Class IntMath

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

    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 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
    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 kth power.
    static int
    saturatedAbs(int x)
    Returns the closest representable int to the absolute value of x.
    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.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • 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.

    • 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 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

      @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. If the RoundingMode is RoundingMode.DOWN, then this method is equivalent to regular Java division, p / q; and if it is RoundingMode.FLOOR, then this method is equivalent to Math.floorDiv(p, q).
      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. This method is equivalent to Math.floorMod(x, m) except that that method also allows negative m. Math.floorMod should be preferred when m is known to be positive.

      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

      @InlineMe(replacement="Math.addExact(a, b)") public static int checkedAdd(int a, int b)
      Returns the sum of a and b, provided it does not overflow.

      Note: this method is now unnecessary and should be treated as deprecated; use Math.addExact(int, int) instead.

      Throws:
      ArithmeticException - if a + b overflows in signed int arithmetic

    • checkedSubtract

      @InlineMe(replacement="Math.subtractExact(a, b)") public static int checkedSubtract(int a, int b)
      Returns the difference of a and b, provided it does not overflow.

      Note: this method is now unnecessary and should be treated as deprecated; use Math.subtractExact(int, int) instead.

      Throws:
      ArithmeticException - if a - b overflows in signed int arithmetic

    • checkedMultiply

      @InlineMe(replacement="Math.multiplyExact(a, b)") public static int checkedMultiply(int a, int b)
      Returns the product of a and b, provided it does not overflow.

      Note: this method is now unnecessary and should be treated as deprecated; use Math.multiplyExact(int, int) instead.

      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

      @GwtIncompatible 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

    • saturatedAbs

      public static int saturatedAbs(int x)
      Returns the closest representable int to the absolute value of x.

      This is the same thing as the true absolute value of x except in the case when x is Integer.MIN_VALUE, in which case this returns Integer.MAX_VALUE. (Note that Integer.MAX_VALUE is mathematically equal to -Integer.MIN_VALUE - 1.)

      There are three common APIs for determining the absolute value of an integer, all of which behave identically except when passed Integer.MIN_VALUE. Those methods are:

      • Math.abs(int), which returns Integer.MIN_VALUE when passed Integer.MIN_VALUE
      • Math.absExact(int), which throws ArithmeticException when passed Integer.MIN_VALUE
      • this method, IntMath.saturatedAbs(int), which returns Integer.MAX_VALUE when passed Integer.MIN_VALUE

      Note that if your only goal is to turn a well-distributed `int` (such as a random number or hash code) into a well-distributed nonnegative number, the most even distribution is achieved not by this method or other absolute value methods, but by x & Integer.MAX_VALUE.

      Since:
      33.5.0