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
    Author:
    Louis Wasserman
    • 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 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 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 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, 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

        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