Many developers will never encounter issues when floating-point math fails to return the correct result. Every once in a while, when you’re expecting to see a number like 10.1 in your trace panel, you might actually see 10.1000000001. This isn’t a specific issue with Flash either. By it’s very nature, any sort of calculation with floating-point numbers can result in tiny, nearly insignificant errors anywhere in modern computing.
In many cases, that number could get corrected the next time you use it in a mathematical operation. Other times, you’ll never notice that something went wrong because you might be animating some object, and the position gets rounded off anyway. You won’t always be so lucky, though. At some point in your future, you may need to display a number to the user. Imagine their look of shock as some crazy number with ten decimal places appears on the screen. “Oh my god! Why is it doing that?” exclaims a user of your cool new Flex app.
It gets worse. When these errors occur, checking if two numbers are equal can fail as well. Now, when you need to know if your function returned a multiple of two, and you get 15.9999999999, bad things can happen. Another problem, which I’ve run into a few times, is when I’m “counting” between two numbers, like two and three:
2 2.1 2.2 2.3 2.4 2.5000000001 2.6 2.7000000001 2.8 2.9 3
Consider the following two functions. I’ve been using them for a while now, and they work great. The first, correctFloatingPointError will manipulate the number (even a fractional one) with some clever multiplication, division, and rounding to try to account for the error. The second fuzzyEquals will check if two numbers are almost equal. In many cases, if two numbers have a difference of 0.00001, they might as well be considered equal. With both of these functions, you can manipulate the precision to allow for more accurate or inaccurate calculations depending on your needs.
/*
Copyright (c) 2007 Josh Tynjala
Permission is hereby granted, free of charge, to any person
obtaining a copy of this software and associated documentation
files (the "Software"), to deal in the Software without
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copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the
Software is furnished to do so, subject to the following
conditions:
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
OTHER DEALINGS IN THE SOFTWARE.
*/
/**
* Corrects errors caused by floating point math.
*/
public function correctFloatingPointError(number:Number, precision:int = 5):Number
{
//default returns (10000 * number) / 10000
//should correct very small floating point errors
var correction:Number = Math.pow(10, precision);
return Math.round(correction * number) / correction;
}
/**
* Tests if two numbers are almost equal.
*/
public function fuzzyEquals(number1:Number, number2:Number, precision:int = 5):Boolean
{
var difference:Number = number1 - number2;
var range:Number = Math.pow(10, -precision);
//default check:
//0.00001 -0.00001
return difference -range;
}
If you have any more tips in this area, I’d like to hear them. Those two functions have been enough for my needs so far, but my toolbox always has room for an extra trick or two.
WTF, I can imagine when perfoming a comparison this could be a nightmare especially if the next time you access it it corrects itself. Havent seen it yet but thanks for the heads up :o)
Like I said, it should rarely affect most developers. Unfortunately, I’m working on a project that displays many numbers, and I need them to stay as accurate as possible.
Here’s the official word from Adobe in TechNote aimed at Flash users, but also includes examples in JavaScript, VBScript, and Perl to help indicate that Flash Player is not the cause.
WTF x 2!! Josh, I’ve never run into this issue before, but it’s enlightening! I’ve added this post to my del.icio.us bookmarks, as I’m sure it will happen someday (just my luck!).
Thanks for the heads-up!
It happens the other way around too.
Try this in a blank flash file:
trace(10.00000000000001);//outputs 10
trace(10.0000000000001);//outputs 10.0000000000001
cheers
Awesome, thanks. I am doing a financial services app in Flex and I can’t just cavalierly wave my hand and say “it’s just the nature of computing” like Adobe does. I was getting something as basic as 0.08 * 0.7 = 0.55999999999999994. This function will come in very handy, thank you!
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Good post, Just covered some other strategies when working with floating points here: http://troyworks.com/blog/?p=70, and here’s a related function for you collection:
public function notClose(number1:Number, number2:Number, precision:int = 0):Boolean { var difference:Number = number1 - number2; var range:Number = Math.pow(10, -precision); trace(-range + " " + difference + " " + range); var res:Boolean = ( difference difference ) ; trace("notClose" + res); return res; }Josh, thanks a lot man! I actually did run into this while trying to do some AS based audio fades. Your “correctFloatingPointError” function smoothed that out nicely.
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Thans man that really worked like magic! dont know what these flex guys doing
This is a great work around for the problem – for calculating taxes, it seems to do the job.
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I’m working on a game in flash, in it I’m having the player fire objects towards objects with gravity as if they were all in outer-space, long story short, I believe my nice, efficient vector-based (as opposed to trig-based) calculations for finding the angle of the trajectory proposed by the player (via mouse click, power designated by length of time the mouse was held) are running into this issue.
At low speeds the trajectory is spot on, hits the mouse cursor every time, but as the speed increases, it flies off course! I might just have to use somewhat less efficient trig functions for it.
Whoops, false alarm… It’s my hard-limit on the speed objects can travel.
Edit: I see you fixed your issue. Leaving this explanation here in case it may help someone else.
I’m not sure if you have collision detection involved in your calculations, Felps, but that kind of reminds me of a common issue. Sometimes an object can be moving so fast that it never actually can be detected in a direct collision. You need to also check to see if the object hasn’t overshot a barrier without actually touching the barrier. Even if it’s not collision detection, if your vector based approach (I’m not sure what that means, exactly) is something like a lookup table, I could see it losing accuracy as you add in increased power values.
You may be right, though. I’m not as familiar with your code as you are. However, for visual positioning, it’s rare that floating point errors will throw an object extremely far away from where it should be. Usually, it’s much less than a pixel for each error, so you would need a great deal of errors accumulating to see a problem.
Wouldnt the part where you divide with the correction:
” / 10000 ”
be nondeterministic in itself? IE the division causing further possible floatpoint errors?
I suppose it could cause further errors. I’ve never seen it happen, though.
This error has become an absolute nightmare for my game. A unit’s walkable range in my rts game is about 8000 pixels, and to keep them in an isometric layout, a frame when the unit is walking looks like
x += .9*speed;
where speed equals 2.
sadly, if the unit’s starting x is 0, the first error is on the 19th frame when I try and add 1.8 to 32.4. Tracing the calculation by itself gives 34.199999
and on my game it turns to 34.15. As the walking progresses, the unit is walking in unwalkable territory before not too long. I could readjust the entire ratio so an integer will be added to the x, but then all of the other units’ speeds must respectively adjust meaning there will just be new instances of this. FUCK YOU FLOATING POINTS.
this is my solution.
private function realPlusEquals(x:Number, addend:Number):Number { return int(x/10+.5)/10 + addend; }oops. i meant
return int(x*10+.5)/10 + addend;
i suppose the best solution is:
function fixPointFloat(x:Number, negativeERoundTo:int):Number
{//if negativeERoundTo is 2 you are rounding to hundreths place.
const figure:int = Math.pow(10, negativeERoundTo);
return int(x*figure+.5)/figure;
}
Seriously? Do I just not know trigonometry?
var m:Number = Math.asin( Math.sin(1.888) );
//m = 1.253