[libre-riscv-dev] 3D Matrix-style operations / primitives

[lkcl]

does anyone know of some mathematics for analysing which would be the best 
"primitives" for Matrix operations, suited to transposition and inversion, 
determinant and normalisation?

for 3D that generally means just 2x2, 3x3 and 4x4.

i'm looking up how matrix inverses are calculated and, hoo-boy :)
https://integratedmlai.com/matrixinverse/
https://www.wikihow.com/Find-the-Inverse-of-a-3x3-Matrix

normalisation looks to be just "divide by the determinant":
http://mymathforum.com/linear-algebra/18218-how-do-i-normalize-matrix.html

so... i am logically deducing that if you wanted something RISC-like, you'd 
have operations for transpose and determinant?  or... can determinant be 
broken down further into something elegant?
https://en.wikipedia.org/wiki/Determinant

whilst 2x2 looks pretty obvious - 0,0 x 1,1 - 1,0 x 0,1 - it looks like it 
goes recursive from there, with permutations:
https://en.wikipedia.org/wiki/Determinant#n_%C3%97_n_matrices

at that point, honestly, i'm scared/alarmed to even recommend a Matrix 
Determinant opcode!

likewise, Transpose appears to be a series of MV operations with offsets, 
which tends to suggest that there may be some vector primitives that would 
be really good to have, that could be added to this:

https://libre-riscv.org/simple_v_extension/specification/mv.x/


a quick search "matrix inverse swizzle" shows this:
https://lxjk.github.io/2017/09/03/Fast-4x4-Matrix-Inverse-with-SSE-SIMD-Explained.html

which mentions __mm_shuffle_epl32, _mm_shuffle_ps, _mm_movelp_ps and that 
leads on a merry search to SSE/AVX/AVX-512:
https://software.intel.com/sites/landingpage/IntrinsicsGuide/#text=_mm_shuffle_ps
https://www.cs.uaf.edu/2006/fall/cs301/lecture/11_17_sse.html

looovely :)

at which point i am definitely lost.  does anyone have any suggestions?

l.