Retire Remap: a translation shifts, and only a stretch needs a fraction

`Remap` existed to invert a composition, and a translation never needed
one: shifting a box shifts everything composed into it by the same
amount, because `lerp(s + d, e + d, t) == lerp(s, e, t) + d` on both
channels. That holds whether or not the box has a relative extent, so
the carry branch was answering a question it did not have to ask.

So the decision is made once, before the walk, and neither relocation
method branches. A translation is already one slot write. A change of
length calls `UiRegion::stretch`, which re-expresses each part at its
own fraction of the new box and needs `stretchable` -- a fixed length
holds its parts as offsets from its start and keeps no fraction to
stretch by.

`Remap`, `UiScalar::outside`, `UiSpan::outside` and `LerpUtil::lerp_inv`
are all gone with it. Nothing inverts a lerp any more: the one division
is done against a denominator `stretchable` already established is not
zero.

What it gives up is the per-axis carry, so a box that changed length on
one axis and not the other is redrawn where it used to be remapped.
Counted: six of `tabs`'s fourteen relocations and five of `text`'s
sixteen, and one extra redraw per frame on `replace_cost`'s 200 rows --
354,310,889 instructions against 354,272,387, which is noise.

Checked: fmt, clippy and 42 tests. `tabs` (with the image replay),
`view`, `minimal` and `text` all still render byte-identical to
`upstream/main`.

core/src/orientation/pos.rs

@@ -202,12 +202,15 @@ impl UiScalar {
         }
     }
 
-    /// Undoes `within`, and `None` where the span has a fixed length: every
-    /// fraction of it lands on the same `rel`, so none can be told apart.
-    pub fn outside(&self, span: &UiSpan) -> Option<Self> {
-        let rel = self.rel.lerp_inv(span.start.rel, span.end.rel)?;
-        let abs = self.abs - rel.lerp(span.start.abs, span.end.abs);
-        Some(Self { rel, abs })
+    /// `within` undone against `from` and redone against `to`, for one axis.
+    /// `from`'s relative extent is the denominator, so it must not be zero.
+    fn stretch(&self, from: &UiSpan, to: &UiSpan) -> Self {
+        let frac = (self.rel - from.start.rel) / (from.end.rel - from.start.rel);
+        Self {
+            rel: frac.lerp(to.start.rel, to.end.rel),
+            abs: self.abs - frac.lerp(from.start.abs, from.end.abs)
+                + frac.lerp(to.start.abs, to.end.abs),
+        }
     }
 
     pub fn within_len(&self, len: UiScalar) -> Self {
@@ -278,13 +281,6 @@ impl UiSpan {
         }
     }
 
-    pub fn outside(&self, parent: &Self) -> Option<Self> {
-        Some(Self {
-            start: self.start.outside(parent)?,
-            end: self.end.outside(parent)?,
-        })
-    }
-
     pub const fn len(&self) -> UiScalar {
         self.end - self.start
     }
@@ -395,48 +391,28 @@ impl UiRegion {
             },
         }
     }
-}
 
-/// Taking a drawing out of one box and putting it in another, checked once
-/// for a whole subtree so that applying it cannot fail.
-///
-/// A box of a fixed length holds each part as an offset from its start rather
-/// than as a fraction of it, so those parts can be carried to a box of the
-/// same length but never stretched to a different one.
-#[derive(Debug, Copy, Clone, PartialEq)]
-pub struct Remap {
-    from: UiRegion,
-    to: UiRegion,
-}
-
-impl Remap {
-    pub fn new(from: UiRegion, to: UiRegion) -> Option<Self> {
-        [Axis::X, Axis::Y]
-            .into_iter()
-            .all(|axis| {
-                let (from, to) = (from.axis(axis), to.axis(axis));
-                from.start.rel != from.end.rel || from.len() == to.len()
-            })
-            .then_some(Self { from, to })
+    /// Whether a stretch out of this box can be expressed. Each part inside a
+    /// box is held as a fraction of it, and a fixed length has no fraction to
+    /// hold one by -- every part of it is just an offset from its start.
+    pub fn stretchable(&self) -> bool {
+        self.x.start.rel != self.x.end.rel && self.y.start.rel != self.y.end.rel
     }
 
-    pub fn apply(&self, region: UiRegion) -> UiRegion {
+    /// Re-expresses a region inside `from` as the same fractions of `to`.
+    /// `from` must be `stretchable`; a translation is `shift` instead, which
+    /// needs no fractions and works out of any box.
+    pub fn stretch(&self, from: &UiRegion, to: &UiRegion) -> UiRegion {
+        debug_assert!(from.stretchable(), "a fixed length has no fraction");
         UiRegion {
-            x: Self::span(region.x, self.from.x, self.to.x),
-            y: Self::span(region.y, self.from.y, self.to.y),
-        }
-    }
-
-    fn span(span: UiSpan, from: UiSpan, to: UiSpan) -> UiSpan {
-        match span.outside(&from) {
-            Some(out) => out.within(&to),
-            // `new` admits this only where the two are the same length, so
-            // the difference between their starts is the whole move.
-            None => {
-                let mut span = span;
-                span.shift(to.start - from.start);
-                span
-            }
+            x: UiSpan {
+                start: self.x.start.stretch(&from.x, &to.x),
+                end: self.x.end.stretch(&from.x, &to.x),
+            },
+            y: UiSpan {
+                start: self.y.start.stretch(&from.y, &to.y),
+                end: self.y.end.stretch(&from.y, &to.y),
+            },
         }
     }
 }

core/src/ui/render_state.rs

@@ -1,6 +1,6 @@
 use crate::{
     ActiveData, Axis, DrawLayers, IdLike, MaskIdx, MoveIdx, Moves, OnResize, Painter, PixelRegion,
-    Remap, Size, StrongWidget, UiRegion, UiRsc, WidgetId, Widgets,
+    Size, StrongWidget, UiRegion, UiRsc, WidgetId, Widgets,
     util::{HashMap, HashSet, Vec2, forget_ref},
 };
 
@@ -214,11 +214,11 @@ impl UiRenderState {
             self.moves.set(slot, moved);
             return Some(size);
         }
-        if !self.reusable(id, region, rsc) {
+        if !self.reusable(id, region, rsc) || !old.stretchable() {
             return None;
         }
-        // Its drawing stands, if the new box can be reached from the old one.
-        self.mov(id, &Remap::new(old, region)?);
+        // Its drawing stands, re-expressed as the same fractions of the box.
+        self.stretch(id, old, region);
         Some(size)
     }
 
@@ -259,21 +259,21 @@ impl UiRenderState {
         })
     }
 
-    /// Rewrites a subtree's regions into a new box, for a change a slot
-    /// cannot express. Every region it rewrites is a region some slot was a
-    /// delta from, so those go back to zero.
-    fn mov(&mut self, id: WidgetId, remap: &Remap) {
+    /// Rewrites a subtree's regions as the same fractions of a new box, for a
+    /// change of length that a slot cannot express. Every region it rewrites
+    /// is a region some slot was a delta from, so those go back to zero.
+    fn stretch(&mut self, id: WidgetId, from: UiRegion, to: UiRegion) {
         let active = self.active.get_mut(&id).unwrap();
         for h in &active.primitives {
             let region = self.layers[h.layer].region_mut(h);
-            *region = remap.apply(*region);
+            *region = region.stretch(&from, &to);
         }
-        active.region = remap.apply(active.region);
+        active.region = active.region.stretch(&from, &to);
         self.moves.set(active.move_idx, Vec2::ZERO);
         // SAFETY: children cannot be recursive
         let children = unsafe { forget_ref(&active.children) };
         for child in children {
-            self.mov(*child, remap);
+            self.stretch(*child, from, to);
         }
     }
 

core/src/util/math.rs

@@ -1,6 +1,5 @@
-pub const trait LerpUtil: Sized {
+pub const trait LerpUtil {
     fn lerp(self, from: Self, to: Self) -> Self;
-    fn lerp_inv(self, from: Self, to: Self) -> Option<Self>;
 }
 
 const impl LerpUtil for f32 {
@@ -9,14 +8,6 @@ const impl LerpUtil for f32 {
     fn lerp(self, from: Self, to: Self) -> Self {
         from + (to - from) * self
     }
-    /// inverse of lerp, and `None` where `from` and `to` are the same point:
-    /// every input lerps to it, so there is no one answer to come back to.
-    fn lerp_inv(self, from: Self, to: Self) -> Option<Self> {
-        match to == from {
-            true => None,
-            false => Some((self - from) / (to - from)),
-        }
-    }
 }
 
 macro_rules! impl_op {