Class LongMath


  • @GwtCompatible(emulated=true)
    public final class LongMath
    extends Object
    A class for arithmetic on values of type long. 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 int and for BigInteger can be found in IntMath and BigIntegerMath respectively. For other common operations on long values, see Longs.

    Since:
    11.0
    Author:
    Louis Wasserman
    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static long binomial​(int n, int k)
      Returns n choose k, also known as the binomial coefficient of n and k, or Long.MAX_VALUE if the result does not fit in a long.
      static long ceilingPowerOfTwo​(long x)
      Returns the smallest power of two greater than or equal to x.
      static long checkedAdd​(long a, long b)
      Returns the sum of a and b, provided it does not overflow.
      static long checkedMultiply​(long a, long b)
      Returns the product of a and b, provided it does not overflow.
      static long checkedPow​(long b, int k)
      Returns the b to the kth power, provided it does not overflow.
      static long checkedSubtract​(long a, long b)
      Returns the difference of a and b, provided it does not overflow.
      static long divide​(long p, long q, RoundingMode mode)
      Returns the result of dividing p by q, rounding using the specified RoundingMode.
      static long factorial​(int n)
      Returns n!, that is, the product of the first n positive integers, 1 if n == 0, or Long.MAX_VALUE if the result does not fit in a long.
      static long floorPowerOfTwo​(long x)
      Returns the largest power of two less than or equal to x.
      static long gcd​(long a, long b)
      Returns the greatest common divisor of a, b.
      static boolean isPowerOfTwo​(long x)
      Returns true if x represents a power of two.
      static boolean isPrime​(long 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​(long x, RoundingMode mode)
      Returns the base-10 logarithm of x, rounded according to the specified rounding mode.
      static int log2​(long x, RoundingMode mode)
      Returns the base-2 logarithm of x, rounded according to the specified rounding mode.
      static long mean​(long x, long y)
      Returns the arithmetic mean of x and y, rounded toward negative infinity.
      static int mod​(long x, int m)
      Returns x mod m, a non-negative value less than m.
      static long mod​(long x, long m)
      Returns x mod m, a non-negative value less than m.
      static long pow​(long b, int k)
      Returns b to the kth power.
      static double roundToDouble​(long x, RoundingMode mode)
      Returns x, rounded to a double with the specified rounding mode.
      static long saturatedAdd​(long a, long b)
      Returns the sum of a and b unless it would overflow or underflow in which case Long.MAX_VALUE or Long.MIN_VALUE is returned, respectively.
      static long saturatedMultiply​(long a, long b)
      Returns the product of a and b unless it would overflow or underflow in which case Long.MAX_VALUE or Long.MIN_VALUE is returned, respectively.
      static long saturatedPow​(long b, int k)
      Returns the b to the kth power, unless it would overflow or underflow in which case Long.MAX_VALUE or Long.MIN_VALUE is returned, respectively.
      static long saturatedSubtract​(long a, long b)
      Returns the difference of a and b unless it would overflow or underflow in which case Long.MAX_VALUE or Long.MIN_VALUE is returned, respectively.
      static long sqrt​(long x, RoundingMode mode)
      Returns the square root of x, rounded with the specified rounding mode.
    • Method Detail

      • ceilingPowerOfTwo

        @Beta
        public static long ceilingPowerOfTwo​(long 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 a long, i.e. when x > 2^62
        Since:
        20.0
      • floorPowerOfTwo

        @Beta
        public static long floorPowerOfTwo​(long 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​(long x)
        Returns true if x represents a power of two.

        This differs from Long.bitCount(x) == 1, because Long.bitCount(Long.MIN_VALUE) == 1, but Long.MIN_VALUE is not a power of two.

      • pow

        @GwtIncompatible
        public static long pow​(long b,
                               int k)
        Returns b to the kth power. Even if the result overflows, it will be equal to BigInteger.valueOf(b).pow(k).longValue(). This implementation runs in O(log k) time.
        Throws:
        IllegalArgumentException - if k < 0
      • divide

        @GwtIncompatible
        public static long divide​(long p,
                                  long 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

        @GwtIncompatible
        public static int mod​(long 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:
        Remainder Operator
      • mod

        @GwtIncompatible
        public static long mod​(long x,
                               long 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:
        Remainder Operator
      • gcd

        public static long gcd​(long a,
                               long 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 long checkedAdd​(long a,
                                      long b)
        Returns the sum of a and b, provided it does not overflow.
        Throws:
        ArithmeticException - if a + b overflows in signed long arithmetic
      • checkedMultiply

        public static long checkedMultiply​(long a,
                                           long b)
        Returns the product of a and b, provided it does not overflow.
        Throws:
        ArithmeticException - if a * b overflows in signed long arithmetic
      • checkedPow

        @GwtIncompatible
        public static long checkedPow​(long b,
                                      int k)
        Returns the b to the kth power, provided it does not overflow.
        Throws:
        ArithmeticException - if b to the kth power overflows in signed long arithmetic
      • saturatedAdd

        @Beta
        public static long saturatedAdd​(long a,
                                        long b)
        Returns the sum of a and b unless it would overflow or underflow in which case Long.MAX_VALUE or Long.MIN_VALUE is returned, respectively.
        Since:
        20.0
      • saturatedSubtract

        @Beta
        public static long saturatedSubtract​(long a,
                                             long b)
        Returns the difference of a and b unless it would overflow or underflow in which case Long.MAX_VALUE or Long.MIN_VALUE is returned, respectively.
        Since:
        20.0
      • saturatedMultiply

        @Beta
        public static long saturatedMultiply​(long a,
                                             long b)
        Returns the product of a and b unless it would overflow or underflow in which case Long.MAX_VALUE or Long.MIN_VALUE is returned, respectively.
        Since:
        20.0
      • saturatedPow

        @Beta
        public static long saturatedPow​(long b,
                                        int k)
        Returns the b to the kth power, unless it would overflow or underflow in which case Long.MAX_VALUE or Long.MIN_VALUE is returned, respectively.
        Since:
        20.0
      • binomial

        public static long binomial​(int n,
                                    int k)
        Returns n choose k, also known as the binomial coefficient of n and k, or Long.MAX_VALUE if the result does not fit in a long.
        Throws:
        IllegalArgumentException - if n < 0, k < 0, or k > n
      • mean

        public static long mean​(long x,
                                long y)
        Returns the arithmetic mean of x and y, rounded toward negative infinity. This method is resilient to overflow.
        Since:
        14.0
      • roundToDouble

        @GwtIncompatible
        public static double roundToDouble​(long x,
                                           RoundingMode mode)
        Returns x, rounded to a double with the specified rounding mode. If x is precisely representable as a double, its double value will be returned; otherwise, the rounding will choose between the two nearest representable values with mode.

        For the case of RoundingMode.HALF_EVEN, this implementation uses the IEEE 754 default rounding mode: if the two nearest representable values are equally near, the one with the least significant bit zero is chosen. (In such cases, both of the nearest representable values are even integers; this method returns the one that is a multiple of a greater power of two.)

        Throws:
        ArithmeticException - if mode is RoundingMode.UNNECESSARY and x is not precisely representable as a double
        Since:
        30.0