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B is for BigDecimal

Continuing the jaunt into the Ruby alphabet we run into BigDecimal and BasicObject. BasicObject is so, well, basic. It is something to take a look at, but I believe that the usage of BigDecimal is one thing that every developer needs in their tool belt.

Have you ever had a problem with a floating point number? Did you even notice the issue? Why don't we try this one on for size.

  1.2-1.0 #=> 0.19999999999999996

What in the heck happened? This is an error in the representation of floating point by binary numbers. To understand the accuracy issues and their underlying causes everyone should read this. Don't go away quite yet. There is a way to solve this problem.

The superhero of our day is BigDecimal. Let's take our example from above.

  BigDecimal.new("1.2") - BigDecimal("1.0") #=> #<BigDecimal:7f809b143930,'0.2E0',9(27)>

  (BigDecimal.new("1.2") - BigDecimal("1.0")).to_s #=> "0.2E0"

You will need to be familiar with scientific notation in order to understand the output.

Notice that the output no longer suffers from the same issues as the above. There is one small issue that I have found in creating a new BigDecimal with a floating point argument.

  BigDecimal.new(1.0) #=> ArgumentError: can't omit precision for a Float.
  BigDecimal.new(1.0, 1) #=> #<BigDecimal:7f809b0671b0,'0.1E1',9(27)>

When providing a floating point number as the input of a new BigDecimal we must also provide the number of significant digits. These digits determine our level of confidence in the numbers after the decimal point. BigDecimal uses the significant digits to determine where to round values when completing computations. Here are a few outputs from irb.

irb(main):031:0> BigDecimal.new(1.2222, 1)
=> #<BigDecimal:7f809b0147d0,'0.1E1',9(27)>

irb(main):032:0> BigDecimal.new(1.2222, 2)
=> #<BigDecimal:7f809a8bb060,'0.12E1',18(27)>

The first input shows 0.1E1 and loses all the information from after the decimal point in 1.2222. This is because our confidence is only one digit. The second version shows a 2 because we include the first digit after the decimal place in our count of significant digits.

The final digit is handled through a rounding mode of the BigDecimal. The default mode is half_up. This means that the BigDecimal is rounded to the nearest neighbor or up if equidistant. This is the same rounding you probably used in school. There are many different versions of rounding that are available to us. For example, we will use Banker's rounding. This is a type of rounding found in many bookkeeping applications. In banker's rounding we round to the nearest number, but if we are equidistant we round to the nearest even number. Don't ask me why this is used. It seems crazy to me.

irb(main):037:0> BigDecimal.new(1.27,2)
=> #<BigDecimal:7f809a883ea8,'0.13E1',18(27)> #default rounding

irb(main):038:0> BigDecimal.mode(BigDecimal::ROUND_MODE, :banker)
=> 7

irb(main):040:0> BigDecimal.new(1.25,2)
=> #<BigDecimal:7f809a84b508,'0.12E1',18(27)>

irb(main):041:0> BigDecimal.new(1.35,2)
=> #<BigDecimal:7f809a842fe8,'0.14E1',18(27)>

I hope that this gets you a good start to using BigDecimal. Next time you are working with floating points you may find that your needs are better suited by BigDecimal.

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