Kenneth Ostby wrote:
Actually when it comes hardware there is surprisingly little matrix
matrix multiplication in the 3D world.
Duck test:
P' = T*P
|p'1| |t11,t12,t13| |p1|
|p'2| = |t21,t22,t23|*|p2|
|p'3| |t31,t32,t33| |p3|
We can write this out explicitly but it is still a matrix * a vector:
p'1 = t11*p1 + t12*p2 + t13*p3
p'2 = t21*p1 + t22*p2 + t23*p3
p'3 = t31*p1 + t32*p2 + t33*p3
IIRC, this is called a linear transform which is a special case of a dot
product.
Note that this can be accomplished by MAC instructions and there are no
dependencies to stall the pipeline.
With a 3-word SIMD you need to:
clear the accumulator
load P in a register
perform 3 MAC vector instructions
If you have a 4-word SIMD you can also do the same for P which is a 4
vector and a 4x4 transform matrix, and it only takes one more MAC.
--
JRT
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