## org.apache.commons.math3.util Class ArithmeticUtils

```java.lang.Object org.apache.commons.math3.util.ArithmeticUtils
```

`public final class ArithmeticUtilsextends Object`

Some useful, arithmetics related, additions to the built-in functions in `Math`.

Version:
\$Id: ArithmeticUtils.java 1422313 2012-12-15 18:53:41Z psteitz \$

Method Summary
`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)```
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.
`static double` ```binomialCoefficientDouble(int n, int k)```
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.
`static double` ```binomialCoefficientLog(int n, int k)```
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.
`static long` `factorial(int n)`
Returns n!.
`static double` `factorialDouble(int n)`
Compute n!, the factorial of `n` (the product of the numbers 1 to n), as a `double`.
`static double` `factorialLog(int n)`
Compute the natural logarithm of the factorial of `n`.
`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)```
Raise an int to a long power.
`static long` ```pow(long k, int e)```
Raise a long to an int power.
`static long` ```pow(long k, long e)```
Raise a long to a long power.
`static long` ```stirlingS2(int n, int k)```
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.
`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

```public static long binomialCoefficient(int n,
int k)
throws NotPositiveException,
NumberIsTooLargeException,
MathArithmeticException```
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

```public static double binomialCoefficientDouble(int n,
int k)
throws NotPositiveException,
NumberIsTooLargeException,
MathArithmeticException```
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

```public static double binomialCoefficientLog(int n,
int k)
throws NotPositiveException,
NumberIsTooLargeException,
MathArithmeticException```
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

```public static long factorial(int n)
throws NotPositiveException,
MathArithmeticException```
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

```public static double factorialDouble(int n)
throws NotPositiveException```
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

```public static double factorialLog(int n)
throws NotPositiveException```
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```
Raise an int 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 int pow(int k,
long e)
throws NotPositiveException```
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```
Raise a long 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 long pow(long k,
long e)
throws NotPositiveException```
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

```public static long stirlingS2(int n,
int k)
throws NotPositiveException,
NumberIsTooLargeException,
MathArithmeticException```
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

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