Compound Numbers

Compound Numbers
A Programming Pattern

Computer Science Department

bernstdh@jmu.edu

Motivation

What is a Compound Number?
- A compound number is a quantity/measure that is expressed in more than one unit
Examples:
- Heights/lengths measured in miles, yards, feet and inches
- Weights measured in tons, pounds and ounces
- Times measured in hours, minutes and seconds
- Volumes measured in gallons, quarts, pints, ounces

Two Observations

Individual Components:
- Are commonly integers (because parts of a whole are usually denominated in different units)
Arithmetic Operations:
- Often involve arithmetic on a circle with "carry"

The Obvious Implementation

The Approach:
- Have an attribute for each of the individual units (e.g., an int for pounds and an int for ounces)
Why it Seems Clever:
- Because we know about the integer division and remainder operators and how to use them for arithmetic on a circle and divisibility checks
A Continuing Example:
- We have 3lbs,12oz of french fries and someone gives us more or takes some away

The Continuing Example

An Example of the Easiest Case:
- We have 3lbs,12oz of french fries and someone gives us 2oz more
Processing this Specific Example:
- ounces = ounces + 2;
Processing this Kind of Example:
- ounces = ounces + deltaounces;

The Continuing Example (cont.)

An More Difficult Example:
- We have 3lbs,12oz of french fries and someone gives us 8oz more
Processing:
- pounds = pounds + (ounces + deltaounces) / 16;
  ounces = (ounces + deltaounces) % 16;
A Word of Caution:
- The following code, while similar, is incorrect!
  ounces = (ounces + deltaounces) % 16;
  pounds = pounds + (ounces + deltaounces) / 16;

The Continuing Example (cont.)

Increasing the Difficulty Further:
- We have 3lbs,12oz of french fries and someone gives us 5lbs,8oz more
Processing:
- pounds = (pounds + deltapounds) + (ounces + deltaounces) / 16;
  ounces = (ounces + deltaounces) % 16;

The Continuing Example (cont.)

Increasing the Difficulty Further:
- We have 1ton,1999lbs,12oz of french fries and someone gives us 8oz more
Processing:
- tons = (tons + deltatons) + (pounds + deltapounds + (ounces + deltaounces) / 16) / 2000;
  pounds = (pounds + deltapounds) + (ounces + deltaounces) / 16;
  ounces = (ounces + deltaounces) % 16;

The Continuing Example (cont.)

Increasing the Difficulty Further:
- We have 1ton,1999lbs,12oz of french fries and someone gives us 1ton,200lbs,8oz more
Increasing the Difficulty Further:
- We have 2tons,1999lbs,12oz of french fries and someone changes the amount by -1ton,353lbs,-15oz
Other Complications:
- Multiplication/division by a constant
- Ratios
- Sign (should all components have the same sign?)
- Comparisons (e.g., equals(), compareTo())

Learning from these Examples

A Conclusion:
- It is possible to use the obvious implementation but there are many ways/places that defects can be introduced
A Hope:
- This situation has arisen frequently in the past and people have developed a solution

A Better Implementation

The Idea:
- Use a single attribute denominated in the "smallest" units and convert when necessary
The Continuing Example Revisited:
- Create a Weight class that has only one attribute measured in ounces, but accessors that can return tons, pounds and ounces and mutators that can be passed tons, pounds, and ounces

A Better Implementation (cont.)

javaexamples/compoundnumbers/Weight.java

Don't Be Confused!

A Common Misconception:
- The shortcomings of the obvious implementation arise only if the objects are mutable
The Reality:
- The shortcomings exist whenever operations are performed on compound numbers (regardless of whether the object is mutable or a new immutable object is created)

There's Always More to Learn