## Class LongMath

• ```@GwtCompatible(emulated=true)
public final class LongMath
extends 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
Author:
Louis Wasserman
• ### Method Summary

All Methods
Modifier and Type Method and 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, 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` `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.
`static int` ```log10(long x, RoundingMode mode)```
Returns the base-10 logarithm of `x`, rounded according to the specified rounding mode.
`static int` ```log2(long x, 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` ```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, 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 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:
`IllegalArgumentException` - if `x <= 0`
`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:
`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.

• #### log2

```public static int log2(long 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(long 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
• #### pow

```@GwtIncompatible
public static long pow(long b,
int k)```
Returns `b` to the `k`th 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:
`IllegalArgumentException` - if `k < 0`
• #### sqrt

```@GwtIncompatible
public static long sqrt(long 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
• #### divide

```@GwtIncompatible
public static long divide(long p,
long 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`
• #### 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:
`ArithmeticException` - if `m <= 0`
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:
`ArithmeticException` - if `m <= 0`
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:
`IllegalArgumentException` - if `a < 0` or `b < 0`

```@GwtIncompatible
long b)```
Returns the sum of `a` and `b`, provided it does not overflow.
Throws:
`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:
`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:
`ArithmeticException` - if `a * b` overflows in signed `long` arithmetic
• #### checkedPow

```@GwtIncompatible
public static long checkedPow(long b,
int k)```
Returns the `b` to the `k`th power, provided it does not overflow.
Throws:
`ArithmeticException` - if `b` to the `k`th power overflows in signed `long` arithmetic

```@Beta
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 `k`th 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:
`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:
`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
• #### 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:
`IllegalArgumentException` - if `n` is negative
Since:
20.0