Split matrix calculation, and FYI: Effectiveness of sparse data structure for double-double and quad-double arithmetics

I got this idea for splitting numbers (but actually only for matrices), like Float64, into two parts, hi and lo (basically the double-double trick), for up to 2x speedup if lo can be Float32, since hi can be in a separate matrix, and it not sparse not dense. Anyone heard of it done? Maybe failed attempt, or a reason it would not work? I asked the AI if this might have been done before, and it gave me this paper, that seems different but maybe similar, and still of possibly of interest to people...