Class LongMath

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

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
  • Nested Class Summary

    Nested Classes
    Modifier and Type
    Class
    Description
    private static enum 
     
  • Field Summary

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

    Constructors
    Modifier
    Constructor
    Description
    private
     
  • Method Summary

    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
    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.
    (package private) static boolean
    fitsInInt(long x)
     
    static long
    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.
    (package private) static int
    lessThanBranchFree(long x, long y)
    Returns 1 if x < y as unsigned longs, and 0 otherwise.
    static int
    log10(long x, RoundingMode mode)
    Returns the base-10 logarithm of x, rounded according to the specified rounding mode.
    (package private) static int
    log10Floor(long x)
     
    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.
    (package private) static long
    multiplyFraction(long x, long numerator, long denominator)
    Returns (x * numerator / denominator), which is assumed to come out to an integral value.
    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.

    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 long MAX_SIGNED_POWER_OF_TWO
      See Also:
    • MAX_POWER_OF_SQRT2_UNSIGNED

      static final long MAX_POWER_OF_SQRT2_UNSIGNED
      The biggest half power of two that fits into an unsigned long
      See Also:
    • maxLog10ForLeadingZeros

      static final byte[] maxLog10ForLeadingZeros
    • powersOf10

      static final long[] powersOf10
    • halfPowersOf10

      static final long[] halfPowersOf10
    • FLOOR_SQRT_MAX_LONG

      static final long FLOOR_SQRT_MAX_LONG
      See Also:
    • factorials

      static final long[] factorials
    • biggestBinomials

      static final int[] biggestBinomials
    • biggestSimpleBinomials

      static final int[] biggestSimpleBinomials
    • SIEVE_30

      private static final int SIEVE_30
      See Also:
    • millerRabinBaseSets

      private static final long[][] millerRabinBaseSets
  • Constructor Details

    • LongMath

      private LongMath()
  • Method Details

    • ceilingPowerOfTwo

      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

      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.

    • lessThanBranchFree

      static int lessThanBranchFree(long x, long y)
      Returns 1 if x < y as unsigned longs, and 0 otherwise. Assumes that x - y fits into a signed long. The implementation is branch-free, and benchmarks suggest it is measurably faster than the straightforward ternary expression.
    • log2

      public static int log2(long 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(long 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

      static int log10Floor(long x)
    • pow

      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
    • sqrt

      public static long sqrt(long 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 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

      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:
    • mod

      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:
    • 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
    • checkedSubtract

      public static long checkedSubtract(long a, long b)
      Returns the difference 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

      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

      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

      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

      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

      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
    • factorial

      public 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.
      Throws:
      IllegalArgumentException - if n < 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
    • multiplyFraction

      static long multiplyFraction(long x, long numerator, long denominator)
      Returns (x * numerator / denominator), which is assumed to come out to an integral value.
    • fitsInInt

      static boolean fitsInInt(long x)
    • 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
    • isPrime

      public 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. 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 BigInteger.isProbablePrime(int).

      Throws:
      IllegalArgumentException - if n is negative
      Since:
      20.0
    • roundToDouble

      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