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)),
+        }
+    }
+}