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

Nested Class Summary

Nested Classes
Modifier and Type Class Description

private static class LongMath.MillerRabinTester

Field Summary

Fields
Modifier and Type	Field	Description
`(package private) static int[]`	`biggestBinomials`
`(package private) static int[]`	`biggestSimpleBinomials`
`(package private) static long[]`	`factorials`
`(package private) static long`	`FLOOR_SQRT_MAX_LONG`
`(package private) static long[]`	`halfPowersOf10`
`(package private) static long`	`MAX_POWER_OF_SQRT2_UNSIGNED`	The biggest half power of two that fits into an unsigned long
`(package private) static long`	`MAX_SIGNED_POWER_OF_TWO`
`(package private) static byte[]`	`maxLog10ForLeadingZeros`
`private static long[][]`	`millerRabinBaseSets`
`(package private) static long[]`	`powersOf10`
`private static int`	`SIEVE_30`

Constructor Summary

Constructors
Modifier Constructor Description

private LongMath()

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`	`ceilingPowerOfTwo(long x)`	Returns the smallest power of two greater than or equal to `x`.
`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`.
`(package private) static boolean`	`fitsInInt(long x)`
`static long`	`floorPowerOfTwo(long x)`	Returns the largest power of two less than or equal to `x`.
`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 boolean`	`isPrime(long n)`	Returns `true` if `n` is a prime number: an integer greater than one that cannot be factored into a product of smaller positive integers.
`(package private) static int`	`lessThanBranchFree(long x, long y)`	Returns 1 if `x < y` as unsigned longs, and 0 otherwise.
`static int`	`log10(long x, java.math.RoundingMode mode)`	Returns the base-10 logarithm of `x`, rounded according to the specified rounding mode.
`(package private) static int`	`log10Floor(long x)`
`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`.
`(package private) static long`	`multiplyFraction(long x, long numerator, long denominator)`	Returns (x * numerator / denominator), which is assumed to come out to an integral value.
`static long`	`pow(long b, int k)`	Returns `b` to the `k`th power.
`static long`	`saturatedAdd(long a, long b)`	Returns the sum of `a` and `b` unless it would overflow or underflow in which case `Long.MAX_VALUE` or `Long.MIN_VALUE` is returned, respectively.
`static long`	`saturatedMultiply(long a, long b)`	Returns the product of `a` and `b` unless it would overflow or underflow in which case `Long.MAX_VALUE` or `Long.MIN_VALUE` is returned, respectively.
`static long`	`saturatedPow(long b, int k)`	Returns the `b` to the `k`th power, unless it would overflow or underflow in which case `Long.MAX_VALUE` or `Long.MIN_VALUE` is returned, respectively.
`static long`	`saturatedSubtract(long a, long b)`	Returns the difference of `a` and `b` unless it would overflow or underflow in which case `Long.MAX_VALUE` or `Long.MIN_VALUE` is returned, respectively.
`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

- Field Detail
  - MAX_SIGNED_POWER_OF_TWO
```
static final long MAX_SIGNED_POWER_OF_TWO
```
    See Also:
    
    Constant Field Values
  - MAX_POWER_OF_SQRT2_UNSIGNED
```
static final long MAX_POWER_OF_SQRT2_UNSIGNED
```
    The biggest half power of two that fits into an unsigned long
    
    See Also:
    
    Constant Field Values
  - maxLog10ForLeadingZeros
```
static final byte[] maxLog10ForLeadingZeros
```
  - powersOf10
```
@GwtIncompatible
static final long[] powersOf10
```
  - halfPowersOf10
```
@GwtIncompatible
static final long[] halfPowersOf10
```
  - FLOOR_SQRT_MAX_LONG
```
static final long FLOOR_SQRT_MAX_LONG
```
    See Also:
    
    Constant Field Values
  - factorials
```
static final long[] factorials
```
  - biggestBinomials
```
static final int[] biggestBinomials
```
  - biggestSimpleBinomials
```
static final int[] biggestSimpleBinomials
```
  - SIEVE_30
```
private static final int SIEVE_30
```
    See Also:
    
    Constant Field Values
  - millerRabinBaseSets
```
private static final long[][] millerRabinBaseSets
```
- Constructor Detail
  - LongMath
```
private LongMath()
```
- Method Detail
  - ceilingPowerOfTwo
```
@Beta
public static long ceilingPowerOfTwo(long x)
```
    Returns the smallest power of two greater than or equal to x. This is equivalent to checkedPow(2, log2(x, CEILING)).
    
    Throws:
    
    java.lang.IllegalArgumentException - if x <= 0
    
    java.lang.ArithmeticException - of the next-higher power of two is not representable as a long, i.e. when x > 2^62
    
    Since:
    
    20.0
  - floorPowerOfTwo
```
@Beta
public static long floorPowerOfTwo(long x)
```
    Returns the largest power of two less than or equal to x. This is equivalent to checkedPow(2, log2(x, FLOOR)).
    
    Throws:
    
    java.lang.IllegalArgumentException - if x <= 0
    
    Since:
    
    20.0
  - 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.
  - lessThanBranchFree
```
static int lessThanBranchFree(long x,
                              long y)
```
    Returns 1 if x < y as unsigned longs, and 0 otherwise. Assumes that x - y fits into a signed long. The implementation is branch-free, and benchmarks suggest it is measurably faster than the straightforward ternary expression.
  - 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
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
  - log10Floor
```
@GwtIncompatible
static int log10Floor(long x)
```
  - pow
```
@GwtIncompatible
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
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
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
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
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
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
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
```
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
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
  - saturatedAdd
```
@Beta
public static long saturatedAdd(long a,
                                long b)
```
    Returns the sum of a and b unless it would overflow or underflow in which case Long.MAX_VALUE or Long.MIN_VALUE is returned, respectively.
    
    Since:
    
    20.0
  - saturatedSubtract
```
@Beta
public static long saturatedSubtract(long a,
                                     long b)
```
    Returns the difference of a and b unless it would overflow or underflow in which case Long.MAX_VALUE or Long.MIN_VALUE is returned, respectively.
    
    Since:
    
    20.0
  - saturatedMultiply
```
@Beta
public static long saturatedMultiply(long a,
                                     long b)
```
    Returns the product of a and b unless it would overflow or underflow in which case Long.MAX_VALUE or Long.MIN_VALUE is returned, respectively.
    
    Since:
    
    20.0
  - saturatedPow
```
@Beta
public static long saturatedPow(long b,
                                int k)
```
    Returns the b to the kth power, unless it would overflow or underflow in which case Long.MAX_VALUE or Long.MIN_VALUE is returned, respectively.
    
    Since:
    
    20.0
  - factorial
```
@GwtIncompatible
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
  - multiplyFraction
```
static long multiplyFraction(long x,
                             long numerator,
                             long denominator)
```
    Returns (x * numerator / denominator), which is assumed to come out to an integral value.
  - fitsInInt
```
static boolean fitsInInt(long x)
```
  - 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
  - isPrime
```
@GwtIncompatible
@Beta
public static boolean isPrime(long n)
```
    Returns true if n is a prime number: an integer greater than one that cannot be factored into a product of smaller positive integers. Returns false if n is zero, one, or a composite number (one which can be factored into smaller positive integers).
    To test larger numbers, use BigInteger.isProbablePrime(int).
    
    Throws:
    
    java.lang.IllegalArgumentException - if n is negative
    
    Since:
    
    20.0

Class LongMath

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

MAX_SIGNED_POWER_OF_TWO

MAX_POWER_OF_SQRT2_UNSIGNED

maxLog10ForLeadingZeros

powersOf10

halfPowersOf10

FLOOR_SQRT_MAX_LONG

factorials

biggestBinomials

biggestSimpleBinomials

SIEVE_30

millerRabinBaseSets

Constructor Detail

LongMath

Method Detail

ceilingPowerOfTwo

floorPowerOfTwo

isPowerOfTwo

lessThanBranchFree

log2

log10

log10Floor

pow

sqrt

divide

mod

mod

gcd

checkedAdd

checkedSubtract

checkedMultiply

checkedPow

saturatedAdd

saturatedSubtract

saturatedMultiply

saturatedPow

factorial

binomial

multiplyFraction

fitsInInt

mean

isPrime