"Any sufficiently advanced bug is indistinguishable from a feature."
- Rich Kulawiec

Shader programming tips #3
Monday, February 9, 2009 | Permalink

Multiplying a vector by a matrix is one of the most common tasks you do in graphics programming. A full matrix multiplication is generally four float4 vector instructions. Depending on whether you have a row major or column major matrix, and whether you multiply the vector from the left or right, the result is either a DP4-DP4-DP4-DP4 or MUL-MAD-MAD-MAD sequence.

In the vast majority of the cases the w component of the vector is 1.0, and in this case you can optimize it down to three instructions. For this to work, declare your matrix as row_major. If you previously was passing a column major matrix you'll need to transpose it before passing it to the shader. You need a matrix that works with mul(vertex, matrix) when declared as row_major. Then you can do something like this to accomplish the transformation in three MAD instructions:
float4 pos;

pos = view_proj[2] * vertex.z + view_proj[3];
pos += view_proj[0] * vertex.x;
pos += view_proj[1] * vertex.y;


It should be mentioned that vs_3_0 has a read port limitation, and since the first line is using two different constant registers, HLSL will put a MOV instruction in there as well. But the hardware can be more flexible (for instance ATI cards are). In vs_4_0 there's no such limitation and HLSL will generate a three instruction sequence.

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