ArithmeticUtils (parent patrimoine de base SIRIUS 3.3 API)

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org.apache.commons.math3.util
Class ArithmeticUtils

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

public final class ArithmeticUtils
extends Object
extends Object

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

Version:: $Id: ArithmeticUtils.java 7721 2013-02-14 14:07:13Z CardosoP $

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:: k^e
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:: k^e
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:: k^e
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:: 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

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

Overview

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SUMMARY: NESTED | FIELD | CONSTR | METHOD

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org.apache.commons.math3.util Class ArithmeticUtils

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

org.apache.commons.math3.util
Class ArithmeticUtils