Class BigIntegerMath


  • @GwtCompatible(emulated=true)
    public final class BigIntegerMath
    extends java.lang.Object
    A class for arithmetic on values of type BigInteger.

    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 long can be found in IntMath and LongMath respectively.

    Since:
    11.0
    Author:
    Louis Wasserman
    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static java.math.BigInteger binomial​(int n, int k)
      Returns n choose k, also known as the binomial coefficient of n and k, that is, n! / (k! (n - k)!).
      static java.math.BigInteger ceilingPowerOfTwo​(java.math.BigInteger x)
      Returns the smallest power of two greater than or equal to x.
      static java.math.BigInteger divide​(java.math.BigInteger p, java.math.BigInteger q, java.math.RoundingMode mode)
      Returns the result of dividing p by q, rounding using the specified RoundingMode.
      static java.math.BigInteger factorial​(int n)
      Returns n!, that is, the product of the first n positive integers, or 1 if n == 0.
      static java.math.BigInteger floorPowerOfTwo​(java.math.BigInteger x)
      Returns the largest power of two less than or equal to x.
      static boolean isPowerOfTwo​(java.math.BigInteger x)
      Returns true if x represents a power of two.
      static int log10​(java.math.BigInteger x, java.math.RoundingMode mode)
      Returns the base-10 logarithm of x, rounded according to the specified rounding mode.
      static int log2​(java.math.BigInteger x, java.math.RoundingMode mode)
      Returns the base-2 logarithm of x, rounded according to the specified rounding mode.
      static double roundToDouble​(java.math.BigInteger x, java.math.RoundingMode mode)
      Returns x, rounded to a double with the specified rounding mode.
      static java.math.BigInteger sqrt​(java.math.BigInteger 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 java.math.BigInteger ceilingPowerOfTwo​(java.math.BigInteger x)
        Returns the smallest power of two greater than or equal to x. This is equivalent to BigInteger.valueOf(2).pow(log2(x, CEILING)).
        Throws:
        java.lang.IllegalArgumentException - if x <= 0
        Since:
        20.0
      • floorPowerOfTwo

        @Beta
        public static java.math.BigInteger floorPowerOfTwo​(java.math.BigInteger x)
        Returns the largest power of two less than or equal to x. This is equivalent to BigInteger.valueOf(2).pow(log2(x, FLOOR)).
        Throws:
        java.lang.IllegalArgumentException - if x <= 0
        Since:
        20.0
      • isPowerOfTwo

        public static boolean isPowerOfTwo​(java.math.BigInteger x)
        Returns true if x represents a power of two.
      • log2

        public static int log2​(java.math.BigInteger 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​(java.math.BigInteger 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
      • sqrt

        @GwtIncompatible
        public static java.math.BigInteger sqrt​(java.math.BigInteger 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
      • roundToDouble

        @GwtIncompatible
        public static double roundToDouble​(java.math.BigInteger x,
                                           java.math.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_DOWN, HALF_UP, and HALF_EVEN, infinite double values are considered infinitely far away. For example, 2^2000 is not representable as a double, but roundToDouble(BigInteger.valueOf(2).pow(2000), HALF_UP) will return Double.MAX_VALUE, not Double.POSITIVE_INFINITY.

        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:
        java.lang.ArithmeticException - if mode is RoundingMode.UNNECESSARY and x is not precisely representable as a double
        Since:
        30.0
      • divide

        @GwtIncompatible
        public static java.math.BigInteger divide​(java.math.BigInteger p,
                                                  java.math.BigInteger 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
      • factorial

        public static java.math.BigInteger factorial​(int n)
        Returns n!, that is, the product of the first n positive integers, or 1 if n == 0.

        Warning: the result takes O(n log n) space, so use cautiously.

        This uses an efficient binary recursive algorithm to compute the factorial with balanced multiplies. It also removes all the 2s from the intermediate products (shifting them back in at the end).

        Throws:
        java.lang.IllegalArgumentException - if n < 0
      • binomial

        public static java.math.BigInteger binomial​(int n,
                                                    int k)
        Returns n choose k, also known as the binomial coefficient of n and k, that is, n! / (k! (n - k)!).

        Warning: the result can take as much as O(k log n) space.

        Throws:
        java.lang.IllegalArgumentException - if n < 0, k < 0, or k > n