Class IntMath

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

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
  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    (package private) static int[]
     
    private static final int[]
     
    (package private) static final int
     
    (package private) static final int[]
     
    (package private) static final int
    The biggest half power of two that can fit in an unsigned int.
    (package private) static final int
     
    (package private) static final byte[]
     
    (package private) static final int[]
     
  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    private
     
  • Method Summary

    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
    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 kth 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
    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.
    (package private) static int
    lessThanBranchFree(int x, int y)
    Returns 1 if x < y as unsigned integers, and 0 otherwise.
    static int
    log10(int x, RoundingMode mode)
    Returns the base-10 logarithm of x, rounded according to the specified rounding mode.
    private static int
    log10Floor(int x)
     
    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 kth 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 kth 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.
    private static int
    sqrtFloor(int x)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
  • Field Details

    • MAX_SIGNED_POWER_OF_TWO

      static final int MAX_SIGNED_POWER_OF_TWO
      See Also:
    • MAX_POWER_OF_SQRT2_UNSIGNED

      static final int MAX_POWER_OF_SQRT2_UNSIGNED
      The biggest half power of two that can fit in an unsigned int.
      See Also:
    • maxLog10ForLeadingZeros

      static final byte[] maxLog10ForLeadingZeros
    • powersOf10

      static final int[] powersOf10
    • halfPowersOf10

      static final int[] halfPowersOf10
    • FLOOR_SQRT_MAX_INT

      static final int FLOOR_SQRT_MAX_INT
      See Also:
    • factorials

      private static final int[] factorials
    • biggestBinomials

      static int[] biggestBinomials
  • Constructor Details

    • IntMath

      private IntMath()
  • Method Details

    • ceilingPowerOfTwo

      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

      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.

    • lessThanBranchFree

      static int lessThanBranchFree(int x, int y)
      Returns 1 if x < y as unsigned integers, and 0 otherwise. Assumes that x - y fits into a signed int. The implementation is branch-free, and benchmarks suggest it is measurably (if narrowly) faster than the straightforward ternary expression.
    • 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

      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
    • log10Floor

      private static int log10Floor(int x)
    • pow

      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:
      IllegalArgumentException - if k < 0
    • sqrt

      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
    • sqrtFloor

      private static int sqrtFloor(int x)
    • 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
      See Also:
    • 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
    • checkedAdd

      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 kth power, provided it does not overflow.

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

      Throws:
      ArithmeticException - if b to the kth power overflows in signed int arithmetic
    • saturatedAdd

      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

      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

      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

      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:
      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

      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