Natural

java.lang.Object
- Natural

All Implemented Interfaces:

java.lang.Comparable
```
public class Natural
extends java.lang.Object
implements java.lang.Comparable
```
A natural number is a non-negative integer. All operations behave like Java's primitive integer types. Natural provides analogues to most of Java's primitive integer operators, and most relevant methods from java.lang.Math. Additionally, Natural provides operations for modular arithmetic.
Semantics of arithmetic operations exactly mimic those of Java's integer arithmetic operators, as defined in The Java Language Specification. For example, division by zero throws an ArithmeticException, and division of a negative by a positive yields a negative (or zero) remainder.
Comparison operations perform signed integer comparisons, analogous to those performed by Java's relational and equality operators.
For the sake of brevity and clarity, pseudo-code is used throughout the descriptions of Natural methods. The pseudo-code expression (i + j) is shorthand for "a Natural whose value is that of the Natural i plus that of the Natural j." The pseudo-code expression (i == j) is shorthand for "true if and only if the Natural i represents the same value as the the Natural j." Other pseudo-code expressions are interpreted similarly.
The MIT License (MIT)
Copyright (c) 2013 John Dalbey
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Version:

1.6 10/19/2013 fixed defect in 2-arg constructor. Implement hashCode().
1.5 3/20/06 added compareTo(int) method.
1.4 3/9/05 modified equals() to not consider maxvalue.
1.3 3/12/05 removed named constants zero and one.
1.2 Enhanced to include a maxvalue.

Author:

John Dalbey, edited by Sean Dinsmore, Thomas Bouldin

Constructor Summary

Constructors
Constructor and Description
`Natural(int val)` Constructs a Natural with the specified int value.
`Natural(int val, int max)` Constructs a Natural with the specified int value and maximum.
`Natural(java.lang.String val)` Translates the decimal String representation of a Natural into a Natural.

Method Summary

Methods
Modifier and Type	Method and Description
`Natural`	`add(Natural val)` Returns a Natural whose value is `(this + val)`.
`int`	`compareTo(int val)` Compares this Natural with the specified integer.
`int`	`compareTo(Natural val)` Compares this Natural with the specified Natural.
`int`	`compareTo(java.lang.Object x)` Same as compareTo() above, just taking an object as parameter.
`void`	`decrement()` Subtracts one from this Natural.
`Natural`	`divide(Natural val)` Returns a Natural whose value is `(this / val)`.
`double`	`doubleValue()` Converts this Natural to a double.
`boolean`	`equals(java.lang.Object x)` Compares this Natural with the specified Object for equality.
`float`	`floatValue()` Converts this Natural to a float.
`int`	`getMax()` Returns the max value of the natural number (-1 means no max)
`int`	`hashCode()` Implementation of hashCode()
`void`	`increment()` Adds one to this Natural.
`int`	`intValue()` Converts this Natural to an int.
`long`	`longValue()` Converts this Natural to a long.
`static void`	`main(java.lang.String[] args)` A local test driver
`Natural`	`max(Natural val)` Returns the maximum of this Natural and `val`.
`Natural`	`min(Natural val)` Returns the minimum of this Natural and `val`.
`Natural`	`multiply(Natural val)` Returns a Natural whose value is `(this * val)`.
`Natural`	`pow(int exponent)` Returns a Natural whose value is `(this^exponent)`.
`Natural`	`remainder(Natural val)` Returns a Natural whose value is `(this % val)`.
`Natural`	`square()` Returns a Natural whose value is `(this²)`.
`Natural`	`subtract(Natural val)` Returns a Natural whose value is `(this - val)`.
`java.lang.String`	`toString()` Returns the decimal String representation of this Natural.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - Natural
```
public Natural(java.lang.String val)
```
    Translates the decimal String representation of a Natural into a Natural. The String representation consists of an optional minus sign followed by a sequence of one or more decimal digits. The character-to-digit mapping is provided by Character.digit. The String may not contain any extraneous characters (whitespace, for example).
    
    Parameters:
    val - decimal String representation of Natural.
    
    Throws:
    
    java.lang.NumberFormatException - val is not a valid representation of a Natural.
    See Also:
    Character.digit(char, int)
  - Natural
```
public Natural(int val)
```
    Constructs a Natural with the specified int value.
    
    Parameters:
    val - int representation of Natural.
    
    Throws:
    
    java.lang.NumberFormatException - if val is negative
  - Natural
```
public Natural(int val,
       int max)
```
    Constructs a Natural with the specified int value and maximum.
    
    Parameters:
    val - int representation of Natural.
    max - int value that is the max this number can take.
    
    Throws:
    
    java.lang.NumberFormatException - if val is negative
    
    java.lang.NumberFormatException - if max is negative
    
    java.lang.NumberFormatException - if val > max
- Method Detail
  - add
```
public Natural add(Natural val)
```
    Returns a Natural whose value is (this + val).
    
    Parameters:
    val - value to be added to this Natural.
    
    Returns:
    this + val
  - increment
```
public void increment()
```
    Adds one to this Natural.
    
    Throws:
    
    ArithmeticException() - if this natural has a maximum value and the result of incrementing exceeds the maximum value.
  - subtract
```
public Natural subtract(Natural val)
```
    Returns a Natural whose value is (this - val).
    
    Parameters:
    val - value to be subtracted from this Natural.
    
    Returns:
    this - val
    
    Throws:
    
    java.lang.ArithmeticException - if result would be negative.
  - decrement
```
public void decrement()
```
    Subtracts one from this Natural.
    
    Throws:
    
    java.lang.ArithmeticException - if result would be negative.
  - multiply
```
public Natural multiply(Natural val)
```
    Returns a Natural whose value is (this * val).
    
    Parameters:
    val - value to be multiplied by this Natural.
    
    Returns:
    this * val
  - square
```
public Natural square()
```
    Returns a Natural whose value is (this²).
    
    Returns:
    this²
  - divide
```
public Natural divide(Natural val)
```
    Returns a Natural whose value is (this / val).
    
    Parameters:
    val - value by which this Natural is to be divided.
    
    Returns:
    this / val
    
    Throws:
    
    java.lang.ArithmeticException - val==0
  - remainder
```
public Natural remainder(Natural val)
```
    Returns a Natural whose value is (this % val).
    
    Parameters:
    val - value by which this Natural is to be divided, and the remainder computed.
    
    Returns:
    this % val
    
    Throws:
    
    java.lang.ArithmeticException - val==0
  - pow
```
public Natural pow(int exponent)
```
    Returns a Natural whose value is (this^exponent). Note that exponent is an integer rather than a Natural.
    
    Parameters:
    exponent - exponent to which this Natural is to be raised.
    
    Returns:
    this^exponent
    
    Throws:
    
    java.lang.ArithmeticException - exponent is negative. (This would cause the operation to yield a non-integer value.)
  - compareTo
```
public int compareTo(Natural val)
```
    Compares this Natural with the specified Natural. This method is provided in preference to individual methods for each of the six boolean comparison operators (<, ==, >, >=, !=, <=). The suggested idiom for performing these comparisons is: (x.compareTo(y) <op> 0), where <op> is one of the six comparison operators.
    
    Parameters:
    val - Natural to which this Natural is to be compared.
    
    Returns:
    -1, 0 or 1 as this Natural is numerically less than, equal to, or greater than val.
  - compareTo
```
public int compareTo(int val)
```
    Compares this Natural with the specified integer.
    
    Parameters:
    val - int to which this Natural is to be compared.
    
    Returns:
    -1, 0 or 1 as this Natural is numerically less than, equal to, or greater than val.
    Precondition:
    
    val >= 0
  - compareTo
```
public int compareTo(java.lang.Object x)
```
    Same as compareTo() above, just taking an object as parameter.
    
    Specified by:
    
    compareTo in interface java.lang.Comparable
  - equals
```
public boolean equals(java.lang.Object x)
```
    Compares this Natural with the specified Object for equality.
    
    Overrides:
    
    equals in class java.lang.Object
    
    Parameters:
    x - Object to which this Natural is to be compared.
    
    Returns:
    true if and only if the specified Object is a Natural whose value is numerically equal to this Natural.
  - hashCode
```
public int hashCode()
```
    Implementation of hashCode()
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    a hash code value for this Natural.
  - min
```
public Natural min(Natural val)
```
    Returns the minimum of this Natural and val.
    
    Parameters:
    val - value with with the minimum is to be computed.
    
    Returns:
    the Natural whose value is the lesser of this Natural and val. If they are equal, either may be returned.
  - max
```
public Natural max(Natural val)
```
    Returns the maximum of this Natural and val.
    
    Parameters:
    val - value with with the maximum is to be computed.
    
    Returns:
    the Natural whose value is the greater of this and val. If they are equal, either may be returned.
  - toString
```
public java.lang.String toString()
```
    Returns the decimal String representation of this Natural. The digit-to-character mapping provided by Character.forDigit is used, and a minus sign is prepended if appropriate. (This representation is compatible with the (String) constructor, and allows for String concatenation with Java's + operator.)
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    decimal String representation of this Natural.
    See Also:
    Character.forDigit(int, int)
  - intValue
```
public int intValue()
```
    Converts this Natural to an int.
    
    Returns:
    this Natural converted to an int.
  - longValue
```
public long longValue()
```
    Converts this Natural to a long.
    
    Returns:
    this Natural converted to a long.
  - floatValue
```
public float floatValue()
```
    Converts this Natural to a float.
    
    Returns:
    this Natural converted to a float.
  - doubleValue
```
public double doubleValue()
```
    Converts this Natural to a double.
    
    Returns:
    this Natural converted to a double.
  - getMax
```
public int getMax()
```
    Returns the max value of the natural number (-1 means no max)
    Returns:
    -1
    if there is no max, otherwise the max
  - main
```
public static void main(java.lang.String[] args)
```
    A local test driver

Class Natural

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

Natural

Natural

Natural

Method Detail

add

increment

subtract

decrement

multiply

square

divide

remainder

pow

compareTo

compareTo

compareTo

equals

hashCode

min

max

toString

intValue

longValue

floatValue

doubleValue

getMax

main