Package org.apache.commons.numbers.core

Class ArithmeticUtils

java.lang.Object

org.apache.commons.numbers.core.ArithmeticUtils

public final class ArithmeticUtils
extends Object

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

Method Summary

Modifier and Type	Method	Description
static int	divideUnsigned(int dividend, int divisor)	Returns the unsigned quotient of dividing the first argument by the second where each argument and the result is interpreted as an unsigned value.
static long	divideUnsigned(long dividend, long divisor)	Returns the unsigned quotient of dividing the first argument by the second where each argument and the result is interpreted as an unsigned value.
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	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 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 BigInteger	pow(BigInteger k, BigInteger e)	Raise a BigInteger to a BigInteger power.
static int	remainderUnsigned(int dividend, int divisor)	Returns the unsigned remainder from dividing the first argument by the second where each argument and the result is interpreted as an unsigned value.
static long	remainderUnsigned(long dividend, long divisor)	Returns the unsigned remainder from dividing the first argument by the second where each argument and the result is interpreted as an unsigned value.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

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:

ArithmeticException - if the result cannot be represented as a non-negative int value.

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:

ArithmeticException - if the result cannot be represented as a non-negative long value.

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:

ArithmeticException - if the result cannot be represented as a non-negative int value.

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:

ArithmeticException - if the result cannot be represented as a non-negative long value.

pow

public static int pow(int k,
                      int e)

Raise an int to an int power.

Special cases:

• k^0 returns 1 (including k=0)
• k^1 returns k (including k=0)
• 0^0 returns 1
• 0^e returns 0
• 1^e returns 1
• (-1)^e returns -1 or 1 if e is odd or even

Parameters:

k - Number to raise.

e - Exponent (must be positive or zero).

Returns:

\( k^e \)

Throws:

IllegalArgumentException - if e < 0.

ArithmeticException - if the result would overflow.

pow

public static long pow(long k,
                       int e)

Raise a long to an int power.

Special cases:

• k^0 returns 1 (including k=0)
• k^1 returns k (including k=0)
• 0^0 returns 1
• 0^e returns 0
• 1^e returns 1
• (-1)^e returns -1 or 1 if e is odd or even

Parameters:

k - Number to raise.

e - Exponent (must be positive or zero).

Returns:

\( k^e \)

Throws:

IllegalArgumentException - if e < 0.

ArithmeticException - if the result would overflow.

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:

IllegalArgumentException - if e < 0.

pow

public static BigInteger pow(BigInteger k,
                             long e)

Raise a BigInteger to a long power.

Parameters:

k - Number to raise.

e - Exponent (must be positive or zero).

Returns:

k^e

Throws:

IllegalArgumentException - if e < 0.

pow

public static BigInteger pow(BigInteger k,
                             BigInteger e)

Raise a BigInteger to a BigInteger power.

Parameters:

k - Number to raise.

e - Exponent (must be positive or zero).

Returns:

k^e

Throws:

IllegalArgumentException - 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

remainderUnsigned

public static int remainderUnsigned(int dividend,
                                    int divisor)

Returns the unsigned remainder from dividing the first argument by the second where each argument and the result is interpreted as an unsigned value.

This method does not use the long datatype.

Parameters:

dividend - the value to be divided

divisor - the value doing the dividing

Returns:

the unsigned remainder of the first argument divided by the second argument.

remainderUnsigned

public static long remainderUnsigned(long dividend,
                                     long divisor)

Returns the unsigned remainder from dividing the first argument by the second where each argument and the result is interpreted as an unsigned value.

This method does not use the BigInteger datatype.

Parameters:

dividend - the value to be divided

divisor - the value doing the dividing

Returns:

the unsigned remainder of the first argument divided by the second argument.

divideUnsigned

public static int divideUnsigned(int dividend,
                                 int divisor)

Returns the unsigned quotient of dividing the first argument by the second where each argument and the result is interpreted as an unsigned value.

Note that in two's complement arithmetic, the three other basic arithmetic operations of add, subtract, and multiply are bit-wise identical if the two operands are regarded as both being signed or both being unsigned. Therefore separate addUnsigned, etc. methods are not provided.

This method does not use the long datatype.

Parameters:

dividend - the value to be divided

divisor - the value doing the dividing

Returns:

the unsigned quotient of the first argument divided by the second argument

divideUnsigned

public static long divideUnsigned(long dividend,
                                  long divisor)

Returns the unsigned quotient of dividing the first argument by the second where each argument and the result is interpreted as an unsigned value.

Note that in two's complement arithmetic, the three other basic arithmetic operations of add, subtract, and multiply are bit-wise identical if the two operands are regarded as both being signed or both being unsigned. Therefore separate addUnsigned, etc. methods are not provided.

This method does not use the BigInteger datatype.

Parameters:

dividend - the value to be divided

divisor - the value doing the dividing

Returns:

the unsigned quotient of the first argument divided by the second argument.