# Floating point precision **URL:** \ **Category:** The Defoldmine\ **Created:** [September 4, 2017, 1:59pm UTC](https://forum.defold.com/t/floating-point-precision/11247 "2017-09-04T13:59:14Z")\ **Posts on this page:** 18\ **Page:** 1
**Author:** ![Mathias\_Westerdahl](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/mathias_westerdahl/32/228_2.png) [@Mathias\_Westerdahl](https://forum.defold.com/u/Mathias_Westerdahl)\ **Post date:** [September 4, 2017, 1:59pm UTC](https://forum.defold.com/t/floating-point-precision/11247/1 "2017-09-04T13:59:14Z")
Every now and then, you’ll see issues that can be described as “choppy” animations, or perhaps your code doesn’t work when comparing various variables. Sometimes, it could be related to something called “[floating point precision](https://en.wikipedia.org/wiki/Single-precision_floating-point_format)”. It stems from the fact that on a computer, real numbers have to be approximated in some way. And as you might imagine, the approximation result might not always be what you intended. (See table at the end) ## TL;DR: Floating point values… - … does not have infinite range - … does not have infinite precision - … exist in most modern engines. - … have better precision when closer to 0 than FLT\_MAX (3.40282e+38) - … should (most often) not be compared using the **==** or **!=** operators - … can be tricky to use, even with operators **\<** and **\>** due to imprecision ## In (only slightly) more detail: You use floating point representations in code (Lua, C++, shaders etc) and data (textures, heightmaps etc). That’s why it’s very good to know about the general workings of them, in order to anticipate any issues that might arise. What we’re using in our C++ engine are [32 bit floating point numbers](https://en.wikipedia.org/wiki/Single-precision_floating-point_format). Lua itself uses 64bit floating point numbers. In OpenGL ES, you can set [lowp / mediump / highp](https://www.khronos.org/files/opengles_shading_language.pdf) precision on your variables. The OpenGL ES standard sets a minumum requirement of the precision so it might still differ between graphics drivers. ## No infinite precision If you think about it, a 32 bit integer can represent the values -2147483647 to 2147483647, that’s it. Then all 32 bits are used. But, if you would also like decimals, how could you fit all those numbers, as well as decimals, in only 32 bits? The answer is, of course, you cannot. You have to make sacrifices. In the single floating point representation (usually refers to the standard [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754)) case, this means that we sacrifice precision the larger the number is. Since the precision varies depending how large your number is, the operators might not work as you’d expect. ## Accumulation Another thing to consider, is how the precision “error” of calculations accumulate. It’s very easy to calculate something that has less precision than you’d like, and use that value in your next calculation, in yet another manner that might introduce even more precision errors. [Small Example](https://stackoverflow.com/a/5694505) ## How to deal with it? A common thing is to keep your data and computations closer to 0 (or Origin) than in world space. - E.g. Moving camera and objects towards Origin (0,0,0). Used for open world games, infinite runners etc. Another way is to increase the number of bits to represent the value - E.g 64 bit precision on CPU, or _highp_ in shaders Each way will come with a drawback, you have to decide which one is the best for you. ## Addendum To give you an idea of how much the precision changes, the larger your numbers get: Table contains: integer, the next 32 bit floating point value after the integer, the difference between the two previous values ```lua f: 0.00 next: 1.4012984643248170709e-45 diff: 1.4012984643248170709237e-45 f: 1.00 next: 1.0000001192092895508 diff: 1.1920928955078125e-07 f: 2.00 next: 2.0000002384185791016 diff: 2.384185791015625e-07 f: 3.00 next: 3.0000002384185791016 diff: 2.384185791015625e-07 f: 4.00 next: 4.0000004768371582031 diff: 4.76837158203125e-07 f: 5.00 next: 5.0000004768371582031 diff: 4.76837158203125e-07 f: 6.00 next: 6.0000004768371582031 diff: 4.76837158203125e-07 f: 7.00 next: 7.0000004768371582031 diff: 4.76837158203125e-07 f: 8.00 next: 8.0000009536743164062 diff: 9.5367431640625e-07 f: 9.00 next: 9.0000009536743164062 diff: 9.5367431640625e-07 f: 10.00 next: 10.000000953674316406 diff: 9.5367431640625e-07 f: 20.00 next: 20.000001907348632812 diff: 1.9073486328125e-06 f: 30.00 next: 30.000001907348632812 diff: 1.9073486328125e-06 f: 40.00 next: 40.000003814697265625 diff: 3.814697265625e-06 f: 50.00 next: 50.000003814697265625 diff: 3.814697265625e-06 f: 60.00 next: 60.000003814697265625 diff: 3.814697265625e-06 f: 70.00 next: 70.00000762939453125 diff: 7.62939453125e-06 f: 80.00 next: 80.00000762939453125 diff: 7.62939453125e-06 f: 90.00 next: 90.00000762939453125 diff: 7.62939453125e-06 f: 100.00 next: 100.00000762939453125 diff: 7.62939453125e-06 f: 200.00 next: 200.0000152587890625 diff: 1.52587890625e-05 f: 300.00 next: 300.000030517578125 diff: 3.0517578125e-05 f: 400.00 next: 400.000030517578125 diff: 3.0517578125e-05 f: 500.00 next: 500.000030517578125 diff: 3.0517578125e-05 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6e+32 next: 6.0000001990881210846e+32 diff: 3.86856e+25 f: 7e+32 next: 7.0000008125538680137e+32 diff: 7.73713e+25 f: 8e+32 next: 8.0000010391633526661e+32 diff: 7.73713e+25 f: 9e+32 next: 9.0000004920603127652e+32 diff: 7.73713e+25 f: 1e+33 next: 1.0000000718669797418e+33 diff: 7.73713e+25 f: 2e+33 next: 2.0000001437339594835e+33 diff: 1.54743e+26 f: 3e+33 next: 3.000000370343444136e+33 diff: 3.09485e+26 f: 4e+33 next: 4.0000002874679189671e+33 diff: 3.09485e+26 f: 5e+33 next: 5.0000002045923937981e+33 diff: 3.09485e+26 f: 6e+33 next: 6.0000007406868882719e+33 diff: 6.1897e+26 f: 7e+33 next: 7.000000657811363103e+33 diff: 6.1897e+26 f: 8e+33 next: 8.0000005749358379341e+33 diff: 6.1897e+26 f: 9e+33 next: 9.0000004920603127652e+33 diff: 6.1897e+26 f: 1e+34 next: 1.0000000409184787596e+34 diff: 6.1897e+26 f: 2e+34 next: 2.0000000818369575193e+34 diff: 1.23794e+27 f: 3e+34 next: 3.000000370343444136e+34 diff: 2.47588e+27 f: 4e+34 next: 4.0000001636739150385e+34 diff: 2.47588e+27 f: 5e+34 next: 5.0000006997684095123e+34 diff: 4.95176e+27 f: 6e+34 next: 6.0000007406868882719e+34 diff: 4.95176e+27 f: 7e+34 next: 7.0000002864293513174e+34 diff: 4.95176e+27 f: 8e+34 next: 8.000000327347830077e+34 diff: 4.95176e+27 f: 9e+34 next: 9.000001358618340265e+34 diff: 9.90352e+27 f: 1e+35 next: 1.0000001399536819025e+35 diff: 9.90352e+27 f: 2e+35 next: 2.0000002799073638049e+35 diff: 1.9807e+28 f: 3e+35 next: 3.0000001227554362789e+35 diff: 1.9807e+28 f: 4e+35 next: 4.0000005598147276098e+35 diff: 3.96141e+28 f: 5e+35 next: 5.0000002045923937981e+35 diff: 3.96141e+28 f: 6e+35 next: 6.0000002455108725578e+35 diff: 3.96141e+28 f: 7e+35 next: 7.0000006825701638887e+35 diff: 7.92282e+28 f: 8e+35 next: 8.0000011196294552197e+35 diff: 7.92282e+28 f: 9e+35 next: 9.000000764407121408e+35 diff: 7.92282e+28 f: 1e+36 next: 1.0000000409184787596e+36 diff: 7.92282e+28 f: 2e+36 next: 2.0000000818369575193e+36 diff: 1.58456e+29 f: 3e+36 next: 3.0000003604399238217e+36 diff: 3.16913e+29 f: 4e+36 next: 4.0000001636739150385e+36 diff: 3.16913e+29 f: 5e+36 next: 5.0000002838205563124e+36 diff: 3.16913e+29 f: 6e+36 next: 6.0000007208798476434e+36 diff: 6.33825e+29 f: 7e+36 next: 7.0000008410264889173e+36 diff: 6.33825e+29 f: 8e+36 next: 8.000000327347830077e+36 diff: 6.33825e+29 f: 9e+36 next: 9.0000004474944713509e+36 diff: 6.33825e+29 f: 1e+37 next: 1.0000000567641112625e+37 diff: 6.33825e+29 f: 2e+37 next: 2.000000113528222525e+37 diff: 1.26765e+30 f: 3e+37 next: 3.0000003604399238217e+37 diff: 2.5353e+30 f: 4e+37 next: 4.0000002270564450499e+37 diff: 2.5353e+30 f: 5e+37 next: 5.0000003472030863238e+37 diff: 5.0706e+30 f: 6e+37 next: 6.0000007208798476434e+37 diff: 5.0706e+30 f: 7e+37 next: 7.0000005874963688716e+37 diff: 5.0706e+30 f: 8e+37 next: 8.0000004541128900999e+37 diff: 5.0706e+30 f: 9e+37 next: 9.0000008277896514194e+37 diff: 1.01412e+31 f: 1e+38 next: 1.0000000694406172648e+38 diff: 1.01412e+31 f: 2e+38 next: 2.0000001388812345295e+38 diff: 2.02824e+31 f: 3e+38 next: 3.0000002083218517943e+38 diff: 2.02824e+31 ``` # Conclusion I hope I at least shed _some_ light on the topic, and you at least know that there is such a thing as “floating point precision errors”. And, now that you’re aware of the topic, you know what to google for 🙂 Here are some reading materials: - [http://gamedevs.org/uploads/numerical-robustness-geometric-calculations.pdf](http://gamedevs.org/uploads/numerical-robustness-geometric-calculations.pdf) - [Single-precision floating-point format - Wikipedia](https://en.wikipedia.org/wiki/Single-precision_floating-point_format) - [Floating Point Visually Explained](http://fabiensanglard.net/floating_point_visually_explained) (Added 1/10/2017) _Please let me know if this topic contains any errors, and I’ll try to correct them asap!_ ---
**Author:** ![britzl](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/britzl/32/23_2.png) [@britzl](https://forum.defold.com/u/britzl)\ **Post date:** [September 4, 2017, 4:18pm UTC](https://forum.defold.com/t/floating-point-precision/11247/2 "2017-09-04T16:18:59Z")
Brilliant write up Mathias! This will be an excellent post to refer to the next time it comes up. ---
**Author:** ![nicloay](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/nicloay/32/1895_2.png) [@nicloay](https://forum.defold.com/u/nicloay)\ **Post date:** [September 26, 2017, 9:30am UTC](https://forum.defold.com/t/floating-point-precision/11247/3 "2017-09-26T09:30:51Z")
> [@Mathias\_Westerdahl](#): > > Another thing to consider, is how the precision “error” of calculations accumulate. > > It’s very easy to calculate something that has Thanks. It’s really useful info. I face this issue quite often. And what i found in another page is that you don’t need to worry about this problem if your action happens within 10 km. or **10 000 points**. in this case you still have 3 numbers after the point (actually you can see that in the table above). If it’s more you will decently need to solve this problem. Below in the video I have 300x1500 tile map, and you can see that i place my character to 70k Y position. but I don’t use built in physics. so everything is still smooth for me. otherwise I think i’ll have some problem in ground check calculations and so on. [![](https://i.ytimg.com/vi/HIZ7XsYojZc/hqdefault.jpg "Defold tile map, no any object bool.") ](https://www.youtube.com/watch?v=HIZ7XsYojZc&t=1m22s) ---
**Author:** ![Mathias\_Westerdahl](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/mathias_westerdahl/32/228_2.png) [@Mathias\_Westerdahl](https://forum.defold.com/u/Mathias_Westerdahl)\ **Post date:** [October 1, 2017, 11:45am UTC](https://forum.defold.com/t/floating-point-precision/11247/4 "2017-10-01T11:45:31Z")
Added link to this great explanation/visualization of floating points: [Floating Point Visually Explained](http://fabiensanglard.net/floating_point_visually_explained/) @nicolay: Your case illustrates quite nicely the problems of accuracy. And it’s very similar to terrain in open world games (Just Cause etc). Instead of having one big terrain map, you have many “patches”. This way you can cull them easily, and LOD them, but also (as discussed here) render them at higher precision by moving the camera to each patch. I.e. each patch is defined in the space (let’s say) [0.0, 512.0]. For instance, in your case, you could have several tilemaps, and move them around and refill them when they are reused. As for where you “don’t have to worry”, it’s very much application specific. In the beginning of Just Cause, the characters were rendered in world space, i.e. [-16384.0, +16384.0], but that really messed up the animations of the characters (they became jerky and ugly). Instead, we had to render the character closer to origin (0,0,0). ---
**Author:** ![sicher](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/sicher/32/8_2.png) [@sicher](https://forum.defold.com/u/sicher)\ **Post date:** [September 24, 2018, 7:38am UTC](https://forum.defold.com/t/floating-point-precision/11247/5 "2018-09-24T07:38:30Z")
Here’s another visualization: [https://twitter.com/D\_M\_Gregory/status/1044008750162604032](https://twitter.com/D_M_Gregory/status/1044008750162604032) ---
**Author:** ![Mathias\_Westerdahl](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/mathias_westerdahl/32/228_2.png) [@Mathias\_Westerdahl](https://forum.defold.com/u/Mathias_Westerdahl)\ **Post date:** [November 29, 2018, 6:08pm UTC](https://forum.defold.com/t/floating-point-precision/11247/6 "2018-11-29T18:08:44Z")
Rest assured, this a topic still tripping up even professional developers, so I can really recommend reading up on it until you feel you get the gist of it. Here’s another good [write up](https://blog.demofox.org/2017/11/21/floating-point-precision/amp/?__twitter_impression=true) ---
**Author:** ![Mathias\_Westerdahl](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/mathias_westerdahl/32/228_2.png) [@Mathias\_Westerdahl](https://forum.defold.com/u/Mathias_Westerdahl)\ **Post date:** [November 29, 2018, 6:10pm UTC](https://forum.defold.com/t/floating-point-precision/11247/7 "2018-11-29T18:10:05Z")
And here’s a little web tool to play around with different values: > **[Float Exposed](https://float.exposed/0x38fffff9)** > > Floating point format explorer – binary representations of common floating point formats. ---
**Author:** ![eklmv](https://forum-defold.b-cdn.net/letter_avatar_proxy/v4/letter/e/e19b73/32.png) [@eklmv](https://forum.defold.com/u/eklmv)\ **Post date:** [December 12, 2018, 5:08pm UTC](https://forum.defold.com/t/floating-point-precision/11247/8 "2018-12-12T17:08:52Z")
Sometimes you just say “hello” to float overflow. Mine problem was false human logic, 9 or 20 not so big numbers. Then you can agree that 1/9 is something infinite 0.11111111 and definetly here is a problem, but what with 1/20 it’s round and nice 0.05, here computers hit you in the face, always remember about floats. Little example which i run into right now: ```lua local step = 1/20 for i = 0, 1, step do pprint(i) end ``` ---
**Author:** ![eklmv](https://forum-defold.b-cdn.net/letter_avatar_proxy/v4/letter/e/e19b73/32.png) [@eklmv](https://forum.defold.com/u/eklmv)\ **Post date:** [December 12, 2018, 5:29pm UTC](https://forum.defold.com/t/floating-point-precision/11247/10 "2018-12-12T17:29:16Z")
Ok, sorry for spamming that much, i found those workarounds: ```lua local steps = 20 local step = 1/steps local res = 0 for i = 0, steps do pprint(res) res = res + step end ``` Or you need to compare numbers with some precision: ```lua function equal(a, b) local precision = 0.00000001 return math.abs(a - b) < precision end local step = 1/20 local i = 0 while i < 1 or equal(i, 1) do pprint(i) i = i + step end ``` Or more cooler coroutine iterator which start with 0 and ends with actual 1 (1 == 1): ```lua local function zero_to_one(float_step) local precision = 0.0000001 local before_last = 1 - float_step return coroutine.wrap(function() local i = 0 while i < before_last or math.abs(i - before_last) < precision do coroutine.yield(i) i = i + float_step end coroutine.yield(1) end) end for i in zero_to_one(1/20) do pprint(i) end ``` ---
**Author:** ![NeZvers](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/nezvers/32/16030_2.png) [@NeZvers](https://forum.defold.com/u/NeZvers)\ **Post date:** [June 25, 2019, 11:42am UTC](https://forum.defold.com/t/floating-point-precision/11247/11 "2019-06-25T11:42:30Z")
> [@Mathias\_Westerdahl](#): > > Table contains: integer, the next 32 bit floating point value after the integer What is that “next 32 bit floating point value”, where you got it from int? ---
**Author:** ![Mathias\_Westerdahl](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/mathias_westerdahl/32/228_2.png) [@Mathias\_Westerdahl](https://forum.defold.com/u/Mathias_Westerdahl)\ **Post date:** [June 25, 2019, 12:02pm UTC](https://forum.defold.com/t/floating-point-precision/11247/12 "2019-06-25T12:02:44Z")
> f: 1.00 next: 1.0000001192092895508 diff: 1.1920928955078125e-07 It means that it cannot represent any number in between E.g. “1.0000000000000001” will become either 1 or 1.0000001192092895508. And when numbers get larger, the precision loss gets bigger: > f: 20000 next: 20000.001953125 diff: 0.00195312 Here, the difference between the two floating point numbers is ~0.002 (or 2 millimeters if you use meters as units). You cannot represent a 32 bit IEEE number in between those to numbers. It might not sound much but it can easily manifest itself as animation jittering, or that geometry edges doesn’t align properly etc. And these “precision errors” will also easily propagate when you do multiplications/divisions/additions. ---
**Author:** ![sicher](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/sicher/32/8_2.png) [@sicher](https://forum.defold.com/u/sicher)\ **Post date:** [June 25, 2019, 2:15pm UTC](https://forum.defold.com/t/floating-point-precision/11247/13 "2019-06-25T14:15:55Z")
[https://twitter.com/schteppe/status/1143111757751357440?s=20](https://twitter.com/schteppe/status/1143111757751357440?s=20) ---
**Author:** ![britzl](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/britzl/32/23_2.png) [@britzl](https://forum.defold.com/u/britzl)\ **Post date:** [June 25, 2019, 4:33pm UTC](https://forum.defold.com/t/floating-point-precision/11247/14 "2019-06-25T16:33:31Z")
And a follow-up: [https://twitter.com/schteppe/status/1142003915208237063](https://twitter.com/schteppe/status/1142003915208237063) ---
**Author:** ![TheKing0x9](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/theking0x9/32/13588_2.png) [@TheKing0x9](https://forum.defold.com/u/TheKing0x9)\ **Post date:** [June 25, 2019, 6:02pm UTC](https://forum.defold.com/t/floating-point-precision/11247/15 "2019-06-25T18:02:43Z")
I wonder then, how do big open world games like GTAs have such a big open worlds loaded at one time, both precision and memory wise? Is it some kind of smart loading that loads a new part of the world when the player gets near it, and unloads the older collection, meanwhile resetting position to origin? ---
**Author:** ![britzl](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/britzl/32/23_2.png) [@britzl](https://forum.defold.com/u/britzl)\ **Post date:** [June 26, 2019, 2:47am UTC](https://forum.defold.com/t/floating-point-precision/11247/16 "2019-06-26T02:47:02Z")
> [@TheKing0x9](#): > > big open worlds loaded at one time The world can be big but I’m sure not all of it is loaded and rendered. You can still load and unload sections of the world and shift the world around without the player noticing. ---
**Author:** ![Mathias\_Westerdahl](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/mathias_westerdahl/32/228_2.png) [@Mathias\_Westerdahl](https://forum.defold.com/u/Mathias_Westerdahl)\ **Post date:** [June 26, 2019, 7:11am UTC](https://forum.defold.com/t/floating-point-precision/11247/17 "2019-06-26T07:11:22Z")
Exactly. In Just Cause they have 32x32km map, and it would produce e.g. Animation artifacts if using positions around 16000meters. So instead, the world is divided into 512meter patches, and when rendering/animating objects, they’re moved closer to origin (0,0,0) to be able to have better precision for all calculations. Also, the patches are unloaded if they are outside of the camera frustum in order ti save memory. Of course, there are several layers of detail for terrain and models (and animations), so the lowest detail is always loaded in memory in order to keep long drawing distances. ---
**Author:** ![Mathias\_Westerdahl](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/mathias_westerdahl/32/228_2.png) [@Mathias\_Westerdahl](https://forum.defold.com/u/Mathias_Westerdahl)\ **Post date:** [November 26, 2019, 1:51pm UTC](https://forum.defold.com/t/floating-point-precision/11247/18 "2019-11-26T13:51:19Z")
@TheKing0x9 Thanks to some old colleagues, I found this presentation about some more detailed insight from another former colleague (Emil “Humus” Persson). It explains some pitfalls we encountered during the development of Just Cause 2 with regards to a huge game world and floating point precision issues: > **[Persson\_CreatingVastGameWorlds.pdf](https://www.humus.name/Articles/Persson_CreatingVastGameWorlds.pdf)** ---
**Author:** ![TheKing0x9](https://forum-defold.b-cdn.net/user_avatar/forum.defold.com/theking0x9/32/13588_2.png) [@TheKing0x9](https://forum.defold.com/u/TheKing0x9)\ **Post date:** [November 27, 2019, 2:06am UTC](https://forum.defold.com/t/floating-point-precision/11247/19 "2019-11-27T02:06:22Z")
Thanks a lot @Mathias_Westerdahl. 😀