IntMath

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

```
@GwtCompatible(emulated=true)
public final class IntMath
extends java.lang.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

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method	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, java.math.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, java.math.RoundingMode mode)`	Returns the base-10 logarithm of `x`, rounded according to the specified rounding mode.
`static int`	`log2(int x, java.math.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, 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
```
@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:
    
    java.lang.IllegalArgumentException - if x <= 0
    
    java.lang.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:
    
    java.lang.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,
                       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(int 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
public static int pow(int b,
                      int k)
```
    Returns b to the kth 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:
    
    java.lang.IllegalArgumentException - if k < 0
  - sqrt
```
@GwtIncompatible
public static int sqrt(int 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
```
public static int divide(int p,
                         int 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
```
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:
    
    java.lang.ArithmeticException - if m <= 0
    
    See Also:
    
    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:
    
    java.lang.IllegalArgumentException - if a < 0 or b < 0
  - checkedAdd
```
public static int checkedAdd(int a,
                             int b)
```
    Returns the sum of a and b, provided it does not overflow.
    
    Throws:
    
    java.lang.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:
    
    java.lang.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:
    
    java.lang.ArithmeticException - if a * b overflows in signed int arithmetic
  - checkedPow
```
public static int checkedPow(int b,
                             int k)
```
    Returns the b to the kth power, provided it does not overflow.
    pow(int, int) may be faster, but does not check for overflow.
    
    Throws:
    
    java.lang.ArithmeticException - if b to the kth power overflows in signed int arithmetic
  - saturatedAdd
```
@Beta
public 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.
    
    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 kth 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:
    
    java.lang.IllegalArgumentException - if n < 0
  - binomial
```
@GwtIncompatible
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:
    
    java.lang.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:
    
    java.lang.IllegalArgumentException - if n is negative
    
    Since:
    
    20.0

Class IntMath

Method Summary

Methods inherited from class java.lang.Object

Method Detail

ceilingPowerOfTwo

floorPowerOfTwo

isPowerOfTwo

log2

log10

pow

sqrt

divide

mod

gcd

checkedAdd

checkedSubtract

checkedMultiply

checkedPow

saturatedAdd

saturatedSubtract

saturatedMultiply

saturatedPow

factorial

binomial

mean

isPrime