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floating_point_comparison [2022/04/29 23:39]
max created 		floating_point_comparison [2022/04/29 23:54] (current)
max
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 +====== Floating-point number comparison ======
 +
 +
 Floating-point numbers are almost always stored inaccurately in computers' memory. This is because of the [[https://en.wikipedia.org/wiki/IEEE_754|IEEE-754]] standard that is used to store the number. Floating-point numbers are almost always stored inaccurately in computers' memory. This is because of the [[https://en.wikipedia.org/wiki/IEEE_754|IEEE-754]] standard that is used to store the number.
  
-It also means that for example, 0.2 + 0.1 is not equal to 0.3; rather it is equal to 0.30000000000000004.+For example, that means ''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. Since computers are exact in comparison by default, you can see how you can run into issues with this.
  
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 The second option is simply the computer's default "==" operator. It is not recommended, but it is marginally faster.  The second option is simply the computer's default "==" operator. It is not recommended, but it is marginally faster. 
  
-==== The absolute method ====+Which method the engine uses can be changed in the source code in the ''IPCommon.h'' file. 
 + 
 +===== 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 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))
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 The absolute method will work, but it does not work on large values. The absolute method will work, but it does not work on large values.
  
-==== The relative method ====+===== 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 relative method takes the absolute method, but 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 drawback to this method is that it does not work on small values.
  
-==== The combined method ====+===== The combined method =====
  
 Considering the strengths and drawbacks of the two methods above, you can combine the two to overcome these limitations.  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.+The combined method takes the relative method, but multiplies the epsilon 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.  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.]] For further reading, please check out [[http://www.realtimecollisiondetection.net/pubs/Tolerances/|Christer Erison's research on this topic.]]
floating_point_comparison.1651275575.txt.gz · Last modified: 2022/04/29 23:39 by max

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