Package org.apache.commons.numbers.core

Class ArithmeticUtils

java.lang.Object
org.apache.commons.numbers.core.ArithmeticUtils
public final class ArithmeticUtils
extends java.lang.Object
Some useful, arithmetics related, additions to the built-in functions in Math.

  • Method Summary

    Modifier and Type Method 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 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 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 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 java.math.BigInteger pow​(java.math.BigInteger k, int e)
    Raise a BigInteger to an int power.
    static java.math.BigInteger pow​(java.math.BigInteger k, long e)
    Raise a BigInteger to a long power.
    static java.math.BigInteger pow​(java.math.BigInteger k, java.math.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.
    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 Details

    • 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:
      java.lang.ArithmeticException - if the result can not be represented as an int.

    • 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:
      java.lang.ArithmeticException - if the result can not be represented as an long

    • 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:
      java.lang.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:
      java.lang.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:
      java.lang.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:
      java.lang.ArithmeticException - if the result cannot be represented as a non-negative long value.

    • 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:
      java.lang.ArithmeticException - if the result can not be represented as an int.

    • 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:
      java.lang.ArithmeticException - if the result can not be represented as a long.

    • 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:
      java.lang.ArithmeticException - if the result can not be represented as an int.

    • 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:
      java.lang.ArithmeticException - if the result can not be represented as a long.

    • pow

      public static int pow​(int k, int e)
      Raise an int to an int power.
      Parameters:
      k - Number to raise.
      e - Exponent (must be positive or zero).
      Returns:
      \( k^e \)
      Throws:
      java.lang.IllegalArgumentException - if e < 0.
      java.lang.ArithmeticException - if the result would overflow.

    • pow

      public static long pow​(long k, int e)
      Raise a long to an int power.
      Parameters:
      k - Number to raise.
      e - Exponent (must be positive or zero).
      Returns:
      \( k^e \)
      Throws:
      java.lang.IllegalArgumentException - if e < 0.
      java.lang.ArithmeticException - if the result would overflow.

    • pow

      public static java.math.BigInteger pow​(java.math.BigInteger k, int e)
      Raise a BigInteger to an int power.
      Parameters:
      k - Number to raise.
      e - Exponent (must be positive or zero).
      Returns:
      ke
      Throws:
      java.lang.IllegalArgumentException - if e < 0.

    • pow

      public static java.math.BigInteger pow​(java.math.BigInteger k, long e)
      Raise a BigInteger to a long power.
      Parameters:
      k - Number to raise.
      e - Exponent (must be positive or zero).
      Returns:
      ke
      Throws:
      java.lang.IllegalArgumentException - if e < 0.

    • pow

      public static java.math.BigInteger pow​(java.math.BigInteger k, java.math.BigInteger e)
      Raise a BigInteger to a BigInteger power.
      Parameters:
      k - Number to raise.
      e - Exponent (must be positive or zero).
      Returns:
      ke
      Throws:
      java.lang.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.