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this is very embarassing to ask about for me but does anyone in my audience understand why Apple's CGAffineTransform is defined as mapping to a matrix where the last column is (0, 0, 1) and the last row is (tx, ty, 1.0); shouldn't it be the other way around? when does this work?
wait. is it just one system uses multiplication by a column vector and the other uses multiplication by a row vector. does that mean that the matrices are equivalent if transposed. is that the monster that's haunted me for checks notes two years? if so then (brb killing myself)
i have this horrible feeling that i came very close to realising this a year ago already and instead blamed myself
the git history of touchHLE's linear algebra code shall forever be a list of reasons i want to die jesus christ
at least it's finally fucking over https://github.com/touchHLE/touchHLE/commit/4c43af4cb8ce4686fd9cf76bb183c65b6355af66
@hikari@social.noyu.me rebase 
@hikari depends whether the coordinates are considered row vectors or column vectors. You need the transpose of the transform entirely depending on the convention.
@porglezomp as i realised in https://social.noyu.me/@hikari/statuses/01JM5Y8ZQB4C7D0MY2MMA84SDV
apple write:
row times matrix
i think i am used to:
matrix times column
if i transpose the matrix are they equivalent?
@hikari yes, A•x = (xT•AT)T
@porglezomp thank you very much