Work a move out once for the subtree, not once for each part

`RegionRemap` re-derived the same things for every scalar of every part of a
moving subtree: the extent it divides by, whether the box only moved, whether
it spans the whole of its parent's, and the two ends of each `lerp`. All of
them are the same for the whole walk, because the walk is one box moving into
one other box. They are worked out once in `RegionRemap::new` now, as an
`AxisRemap` per axis that is either a translation or a scale.

Identical arithmetic in the same order, so the answers are unchanged: 500
frames of the `many` phase went from 1,886,328,855 instructions to
1,815,666,327, 3.8% fewer, and `tabs`, `text` and `random` are byte-identical
at 1920x1200.

Cycles moved 0.8%, which is the finding worth keeping: the surrounding
arithmetic was never the cost. The `i64` division is, and it is still there.

Checked: fmt, clippy, 105 tests, all five shrinker cases at 300 seeds.

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

core/src/ui/render_state.rs

@@ -3,7 +3,7 @@ use crate::layout_diagnostics::{self as diag, Counter, ReuseOutcome, TimerKind};
 use crate::ui::painter::{declared_box, declared_lens, placed_box};
 use crate::{
     ActiveData, Axis, DrawLayers, Holds, IdLike, LayoutLen, Len, MaskIdx, MoveIdx, Moves, Painter,
-    PixelRegion, PxVec2, RegionAlign, Rel, Size, StrongWidget, UiRegion, UiRsc, UiSpan, Weight,
+    PixelRegion, Px, PxVec2, RegionAlign, Rel, Size, StrongWidget, UiRegion, UiRsc, UiSpan, Weight,
     WidgetId, Widgets,
     util::{HashMap, Vec2},
 };
@@ -632,7 +632,7 @@ impl UiRenderState {
                 self.moves.set(slot, region);
             } else {
                 let remap = RegionRemap::new(old_region, region)?;
-                self.remap_subtree(id, remap, info.parent_move, mask, rsc);
+                self.remap_subtree(id, &remap, info.parent_move, mask, rsc);
             }
         }
         let active = self.active.get_mut(&id).unwrap();
@@ -668,7 +668,7 @@ impl UiRenderState {
     fn remap_subtree(
         &mut self,
         id: WidgetId,
-        remap: RegionRemap,
+        remap: &RegionRemap,
         parent_move: MoveIdx,
         inherited_mask: MaskIdx,
         rsc: &mut dyn UiRsc,
@@ -1045,55 +1045,102 @@ fn same_pixel_region(a: PixelRegion, b: PixelRegion) -> bool {
 /// source extent can be translated but cannot recover fractions for a resize.
 #[derive(Clone, Copy)]
 struct RegionRemap {
-    from: UiRegion,
+    axes: [AxisRemap; 2],
-    to: UiRegion,
+}
+
+/// Moving one axis of a box into another, worked out once for the whole
+/// subtree that moves with it. Every part of that subtree is divided by the
+/// same extent and placed between the same two ends, so the ends and the
+/// divisor belong here rather than in each part's arithmetic.
+#[derive(Clone, Copy)]
+enum AxisRemap {
+    /// A box that kept its length carries its parts by moving them, which is
+    /// exact. Dividing to find the fraction each sits at and multiplying to
+    /// place it again are two roundings, and they land a step from where
+    /// growing the tree that way does.
+    Translate(Len),
+    /// A box that changed length has to re-express each part as a fraction of
+    /// the new one, which is what a part of a box means.
+    Scale(AxisScale),
+}
+
+#[derive(Clone, Copy)]
+struct AxisScale {
+    /// What the fraction is measured from, and what divides it. `whole` is
+    /// the common case of a box spanning the whole of its parent's, where
+    /// dividing by one is the expensive way to write a subtraction.
+    start_rel: Rel,
+    extent: Rel,
+    whole: bool,
+    /// `lerp` is `a + (b - a) * fraction`, and both ends are the same for
+    /// every part, so each is kept as its near end and its span.
+    from_px: Px,
+    from_px_span: Px,
+    to_rel: Rel,
+    to_rel_span: Rel,
+    to_px: Px,
+    to_px_span: Px,
 }
 
 impl RegionRemap {
     fn new(from: UiRegion, to: UiRegion) -> Option<Self> {
-        AXES.into_iter()
+        Some(Self {
-            .all(|axis| {
+            axes: [AxisRemap::new(from.x, to.x)?, AxisRemap::new(from.y, to.y)?],
-                let from = from.axis(axis);
-                from.start.rel != from.end.rel || from.len() == to.axis(axis).len()
         })
-            .then_some(Self { from, to })
     }
 
-    fn apply(self, region: UiRegion) -> UiRegion {
+    fn apply(&self, region: UiRegion) -> UiRegion {
         UiRegion {
-            x: self.apply_span(region.x, self.from.x, self.to.x),
+            x: self.axes[0].apply_span(region.x),
-            y: self.apply_span(region.y, self.from.y, self.to.y),
+            y: self.axes[1].apply_span(region.y),
+        }
     }
 }
 
-    fn apply_span(self, span: UiSpan, from: UiSpan, to: UiSpan) -> UiSpan {
+impl AxisRemap {
-        UiSpan {
+    fn new(from: UiSpan, to: UiSpan) -> Option<Self> {
-            start: self.apply_scalar(span.start, from, to),
+        if from.len() == to.len() {
-            end: self.apply_scalar(span.end, from, to),
+            return Some(Self::Translate(to.start - from.start));
         }
-    }
-
-    fn apply_scalar(self, scalar: Len, from: UiSpan, to: UiSpan) -> Len {
         let extent = from.end.rel - from.start.rel;
-        // A box that only moved, or that has no relative extent to divide,
+        // Without a relative extent there is no fraction to re-express: a box
-        // carries its parts by moving them, which is exact. Dividing to find
+        // of fixed length cannot say where its parts sit in a different one.
-        // the fraction each sits at and multiplying to place it again are two
+        if extent == Rel::ZERO {
-        // roundings, and they land a step from where growing the tree that
+            return None;
-        // way does. Where the box changed length there is nothing else to do,
-        // and the fraction is what a part means.
-        if from.len() == to.len() || extent == Rel::ZERO {
-            return scalar + to.start - from.start;
         }
-        // A box that spans the whole of its parent's is the common one, and
+        Some(Self::Scale(AxisScale {
-        // dividing by one is the expensive way to write a subtraction.
+            start_rel: from.start.rel,
-        let offset = scalar.rel - from.start.rel;
+            extent,
-        let fraction = match extent == Rel::ONE {
+            whole: extent == Rel::ONE,
-            true => offset,
+            from_px: from.start.px,
-            false => offset / extent,
+            from_px_span: from.end.px - from.start.px,
+            to_rel: to.start.rel,
+            to_rel_span: to.end.rel - to.start.rel,
+            to_px: to.start.px,
+            to_px_span: to.end.px - to.start.px,
+        }))
+    }
+
+    fn apply_span(&self, span: UiSpan) -> UiSpan {
+        UiSpan {
+            start: self.apply_scalar(span.start),
+            end: self.apply_scalar(span.end),
+        }
+    }
+
+    fn apply_scalar(&self, scalar: Len) -> Len {
+        let scale = match self {
+            Self::Translate(by) => return scalar + *by,
+            Self::Scale(scale) => scale,
         };
-        let from_px = fraction.lerp(from.start.px, from.end.px);
+        let offset = scalar.rel - scale.start_rel;
-        let to_rel = fraction.lerp(to.start.rel, to.end.rel);
+        let fraction = match scale.whole {
-        let to_px = fraction.lerp(to.start.px, to.end.px);
+            true => offset,
+            false => offset / scale.extent,
+        };
+        let from_px = scale.from_px + scale.from_px_span.mul(fraction);
+        let to_rel = scale.to_rel + scale.to_rel_span.mul(fraction);
+        let to_px = scale.to_px + scale.to_px_span.mul(fraction);
         Len::from_parts(to_rel, scalar.px - from_px + to_px)
     }
 }