org.apache.commons.math3.util
Class ArithmeticUtils

java.lang.Object
  extended by org.apache.commons.math3.util.ArithmeticUtils

public final class ArithmeticUtils
extends 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:

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:

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:

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:

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:

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:

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:

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:

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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