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copied!<p>There are two common pitfalls when working with floating point arithmetic.</p> <p><strong>The first problem</strong> is that Ruby floating points have fixed precision. In practice this will either be 1) no problem for you or 2) disastrous, or 3) something in between. Consider the following:</p> <pre><code># float 1.0e+25 - 9999999999999999900000000.0 #=> 0.0 # bigdecimal BigDecimal("1.0e+25") - BigDecimal("9999999999999999900000000.0") #=> 100000000 </code></pre> <p>A precision difference of 100 million! Pretty serious, right?</p> <p>Except the precision error is only about 0.000000000000001% of the original number. It really is up to you to decide if this is a problem or not. But the problem is removed by using <code>BigDecimal</code> because it has arbitrary precision. Your only limit is memory available to Ruby.</p> <p><strong>The second problem</strong> is that floating points cannot express all fractions accurately. In particular, they have problems with <em>decimal</em> fractions, because floats in Ruby (and most other languages) are <em>binary</em> floating points. For example, the decimal fraction <code>0.2</code> is an eternally-repeating binary fraction (<code>0.001100110011...</code>). This can never be stored accurately in a binary floating point, no matter what the precision is.</p> <p>This can make a big difference when you're rounding numbers. Consider:</p> <pre><code># float (0.29 * 50).round #=> 14 # not correct # bigdecimal (BigDecimal("0.29") * 50).round #=> 15 # correct </code></pre> <p>A <code>BigDecimal</code> can describe <em>decimal</em> fractions precisely. However, there are fractions that cannot be described precisely with a decimal fraction either. For example <code>1/9</code> is an eternally-repeating decimal fraction (<code>0.1111111111111...</code>). </p> <p>Again, this will bite you when you round a number. Consider:</p> <pre><code># bigdecimal (BigDecimal("1") / 9 * 9 / 2).round #=> 0 # not correct </code></pre> <p>In this case, using decimal floating points will <strong>still</strong> give a rounding error.</p> <p>Some conclusions:</p> <ul> <li>Decimal floats are awesome if you do calculations with decimal fractions (money, for example).</li> <li>Ruby's <code>BigDecimal</code> also works well if you need arbitrary precision floating points, and don't really care if they are decimal or binary floating points.</li> <li>If you work with (scientific) data, you're typically dealing with fixed precision numbers; Ruby's built-in floats will probably suffice.</li> <li>You can never expect arithmetic with <em>any</em> kind of floating point to be precise in all situations.</li> </ul>

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