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I guess I just never encountered the 3,5,6,7 bytes word types.

24-bit floats "FP24" at least have been a thing in some ATI graphics cards (R300 & R420) 15+ years ago. Some DSPs have also used (some still do?) 24-bit word width.

These odd word widths are anything but common, though.

Modern AMD GPUs still support 24 bit integers, see https://rocm.github.io/GCN_Float16.html.

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