nx_kp_break.nx

nx_kp_break.nx -- KNUTH-PLASS OPTIMAL LINE BREAKING, integer-exact. WHY: every browser, and almost every renderer, breaks lines FIRST-FIT -- it fills the current line until the next word does not fit, then breaks, and never reconsiders. That is a greedy choice made with no knowledge of the rest of the paragraph, and it is why justified text on the web has rivers of white and books do not. Knuth and Plass (1981, the TeX line breaker) instead model the paragraph as BOXES (words), GLUE (spaces that can stretch and shrink) and PENALTIES (places a break is discouraged or encouraged), then choose the set of breakpoints that minimises TOTAL badness over the WHOLE paragraph by dynamic programming. Accepting a slightly worse line early to avoid a terrible line later is a trade a greedy algorithm cannot make. This is the piece CSS cannot reach. `hyphens:auto` and `text-align:justify` only make the browser's greedy result less ugly; they do not change the algorithm. Owning the line breaker is what makes a Nishi reading surface typographically book-grade rather than screen-grade. INTEGER-EXACT: badness is TeX's 100*r^3 evaluated in fixed point, so a paragraph lays out identically on every host. Widths are in milli-units (one character = 1000) which keeps the arithmetic exact without float. nx_kp_break fit <cols> <text> -- optimal layout, one line per output line nx_kp_break compare <cols> <text> -- Knuth-Plass vs greedy first-fit, with the measured difference nx_kp_break selftest -- the gate license_tier: ORIGINAL