A critical design decision is how to extract the file and rank from a square index. In most languages, you’d write file = (sq - 1) % 8 + 1 and rank = (sq - 1) / 8 + 1. But TeX’s \numexpr division rounds instead of truncating: 63/8 gives 8 (rounding 7.875 up), not 7. This was the source of one of the first nasty bugs. The fix: precompute lookup tables at load time using \divide (which truncates) and store results in \csname control sequences:
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