# D3DXMatrixMultiply implimentation?

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Does anyone know how D3DXMatrixMultiply is implimented? I can't find any information on what alrogrithm it uses, but it is definitely faster than just a naive matrix multiplication in C++. Could it even be implimented in assembly?

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I'm fairly certain that the matrix multiplication, along with a number of other functions, is written to use SSE when available. You're not likely to beat it any time soon, as it's tuned by guys who know processors like whoa.

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Wow, you were right, that took a long time, but I did some heavy research on the SSE and 3DNow! SIMD instruction sets and I've finally got an implimentation that equals D3DMatrixMultiply's performance. I'm developing on an AMD processor so this is in 3DNow! MMX assembly. I don't know if it would work on an Intel or not. DX looks up your processor internally and probably chooses an SSE or 3DNow! implimentation depending on what your processor supports. I will probably do something similar if I can figure out how to test it on an Intel (though supposedly AMD processors now support SSE instructions, but I'm not sure if there is a large performance difference compared to 3DNow! on these machines).

Anyway, for anyone who wishes to use this in a math library, feel free.

enum MPARTS { MP_11=0, MP_12=4, MP_13=8, MP_14=12,	      MP_21=16, MP_22=20, MP_23=24, MP_24=28,	      MP_31=32, MP_32=36, MP_33=40, MP_34=44,	      MP_41=48, MP_42=52, MP_43=56, MP_44=60 };enum MROWS { MR_1=0, MR_2=16, MR_3=32, MR_4=48 };inline Matrix& Matrix::operator *=(const Matrix& rhs){	__asm	{		FEMMS		mov edi, this		mov esi, rhs		MOVQ MM1, [esi+MR_1]		MOVQ MM2, [esi+MR_1+8]		MOVQ MM3, [esi+MR_2]		PSHUFW MM6, [edi+MP_11], 0x44		MOVQ MM7, MM6		PFMUL MM6, MM1		PFMUL MM7, MM2		PSHUFW MM4, [edi+MP_12], 0x44		MOVQ MM5, MM4		PFMUL MM4, MM3		MOVQ MM0, [esi+MR_2+8]		PFMUL MM5, MM0		PFADD MM6, MM4		PFADD MM7, MM5		PSHUFW MM4, [edi+MP_13], 0x44		MOVQ MM5, MM4		MOVQ MM0, [esi+MR_3]		PFMUL MM4, MM0		MOVQ MM0, [esi+MR_3+8]		PFMUL MM5, MM2		PFADD MM6, MM4		PFADD MM7, MM5		PSHUFW MM4, [edi+MP_14], 0x44		MOVQ MM5, MM4		MOVQ MM0, [esi+MR_4]		PFMUL MM4, MM0		MOVQ MM0, [esi+MR_4+8]		PFMUL MM5, MM2		PFADD MM6, MM4		PFADD MM7, MM5				MOVQ [edi+MR_1], MM6		MOVQ [edi+MR_1+8], MM7		PSHUFW MM6, [edi+MP_21], 0x44		MOVQ MM7, MM6		PFMUL MM6, MM1		PFMUL MM7, MM2		PSHUFW MM4, [edi+MP_22], 0x44		MOVQ MM5, MM4		PFMUL MM4, MM3		MOVQ MM0, [esi+MR_2+8]		PFMUL MM5, MM0		PFADD MM6, MM4		PFADD MM7, MM5		PSHUFW MM4, [edi+MP_23], 0x44		MOVQ MM5, MM4		MOVQ MM0, [esi+MR_3]		PFMUL MM4, MM0		MOVQ MM0, [esi+MR_3+8]		PFMUL MM5, MM2		PFADD MM6, MM4		PFADD MM7, MM5		PSHUFW MM4, [edi+MP_24], 0x44		MOVQ MM5, MM4		MOVQ MM0, [esi+MR_4]		PFMUL MM4, MM0		MOVQ MM0, [esi+MR_4+8]		PFMUL MM5, MM2		PFADD MM6, MM4		PFADD MM7, MM5				MOVQ [edi+MR_2], MM6		MOVQ [edi+MR_2+8], MM7		PSHUFW MM6, [edi+MP_31], 0x44		MOVQ MM7, MM6		PFMUL MM6, MM1		PFMUL MM7, MM2		PSHUFW MM4, [edi+MP_32], 0x44		MOVQ MM5, MM4		PFMUL MM4, MM3		MOVQ MM0, [esi+MR_2+8]		PFMUL MM5, MM0		PFADD MM6, MM4		PFADD MM7, MM5		PSHUFW MM4, [edi+MP_33], 0x44		MOVQ MM5, MM4		MOVQ MM0, [esi+MR_3]		PFMUL MM4, MM0		MOVQ MM0, [esi+MR_3+8]		PFMUL MM5, MM2		PFADD MM6, MM4		PFADD MM7, MM5		PSHUFW MM4, [edi+MP_34], 0x44		MOVQ MM5, MM4		MOVQ MM0, [esi+MR_4]		PFMUL MM4, MM0		MOVQ MM0, [esi+MR_4+8]		PFMUL MM5, MM2		PFADD MM6, MM4		PFADD MM7, MM5				MOVQ [edi+MR_3], MM6		MOVQ [edi+MR_3+8], MM7		PSHUFW MM6, [edi+MP_41], 0x44		MOVQ MM7, MM6		PFMUL MM6, MM1		PFMUL MM7, MM2		PSHUFW MM4, [edi+MP_42], 0x44		MOVQ MM5, MM4		PFMUL MM4, MM3		MOVQ MM0, [esi+MR_2+8]		PFMUL MM5, MM0		PFADD MM6, MM4		PFADD MM7, MM5		PSHUFW MM4, [edi+MP_43], 0x44		MOVQ MM5, MM4		MOVQ MM0, [esi+MR_3]		PFMUL MM4, MM0		MOVQ MM0, [esi+MR_3+8]		PFMUL MM5, MM2		PFADD MM6, MM4		PFADD MM7, MM5		PSHUFW MM4, [edi+MP_44], 0x44		MOVQ MM5, MM4		MOVQ MM0, [esi+MR_4]		PFMUL MM4, MM0		MOVQ MM0, [esi+MR_4+8]		PFMUL MM5, MM2		PFADD MM6, MM4		PFADD MM7, MM5				MOVQ [edi+MR_4], MM6		MOVQ [edi+MR_4+8], MM7		FEMMS	}	return *this;}

Matrix's data here is just an array of 16 floats. This is the *= version, a generic multimatrix(m1, m2, out) would be simply to make from this.

Please post any improvements and optimizations, I'm only a beginnner in assembly. If anyone wants me to post the complete matrix class to test the code let me know. I tested this against D3DXMatrixMultiply and even doing 10000 multiplications per frame they performed extremely close (sometimes over, sometimes under, averaging nearly identical).

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Most impressive. :)

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Only thing is, this won't compile on a x64 platform. Microsoft pulled asm support for x64 platforms. This has forced me to not use asm, if I want to build a x64 application.

Edit: Not to sound like a real downer[smile].

[Edited by - exorcist_bob on January 3, 2007 8:19:44 PM]

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1. Unless you have good reason to (e.g. for self-education on how to implement such a thing, or for use on Linux PCs), for single operations like matrix multiplication and inversion I'd still advise using the D3DX maths functions: they're well tested, extremely optimal for a general purpose library, somebody else fixes the bugs, less memory is used for code if any other running application has the same D3DX DLL loaded.

2. To use Gondolin's code on x64, you'll either have to use a standalone assembler and put a function call to the ASM function inside the inline C++ or use intrinsics.

Incidentally, when you want to mix ASM and C/C++ in the same function, intrinsics can actually provide better performance because you leave the choice of register assignment up to the compiler, so it can do a better job of assigning C/C++ variables to registers that your low-level code uses.

3. writing, and hand-tuning ASM can be a fun activity, and it's often useful to understand ASM for debugging purposes, but do remember that the CPU manufacturers are more 'l33t' at ASM than you are, so it's always worth checking whether they've already done the hard work for you, e.g.:
http://www.intel.com/design/PentiumIII/sml/

http://www.amd.com/us-en/assets/content_type/white_papers_and_tech_docs/22007.pdf (See chapter 10, the principles behind the Matrix-Vector multiply can be expanded to a Matrix-Matrix multiply. Also check out AMD's ACML library).

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Quote:
 Unless you have good reason to (e.g. for self-education on how to implement such a thing

Yep, this is more of a self-education implimentation. You're right, its a lot of fun tuning in ASM and when you're done you have a much better understanding of the general algorithm along with how to optimize it.

My original idea was that a game server would not have to load any DirectX DLLs...as from a design standpoint every component of DirectX is aimed for client presentation, not CPU calculations such as physics and scene management that the server does. Unfortunately including the D3DX math header seems to load the whole D3D dll which seems a waste. There are lots of math libraries out there but I was attempting to write my own that essentially impliments DX math. Even though its a lot of work and probably pointless, I'm finding that there are a few things that DX doesn't fully optimize, so its interesting to see what works better and what doesn't, even if I don't end up using this.