Push 3 Standard-tier: optimal break search (replace greedy first-fit)

Casting-off's greedy first-fit + tail-only widow rebalance is replaced by a
deterministic badness-minimizing break search (optimal_breaks, a Knuth-Plass-
style dynamic program over the measure boundaries). ENGRAVER_VERSION 9 -> 10.

Objective: minimize the sum over ALL systems of the squared normalized underfill
((width_limit - w)/width_limit)^2. Squaring evens the systems; including the
FINAL system in the sum subsumes the old widow rebalance (the optimizer won't
leave a narrow final stub if a balanced partition is cheaper). It is the
additive, DP-tractable analog of the retired distribution_cost (max of the
catalog's break penalty and width-CV imbalance). On the ten-measure fixture the
search settles on 5/4 measures where greedy left a fuller-then-shorter split,
filling the final system more and pulling casting_off_quality down (~0.80 ->
~0.61) — the payoff, visible now that horizontal justification drives
system_break to ~0 so casting_off mostly sees the last system's fullness.

Break requirements (hard/soft/page) bound the DP's segments — a system may not
span a forced break — and walk_region still honours them and records skipped
content-less soft breaks as IrOverride, unchanged; optimal_breaks reports only
the automatic breaks. A system may exceed the width only as a single
unsplittable measure. Minimal still makes no optimality claim.

Deterministic: minimizes lexicographic (cost, system_count). Tests:
optimal_breaks_{balances_systems_and_avoids_a_final_widow, never_spans_a_forced_
break, is_deterministic_and_empty_when_unbounded}; the widow test now checks the
balanced measure distribution; wrapping-fixture metrics updated (casting_off
improved). Removed rebalance_widows/rebalance_region/distribution_cost + their
tests. Goldens regenerated (balanced systems; view_box stable — justification
still fills to width). 944 tests, clippy 0, docs -D warnings, conformance 8/8.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
This commit is contained in:
Levi Neuwirth 2026-07-08 21:29:08 -04:00
parent 0db005db9a
commit c818992835
8 changed files with 704 additions and 738 deletions

View File

@ -22,14 +22,15 @@ first axis of the planned two-pass spring layout — later joined by real
hard-constraint evaluation (which earned the `Minimal` tier).
**Phase 3's layout track adds CASTING-OFF** (see "Casting-off (2026-07)" below):
greedy system breaking at measure boundaries, vertical system stacking, page
system breaking at measure boundaries, vertical system stacking, page
assignment, a populated `ResolvedPage`/`ResolvedSystem` tree, and full break-
constraint evaluation. **Push 3's Standard-tier track then adds per-system
JUSTIFICATION** (see "Per-system justification (Push 3)" below): every non-final
system stretches to fill the content width; and **vertical justification** (same
section): the systems of a non-final page spread to fill the page height. Still
deferred: the inter-staff soft-spring solve *within* a system (band-height
renegotiation), and optimal (lookahead) break search.
section): the systems of a non-final page spread to fill the page height; and
**optimal break search** (see "Optimal break search (Push 3)" below) replaces
greedy first-fit + widow rebalance. Still deferred: the inter-staff soft-spring
solve *within* a system (band-height renegotiation).
### Honest tier
@ -39,8 +40,8 @@ report `SolverTier::Stub`, never `Minimal` (Chapter 9 §"Conformance Tiers").
`Engraver::tier()` reported `Stub` until real hard-constraint satisfaction
landed and now reports `Minimal` — which it fully earns after casting-off: the
break constraint family is genuinely supported (spec §"Conformance Tiers",
Minimal row), and `Minimal` makes no optimality claim, so greedy first-fit
casting-off is legitimate. Since the Quality Metric Catalog companion's
Minimal row), and `Minimal` makes no optimality claim, so the break search
(originally greedy first-fit, now a badness-minimizing search) is legitimate. Since the Quality Metric Catalog companion's
ratification, the solve also reports a **real quality-metric vector**
accurate metric vectors are part of the Minimal claim — computed per the
catalog's formulas (see "Quality metrics (2026-07)" below). The all-worst
@ -82,19 +83,15 @@ inputs the solver cannot measure.
## Casting-off (2026-07) — decisions
1. **Greedy first-fit system breaking, at measure boundaries.** The casting-off
walk visits each region's spaced spring-slot columns in x order and breaks
before a **barline column** (this projection draws each measure's barline at
its *start* column, so breaking before the barline keeps every measure
intact; the region-final barline closes the region and is never a
candidate) whenever the measure beginning there would overflow the page
content width. Rationale: `SolverTier::Minimal` requires the break family
supported and hard constraints satisfied, with **no optimality claim**
(Chapter 9 §"Conformance Tiers"), so an optimal (KnuthPlass-style) search
is deliberately rejected at this tier — greedy first-fit is deterministic,
linear, and easy to validate. Consequences accepted and documented:
a region with no measures never wraps automatically; a single measure wider
than the page yields an overfull system (no mid-measure emergency break).
1. **System breaking at measure boundaries.** Breaks fall only before a
**barline column** (this projection draws each measure's barline at its
*start* column, so breaking before the barline keeps every measure intact;
the region-final barline closes the region and is never a candidate).
*Originally greedy first-fit; replaced in Push 3 by an optimal break search
— see "Optimal break search (Push 3)" below.* Consequences accepted and
documented: a region with no measures never wraps automatically; a single
measure wider than the page yields an overfull system (no mid-measure
emergency break).
2. **Break-constraint semantics: "breaks at slot S" ⇔ S starts a system.** A
`SystemBreakAt`/`PageBreakAt` is satisfied iff the final layout starts a
system/page at that slot (a region's first slot is trivially at a
@ -642,3 +639,43 @@ stage's staff stacking is preserved verbatim; `vertical_density_penalty`
measures it but nothing renegotiates it). That needs vertical pressure — a
collision or a target — to be meaningful, and multi-staff systems to exercise;
a later tranche.
## Optimal break search (Push 3, 2026-07-08)
Casting-off's greedy first-fit + tail-only widow rebalance is replaced by a
deterministic **badness-minimizing break search** (`optimal_breaks`, a
KnuthPlass-style dynamic program). `ENGRAVER_VERSION` 9 → 10 (a wrapping
score's measures partition into different, more balanced systems, so its breaks
and all flowing geometry differ; a non-wrapping score is unchanged).
**Objective.** Minimize the sum over ALL systems of the squared normalized
underfill `((width_limit w)/width_limit)²`. Squaring evens the systems (a
lopsided split costs more than a balanced one); including the FINAL system in
the sum is what subsumes the old `rebalance_widows` (the optimizer will not
leave a narrow final stub if a more balanced partition is cheaper). It is the
additive, DP-tractable analog of the retired `distribution_cost` (max of the
catalog's break penalty and width-CV imbalance): both reward filled, even
systems, but the additive form admits a polynomial DP over the measure
boundaries. On the ten-measure fixture the search settles on **5/4 measures**
where greedy + rebalance left a fuller-then-shorter split, which fills the final
system more and pulls `casting_off_quality` down (~0.80 → ~0.61) — the payoff,
visible now that horizontal justification has driven `system_break` to ~0 so
the last system's fullness is what `casting_off` mostly sees.
**Requirements and overfull.** The break REQUIREMENTS (hard / soft / page)
bound the DP's segments — a system may not span a forced break — and
`walk_region` still honours them (and records a skipped content-less soft break
as an `IrOverride`, unchanged); `optimal_breaks` reports only the AUTOMATIC
breaks. A system may not exceed the content width unless it is a **single
unsplittable measure** (an overfull lone measure, which greedy also emitted; not
charged, since nothing can be done). `Minimal` still makes **no optimality
claim** — this is a deterministic global heuristic, an honest improvement on
first-fit, not a formal guarantee.
**Determinism.** A pure function of the slot extents and requirements; the DP
minimizes lexicographic `(cost, system_count)` (fewer systems — hence fewer
pages — breaks ties), and among equal `(cost, count)` the earliest-considered
predecessor wins. Tests: `optimal_breaks_balances_systems_and_avoids_a_final_
widow`, `optimal_breaks_never_spans_a_forced_break`,
`optimal_breaks_is_deterministic_and_empty_when_unbounded`; the widow test now
checks the balanced measure distribution the DP produces.

View File

@ -3,30 +3,33 @@
//! "resolve\[s\] page and system breaks"; Chapter 7 §"ResolvedLayoutIR" defines
//! the page/system tree this pass populates).
//!
//! ## The algorithm (greedy first-fit, then a widow rebalance)
//! ## The algorithm (optimal break search)
//!
//! [`SolverTier::Minimal`](epiphany_layout_ir::SolverTier) requires the break
//! constraint family to be supported and every hard constraint satisfied (or an
//! honest `Unsatisfiable`); it makes **no optimality claim**, so casting-off is
//! a deterministic two-phase heuristic, not an optimal (KnuthPlass-style) break
//! search. Phase 1 is greedy first-fit; phase 2 (`rebalance_widows`) evens the
//! system widths so the final system is not left a narrow stub. Phase 1:
//! honest `Unsatisfiable`); it makes **no optimality claim**. Casting-off uses a
//! deterministic **badness-minimizing break search** (`optimal_breaks`, a
//! KnuthPlass-style dynamic program) — an honest improvement on the earlier
//! greedy-first-fit-plus-widow-rebalance, not a formal optimality guarantee.
//!
//! 1. **System breaking.** Per region, walk the spaced spring-slot columns in x
//! order. Break into systems at **measure boundaries** — the barline columns
//! (`to_constrained` draws each measure's barline at its start column; the
//! region-final barline closes the region and is never a break candidate) —
//! whenever the measure beginning at a barline would overflow the page
//! content width. A **hard** `SystemBreakAt`/`PageBreakAt` is *always*
//! honoured at its slot (the slot begins a new system/page); a **soft** one
//! is honoured unless doing so would close a system with no musical content
//! (no notehead/rest column) — the documented exceptional path, recorded as
//! an [`EngravingDecision`] with [`DecisionSource::IrOverride`] per the
//! spec's override-resolution rule (an unhonoured override is recorded, not
//! silently dropped). A region with no measures has no automatic break
//! candidates: it stays one (possibly overfull) system unless breaks force
//! otherwise. A single measure wider than the page yields an overfull
//! system — Minimal does not break mid-measure on its own.
//! 1. **System breaking.** Per region, partition the measures into systems to
//! minimize the total squared normalized underfill over ALL systems — which
//! evens them (no lopsided split) and fills them (no needless breaks), the
//! additive analog of the Quality Metric Catalog's break/imbalance
//! distribution cost; including the final system in the sum is what removes
//! the old separate widow rebalance. Breaks fall only at **measure
//! boundaries** — the barline columns (`to_constrained` draws each measure's
//! barline at its start column; the region-final barline closes the region
//! and is never a break candidate). A **hard** `SystemBreakAt`/`PageBreakAt`
//! is *always* honoured at its slot (and bounds the search's segments); a
//! **soft** one is honoured unless doing so would close a system with no
//! musical content (no notehead/rest column) — the documented exceptional
//! path, recorded as an [`EngravingDecision`] with
//! [`DecisionSource::IrOverride`] per the spec's override-resolution rule (an
//! unhonoured override is recorded, not silently dropped). A region with no
//! measures has no break candidates: it stays one (possibly overfull) system
//! unless breaks force otherwise. A single measure wider than the page yields
//! an overfull system — Minimal does not break mid-measure on its own.
//! 2. **Vertical stacking.** Each system's height is its real content extent
//! (glyph boxes plus stroke extents — the vertical spring solve that would
//! renegotiate band heights is deferred, so the constrained `y` geometry is
@ -44,15 +47,6 @@
//! flat glyph/stroke lists remain the renderer's and hit-tester's single
//! coordinate space — no per-page transform exists anywhere downstream.
//!
//! Phase 2 (`rebalance_widows`, run between system breaking and stacking)
//! moves whole trailing measures from a region's penultimate system into its
//! final one to even their widths — the anti-widow refinement, choosing the
//! shift that minimizes the larger of the two distribution penalties the
//! Quality Metric Catalog defines for the break family (width imbalance vs
//! non-final underfill). It leaves the system *count* unchanged and never
//! disturbs a constraint-pinned boundary, so the break structure phase 1
//! established still holds.
//!
//! ## Region-spanning strokes
//!
//! A stroke confined to one system (a stem, a ledger, a barline-anchored mark)
@ -547,11 +541,9 @@ pub(crate) fn cast_off(
);
}
// ---- Widow rebalance (casting-off phase 2) ----------------------------
// Greedy first-fit fills every non-final system maximally, which can leave
// a region's final system a narrow stub; even the system widths without
// moving any constraint-pinned boundary or changing the system count.
rebalance_widows(&mut systems, &region_slots, &reqs, width_limit);
// (The old greedy pass needed a second widow-rebalance phase here; the
// optimal break search evens the final system directly — see
// `optimal_breaks`.)
// ---- Stroke fates ------------------------------------------------------
// Which system each slot landed in, and each region's slot span / per-system
@ -1030,7 +1022,110 @@ fn page_top_content(p: usize, geometry: &PageGeometry) -> f32 {
-(p as f32) * (geometry.size.height.0 + INTER_PAGE_GAP) - geometry.margins.top.0
}
/// Greedy first-fit walk over one region's slots (see the module docs).
/// Optimal automatic system breaks for one region: a badness-minimizing
/// (KnuthPlass-style) partition of the region's measures into systems,
/// replacing greedy first-fit. Returns the slot ids at which an AUTOMATIC break
/// opens a system — the break REQUIREMENTS (hard / soft / page, which bound the
/// DP's segments) are honoured by [`walk_region`] itself, and never appear here.
///
/// **Objective.** Minimize the sum over ALL systems of the squared normalized
/// underfill `((width_limit w) / width_limit)²`. Squaring evens the systems
/// (a lopsided split costs more than a balanced one), and including the *final*
/// system in the sum is what subsumes the old tail-only widow rebalance — the
/// optimizer will not leave a narrow final stub if a more even partition is
/// cheaper. It is the additive, DP-tractable analog of the catalog's
/// break/imbalance distribution cost (`distribution_cost`, now retired): both
/// reward filled, even systems. A system may not exceed the content width unless
/// it is a **single unsplittable measure** (an overfull lone measure, which the
/// greedy pass also emitted). `Minimal` still makes no optimality *claim*; this
/// is a deterministic global heuristic, an honest improvement on first-fit.
///
/// **Determinism.** A pure function of the slot extents and requirements; the
/// DP minimizes the lexicographic `(cost, system_count)` (fewer systems breaks
/// ties, so ties favour fewer pages), and among equal `(cost, count)` the
/// earliest-considered predecessor (the largest final system) wins.
fn optimal_breaks(
slots: &[SlotInfo],
reqs: &BTreeMap<SpringSlotId, Vec<BreakReq>>,
width_limit: f32,
) -> BTreeSet<SpringSlotId> {
let mut automatic = BTreeSet::new();
if !width_limit.is_finite() || width_limit <= 0.0 || slots.is_empty() {
return automatic; // unbounded width: nothing wraps
}
let breakable = |slot: &SlotInfo| slot.barline && !slot.final_barline;
// Measure-boundary positions in slot-index space: region start, each
// breakable barline, region end. `forced[k]` marks a boundary carrying a
// break requirement (the DP may not span it). The region end is a boundary.
let mut pts: Vec<usize> = vec![0];
let mut forced: Vec<bool> = vec![false];
for (i, slot) in slots.iter().enumerate() {
if i > 0 && breakable(slot) {
pts.push(i);
forced.push(reqs.contains_key(&slot.id));
}
}
pts.push(slots.len());
forced.push(true);
let n = pts.len(); // n - 1 measures between the n boundaries
// A system spanning boundaries [a, b): its ink extent over slots
// `[pts[a] .. pts[b])`.
let width = |a: usize, b: usize| -> f32 {
let range = &slots[pts[a]..pts[b]];
let lo = range.iter().map(|s| s.lo).fold(f32::INFINITY, f32::min);
let hi = range.iter().map(|s| s.hi).fold(f32::NEG_INFINITY, f32::max);
(hi - lo).max(0.0)
};
// dp[b] = the min `(cost, system_count)` to partition measures [0, b).
let mut dp: Vec<(f64, usize)> = vec![(f64::INFINITY, usize::MAX); n];
let mut from: Vec<usize> = vec![0; n];
dp[0] = (0.0, 0);
for b in 1..n {
for a in 0..b {
// A system may not skip a forced break at an interior boundary.
if (a + 1..b).any(|k| forced[k]) {
continue;
}
let (prev_cost, prev_count) = dp[a];
if !prev_cost.is_finite() {
continue;
}
let w = width(a, b);
let bad = if w <= width_limit {
let u = f64::from((width_limit - w) / width_limit);
u * u
} else if b - a == 1 {
0.0 // a lone measure wider than the page: unavoidable, not charged
} else {
continue; // overfull and splittable: not a valid system
};
let cand = (prev_cost + bad, prev_count + 1);
if cand < dp[b] {
dp[b] = cand;
from[b] = a;
}
}
}
// Reconstruct the partition; its non-forced boundaries are the automatic
// breaks `walk_region` adds to its requirement-driven ones.
if dp[n - 1].0.is_finite() {
let mut b = n - 1;
while b > 0 {
let a = from[b];
if a > 0 && !forced[a] {
automatic.insert(slots[pts[a]].id);
}
b = a;
}
}
automatic
}
/// Walks one region's slots, opening a system at each break requirement and at
/// each optimal automatic break (`optimal_breaks`).
#[allow(clippy::too_many_arguments)]
fn walk_region(
region: usize,
@ -1042,25 +1137,13 @@ fn walk_region(
systems: &mut Vec<SystemPlan>,
skipped: &mut Vec<EngravingDecision>,
) {
// Measure look-ahead: `chunk_hi[i]` is the rightmost content edge of the
// chunk beginning at slot `i` — through the slot before the next breakable
// barline (the region-final barline closes the last chunk, so it never
// starts one).
let breakable = |slot: &SlotInfo| slot.barline && !slot.final_barline;
let mut chunk_hi = vec![f32::NEG_INFINITY; slots.len()];
for i in (0..slots.len()).rev() {
let next = if i + 1 < slots.len() && !breakable(&slots[i + 1]) {
chunk_hi[i + 1]
} else {
f32::NEG_INFINITY
};
chunk_hi[i] = slots[i].hi.max(next);
}
// The optimal automatic breaks (a global badness-minimizing partition,
// bounded by the break requirements); the walk opens a system at each.
let automatic = optimal_breaks(slots, reqs, width_limit);
let mut local = 0usize;
let mut current: Vec<usize> = Vec::new();
let mut has_note = false;
let mut current_lo = f32::INFINITY;
let mut open_boundary: Option<Boundary> = None;
let mut open_page_forced = false;
let mut open_page_source = DecisionSource::Automatic;
@ -1081,7 +1164,6 @@ fn walk_region(
}
current.push(i);
has_note = slot.note;
current_lo = slot.lo;
continue;
}
let mut break_here = false;
@ -1111,9 +1193,10 @@ fn walk_region(
source = origin_source(origins, slot.id, req.page);
}
}
// Greedy first-fit: at a measure boundary, break when the measure
// beginning here would overflow the content width.
if !break_here && breakable(slot) && has_note && chunk_hi[i] - current_lo > width_limit {
// Optimal casting-off: open a system at a chosen automatic break, as
// long as the closing system carries musical content (a lead-only
// system is never torn off — matching the requirement path's rule).
if !break_here && has_note && automatic.contains(&slot.id) {
break_here = true;
}
if break_here {
@ -1138,11 +1221,9 @@ fn walk_region(
};
current.push(i);
has_note = slot.note;
current_lo = slot.lo;
} else {
current.push(i);
has_note |= slot.note;
current_lo = current_lo.min(slot.lo);
}
}
// The region's last system — or, for a region with no slots at all, its
@ -1157,197 +1238,6 @@ fn walk_region(
});
}
/// **Widow rebalance** — the casting-off pass's second phase (module docs). The
/// greedy first-fit walk fills each non-final system as full as the content
/// width allows, which is optimal for *page fill* but can leave the region's
/// **final** system a narrow stub (a "widow") — exactly what the Quality Metric
/// Catalog's `casting_off_quality` axis penalizes. This pass evens the region's
/// system widths by moving whole trailing measures from the penultimate system
/// into the final one.
///
/// The shift is chosen to **minimize the larger of the two distribution
/// penalties the catalog defines for the break family**: the system-width
/// *imbalance* (`casting_off_quality`, the coefficient of variation of the
/// region's system widths) and the non-final *break* penalty
/// (`system_break_penalty`, the mean of `|W w|/W` over non-final systems).
/// Each is computed by the same formula the metric census uses (see
/// [`distribution_cost`]). The two axes pull against each other —
/// filling non-final systems (few, wide systems) worsens imbalance; equalizing
/// widths (empty non-final systems) worsens underfill — and both share the
/// catalog's `0.5` worst-tolerable anchor, so their raw quantities are compared
/// directly and the minimizer of their maximum is the width that best satisfies
/// both. It is not a claim of optimality (Minimal makes none); it is a
/// deterministic anti-widow heuristic.
///
/// Only a region's **last** boundary moves, and only when greedy placed it — an
/// `Automatic` boundary with no break requirement or page force pinned to its
/// slot. A user/IR-anchored or page-forced boundary is never disturbed, and the
/// **system count is unchanged**, so page assignment and every break-count
/// invariant the walk established still hold. The penultimate system keeps at
/// least its own first measure (never emptied), and the final system never
/// grows wider than its predecessor (no mirror-image imbalance).
fn rebalance_widows(
systems: &mut [SystemPlan],
region_slots: &[Vec<SlotInfo>],
reqs: &BTreeMap<SpringSlotId, Vec<BreakReq>>,
width_limit: f32,
) {
if !(width_limit.is_finite() && width_limit > 0.0) {
return; // unbounded width: nothing wraps, nothing to even out
}
let w_limit = f64::from(width_limit);
// A region's systems are a contiguous run in `systems` (walk_region appends
// them per region, in region order); rebalance each run independently.
let mut start = 0;
while start < systems.len() {
let region = systems[start].region;
let mut end = start;
while end < systems.len() && systems[end].region == region {
end += 1;
}
rebalance_region(
&mut systems[start..end],
&region_slots[region],
reqs,
w_limit,
);
start = end;
}
}
/// Rebalances one region's contiguous run of systems (see [`rebalance_widows`]).
fn rebalance_region(
run: &mut [SystemPlan],
slots: &[SlotInfo],
reqs: &BTreeMap<SpringSlotId, Vec<BreakReq>>,
w_limit: f64,
) {
let n = run.len();
if n < 2 {
return; // a single system has no widow to fix
}
let (prev, last) = (n - 2, n - 1);
// The final boundary must be a greedy one to move it: an `Automatic` system
// break with no break requirement or page force pinned to its slot.
let Some(boundary) = run[last].boundary else {
return;
};
if boundary.source != DecisionSource::Automatic
|| run[last].page_forced
|| reqs.contains_key(&boundary.slot)
{
return;
}
let width = |idx: &[usize]| -> f64 {
let lo = idx
.iter()
.map(|&k| slots[k].lo)
.fold(f32::INFINITY, f32::min);
let hi = idx
.iter()
.map(|&k| slots[k].hi)
.fold(f32::NEG_INFINITY, f32::max);
if hi > lo {
f64::from(hi - lo)
} else {
0.0
}
};
// Widths of the systems before the penultimate stay fixed (only the last
// boundary moves); the objective's coefficient of variation ranges over all.
let fixed: Vec<f64> = run[..prev].iter().map(|p| width(&p.slots)).collect();
// Measure-start positions within the penultimate system — local indices into
// its slot list. The first is the system's own opening (immovable); a split
// at a later one moves that measure and the rest into the final system.
let starts: Vec<usize> = run[prev]
.slots
.iter()
.enumerate()
.filter(|(_, &k)| slots[k].measure_barline.is_some())
.map(|(local, _)| local)
.collect();
if starts.len() < 2 {
return; // the penultimate system has one measure — nothing to lend
}
// Baseline: the greedy split (move nothing). Iterate candidate splits from
// the fewest measures moved (latest start) so ties keep the fuller
// predecessor; accept only a strict improvement.
let mut best_cost = distribution_cost(
&fixed,
width(&run[prev].slots),
width(&run[last].slots),
w_limit,
);
let mut best_split: Option<usize> = None;
for &split in starts.iter().skip(1).rev() {
let kept = &run[prev].slots[..split];
let moved = &run[prev].slots[split..];
let last_slots: Vec<usize> = moved.iter().chain(&run[last].slots).copied().collect();
let (w_prev, w_last) = (width(kept), width(&last_slots));
if w_last > w_prev {
continue; // never grow the final system past its predecessor
}
let cost = distribution_cost(&fixed, w_prev, w_last, w_limit);
if cost < best_cost - 1e-9 {
best_cost = cost;
best_split = Some(split);
}
}
if let Some(split) = best_split {
let moved: Vec<usize> = run[prev].slots[split..].to_vec();
let new_boundary_slot = slots[run[prev].slots[split]].id;
run[prev].slots.truncate(split);
let mut new_last = moved;
new_last.extend_from_slice(&run[last].slots);
run[last].slots = new_last;
run[last].boundary = Some(Boundary {
slot: new_boundary_slot,
source: DecisionSource::Automatic,
});
}
}
/// The rebalance objective (see [`rebalance_widows`]): the larger of the two raw
/// distribution penalties over a region's system widths — the **break** penalty
/// and the width **imbalance**. Both normalize against the catalog's shared
/// `0.5` anchor, so comparing and taking the max of the raw quantities orders
/// candidates exactly as the max of the two normalized metrics does. Each raw is
/// computed by the *same* formula as the axis it stands in for, so the rebalance
/// optimizes against the values the `quality` module will report:
///
/// * **break** — `quality::system_break_raw`'s mean of `|W w| / W` over the
/// **non-final** systems (absolute, so an overfull non-final system is
/// penalized too);
/// * **imbalance** — `quality::casting_off_raw`'s coefficient of variation over
/// **all** the region's system widths.
fn distribution_cost(fixed: &[f64], w_prev: f64, w_last: f64, w_limit: f64) -> f64 {
let mut widths: Vec<f64> = fixed.to_vec();
widths.push(w_prev);
widths.push(w_last);
let count = widths.len();
// Break penalty: mean absolute deviation from the content width over the
// non-final systems (the final system is exempt) — `system_break_raw`.
let non_final = &widths[..count - 1];
let breaks = if non_final.is_empty() {
0.0
} else {
non_final
.iter()
.map(|&w| (w_limit - w).abs() / w_limit)
.sum::<f64>()
/ non_final.len() as f64
};
// Imbalance: the coefficient of variation of all system widths — `casting_off_raw`.
let mean = widths.iter().sum::<f64>() / count as f64;
let imbalance = if mean > 0.0 {
let variance = widths.iter().map(|w| (w - mean) * (w - mean)).sum::<f64>() / count as f64;
variance.sqrt() / mean
} else {
0.0
};
breaks.max(imbalance)
}
/// Decides how a stroke rides the cast systems (see [`StrokeFate`]).
fn stroke_fate(
stroke: &Stroke,
@ -1847,49 +1737,81 @@ mod tests {
);
}
/// A uniform test measure: one break-candidate barline slot per measure,
/// spanning `[i·10, i·10 + 9]` (each measure ~9 wide, step 10).
fn measure_slot(i: usize) -> SlotInfo {
SlotInfo {
id: SpringSlotId(i as u128 + 1),
x: i as f32 * 10.0,
lo: i as f32 * 10.0,
hi: i as f32 * 10.0 + 9.0,
members: Vec::new(),
barline: true,
final_barline: false,
note: true,
measure_barline: None,
}
}
#[test]
fn distribution_cost_prefers_the_even_split_over_greedy_and_full_balance() {
// The RS-1 two-system candidates, glyph-ink widths (staff spaces) from
// the ten-measure fixture at the default 90-wide content area. The
// widow rebalance minimizes the larger of imbalance (CV) and worst
// non-final underfill; the greedy 8/2 stub and the fully balanced 5/5
// both score worse than the six/four split it settles on.
let w = 90.0;
let greedy = distribution_cost(&[], 78.57, 18.76, w); // 8/2 stub
let six_four = distribution_cost(&[], 59.52, 37.80, w); // rebalanced
let five_five = distribution_cost(&[], 50.00, 47.33, w); // full balance
fn optimal_breaks_balances_systems_and_avoids_a_final_widow() {
// Six uniform measures; the content width fits four (4 measures span 39,
// 5 span 49). Greedy first-fit packs [4, 2] — a short final system;
// the optimal search balances to [3, 3] (lower total squared underfill),
// subsuming the old widow rebalance. One automatic break, before the
// fourth measure.
let slots: Vec<SlotInfo> = (0..6).map(measure_slot).collect();
let breaks = optimal_breaks(&slots, &BTreeMap::new(), 42.0);
assert_eq!(
breaks.len(),
1,
"one automatic break → two systems: {breaks:?}"
);
assert!(
six_four < greedy && six_four < five_five,
"6/4 ({six_four:.4}) must beat greedy ({greedy:.4}) and 5/5 ({five_five:.4})"
breaks.contains(&slots[3].id),
"the break is before the 4th measure (a 3/3 split): {breaks:?}"
);
}
#[test]
fn distribution_cost_uses_the_mean_break_penalty_not_the_worst() {
// For three or more systems the break term must be the MEAN of |W-w|/W
// over the non-final systems — the same quantity `quality::system_break_raw`
// reports — not the worst single system. With one full leading system
// fixed at W, the balanced 45/45 tail must beat the 60/30 tail: its width
// CV is lower, and the mean break penalty (diluted by the full leading
// system) does not dominate. A worst-underfill proxy would wrongly prefer
// 60/30 (its lone short system is less empty), inverting the choice.
let w = 90.0;
let fixed = [90.0]; // one full non-final system
let balanced = distribution_cost(&fixed, 45.0, 45.0, w);
let uneven = distribution_cost(&fixed, 60.0, 30.0, w);
assert!(
balanced < uneven,
"the mean break penalty prefers the balanced tail: {balanced:.4} vs {uneven:.4}"
fn optimal_breaks_never_spans_a_forced_break() {
// A break requirement at the 2nd measure partitions the DP: the first
// segment is a lone measure [0,1); the optimizer works only within
// [1,6). So measure 0 stands alone even though it would pack with more,
// and no automatic break coincides with the forced one.
let slots: Vec<SlotInfo> = (0..6).map(measure_slot).collect();
let mut reqs: BTreeMap<SpringSlotId, Vec<BreakReq>> = BTreeMap::new();
reqs.insert(
slots[1].id,
vec![BreakReq {
page: false,
hard: true,
}],
);
// Pin the mean-not-max semantics exactly: over the non-final systems
// [90, 45] the break penalty is mean(0, 0.5) = 0.25, below the width CV,
// so the objective here is the CV of [90, 45, 45].
let widths = [90.0_f64, 45.0, 45.0];
let mean = widths.iter().sum::<f64>() / 3.0;
let cv = (widths.iter().map(|x| (x - mean).powi(2)).sum::<f64>() / 3.0).sqrt() / mean;
let breaks = optimal_breaks(&slots, &reqs, 42.0);
assert!(
(balanced - cv).abs() < 1e-12,
"the objective should equal the width CV here: {balanced} vs {cv}"
!breaks.contains(&slots[1].id),
"the forced break is walk_region's, never reported here: {breaks:?}"
);
// The remaining measures [1..6) (5 of them, width 49 > 42) split
// optimally within their segment — every reported break is inside it.
for id in &breaks {
assert!(
slots[2..].iter().any(|s| s.id == *id),
"an automatic break stays inside the post-requirement segment: {id:?}"
);
}
}
#[test]
fn optimal_breaks_is_deterministic_and_empty_when_unbounded() {
let slots: Vec<SlotInfo> = (0..6).map(measure_slot).collect();
let a = optimal_breaks(&slots, &BTreeMap::new(), 42.0);
let b = optimal_breaks(&slots, &BTreeMap::new(), 42.0);
assert_eq!(a, b, "a pure function of the inputs");
assert!(
optimal_breaks(&slots, &BTreeMap::new(), f32::INFINITY).is_empty(),
"an unbounded width wraps nothing"
);
}

View File

@ -195,8 +195,13 @@ pub struct Engraver {
/// non-final page spread so the last one's bottom reaches the content bottom,
/// filling the page height; a multi-page score's baked geometry differs, while
/// a single-page score — whose only page is ragged-bottom by convention — is
/// unchanged), and to `10` when casting-off replaced greedy first-fit + widow
/// rebalance with an **optimal (badness-minimizing) break search** (a wrapping
/// score's measures partition into more balanced systems — e.g. a 5/4 split
/// where greedy left a fuller-then-stub one — so its system breaks, and every
/// geometry that flows from them, differ; a score that does not wrap is
/// unchanged).
pub const ENGRAVER_VERSION: SolverVersion = SolverVersion(9);
pub const ENGRAVER_VERSION: SolverVersion = SolverVersion(10);
impl Engraver {
/// An engraver casting off against the given page geometry.

View File

@ -681,21 +681,22 @@ mod tests {
"the non-final system fills the width after justification: {}",
vector.system_break_penalty.0
);
// The width-uniformity axes RISE as a consequence: the justified
// non-final system now spans the full width while the last stays
// ragged-right, so the two systems' ink widths (and their glyph
// densities) differ more than the rebalanced natural widths did. This
// is honest for a two-system score (one full line, one short last
// line); a metric refinement that scores casting-off on natural widths
// or excludes the intentionally-ragged final system is a follow-up (see
// DECISIONS).
// The width-uniformity axes are non-zero: the justified non-final system
// spans the full width while the last stays ragged-right, so the two
// systems' ink widths (and their glyph densities) differ. Optimal
// casting-off balances the split (5/4 measures, not greedy's 6-plus/stub),
// which fills the final system more and pulls casting_off DOWN from the
// greedy value (~0.80 → ~0.61) — the break search's payoff. Still honest
// for a two-system score (one full line, one shorter last line); a metric
// refinement that scores casting-off on natural widths or excludes the
// intentionally-ragged final system is a follow-up (see DECISIONS).
assert!(
(0.7..0.9).contains(&vector.casting_off_quality.0),
"the full non-final system contrasts with the ragged last: {}",
(0.5..0.7).contains(&vector.casting_off_quality.0),
"the balanced split leaves a moderate full-vs-ragged contrast: {}",
vector.casting_off_quality.0
);
assert!(
(0.3..0.5).contains(&vector.symbol_density_uniformity.0),
(0.45..0.65).contains(&vector.symbol_density_uniformity.0),
"density differs between the stretched and the ragged system: {}",
vector.symbol_density_uniformity.0
);
@ -767,12 +768,13 @@ mod tests {
.events
.clone();
let id: SlurId = score.identity.mint();
// Events 22→26 straddle the fixture's two-system break (a ~one-measure
// span, wide enough that the height clamp does not bind → ρ ≈ 0.16).
// Events 14→24 straddle the fixture's centred two-system break (optimal
// casting-off balances to ~5/4 measures), wide enough that the height
// clamp does not bind → ρ ≈ 0.16.
score.cross_cutting.slurs.push(Slur {
id,
start_event: ev[22],
end_event: ev[26],
start_event: ev[14],
end_event: ev[24],
kind: SlurKind::Legato,
curvature_override: None,
style: SpanStyle::default(),

View File

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