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--- math_library [2022/04/29 23:39]
max [Float comparison]
+++ math_library [2022/04/29 23:41]
max
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 To learn which methods Impulse Physics offers to compare floating-point numbers, visit [[floating point comparison]].
-It also means that for example, 0.2 + 0.1 is not equal to 0.3; rather it is equal to 0.30000000000000004.
-Since computers are exact in comparison by default, you can see how you can run into issues with this.
-Impulse, therefore, offers two methods of float comparison by default.
-The default option is a combination of both the absolute and relative methods of epsilon comparison. ((http://www.realtimecollisiondetection.net/pubs/Tolerances/))
-The second option is simply the computer's default "==" operator. It is not recommended, but it is marginally faster.
-==== The absolute method ====
-The absolute method takes the absolute value of ''x - y'', then checks if they are less than or equal to the FLT_EPSILON preprocessor definition. ((FLT_EPSILON is defined as 1.192092896e-07F))
-The absolute method will work, but it does not work on large values.
-==== The relative method ====
-The relative method takes the result of the absolute method and multiplies the epsilon by ''x'' or ''y'', depending on which is larger.
-The drawback to this method is that it does not work on small values.
-==== The combined method ====
-Considering the strengths and drawbacks of the two methods above, you can combine the two to overcome these limitations.
-The combined method takes the result of the absolute method and multiplies it by the largest absolute number out of a set of ''1'', ''x'', or ''y''. Very similar to the relative method.
-This method gives us good results, but it is not without its drawbacks since it uses the same epsilon for the relative and the absolute tolerance.
-For further reading, please check out [[http://www.realtimecollisiondetection.net/pubs/Tolerances/|Christer Erison's research on this topic.]]

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