Package com.google.common.math

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

    • Constructor Summary

      Constructors 
      Modifier Constructor Description
      private BigIntegerMath()  

    • 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.
      (package private) static boolean fitsInLong​(java.math.BigInteger x)  
      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.
      (package private) static java.math.BigInteger listProduct​(java.util.List<java.math.BigInteger> nums)  
      (package private) static java.math.BigInteger listProduct​(java.util.List<java.math.BigInteger> nums, int start, int end)  
      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 java.math.BigInteger sqrt​(java.math.BigInteger x, java.math.RoundingMode mode)
      Returns the square root of x, rounded with the specified rounding mode.
      private static java.math.BigInteger sqrtApproxWithDoubles​(java.math.BigInteger x)  
      private static java.math.BigInteger sqrtFloor​(java.math.BigInteger x)  

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    • Field Detail

      • SQRT2_PRECOMPUTE_THRESHOLD

        static final int SQRT2_PRECOMPUTE_THRESHOLD
        See Also:
        Constant Field Values

      • SQRT2_PRECOMPUTED_BITS

        static final java.math.BigInteger SQRT2_PRECOMPUTED_BITS

      • LN_10

        private static final double LN_10

      • LN_2

        private static final double LN_2

    • Constructor Detail

      • BigIntegerMath

        private BigIntegerMath()

    • 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

      • sqrtFloor

        @GwtIncompatible
private static java.math.BigInteger sqrtFloor​(java.math.BigInteger x)

      • sqrtApproxWithDoubles

        @GwtIncompatible
private static java.math.BigInteger sqrtApproxWithDoubles​(java.math.BigInteger x)

      • 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

      • listProduct

        static java.math.BigInteger listProduct​(java.util.List<java.math.BigInteger> nums)

      • listProduct

        static java.math.BigInteger listProduct​(java.util.List<java.math.BigInteger> nums,
                                        int start,
                                        int end)

      • 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

      • fitsInLong

        @GwtIncompatible
static boolean fitsInLong​(java.math.BigInteger x)