fr.cnes.sirius.patrius.math.util

Class ArithmeticUtils

java.lang.Object

fr.cnes.sirius.patrius.math.util.ArithmeticUtils

public final class ArithmeticUtils
extends Object

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

Version:

$Id: ArithmeticUtils.java 18108 2017-10-04 06:45:27Z bignon $

Method Summary

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) 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 eIn) 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 eIn) Raise a BigInteger to a long power.
static int	pow(int k, int eIn) Raise an int to an int power.
static int	pow(int k, long eIn) Raise an int to a long power.
static long	pow(long k, int eIn) Raise a long to an int power.
static long	pow(long k, long eIn) 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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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 eIn)

Raise an int to an int power.

Parameters:

k - Number to raise.

eIn - Exponent (must be positive or zero).

Returns:

k^e

Throws:

NotPositiveException - if e < 0.

pow

public static int pow(int k,
                      long eIn)

Raise an int to a long power.

Parameters:

k - Number to raise.

eIn - Exponent (must be positive or zero).

Returns:

k^e

Throws:

NotPositiveException - if e < 0.

pow

public static long pow(long k,
                       int eIn)

Raise a long to an int power.

Parameters:

k - Number to raise.

eIn - Exponent (must be positive or zero).

Returns:

k^e

Throws:

NotPositiveException - if e < 0.

pow

public static long pow(long k,
                       long eIn)

Raise a long to a long power.

Parameters:

k - Number to raise.

eIn - Exponent (must be positive or zero).

Returns:

k^e

Throws:

NotPositiveException - if e < 0.

pow

public static BigInteger pow(BigInteger k,
                             int e)

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 eIn)

Raise a BigInteger to a long power.

Parameters:

k - Number to raise.

eIn - Exponent (must be positive or zero).

Returns:

k^e

Throws:

NotPositiveException - if e < 0.

pow

public static BigInteger pow(BigInteger k,
                             BigInteger eIn)

Raise a BigInteger to a BigInteger power.

Parameters:

k - Number to raise.

eIn - Exponent (must be positive or zero).

Returns:

k^e

Throws:

NotPositiveException - if e < 0.

stirlingS2

public 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.

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