Package org.apache.commons.math3.util

Class ArithmeticUtils

java.lang.Object
org.apache.commons.math3.util.ArithmeticUtils
public final class ArithmeticUtils extends Object
Some useful, arithmetics related, additions to the built-in functions in Math.

  • Method Details

    • addAndCheck

      public static int addAndCheck(int x, int y) throws MathArithmeticException
      Add two integers, checking for overflow.
      Parameters:
      x - an addend
      y - an addend
      Returns:
      the sum x+y
      Throws:
      MathArithmeticException - if the result can not be represented as an int.
      Since:
      1.1

    • addAndCheck

      public static long addAndCheck(long a, long b) throws MathArithmeticException
      Add two long integers, checking for overflow.
      Parameters:
      a - an addend
      b - an addend
      Returns:
      the sum a+b
      Throws:
      MathArithmeticException - if the result can not be represented as an long
      Since:
      1.2

    • binomialCoefficient

      @Deprecated public static long binomialCoefficient(int n, int k) throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException
      Deprecated.
      use CombinatoricsUtils.binomialCoefficient(int, int)
      Returns an exact representation of the Binomial Coefficient, "n choose k", the number of k-element subsets that can be selected from an n-element set.

      Preconditions:

      • 0 <= k <= n (otherwise IllegalArgumentException is thrown)
      • The result is small enough to fit into a long. The largest value of n for which all coefficients are < Long.MAX_VALUE is 66. If the computed value exceeds Long.MAX_VALUE an ArithMeticException is thrown.

      Parameters:
      n - the size of the set
      k - the size of the subsets to be counted
      Returns:
      n choose k
      Throws:
      NotPositiveException - if n < 0.
      NumberIsTooLargeException - if k > n.
      MathArithmeticException - if the result is too large to be represented by a long integer.

    • binomialCoefficientDouble

      @Deprecated public static double binomialCoefficientDouble(int n, int k) throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException
      Deprecated.
      use CombinatoricsUtils.binomialCoefficientDouble(int, int)
      Returns a double representation of the Binomial Coefficient, "n choose k", the number of k-element subsets that can be selected from an n-element set.

      Preconditions:

      • 0 <= k <= n (otherwise IllegalArgumentException is thrown)
      • The result is small enough to fit into a double. The largest value of n for which all coefficients are invalid input: '<' Double.MAX_VALUE is 1029. If the computed value exceeds Double.MAX_VALUE, Double.POSITIVE_INFINITY is returned

      Parameters:
      n - the size of the set
      k - the size of the subsets to be counted
      Returns:
      n choose k
      Throws:
      NotPositiveException - if n < 0.
      NumberIsTooLargeException - if k > n.
      MathArithmeticException - if the result is too large to be represented by a long integer.

    • binomialCoefficientLog

      @Deprecated public static double binomialCoefficientLog(int n, int k) throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException
      Deprecated.
      use CombinatoricsUtils.binomialCoefficientLog(int, int)
      Returns the natural log of the Binomial Coefficient, "n choose k", the number of k-element subsets that can be selected from an n-element set.

      Preconditions:

      • 0 <= k <= n (otherwise IllegalArgumentException is thrown)

      Parameters:
      n - the size of the set
      k - the size of the subsets to be counted
      Returns:
      n choose k
      Throws:
      NotPositiveException - if n < 0.
      NumberIsTooLargeException - if k > n.
      MathArithmeticException - if the result is too large to be represented by a long integer.

    • factorial

      @Deprecated public static long factorial(int n) throws NotPositiveException, MathArithmeticException
      Deprecated.
      use CombinatoricsUtils.factorial(int)
      Returns n!. Shorthand for n Factorial, the product of the numbers 1,...,n.

      Preconditions:

      • n >= 0 (otherwise IllegalArgumentException is thrown)
      • The result is small enough to fit into a long. The largest value of n for which n! invalid input: '<' Long.MAX_VALUE} is 20. If the computed value exceeds Long.MAX_VALUE an ArithMeticException is thrown.

      Parameters:
      n - argument
      Returns:
      n!
      Throws:
      MathArithmeticException - if the result is too large to be represented by a long.
      NotPositiveException - if n < 0.
      MathArithmeticException - if n > 20: The factorial value is too large to fit in a long.

    • factorialDouble

      @Deprecated public static double factorialDouble(int n) throws NotPositiveException
      Deprecated.
      use CombinatoricsUtils.factorialDouble(int)
      Compute n!, the factorial of n (the product of the numbers 1 to n), as a double. The result should be small enough to fit into a double: The largest n for which n! < Double.MAX_VALUE is 170. If the computed value exceeds Double.MAX_VALUE, Double.POSITIVE_INFINITY is returned.
      Parameters:
      n - Argument.
      Returns:
      n!
      Throws:
      NotPositiveException - if n < 0.

    • factorialLog

      @Deprecated public static double factorialLog(int n) throws NotPositiveException
      Deprecated.
      use CombinatoricsUtils.factorialLog(int)
      Compute the natural logarithm of the factorial of n.
      Parameters:
      n - Argument.
      Returns:
      n!
      Throws:
      NotPositiveException - if n < 0.

    • gcd

      public static int gcd(int p, int q) throws MathArithmeticException
      Computes the greatest common divisor of the absolute value of two numbers, using a modified version of the "binary gcd" method. See Knuth 4.5.2 algorithm B. The algorithm is due to Josef Stein (1961).
      Special cases:
      • The invocations gcd(Integer.MIN_VALUE, Integer.MIN_VALUE), gcd(Integer.MIN_VALUE, 0) and gcd(0, Integer.MIN_VALUE) throw an ArithmeticException, because the result would be 2^31, which is too large for an int value.
      • The result of gcd(x, x), gcd(0, x) and gcd(x, 0) is the absolute value of x, except for the special cases above.
      • The invocation gcd(0, 0) is the only one which returns 0.
      Parameters:
      p - Number.
      q - Number.
      Returns:
      the greatest common divisor (never negative).
      Throws:
      MathArithmeticException - if the result cannot be represented as a non-negative int value.
      Since:
      1.1

    • gcd

      public static long gcd(long p, long q) throws MathArithmeticException

      Gets the greatest common divisor of the absolute value of two numbers, using the "binary gcd" method which avoids division and modulo operations. See Knuth 4.5.2 algorithm B. This algorithm is due to Josef Stein (1961).

      Special cases:
      • The invocations gcd(Long.MIN_VALUE, Long.MIN_VALUE), gcd(Long.MIN_VALUE, 0L) and gcd(0L, Long.MIN_VALUE) throw an ArithmeticException, because the result would be 2^63, which is too large for a long value.
      • The result of gcd(x, x), gcd(0L, x) and gcd(x, 0L) is the absolute value of x, except for the special cases above.
      • The invocation gcd(0L, 0L) is the only one which returns 0L.
      Parameters:
      p - Number.
      q - Number.
      Returns:
      the greatest common divisor, never negative.
      Throws:
      MathArithmeticException - if the result cannot be represented as a non-negative long value.
      Since:
      2.1

    • lcm

      public static int lcm(int a, int b) throws MathArithmeticException

      Returns the least common multiple of the absolute value of two numbers, using the formula lcm(a,b) = (a / gcd(a,b)) * b.

      Special cases:
      • The invocations lcm(Integer.MIN_VALUE, n) and lcm(n, Integer.MIN_VALUE), where abs(n) is a power of 2, throw an ArithmeticException, because the result would be 2^31, which is too large for an int value.
      • The result of lcm(0, x) and lcm(x, 0) is 0 for any x.
      Parameters:
      a - Number.
      b - Number.
      Returns:
      the least common multiple, never negative.
      Throws:
      MathArithmeticException - if the result cannot be represented as a non-negative int value.
      Since:
      1.1

    • lcm

      public static long lcm(long a, long b) throws MathArithmeticException

      Returns the least common multiple of the absolute value of two numbers, using the formula lcm(a,b) = (a / gcd(a,b)) * b.

      Special cases:
      • The invocations lcm(Long.MIN_VALUE, n) and lcm(n, Long.MIN_VALUE), where abs(n) is a power of 2, throw an ArithmeticException, because the result would be 2^63, which is too large for an int value.
      • The result of lcm(0L, x) and lcm(x, 0L) is 0L for any x.
      Parameters:
      a - Number.
      b - Number.
      Returns:
      the least common multiple, never negative.
      Throws:
      MathArithmeticException - if the result cannot be represented as a non-negative long value.
      Since:
      2.1

    • mulAndCheck

      public static int mulAndCheck(int x, int y) throws MathArithmeticException
      Multiply two integers, checking for overflow.
      Parameters:
      x - Factor.
      y - Factor.
      Returns:
      the product x * y.
      Throws:
      MathArithmeticException - if the result can not be represented as an int.
      Since:
      1.1

    • mulAndCheck

      public static long mulAndCheck(long a, long b) throws MathArithmeticException
      Multiply two long integers, checking for overflow.
      Parameters:
      a - Factor.
      b - Factor.
      Returns:
      the product a * b.
      Throws:
      MathArithmeticException - if the result can not be represented as a long.
      Since:
      1.2

    • subAndCheck

      public static int subAndCheck(int x, int y) throws MathArithmeticException
      Subtract two integers, checking for overflow.
      Parameters:
      x - Minuend.
      y - Subtrahend.
      Returns:
      the difference x - y.
      Throws:
      MathArithmeticException - if the result can not be represented as an int.
      Since:
      1.1

    • subAndCheck

      public static long subAndCheck(long a, long b) throws MathArithmeticException
      Subtract two long integers, checking for overflow.
      Parameters:
      a - Value.
      b - Value.
      Returns:
      the difference a - b.
      Throws:
      MathArithmeticException - if the result can not be represented as a long.
      Since:
      1.2

    • pow

      public static int pow(int k, int e) throws NotPositiveException, MathArithmeticException
      Raise an int to an int power.
      Parameters:
      k - Number to raise.
      e - Exponent (must be positive or zero).
      Returns:
      \( k^e \)
      Throws:
      NotPositiveException - if e < 0.
      MathArithmeticException - if the result would overflow.

    • pow

      @Deprecated public static int pow(int k, long e) throws NotPositiveException
      Deprecated.
      As of 3.3. Please use pow(int,int) instead.
      Raise an int to a long power.
      Parameters:
      k - Number to raise.
      e - Exponent (must be positive or zero).
      Returns:
      ke
      Throws:
      NotPositiveException - if e < 0.

    • pow

      public static long pow(long k, int e) throws NotPositiveException, MathArithmeticException
      Raise a long to an int power.
      Parameters:
      k - Number to raise.
      e - Exponent (must be positive or zero).
      Returns:
      \( k^e \)
      Throws:
      NotPositiveException - if e < 0.
      MathArithmeticException - if the result would overflow.

    • pow

      @Deprecated public static long pow(long k, long e) throws NotPositiveException
      Deprecated.
      As of 3.3. Please use pow(long,int) instead.
      Raise a long to a long power.
      Parameters:
      k - Number to raise.
      e - Exponent (must be positive or zero).
      Returns:
      ke
      Throws:
      NotPositiveException - if e < 0.

    • pow

      public static BigInteger pow(BigInteger k, int e) throws NotPositiveException
      Raise a BigInteger to an int power.
      Parameters:
      k - Number to raise.
      e - Exponent (must be positive or zero).
      Returns:
      ke
      Throws:
      NotPositiveException - if e < 0.

    • pow

      public static BigInteger pow(BigInteger k, long e) throws NotPositiveException
      Raise a BigInteger to a long power.
      Parameters:
      k - Number to raise.
      e - Exponent (must be positive or zero).
      Returns:
      ke
      Throws:
      NotPositiveException - if e < 0.

    • pow

      public static BigInteger pow(BigInteger k, BigInteger e) throws NotPositiveException
      Raise a BigInteger to a BigInteger power.
      Parameters:
      k - Number to raise.
      e - Exponent (must be positive or zero).
      Returns:
      ke
      Throws:
      NotPositiveException - if e < 0.

    • stirlingS2

      @Deprecated public static long stirlingS2(int n, int k) throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException
      Deprecated.
      use CombinatoricsUtils.stirlingS2(int, int)
      Returns the Stirling number of the second kind, "S(n,k)", the number of ways of partitioning an n-element set into k non-empty subsets.

      The preconditions are 0 <= k <= n (otherwise NotPositiveException is thrown)

      Parameters:
      n - the size of the set
      k - the number of non-empty subsets
      Returns:
      S(n,k)
      Throws:
      NotPositiveException - if k < 0.
      NumberIsTooLargeException - if k > n.
      MathArithmeticException - if some overflow happens, typically for n exceeding 25 and k between 20 and n-2 (S(n,n-1) is handled specifically and does not overflow)
      Since:
      3.1

    • isPowerOfTwo

      public static boolean isPowerOfTwo(long n)
      Returns true if the argument is a power of two.
      Parameters:
      n - the number to test
      Returns:
      true if the argument is a power of two