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    <p>Huge difference.</p> <p>As the name implies, a <a href="http://en.wikipedia.org/wiki/Double_precision_floating-point_format" rel="noreferrer"><code>double</code></a> has 2x the precision of <a href="http://en.wikipedia.org/wiki/Single_precision_floating-point_format" rel="noreferrer"><code>float</code></a><sup>[1]</sup>. In general a <code>double</code> has 15 decimal digits of precision, while <code>float</code> has 7.</p> <p>Here's how the number of digits are calculated:</p> <blockquote> <p><code>double</code> has 52 mantissa bits + 1 hidden bit: log(2<sup>53</sup>)÷log(10) = 15.95 digits</p> <p><code>float</code> has 23 mantissa bits + 1 hidden bit: log(2<sup>24</sup>)÷log(10) = 7.22 digits</p> </blockquote> <p>This precision loss could lead to truncation errors much easier to float up, e.g.</p> <pre><code>float a = 1.f / 81; float b = 0; for (int i = 0; i &lt; 729; ++ i) b += a; printf("%.7g\n", b); // prints 9.000023 </code></pre> <p>while</p> <pre><code>double a = 1.0 / 81; double b = 0; for (int i = 0; i &lt; 729; ++ i) b += a; printf("%.15g\n", b); // prints 8.99999999999996 </code></pre> <p>Also, the maximum value of float is about <code>3e38</code>, but double is about <code>1.7e308</code>, so using <code>float</code> can hit "infinity" (i.e. a special floating-point number) much more easily than <code>double</code> for something simple, e.g. computing the factorial of 60.</p> <p>During testing, maybe a few test cases contain these huge numbers, which may cause your programs to fail if you use floats.</p> <hr> <p>Of course, sometimes, even <code>double</code> isn't accurate enough, hence we sometimes have <code>long double</code><sup>[1]</sup> (the above example gives 9.000000000000000066 on Mac), but all floating point types suffer from <em>round-off errors</em>, so if precision is very important (e.g. money processing) you should use <code>int</code> or a fraction class.</p> <hr> <p>Furthermore, don't use <code>+=</code> to sum lots of floating point numbers, as the errors accumulate quickly. If you're using Python, use <code>fsum</code>. Otherwise, try to implement the <a href="http://en.wikipedia.org/wiki/Kahan_summation_algorithm" rel="noreferrer">Kahan summation algorithm</a>.</p> <hr> <p><sup>[1]: The C and C++ standards do not specify the representation of <code>float</code>, <code>double</code> and <code>long double</code>. It is possible that all three are implemented as IEEE double-precision. Nevertheless, for most architectures (gcc, MSVC; x86, x64, ARM) <code>float</code> <em>is</em> indeed a IEEE single-precision floating point number (binary32), and <code>double</code> <em>is</em> a IEEE double-precision floating point number (binary64).</sup></p>
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    1. COThe usual advice for summation is to sort your floating point numbers by magnitude (smallest first) before summing.
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