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Quake III Arena, a first-person shooter video game, was released in 1999 by id Software and used the algorithm. Brian Hook may have brought the algorithm from 3dfx to id Software.[6] A discussion of the code appeared on the Chinese developer forum CSDN in 2000,[10] and Usenet and the gamedev.net forum spread the code widely in 2002 and 2003.[11] Speculation arose as to who wrote the algorithm and how the constant was derived; some guessed John Carmack.[7] Quake III's full source code was released at QuakeCon 2005, but provided no answers. The authorship question was answered in 2006 when Greg Walsh contacted Beyond3D as their speculation gained popularity on Slashdot.[6]

The inverse square root of a floating point number is used in digital signal processing to normalize a vector, scaling it to length 1 to produce a unit vector.[14] For example, computer graphics programs use inverse square roots to compute angles of incidence and reflection for lighting and shading. 3D graphics programs must perform millions of these calculations every second to simulate lighting. When the code was developed in the early 1990s, most floating point processing power lagged the speed of integer processing.[7] This was troublesome for 3D graphics programs before the advent of specialized hardware to handle transform and lighting. Computation of square roots usually depends upon many division operations, which for floating point numbers are computationally expensive. The fast inverse square generates a good approximation with only one division step.

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The advantages in speed offered by the fast inverse square root trick came from treating the 32-bit floating-point word[note 1] as an integer, then subtracting it from a "magic" constant, 0x5F3759DF.[7][19][20][21] This integer subtraction and bit shift results in a bit pattern which, when re-defined as a floating-point number, is a rough approximation for the inverse square root of the number. One iteration of Newton's method is performed to gain some accuracy, and the code is finished. The algorithm generates reasonably accurate results using a unique first approximation for Newton's method; however, it is much slower and less accurate than using the SSE instruction rsqrtss on x86 processors also released in 1999.[1][22]

Since this algorithm relies heavily on the bit-level representation of single-precision floating-point numbers, a short overview of this representation is provided here. To encode a non-zero real number x {\displaystyle x} as a single precision float, the first step is to write x {\displaystyle x} as a normalized binary number:[23]

By repeating this step, using the output of the function ( y n + 1 {\displaystyle y_{n+1}} ) as the input of the next iteration, the algorithm causes y {\displaystyle y} to converge to the inverse square root.[29] For the purposes of the Quake III engine, only one iteration was used. A second iteration remained in the code but was commented out.[21]

I was particularly impressed by : The virtual machines system and the associated toolchain that altogether account for 30% of the code released. Under this perspective idTech3 is a mini operating system providing system calls to three processes. The elegant network system based on snapshots and memory introspection.As usual I wrote numerous notes that I have cleaned up and synthesized into drawings. I hope it will save time to some people but also encourage others to read more code and become better engineers.

Edit : Thanks for the support :) !

The first striking thing is that the Visual Studio workspace is not made of one project but eight. Not all of them are used depending if the build is DEBUG or RELEASE (especially game,cgame and q3_ui : the virtual machines projects). Some of the projects are never used (splines and ui).

A table is better to summarize what project is contributing to which module:

Projects Type DEBUG Builds RELEASE Builds Comments botlib Static Library botlib.lib botlib.lib A.I cgame Dynamic Libary/Bytecode cgamex86.dll - game Dynamic Libary/Bytecode qagamex86.dll - q3_ui Dynamic Libary/Bytecode uix86.dll - quake3 Executable quake3.exe quake3.exe renderer Static Library renderer.lib renderer.lib OpenGL based Splines Static Library Splines.lib Splines.lib Used NOWHERE ! ui Dynamic Libary/Bytecode uix86_new.dll - Used for Quake III Arena.

Trivia : idTech3 working title was "Trinity". Since idTech4 was called "Neo" I assumed it was from the "Matrix" franchise...but id Software stated in interview with firingsquad.com thatit was named after "Trinity River in Dallas":

John : I've got a couple of engine things that I'm working on, as far as research. FS : So is one of those things Trinity? I think there's been a little confusion about "Trinity." John : I was never really certain how this got as confusing as it did to everybody. After Quake, when I was starting on new rendering technologies and everything, everybody was just calling it "the next engine" or whatever. Michael Abrash suggested we just take Intel's tack of naming your next project after a river near you. We have the Trinity River in Dallas, and so it was just like "Trinity Engine," the next step.

Edit ( July 07, 2012 ) : Jeremiah Sypult contacted me after publication of this article: He "unrotted" the Mac OS X build with an XCode 4.0 project for Quake3. I have fixed it further and you can get it on here on github. You will need the Quake III Arena baseq3 (not the demo version) and be sure to use the parameters "+set vm_game 0 +set vm_cgame 0 +set vm_ui 0" in order to use the dylib virtual machines. Open /code/quake3.xcworkspace and it builds in one click !!

Here is a fully unrolled loop that I used a a map while digging into the source code.

An interesting thing to notice here that perfectly illustrates how paramount the virtual machines are: Nowhere we see a call to RE_RenderScene: the function that performs culling and issue OpenGL commands. Instead what happen is:

Quake3.exe sends a message to the Client VM: CG_DRAW_ACTIVE_FRAME which signal that a refresh is needed. The Virtual Machine performs some entity culling and prediction then call for OpenGL rendition via a Quake3 system call (CG_R_RENDERSCENE). Quake3.exe receives the system call and actually calls RE_RenderScene. OpenGL Quake3.exe Client Virtual machine -------- ---------- ---------------------- | | | | | | | VM_Call(CG_DRAW_ACTIVE_FRAME)-----------------> CG_DrawActiveFrame | | CG_DrawActive | | trap_R_RenderScene | | syscall( CG_R_RENDERSCENE, fd ) | RE_RenderScene

On a pie chart we can vividly see how unusual the proportion are since 30% of the codebase is dedicated to tools:

This is explained partly because idtech3 features a ANSI C compiler: The open source Little C Compiler (LCC) is used to generate bytecode for the virtual machines.

I studied Quake World, openGL rendered ; Upon opening the solution, 4 sub-projects can be seen:gas2asm - Utility to port assembler code from GNU ASM to x86 ASMqwcl - The client part of QuakeQWFwd - Proxy sitting in front of Quake Serversqwsv - The server part of Quake

John Carmack has a special function in the Quake III source code which calculates the inverse square root of a float, 4x faster than regular (float)(1.0/sqrt(x)), including a strange 0x5f3759df constant. See the code below. Can someone explain line by line what exactly is going on here and why this works so much faster than the regular implementation?

The magic of the code, even if you can't follow it, stands out as the i = 0x5f3759df - (i>>1); line. Simplified, Newton-Raphson is an approximation that starts off with a guess and refines it with iteration. Taking advantage of the nature of 32-bit x86 processors, i, an integer, is initially set to the value of the floating point number you want to take the inverse square of, using an integer cast. i is then set to 0x5f3759df, minus itself shifted one bit to the right. The right shift drops the least significant bit of i, essentially halving it.

Questions about debugging a problem in your project must present a concise selection of code and context so as to allow a reader to diagnose the issue without needing to read all of your code or to engage in extensive back-and-forth dialog. For more information, see this meta thread.

I followed the code and found that the exception was generated in int VM_CallCompiled(vm_t *vm, int *args), when executing call entryPoint in the __asm block, located in line 1148 of vm_x86.c. Since it's assembler code, I don't know how to debug it.

But instead of explicitly doing division (expensive for the CPU), the code uses another clever hack: it shifts bits. Right-shifting by one position is the same as dividing by two (you can try this for any power of 2, but it will truncate the remainder). And if you want to get a negative number, instead of multiplying by -1 (multiplications are expensive), just subtract the number from "0" (subtractions are cheap).

So, the code converts the floating-point number into an integer. It then shifts the bits by one, which means the exponent bits are divided by 2 (when we eventually turn the bits back into a float). And lastly, to negate the exponent, we subtract from the magic number 0x5f3759df. This does a few things: it preserves the mantissa (the non-exponent part, aka 5 in: $5 \cdot 10^6$), handles odd-even exponents, shifting bits from the exponent into the mantissa, and all sorts of funky stuff. The paper has more details and explanation, I didn't catch all of it the first time around. As always, feel free to comment if you have a better explanation of what's happening.

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