ArithmeticUtils (Apache Commons Math 4.0-SNAPSHOT API)

java.lang.Object
- org.apache.commons.math4.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 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 long`	`pow(long k, int e)` Raise a long to an int power.
`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
  - 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
```
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
```
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.
  - 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

gcd

gcd

lcm

lcm

mulAndCheck

mulAndCheck

subAndCheck

subAndCheck

pow

pow

pow

pow

pow

isPowerOfTwo