Compose a box down its chain once, not once a level

Bryan's call, 2026-09-16, for correctness. `Moves` walked the move chain in
`Len`, so every level's four multiplies landed back on the grid before the
next started and the residue grew with the depth of the tree. `WideLen`
carries a length through the walk on a grid twenty-four bits of a box and
twenty-two of a pixel finer, and rounds once at the end.

What it buys, measured rather than argued: `Holds::through`'s allowance for
the two routes to a length drops from three half steps to two, and the whole
of a box now maps back to a range one step wide rather than one step per
level of nesting. One half step further is arithmetically available -- the
`Holds` assertion is quiet there and the whole-box case becomes an exact
identity -- and it is **not taken**, because shrinker seed 220 then lays out
differently warm than cold. Too narrow is meant to cost a redraw and no more;
there it re-breaks a wrapping text, whose reported width moves a `Branch`
onto its other subtree. That is the unsettled-text family, and closing it is
what would let this go lower. The note is in `through`.

`Moves` now answers three questions instead of one, and they are different
questions: `size_of` for how long a box is, which is what reads a box in
pixels; `compose` for where both of its ends are, which is what compares two
boxes; and `resolve`, unchanged, for the `Len` walk the vertex shader does
again in floats. A length composes on its own in two multiplies a level
rather than four, since where the parent sits falls out of the difference --
which is most of why this is not slower.

Measured on the fixed-shape fixture, seed 1 depth 8, 500 frames of `many`,
medians of 25 runs with all twenty-five work counters identical between the
two: 1,880M instructions and 755M cycles against 1,908M and 760M. So it is
free, and a little better on instructions. Three things were tried on the way
and two kept: composing the length alone rather than both ends (-111M
instructions), taking the pixel term's fraction on the ordinary grid so it
stays in an `i64` (-2M instructions, -8M cycles), and skipping a parent that
spans its own box, which **cost** 18M instructions and is not here -- the
same verdict a short-circuit got in `UiSpan::within`.

Checked: fmt, clippy, 83 suite tests, 17 core unit tests, the release oracle
at 100 seeds and at 1000 seeds of depth 6, all fifteen shrinker cases at 400
seeds of depth 5, and `tabs`, `view`, `minimal`, `text` and `random`
byte-identical at 1920x1200 against `d21a215`.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

core/src/orientation/mod.rs

@@ -2,6 +2,7 @@ mod align;
 mod axis;
 mod len;
 mod pos;
+mod wide;
 
 use crate::util::Vec2;
 
@@ -9,3 +10,4 @@ pub use align::*;
 pub use axis::*;
 pub use len::*;
 pub use pos::*;
+pub use wide::*;

core/src/orientation/wide.rs

@@ -0,0 +1,167 @@
+use crate::{PX_SHIFT, PixelRegion, Px, PxVec2, REL_SHIFT, UiRegion, UiSpan};
+
+use super::Len;
+
+/// How many bits of a box a [`WideLen`] keeps, and how many of a pixel. Both
+/// are the grid's own shift plus the room an `i64` has left over: a `Rel` is
+/// a fraction of a box and needs eight bits above the point, a `Px` counts up
+/// to two million of them and needs twenty-two.
+const WIDE_REL: u32 = 48;
+const WIDE_PX: u32 = 32;
+const REL_GAIN: u32 = WIDE_REL - REL_SHIFT;
+const PX_GAIN: u32 = WIDE_PX - PX_SHIFT;
+
+/// A length part-way through a composition, on a finer grid than the [`Len`]
+/// it came from and will go back to.
+///
+/// Composing a box through its ancestors is four multiplies a level, and in
+/// `Len` every one of them lands back on the grid before the next starts, so
+/// the error grows with the depth of the tree. Stepping through this instead
+/// rounds once, at the end -- which matters because the same box is reached
+/// two ways, composed down the chain and measured against the window, and a
+/// structural layout decision turns on the two being one number.
+///
+/// Twenty-four extra bits of a box and twenty-two of a pixel are far more
+/// than a chain can spend: the residue is `2^-48` of a box a level, against
+/// `2^-24` before.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub struct WideLen {
+    /// Counts `1/2^WIDE_REL` of the box this length is a part of.
+    rel: i64,
+    /// Counts `1/2^WIDE_PX` of a pixel.
+    px: i64,
+}
+
+impl WideLen {
+    pub const fn of(len: Len) -> Self {
+        Self {
+            rel: (len.rel.raw() as i64) << REL_GAIN,
+            px: (len.px.raw() as i64) << PX_GAIN,
+        }
+    }
+
+    /// This length composed through the box it sits in, which is the same
+    /// expression [`Len::within`] uses with the rounding left out. The parent
+    /// is a stored box and so is on the ordinary grid; only the part being
+    /// carried needs the room.
+    pub const fn within(self, parent: &UiSpan) -> Self {
+        let rel_span = (parent.end.rel.raw() - parent.start.rel.raw()) as i128;
+        let px_span = (parent.end.px.raw() - parent.start.px.raw()) as i128;
+        let rel = ((parent.start.rel.raw() as i64) << REL_GAIN)
+            + ((rel_span * self.rel as i128) >> REL_SHIFT) as i64;
+        // A pixel span of the parent, taken at this length's fraction of it:
+        // the product is `WIDE_REL + PX_SHIFT` bits under the point and the
+        // answer is `WIDE_PX`, so what comes off is the difference.
+        let px = self.px
+            + ((parent.start.px.raw() as i64) << PX_GAIN)
+            + ((px_span * self.rel as i128) >> (WIDE_REL + PX_SHIFT - WIDE_PX)) as i64;
+        Self { rel, px }
+    }
+
+    /// Back onto the grid against a box of `len` pixels, which is the one
+    /// rounding a whole composition gets. Both parts are put over
+    /// `WIDE_REL + PX_SHIFT` first so that it is one and not two.
+    pub const fn to_px(self, len: Px) -> Px {
+        let px = (self.px as i128) << (WIDE_REL + PX_SHIFT - WIDE_PX);
+        let rel = self.rel as i128 * len.raw() as i128;
+        Px::from_raw(((px + rel) >> WIDE_REL) as i32)
+    }
+
+    /// A *length* composed through the box it sits in, which is half of what
+    /// the two ends of that box cost: where the parent sits falls out of the
+    /// difference, so a length carries the parent's extent and its pixel span
+    /// and nothing else. Two multiplies a level rather than four.
+    pub const fn len_within(self, parent: &UiSpan) -> Self {
+        let rel_span = (parent.end.rel.raw() - parent.start.rel.raw()) as i128;
+        let px_span = (parent.end.px.raw() - parent.start.px.raw()) as i64;
+        Self {
+            rel: ((rel_span * self.rel as i128) >> REL_SHIFT) as i64,
+            // The pixel term takes the fraction on the ordinary grid, which
+            // keeps it inside an `i64`. Only the fraction itself compounds
+            // multiplicatively and so needs the room: an error of a `Rel`
+            // step here is that step times a pixel span, which is a ten
+            // thousandth of a pixel over a whole window.
+            px: self.px + ((px_span * (self.rel >> REL_GAIN)) >> (PX_SHIFT + REL_SHIFT - WIDE_PX)),
+        }
+    }
+}
+
+/// The two ends of a box, part-way through a composition.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub struct WideSpan {
+    pub start: WideLen,
+    pub end: WideLen,
+}
+
+impl WideSpan {
+    pub const fn of(span: UiSpan) -> Self {
+        Self {
+            start: WideLen::of(span.start),
+            end: WideLen::of(span.end),
+        }
+    }
+
+    pub const fn within(self, parent: &UiSpan) -> Self {
+        Self {
+            start: self.start.within(parent),
+            end: self.end.within(parent),
+        }
+    }
+}
+
+/// How long a box is on each axis, part-way through a composition. What
+/// reads a box in pixels almost always wants this and not where it sits.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub struct WideSize {
+    pub x: WideLen,
+    pub y: WideLen,
+}
+
+impl WideSize {
+    pub const fn of(region: UiRegion) -> Self {
+        Self {
+            x: WideLen::of(region.x.len()),
+            y: WideLen::of(region.y.len()),
+        }
+    }
+
+    pub const fn within(self, parent: &UiRegion) -> Self {
+        Self {
+            x: self.x.len_within(&parent.x),
+            y: self.y.len_within(&parent.y),
+        }
+    }
+
+    pub fn to_px(self, window: PxVec2) -> PxVec2 {
+        PxVec2::new(self.x.to_px(window.x), self.y.to_px(window.y))
+    }
+}
+
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub struct WideRegion {
+    pub x: WideSpan,
+    pub y: WideSpan,
+}
+
+impl WideRegion {
+    pub const fn of(region: UiRegion) -> Self {
+        Self {
+            x: WideSpan::of(region.x),
+            y: WideSpan::of(region.y),
+        }
+    }
+
+    pub const fn within(self, parent: &UiRegion) -> Self {
+        Self {
+            x: self.x.within(&parent.x),
+            y: self.y.within(&parent.y),
+        }
+    }
+
+    pub fn to_px(self, window: PxVec2) -> PixelRegion {
+        PixelRegion {
+            top_left: PxVec2::new(self.x.start.to_px(window.x), self.y.start.to_px(window.y)),
+            bot_right: PxVec2::new(self.x.end.to_px(window.x), self.y.end.to_px(window.y)),
+        }
+    }
+}

core/src/ui/holds.rs

@@ -55,28 +55,40 @@ impl Holds {
         if rel == 0 {
             return Self::ANY;
         }
-        // In half steps, and no more than the arithmetic needs: too wide a
+        // In half steps, and both at the floor: one less on either and the
-        // range admits reusing a drawing where it does not hold, and too
+        // `Holds` assertion in `draw_at` fires, because the range stops
-        // narrow a one leaves out the box a drawing was made in, which the
+        // containing the box a drawing was made in. Wider is the unsound
-        // `Holds` assertion in `draw_at` catches. `ROUTES` is at that floor
+        // side -- it admits reusing a drawing where it does not hold -- and
-        // -- two half steps fires it -- and tightening both ends moved not
+        // neither end buys any reuse, since tightening them moves none of
-        // one of the rig's work counters, so the slack is not buying reuse.
+        // the rig's work counters.
         //
         // `ROUTES` covers a box composed down the chain against the same box
-        // measured against the window: two routes to one number, each
+        // measured against the window. It was three half steps while
-        // rounding where the other does not. `way_in` covers the multiply
+        // composing rounded four multiplies a level; `Moves::compose` now
-        // this inverts, which drops a step and only ever downward, so it
+        // rounds the whole walk once, which took one off. One more is
-        // belongs at the top of the range alone -- and the whole of a box has
+        // arithmetically available -- the `Holds` assertion is quiet at one
-        // no multiply in it, however many pixels were added to it, since
+        // half step, and the whole-of-a-box case maps back to itself exactly
-        // multiplying by one is exact and taking the pixels off again is too.
+        // -- and it is **not** taken, because a range that tight makes
-        // Allowing for it there anyway compounded, a step a level down a
+        // shrinker seed 220 lay out differently warm than cold. Too narrow
-        // chain of widgets each taking the whole of its parent.
+        // is supposed to cost only a redraw; there it re-breaks a wrapping
+        // text, whose reported width then moves a `Branch` onto its other
+        // subtree. That is the unsettled-text family rather than a rounding
+        // question, and closing it is what would let this go lower.
+        //
+        // `way_in` covers the multiply this inverts, which drops a step and
+        // only ever downward, so it belongs at the top of the range alone.
+        // It is irreducible for the same reason a floor is not invertible:
+        // many boxes give one length. The whole of a box has no multiply in
+        // it, however many pixels were added to it, since multiplying by one
+        // is exact and taking the pixels off again is too -- allowing for it
+        // there anyway compounded, a step a level down a chain of widgets
+        // each taking the whole of its parent.
         //
         // Shifted by half of what a `Rel` counts in, to divide by the
         // fraction: exact until the division takes it back to the grid.
-        const ROUTES: i64 = 3;
         let px = len.px.raw() as i64;
         let half_rel = REL_SHIFT - 1;
+        const ROUTES: i64 = 2;
         let way_in = match rel == Rel::ONE.raw() as i64 {
             true => 0,
             false => 2,
@@ -136,11 +148,10 @@ mod tests {
     }
 
     /// A widget handed the whole of its parent's box, with or without pixels
-    /// taken off it, brings no multiply of its own: only the two routes to
+    /// taken off it, brings no multiply of its own, so it allows for the two
-    /// the same length are left to allow for, and not a rounding that did
+    /// routes and nothing else -- one step, where it was one a level of
-    /// not happen. Widening for it as well grew the interval a level at a
+    /// nesting before `Moves::compose`. The identity is what the arithmetic
-    /// time down a chain of them. Three half steps come back as one whole
+    /// would allow; see `through` for why it is not taken.
-    /// one, since dividing by a whole box is dividing by one.
     #[test]
     fn the_whole_of_a_box_widens_by_the_routes_alone() {
         let at = Px::from_int(956);

core/src/ui/mod.rs

@@ -1,6 +1,6 @@
 use crate::{
     Mask, MoveIdx, MoveOffset, PrimitiveRegistry, TextData, Textures, UiRegion, WeakWidget,
-    WidgetId, Widgets,
+    WideRegion, WideSize, WidgetId, Widgets,
     util::{Arena, Id, TrackedArena},
 };
 
@@ -68,17 +68,46 @@ impl Moves {
         }
     }
 
-    /// Composes a region held in `idx`'s coordinates down the chain, which is
+    /// Composes a region held in `idx`'s coordinates down the chain, on a
-    /// the same walk the vertex shader does.
+    /// grid fine enough that the whole walk rounds once. Composing in `Len`
+    /// rounds four multiplies a level, so the residue grew with the depth of
+    /// the tree -- and it is the box this produces that layout takes a
+    /// structural decision on.
+    pub fn compose(&self, idx: MoveIdx, local: UiRegion) -> WideRegion {
+        let mut region = WideRegion::of(local);
+        self.walk(idx, |entry| region = region.within(entry));
+        region
+    }
+
+    /// How long a region held in `idx`'s coordinates is, composed down the
+    /// chain on the same fine grid as [`Self::compose`] and for the same
+    /// reason. Half the multiplies of composing the box, since a length does
+    /// not need to know where the box sits -- and what reads a box in pixels
+    /// nearly always wants only this.
+    pub fn size_of(&self, idx: MoveIdx, local: UiRegion) -> WideSize {
+        let mut size = WideSize::of(local);
+        self.walk(idx, |entry| size = size.within(entry));
+        size
+    }
+
+    /// The same walk the vertex shader does, in the same `Len` the shader is
+    /// handed. What layout decides on is [`Self::compose`]; this is for
+    /// asking where the drawing will actually land, which the shader works
+    /// out again in floats from these same entries.
     pub fn resolve(&self, idx: MoveIdx, local: UiRegion) -> UiRegion {
         let mut region = local;
+        self.walk(idx, |entry| region = region.within(entry));
+        region
+    }
+
+    fn walk(&self, idx: MoveIdx, mut step: impl FnMut(&UiRegion)) {
         let mut at = idx;
         for _ in 0..CHAIN_LIMIT {
             if at == MoveIdx::NONE {
-                return region;
+                return;
             }
-            let entry = self.arena[at.idx()];
+            let entry = &self.arena[at.idx()];
-            region = region.within(&entry.region);
+            step(&entry.region);
             at = entry.parent;
         }
         debug_assert!(
@@ -86,7 +115,6 @@ impl Moves {
             "a move chain longer than {CHAIN_LIMIT} resolves to the wrong place, \
              and the shader stops at the same depth"
         );
-        region
     }
 
     /// How many slots a region in `idx` is composed through, which is what

core/src/ui/render_state.rs

@@ -462,16 +462,14 @@ impl UiRenderState {
 
     /// The pixel size of a region held in `slot`'s coordinates.
     pub(super) fn px_of(&self, slot: MoveIdx, region: UiRegion) -> PxVec2 {
-        self.moves
+        self.moves.size_of(slot, region).to_px(self.output_size)
-            .resolve(slot, region)
-            .size()
-            .to_px(self.output_size)
     }
 
-    /// Where a region held in `slot`'s coordinates lands on screen, which is
+    /// Where a region held in `slot`'s coordinates lands on screen, to
-    /// the walk the vertex shader does.
+    /// compare one box against another. Both ends of it, where
+    /// [`Self::px_of`] wants only the length between them.
     fn px_region(&self, slot: MoveIdx, region: UiRegion) -> PixelRegion {
-        self.moves.resolve(slot, region).to_px(self.output_size)
+        self.moves.compose(slot, region).to_px(self.output_size)
     }
 
     /// A clean widget's retained answer, if that answer holds for a box of