ArithmeticUtils (Apache Commons Math 3.6.1 API)

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 Summary

Methods
Modifier and Type	Method and Description
`static int`	`addAndCheck(int x, int y)` Add two integers, checking for overflow.
`static long`	`addAndCheck(long a, long b)` Add two long integers, checking for overflow.
`static long`	`binomialCoefficient(int n, int k)` Deprecated. use `CombinatoricsUtils.binomialCoefficient(int, int)`
`static double`	`binomialCoefficientDouble(int n, int k)` Deprecated. use `CombinatoricsUtils.binomialCoefficientDouble(int, int)`
`static double`	`binomialCoefficientLog(int n, int k)` Deprecated. use `CombinatoricsUtils.binomialCoefficientLog(int, int)`
`static long`	`factorial(int n)` Deprecated. use `CombinatoricsUtils.factorial(int)`
`static double`	`factorialDouble(int n)` Deprecated. use `CombinatoricsUtils.factorialDouble(int)`
`static double`	`factorialLog(int n)` Deprecated. use `CombinatoricsUtils.factorialLog(int)`
`static int`	`gcd(int p, int q)` Computes the greatest common divisor of the absolute value of two numbers, using a modified version of the "binary gcd" method.
`static long`	`gcd(long p, long q)` Gets the greatest common divisor of the absolute value of two numbers, using the "binary gcd" method which avoids division and modulo operations.
`static boolean`	`isPowerOfTwo(long n)` Returns true if the argument is a power of two.
`static int`	`lcm(int a, int b)` Returns the least common multiple of the absolute value of two numbers, using the formula `lcm(a,b) = (a / gcd(a,b)) * b`.
`static long`	`lcm(long a, long b)` Returns the least common multiple of the absolute value of two numbers, using the formula `lcm(a,b) = (a / gcd(a,b)) * b`.
`static int`	`mulAndCheck(int x, int y)` Multiply two integers, checking for overflow.
`static long`	`mulAndCheck(long a, long b)` Multiply two long integers, checking for overflow.
`static BigInteger`	`pow(BigInteger k, BigInteger e)` Raise a BigInteger to a BigInteger power.
`static BigInteger`	`pow(BigInteger k, int e)` Raise a BigInteger to an int power.
`static BigInteger`	`pow(BigInteger k, long e)` Raise a BigInteger to a long power.
`static int`	`pow(int k, int e)` Raise an int to an int power.
`static int`	`pow(int k, long e)` Deprecated. As of 3.3. Please use `pow(int,int)` instead.
`static long`	`pow(long k, int e)` Raise a long to an int power.
`static long`	`pow(long k, long e)` Deprecated. As of 3.3. Please use `pow(long,int)` instead.
`static long`	`stirlingS2(int n, int k)` Deprecated. use `CombinatoricsUtils.stirlingS2(int, int)`
`static int`	`subAndCheck(int x, int y)` Subtract two integers, checking for overflow.
`static long`	`subAndCheck(long a, long b)` Subtract two long integers, checking for overflow.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Method Detail
  - 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 < 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! < 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:
    k^e
    
    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:
    k^e
    
    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:
    k^e
    
    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:
    k^e
    
    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:
    k^e
    
    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

Class ArithmeticUtils

Method Summary

Methods inherited from class java.lang.Object

Method Detail

addAndCheck

addAndCheck

binomialCoefficient

binomialCoefficientDouble

binomialCoefficientLog

factorial

factorialDouble

factorialLog

gcd

gcd

lcm

lcm

mulAndCheck

mulAndCheck

subAndCheck

subAndCheck

pow

pow

pow

pow

pow

pow

pow

stirlingS2

isPowerOfTwo