Class 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 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, 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 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 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.
      static int pow​(int b, int k)
      Returns b to the kth power.
      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

        equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
    • Method Detail

      • 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("need BigIntegerMath to adequately test")
        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("failing tests")
        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("need BigIntegerMath to adequately test")
        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. This differs from x % m in that it always returns a non-negative result.

        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
      • 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
      • 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("need BigIntegerMath to adequately test")
        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