So the guarantee is really that the same machine code will produce the same results, as long as you don’t do something wacky. I expected it to be false | SevenNet, Floating Point in the Browser, Part 3: When x+y=x (y != 0), Floating Point in the Browser, Part 2: Bad Epsilon, Windows Timer Resolution: The Great Rule Change, Floating Point in the Browser, Part 1: Impossible Expectations, 10/7 = 1+3/7 (discard integer part, multiply by ten, next digit is one), 0.2 (multiply by two, first digit is zero), 0.4 (discard integer part, then multiply by two, next digit is zero), 0.8 (multiply by two, next digit is zero). Pingback: Float Precision Revisited: Nine Digit Float Portability | Random ASCII, Pingback: Comparing Floating Point Numbers, 2012 Edition | Random ASCII. The slight breaking of the pattern at the end of both numbers is because the conversion is done with round-to-nearest rather than truncation, in order to minimize the error in the approximation, and in both cases it is rounded up. I just changed it to make them consistent in order to avoid any possible confusion. Forecast for randomascii: programming, tech topics, with a chance of unicycling. Thank you so much. 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). New comments cannot be posted and votes cannot be cast. An awesome reminder of how to do base conversion and why we had to learn it in the first place! After each multiply we take the integer portion of the result as our next digit, and discard the integer portion before the next multiply: Notice that the steps in bold (3-6) repeat endlessly, so the binary representation of 1.1 repeats endlessly. Floats are normally OK for games but if you are writing financial software you will want to use Decimal. Very clear and point to point reply. Double: The double accommodates 15 to 16 digits, compared with float's seven. The problem is that there are two main floating-point types in most C/C++ implementations. Clustering is totally transparent to users, it runs in the background and you won’t see it. Excellent discussion. If you do the same calculation in a slightly different way then it is normal and expected that you might get slightly different results. After each step the integer portion is the next digit. Basically you need to use 2 coordinate systems and move all the object in your current cluster (first coordinate Double) to 0,0,0 in unity and use your coordinates relative to the cluster center(2nd coordinate Float) as the actual transform coordinates. Float is a single-precision, 32-bit floating point data type; double is a double-precision, 64-bit floating point data type. In programming, it is required to store data. Thanks for tuning in! Int - represent whole integer numbers. Unity allows you to place objects anywhere within the limitations of the float-based coordinate system. I talked to somebody who had spent weeks trying to understand how to deal with floating-point instability in his code – different results on different machines from the same machine code – when it was clear to me that the results should have been identical. This makes for a fascinating problem then. No epsilon required. Then somebody inevitably points them to my article and tells them to use an epsilon, and whenever that happens another angel loses their wings. The main barrier to Unity using doubles to track positions would be that doing so would mean a performance decrease for all projects using Unity, regardless if they need the changes or not, and 99% (possibly higher) of games don't actually need worlds in excess of what can be achieved with the current floating point limitations (I.E. 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. Cookies help us deliver our Services. http://blog.marekrosa.org/2014/12/space-engineers-super-large-worlds_17.html. The biggest differences are in precision and range. I would guess that that is because the ‘int’ type is the size of a pointer so ‘float’ might as well be also, but still. Select an object in your Unity project. Switch to Manual. I'm fairly new to Unity, but have a decent programming background. 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™. A User Showcase of the Unity Game Engine. (See also PEP 393 strings. As a programmer who used to avoid floats and doubles whenever possible (because I didn’t understand the “magic” behind them) and is getting to C/C++ game programming, this post and all the others about the subject taught me I was doing it wrong. 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. Instead those same six digits will repeat forever. Floating-point constants in C/C++ are double precision, so the code above is equivalent to: if (float(1.1) != double(1.1))    printf(“OMG! Floating point is subtle, but it’s not inherently nondeterministic. Ever wanted to make an object float up and down while spinning in Unity? Decided to start learning Unity to refresh my programming skills (after a few years doing SE) and make myself a bit more marketable to some more creative fields. Most FPUs have a (per-thread) setting to control the rounding mode, and x87 FPUs have a setting to control register precision. Memory size for each data type is different. You can take advantage of this to create some nifty smooth transition functions. On Intel Haswell the difference between float and double is small, but on ARM Cortex-A9 the difference is big. 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. As you probably know, both of these types are 32-bits. Floats suck!\n”); In other words, if 1.1 is not the same when stored as a float as when stored as a double then the message will be printed. Cancel. Python has only one ‘float’ type (with at least as much as IEEE double precision, but maybe more); Pike has one ‘float’ type plus ‘mpf’, a multi-precision float (allowing you to go to arbitrarily large precision if you wish). Two reasonable ways to fix the initial code would be: float x = 1.1f; // Float constantif (x != 1.1f) // Float constant    printf(“OMG! Or better still, switch to a language like Pike, where the default float type is double precision, AND you get an arbitrary-precision float type (Gmp.mpf, using the GNU Multiprecision Library). Here's a few of the basic types: As you say at the end, the solution is to match constants and variables; either use 1.1f or use a double. Of course, most of this trouble disappears if you use a high level language. 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. And no angels harmed. Life will be better. How is it possible then that the max value of int is 2 31, and the max value of float is 3.4*10 38, while both of them are 32 bits? 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). Generally if you want mathematical precision, you would not use a game engine to do it. The primary difference between float and double is that the float type has 32-bit storage. Even knowing some of this stuff, it’s easy to forget day-to-day. Float vs. The double data type is more precise than float in Java. else The more logical conclusion – rather than “OMG! I'm curious how we can improve on this. Usage. 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). printf(“ELSE IF”); The examples are extremely valuable when one’s thinking isn’t as clear as it should be. For example, the following declarations declare variables of the same type:The default value of each floating-point type is zero, 0. 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. public static float Floor (float f); Description. float means that sizeModifierstores a floatin… The double is 8 bytes long. If you want begin representing AU roughly accurately you're going to need a bit more than doubles, From Marek Rosa's Blog on Space Engineers (6.6AU infinite worlds](http://blog.marekrosa.org/2014/12/space-engineers-super-large-worlds_17.html). Change ), You are commenting using your Facebook account. I've seen this question pop up a few times and every time I see people saying to check out the articles Kerbal Space Program devs wrote about how they solved it. Each of the floating-point types has the MinValue and MaxValue constants that provide the minimum and maximum finite value of that type. I think the real problem is with the over-simplistic design of operator overloading and promotion. inputs to serialization or comparison functions). Ignore C’s float and just use double instead. I agree that using 1.1 as a float constant is the problem. Reply. Add Component > New Script Name: Floater; Language: C-Sharp; Edit the script; Copy & Paste the code below into your script editor. And yet, other developers manage to get excellent results from it. Otherwise, if you have time to do the cleanup earlier, that would be awesome. We can create a variable to store a change in size. When reading JSON we see a floating point number and we can deserialize it as a double or a float. There seems to be a belief that if you redo the exact same calculation with the exact same inputs then you might get a different answer. Depending on dynamic objects density, cluster size can increase its size without limits. 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. 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. Very clear and point to point reply. John Payson says: May 28, 2016 at 2:01 pm. Close. float x = 0.5; Here's a talk where KSP devs discuss it. But flexibility comes at the cost of a LOT of work: with surface shaders, Unity takes care of all (almost) the PBR lighting and shadowing so you just have to worry about the shader itself. One quibble: in the Floating-point-quiz you say “For a decimal number to be representable as a (base 2) floating-point number, its decimal expansion has to end in 5” but that is only true if there is a fractional part. In one of the examples, why do you use float(1.1) and (double)1.1, and thus not double(1.1)? Float, Double, and Decimal - represents real world numbers, precision and size distinguish these types from each other. Realistically, you won't notice a planet wiggling by a few hundred meters, let alone a few cm, out to a much larger distance. If floating-point math is incapable of getting correct results when there are no calculations (except for a conversion) involved then it is completely broken. 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. In programming languages such as Python, the programmer does not need to declare the type of the variable. Post was not sent - check your email addresses! printf(“ELSE”); When you assign a floating-point value, it is what it is. By default, floating point numbers are double in Java. Unity is the ultimate game development platform. And these days, most high level languages are doing the same thing; the ‘float’ type in Python, Pike, and (I think) JavaScript/ECMAScript (where it’s just called a number) is double-precision. The range of double is 5.0 × 10 −345 to 1.7 × 10 308. I can probably tackle this next week if you need me to. Thank you! the game world in Skyrim is something like 5 km x 5 km). The first thing we're gonna do is create a new “Standard Surface Shader”.Some people may prefer a fixed-function shader for this particular case, as those are more flexible. There are some situations where floats should silently promote to doubles, others where doubles should silently demote to floats, and others where the compiler should demand an explicit conversion. Make your own math library with arbitrary precision, unless you're going to run thousands of small asteroids and stuff, and mostly focus on planets/moons, just make some 256bit fixed point number system by hand, something like Q128.128 should give you more precision than you need (i think). In some cases, comparing floating-point numbers for exact equality is actually correct. In C#, the naming convention for variables is to capitalize the first letter of every word after the first word. Default Values: The default value of float is 0.0f. 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. More generally, I’d allow parameters to functions to indicate whether they should allow or disallow explicit casts, since there are situations where double-to-float should be accepted silently (e.g. The net result is that the binary representations of 1.1 in float (24-bit mantissa) and double (53-bit mantissa) precision are: double(1.1) = %1.0001100110011001100110011001100110011001100110011010. Anyway, thanks for your help and the resource. Reply. Cancel. Floating Point Accuracy. As a case in point, all of Relic’s games have used floating-point extensively in gameplay code, but are still completely deterministic across CPUs from the Pentium II through the i7 — we know this because you can play networked games and replays on different generations of machine without desyncing. 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. The double is a double precision 64 bit IEEE 754 floating point data type. As a result Havok doesn’t need to use double-precision math (physics calculations are faster in single-precision mode). I can make a GUI program that displays a colorful Mandelbrot image in a screenful of Pike code, but the boilerplate to just create a window would be more than that in C. With float vs double, I don’t remember ever working with floats for performance – I just always go double for accuracy. Change ). 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. Perfomance impact of calculating using float vs double. Making a countdown timer in Unity involves storing a float time value and subtracting the duration of the last frame (the delta time) ... made up of two double-digit numbers that are separated by a colon (00:00). A double loses precision as the value it is approximating increases, of course, but an IEEE 754 64-bit double will still be within 1 of any number less than, say, 2^53, or 9*1015. The other example I’ve seen where people are too quick to pull out an epsilon value is comparing a constant to itself. Floats suck!\n”); double x = 1.1;if (x != 1.1)    printf(“OMG! Sometimes people think that floating-point numbers are magically error prone. This is due to a hardware limitation. Really you'd have to change the Transform component and the global 3d space it is used in. Double vs float. 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! If not, the difference might be much smaller, but it is very dependent on your CPU. But first let’s practice base conversion. else if (x == 0.5f) Switch to Manual. Your name Your email Suggestion * Submit suggestion. 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. Decimal vs Double vs Float, unless you have a case where it isn't accurate enough. The difference between the two is in the size of the numbers that they can hold. In that case a thoughtful comparison of the two results with a carefully chosen relative and/or absolute epsilon value is entirely appropriate. C# supports the following predefined floating-point types:In the preceding table, each C# type keyword from the leftmost column is an alias for the corresponding .NET type. How did we increase the precision of numerical computations? Memory locations that store data are called variables. Floats definitely still have significant advantages. A good language should squawk in cases where there is genuine ambiguity about what a programmer most likely meant. 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. By using our Services or clicking I agree, you agree to our use of cookies. 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. All binary numbers can be exactly represented in decimal, but not all decimal numbers can be exactly represented in binary. ( Log Out /  Which is poor odds. 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. The confusion, presumably, comes from the fact that 1.1 looks like such a simple number, and therefore the naive expectation is that it can trivially be stored in a float. Then again, sometimes using double really is the right solution, or at least really does solve the problem. Hm. I work in games and for most of our data we absolutely cannot use double. Here is a typical example of the code that triggers this: float x = 1.1;if (x != 1.1)    printf(“OMG! A physics engine is overkill and will impose limitations on what you will be able to do. 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. Running double calculations on a commercial graphics card will result in 100-300% additional render time per frame. On 32-bit systems float is 32-bit, on 64-bit systems float is 64-bit. Anyone know? In order to store them into float variable, you need to cast them explicitly or suffix with ‘f’ or ‘F’. These are float (32 bits) and double (64 bits). ( Log Out /  The Decimal, Double, and Float variable types are different in the way that they store the values. There are caveats: the way some SSE instructions are specified is a bit of a minefield, and we’re trying to figure out now how we can make things work reliably across architectures, but the main point is valid. 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.