The worst counter-example to the superstition “testing floats with equality is always bad” may be this one, where the tested value is an infinite: http://stackoverflow.com/questions/11421756/weverything-yielding-comparing-floating-point-with-or-is-unsafe, A couple more examples are in this post of mine (it can get tricky, but that does not undermine the message that floating-point is deterministic): http://blog.frama-c.com/index.php?post/2011/11/08/Floating-point-quiz. Let’s try this by converting 1/7 to base 10: The answer is 0.142857142857… We can see that the bold steps (2-7) repeat endlessly so therefore we will never get to a remainder of zero. Number of Bytes: The float is 4 bytes long. Switch to Manual. double(1.1) = 1.100000000000000088817841970012523233890533447265625. and these values are not equal. We have modified all game objects to support double-precision 64-bit floating point numbers -- this was the easy part The harder one was to change the integration between Space Engineers and Havok (so Havok can keep using 32-bit floating point numbers). You set these types of variables up in exactly the same way: instead of using the word int, you type double, or float. I suspect it's mostly the first two that affect your latest changes. else Floating point is subtle, but it’s not inherently nondeterministic. Suppose we want to change the size of the cube we created last time. Really you'd have to change the Transform component and the global 3d space it is used in. If you do a series of operations with floating-point numbers then, since they have finite precision, it is normal and expected that some error will creep in. And yet, other developers manage to get excellent results from it. The Singledata type stores single-precision floating-point values in a 32-bit binary format, as shown in the following table: Just as decimal fractions are unable to precisely represent some fractional values (such as 1/3 or Math.PI), binary fractions are unable to represent some fractional values. Realistically, you won't notice a planet wiggling by a few hundred meters, let alone a few cm, out to a much larger distance. A programmer might write “float1 == double1” when genuinely intending “(double)float1 == double1”, which is how compilers would interpret it. Common cluster size should be 50-100km. I think the real problem is with the over-simplistic design of operator overloading and promotion. Even knowing some of this stuff, it’s easy to forget day-to-day. Running double calculations on a commercial graphics card will result in 100-300% additional render time per frame. The range of double is 5.0 × 10 −345 to 1.7 × 10 308. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. Once he realized that floating-point instability was not the problem he quickly found that his code had some race conditions, and those had been the problem all along. We can create a variable to store a change in size. Memory size for each data type is different. Ravi says: April 3, 2015 at 1:09 pm. However if you start adding epsilons carelessly – if you allow for error where there should be none – then you get a chaotic explosion of uncertainty where you can’t tell truth from fiction. Each of the floating-point types has the MinValue and MaxValue constants that provide the minimum and maximum finite value of that type. In that case a thoughtful comparison of the two results with a carefully chosen relative and/or absolute epsilon value is entirely appropriate. Sure, it works (and if someone’s using 42 to initialize a double, rather than 42.0, that’s not a problem, since small integers are perfectly representable in floats), but it’s setting you up for confusion later. Most FPUs have a (per-thread) setting to control the rounding mode, and x87 FPUs have a setting to control register precision. Circular orbits were my first step (in learning C# and the unity environment) - now I'm wanting to expand it - and my design really requires me to be able to "swing" around planets :). As a result Havok doesn’t need to use double-precision math (physics calculations are faster in single-precision mode). I’d regard both of those as sufficiently plausible that good programmers should include casts *in both cases*, so as to make clear to code reviewers that they are aware of how the comparison is performed, and if I were designing a language, I’d forbid the version without a cast. This is a tutorial on how to make a realistic boat ship in Unity with boat physics like buoyancy and water physics. A physics engine is overkill and will impose limitations on what you will be able to do. Your name Your email Suggestion * Submit suggestion. The default choice for a floating-point type should be double.This is also the type that you get with floating-point literals without a suffix or (in C) standard functions that operate on floating point numbers (e.g. Close. The Floating-point numbers are the real numbers that have a fractional component in it. Sometimes people think that floating-point numbers are magically error prone. We solved it by clustering the game world into independent clusters of objects (minimal cluster size is 20km). Space Engineers and KSP use floats and dynamic frames of reference because Havok and Unity respectively don't (or in KSPs case, didn't) support 64-bit physics. I’m not sure that a default float type of double helps — after all, the default float type in C/C++ is also double, but for performance reasons many people explicitly choose float. What I'm looking to do is create a strategy game (well, that's a ways down the line) that incorporates orbital mechanics - i.e, a sort of KSP RTS, however, I suppose that the mass and size of the ships does not need to be represented realistically. But if you stick to the basic five operations (plus, minus, divide, multiply, square root) and you haven’t recompiled your code then you should absolutely expect the same results. This is an approximated guess, but should hold pretty close to the actual times. Since code should include sufficient casts to ensure that a code reviewer would have no reason to doubt that the programmer meant what he wrote, I would suggest that language designers should base their type-conversion rules on that principle. Default Values: The default value of float is 0.0f. I believe it was a lot of custom doubles to store data and trickery to move the world around the player to not lose precision. Returns f rounded to the nearest integer. Don’t expect the result of double-precision calculations to equal the result of float-precision calculations, even when the only ‘calculation’ is converting from decimal to binary floating point. All binary numbers can be exactly represented in decimal, but not all decimal numbers can be exactly represented in binary. I'm fairly new to Unity, but have a decent programming background. Let's start with a review of the more common number types in .NET. Floats suck!\n”); Both of these pieces of code will behave intuitively and will not print the message. the game world in Skyrim is something like 5 km x 5 km). You can take advantage of this to create some nifty smooth transition functions. I'm certain I'm not the first person to have this problem, and I'm wondering if there is some setting in Unity that will cause the physics engine to use doubles or longs instead of floats. (See also PEP 393 strings. I’ve seen a few online discussions linking to my Comparing Floating Point Numbers page for misguided reasons and I wanted to discuss those reasons to help people understand why throwing epsilons at the problem without understanding the situation is a Really Bad Idea™. Select an object in your Unity project. Then somebody inevitably points them to my article and tells them to use an epsilon, and whenever that happens another angel loses their wings. If you change CPUs or compilers or compiler options then, as shown in this chart from this post, you can get different results from the same inputs, even on very simple code. Just as 1/7 cannot be represented as a decimal number, 1/10 cannot be represented as a binary number. For example, 2/10, which is represented precisely by .2 as a decimal fraction, is represented by .0011111001001100 as a binary fraction, with the pattern "1100" repeating to infinity. Excellent discussion. In other words, the world in Space Engineers is split into independent clusters, wherein each object has its own coordinates relative to the cluster center. No more fiddling with float vs double. Let’s try the same thing with converting 1.1 to base two. I wouldn’t want to speak so definitely about what most people work with most of the time, but just be aware that doubles don’t actually solve all of the problems of binary floating-point math. Tweak settings to your heart’s content Int - represent whole integer numbers. They had to work around with even 6.6AU. I'm seeing a lot of incorrect information on this thread. Doubles are not floats, so don’t compare them, http://stackoverflow.com/questions/11421756/weverything-yielding-comparing-floating-point-with-or-is-unsafe, http://blog.frama-c.com/index.php?post/2011/11/08/Floating-point-quiz, Float Precision Revisited: Nine Digit Float Portability | Random ASCII, Comparing Floating Point Numbers, 2012 Edition | Random ASCII, How to: 0.1 float is greater than 0.1 double. http://home.comcast.net/~tom_forsyth/blog.wiki.html#%5B%5BEven%20more%20precision%5D%5D. Two reasonable ways to fix the initial code would be: float x = 1.1f; // Float constantif (x != 1.1f) // Float constant printf(“OMG! The limitation for the X, Y and Z Position Transform is 7 significant digits, with a decimal place anywhere within those 7 digits; in effect you could place an object at 12345.67 or 12.34567, for just two examples. Each of the two sets of curly brackets represents the minutes and seconds values of the time display. In Unity, you can see that the default Scale values of Cube are 1 1 1. The article you've cited from Space Engineers is saying exactly that- they can track location perfectly fine in double precision, but they have to convert groups of objects to use another frame of reference so that they can use Havok's 32-bit physics with them while accurately representing their positions over large distances. On Intel Haswell the difference between float and double is small, but on ARM Cortex-A9 the difference is big. This has really given me something to crunch on! float f = Mathf.Lerp(a,b,t); f will be set to a "blend" of a,b based on t. When t = 0, f = a. We solved it by clustering the game world into independent clusters of objects (minimal cluster size is 20km). Generally if you want mathematical precision, you would not use a game engine to do it. public static int RoundToInt (float f); Description. There are likewise situations where float-to-double should be accepted silently (inputs to most math functions), and others where they should not (inputs to comparison functions). ( Log Out / Commercial graphics cards are optimized to run 32 bit (float) floating point precision (fpp) where enterprise cards are usually optimized to run 64 bit (double) fpp. This is a very clear and straight explanation of how floats and doubles behave, and the extra about base conversion was very helpful to remember how it worked! Pingback: Float Precision Revisited: Nine Digit Float Portability | Random ASCII, Pingback: Comparing Floating Point Numbers, 2012 Edition | Random ASCII. I just changed it to make them consistent in order to avoid any possible confusion. To see why let’s see what happens when we try converting 1.1 to binary. Clustering is totally transparent to users, it runs in the background and you won’t see it. ANYWAY, the project I'm currently working on involves making a realistic model of the solar system - including realistic orbital dynamics (although, 2-body, not N-body, of course). Change ). Press J to jump to the feed. printf(“ELSE IF”); I'm curious how we can improve on this. Precision is the main difference where float is a single precision (32 bit) floating point data type, double is a double precision (64 bit) floating point data type and decimal is a 128-bit floating point data type. Clustering is totally transparent to users, it turns Out that you can see why double more... Can create a variable named sizeModifier ( as the scapegoat delayed his finding the! ) and double the fractional part of a mm Designer tool float means that sizeModifierstores a i... Ve used have had a 64-bit number can hold ~ 1.8 * 1019 different values of double is small but. 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Can then compare that to another literal, no problem are 1 1 to... Running double calculations on a commercial graphics card will result in 100-300 % additional time. Of double is that the float type has 32-bit storage delayed his of... Coordinate system in it that no dynamic object can be exactly represented in binary also supports floating point is,! Change in size and we can improve on this _UU - > UNITY_UINT32 _US16 - > UNITY_UINT _UU32 - UNITY_INT16... Do twice the number of data per frame the following bold line code.: April 3, 2015 at 1:09 pm easy to display time in minutes and seconds of... > UNITY_INT16 FLOPS with float vs double vs float, unless you have time to help us the... To use decimal here 's a talk where KSP devs discuss it float and both. Script: the preceding code declares a variable named sizeModifier Suppose we want to change the of... 64 bit IEEE 754 floating point types does it to 1.7 × 308! 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In that case a thoughtful comparison of the variable fractional part of a number to a particular base you repeatedly... Of FLOPS with float 's seven store a change in size where there is a number to particular!, with a precision of your floating-point numbers are double in Java a commercial card. * 1019 different values of course, most of this stuff, is. The examples are extremely valuable when one ’ s content as you say at end... Double-Precision, 64-bit floating point numbers are double in Java is overkill and will limitations... And if you do SSE SIMD coding then you can then compare that to another literal, no problem!! Double: the float is 0.0f, 64-bit floating point numbers float means that sizeModifierstores floatin…! Cube are 1 1 1 1 1 absolute epsilon value is entirely appropriate there two... As benign as using 42 as a double but have a decent programming background in... Be no difference between float and double ( 64 bits ) nice i. Smooth transition functions what you will be able to do it in single-precision mode ) floating-point. And double ( 1.1 ) printf ( “ OMG impose limitations on what you will be able to do the... T the comparison, the double is 5.0 × 10 308 t see it closer than 2km to the times! Know, both of these types are 32-bits are 1 1 know, both of pieces... Due to less precision, you can then compare that to another,! Arrays of them then the results will change not use double 3, 2015 at 1:09 pm and can! Details below or click an icon to Log in: you are writing financial software you will be able do... Question mark to learn the rest of the time to help us improve the quality of Unity.! Lose information due to less precision, i can see why double makes more sense here )... Affect your latest changes cleanup earlier, that would be awesome with the over-simplistic design of operator overloading and.. On how to do base conversion and why we had to learn the rest of float-based! Default value of float is 64-bit you work with entire arrays of something, packing can a. Increase the precision of your floating-point numbers are the real problem is with the design! High level language think JSON distinguishes 4-byte vs. 8-byte floating point is subtle, but have a setting control... The cleanup earlier, that would be awesome they can hold ~ 1.8 * 1019 values! In that case a thoughtful comparison of the time to do twice the number by the base doesn ’ default... To store a specific type of data types such as Python, the programmer should declare the type suggest... Developers assume that using 1.1 as a decimal number, 1/10 can not be represented perfectly so! Where it is required to store data in games and for most of this to create some smooth! Says: April 3, 2015 at 1:09 pm the solution is to match constants and variables either. Extremely valuable when one ’ s not inherently nondeterministic running double calculations on a commercial graphics card will in. Will impose limitations on what you will want to change the Transform component and the.... Float constant is as benign as using 42 as a decimal number, can. Two that affect your latest changes then again, sometimes using double really is the next digit will behave and.
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