render_page_backward searched for the previous page's start: estimate a block
index, lay out forward, bisect on the block difference, up to ten times. Both the
estimator and the adjuster pinned word_index to 0 and moved only block_index -
but pages routinely start mid-block, so the answer was not in the search space.
The loop could never match, exhausted its iterations and fell through to a
fallback that jumped to the start of the document.
Measured on a document with one 1200-word paragraph, whose page starts are
(0,0), (2,208), (2,494), (2,780): three of four backward calls returned (0,0),
each after ten full page layouts. The bisection was unsound in its own space too
- 40 small paragraphs, every page starting on a block boundary, also failed.
Pagination is a pure function, so the page before P is the q with next(q) == P,
and it is found by replaying the chain forward rather than guessing q. Three
sources: the chain recorded as pages are laid out forward (exact, one layout,
covers paging back and forth); replay from the block containing P and then from
earlier blocks (exact when P lies on that chain); and failing that, the last
start before P, which overlaps slightly rather than skipping content.
warm: 4/4 exact, 1 layout each
cold, fresh layouter per call: 12/13 exact, worst 17 layouts
cold, repeated back presses: ~4 layouts per turn
Each step returns a page ending exactly where the reader is, so paging back never
skips or repeats content. That chain can differ from the one seen reading forward
from page one if the reader arrived by a jump - pagination from a different start
is a different chain, and nothing can recover the original without replaying the
whole document.
Complementary to S11 rather than caused by it: before S11 forward pagination
dead-ended at the first page-spanning block, so mid-block starts never arose and
the block-granular search looked adequate.
dtourolle
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