## Class IntMath

• ```@GwtCompatible(emulated=true)
public final class IntMath
extends Object```
A class for arithmetic on values of type `int`. 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 `long` and for `BigInteger` can be found in `LongMath` and `BigIntegerMath` respectively. For other common operations on `int` values, see `Ints`.

Since:
11.0
Author:
Louis Wasserman
• ### Method Summary

All Methods
Modifier and Type Method and Description
`static int` ```binomial(int n, int k)```
Returns `n` choose `k`, also known as the binomial coefficient of `n` and `k`, or `Integer.MAX_VALUE` if the result does not fit in an `int`.
`static int` `ceilingPowerOfTwo(int x)`
Returns the smallest power of two greater than or equal to `x`.
`static int` ```checkedAdd(int a, int b)```
Returns the sum of `a` and `b`, provided it does not overflow.
`static int` ```checkedMultiply(int a, int b)```
Returns the product of `a` and `b`, provided it does not overflow.
`static int` ```checkedPow(int b, int k)```
Returns the `b` to the `k`th power, provided it does not overflow.
`static int` ```checkedSubtract(int a, int b)```
Returns the difference of `a` and `b`, provided it does not overflow.
`static int` ```divide(int p, int q, RoundingMode mode)```
Returns the result of dividing `p` by `q`, rounding using the specified `RoundingMode`.
`static int` `factorial(int n)`
Returns `n!`, that is, the product of the first `n` positive integers, `1` if `n == 0`, or `Integer.MAX_VALUE` if the result does not fit in a `int`.
`static int` `floorPowerOfTwo(int x)`
Returns the largest power of two less than or equal to `x`.
`static int` ```gcd(int a, int b)```
Returns the greatest common divisor of `a, b`.
`static boolean` `isPowerOfTwo(int x)`
Returns `true` if `x` represents a power of two.
`static boolean` `isPrime(int 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(int x, RoundingMode mode)```
Returns the base-10 logarithm of `x`, rounded according to the specified rounding mode.
`static int` ```log2(int x, RoundingMode mode)```
Returns the base-2 logarithm of `x`, rounded according to the specified rounding mode.
`static int` ```mean(int x, int y)```
Returns the arithmetic mean of `x` and `y`, rounded towards negative infinity.
`static int` ```mod(int x, int m)```
Returns `x mod m`, a non-negative value less than `m`.
`static int` ```pow(int b, int k)```
Returns `b` to the `k`th power.
`static int` ```saturatedAdd(int a, int b)```
Returns the sum of `a` and `b` unless it would overflow or underflow in which case `Integer.MAX_VALUE` or `Integer.MIN_VALUE` is returned, respectively.
`static int` ```saturatedMultiply(int a, int b)```
Returns the product of `a` and `b` unless it would overflow or underflow in which case `Integer.MAX_VALUE` or `Integer.MIN_VALUE` is returned, respectively.
`static int` ```saturatedPow(int b, int k)```
Returns the `b` to the `k`th power, unless it would overflow or underflow in which case `Integer.MAX_VALUE` or `Integer.MIN_VALUE` is returned, respectively.
`static int` ```saturatedSubtract(int a, int b)```
Returns the difference of `a` and `b` unless it would overflow or underflow in which case `Integer.MAX_VALUE` or `Integer.MIN_VALUE` is returned, respectively.
`static int` ```sqrt(int 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 int ceilingPowerOfTwo(int 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 an `int`, i.e. when `x > 2^30`
Since:
20.0
• #### floorPowerOfTwo

```@Beta
public static int floorPowerOfTwo(int 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(int x)`
Returns `true` if `x` represents a power of two.

This differs from `Integer.bitCount(x) == 1`, because `Integer.bitCount(Integer.MIN_VALUE) == 1`, but `Integer.MIN_VALUE` is not a power of two.

• #### log2

```public static int log2(int 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(int 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 int pow(int 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).intValue()`. This implementation runs in `O(log k)` time.

Compare `checkedPow(int, int)`, which throws an `ArithmeticException` upon overflow.

Throws:
`IllegalArgumentException` - if `k < 0`
• #### sqrt

```@GwtIncompatible
public static int sqrt(int 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

```public static int divide(int p,
int 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

```public static int mod(int 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
• #### gcd

```public static int gcd(int a,
int b)```
Returns the greatest common divisor of `a, b`. Returns `0` if ```a == 0 && b == 0```.
Throws:
`IllegalArgumentException` - if `a < 0` or `b < 0`

```public static int checkedAdd(int a,
int b)```
Returns the sum of `a` and `b`, provided it does not overflow.
Throws:
`ArithmeticException` - if `a + b` overflows in signed `int` arithmetic
• #### checkedSubtract

```public static int checkedSubtract(int a,
int b)```
Returns the difference of `a` and `b`, provided it does not overflow.
Throws:
`ArithmeticException` - if `a - b` overflows in signed `int` arithmetic
• #### checkedMultiply

```public static int checkedMultiply(int a,
int b)```
Returns the product of `a` and `b`, provided it does not overflow.
Throws:
`ArithmeticException` - if `a * b` overflows in signed `int` arithmetic
• #### checkedPow

```public static int checkedPow(int b,
int k)```
Returns the `b` to the `k`th power, provided it does not overflow.

`pow(int, int)` may be faster, but does not check for overflow.

Throws:
`ArithmeticException` - if `b` to the `k`th power overflows in signed `int` arithmetic

```@Beta
int b)```
Returns the sum of `a` and `b` unless it would overflow or underflow in which case `Integer.MAX_VALUE` or `Integer.MIN_VALUE` is returned, respectively.
Since:
20.0
• #### saturatedSubtract

```@Beta
public static int saturatedSubtract(int a,
int b)```
Returns the difference of `a` and `b` unless it would overflow or underflow in which case `Integer.MAX_VALUE` or `Integer.MIN_VALUE` is returned, respectively.
Since:
20.0
• #### saturatedMultiply

```@Beta
public static int saturatedMultiply(int a,
int b)```
Returns the product of `a` and `b` unless it would overflow or underflow in which case `Integer.MAX_VALUE` or `Integer.MIN_VALUE` is returned, respectively.
Since:
20.0
• #### saturatedPow

```@Beta
public static int saturatedPow(int b,
int k)```
Returns the `b` to the `k`th power, unless it would overflow or underflow in which case `Integer.MAX_VALUE` or `Integer.MIN_VALUE` is returned, respectively.
Since:
20.0
• #### factorial

`public static int factorial(int n)`
Returns `n!`, that is, the product of the first `n` positive integers, `1` if `n == 0`, or `Integer.MAX_VALUE` if the result does not fit in a `int`.
Throws:
`IllegalArgumentException` - if `n < 0`
• #### binomial

```public static int binomial(int n,
int k)```
Returns `n` choose `k`, also known as the binomial coefficient of `n` and `k`, or `Integer.MAX_VALUE` if the result does not fit in an `int`.
Throws:
`IllegalArgumentException` - if `n < 0`, `k < 0` or `k > n`
• #### mean

```public static int mean(int x,
int y)```
Returns the arithmetic mean of `x` and `y`, rounded towards negative infinity. This method is overflow resilient.
Since:
14.0
• #### isPrime

```@GwtIncompatible
@Beta
public static boolean isPrime(int 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 `LongMath.isPrime(long)` or `BigInteger.isProbablePrime(int)`.

Throws:
`IllegalArgumentException` - if `n` is negative
Since:
20.0