
@GwtIncompatible("TODO")
public static int mod(long x,
                      int m)
```
    Returns x mod m, a non-negative value less than m. This differs from x % m, which might be negative.
    For example:
    mod(7, 4) == 3 mod(-7, 4) == 1 mod(-1, 4) == 3 mod(-8, 4) == 0 mod(8, 4) == 0
    Throws:
    
    java.lang.ArithmeticException - if m <= 0
    
    See Also:
    
    Remainder Operator
  - mod
```
@GwtIncompatible("TODO")
public static long mod(long x,
                       long m)
```
    Returns x mod m, a non-negative value less than m. This differs from x % m, which might be negative.
    For example:
    mod(7, 4) == 3 mod(-7, 4) == 1 mod(-1, 4) == 3 mod(-8, 4) == 0 mod(8, 4) == 0
    Throws:
    
    java.lang.ArithmeticException - if m <= 0
    
    See Also:
    
    Remainder Operator
  - gcd
```
public static long gcd(long a,
                       long b)
```
    Returns the greatest common divisor of a, b. Returns 0 if a == 0 && b == 0.
    
    Throws:
    
    java.lang.IllegalArgumentException - if a < 0 or b < 0
  - checkedAdd
```
@GwtIncompatible("TODO")
public static long checkedAdd(long a,
                              long b)
```
    Returns the sum of a and b, provided it does not overflow.
    
    Throws:
    
    java.lang.ArithmeticException - if a + b overflows in signed long arithmetic
  - checkedSubtract
```
@GwtIncompatible("TODO")
public static long checkedSubtract(long a,
                                   long b)
```
    Returns the difference of a and b, provided it does not overflow.
    
    Throws:
    
    java.lang.ArithmeticException - if a - b overflows in signed long arithmetic
  - checkedMultiply
```
@GwtIncompatible("TODO")
public static long checkedMultiply(long a,
                                   long b)
```
    Returns the product of a and b, provided it does not overflow.
    
    Throws:
    
    java.lang.ArithmeticException - if a * b overflows in signed long arithmetic
  - checkedPow
```
@GwtIncompatible("TODO")
public static long checkedPow(long b,
                              int k)
```
    Returns the b to the kth power, provided it does not overflow.
    
    Throws:
    
    java.lang.ArithmeticException - if b to the kth power overflows in signed long arithmetic
  - factorial
```
@GwtIncompatible("TODO")
public static long factorial(int n)
```
    Returns n!, that is, the product of the first n positive integers, 1 if n == 0, or Long.MAX_VALUE if the result does not fit in a long.
    
    Throws:
    
    java.lang.IllegalArgumentException - if n < 0
  - binomial
```
public static long binomial(int n,
                            int k)
```
    Returns n choose k, also known as the binomial coefficient of n and k, or Long.MAX_VALUE if the result does not fit in a long.
    
    Throws:
    
    java.lang.IllegalArgumentException - if n < 0, k < 0, or k > n
  - mean
```
public static long mean(long x,
                        long y)
```
    Returns the arithmetic mean of x and y, rounded toward negative infinity. This method is resilient to overflow.
    
    Since:
    
    14.0

Class LongMath

Method Summary

Methods inherited from class java.lang.Object

Method Detail

isPowerOfTwo

log2

log10

pow

sqrt

divide

mod

mod

gcd

checkedAdd

checkedSubtract

checkedMultiply

checkedPow

factorial

binomial

mean