WIP: a stack does not take its sizing child's fraction twice

Every child gets the whole of the stack's box rather than `box_of(size)`,
and `widget_at` does not resolve a rule into a box already chosen from it.
Fixes half a row becoming a quarter, which no oracle can see because warm
and cold shrink alike. Pinned by
`a_stack_sized_by_a_child_does_not_take_that_childs_fraction_twice`.

Not landed. Seed 1091 at depth 4, `shuffle-swap-for-three`, disagrees by
three steps of the grid -- warm 1053.9971 against cold 1054 -- where the
oracle tolerates two. Not a structural divergence: `box_of` was also making
a child's placement exact, by handing it a box of exactly the length it
asked for, and giving it the whole box instead puts a rounding back at each
nesting level. Two nested stacks is three steps. Widening AGREE_STEPS is
not the answer; finding the composition that went from exact to rounded is.

Everything else is green: suite, shrinker at 400 seeds of depth 5, oracle at
1000 seeds of depth 6, and the rest of 2000 seeds at depth 4.

Also carries examples/text.rs's top panel taking the full width.

Cargo.toml

@@ -3,6 +3,9 @@ name = "iris"
 version.workspace = true
 edition.workspace = true
 
+[features]
+layout-diagnostics = ["iris-core/layout-diagnostics"]
+
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
 [dependencies]
@@ -22,6 +25,12 @@ tokio = { workspace = true, features = ["sync", "rt", "rt-multi-thread", "time"]
 [workspace]
 members = ["core", "macro", "rig-input"]
 
+[profile.dev]
+debug = 1
+
+[profile.test]
+debug = "line-tables-only"
+
 [workspace.package]
 version = "0.1.0"
 edition = "2024"

core/Cargo.toml

@@ -3,6 +3,9 @@ name = "iris-core"
 version.workspace = true
 edition.workspace = true
 
+[features]
+layout-diagnostics = []
+
 [dependencies]
 wgpu = { workspace = true }
 bytemuck ={ workspace = true }

core/src/fixed.rs

@@ -0,0 +1,574 @@
+use crate::{UiNum, util::Vec2};
+use std::{
+    fmt::{Debug, Display, Formatter},
+    ops::{Add, AddAssign, Div, Mul, Neg, Sub, SubAssign},
+};
+
+/// A number held as a whole count of `1 / 2^SHIFT`.
+///
+/// Layout reaches one place by more than one route -- a box composed down the
+/// chain, and the same box summed from what its children asked for -- and has
+/// to decide whether the two are the same place. In floats they land a few
+/// bits apart, which is a defect wherever the answer changes what is drawn
+/// rather than where. Here adding and subtracting are exact, a multiply
+/// drops to the step below, and a conversion between grids takes the nearest
+/// one, so two routes to one place land on one number and everything
+/// downstream compares for equality instead of for nearness.
+///
+/// `SHIFT` is the number of fractional bits, which is what makes the steps
+/// divide a whole number: a power of two also converts to `f32` without
+/// rounding while the value fits in its mantissa.
+///
+/// Arithmetic wraps at the ends of the range, the way the `i32` underneath
+/// does. Saturating instead was measured at a twelfth of layout's
+/// instructions -- five per add against one -- to keep the ordering of
+/// coordinates two million pixels out, where nothing draws anyway. A value
+/// off the end is a defect either way; wrapping makes it an obvious one.
+/// Only [`Self::from_f32`] clamps, since a float has further to come from.
+#[repr(transparent)]
+#[derive(
+    Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash, Default, bytemuck::Pod, bytemuck::Zeroable,
+)]
+pub struct Fixed<const SHIFT: u32>(i32);
+
+/// A length or a coordinate in pixels, in steps of `1/1024`. Finer than
+/// anything a display can show, and exact in `f32` up to 16,384 px, which is
+/// what lets the same number reach the GPU.
+pub type Px = Fixed<PX_SHIFT>;
+
+/// How many bits of a pixel a [`Px`] keeps. One place, because [`PxVec2`]
+/// and the shader's own decoding are the same grid or nothing lines up.
+pub const PX_SHIFT: u32 = 10;
+
+/// A share of what a box has left over, which is a weight beside its
+/// siblings rather than a fraction of anything: a list divides its room by
+/// the total of these, so the range has to hold a whole list's worth and the
+/// precision only has to tell two weights apart.
+pub type Weight = Fixed<16>;
+
+/// A fraction of a box. Twenty-four bits of it, which matches `f32` around a
+/// half and beats it above one -- where anchors actually sit -- and leaves
+/// +/-128 of range, enough to sum a hundred children each asking for a whole
+/// box. A `leftover` weight is not one of these: it is a share of what is
+/// left rather than a fraction of anything, and it sums over a whole list.
+pub type Rel = Fixed<REL_SHIFT>;
+
+/// How many bits of a box a [`Rel`] keeps, beside [`PX_SHIFT`] and for the
+/// same reason.
+pub const REL_SHIFT: u32 = 24;
+
+impl<const SHIFT: u32> Fixed<SHIFT> {
+    pub const ZERO: Self = Self(0);
+    pub const ONE: Self = Self::one();
+    /// The gap between neighbouring values, which is also how far apart two
+    /// numbers can be and still mean the same place.
+    pub const STEP: Self = Self(1);
+    /// Also what stands in for an unbounded end: compared against, never
+    /// added to, since arithmetic wraps past it.
+    pub const MIN: Self = Self(i32::MIN);
+    pub const MAX: Self = Self(i32::MAX);
+
+    const fn one() -> Self {
+        assert!(SHIFT < 31, "a Fixed needs a bit for the whole part");
+        Self(1 << SHIFT)
+    }
+
+    pub const fn from_raw(raw: i32) -> Self {
+        Self(raw)
+    }
+
+    /// The count of steps, for a caller that needs the representation rather
+    /// than the number.
+    pub const fn raw(self) -> i32 {
+        self.0
+    }
+
+    pub const fn from_int(v: i32) -> Self {
+        Self(v.wrapping_mul(Self::one().0))
+    }
+
+    /// Rounds to the nearest step, and clamps to the ends of the grid rather
+    /// than wrapping: this is where a number from outside arrives, and a float
+    /// has the range to be anywhere. A NaN has no nearest step and becomes
+    /// zero, which is a caller's mistake rather than a value worth carrying.
+    ///
+    /// Half-away is written out rather than called through `f32::round`,
+    /// which is not `const`: a layout constant has to stay a constant.
+    pub const fn from_f32(v: f32) -> Self {
+        debug_assert!(!v.is_nan(), "a NaN has no place on the grid");
+        let scaled = v * Self::one().0 as f32;
+        // Above 2^23 an `f32` has no fractional part left to round, and
+        // adding a half there rounds the number itself up instead. The cast
+        // saturates at both ends and sends NaN to zero, which is the
+        // behaviour wanted at both.
+        const WHOLE: f32 = (1 << 23) as f32;
+        Self(match (scaled >= WHOLE, scaled <= -WHOLE, scaled < 0.0) {
+            (true, _, _) | (_, true, _) => scaled as i32,
+            (_, _, true) => (scaled - 0.5) as i32,
+            _ => (scaled + 0.5) as i32,
+        })
+    }
+
+    /// The first step at or above `v`, where [`Self::from_f32`] takes the
+    /// nearest one and is below it half the time. For a bound that has to
+    /// admit the value it came from: a measurement rounded down is a bound
+    /// that leaves out the thing it was measured from.
+    pub const fn ceil_from_f32(v: f32) -> Self {
+        let nearest = Self::from_f32(v);
+        match nearest.to_f32() < v {
+            true => nearest.next_up(),
+            false => nearest,
+        }
+    }
+
+    /// From a number as it is written in source -- `16`, `1.5` -- which is
+    /// the other place a value enters the grid.
+    pub fn from_num(v: impl UiNum) -> Self {
+        Self::from_f32(v.to_f32())
+    }
+
+    pub const fn to_f32(self) -> f32 {
+        self.0 as f32 / Self::one().0 as f32
+    }
+
+    /// The same value on another grid, rounded where the new one is coarser.
+    pub const fn to_scale<const TO: u32>(self) -> Fixed<TO> {
+        Fixed(match TO >= SHIFT {
+            true => self.0 << (TO - SHIFT),
+            false => shift_round(self.0 as i64, SHIFT - TO) as i32,
+        })
+    }
+
+    pub const fn add(self, rhs: Self) -> Self {
+        Self(self.0.wrapping_add(rhs.0))
+    }
+
+    pub const fn sub(self, rhs: Self) -> Self {
+        Self(self.0.wrapping_sub(rhs.0))
+    }
+
+    pub const fn neg(self) -> Self {
+        Self(self.0.wrapping_neg())
+    }
+
+    /// Scaled by a number on any grid, which is how a length takes a fraction
+    /// of itself and keeps being a length: the product is measured in the
+    /// receiver's steps.
+    ///
+    /// Dropped to the step below rather than taken to the nearest one
+    /// (Bryan, 2026-09-16), which costs a share a thousandth of a pixel of
+    /// its row -- less than an even number of pixels draws. Toward negative
+    /// infinity on both sides of zero, since that is a shift and nothing
+    /// else: a value and its negation therefore land different distances
+    /// from where they came, so a flipped span can sit a step from its
+    /// mirror image.
+    pub const fn mul<const BY: u32>(self, by: Fixed<BY>) -> Self {
+        Self(((self.0 as i64 * by.0 as i64) >> BY) as i32)
+    }
+
+    /// Repeated a whole number of times, which no grid rounds.
+    pub const fn mul_int(self, by: i32) -> Self {
+        Self(self.0.wrapping_mul(by))
+    }
+
+    /// Divided into a whole number of parts, rounded to the nearest step.
+    pub const fn div_int(self, by: i32) -> Self {
+        debug_assert!(by != 0, "no part of nothing");
+        if by == 0 {
+            return Self::ZERO;
+        }
+        Self(div_round(self.0 as i64, by as i64) as i32)
+    }
+
+    /// Divided by a number on any grid. A zero divisor is a caller bug -- a
+    /// box of no length has no fraction of itself -- and answers with the end
+    /// of the range so that a release build lays out something absurd rather
+    /// than dying.
+    pub const fn div<const BY: u32>(self, by: Fixed<BY>) -> Self {
+        debug_assert!(by.0 != 0, "dividing by a length of zero");
+        if by.0 == 0 {
+            return match self.0 < 0 {
+                true => Self::MIN,
+                false => Self::MAX,
+            };
+        }
+        Self(div_round((self.0 as i64) << BY, by.0 as i64) as i32)
+    }
+
+    /// `num / den` on *this* grid rather than on theirs, for weights coarser
+    /// than the share they divide.
+    pub const fn ratio<const OF: u32>(num: Fixed<OF>, den: Fixed<OF>) -> Self {
+        debug_assert!(den.0 != 0, "no part of a whole of nothing");
+        if den.0 == 0 {
+            return Self::ZERO;
+        }
+        Self(div_round((num.0 as i64) << SHIFT, den.0 as i64) as i32)
+    }
+
+    /// `from` and `to` a fraction of the way apart, the fraction being the
+    /// receiver -- the argument order [`crate::util::LerpUtil`] already uses.
+    pub const fn lerp<const OF: u32>(self, from: Fixed<OF>, to: Fixed<OF>) -> Fixed<OF> {
+        from.add(to.sub(from).mul(self))
+    }
+
+    pub const fn min(self, other: Self) -> Self {
+        match self.0 < other.0 {
+            true => self,
+            false => other,
+        }
+    }
+
+    pub const fn max(self, other: Self) -> Self {
+        match self.0 > other.0 {
+            true => self,
+            false => other,
+        }
+    }
+
+    pub const fn abs(self) -> Self {
+        Self(self.0.wrapping_abs())
+    }
+
+    pub const fn clamp(self, lo: Self, hi: Self) -> Self {
+        debug_assert!(lo.0 <= hi.0, "an empty clamp has no answer");
+        self.max(lo).min(hi)
+    }
+
+    /// The next value along, for an interval that must not admit its own
+    /// boundary. The step is the whole gap, so there is nothing to exclude
+    /// between this and the boundary itself.
+    pub const fn next_up(self) -> Self {
+        Self(self.0.wrapping_add(1))
+    }
+
+    pub const fn next_down(self) -> Self {
+        Self(self.0.wrapping_sub(1))
+    }
+}
+
+/// Back to a single step, rounding halves away from zero so that a value and
+/// its negation round to the same distance.
+const fn shift_round(v: i64, bits: u32) -> i64 {
+    let half = (1i64 << bits) >> 1;
+    match v < 0 {
+        true => -((-v + half) >> bits),
+        false => (v + half) >> bits,
+    }
+}
+
+const fn div_round(num: i64, den: i64) -> i64 {
+    let (q, rem) = (num / den, num % den);
+    match rem.unsigned_abs() * 2 >= den.unsigned_abs() {
+        true => match (num < 0) == (den < 0) {
+            true => q + 1,
+            false => q - 1,
+        },
+        false => q,
+    }
+}
+
+/// Toward positive infinity when `up`, toward negative infinity otherwise.
+pub(crate) const fn div_toward(num: i64, den: i64, up: bool) -> i64 {
+    let (q, rem) = (num / den, num % den);
+    if rem == 0 {
+        return q;
+    }
+    match (rem < 0) == (den < 0) {
+        true => q + up as i64,
+        false => q - !up as i64,
+    }
+}
+
+/// Clamped to the ends, unlike a [`Fixed`]'s own arithmetic: a range of box
+/// lengths that runs past `i32` really is unbounded.
+pub(crate) const fn narrow(v: i64) -> i32 {
+    if v > i32::MAX as i64 {
+        return i32::MAX;
+    }
+    if v < i32::MIN as i64 {
+        return i32::MIN;
+    }
+    v as i32
+}
+
+const impl<const SHIFT: u32> Add for Fixed<SHIFT> {
+    type Output = Self;
+
+    fn add(self, rhs: Self) -> Self {
+        Fixed::add(self, rhs)
+    }
+}
+
+const impl<const SHIFT: u32> Sub for Fixed<SHIFT> {
+    type Output = Self;
+
+    fn sub(self, rhs: Self) -> Self {
+        Fixed::sub(self, rhs)
+    }
+}
+
+const impl<const SHIFT: u32> Neg for Fixed<SHIFT> {
+    type Output = Self;
+
+    fn neg(self) -> Self {
+        Fixed::neg(self)
+    }
+}
+
+const impl<const SHIFT: u32> AddAssign for Fixed<SHIFT> {
+    fn add_assign(&mut self, rhs: Self) {
+        *self = Fixed::add(*self, rhs);
+    }
+}
+
+const impl<const SHIFT: u32> SubAssign for Fixed<SHIFT> {
+    fn sub_assign(&mut self, rhs: Self) {
+        *self = Fixed::sub(*self, rhs);
+    }
+}
+
+const impl<const SHIFT: u32, const BY: u32> Mul<Fixed<BY>> for Fixed<SHIFT> {
+    type Output = Self;
+
+    fn mul(self, rhs: Fixed<BY>) -> Self {
+        Fixed::mul(self, rhs)
+    }
+}
+
+const impl<const SHIFT: u32, const BY: u32> Div<Fixed<BY>> for Fixed<SHIFT> {
+    type Output = Self;
+
+    fn div(self, rhs: Fixed<BY>) -> Self {
+        Fixed::div(self, rhs)
+    }
+}
+
+impl<const SHIFT: u32> Display for Fixed<SHIFT> {
+    fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
+        Display::fmt(&self.to_f32(), f)
+    }
+}
+
+/// Prints the number rather than the count of steps: a failing layout test
+/// reports boxes, and `1126` is not a height anybody can read.
+impl<const SHIFT: u32> Debug for Fixed<SHIFT> {
+    fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
+        Display::fmt(&self.to_f32(), f)
+    }
+}
+
+/// Two of them, for the places a size or a position needs both axes: a
+/// window, a box in pixels, a pointer. Held apart from [`crate::util::Vec2`]
+/// because that one is what the GPU and the platform speak.
+#[repr(C)]
+#[derive(Clone, Copy, PartialEq, Eq, Hash, Default)]
+pub struct FixedVec2<const SHIFT: u32> {
+    pub x: Fixed<SHIFT>,
+    pub y: Fixed<SHIFT>,
+}
+
+pub type PxVec2 = FixedVec2<PX_SHIFT>;
+
+impl<const SHIFT: u32> FixedVec2<SHIFT> {
+    pub const ZERO: Self = Self::splat(Fixed::ZERO);
+
+    pub const fn new(x: Fixed<SHIFT>, y: Fixed<SHIFT>) -> Self {
+        Self { x, y }
+    }
+
+    pub const fn splat(v: Fixed<SHIFT>) -> Self {
+        Self { x: v, y: v }
+    }
+
+    pub fn from_f32(v: Vec2) -> Self {
+        Self::new(Fixed::from_f32(v.x), Fixed::from_f32(v.y))
+    }
+
+    /// The first step at or above each part, for a measurement reported as a
+    /// box: what it occupies is not less than what was measured.
+    pub fn ceil_from_f32(v: Vec2) -> Self {
+        Self::new(Fixed::ceil_from_f32(v.x), Fixed::ceil_from_f32(v.y))
+    }
+
+    pub fn to_f32(self) -> Vec2 {
+        Vec2::new(self.x.to_f32(), self.y.to_f32())
+    }
+
+    pub const fn div_int(self, by: i32) -> Self {
+        Self::new(self.x.div_int(by), self.y.div_int(by))
+    }
+
+    pub const fn min(self, other: Self) -> Self {
+        Self::new(self.x.min(other.x), self.y.min(other.y))
+    }
+
+    pub const fn max(self, other: Self) -> Self {
+        Self::new(self.x.max(other.x), self.y.max(other.y))
+    }
+}
+
+// `impl_op!` names one concrete type, and this one is generic.
+const impl<const SHIFT: u32> Add for FixedVec2<SHIFT> {
+    type Output = Self;
+
+    fn add(self, rhs: Self) -> Self {
+        Self::new(self.x.add(rhs.x), self.y.add(rhs.y))
+    }
+}
+
+const impl<const SHIFT: u32> Sub for FixedVec2<SHIFT> {
+    type Output = Self;
+
+    fn sub(self, rhs: Self) -> Self {
+        Self::new(self.x.sub(rhs.x), self.y.sub(rhs.y))
+    }
+}
+
+const impl<const SHIFT: u32> AddAssign for FixedVec2<SHIFT> {
+    fn add_assign(&mut self, rhs: Self) {
+        *self = Add::add(*self, rhs);
+    }
+}
+
+const impl<const SHIFT: u32> SubAssign for FixedVec2<SHIFT> {
+    fn sub_assign(&mut self, rhs: Self) {
+        *self = Sub::sub(*self, rhs);
+    }
+}
+
+impl<const SHIFT: u32> Debug for FixedVec2<SHIFT> {
+    fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
+        write!(f, "({}, {})", self.x, self.y)
+    }
+}
+
+impl<const SHIFT: u32> Display for FixedVec2<SHIFT> {
+    fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
+        write!(f, "({}, {})", self.x, self.y)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn a_sum_of_steps_does_not_drift() {
+        let mut at = Px::ZERO;
+        for _ in 0..20_000 {
+            at += Px::from_raw(3);
+        }
+        assert_eq!(at, Px::from_raw(60_000));
+        for _ in 0..20_000 {
+            at -= Px::from_raw(3);
+        }
+        assert_eq!(at, Px::ZERO);
+    }
+
+    #[test]
+    fn a_pixel_survives_the_trip_through_f32() {
+        for raw in [0, 1, -1, 64, -1000, 16_777_215, -16_777_215] {
+            let px = Px::from_raw(raw);
+            assert_eq!(Px::from_f32(px.to_f32()), px);
+        }
+    }
+
+    #[test]
+    fn a_fraction_of_a_length_is_a_length() {
+        let half = Px::from_int(100) * Rel::from_f32(0.5);
+        assert_eq!(half, Px::from_int(50));
+        assert_eq!(Px::from_int(100) * Rel::ONE, Px::from_int(100));
+        assert_eq!(Px::from_int(100) * Rel::ZERO, Px::ZERO);
+    }
+
+    /// Toward negative infinity on both sides of zero, which is what makes
+    /// it a shift rather than a shift and a sign branch -- and what makes a
+    /// value and its negation land different distances from where they came,
+    /// so a flipped span can sit a step from its mirror image.
+    #[test]
+    fn a_multiply_drops_to_the_step_below_on_both_sides_of_zero() {
+        // A step and a half of one, which has no step of its own.
+        let step_and_a_half = Rel::from_f32(1.5).div_int(Px::ONE.raw());
+        assert_eq!(Px::ONE * step_and_a_half, Px::from_raw(1));
+        assert_eq!(Px::ONE.neg() * step_and_a_half, Px::from_raw(-2));
+    }
+
+    /// A division rounds to the nearest step, so it cannot put back the
+    /// steps a truncating multiply dropped: a round trip comes back short,
+    /// never long, and by the few steps the two operations gave up.
+    #[test]
+    fn dividing_by_a_fraction_cannot_undo_a_truncating_multiply() {
+        let third = Rel::ONE / Rel::from_int(3);
+        let len = Px::from_int(300);
+        let back = len * third / third;
+        assert!(back <= len, "{back:?} is longer than {len:?}");
+        assert!(len - back <= Px::from_raw(3), "{back:?} against {len:?}");
+        assert_eq!(Px::from_int(100) / Rel::from_f32(0.5), Px::from_int(200));
+    }
+
+    /// The bound a greedy line break needs: the width it was measured at is
+    /// not on the grid, and the narrowest box the break still holds for is
+    /// the step at or above it, never the one below.
+    #[test]
+    fn a_ceiling_never_lands_below_the_number_it_came_from() {
+        let step = 1.0 / (1 << PX_SHIFT) as f32;
+        for n in 0..64 {
+            let v = 189.0 + n as f32 * step / 3.0;
+            let up = Px::ceil_from_f32(v);
+            assert!(up.to_f32() >= v, "{up:?} is below {v}");
+            assert!(
+                up.to_f32() - v < step,
+                "{up:?} is more than a step above {v}"
+            );
+        }
+        // An exact step is its own ceiling.
+        assert_eq!(Px::ceil_from_f32(189.5), Px::from_f32(189.5));
+    }
+
+    #[test]
+    fn a_number_from_outside_is_clamped_to_the_grid() {
+        assert_eq!(Px::from_f32(1e12), Px::MAX);
+        assert_eq!(Px::from_f32(-1e12), Px::MIN);
+    }
+
+    #[test]
+    fn a_coarser_grid_rounds_and_a_finer_one_does_not() {
+        // A third, which neither grid holds exactly.
+        let third = Rel::ONE / Rel::from_int(3);
+        assert_eq!(third.to_scale::<6>(), Fixed::<6>::from_raw(21));
+        let coarse = Fixed::<6>::from_raw(21);
+        assert_eq!(coarse.to_scale::<24>().to_scale::<6>(), coarse);
+    }
+
+    #[test]
+    fn lerp_takes_the_fraction_as_the_receiver() {
+        let (from, to) = (Px::from_int(10), Px::from_int(20));
+        assert_eq!(Rel::ZERO.lerp(from, to), from);
+        assert_eq!(Rel::ONE.lerp(from, to), to);
+        assert_eq!(Rel::from_f32(0.5).lerp(from, to), Px::from_int(15));
+        assert_eq!(Rel::from_f32(0.5).lerp(to, from), Px::from_int(15));
+    }
+
+    #[test]
+    fn a_ratio_is_finer_than_the_weights_it_divides() {
+        let (one, three) = (Weight::ONE, Weight::from_int(3));
+        // A third, which the weights' own grid could only hold to 1/65536.
+        assert_eq!(Rel::ratio(one, three), Rel::from_raw(5592405));
+        assert_eq!(Rel::ratio(three, three), Rel::ONE);
+        assert_eq!(Rel::ratio(Weight::ZERO, three), Rel::ZERO);
+    }
+
+    #[test]
+    fn nothing_sits_between_a_value_and_the_next_one() {
+        let at = Px::from_int(3);
+        assert_eq!(at.next_up().next_down(), at);
+        assert_eq!(at.next_up().raw() - at.raw(), 1);
+        assert!(at.next_down() < at && at < at.next_up());
+    }
+
+    #[test]
+    fn it_prints_the_number_rather_than_the_steps() {
+        assert_eq!(format!("{:?}", Px::from_f32(17.59375)), "17.59375");
+        assert_eq!(format!("{}", Px::from_int(-2)), "-2");
+    }
+}

core/src/layout_diagnostics.rs

@@ -0,0 +1,483 @@
+//! Opt-in counters and coarse timers for explaining CPU layout cost.
+//!
+//! Enable the `layout-diagnostics` feature. With it disabled, none of the
+//! instrumentation is compiled into Iris. The retained rig in
+//! `tests/layout_diagnostics.rs` is the ordinary entry point.
+//!
+//! Timers are inclusive: `update total` contains `full layout` or
+//! `incremental layout`, and `text render` contains shaping and glyph
+//! placement. They locate cost within one instrumented run and must not be
+//! added together. Use an uninstrumented build under `perf` for final CPU
+//! totals; counting every primitive and distinct widget deliberately perturbs
+//! the instrumented run.
+//!
+//! Call [`trace_widget`] before a frame to retain the ordered constraint,
+//! reuse, size, placement, and text events for one suspicious widget. The
+//! selection is a set and survives [`take`] until cleared.
+
+use crate::{Axis, LayoutLen, PxVec2, Size, UiRegion, WidgetId};
+use std::{
+    cell::RefCell,
+    collections::{HashMap, HashSet},
+    fmt::Write,
+    time::Instant,
+};
+
+#[derive(Clone, Copy)]
+pub(crate) enum Counter {
+    Updates,
+    DrawRequests,
+    WidgetDraws,
+    RegionNodeDraws,
+    SizeReads,
+    HintHits,
+    HintMisses,
+    RetainedSizeHits,
+    ReuseAttempts,
+    ReuseExact,
+    ReuseMoved,
+    ReuseDirty,
+    ReuseWrongParent,
+    ReuseRemapped,
+    ReuseOutside,
+    ReuseWrongLayer,
+    ReuseWrongNode,
+    PlaceRedraws,
+    QueuePops,
+    DepthReads,
+    LocalRedraws,
+    SizeChanges,
+    ReaderEdges,
+    PrimitiveWrites,
+    TextRenders,
+    TextShapeHits,
+    TextShapes,
+    TextBreaks,
+    GlyphPlacements,
+}
+
+impl Counter {
+    const COUNT: usize = Self::GlyphPlacements as usize + 1;
+
+    const NAMES: [&'static str; Self::COUNT] = [
+        "updates",
+        "draw requests",
+        "widget draws",
+        "region-node draws",
+        "draw-result size reads",
+        "hint hits",
+        "hint misses",
+        "retained size hits",
+        "reuse attempts",
+        "reuse exact",
+        "reuse moved",
+        "reuse: dirty",
+        "reuse: wrong parent",
+        "reuse remapped",
+        "reuse: outside what it holds for",
+        "reuse: another layer",
+        "reuse: region-node choice changed",
+        "placed by redrawing",
+        "redraw queue pops",
+        "depth reads",
+        "local redraws",
+        "size changes",
+        "reader edges",
+        "primitive writes",
+        "text renders",
+        "text shape hits",
+        "text shapes",
+        "text line breaks",
+        "glyph placements",
+    ];
+}
+
+#[derive(Clone, Copy)]
+pub(crate) enum TimerKind {
+    Update,
+    FullLayout,
+    IncrementalLayout,
+    TextRender,
+    TextShape,
+    TextBreak,
+    GlyphPlacement,
+}
+
+impl TimerKind {
+    const COUNT: usize = Self::GlyphPlacement as usize + 1;
+
+    const NAMES: [&'static str; Self::COUNT] = [
+        "update total",
+        "full layout",
+        "incremental layout",
+        "text render",
+        "text shape",
+        "text line break",
+        "glyph placement",
+    ];
+}
+
+#[derive(Clone)]
+pub struct Report {
+    counters: [u64; Counter::COUNT],
+    nanos: [u64; TimerKind::COUNT],
+    distinct_widgets: usize,
+    distinct_text_widgets: usize,
+    hot_widgets: Vec<Callsite>,
+    hot_text: Vec<Callsite>,
+    traces: Vec<TraceEvent>,
+}
+
+impl Default for Report {
+    fn default() -> Self {
+        Self {
+            counters: [0; Counter::COUNT],
+            nanos: [0; TimerKind::COUNT],
+            distinct_widgets: 0,
+            distinct_text_widgets: 0,
+            hot_widgets: Vec::new(),
+            hot_text: Vec::new(),
+            traces: Vec::new(),
+        }
+    }
+}
+
+impl Report {
+    pub fn counters(&self) -> impl Iterator<Item = (&'static str, u64)> + '_ {
+        Counter::NAMES.into_iter().zip(self.counters)
+    }
+
+    /// Inclusive elapsed time accumulated for each targeted operation.
+    pub fn timings_ns(&self) -> impl Iterator<Item = (&'static str, u64)> + '_ {
+        TimerKind::NAMES.into_iter().zip(self.nanos)
+    }
+
+    pub fn distinct_widgets(&self) -> usize {
+        self.distinct_widgets
+    }
+
+    pub fn distinct_text_widgets(&self) -> usize {
+        self.distinct_text_widgets
+    }
+
+    pub fn hot_widgets(&self) -> &[Callsite] {
+        &self.hot_widgets
+    }
+
+    pub fn hot_text(&self) -> &[Callsite] {
+        &self.hot_text
+    }
+
+    /// Ordered layout events for widgets selected with [`trace_widget`].
+    pub fn traces(&self) -> &[TraceEvent] {
+        &self.traces
+    }
+
+    /// Formats nonzero totals divided by `frames`.
+    pub fn per_frame(&self, frames: usize) -> String {
+        let divisor = frames.max(1) as f64;
+        let mut out = String::new();
+        for (name, value) in self.counters() {
+            if value != 0 {
+                let _ = writeln!(out, "  {name:<27} {:>12.2}", value as f64 / divisor);
+            }
+        }
+        if self.distinct_widgets != 0 {
+            let _ = writeln!(
+                out,
+                "  {:<27} {:>12}",
+                "distinct widgets", self.distinct_widgets
+            );
+        }
+        if self.distinct_text_widgets != 0 {
+            let _ = writeln!(
+                out,
+                "  {:<27} {:>12}",
+                "distinct text widgets", self.distinct_text_widgets
+            );
+        }
+        for (name, nanos) in self.timings_ns() {
+            if nanos != 0 {
+                let ms = nanos as f64 / divisor / 1_000_000.0;
+                let _ = writeln!(out, "  {name:<27} {ms:>12.3} ms");
+            }
+        }
+        if !self.hot_widgets.is_empty() {
+            let _ = writeln!(out, "  hottest widget draws:");
+            for callsite in &self.hot_widgets {
+                let calls = callsite.calls as f64 / divisor;
+                let _ = writeln!(
+                    out,
+                    "    {calls:>9.2}  {:?} {}",
+                    callsite.id, callsite.label
+                );
+            }
+        }
+        if !self.hot_text.is_empty() {
+            let _ = writeln!(out, "  hottest text renders:");
+            for callsite in &self.hot_text {
+                let calls = callsite.calls as f64 / divisor;
+                let _ = writeln!(
+                    out,
+                    "    {calls:>9.2}  {:>3} widths  {:?} {}",
+                    callsite.distinct_widths, callsite.id, callsite.label
+                );
+            }
+        }
+        if !self.traces.is_empty() {
+            let _ = writeln!(out, "  targeted layout trace:");
+            for event in &self.traces {
+                let _ = writeln!(out, "    {event:?}");
+            }
+        }
+        out
+    }
+}
+
+#[derive(Clone)]
+pub struct Callsite {
+    pub id: WidgetId,
+    pub label: String,
+    pub calls: u64,
+    pub distinct_widths: usize,
+}
+
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub enum ReuseOutcome {
+    Exact,
+    Moved,
+    Dirty,
+    WrongParent,
+    WrongLayer,
+    Remapped,
+    Outside,
+    Undrawn,
+}
+
+/// One targeted layout event. Events are retained in execution order, making
+/// repeated constraint paths visible without logging every widget globally.
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub enum TraceEvent {
+    DrawRequest {
+        id: WidgetId,
+        parent: Option<WidgetId>,
+        region: UiRegion,
+        pixel_size: PxVec2,
+        region_node: bool,
+    },
+    Reuse {
+        id: WidgetId,
+        outcome: ReuseOutcome,
+    },
+    SizeReported {
+        id: WidgetId,
+        size: Size,
+    },
+    RegionNode {
+        id: WidgetId,
+        parent: WidgetId,
+        region: UiRegion,
+    },
+    SizeRead {
+        id: WidgetId,
+        reader: WidgetId,
+        size: Size,
+    },
+    HintRead {
+        id: WidgetId,
+        reader: WidgetId,
+        axis: Axis,
+        hint: Option<LayoutLen>,
+    },
+    TextRendered {
+        id: WidgetId,
+        width: Option<f32>,
+    },
+}
+
+#[derive(Default)]
+struct Calls {
+    label: String,
+    count: u64,
+    widths: HashSet<Option<u32>>,
+}
+
+#[derive(Default)]
+struct Current {
+    report: Report,
+    widgets: HashMap<WidgetId, Calls>,
+    text_widgets: HashMap<WidgetId, Calls>,
+    traced: HashSet<WidgetId>,
+}
+
+thread_local! {
+    static CURRENT: RefCell<Current> = RefCell::new(Current::default());
+}
+
+pub(crate) fn bump(counter: Counter) {
+    CURRENT.with_borrow_mut(|current| current.report.counters[counter as usize] += 1);
+}
+
+pub(crate) fn draw_widget(id: WidgetId, label: &str) {
+    CURRENT.with_borrow_mut(|current| {
+        let calls = current.widgets.entry(id).or_default();
+        if calls.label.is_empty() {
+            calls.label = label.to_owned();
+        }
+        calls.count += 1;
+    });
+}
+
+/// Adds a widget to the targeted trace set. Selection survives [`take`]
+/// until explicitly removed or cleared.
+pub fn trace_widget(id: impl Into<WidgetId>) {
+    CURRENT.with_borrow_mut(|current| {
+        current.traced.insert(id.into());
+    });
+}
+
+pub fn untrace_widget(id: impl Into<WidgetId>) {
+    CURRENT.with_borrow_mut(|current| {
+        current.traced.remove(&id.into());
+    });
+}
+
+pub fn clear_traced_widgets() {
+    CURRENT.with_borrow_mut(|current| current.traced.clear());
+}
+
+fn trace(id: WidgetId, event: TraceEvent) {
+    CURRENT.with_borrow_mut(|current| {
+        if current.traced.contains(&id) {
+            current.report.traces.push(event);
+        }
+    });
+}
+
+pub(crate) fn draw_request(
+    id: WidgetId,
+    parent: Option<WidgetId>,
+    region: UiRegion,
+    pixel_size: PxVec2,
+    region_node: bool,
+) {
+    trace(
+        id,
+        TraceEvent::DrawRequest {
+            id,
+            parent,
+            region,
+            pixel_size,
+            region_node,
+        },
+    );
+}
+
+pub(crate) fn reuse(id: WidgetId, outcome: ReuseOutcome) {
+    trace(id, TraceEvent::Reuse { id, outcome });
+}
+
+pub(crate) fn size_reported(id: WidgetId, size: Size) {
+    trace(id, TraceEvent::SizeReported { id, size });
+}
+
+pub(crate) fn region_node(id: WidgetId, parent: WidgetId, region: UiRegion) {
+    trace(id, TraceEvent::RegionNode { id, parent, region });
+}
+
+pub(crate) fn size_read(id: WidgetId, reader: WidgetId, size: Size) {
+    trace(id, TraceEvent::SizeRead { id, reader, size });
+}
+
+pub(crate) fn hint_read(id: WidgetId, reader: WidgetId, axis: Axis, hint: Option<LayoutLen>) {
+    trace(
+        id,
+        TraceEvent::HintRead {
+            id,
+            reader,
+            axis,
+            hint,
+        },
+    );
+}
+
+pub(crate) fn render_text(id: WidgetId, label: &str, width: Option<f32>) {
+    CURRENT.with_borrow_mut(|current| {
+        let calls = current.text_widgets.entry(id).or_default();
+        if calls.label.is_empty() {
+            calls.label = label.to_owned();
+        }
+        calls.count += 1;
+        calls.widths.insert(width.map(f32::to_bits));
+        if current.traced.contains(&id) {
+            current
+                .report
+                .traces
+                .push(TraceEvent::TextRendered { id, width });
+        }
+    });
+}
+
+pub(crate) struct Timer {
+    kind: TimerKind,
+    start: Instant,
+}
+
+pub(crate) fn timer(kind: TimerKind) -> Timer {
+    Timer {
+        kind,
+        start: Instant::now(),
+    }
+}
+
+impl Drop for Timer {
+    fn drop(&mut self) {
+        let nanos = self.start.elapsed().as_nanos().min(u64::MAX as u128) as u64;
+        CURRENT.with_borrow_mut(|current| current.report.nanos[self.kind as usize] += nanos);
+    }
+}
+
+/// Takes all diagnostics accumulated on this thread and resets them.
+pub fn take() -> Report {
+    CURRENT.with_borrow_mut(|current| {
+        current.report.distinct_widgets = current.widgets.len();
+        current.report.distinct_text_widgets = current.text_widgets.len();
+        current.report.hot_widgets = hottest(&current.widgets);
+        current.report.hot_text = hottest(&current.text_widgets);
+        let report = std::mem::take(&mut current.report);
+        current.widgets.clear();
+        current.text_widgets.clear();
+        report
+    })
+}
+
+fn hottest(calls: &HashMap<WidgetId, Calls>) -> Vec<Callsite> {
+    let mut calls: Vec<_> = calls
+        .iter()
+        .map(|(&id, calls)| Callsite {
+            id,
+            label: calls.label.clone(),
+            calls: calls.count,
+            distinct_widths: calls.widths.len(),
+        })
+        .collect();
+    calls.sort_by(|a, b| b.calls.cmp(&a.calls).then_with(|| a.label.cmp(&b.label)));
+    calls.truncate(8);
+    calls
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn taking_a_report_resets_its_counters() {
+        let _ = take();
+        bump(Counter::Updates);
+        bump(Counter::Updates);
+
+        let report = take();
+        assert_eq!(report.counters().next(), Some(("updates", 2)));
+        assert!(take().counters().all(|(_, count)| count == 0));
+    }
+}

core/src/lib.rs

@@ -10,8 +10,12 @@
 #![feature(coerce_unsized)]
 #![feature(option_into_flat_iter)]
 
+#[cfg(feature = "layout-diagnostics")]
+pub mod layout_diagnostics;
+
 mod attr;
 mod event;
+mod fixed;
 mod num;
 mod orientation;
 mod primitive;
@@ -23,6 +27,7 @@ pub mod util;
 
 pub use attr::*;
 pub use event::*;
+pub use fixed::*;
 pub use num::*;
 pub use orientation::*;
 pub use primitive::*;

core/src/orientation/align.rs

@@ -1,8 +1,8 @@
-use crate::vec2;
+use crate::{Px, Rel};
 
 use super::*;
 
-#[derive(Clone, Copy, PartialEq, Eq)]
+#[derive(Clone, Copy, PartialEq)]
 pub struct Align {
     pub x: Option<AxisAlign>,
     pub y: Option<AxisAlign>,
@@ -30,20 +30,32 @@ impl Align {
     }
 }
 
-#[derive(Clone, Copy, PartialEq, Eq)]
-pub enum AxisAlign {
-    Neg,
-    Center,
-    Pos,
-}
+/// Where a widget sits in a box longer than it is. The default is the middle,
+/// because the two edges are the ones that assume a direction: which of them
+/// is the near one depends on the writing system and on which way a container
+/// runs, and the middle is the same either way.
+#[derive(Debug, Clone, Copy, PartialEq)]
+pub struct AxisAlign(Rel);
 
 impl AxisAlign {
-    pub const fn rel(&self) -> f32 {
-        match self {
-            Self::Neg => 0.0,
-            Self::Center => 0.5,
-            Self::Pos => 1.0,
-        }
+    pub const NEG: Self = Self::new(0.0);
+    pub const CENTER: Self = Self::new(0.5);
+    pub const POS: Self = Self::new(1.0);
+
+    pub const fn new(rel: f32) -> Self {
+        Self(Rel::from_f32(rel))
+    }
+
+    /// A fraction of the room left over, which is what the layout reads: the
+    /// three constants are the familiar places along it, not the only ones.
+    pub const fn rel(&self) -> Rel {
+        self.0
+    }
+}
+
+impl Default for AxisAlign {
+    fn default() -> Self {
+        Self::CENTER
     }
 }
 
@@ -53,41 +65,60 @@ pub struct CardinalAlign {
 }
 
 impl CardinalAlign {
-    pub const LEFT: Self = Self::new(Axis::X, AxisAlign::Neg);
-    pub const H_CENTER: Self = Self::new(Axis::X, AxisAlign::Center);
-    pub const RIGHT: Self = Self::new(Axis::X, AxisAlign::Pos);
-    pub const TOP: Self = Self::new(Axis::Y, AxisAlign::Neg);
-    pub const V_CENTER: Self = Self::new(Axis::Y, AxisAlign::Center);
-    pub const BOT: Self = Self::new(Axis::Y, AxisAlign::Pos);
+    pub const LEFT: Self = Self::new(Axis::X, AxisAlign::NEG);
+    pub const H_CENTER: Self = Self::new(Axis::X, AxisAlign::CENTER);
+    pub const RIGHT: Self = Self::new(Axis::X, AxisAlign::POS);
+    pub const TOP: Self = Self::new(Axis::Y, AxisAlign::NEG);
+    pub const V_CENTER: Self = Self::new(Axis::Y, AxisAlign::CENTER);
+    pub const BOT: Self = Self::new(Axis::Y, AxisAlign::POS);
 
     pub const fn new(axis: Axis, align: AxisAlign) -> Self {
         Self { axis, align }
     }
 }
 
-#[derive(Clone, Copy, PartialEq, Eq)]
+#[derive(Debug, Clone, Copy, PartialEq, Default)]
 pub struct RegionAlign {
     pub x: AxisAlign,
     pub y: AxisAlign,
 }
 
 impl RegionAlign {
-    pub const TOP_LEFT: Self = Self::new(AxisAlign::Neg, AxisAlign::Neg);
-    pub const TOP_CENTER: Self = Self::new(AxisAlign::Center, AxisAlign::Neg);
-    pub const TOP_RIGHT: Self = Self::new(AxisAlign::Pos, AxisAlign::Neg);
-    pub const CENTER_LEFT: Self = Self::new(AxisAlign::Neg, AxisAlign::Center);
-    pub const CENTER: Self = Self::new(AxisAlign::Center, AxisAlign::Center);
-    pub const CENTER_RIGHT: Self = Self::new(AxisAlign::Pos, AxisAlign::Center);
-    pub const BOT_LEFT: Self = Self::new(AxisAlign::Neg, AxisAlign::Pos);
-    pub const BOT_CENTER: Self = Self::new(AxisAlign::Center, AxisAlign::Pos);
-    pub const BOT_RIGHT: Self = Self::new(AxisAlign::Pos, AxisAlign::Pos);
+    /// Both axes at the near edge: the start of a box in its own orientation.
+    pub const NEAR: Self = Self {
+        x: AxisAlign::NEG,
+        y: AxisAlign::NEG,
+    };
+
+    pub fn axis(&self, axis: Axis) -> AxisAlign {
+        match axis {
+            Axis::X => self.x,
+            Axis::Y => self.y,
+        }
+    }
+
+    pub fn axis_mut(&mut self, axis: Axis) -> &mut AxisAlign {
+        match axis {
+            Axis::X => &mut self.x,
+            Axis::Y => &mut self.y,
+        }
+    }
+}
+
+impl RegionAlign {
+    pub const TOP_LEFT: Self = Self::new(AxisAlign::NEG, AxisAlign::NEG);
+    pub const TOP_CENTER: Self = Self::new(AxisAlign::CENTER, AxisAlign::NEG);
+    pub const TOP_RIGHT: Self = Self::new(AxisAlign::POS, AxisAlign::NEG);
+    pub const CENTER_LEFT: Self = Self::new(AxisAlign::NEG, AxisAlign::CENTER);
+    pub const CENTER: Self = Self::new(AxisAlign::CENTER, AxisAlign::CENTER);
+    pub const CENTER_RIGHT: Self = Self::new(AxisAlign::POS, AxisAlign::CENTER);
+    pub const BOT_LEFT: Self = Self::new(AxisAlign::NEG, AxisAlign::POS);
+    pub const BOT_CENTER: Self = Self::new(AxisAlign::CENTER, AxisAlign::POS);
+    pub const BOT_RIGHT: Self = Self::new(AxisAlign::POS, AxisAlign::POS);
 
     pub const fn new(x: AxisAlign, y: AxisAlign) -> Self {
         Self { x, y }
     }
-    pub const fn rel(&self) -> Vec2 {
-        vec2(self.x.rel(), self.y.rel())
-    }
 }
 
 impl UiVec2 {
@@ -140,16 +171,15 @@ impl Vec2 {
     }
 }
 
-impl UiScalar {
+impl Len {
     pub const fn align(&self, align: AxisAlign) -> UiSpan {
         let rel = align.rel();
-        let mut start = UiScalar::rel(rel);
-        start.abs -= self.abs * rel;
-        start.rel -= self.rel * rel;
-        let mut end = UiScalar::rel(rel);
-        end.abs += self.abs * (1.0 - rel);
-        end.rel += self.rel * (1.0 - rel);
-        UiSpan { start, end }
+        let rest = Rel::ONE.sub(rel);
+        let at = Len::from_parts(rel, Px::ZERO);
+        UiSpan {
+            start: Len::from_parts(at.rel.sub(self.rel.mul(rel)), at.px.sub(self.px.mul(rel))),
+            end: Len::from_parts(at.rel.add(self.rel.mul(rest)), at.px.add(self.px.mul(rest))),
+        }
     }
 }
 
@@ -165,8 +195,8 @@ impl From<RegionAlign> for Align {
 impl From<Align> for RegionAlign {
     fn from(align: Align) -> Self {
         Self {
-            x: align.x.unwrap_or(AxisAlign::Center),
-            y: align.y.unwrap_or(AxisAlign::Center),
+            x: align.x.unwrap_or(AxisAlign::CENTER),
+            y: align.y.unwrap_or(AxisAlign::CENTER),
         }
     }
 }
@@ -189,7 +219,10 @@ impl From<CardinalAlign> for Align {
 
 const impl From<RegionAlign> for UiVec2 {
     fn from(align: RegionAlign) -> Self {
-        Self::rel(align.rel())
+        Self::new(
+            Len::from_parts(align.x.rel(), Px::ZERO),
+            Len::from_parts(align.y.rel(), Px::ZERO),
+        )
     }
 }
 

core/src/orientation/axis.rs

@@ -1,6 +1,7 @@
 use super::*;
+use crate::{Fixed, FixedVec2};
 
-#[derive(Copy, Clone, Eq, PartialEq)]
+#[derive(Copy, Clone, Debug, Eq, PartialEq)]
 pub enum Axis {
     X,
     Y,
@@ -40,6 +41,29 @@ pub enum Sign {
     Pos,
 }
 
+impl<const SHIFT: u32> FixedVec2<SHIFT> {
+    pub const fn axis(&self, axis: Axis) -> Fixed<SHIFT> {
+        match axis {
+            Axis::X => self.x,
+            Axis::Y => self.y,
+        }
+    }
+
+    pub const fn axis_mut(&mut self, axis: Axis) -> &mut Fixed<SHIFT> {
+        match axis {
+            Axis::X => &mut self.x,
+            Axis::Y => &mut self.y,
+        }
+    }
+
+    pub const fn from_axis(axis: Axis, aligned: Fixed<SHIFT>, ortho: Fixed<SHIFT>) -> Self {
+        match axis {
+            Axis::X => Self::new(aligned, ortho),
+            Axis::Y => Self::new(ortho, aligned),
+        }
+    }
+}
+
 impl Vec2 {
     pub fn axis(&self, axis: Axis) -> f32 {
         match axis {

core/src/orientation/len.rs

@@ -1,22 +1,30 @@
 use super::*;
-use crate::{UiNum, util::impl_op};
+use crate::{Px, PxVec2, Rel, UiNum, Weight, util::impl_op};
 
 #[derive(Debug, Default, Clone, Copy, PartialEq)]
 pub struct Size {
-    pub x: Len,
-    pub y: Len,
+    pub x: LayoutLen,
+    pub y: LayoutLen,
 }
 
-#[derive(Debug, Clone, Copy, PartialEq)]
-pub struct Len {
-    pub abs: f32,
-    pub rel: f32,
-    pub rest: f32,
+/// What a widget asks for along one axis: a [`Len`] -- pixels and a fraction
+/// of the box it is given -- plus a share of whatever is left over once
+/// everything fixed has been taken. The parts add up rather than choosing
+/// between one another.
+///
+/// Only a container dividing its room can answer a share, so a length nobody
+/// divides is a `Len`: a position, a padding, a cap, anything already
+/// resolved.
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
+pub struct LayoutLen {
+    pub px: Px,
+    pub rel: Rel,
+    pub leftover: Weight,
 }
 
-impl<N: UiNum> From<N> for Len {
+impl<N: UiNum> From<N> for LayoutLen {
     fn from(value: N) -> Self {
-        Len::abs(value.to_f32())
+        LayoutLen::px(value.to_f32())
     }
 }
 
@@ -29,52 +37,76 @@ impl<Nx: UiNum, Ny: UiNum> From<(Nx, Ny)> for Size {
     }
 }
 
-impl From<Len> for Size {
-    fn from(value: Len) -> Self {
+/// A length with no share in it is a length a container does not have to
+/// divide, which is one it can always give.
+impl From<Len> for LayoutLen {
+    fn from(len: Len) -> Self {
+        Self {
+            px: len.px,
+            rel: len.rel,
+            leftover: Weight::ZERO,
+        }
+    }
+}
+
+impl From<LayoutLen> for Size {
+    fn from(value: LayoutLen) -> Self {
         Self { x: value, y: value }
     }
 }
 
 impl Size {
     pub const ZERO: Self = Self {
-        x: Len::ZERO,
-        y: Len::ZERO,
+        x: LayoutLen::ZERO,
+        y: LayoutLen::ZERO,
     };
 
-    pub const REST: Self = Self {
-        x: Len::REST,
-        y: Len::REST,
+    pub const LEFTOVER: Self = Self {
+        x: LayoutLen::LEFTOVER,
+        y: LayoutLen::LEFTOVER,
     };
 
-    pub fn abs(v: Vec2) -> Self {
+    /// From something measured outside layout -- a texture, a shaped line --
+    /// which is where a size in floats comes from.
+    pub fn px(v: Vec2) -> Self {
+        Self::from_px(PxVec2::from_f32(v))
+    }
+
+    pub const fn from_px(v: PxVec2) -> Self {
         Self {
-            x: Len::abs(v.x),
-            y: Len::abs(v.y),
+            x: LayoutLen {
+                px: v.x,
+                ..LayoutLen::ZERO
+            },
+            y: LayoutLen {
+                px: v.y,
+                ..LayoutLen::ZERO
+            },
         }
     }
 
     pub fn rel(v: Vec2) -> Self {
         Self {
-            x: Len::rel(v.x),
-            y: Len::rel(v.y),
+            x: LayoutLen::rel(v.x),
+            y: LayoutLen::rel(v.y),
         }
     }
 
-    pub fn rest(v: Vec2) -> Self {
+    pub fn leftover(v: Vec2) -> Self {
         Self {
-            x: Len::rest(v.x),
-            y: Len::rest(v.y),
+            x: LayoutLen::leftover(v.x),
+            y: LayoutLen::leftover(v.y),
         }
     }
 
     pub fn to_uivec2(self) -> UiVec2 {
         UiVec2 {
-            x: self.x.apply_rest(),
-            y: self.y.apply_rest(),
+            x: self.x.apply_leftover(),
+            y: self.y.apply_leftover(),
         }
     }
 
-    pub fn from_axis(axis: Axis, aligned: Len, ortho: Len) -> Self {
+    pub fn from_axis(axis: Axis, aligned: LayoutLen, ortho: LayoutLen) -> Self {
         match axis {
             Axis::X => Self {
                 x: aligned,
@@ -87,53 +119,73 @@ impl Size {
         }
     }
 
-    pub fn axis(&self, axis: Axis) -> Len {
+    pub fn axis(&self, axis: Axis) -> LayoutLen {
         match axis {
             Axis::X => self.x,
             Axis::Y => self.y,
         }
     }
+
+    pub fn axis_mut(&mut self, axis: Axis) -> &mut LayoutLen {
+        match axis {
+            Axis::X => &mut self.x,
+            Axis::Y => &mut self.y,
+        }
+    }
 }
 
-impl Len {
+impl LayoutLen {
     pub const ZERO: Self = Self {
-        abs: 0.0,
-        rel: 0.0,
-        rest: 0.0,
+        px: Px::ZERO,
+        rel: Rel::ZERO,
+        leftover: Weight::ZERO,
     };
 
-    pub const REST: Self = Self {
-        abs: 0.0,
-        rel: 0.0,
-        rest: 1.0,
+    pub const LEFTOVER: Self = Self {
+        px: Px::ZERO,
+        rel: Rel::ZERO,
+        leftover: Weight::ONE,
     };
 
-    pub fn apply_rest(&self) -> UiScalar {
-        UiScalar {
-            rel: self.rel + if self.rest > 0.0 { 1.0 } else { 0.0 },
-            abs: self.abs,
+    /// The whole of what is left over counts as the whole box, which is what
+    /// a length means to something that is not dividing a box between
+    /// siblings -- a scroll asking how long its content is.
+    pub fn apply_leftover(&self) -> Len {
+        let share = match self.leftover > Weight::ZERO {
+            true => Rel::ONE,
+            false => Rel::ZERO,
+        };
+        Len::from_parts(self.rel.add(share), self.px)
+    }
+
+    /// This length, given as a part of a box `len` long, as a part of the
+    /// box `len` is itself a part of. The share is untouched: it is a claim
+    /// on whoever divides the room, not a fraction of anything.
+    pub const fn within_len(self, len: Len) -> Self {
+        let part = Len::from_parts(self.rel, self.px).within_len(len);
+        Self {
+            px: part.px,
+            rel: part.rel,
+            leftover: self.leftover,
         }
     }
 
-    pub fn abs(abs: impl UiNum) -> Self {
+    pub fn px(px: impl UiNum) -> Self {
         Self {
-            abs: abs.to_f32(),
-            rel: 0.0,
-            rest: 0.0,
+            px: Px::from_num(px),
+            ..Self::ZERO
         }
     }
     pub fn rel(rel: impl UiNum) -> Self {
         Self {
-            abs: 0.0,
-            rel: rel.to_f32(),
-            rest: 0.0,
+            rel: Rel::from_num(rel),
+            ..Self::ZERO
         }
     }
-    pub fn rest(ratio: impl UiNum) -> Self {
+    pub fn leftover(ratio: impl UiNum) -> Self {
         Self {
-            abs: 0.0,
-            rel: 0.0,
-            rest: ratio.to_f32(),
+            leftover: Weight::from_num(ratio),
+            ..Self::ZERO
         }
     }
 }
@@ -141,38 +193,26 @@ impl Len {
 pub mod len_fns {
     use super::*;
 
-    pub fn abs(abs: impl UiNum) -> Len {
-        Len {
-            abs: abs.to_f32(),
-            rel: 0.0,
-            rest: 0.0,
-        }
+    pub fn px(px: impl UiNum) -> LayoutLen {
+        LayoutLen::px(px)
     }
-    pub fn rel(rel: impl UiNum) -> Len {
-        Len {
-            abs: 0.0,
-            rel: rel.to_f32(),
-            rest: 0.0,
-        }
+    pub fn rel(rel: impl UiNum) -> LayoutLen {
+        LayoutLen::rel(rel)
     }
-    pub fn rest(ratio: impl UiNum) -> Len {
-        Len {
-            abs: 0.0,
-            rel: 0.0,
-            rest: ratio.to_f32(),
-        }
+    pub fn leftover(ratio: impl UiNum) -> LayoutLen {
+        LayoutLen::leftover(ratio)
     }
 }
 
-impl_op!(Len Add add; abs rel rest);
-impl_op!(Len Sub sub; abs rel rest);
+impl_op!(same LayoutLen Add add; px rel leftover);
+impl_op!(same LayoutLen Sub sub; px rel leftover);
 
-impl_op!(Size Add add; x y);
-impl_op!(Size Sub sub; x y);
+impl_op!(same Size Add add; x y);
+impl_op!(same Size Sub sub; x y);
 
-impl Default for Len {
+impl Default for LayoutLen {
     fn default() -> Self {
-        Self::rest(1.0)
+        Self::leftover(1.0)
     }
 }
 
@@ -182,16 +222,16 @@ impl std::fmt::Display for Size {
     }
 }
 
-impl std::fmt::Display for Len {
+impl std::fmt::Display for LayoutLen {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
-        if self.abs != 0.0 {
-            write!(f, "{} abs;", self.abs)?;
+        if self.px != Px::ZERO {
+            write!(f, "{} px;", self.px)?;
         }
-        if self.rel != 0.0 {
+        if self.rel != Rel::ZERO {
             write!(f, "{} rel;", self.rel)?;
         }
-        if self.rest != 0.0 {
-            write!(f, "{} rest;", self.rest)?;
+        if self.leftover != Weight::ZERO {
+            write!(f, "{} leftover;", self.leftover)?;
         }
         Ok(())
     }

core/src/orientation/pos.rs

@@ -1,41 +1,46 @@
-use std::{fmt::Display, hash::Hash, marker::Destruct};
+use std::{fmt::Display, marker::Destruct};
 
 use super::*;
-use crate::{
-    UiNum,
-    util::{LerpUtil, impl_op},
-};
+use crate::{Px, PxVec2, Rel, UiNum, util::impl_op};
 
 #[repr(C)]
 #[derive(Debug, Copy, Clone, PartialEq, Eq, Hash, bytemuck::Pod, bytemuck::Zeroable, Default)]
 pub struct UiVec2 {
-    pub x: UiScalar,
-    pub y: UiScalar,
+    pub x: Len,
+    pub y: Len,
 }
 
 impl UiVec2 {
     pub const ZERO: Self = Self {
-        x: UiScalar::ZERO,
-        y: UiScalar::ZERO,
+        x: Len::ZERO,
+        y: Len::ZERO,
     };
 
-    pub const fn new(x: UiScalar, y: UiScalar) -> Self {
+    pub const fn new(x: Len, y: Len) -> Self {
         Self { x, y }
     }
 
-    pub const fn abs(abs: impl const Into<Vec2>) -> Self {
-        let abs = abs.into();
+    pub const fn px(px: impl const Into<Vec2>) -> Self {
+        let px = px.into();
         Self {
-            x: UiScalar::abs(abs.x),
-            y: UiScalar::abs(abs.y),
+            x: Len::px(px.x),
+            y: Len::px(px.y),
+        }
+    }
+
+    /// From lengths already on the grid, with no fraction of a box.
+    pub const fn from_px(px: PxVec2) -> Self {
+        Self {
+            x: Len::from_parts(Rel::ZERO, px.x),
+            y: Len::from_parts(Rel::ZERO, px.y),
         }
     }
 
     pub const fn rel(rel: impl const Into<Vec2>) -> Self {
         let rel = rel.into();
         Self {
-            x: UiScalar::rel(rel.x),
-            y: UiScalar::rel(rel.y),
+            x: Len::rel(rel.x),
+            y: Len::rel(rel.y),
         }
     }
 
@@ -56,30 +61,29 @@ impl UiVec2 {
         }
     }
 
-    pub fn axis_mut(&mut self, axis: Axis) -> &mut UiScalar {
+    pub fn axis_mut(&mut self, axis: Axis) -> &mut Len {
         match axis {
             Axis::X => &mut self.x,
             Axis::Y => &mut self.y,
         }
     }
 
-    pub fn axis(&self, axis: Axis) -> UiScalar {
+    pub fn axis(&self, axis: Axis) -> Len {
         match axis {
             Axis::X => self.x,
             Axis::Y => self.y,
         }
     }
 
-    pub fn to_abs(&self, rel: Vec2) -> Vec2 {
-        Vec2 {
-            x: self.x.to_abs(rel.x),
-            y: self.y.to_abs(rel.y),
-        }
+    /// Resolved against a box of `size`, which is where a fraction stops
+    /// being one and becomes a place.
+    pub fn to_px(&self, size: PxVec2) -> PxVec2 {
+        PxVec2::new(self.x.to_px(size.x), self.y.to_px(size.y))
     }
 
     pub const FULL_SIZE: Self = Self::rel(Vec2::ONE);
 
-    pub const fn from_axis(axis: Axis, aligned: UiScalar, ortho: UiScalar) -> Self {
+    pub const fn from_axis(axis: Axis, aligned: Len, ortho: Len) -> Self {
         match axis {
             Axis::X => Self {
                 x: aligned,
@@ -92,34 +96,27 @@ impl UiVec2 {
         }
     }
 
-    pub fn get_abs(&self) -> Vec2 {
-        (self.x.abs, self.y.abs).into()
+    pub fn get_px(&self) -> Vec2 {
+        (self.x.px.to_f32(), self.y.px.to_f32()).into()
     }
 
     pub fn get_rel(&self) -> Vec2 {
-        (self.x.rel, self.y.rel).into()
-    }
-
-    pub fn abs_mut(&mut self) -> Vec2View<'_> {
-        Vec2View {
-            x: &mut self.x.abs,
-            y: &mut self.y.abs,
-        }
+        (self.x.rel.to_f32(), self.y.rel.to_f32()).into()
     }
 }
 
 impl Display for UiVec2 {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
-        write!(f, "rel{};abs{}", self.get_rel(), self.get_abs())
+        write!(f, "rel{};px{}", self.get_rel(), self.get_px())
     }
 }
 
-impl_op!(UiVec2 Add add; x y);
-impl_op!(UiVec2 Sub sub; x y);
+impl_op!(same UiVec2 Add add; x y);
+impl_op!(same UiVec2 Sub sub; x y);
 
 const impl From<Vec2> for UiVec2 {
-    fn from(abs: Vec2) -> Self {
-        Self::abs(abs)
+    fn from(px: Vec2) -> Self {
+        Self::px(px)
     }
 }
 
@@ -127,135 +124,149 @@ const impl<T: const UiNum, U: const UiNum> From<(T, U)> for UiVec2
 where
     (T, U): const Destruct,
 {
-    fn from(abs: (T, U)) -> Self {
-        Self::abs(abs)
+    fn from(px: (T, U)) -> Self {
+        Self::px(px)
     }
 }
 
+/// A length along one axis: a fraction of the box it is measured in plus an
+/// offset, `rel * box + px`. A position is the same number -- the length from
+/// the start of the box to the point -- which is why a [`UiSpan`] is two of
+/// these. Both parts are fixed point, so composing one through a chain of
+/// boxes rounds only where it multiplies, and lands on the same number as any
+/// other route to the same place.
+///
+/// It carries no claim on what a container has left over. That is
+/// [`crate::LayoutLen`], which is this plus a weight, and which means nothing
+/// to anyone but whoever divides the room.
 #[repr(C)]
-#[derive(Debug, Copy, Clone, PartialEq, bytemuck::Pod, Default, bytemuck::Zeroable)]
-pub struct UiScalar {
-    pub rel: f32,
-    pub abs: f32,
+#[derive(Debug, Copy, Clone, PartialEq, Eq, Hash, bytemuck::Pod, Default, bytemuck::Zeroable)]
+pub struct Len {
+    pub rel: Rel,
+    pub px: Px,
 }
 
-impl Eq for UiScalar {}
-impl Hash for UiScalar {
-    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
-        state.write_u32(self.rel.to_bits());
-        state.write_u32(self.abs.to_bits());
+impl_op!(same Len Add add; rel px);
+impl_op!(same Len Sub sub; rel px);
+
+impl Len {
+    pub const ZERO: Self = Self {
+        rel: Rel::ZERO,
+        px: Px::ZERO,
+    };
+    pub const FULL: Self = Self {
+        rel: Rel::ONE,
+        px: Px::ZERO,
+    };
+
+    pub const fn new(rel: f32, px: f32) -> Self {
+        Self::from_parts(Rel::from_f32(rel), Px::from_f32(px))
     }
-}
 
-impl_op!(UiScalar Add add; rel abs);
-impl_op!(UiScalar Sub sub; rel abs);
-
-impl UiScalar {
-    pub const ZERO: Self = Self { rel: 0.0, abs: 0.0 };
-    pub const FULL: Self = Self { rel: 1.0, abs: 0.0 };
-
-    pub const fn new(rel: f32, abs: f32) -> Self {
-        Self { rel, abs }
+    /// From parts already on the grid, rather than numbers to be put on it.
+    pub const fn from_parts(rel: Rel, px: Px) -> Self {
+        Self { rel, px }
     }
 
     pub const fn rel(rel: f32) -> Self {
-        Self { rel, abs: 0.0 }
+        Self::from_parts(Rel::from_f32(rel), Px::ZERO)
     }
 
-    pub const fn abs(abs: f32) -> Self {
-        Self { rel: 0.0, abs }
+    pub const fn px(px: f32) -> Self {
+        Self::from_parts(Rel::ZERO, Px::from_f32(px))
     }
 
     pub const fn rel_min() -> Self {
-        Self::new(0.0, 0.0)
+        Self::ZERO
     }
 
     pub const fn rel_max() -> Self {
-        Self::new(1.0, 0.0)
+        Self::FULL
     }
 
     pub const fn max(&self, other: Self) -> Self {
         Self {
             rel: self.rel.max(other.rel),
-            abs: self.abs.max(other.abs),
+            px: self.px.max(other.px),
         }
     }
 
     pub const fn min(&self, other: Self) -> Self {
         Self {
             rel: self.rel.min(other.rel),
-            abs: self.abs.min(other.abs),
+            px: self.px.min(other.px),
         }
     }
 
-    pub const fn offset(mut self, amt: f32) -> Self {
-        self.abs += amt;
+    /// Both parts by the same fraction, which is what a part of a length
+    /// means when the length is part pixels and part a fraction of a box.
+    pub const fn scale(&self, by: Rel) -> Self {
+        Self {
+            rel: self.rel.mul(by),
+            px: self.px.mul(by),
+        }
+    }
+
+    pub const fn offset(mut self, amt: Px) -> Self {
+        self.px = self.px.add(amt);
         self
     }
 
     pub const fn within(&self, span: &UiSpan) -> Self {
-        let anchor = self.rel.lerp(span.start.rel, span.end.rel);
-        let offset = self.abs + self.rel.lerp(span.start.abs, span.end.abs);
         Self {
-            rel: anchor,
-            abs: offset,
+            rel: self.rel.lerp(span.start.rel, span.end.rel),
+            px: self.px.add(self.rel.lerp(span.start.px, span.end.px)),
         }
     }
 
-    /// 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 })
-    }
-
-    pub fn within_len(&self, len: UiScalar) -> Self {
+    pub const fn within_len(&self, len: Len) -> Self {
         self.within(&UiSpan {
-            start: UiScalar::ZERO,
+            start: Len::ZERO,
             end: len,
         })
     }
 
-    pub fn select_len(&self, len: UiScalar) -> Self {
+    pub fn select_len(&self, len: Len) -> Self {
         len.within_len(*self)
     }
 
     pub const fn flip(&mut self) {
-        self.rel = 1.0 - self.rel;
-        self.abs = -self.abs;
+        self.rel = Rel::ONE.sub(self.rel);
+        self.px = self.px.neg();
     }
 
     pub const fn to(&self, end: Self) -> UiSpan {
         UiSpan { start: *self, end }
     }
 
-    pub const fn to_abs(&self, rel: f32) -> f32 {
-        self.rel * rel + self.abs
+    /// Resolved against a box of `len`, which is the only place a fraction
+    /// becomes a number of pixels.
+    pub const fn to_px(&self, len: Px) -> Px {
+        self.px.add(len.mul(self.rel))
     }
 }
 
 #[repr(C)]
 #[derive(Debug, Copy, Clone, PartialEq, bytemuck::Pod, bytemuck::Zeroable)]
 pub struct UiSpan {
-    pub start: UiScalar,
-    pub end: UiScalar,
+    pub start: Len,
+    pub end: Len,
 }
 
 impl UiSpan {
     pub const FULL: Self = Self {
-        start: UiScalar::ZERO,
-        end: UiScalar::FULL,
+        start: Len::ZERO,
+        end: Len::FULL,
     };
 
     pub const fn rel(rel: f32) -> Self {
         Self {
-            start: UiScalar::rel(rel),
-            end: UiScalar::rel(rel),
+            start: Len::rel(rel),
+            end: Len::rel(rel),
         }
     }
 
-    pub const fn new(start: UiScalar, end: UiScalar) -> Self {
+    pub const fn new(start: Len, end: Len) -> Self {
         Self { start, end }
     }
 
@@ -263,14 +274,19 @@ impl UiSpan {
         self.start.flip();
         self.end.flip();
         std::mem::swap(&mut self.start.rel, &mut self.end.rel);
-        std::mem::swap(&mut self.start.abs, &mut self.end.abs);
+        std::mem::swap(&mut self.start.px, &mut self.end.px);
     }
 
-    pub const fn shift(&mut self, offset: UiScalar) {
+    pub const fn shift(&mut self, offset: Len) {
         self.start += offset;
         self.end += offset;
     }
 
+    /// Composing a box through the one it sits in, and the hottest line in
+    /// layout. It used to skip the multiplies where a span was the whole of
+    /// its parent or the parent the whole of its own; both come out of the
+    /// multiply unchanged anyway, and the body those comparisons cost was
+    /// what kept the inliner from taking this at all.
     pub const fn within(&self, parent: &Self) -> Self {
         Self {
             start: self.start.within(parent),
@@ -278,15 +294,17 @@ 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) -> Len {
+        self.end - self.start
     }
 
-    pub const fn len(&self) -> UiScalar {
-        self.end - self.start
+    /// Both ends by the same amount, which is what moving a box without
+    /// changing its length does to every part of it.
+    pub const fn translated(self, by: Len) -> Self {
+        Self {
+            start: self.start + by,
+            end: self.end + by,
+        }
     }
 }
 
@@ -298,6 +316,17 @@ pub struct UiRegion {
 }
 
 impl UiRegion {
+    /// Every part of the box by the same amount on each axis. Done to the
+    /// whole region rather than an end at a time, because that is what it is
+    /// -- and because four adds in a row are four adds, where four asked for
+    /// separately are four sequences.
+    pub const fn translated(self, x: Len, y: Len) -> Self {
+        Self {
+            x: self.x.translated(x),
+            y: self.y.translated(y),
+        }
+    }
+
     pub const FULL: Self = Self {
         x: UiSpan::FULL,
         y: UiSpan::FULL,
@@ -351,10 +380,10 @@ impl UiRegion {
         self
     }
 
-    pub fn to_px(&self, size: Vec2) -> PixelRegion {
+    pub fn to_px(&self, size: PxVec2) -> PixelRegion {
         PixelRegion {
-            top_left: self.top_left().get_rel() * size + self.top_left().get_abs(),
-            bot_right: self.bot_right().get_rel() * size + self.bot_right().get_abs(),
+            top_left: self.top_left().to_px(size),
+            bot_right: self.bot_right().to_px(size),
         }
     }
 
@@ -397,50 +426,6 @@ 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 })
-    }
-
-    pub fn apply(&self, region: UiRegion) -> UiRegion {
-        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
-            }
-        }
-    }
-}
-
 impl Display for UiRegion {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
         write!(
@@ -453,21 +438,21 @@ impl Display for UiRegion {
     }
 }
 
-#[derive(Debug, Clone, Copy, PartialEq)]
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
 pub struct PixelRegion {
-    pub top_left: Vec2,
-    pub bot_right: Vec2,
+    pub top_left: PxVec2,
+    pub bot_right: PxVec2,
 }
 
 impl PixelRegion {
-    pub fn contains(&self, pos: Vec2) -> bool {
+    pub fn contains(&self, pos: PxVec2) -> bool {
         pos.x >= self.top_left.x
             && pos.x <= self.bot_right.x
             && pos.y >= self.top_left.y
             && pos.y <= self.bot_right.y
     }
 
-    pub fn size(&self) -> Vec2 {
+    pub fn size(&self) -> PxVec2 {
         self.bot_right - self.top_left
     }
 }
@@ -477,20 +462,3 @@ impl Display for PixelRegion {
         write!(f, "{} -> {}", self.top_left, self.bot_right)
     }
 }
-
-pub struct Vec2View<'a> {
-    pub x: &'a mut f32,
-    pub y: &'a mut f32,
-}
-
-impl Vec2View<'_> {
-    pub fn set(&mut self, other: Vec2) {
-        *self.x = other.x;
-        *self.y = other.y;
-    }
-
-    pub fn add(&mut self, other: Vec2) {
-        *self.x += other.x;
-        *self.y += other.y;
-    }
-}

core/src/primitive/layer.rs

@@ -120,6 +120,10 @@ impl<T: Default> Layers<T> {
 }
 
 impl DrawLayers {
+    /// Inlined on purpose: it is one call per glyph, the innermost thing a
+    /// frame does, and whether the inliner takes it turns out to depend on
+    /// unrelated code elsewhere in the crate -- 12% of a resize frame.
+    #[inline]
     pub fn write<P: Primitive>(
         &mut self,
         layer: LayerId,

core/src/primitive/text.rs

@@ -1,11 +1,17 @@
+#[cfg(feature = "layout-diagnostics")]
+use crate::layout_diagnostics::{self as diag, Counter, TimerKind};
 use crate::{
-    Align, GlyphAtlas, GlyphEntry, GlyphKey, PlacedGlyph, RegionAlign, UiColor, util::Vec2,
+    Align, GlyphAtlas, GlyphEntry, GlyphKey, PlacedGlyph, Px, PxVec2, RegionAlign, UiColor,
+    util::Vec2,
 };
 use parley::{
     Alignment, AlignmentOptions, FontContext, FontFamily, FontFamilyName, GenericFamily, Layout,
     LayoutContext, LineHeight, PositionedLayoutItem, StyleProperty,
 };
-use std::hash::{DefaultHasher, Hash, Hasher};
+use std::{
+    collections::VecDeque,
+    hash::{DefaultHasher, Hash, Hasher},
+};
 use swash::{
     FontRef,
     scale::{Render, ScaleContext, Source, StrikeWith},
@@ -17,8 +23,32 @@ pub struct TextData {
     pub layout_ctx: LayoutContext<UiColor>,
     scale_ctx: ScaleContext,
     pub atlas: GlyphAtlas,
+    spare: VecDeque<Placed>,
 }
 
+/// The glyphs of one text at one width. A buffer holds the ones it is drawn
+/// as; these are the ones it had before, kept because a container measures a
+/// child by drawing it in a box it may not keep, and so comes back to widths
+/// it has already asked for.
+struct Placed {
+    /// Where the glyphs land is a function of these three and nothing else,
+    /// so no widget or buffer identity is involved and two texts of the same
+    /// words share an answer.
+    text: String,
+    key: LayoutKey,
+    glyphs: RenderedText,
+}
+
+/// How many to keep. Bounding the whole store rather than each buffer is what
+/// makes this a fixed cost instead of one a tree of ten thousand texts pays
+/// ten thousand times; the re-asks come from laying out one subtree, so they
+/// are close together and few are needed. Instructions over 500 resize frames
+/// of `tests/revision_cost.rs`, both the repeating widths and the sweep that
+/// cannot hit across frames: 13.7B at 32, 12.1B at 64, 10.4B and 12.1B at 128,
+/// and nothing past that -- so 128, which is no worse in the case that never
+/// repeats and better in the one that does.
+const SPARE_PLACED: usize = 128;
+
 impl Default for TextData {
     fn default() -> Self {
         Self {
@@ -26,6 +56,7 @@ impl Default for TextData {
             layout_ctx: LayoutContext::new(),
             scale_ctx: ScaleContext::new(),
             atlas: GlyphAtlas::default(),
+            spare: VecDeque::new(),
         }
     }
 }
@@ -81,6 +112,9 @@ pub struct TextBuffer {
     text: String,
     layout: Layout<UiColor>,
     layout_key: Option<LayoutKey>,
+    /// The glyphs placed from `layout`, so drawing this text again at the
+    /// width it already has places them once.
+    placed: Option<RenderedText>,
 }
 
 #[derive(PartialEq)]
@@ -95,6 +129,7 @@ impl TextBuffer {
             text: text.into(),
             layout: Layout::new(),
             layout_key: None,
+            placed: None,
         }
     }
 
@@ -119,15 +154,28 @@ impl TextBuffer {
         if text != self.text {
             self.text = text;
             self.layout_key = None;
+            self.placed = None;
         }
     }
 
     /// Invalidates the layout and returns the underlying string for editing.
     pub fn edit(&mut self) -> &mut String {
         self.layout_key = None;
+        self.placed = None;
         &mut self.text
     }
 
+    /// The glyphs of the shaping it is drawn as, once they are placed.
+    pub fn rendered(&self) -> Option<&RenderedText> {
+        self.placed.as_ref()
+    }
+
+    /// The width its shaping wraps at, and `None` where it does not wrap or
+    /// has not been shaped.
+    pub fn wrap_width(&self) -> Option<f32> {
+        self.layout_key.as_ref()?.max_width
+    }
+
     pub fn size(&self) -> Vec2 {
         Vec2::new(self.layout.width(), self.layout.height())
     }
@@ -138,8 +186,62 @@ impl TextBuffer {
             max_width: width,
         };
         if self.layout_key.as_ref() == Some(&layout_key) {
+            #[cfg(feature = "layout-diagnostics")]
+            diag::bump(Counter::TextShapeHits);
             return;
         }
+        // A greedy break at one width is the same break at every width down
+        // to the longest line it produced: each line still fits, and none can
+        // take a word that would not fit in the wider box. So the layout in
+        // hand already answers, and re-breaking would only be work.
+        //
+        // At the longest line exactly, with no margin below it. A narrower
+        // width really does break differently, so answering one from the
+        // break in hand is how a warm tree keeps lines a cold tree would
+        // never produce. The margin was here because a text reports the
+        // width it used and a parent hands that back; the report is the step
+        // at or above its longest line now, so what comes back fits.
+        if let Some(key) = &self.layout_key
+            && key.attrs == *attrs
+            && let (Some(broke_at), Some(want)) = (key.max_width, width)
+            && want <= broke_at
+            && want >= self.layout.width()
+        {
+            #[cfg(feature = "layout-diagnostics")]
+            diag::bump(Counter::TextShapeHits);
+            return;
+        }
+        let same_shaping = self
+            .layout_key
+            .as_ref()
+            .is_some_and(|key| key.attrs == *attrs);
+        let old_key = self.layout_key.replace(layout_key);
+        // The glyphs it holds are of the width it held, which the layout may
+        // well come back to.
+        if let Some(key) = old_key
+            && let Some(glyphs) = self.placed.take()
+        {
+            data.keep_placed(Placed {
+                text: self.text.clone(),
+                key,
+                glyphs,
+            });
+        }
+        // Only the line breaking depends on the width: the shaped runs under
+        // it are a function of the text and the attrs, and parley re-breaks
+        // them in place. So a new width is a break, not a shaping.
+        if same_shaping {
+            #[cfg(feature = "layout-diagnostics")]
+            diag::bump(Counter::TextBreaks);
+            #[cfg(feature = "layout-diagnostics")]
+            let _break = diag::timer(TimerKind::TextBreak);
+            self.break_lines(width);
+            return;
+        }
+        #[cfg(feature = "layout-diagnostics")]
+        diag::bump(Counter::TextShapes);
+        #[cfg(feature = "layout-diagnostics")]
+        let _shape = diag::timer(TimerKind::TextShape);
         let mut builder = data
             .layout_ctx
             .ranged_builder(&mut data.font_ctx, &self.text, 1.0, true);
@@ -150,10 +252,13 @@ impl TextBuffer {
         )));
         builder.push_default(StyleProperty::Brush(attrs.color));
         builder.build_into(&mut self.layout, &self.text);
+        self.break_lines(width);
+    }
+
+    fn break_lines(&mut self, width: Option<f32>) {
         self.layout.break_all_lines(width);
         self.layout
             .align(Alignment::Start, AlignmentOptions::default());
-        self.layout_key = Some(layout_key);
     }
 }
 
@@ -196,9 +301,9 @@ impl TextData {
                     };
                     placed.push(PlacedGlyph {
                         entry,
-                        offset: Vec2::new(
-                            glyph.x.floor() + entry.left as f32,
-                            glyph.y.floor() - entry.top as f32,
+                        offset: PxVec2::new(
+                            Px::from_int(glyph.x.floor() as i32 + entry.left),
+                            Px::from_int(glyph.y.floor() as i32 - entry.top),
                         ),
                     });
                 }
@@ -265,18 +370,54 @@ pub struct RenderedText {
 }
 
 impl TextData {
-    pub fn render(
+    /// The glyphs of this text at this width, taken out of what is kept.
+    fn take_placed(&mut self, text: &str, key: &LayoutKey) -> Option<RenderedText> {
+        // From the newest, since a re-ask is usually of something recent.
+        let at = self
+            .spare
+            .iter()
+            .rposition(|spare| spare.key == *key && spare.text == text)?;
+        self.spare.remove(at).map(|spare| spare.glyphs)
+    }
+
+    fn keep_placed(&mut self, placed: Placed) {
+        if self.spare.len() >= SPARE_PLACED {
+            self.spare.pop_front();
+        }
+        self.spare.push_back(placed);
+    }
+
+    pub fn render<'b>(
         &mut self,
-        buffer: &mut TextBuffer,
+        buffer: &'b mut TextBuffer,
         attrs: &TextAttrs,
         width: Option<f32>,
-    ) -> RenderedText {
+    ) -> &'b RenderedText {
+        #[cfg(feature = "layout-diagnostics")]
+        diag::bump(Counter::TextRenders);
+        #[cfg(feature = "layout-diagnostics")]
+        let _render = diag::timer(TimerKind::TextRender);
         buffer.shape(self, attrs, width);
-        let glyphs = self.place(buffer);
-        RenderedText {
-            glyphs,
-            size: buffer.size(),
-            color: attrs.color,
-        }
+        // Only asked for when the buffer no longer holds them: taking one out
+        // of the store to then drop it would throw an answer away.
+        let placed = buffer.placed.take().or_else(|| {
+            let key = buffer.layout_key.as_ref()?;
+            self.take_placed(&buffer.text, key)
+        });
+        let placed = match placed {
+            Some(placed) => placed,
+            None => {
+                #[cfg(feature = "layout-diagnostics")]
+                diag::bump(Counter::GlyphPlacements);
+                #[cfg(feature = "layout-diagnostics")]
+                let _place = diag::timer(TimerKind::GlyphPlacement);
+                RenderedText {
+                    glyphs: self.place(buffer),
+                    size: buffer.size(),
+                    color: attrs.color,
+                }
+            }
+        };
+        buffer.placed.insert(placed)
     }
 }

core/src/render/atlas.rs

@@ -1,5 +1,5 @@
 use crate::{
-    PatchRect,
+    PatchRect, PxVec2,
     util::{HashMap, Vec2},
 };
 use image::RgbaImage;
@@ -241,5 +241,7 @@ fn write_glyph(page: &mut RgbaImage, image: &Image, x: u32, y: u32) {
 #[derive(Clone, Copy)]
 pub struct PlacedGlyph {
     pub entry: GlyphEntry,
-    pub offset: Vec2,
+    /// Whole pixels from the origin of the text to this glyph's top-left,
+    /// on the grid once here rather than on every frame that draws it.
+    pub offset: PxVec2,
 }

core/src/render/data.rs

@@ -1,11 +1,10 @@
-use crate::{UiRegion, util::Id};
+use crate::{UiRegion, util::Id, util::Vec2};
 use wgpu::*;
 
 #[repr(C)]
 #[derive(Copy, Clone, bytemuck::Pod, bytemuck::Zeroable, Default)]
 pub struct WindowUniform {
-    pub width: f32,
-    pub height: f32,
+    pub dim: Vec2,
 }
 
 #[repr(C)]
@@ -13,15 +12,19 @@ pub struct WindowUniform {
 pub struct PrimitiveInstance {
     pub region: UiRegion,
     pub mask_idx: MaskIdx,
+    pub move_idx: MoveIdx,
 }
 
 impl PrimitiveInstance {
-    const ATTRIBS: [VertexAttribute; 5] = vertex_attr_array![
-        0 => Float32x2,
-        1 => Float32x2,
-        2 => Float32x2,
-        3 => Float32x2,
+    // The region's four scalars, each a `Rel` beside a `Px`: whole counts
+    // that the shader decodes, rather than the numbers themselves.
+    const ATTRIBS: [VertexAttribute; 6] = vertex_attr_array![
+        0 => Sint32x2,
+        1 => Sint32x2,
+        2 => Sint32x2,
+        3 => Sint32x2,
         4 => Uint32,
+        5 => Uint32,
     ];
 
     pub fn desc() -> VertexBufferLayout<'static> {
@@ -43,4 +46,45 @@ impl MaskIdx {
 #[derive(Debug, Copy, Clone, bytemuck::Pod, bytemuck::Zeroable)]
 pub struct Mask {
     pub region: UiRegion,
+    pub move_idx: MoveIdx,
+}
+
+/// Its own type rather than another `Id<u32>`, because it sits beside
+/// `MaskIdx` in an instance and the two must not be swappable.
+#[repr(transparent)]
+#[derive(Debug, Copy, Clone, PartialEq, Eq, Hash, bytemuck::Pod, bytemuck::Zeroable)]
+pub struct MoveIdx(u32);
+
+impl MoveIdx {
+    pub const NONE: Self = Self(u32::MAX);
+
+    pub(crate) fn slot(idx: usize) -> Self {
+        Self(idx as u32)
+    }
+
+    pub(crate) fn idx(self) -> usize {
+        self.0 as usize
+    }
+}
+
+/// One link of the chain a primitive's position is resolved through: the box
+/// its contents are placed within, given in the coordinates of the slot it
+/// names. Moving or resizing a subtree writes its own slot and nothing else.
+///
+/// The identity is `UiRegion::FULL`, not zero: a zeroed entry is a box of no
+/// extent, which collapses everything under it to a point.
+#[repr(C)]
+#[derive(Debug, Copy, Clone)]
+pub struct MoveOffset {
+    pub region: UiRegion,
+    pub parent: MoveIdx,
+}
+
+unsafe impl bytemuck::Pod for MoveOffset {}
+unsafe impl bytemuck::Zeroable for MoveOffset {}
+
+impl MoveOffset {
+    pub fn new(parent: MoveIdx, region: UiRegion) -> Self {
+        Self { region, parent }
+    }
 }

core/src/render/mod.rs

@@ -17,11 +17,22 @@ mod texture;
 mod util;
 
 pub use atlas::*;
-pub use data::{Mask, MaskIdx};
+pub use data::{Mask, MaskIdx, MoveIdx, MoveOffset};
 pub use primitive::*;
 
 const PRELUDE: &str = include_str!("./shader/prelude.wgsl");
 
+fn module_source(wgsl: &str) -> String {
+    // The steps come from the same constants the CPU counts in, rather than
+    // a second copy of them written into the shader: a grid the two disagree
+    // about puts every coordinate somewhere else.
+    format!(
+        "const PX_STEP: f32 = 1.0 / {}.0;\nconst REL_STEP: f32 = 1.0 / {}.0;\n{PRELUDE}\n{wgsl}",
+        1u32 << crate::PX_SHIFT,
+        1u32 << crate::REL_SHIFT,
+    )
+}
+
 pub struct UiRenderNode {
     shared_layout: BindGroupLayout,
     shared_group: BindGroup,
@@ -34,6 +45,7 @@ pub struct UiRenderNode {
     active: Vec<usize>,
     window_buffer: Buffer,
     masks: ArrBuf<Mask>,
+    moves: ArrBuf<MoveOffset>,
 }
 
 struct RenderLayer {
@@ -127,32 +139,35 @@ impl UiRenderNode {
         for primitive in &mut self.primitives {
             primitive.render.update(ui);
         }
+        let mut regroup = false;
         if ui.masks.changed {
             ui.masks.changed = false;
-            if self.masks.update(device, queue, &ui.masks[..]) {
-                self.shared_group = Self::shared_group(
-                    device,
-                    &self.shared_layout,
-                    &self.window_buffer,
-                    &self.masks,
-                );
-            }
+            regroup |= self.masks.update(device, queue, &ui.masks[..]);
+        }
+        if ui_render.moves.changed {
+            ui_render.moves.changed = false;
+            regroup |= self.moves.update(device, queue, ui_render.moves.entries());
+        }
+        if regroup {
+            self.shared_group = Self::shared_group(
+                device,
+                &self.shared_layout,
+                &self.window_buffer,
+                &self.masks,
+                &self.moves,
+            );
         }
     }
 
     pub fn resize(&mut self, size: impl Into<Vec2>, queue: &Queue) {
         let size = size.into();
-        let slice = &[WindowUniform {
-            width: size.x,
-            height: size.y,
-        }];
+        let slice = &[WindowUniform { dim: size }];
         queue.write_buffer(&self.window_buffer, 0, bytemuck::cast_slice(slice));
     }
 
     pub fn new(device: &Device, config: &SurfaceConfiguration) -> Self {
         let window_uniform = WindowUniform {
-            width: config.width as f32,
-            height: config.height as f32,
+            dim: Vec2::new(config.width as f32, config.height as f32),
         };
         let window_buffer = device.create_buffer_init(&BufferInitDescriptor {
             label: Some("window"),
@@ -166,7 +181,13 @@ impl UiRenderNode {
             BufferUsages::STORAGE | BufferUsages::COPY_DST,
             "ui masks",
         );
-        let shared_group = Self::shared_group(device, &shared_layout, &window_buffer, &masks);
+        let moves = ArrBuf::new(
+            device,
+            BufferUsages::STORAGE | BufferUsages::COPY_DST,
+            "ui move offsets",
+        );
+        let shared_group =
+            Self::shared_group(device, &shared_layout, &window_buffer, &masks, &moves);
 
         Self {
             shared_layout,
@@ -177,6 +198,7 @@ impl UiRenderNode {
             layers: HashMap::default(),
             active: Vec::new(),
             masks,
+            moves,
         }
     }
 
@@ -211,7 +233,7 @@ impl UiRenderNode {
     ) -> RenderPipeline {
         let module = device.create_shader_module(ShaderModuleDescriptor {
             label: Some(label),
-            source: ShaderSource::Wgsl(format!("{PRELUDE}\n{wgsl}").into()),
+            source: ShaderSource::Wgsl(module_source(wgsl).into()),
         });
         device.create_render_pipeline(&RenderPipelineDescriptor {
             label: Some(label),
@@ -252,7 +274,8 @@ impl UiRenderNode {
         })
     }
 
-    /// What every draw in the ui is given: the window and the masks.
+    /// What every draw in the ui is given: the window, the masks and the
+    /// move chain every position is resolved through.
     fn shared_layout(device: &Device) -> BindGroupLayout {
         device.create_bind_group_layout(&BindGroupLayoutDescriptor {
             entries: &[
@@ -276,6 +299,16 @@ impl UiRenderNode {
                     },
                     count: None,
                 },
+                BindGroupLayoutEntry {
+                    binding: 2,
+                    visibility: ShaderStages::VERTEX | ShaderStages::FRAGMENT,
+                    ty: BindingType::Buffer {
+                        ty: BufferBindingType::Storage { read_only: true },
+                        has_dynamic_offset: false,
+                        min_binding_size: BufferSize::new(size_of::<MoveOffset>() as u64),
+                    },
+                    count: None,
+                },
             ],
             label: Some("ui shared"),
         })
@@ -286,6 +319,7 @@ impl UiRenderNode {
         layout: &BindGroupLayout,
         window: &Buffer,
         masks: &ArrBuf<Mask>,
+        moves: &ArrBuf<MoveOffset>,
     ) -> BindGroup {
         device.create_bind_group(&BindGroupDescriptor {
             layout,
@@ -298,6 +332,10 @@ impl UiRenderNode {
                     binding: 1,
                     resource: masks.buffer.as_entire_binding(),
                 },
+                BindGroupEntry {
+                    binding: 2,
+                    resource: moves.buffer.as_entire_binding(),
+                },
             ],
             label: Some("ui shared"),
         })
@@ -374,3 +412,35 @@ impl ListBuffers {
         }
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use super::module_source;
+    use wgpu::naga::{
+        front::wgsl,
+        valid::{Capabilities, ValidationFlags, Validator},
+    };
+
+    /// Every shader file, composed as the renderer composes it, parses and
+    /// validates with no device -- so an edit that breaks one fails here and
+    /// not in the first window opened.
+    #[test]
+    fn every_shader_validates() {
+        let dir = concat!(env!("CARGO_MANIFEST_DIR"), "/src/render/shader");
+        let mut checked = 0;
+        for entry in std::fs::read_dir(dir).unwrap() {
+            let path = entry.unwrap().path();
+            if path.extension().is_none_or(|e| e != "wgsl") || path.ends_with("prelude.wgsl") {
+                continue;
+            }
+            let source = module_source(&std::fs::read_to_string(&path).unwrap());
+            let module = wgsl::parse_str(&source)
+                .unwrap_or_else(|e| panic!("{}: {}", path.display(), e.emit_to_string(&source)));
+            Validator::new(ValidationFlags::all(), Capabilities::all())
+                .validate(&module)
+                .unwrap_or_else(|e| panic!("{}: {e:?}", path.display()));
+            checked += 1;
+        }
+        assert!(checked > 0, "no shaders found in {dir}");
+    }
+}

core/src/render/primitive.rs

@@ -3,7 +3,7 @@ use std::{any::TypeId, marker::PhantomData};
 use crate::{
     Color, TextureHandle, UiData, UiRegion, WidgetId,
     render::{
-        data::{MaskIdx, PrimitiveInstance},
+        data::{MaskIdx, MoveIdx, PrimitiveInstance},
         page::GlyphRender,
         texture::ImageRender,
     },
@@ -246,6 +246,7 @@ impl LayerDraws {
             primitive,
             region,
             mask_idx,
+            move_idx,
         }: PrimitiveInst<P>,
     ) -> PrimitiveHandle {
         self.updated = true;
@@ -258,7 +259,11 @@ impl LayerDraws {
             .get_or_insert_with(InstanceList::new::<P>)
             .push(
                 id,
-                PrimitiveInstance { region, mask_idx },
+                PrimitiveInstance {
+                    region,
+                    mask_idx,
+                    move_idx,
+                },
                 bytemuck::bytes_of(&primitive),
             );
         PrimitiveHandle {
@@ -304,6 +309,7 @@ pub struct PrimitiveInst<P> {
     pub primitive: P,
     pub region: UiRegion,
     pub mask_idx: MaskIdx,
+    pub move_idx: MoveIdx,
 }
 
 pub struct PrimitiveChange {
@@ -347,7 +353,7 @@ impl RectPrimitive {
 
 /// `color` is multiplied by the atlas alpha for a mask glyph; a colour glyph
 /// takes the texel unchanged, which `GlyphEntry::IS_COLORED` selects.
-#[repr(C, align(8))]
+#[repr(C)]
 #[derive(Debug, Copy, Clone)]
 pub struct GlyphPrimitive {
     pub uv_min: Vec2,
@@ -358,8 +364,8 @@ pub struct GlyphPrimitive {
     pub flags: u32,
 }
 
-// Manual rather than derived: the align(8) leaves four bytes of padding, which
-// is how WGSL lays the struct out.
+// Manual rather than derived: `Vec2`'s alignment leaves four bytes of padding
+// here, which is how WGSL lays the struct out.
 unsafe impl bytemuck::Pod for GlyphPrimitive {}
 unsafe impl bytemuck::Zeroable for GlyphPrimitive {}
 impl Primitive for GlyphPrimitive {

core/src/render/shader/prelude.wgsl

@@ -7,32 +7,121 @@
 var<uniform> window: WindowUniform;
 @group(0) @binding(1)
 var<storage> masks: array<Mask>;
+@group(0) @binding(2)
+var<storage> move_offsets: array<MoveOffset>;
 
 struct WindowUniform {
     dim: vec2<f32>,
 };
 
 struct Mask {
+    x: RawSpan,
+    y: RawSpan,
+    move_idx: u32,
+}
+
+struct MoveOffset {
+    x: RawSpan,
+    y: RawSpan,
+    parent: u32,
+}
+
+// `PX_STEP` and `REL_STEP` are prepended from `iris_core`'s own constants:
+// what it stores is a whole count of each, both powers of two, so decoding
+// is exact and the number here is the number the CPU decided.
+
+// Every coordinate the CPU decided is a whole count of `PX_STEP`, so one that
+// composes to within half a step of a pixel boundary is on that boundary and
+// belongs to the pixel above it. Flooring the product instead drops a pixel
+// wherever a fraction divides a window exactly: a fifth of 1920 comes out of
+// `REL_STEP` as 383.99998, and five tabs each lose their last column.
+//
+// Taken over the whole coordinate, fraction and pixels summed, since a floor
+// does not distribute over a sum: floored apart, a half of one and a half of
+// the other lose the pixel the two together make.
+fn snap_floor(v: vec2<f32>) -> vec2<f32> {
+    return floor(v + PX_STEP * 0.5);
+}
+
+struct RawScalar {
+    rel: i32,
+    px: i32,
+}
+
+struct RawSpan {
+    start: RawScalar,
+    end: RawScalar,
+}
+
+fn scalar_of(raw: RawScalar) -> Len {
+    return Len(f32(raw.rel) * REL_STEP, f32(raw.px) * PX_STEP);
+}
+
+fn span_of(raw: RawSpan) -> UiSpan {
+    return UiSpan(scalar_of(raw.start), scalar_of(raw.end));
+}
+
+fn scalar_of_pair(raw: vec2<i32>) -> Len {
+    return Len(f32(raw.x) * REL_STEP, f32(raw.y) * PX_STEP);
+}
+
+struct Region {
     x: UiSpan,
     y: UiSpan,
 }
 
-struct UiSpan {
-    start: UiScalar,
-    end: UiScalar,
+const MOVE_NONE: u32 = 4294967295u;
+// Keep in step with `iris_core::CHAIN_LIMIT`. It bounds a malformed cycle
+// rather than any real tree, and the CPU walk uses the same number so both
+// resolve a deep one the same way.
+const CHAIN_LIMIT: u32 = 64u;
+
+// The same expression `Len::within` uses, in floats rather than on the
+// CPU's grid: a move is resolved here so that scrolling a subtree writes one
+// entry instead of walking it. What has to hold is that this agrees with
+// itself frame to frame, not that it matches the CPU to the last bit.
+fn scalar_within(s: Len, p: UiSpan) -> Len {
+    return Len(
+        p.start.rel + (p.end.rel - p.start.rel) * s.rel,
+        s.px + (p.start.px + (p.end.px - p.start.px) * s.rel),
+    );
 }
 
-struct UiScalar {
+fn span_within(s: UiSpan, p: UiSpan) -> UiSpan {
+    return UiSpan(scalar_within(s.start, p), scalar_within(s.end, p));
+}
+
+fn resolve_move(idx: u32, local: Region) -> Region {
+    var r = local;
+    var at = idx;
+    for (var step = 0u; step < CHAIN_LIMIT; step++) {
+        if at == MOVE_NONE {
+            break;
+        }
+        let entry = move_offsets[at];
+        r = Region(span_within(r.x, span_of(entry.x)), span_within(r.y, span_of(entry.y)));
+        at = entry.parent;
+    }
+    return r;
+}
+
+struct UiSpan {
+    start: Len,
+    end: Len,
+}
+
+struct Len {
     rel: f32,
-    abs: f32,
+    px: f32,
 }
 
 struct InstanceInput {
-    @location(0) x_start: vec2<f32>,
-    @location(1) x_end: vec2<f32>,
-    @location(2) y_start: vec2<f32>,
-    @location(3) y_end: vec2<f32>,
+    @location(0) x_start: vec2<i32>,
+    @location(1) x_end: vec2<i32>,
+    @location(2) y_start: vec2<i32>,
+    @location(3) y_end: vec2<i32>,
     @location(4) mask_idx: u32,
+    @location(5) move_idx: u32,
 }
 
 struct VertexOutput {
@@ -52,13 +141,18 @@ fn vs_main(
 ) -> VertexOutput {
     var out: VertexOutput;
 
-    let top_left_rel = vec2(in.x_start.x, in.y_start.x);
-    let top_left_abs = vec2(in.x_start.y, in.y_start.y);
-    let bot_right_rel = vec2(in.x_end.x, in.y_end.x);
-    let bot_right_abs = vec2(in.x_end.y, in.y_end.y);
+    let local = Region(
+        UiSpan(scalar_of_pair(in.x_start), scalar_of_pair(in.x_end)),
+        UiSpan(scalar_of_pair(in.y_start), scalar_of_pair(in.y_end)),
+    );
+    let r = resolve_move(in.move_idx, local);
+    let top_left_rel = vec2(r.x.start.rel, r.y.start.rel);
+    let top_left_px = vec2(r.x.start.px, r.y.start.px);
+    let bot_right_rel = vec2(r.x.end.rel, r.y.end.rel);
+    let bot_right_px = vec2(r.x.end.px, r.y.end.px);
 
-    let top_left = floor(top_left_rel * window.dim) + floor(top_left_abs);
-    let bot_right = floor(bot_right_rel * window.dim) + floor(bot_right_abs);
+    let top_left = snap_floor(top_left_rel * window.dim + top_left_px);
+    let bot_right = snap_floor(bot_right_rel * window.dim + bot_right_px);
     let size = bot_right - top_left;
 
     let uv = vec2<f32>(
@@ -81,13 +175,16 @@ fn masked(in: VertexOutput, color: vec4<f32>) -> vec4<f32> {
         return color;
     }
     let mask = masks[in.mask_idx];
-    let tl = vec2(mask.x.start.rel, mask.y.start.rel);
-    let tl_abs = vec2(mask.x.start.abs, mask.y.start.abs);
-    let br = vec2(mask.x.end.rel, mask.y.end.rel);
-    let br_abs = vec2(mask.x.end.abs, mask.y.end.abs);
+    // Its own chain, not the drawn primitive's, so a stationary viewport
+    // clips content that moves inside it.
+    let m = resolve_move(mask.move_idx, Region(span_of(mask.x), span_of(mask.y)));
+    let tl = vec2(m.x.start.rel, m.y.start.rel);
+    let tl_px = vec2(m.x.start.px, m.y.start.px);
+    let br = vec2(m.x.end.rel, m.y.end.rel);
+    let br_px = vec2(m.x.end.px, m.y.end.px);
 
-    let top_left = floor(tl * window.dim) + floor(tl_abs);
-    let bot_right = floor(br * window.dim) + floor(br_abs);
+    let top_left = snap_floor(tl * window.dim + tl_px);
+    let bot_right = snap_floor(br * window.dim + br_px);
     let pos = in.clip_position.xy;
     if pos.x < top_left.x || pos.x > bot_right.x || pos.y < top_left.y || pos.y > bot_right.y {
         return color * 0.0;

core/src/ui/active.rs

@@ -1,20 +1,77 @@
-use crate::{LayerId, MaskIdx, PrimitiveHandle, Size, TextureHandle, UiRegion, WidgetId};
+use crate::{
+    Holds, LayerId, LayoutLen, MaskIdx, MoveIdx, PrimitiveHandle, RegionAlign, Size, TextureHandle,
+    UiRegion, UiVec2, WidgetId,
+};
 
-/// important non rendering data for retained drawing
+/// What is kept of a widget its parent has asked about. `drawn` says whether
+/// it currently draws; one that does not is kept so that a change to it, or
+/// under it, still reaches whoever asked.
 #[derive(Debug)]
 pub struct ActiveData {
     pub id: WidgetId,
+    /// The box its drawing is in, in `parent_move`'s coordinates.
     pub region: UiRegion,
-    /// What the widget said it used of `region`, the last time it drew.
+    /// The box its parent gave it, in the same coordinates: what it was
+    /// asked about, before its own answer placed its drawing inside it.
+    /// `region` is that placement, and a local redraw asks here.
+    pub given: UiRegion,
+    /// The same box as lengths of its parent's box, which is the one route
+    /// to a box in pixels: a draw threads these down a level at a time, and
+    /// [`crate::UiRenderState::redraw`] takes the same steps back up.
+    pub given_len: UiVec2,
+    /// The lengths of the box its parent first asked about it in, as
+    /// lengths of the box the parent was itself offered. Any later box it
+    /// was given was decided knowing its answer, so this is the question
+    /// asked again -- and a chain of fractions has no frame in it, which is
+    /// why a region node between two widgets cannot break it.
+    pub offer_len: UiVec2,
+    /// What it answered there: the size and what that held for.
+    pub answer: (Size, [Holds; 2]),
+    /// What the widget said it used of its box, the last time it drew.
     pub size: Size,
+    /// The pixel lengths of `region`, per axis, that its drawing and `size`
+    /// hold for.
+    pub holds: [Holds; 2],
+    pub drawn: bool,
     pub parent: Option<WidgetId>,
+    /// How far down the tree it was drawn, the root being 1. Carried down a
+    /// draw rather than worked out by walking up, so it is right for every
+    /// widget a frame visits and cannot drift while one is being drawn.
+    pub depth: usize,
     pub textures: Vec<TextureHandle>,
     pub primitives: Vec<PrimitiveHandle>,
     pub children: Vec<WidgetId>,
     /// The children whose size this widget read while drawing.
     pub size_deps: Vec<WidgetId>,
-    /// Whether it read the output's size, and so is wrong when that changes.
-    pub reads_output: bool,
+    /// The movable region its primitives are positioned through: its own when
+    /// opted in, otherwise the nearest ancestor's.
+    pub move_idx: MoveIdx,
+    /// The declared lengths whoever drew this widget resolved into its box.
+    /// A change to one moves a box this widget cannot fix by drawing again,
+    /// and comparing them is what says so.
+    pub declared: [Option<LayoutLen>; 2],
+    /// The axes along which its parent chose its box from its own answer,
+    /// so a local redraw asks the question its parent asked.
+    pub decided: [bool; 2],
+    /// Its alignment when it was last drawn, which a change to the property
+    /// is found against.
+    pub own_align: RegionAlign,
+    /// The movable region whose coordinates `region` uses.
+    pub parent_move: MoveIdx,
+    /// The mask its drawing is clipped to: one it set itself, or the one it
+    /// inherited from whoever drew it.
     pub mask: MaskIdx,
+    /// That inherited one. The two differ exactly where the widget set a
+    /// mask of its own, which is the one it owns and the one a move rewrites
+    /// -- and the one a redraw of it must not be handed back, since setting
+    /// a mask asserts there is none.
+    pub parent_mask: MaskIdx,
     pub layer: LayerId,
 }
+
+impl ActiveData {
+    /// Whether its drawing and size hold for a box of these pixel lengths.
+    pub fn holds_at(&self, px: crate::PxVec2) -> bool {
+        self.holds[0].contains(px.x) && self.holds[1].contains(px.y)
+    }
+}

core/src/ui/holds.rs

@@ -0,0 +1,165 @@
+use crate::{Len, Px, REL_SHIFT, fixed::div_toward, fixed::narrow};
+use std::ops::RangeInclusive;
+
+/// The lengths of a box, in pixels, that one drawing of a widget holds for:
+/// give the widget any box in this range and it draws the same thing and
+/// reports the same size. A widget that never reads its box in pixels holds
+/// for every length; one that does holds for the one it read unless it says
+/// otherwise, and a parent holds for whatever keeps every child it asked
+/// about or drew inside its own range.
+///
+/// The ends are lengths on the grid rather than floats with a tolerance
+/// around them: a box offered back at the length a widget reported comes back
+/// as the same number, so a range means what it says. The one place a range
+/// is wider than the length it came from is [`Self::through`], and what it is
+/// wider by is the floor that inverting a fraction undoes.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub struct Holds {
+    pub lo: Px,
+    pub hi: Px,
+}
+
+impl Holds {
+    pub const ANY: Self = Self {
+        lo: Px::MIN,
+        hi: Px::MAX,
+    };
+
+    pub const fn at(len: Px) -> Self {
+        Self { lo: len, hi: len }
+    }
+
+    pub const fn contains(&self, len: Px) -> bool {
+        len.raw() >= self.lo.raw() && len.raw() <= self.hi.raw()
+    }
+
+    pub const fn and(self, other: Self) -> Self {
+        Self {
+            lo: self.lo.max(other.lo),
+            hi: self.hi.min(other.hi),
+        }
+    }
+
+    /// What a box has to be for a part of it, `len` of the box long, to stay
+    /// in this range: the exact preimage of `px + floor(rel * box)`, which is
+    /// the one way a box in pixels is reached. A part with no relative extent
+    /// is a fixed length -- it was drawn at that length and any box keeps it
+    /// there.
+    ///
+    /// The answer is an interval even where this range is a single length,
+    /// because the multiply on the way in drops to the step below and many
+    /// boxes therefore give one length. That is a floor rather than an
+    /// allowance: inverting it is two divisions and nothing else, and the
+    /// whole of a box maps back to itself.
+    pub const fn through(self, len: Len) -> Self {
+        let rel = len.rel.raw() as i64;
+        if rel == 0 {
+            return Self::ANY;
+        }
+        let px = len.px.raw() as i64;
+        // `floor(rel * box) >= lo - px` is `rel * box >= (lo - px) << REL`, and
+        // `floor(rel * box) <= hi - px` is `rel * box < (hi - px + 1) << REL`.
+        let lo = (self.lo.raw() as i64 - px) << REL_SHIFT;
+        let hi = (((self.hi.raw() as i64 - px) + 1) << REL_SHIFT) - 1;
+        // Dividing by a negative fraction turns the ends around, so which
+        // bound each comes from is decided before dividing rather than by
+        // taking the min and max of four divisions.
+        match rel > 0 {
+            true => Self::raws(div_toward(lo, rel, true), div_toward(hi, rel, false)),
+            false => Self::raws(div_toward(hi, rel, true), div_toward(lo, rel, false)),
+        }
+    }
+
+    const fn raws(lo: i64, hi: i64) -> Self {
+        Self {
+            lo: Px::from_raw(narrow(lo)),
+            hi: Px::from_raw(narrow(hi)),
+        }
+    }
+}
+
+impl From<RangeInclusive<Px>> for Holds {
+    fn from(range: RangeInclusive<Px>) -> Self {
+        Self {
+            lo: *range.start(),
+            hi: *range.end(),
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::Rel;
+
+    #[test]
+    fn through_reverses_a_range_for_a_negative_fraction() {
+        // `10 - box / 2` is between 20 and 40 for boxes from -60 to -20.
+        let part = Len::from_parts(Rel::from_f32(-0.5), Px::from_int(10));
+        let holds = Holds::from(Px::from_int(20)..=Px::from_int(40)).through(part);
+        assert!(holds.contains(Px::from_int(-60)) && holds.contains(Px::from_int(-20)));
+        assert!(!holds.contains(Px::from_int(-61)) && !holds.contains(Px::from_int(-19)));
+    }
+
+    /// The case the widening is for: a part that holds only for the length it
+    /// was drawn at has to hold for the box it was drawn in, and a third of a
+    /// box is not a whole number of steps.
+    #[test]
+    fn a_part_maps_back_onto_the_box_it_was_measured_in() {
+        let part = Len::from_parts(Rel::from_f32(1.0 / 3.0), Px::from_int(-146));
+        for box_len in (440..460).map(Px::from_int) {
+            let holds = Holds::at(part.to_px(box_len)).through(part);
+            assert!(holds.contains(box_len), "{box_len:?} left out by {holds:?}");
+        }
+    }
+
+    /// A widget handed the whole of its parent's box, with or without pixels
+    /// taken off it, has no fraction to invert: multiplying by one is exact
+    /// and taking the pixels off again is too, so the box maps back to
+    /// itself. Allowing for anything here compounded a step a level down a
+    /// chain of widgets each taking the whole of its parent.
+    #[test]
+    fn the_whole_of_a_box_maps_back_to_itself() {
+        let at = Px::from_int(956);
+        assert_eq!(Holds::at(at).through(Len::FULL), Holds::at(at));
+        let less_eight = Len::from_parts(Rel::ONE, Px::from_int(-8));
+        assert_eq!(
+            Holds::at(at).through(less_eight),
+            Holds::at(at + Px::from_int(8))
+        );
+    }
+
+    /// The range is the exact preimage at both ends, so a box one step
+    /// outside it really does give a length outside this range. What a wider
+    /// range costs is a drawing reused where it does not hold.
+    #[test]
+    fn a_box_one_step_outside_the_range_is_outside_it() {
+        let part = Len::from_parts(Rel::from_f32(1.0 / 3.0), Px::from_int(-146));
+        let at = Px::from_int(300);
+        let holds = Holds::at(at).through(part);
+        for inside in [holds.lo, holds.hi] {
+            assert_eq!(part.to_px(inside), at, "{inside:?} left out of {holds:?}");
+        }
+        for outside in [holds.lo.next_down(), holds.hi.next_up()] {
+            assert_ne!(part.to_px(outside), at, "{outside:?} admitted by {holds:?}");
+        }
+    }
+
+    /// A truncating multiply only ever drops, so the step it needs allowing
+    /// for on the way in belongs at the top of the range and not the bottom.
+    #[test]
+    fn a_fraction_widens_further_up_than_down() {
+        let half = Len::from_parts(Rel::from_f32(0.5), Px::ZERO);
+        let holds = Holds::at(Px::from_int(100)).through(half);
+        let box_len = Px::from_int(200);
+        assert!(holds.hi - box_len > box_len - holds.lo, "{holds:?}");
+    }
+
+    #[test]
+    fn a_boundary_the_next_step_along_does_not_admit_it() {
+        let boundary = Px::from_int(10);
+        let above = Holds::from(boundary.next_up()..=Px::MAX);
+        assert!(!above.contains(boundary));
+        assert!(above.contains(boundary.next_up()));
+    }
+}

core/src/ui/mod.rs

@@ -1,12 +1,21 @@
 use crate::{
-    Mask, PrimitiveRegistry, TextData, Textures, WeakWidget, WidgetId, Widgets, util::TrackedArena,
+    Mask, MoveIdx, MoveOffset, PrimitiveRegistry, TextData, Textures, UiRegion, WeakWidget,
+    WidgetId, Widgets,
+    util::{Arena, Id, TrackedArena},
 };
 
+/// How far the shader will walk a move chain. It bounds a malformed cycle
+/// rather than any real tree; `Moves::resolve` uses the same number so the
+/// two agree on what a deep tree resolves to.
+pub const CHAIN_LIMIT: u32 = 64;
+
 mod active;
+mod holds;
 mod painter;
 mod render_state;
 
 pub use active::*;
+pub use holds::*;
 pub use painter::{Painter, PrimitiveLike};
 pub use render_state::*;
 
@@ -20,6 +29,94 @@ pub struct UiData {
     pub masks: TrackedArena<Mask, u32>,
 }
 
+/// Where each widget's drawing sits relative to its parent's slot, so moving
+/// a subtree writes one entry rather than every descendant's primitives.
+#[derive(Default)]
+pub struct Moves {
+    arena: Arena<MoveOffset, u32>,
+    pub changed: bool,
+}
+
+impl Moves {
+    pub fn push(&mut self, parent: MoveIdx, region: UiRegion) -> MoveIdx {
+        self.changed = true;
+        MoveIdx::slot(self.arena.push(MoveOffset::new(parent, region)).idx())
+    }
+
+    /// Re-points a slot at a different parent, for a widget drawn somewhere
+    /// else in the tree than it was.
+    pub fn set_parent(&mut self, idx: MoveIdx, parent: MoveIdx) {
+        let entry = self.arena.get_mut(Id::preset(idx.idx() as u32));
+        if entry.parent != parent {
+            entry.parent = parent;
+            self.changed = true;
+        }
+    }
+
+    pub fn remove(&mut self, idx: MoveIdx) {
+        self.changed = true;
+        self.arena.remove(Id::preset(idx.idx() as u32));
+    }
+
+    /// Sets the box a slot's contents are placed within, itself given in the
+    /// coordinates of its parent slot.
+    pub fn set(&mut self, idx: MoveIdx, region: UiRegion) {
+        let entry = self.arena.get_mut(Id::preset(idx.idx() as u32));
+        if entry.region != region {
+            entry.region = region;
+            self.changed = true;
+        }
+    }
+
+    /// The same walk the vertex shader does, in the same `Len` the shader is
+    /// handed, for asking where a drawing will actually land -- hit testing,
+    /// and nothing layout decides on. Layout threads its lengths down the
+    /// draw instead, so no box it compares is composed back up this chain.
+    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;
+            }
+            let entry = &self.arena[at.idx()];
+            step(&entry.region);
+            at = entry.parent;
+        }
+        debug_assert!(
+            at == MoveIdx::NONE,
+            "a move chain longer than {CHAIN_LIMIT} resolves to the wrong place, \
+             and the shader stops at the same depth"
+        );
+    }
+
+    /// How many slots a region in `idx` is composed through, which is what
+    /// the shader's walk costs per primitive.
+    pub fn depth(&self, idx: MoveIdx) -> usize {
+        let mut depth = 0;
+        let mut at = idx;
+        while at != MoveIdx::NONE && depth < CHAIN_LIMIT as usize {
+            at = self.arena[at.idx()].parent;
+            depth += 1;
+        }
+        depth
+    }
+
+    pub fn entries(&self) -> &[MoveOffset] {
+        &self.arena
+    }
+
+    pub fn clear(&mut self) {
+        self.changed = true;
+        self.arena = Arena::default();
+    }
+}
+
 pub trait UiRsc {
     fn ui(&self) -> &UiData;
     fn ui_mut(&mut self) -> &mut UiData;

core/src/ui/painter.rs

@@ -1,27 +1,58 @@
+#[cfg(feature = "layout-diagnostics")]
+use crate::layout_diagnostics::{self as diag, Counter};
 use crate::{
-    Axis, Len, RenderedText, Size, StrongWidget, TextAttrs, TextBuffer, TextData, TextureHandle,
-    UiRegion, UiRenderState, UiRsc, UiScalar, UiVec2, WidgetId,
+    Axis, Holds, LayoutLen, Len, Px, PxVec2, RegionAlign, RenderedText, Size, StrongWidget,
+    TextAttrs, TextBuffer, TextData, TextureHandle, UiRegion, UiRenderState, UiRsc, UiVec2, Weight,
+    WidgetId, Widgets,
     render::{
-        GlyphPrimitive, Mask, MaskIdx, Primitive, PrimitiveHandle, PrimitiveInst, PrimitiveKind,
-        TexturePrimitive,
+        GlyphPrimitive, Mask, MaskIdx, MoveIdx, Primitive, PrimitiveHandle, PrimitiveInst,
+        PrimitiveKind, TexturePrimitive,
     },
-    util::Vec2,
+    ui::render_state::DrawInfo,
 };
+const AXES: [Axis; 2] = [Axis::X, Axis::Y];
 
 /// makes your surfaces look pretty
 pub struct Painter<'a> {
     pub(super) state: &'a mut UiRenderState,
     pub(super) rsc: &'a mut dyn UiRsc,
 
+    /// This widget's box, in the coordinates of `move_idx`.
     pub(super) region: UiRegion,
+    /// That box in pixels, which its children's are a length of: threaded
+    /// down from the box this widget was given rather than composed back up
+    /// the chain, so every length in layout is one multiply from its
+    /// parent's and [`Holds::through`] inverts exactly that.
+    pub(super) px: PxVec2,
     pub(super) mask: MaskIdx,
     pub(super) textures: Vec<TextureHandle>,
     pub(super) primitives: Vec<PrimitiveHandle>,
     pub(super) children: Vec<WidgetId>,
+    /// The children asked about so far, so the first box each was asked in
+    /// is the one recorded as its offer.
+    pub(super) offered: Vec<WidgetId>,
+    /// The lengths of the box this widget was first asked about in, in
+    /// pixels. Its children's offers are a fraction of it.
+    pub(super) offered_px: PxVec2,
+    /// Whether this draw is in a box of those lengths, which makes the
+    /// questions it asks the ones a cold layout asks and their answers the
+    /// ones to keep.
+    pub(super) at_offer: bool,
     /// The children whose size this widget read while drawing.
     pub(super) size_deps: Vec<WidgetId>,
-    pub(super) reads_output: bool,
+    /// What this draw itself read of its box in pixels, per axis: every
+    /// length until it reads one, then that one, unless it says otherwise.
+    pub(super) own: [Holds; 2],
+    /// What the children it asked about and drew keep it to.
+    pub(super) under: [Holds; 2],
+    /// The movable region this widget's primitives are positioned through:
+    /// its own when opted in, otherwise the nearest ancestor's.
+    pub(super) move_idx: MoveIdx,
     pub layer: usize,
+    /// The layer this widget was entered on, which its children's layers are
+    /// counted from however far `layer` has walked.
+    pub(super) own_layer: usize,
+    pub(super) depth: usize,
     pub(super) id: WidgetId,
 }
 
@@ -33,6 +64,8 @@ impl<'a> Painter<'a> {
 
     /// Takes the kind, for a caller writing many of one primitive.
     fn write<P: Primitive>(&mut self, kind: PrimitiveKind<P>, primitive: P, region: UiRegion) {
+        #[cfg(feature = "layout-diagnostics")]
+        diag::bump(Counter::PrimitiveWrites);
         let h = self.state.layers.write(
             self.layer,
             PrimitiveInst {
@@ -41,6 +74,7 @@ impl<'a> Painter<'a> {
                 primitive,
                 region,
                 mask_idx: self.mask,
+                move_idx: self.move_idx,
             },
         );
         self.push_primitive(h);
@@ -67,70 +101,245 @@ impl<'a> Painter<'a> {
 
     pub fn set_mask(&mut self, region: UiRegion) {
         assert!(self.mask == MaskIdx::NONE);
-        self.mask = self.rsc.ui_mut().masks.push(Mask { region });
+        self.mask = self.rsc.ui_mut().masks.push(Mask {
+            region,
+            move_idx: self.move_idx,
+        });
     }
 
     /// Draws a widget within this widget's region.
     pub fn widget<'s, W: ?Sized>(&'s mut self, id: &'s StrongWidget<W>) -> DrawResult<'s, 'a, W> {
-        self.widget_at(id, self.region)
+        self.widget_within(id, UiRegion::FULL)
     }
 
-    /// Draws a widget somewhere within this one. Drawing one a second time
-    /// gives it a new box, keeping the drawing it already has where it can.
+    /// What a widget's rules declare its lengths to be, which whoever draws
+    /// it resolves into its box. Reading them depends on nothing -- the box
+    /// that comes of them is kept on the child, and `redraw` compares it
+    /// there.
+    fn declared_lens<W: ?Sized>(&self, id: &StrongWidget<W>) -> [Option<LayoutLen>; 2] {
+        declared_lens(self.rsc.widgets(), id.id())
+    }
+
+    /// Takes back a child that was drawn only to find out how long it is.
+    /// Its drawing is dropped and it is not one of this widget's children
+    /// this frame; what it answered is still something this widget asked.
+    pub fn undraw<W: ?Sized>(&mut self, id: &StrongWidget<W>) {
+        self.children.retain(|child| *child != id.id());
+        self.state.undraw_rec(id.id(), self.rsc);
+    }
+
+    /// Draws a widget somewhere within this one. `region` is in this widget's
+    /// own coordinates, and the child's declared lengths are still to be
+    /// taken from it. Where the child's drawing sits inside what it is given
+    /// is the child's alignment, applied where the child is drawn, so a
+    /// container positions a child either by handing it a box of exactly its
+    /// length or by leaving it room and letting its alignment decide.
     pub fn widget_within<'s, W: ?Sized>(
         &'s mut self,
         id: &'s StrongWidget<W>,
         region: UiRegion,
     ) -> DrawResult<'s, 'a, W> {
-        let region = region.within(&self.region);
-        self.widget_at(id, region)
+        self.widget_at(id, region, region.size(), [false; 2])
     }
 
-    fn widget_at<'s, W: ?Sized>(
+    /// Draws a widget in `region`, saying what the answer means.
+    ///
+    /// `reports_of` is what a fraction the child reports is a fraction of, as
+    /// lengths of this widget's own box. It is the box the child was given
+    /// wherever that box is the child's whole area -- a pad's inset, a stack
+    /// child, a scroll's content -- and a span passes its own extent along
+    /// the row instead: it offers each child the room left from its cursor,
+    /// because a text has to wrap at the width actually there, while
+    /// `rel(0.5)` still means half the span wherever the child sits in it.
+    ///
+    /// A `decided` axis is one where this box was chosen from the widget's
+    /// own answer. On those the answer is not placed inside the box again: it
+    /// already is the box, and a fraction taken of it a second time would
+    /// shrink it twice. A container uses that where it hands back exactly
+    /// what a child asked for -- a span placing a child at the length it
+    /// reported, a scroll giving its content the content's own length.
+    pub fn widget_at<'s, W: ?Sized>(
         &'s mut self,
         id: &'s StrongWidget<W>,
         region: UiRegion,
+        reports_of: UiVec2,
+        decided: [bool; 2],
     ) -> DrawResult<'s, 'a, W> {
+        let region_node = self.rsc.widgets().is_region_node(id.id());
+        let declared = self.declared_lens(id);
+        let align = self.rsc.widgets().alignment(id.id());
+        // A rule this box was already chosen from is not resolved into it a
+        // second time. The box is that rule's length already, so resolving
+        // it again takes the fraction twice -- a widget declaring half of a
+        // stack, in the stack its own answer made half a row, is a quarter
+        // of the row. Pixels survive it, being the same length wherever they
+        // are taken from, which is why only a share ever shrank.
+        let resolve = AXES.map(|axis| match decided[axis as usize] {
+            true => None,
+            false => declared[axis as usize],
+        });
+        // Composing `FULL` through a box is not quite the identity in f32,
+        // so a child with nothing declared keeps the box it would have had.
+        let local = match resolve.iter().any(Option::is_some) {
+            true => declared_box(region, resolve, align),
+            false => region,
+        };
+        let within = match local == UiRegion::FULL {
+            true => self.region,
+            false => local.within(&self.region),
+        };
+        #[cfg(feature = "layout-diagnostics")]
+        if region_node {
+            diag::bump(Counter::RegionNodeDraws);
+            diag::region_node(id.id(), self.id, within);
+        }
         // A child listed twice would be moved twice.
         if !self.children.contains(&id.id()) {
             self.children.push(id.id());
         }
-        let size = self.state.draw_inner(
-            self.layer,
+        let first_ask = self.offer(id.id());
+        let given_len = local.size();
+        let offer_len = match first_ask {
+            true => given_len,
+            false => self
+                .state
+                .active
+                .get(&id.id())
+                .map_or(given_len, |a| a.offer_len),
+        };
+        let px = given_len.to_px(self.px);
+        let offered_px = offer_len.to_px(self.offered_px);
+        // Whether this ask is the child's offer question, which is a question
+        // about lengths: the same lengths somewhere else is the same question.
+        let answers_offer = self.at_offer && px == offered_px;
+        // The answer and what it holds for, both about the box asked in. The
+        // child's record may say something else once its drawing has been
+        // placed: a drawing made again in its placed box holds for that box.
+        let (size, holds) = self.state.draw_inner(
             id.id(),
-            region,
-            Some(self.id),
-            self.mask,
+            within,
+            DrawInfo {
+                layer: self.layer,
+                parent: Some(self.id),
+                depth: self.depth + 1,
+                parent_move: self.move_idx,
+                region_node,
+                mask: self.mask,
+                given_len,
+                offer_len,
+                px,
+                offered_px,
+                decided,
+            },
             None,
             self.rsc,
         );
+        if answers_offer {
+            self.state.active.get_mut(&id.id()).unwrap().answer = (size, holds);
+        }
+        // Whatever the child's answer holds for keeps this one to the boxes
+        // that give the child a length inside it.
+        for (axis, under) in AXES.into_iter().zip(self.under.iter_mut()) {
+            *under = under.and(holds[axis as usize].through(local.axis(axis).len()));
+        }
         DrawResult {
             child: id,
             painter: self,
-            size,
+            size: in_parent_frame(size, reports_of, declared),
         }
     }
 
     /// What a child says its length is without being drawn, if it can say.
     /// Asking counts as reading its size.
-    pub fn size_hint<W: ?Sized>(&mut self, id: &StrongWidget<W>, axis: Axis) -> Option<Len> {
-        let hint = self.rsc.widgets().get_dyn(id.id())?.size_hint(axis)?;
-        self.depend_on_size(id);
-        Some(hint)
+    pub fn size_hint<W: ?Sized>(&mut self, id: &StrongWidget<W>, axis: Axis) -> Option<LayoutLen> {
+        let widgets = self.rsc.widgets();
+        // A rule is the answer where there is one: it wins over whatever the
+        // widget would draw, so it has to win over what the widget says too.
+        let hint = widgets.size_rules(id.id()).axis(axis).exact().or_else(|| {
+            widgets
+                .get_dyn(id.id())
+                .and_then(|widget| widget.size_hint(axis))
+        });
+        #[cfg(feature = "layout-diagnostics")]
+        diag::hint_read(id.id(), self.id, axis, hint);
+        match hint {
+            Some(hint) => {
+                #[cfg(feature = "layout-diagnostics")]
+                diag::bump(Counter::HintHits);
+                self.depend_on(id);
+                Some(hint)
+            }
+            None => {
+                #[cfg(feature = "layout-diagnostics")]
+                diag::bump(Counter::HintMisses);
+                None
+            }
+        }
     }
 
-    fn depend_on_size<W: ?Sized>(&mut self, child: &StrongWidget<W>) {
+    /// A child's length in the box it is about to be offered, if it can be
+    /// had without drawing it: from its hint, or from a drawing it already
+    /// has that holds for that box. `reports_of` is what a fraction in the
+    /// answer is a fraction of, as it is for [`Self::widget_at`].
+    pub fn known_len<W: ?Sized>(
+        &mut self,
+        child: &StrongWidget<W>,
+        axis: Axis,
+        region: UiRegion,
+        reports_of: UiVec2,
+    ) -> Option<LayoutLen> {
+        let declared = self.declared_lens(child);
+        let align = self.rsc.widgets().alignment(child.id());
+        let local = declared_box(region, declared, align);
+        let first_ask = self.offer(child.id());
+        if first_ask && let Some(active) = self.state.active.get_mut(&child.id()) {
+            active.offer_len = local.size();
+        }
+        if let Some(hint) = self.size_hint(child, axis) {
+            return Some(hint);
+        }
+        let px = local.size().to_px(self.px);
+        let (size, holds) =
+            self.state
+                .retained_size(child.id(), px, self.move_idx, self.rsc.widgets())?;
+        #[cfg(feature = "layout-diagnostics")]
+        diag::bump(Counter::RetainedSizeHits);
+        self.depend_on(child);
+        if first_ask {
+            let active = self.state.active.get_mut(&child.id()).unwrap();
+            active.answer = (size, holds);
+        }
+        for (axis, under) in AXES.into_iter().zip(self.under.iter_mut()) {
+            *under = under.and(holds[axis as usize].through(local.axis(axis).len()));
+        }
+        Some(in_parent_frame(size, reports_of, declared).axis(axis))
+    }
+
+    /// Whether this is the first box a child is asked about in during a draw
+    /// that is itself in the box it was asked in -- the question a cold
+    /// layout asks, whose answer is the one to keep.
+    fn offer(&mut self, child: WidgetId) -> bool {
+        if !self.at_offer || self.offered.contains(&child) {
+            return false;
+        }
+        self.offered.push(child);
+        true
+    }
+
+    fn depend_on<W: ?Sized>(&mut self, child: &StrongWidget<W>) {
         if !self.size_deps.contains(&child.id()) {
             self.size_deps.push(child.id());
         }
     }
 
-    pub fn render_text(
+    pub fn render_text<'b>(
         &mut self,
-        buffer: &mut TextBuffer,
+        buffer: &'b mut TextBuffer,
         attrs: &TextAttrs,
         width: Option<f32>,
-    ) -> RenderedText {
+    ) -> &'b RenderedText {
+        #[cfg(feature = "layout-diagnostics")]
+        diag::render_text(self.id, self.rsc.widgets().label(self.id), width);
         let ui = self.rsc.ui_mut();
         ui.text.render(buffer, attrs, width)
     }
@@ -142,9 +351,13 @@ impl<'a> Painter<'a> {
             let mut region = origin;
             region.x.end = region.x.start;
             region.y.end = region.y.start;
-            let mut region = region.offset(UiVec2::abs(glyph.offset));
-            region.x.end = region.x.start + UiScalar::abs(glyph.entry.width as f32);
-            region.y.end = region.y.start + UiScalar::abs(glyph.entry.height as f32);
+            let mut region = region.offset(UiVec2::from_px(glyph.offset));
+            let size = PxVec2::new(
+                Px::from_int(glyph.entry.width as i32),
+                Px::from_int(glyph.entry.height as i32),
+            );
+            region.x.end = region.x.start.offset(size.x);
+            region.y.end = region.y.start.offset(size.y);
             self.write(
                 kind,
                 GlyphPrimitive {
@@ -159,22 +372,72 @@ impl<'a> Painter<'a> {
         }
     }
 
+    /// This widget's box, in the coordinates its own primitives are written
+    /// in -- so a region composed `within` it may be drawn directly.
     pub fn region(&self) -> UiRegion {
         self.region
     }
 
-    /// The output's size in pixels. A widget that reads it draws again when
-    /// the output changes, since nothing else can put that right.
-    pub fn output_size(&mut self) -> Vec2 {
-        self.reads_output = true;
-        self.state.output_size
+    /// Where this widget sits in a box longer than the length it takes. A
+    /// widget that positions its own content reads it to place that content
+    /// the way the box around it would have placed the widget.
+    pub fn alignment(&self) -> RegionAlign {
+        self.rsc.widgets().alignment(self.id)
     }
 
-    /// This widget's box in pixels. Resolved against the output's size, so a
-    /// widget that reads it draws again when the output changes.
-    pub fn px_size(&mut self) -> Vec2 {
-        self.reads_output = true;
-        self.region.size().to_abs(self.state.output_size)
+    /// Whether a rule beside this widget gives its length on `axis` outright,
+    /// which makes whatever it reports for that axis moot. A rule that only
+    /// bounds the length is not one of these: the answer is still the
+    /// widget's to give, and something still has to work it out.
+    ///
+    /// The widget under a rule does not otherwise learn of it -- this is for
+    /// a container deciding whether reading its children across an axis is
+    /// worth anything, since reading one is also what makes its own size
+    /// depend on it.
+    pub fn has_exact_size(&self, axis: Axis) -> bool {
+        self.rsc
+            .widgets()
+            .size_rules(self.id)
+            .axis(axis)
+            .exact()
+            .is_some()
+    }
+
+    /// This widget's box in pixels. Reading it makes the drawing one that
+    /// holds for this box only, until `holds` says how far it goes.
+    pub fn px_size(&mut self) -> PxVec2 {
+        for (own, len) in self.own.iter_mut().zip([self.px.x, self.px.y]) {
+            if *own == Holds::ANY {
+                *own = Holds::at(len);
+            }
+        }
+        self.px
+    }
+
+    /// One axis of this widget's box in pixels. Prefer this to
+    /// [`Self::px_size`] when the other axis cannot affect the drawing.
+    pub fn px_len(&mut self, axis: Axis) -> Px {
+        let len = self.px.axis(axis);
+        let own = &mut self.own[axis as usize];
+        if *own == Holds::ANY {
+            *own = Holds::at(len);
+        }
+        len
+    }
+
+    /// The lengths of this widget's box on `axis` that what it is drawing
+    /// holds for -- the same primitives, in the same fractions and offsets
+    /// of the box, and the same reported size. A widget that read its
+    /// length in pixels holds for that one alone until it says otherwise.
+    pub fn holds(&mut self, axis: Axis, holds: impl Into<Holds>) {
+        let holds = holds.into();
+        debug_assert!(
+            holds.contains(self.px.axis(axis)),
+            "'{}' ({:?}) says its drawing holds for lengths that leave out its own box",
+            self.label(),
+            self.id
+        );
+        self.own[axis as usize] = holds;
     }
 
     pub fn text_data(&mut self) -> &mut TextData {
@@ -185,6 +448,18 @@ impl<'a> Painter<'a> {
         self.layer = self.state.layers.child(self.layer);
     }
 
+    /// The layer this widget's `n`th child draws on, addressed rather than
+    /// walked to. A container that measures one child by drawing it can ask
+    /// on the layer that child will end up on, and then the second ask is a
+    /// reuse rather than a second drawing on another layer.
+    pub fn child_layer_at(&mut self, n: usize) {
+        let mut at = self.state.layers.child(self.own_layer);
+        for _ in 0..n {
+            at = self.state.layers.next(at);
+        }
+        self.layer = at;
+    }
+
     pub fn next_layer(&mut self) {
         self.layer = self.state.layers.next(self.layer);
     }
@@ -209,11 +484,16 @@ pub struct DrawResult<'p, 'a, W: ?Sized> {
 
 impl<W: ?Sized> DrawResult<'_, '_, W> {
     pub fn size(self) -> Size {
-        self.painter.depend_on_size(self.child);
+        #[cfg(feature = "layout-diagnostics")]
+        {
+            diag::bump(Counter::SizeReads);
+            diag::size_read(self.child.id(), self.painter.id, self.size);
+        }
+        self.painter.depend_on(self.child);
         self.size
     }
 
-    pub fn len(self, axis: Axis) -> Len {
+    pub fn len(self, axis: Axis) -> LayoutLen {
         self.size().axis(axis)
     }
 }
@@ -242,3 +522,113 @@ impl PrimitiveLike for &TextureHandle {
         self.into()
     }
 }
+
+/// A child's answer as lengths of the parent's own box. A widget reports a
+/// fraction, and `reports_of` is the length that fraction is of: the box the
+/// child was given wherever that is the child's whole area, and the parent's
+/// own extent wherever the box is a positional remainder, as a span's is
+/// after an earlier child. Pixels come through untouched either way, being
+/// that many pixels wherever they end up. A declared axis is already the
+/// parent's: it resolved the rule in its own box, and the rule is what the
+/// report says.
+fn in_parent_frame(size: Size, reports_of: UiVec2, declared: [Option<LayoutLen>; 2]) -> Size {
+    let mut size = size;
+    for (axis, declared) in AXES.into_iter().zip(declared) {
+        if declared.is_none() {
+            *size.axis_mut(axis) = size.axis(axis).within_len(reports_of.axis(axis));
+        }
+    }
+    size
+}
+
+/// What a widget declares a length of its box to be. `leftover` is not one: a
+/// share of what is left over is only a length to the widget dividing one,
+/// so it passes up in the size instead.
+pub(crate) fn declared_lens(widgets: &Widgets, id: WidgetId) -> [Option<LayoutLen>; 2] {
+    let rules = widgets.size_rules(id);
+    let widget = widgets.get_dyn(id);
+    AXES.map(|axis| {
+        rules.axis(axis).declared().or_else(|| {
+            // A hint still narrows the box where no rule does, which is how a
+            // widget with a natural pixel size -- an image, a gap -- gets that
+            // size rather than the whole offer. That is the offer's business
+            // rather than a declaration's, and this falls away once a widget
+            // occupies its reported size inside the box it was offered.
+            widget
+                .and_then(|widget| widget.size_hint(axis))
+                .filter(|len| len.leftover == Weight::ZERO)
+        })
+    })
+}
+
+/// Whether what a widget reported along an axis is the whole of the box it
+/// is in rather than a part to be placed inside it. A share fills, because a
+/// share is a length only to whoever divides one, and whoever did is the one
+/// that handed down this box. A declared axis does too: `declared_box`
+/// already placed it, in the parent's box, and the rule's length is what the
+/// widget reports there. And an axis the parent decided from the answer is
+/// the answer already.
+pub(crate) fn fills(reported: LayoutLen, declared: Option<LayoutLen>, decided: bool) -> bool {
+    reported.leftover != Weight::ZERO || declared.is_some() || decided
+}
+
+/// What of the box it was given a widget's drawing occupies, as lengths of
+/// that box: the size it reported wherever that is a part to be placed, and
+/// the whole of the box wherever the answer fills it.
+///
+/// A reported fraction is a fraction of the box the widget drew in, where a
+/// declared one is a fraction of the box its parent handed down -- a span
+/// reporting `rel(1.0)` means all of what it was given, whatever that was a
+/// fraction of. So this is a length of the box rather than a length composed
+/// into it, and a box in pixels is this step from the given box's pixels.
+pub(crate) fn placed_lens(
+    size: Size,
+    declared: [Option<LayoutLen>; 2],
+    decided: [bool; 2],
+) -> UiVec2 {
+    let mut lens = UiVec2::FULL_SIZE;
+    for (axis, (declared, decided)) in AXES.into_iter().zip(declared.into_iter().zip(decided)) {
+        let reported = size.axis(axis);
+        if !fills(reported, declared, decided) {
+            *lens.axis_mut(axis) = Len::from_parts(reported.rel, reported.px);
+        }
+    }
+    lens
+}
+
+/// Where that drawing sits: those lengths taken of the box the widget was
+/// asked in, on the side of it that the widget's alignment says.
+pub(crate) fn placed_box(region: UiRegion, lens: UiVec2, align: RegionAlign) -> UiRegion {
+    let mut placed = region;
+    for axis in AXES {
+        // The whole of the box is already where it sits, and the arithmetic
+        // below is the identity for it.
+        if lens.axis(axis) == Len::FULL {
+            continue;
+        }
+        let span = placed.axis_mut(axis);
+        let len = lens.axis(axis).within_len(span.len());
+        span.start += (span.len() - len).scale(align.axis(axis).rel());
+        span.end = span.start + len;
+    }
+    placed
+}
+
+/// Takes a widget's declared lengths in the box `region` is given in, since a
+/// fraction of a length means a fraction of that one, and puts what is left
+/// over on the side its alignment says. A caller that already reserved the
+/// space hands back the same length, so this is the identity for it.
+pub(crate) fn declared_box(
+    mut region: UiRegion,
+    declared: [Option<LayoutLen>; 2],
+    align: RegionAlign,
+) -> UiRegion {
+    for (axis, len) in AXES.into_iter().zip(declared) {
+        let Some(len) = len else { continue };
+        let span = region.axis_mut(axis);
+        let len = Len::from_parts(len.rel, len.px);
+        span.start += (span.len() - len).scale(align.axis(axis).rel());
+        span.end = span.start + len;
+    }
+    region
+}

core/src/util/arena.rs

@@ -34,6 +34,10 @@ impl<T, I: IdNum> Arena<T, I> {
         self.tracker.free(id);
         self.data[i]
     }
+
+    pub(crate) fn get_mut(&mut self, id: Id<I>) -> &mut T {
+        &mut self.data[id.idx()]
+    }
 }
 
 impl<T, I: IdNum> Default for Arena<T, I> {
@@ -71,6 +75,11 @@ impl<T, I: IdNum> TrackedArena<T, I> {
         self.refs[i.idx()] += 1;
     }
 
+    pub fn get_mut(&mut self, id: Id<I>) -> &mut T {
+        self.changed = true;
+        self.inner.get_mut(id)
+    }
+
     pub fn remove(&mut self, id: Id<I>) -> T
     where
         T: Copy,

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 {
@@ -65,6 +56,34 @@ macro_rules! impl_op {
             }
         }
     };
+    // Without the `f32` operations, for a type whose fields are not all the
+    // same kind of number: there is nothing a bare float means to a fraction
+    // and an offset at once.
+    (same $T:ident $op:ident $fn:ident $opa:ident $fna:ident; $($field:ident)*) => {
+        #[allow(non_snake_case)]
+        mod ${concat($T, _op_, $fn, _same_impl)} {
+            use super::*;
+            #[allow(unused_imports)]
+            use std::ops::*;
+            const impl $op for $T {
+                type Output = Self;
+
+                fn $fn(self, rhs: Self) -> Self::Output {
+                    Self {
+                        $($field: self.$field.$fn(rhs.$field),)*
+                    }
+                }
+            }
+            const impl $opa for $T {
+                fn $fna(&mut self, rhs: Self) {
+                    *self = self.$fn(rhs);
+                }
+            }
+        }
+    };
+    (same $T:ident $op:ident $fn:ident; $($field:ident)*) => {
+        impl_op!(same $T $op $fn ${concat($op,Assign)} ${concat($fn,_assign)}; $($field)*);
+    };
     ($T:ident $op:ident $fn:ident; $($field:ident)*) => {
         impl_op!($T $op $fn ${concat($op,Assign)} ${concat($fn,_assign)}; $($field)*);
     };

core/src/util/trust.rs

@@ -1,8 +1,3 @@
-#[allow(clippy::missing_safety_doc)]
-pub(crate) unsafe fn forget_ref<'a, T>(x: &T) -> &'a T {
-    unsafe { std::mem::transmute::<&T, &T>(x) }
-}
-
 #[allow(clippy::missing_safety_doc)]
 pub(crate) unsafe fn forget_mut<'a, T>(x: &mut T) -> &'a mut T {
     unsafe { std::mem::transmute::<&mut T, &mut T>(x) }

core/src/util/vec2.rs

@@ -1,7 +1,11 @@
 use crate::util::impl_op;
 use std::{hash::Hash, ops::*};
 
-#[repr(C)]
+/// `align(8)` because that is WGSL's alignment for a `vec2<f32>`, so any GPU
+/// struct holding one is laid out the way its shader reads it without having
+/// to say so itself. Those structs still need a manual `unsafe impl Pod`,
+/// since the trailing padding this introduces is what `derive(Pod)` refuses.
+#[repr(C, align(8))]
 #[derive(Clone, Copy, PartialEq, Default, bytemuck::Pod, bytemuck::Zeroable)]
 pub struct Vec2 {
     pub x: f32,

core/src/widget/data.rs

@@ -1,8 +1,11 @@
-use crate::Widget;
+use crate::{RegionAlign, SizeRules, Widget};
 
 pub struct WidgetData {
     pub widget: Box<dyn Widget>,
     pub label: String,
+    pub(super) region_node: bool,
+    pub(super) size: SizeRules,
+    pub(super) align: RegionAlign,
     /// dynamic borrow checking
     pub borrowed: bool,
 }
@@ -16,6 +19,9 @@ impl WidgetData {
         Self {
             widget: Box::new(widget),
             label,
+            region_node: false,
+            size: SizeRules::default(),
+            align: RegionAlign::default(),
             borrowed: false,
         }
     }

core/src/widget/mod.rs

@@ -1,9 +1,10 @@
-use crate::{Axis, Len, Painter, Size};
+use crate::{Axis, LayoutLen, Painter, Size};
 use std::any::Any;
 
 mod data;
 mod handle;
 mod like;
+mod size_rule;
 mod tag;
 mod view;
 mod widgets;
@@ -11,21 +12,11 @@ mod widgets;
 pub use data::*;
 pub use handle::*;
 pub use like::*;
+pub use size_rule::*;
 pub use tag::*;
 pub use view::*;
 pub use widgets::*;
 
-/// What may be done to a widget's drawing when the box it was given changes
-/// on this axis, instead of drawing it again. Asked per axis, because wrapped
-/// text reads the width it is offered and not the height.
-#[derive(Clone, Copy, Debug, Default, PartialEq, Eq)]
-pub enum OnResize {
-    Scale,
-    Translate,
-    #[default]
-    Redraw,
-}
-
 pub trait Widget: Any {
     /// Draws the widget, and returns what it used of the box it was given.
     fn draw(&mut self, painter: &mut Painter) -> Size;
@@ -33,13 +24,9 @@ pub trait Widget: Any {
     /// An exact length the widget can give without a painter or its children.
     /// Optional, and saves a draw rather than changing one: a hint that
     /// disagrees with the eventual draw fails a debug assertion.
-    fn size_hint(&self, _axis: Axis) -> Option<Len> {
+    fn size_hint(&self, _axis: Axis) -> Option<LayoutLen> {
         None
     }
-
-    fn on_resize(&self, _axis: Axis) -> OnResize {
-        OnResize::default()
-    }
 }
 
 impl Widget for () {
@@ -48,12 +35,8 @@ impl Widget for () {
         Size::default()
     }
 
-    fn size_hint(&self, _axis: Axis) -> Option<Len> {
-        Some(Len::default())
-    }
-
-    fn on_resize(&self, _axis: Axis) -> OnResize {
-        OnResize::Scale
+    fn size_hint(&self, _axis: Axis) -> Option<LayoutLen> {
+        Some(LayoutLen::default())
     }
 }
 

core/src/widget/size_rule.rs

@@ -0,0 +1,87 @@
+use crate::{Axis, LayoutLen, Weight};
+
+/// What a widget's length on one axis is, as a rule its parent applies where
+/// it draws it rather than an answer the widget gives about itself.
+///
+/// A rule and a drawn size are not two opinions to reconcile: a rule wins on
+/// the axis it names, and the `Size` returned by `draw` answers only the axes
+/// with no rule. That is what lets a span divide its space around a length
+/// nobody has drawn yet, and it is why a rule lives beside the widget rather
+/// than inside it -- the widget under the rule never has to know about it.
+#[derive(Debug, Clone, Copy, PartialEq, Default)]
+pub enum SizeRule {
+    /// Whatever the widget reports from drawing.
+    #[default]
+    Free,
+    /// This length, whatever the widget reports.
+    Exact(LayoutLen),
+}
+
+impl SizeRule {
+    /// The length this rule gives without the widget being drawn, if it can
+    /// give one. `leftover` is never among them: a share is a length only to
+    /// whoever divides one, so it passes up in the reported size instead and
+    /// is resolved there.
+    pub fn declared(&self) -> Option<LayoutLen> {
+        match self {
+            Self::Exact(len) if len.leftover == Weight::ZERO => Some(*len),
+            _ => None,
+        }
+    }
+
+    /// The length this rule gives outright, whatever the widget reports --
+    /// which makes the widget's answer on that axis moot. A share counts: it
+    /// is a length the widget's parent still has to divide, so it is exact
+    /// here and resolved there, unlike `declared`, which is only the ones
+    /// that give a box directly.
+    pub fn exact(&self) -> Option<LayoutLen> {
+        match self {
+            Self::Free => None,
+            Self::Exact(len) => Some(*len),
+        }
+    }
+
+    /// The length a widget reporting `reported` ends up with.
+    pub fn apply(&self, reported: LayoutLen) -> LayoutLen {
+        match self {
+            Self::Free => reported,
+            Self::Exact(len) => *len,
+        }
+    }
+}
+
+impl From<LayoutLen> for SizeRule {
+    fn from(len: LayoutLen) -> Self {
+        Self::Exact(len)
+    }
+}
+
+impl From<Option<LayoutLen>> for SizeRule {
+    fn from(len: Option<LayoutLen>) -> Self {
+        len.map_or(Self::Free, Self::Exact)
+    }
+}
+
+/// One rule per axis, which is how a widget carries a length on one axis and
+/// leaves the other to whatever it draws.
+#[derive(Debug, Clone, Copy, PartialEq, Default)]
+pub struct SizeRules {
+    pub x: SizeRule,
+    pub y: SizeRule,
+}
+
+impl SizeRules {
+    pub fn axis(&self, axis: Axis) -> SizeRule {
+        match axis {
+            Axis::X => self.x,
+            Axis::Y => self.y,
+        }
+    }
+
+    pub fn axis_mut(&mut self, axis: Axis) -> &mut SizeRule {
+        match axis {
+            Axis::X => &mut self.x,
+            Axis::Y => &mut self.y,
+        }
+    }
+}

core/src/widget/widgets.rs

@@ -1,7 +1,8 @@
 use std::sync::mpsc::{Receiver, Sender, channel};
 
 use crate::{
-    IdLike, StrongWidget, WeakWidget, Widget, WidgetData, WidgetId,
+    Axis, AxisAlign, IdLike, RegionAlign, SizeRule, SizeRules, StrongWidget, WeakWidget, Widget,
+    WidgetData, WidgetId,
     util::{DynBorrower, HashSet, SlotVec, forget_mut, to_mut},
 };
 
@@ -100,6 +101,71 @@ impl Widgets {
         self.data_mut(id.id()).unwrap().label = label;
     }
 
+    /// Whether this widget owns a movable retained region.
+    pub fn is_region_node(&self, id: impl IdLike) -> bool {
+        self.data(id).unwrap().region_node
+    }
+
+    /// Chooses whether this widget's retained drawing has one movable region
+    /// of its own. Changing the boundary redraws the subtree once so every
+    /// primitive names the right coordinate space.
+    pub fn set_region_node(&mut self, id: impl IdLike, region_node: bool) {
+        let id = id.id();
+        let data = self.data_mut(id).unwrap();
+        if data.region_node == region_node {
+            return;
+        }
+        data.region_node = region_node;
+        self.needs_redraw.insert(id);
+    }
+
+    /// The length rules whoever draws this widget applies to its box.
+    pub fn size_rules(&self, id: impl IdLike) -> SizeRules {
+        self.data(id).unwrap().size
+    }
+
+    /// Sets one axis's rule. The widget is marked rather than its parent
+    /// because the parent is not known here; `redraw` escalates a changed
+    /// declared length to whoever resolves it.
+    pub fn set_size_rule(&mut self, id: impl IdLike, axis: Axis, rule: SizeRule) {
+        let id = id.id();
+        let data = self.data_mut(id).unwrap();
+        if *data.size.axis_mut(axis) == rule {
+            return;
+        }
+        *data.size.axis_mut(axis) = rule;
+        self.needs_redraw.insert(id);
+    }
+
+    /// Where this widget sits in a box longer than the length it takes.
+    pub fn alignment(&self, id: impl IdLike) -> RegionAlign {
+        self.data(id).unwrap().align
+    }
+
+    /// Sets one axis's alignment. Which box a widget ends up in is its
+    /// parent's to decide, so this is escalated the way a length rule is.
+    pub fn set_alignment(&mut self, id: impl IdLike, axis: Axis, align: AxisAlign) {
+        let id = id.id();
+        let data = self.data_mut(id).unwrap();
+        if *data.align.axis_mut(axis) == align {
+            return;
+        }
+        *data.align.axis_mut(axis) = align;
+        self.needs_redraw.insert(id);
+    }
+
+    /// Both axes at once, for a caller holding a pair.
+    pub fn set_size_rules(
+        &mut self,
+        id: impl IdLike,
+        x: impl Into<SizeRule>,
+        y: impl Into<SizeRule>,
+    ) {
+        let id = id.id();
+        self.set_size_rule(id, Axis::X, x.into());
+        self.set_size_rule(id, Axis::Y, y.into());
+    }
+
     pub fn data_mut(&mut self, id: impl IdLike) -> Option<&mut WidgetData> {
         self.vec.get_mut(id.id())
     }

examples/random.rs

@@ -0,0 +1,31 @@
+//! The seeded random tree `tests/generated.rs` checks, drawn so it can be
+//! looked at. `IRIS_SEED` and `IRIS_DEPTH` choose which one.
+
+use iris::prelude::*;
+use iris::random::Edits;
+
+fn env(name: &str, fallback: u64) -> u64 {
+    std::env::var(name)
+        .ok()
+        .and_then(|v| v.parse().ok())
+        .unwrap_or(fallback)
+}
+
+fn main() {
+    DefaultApp::<State>::run();
+}
+
+#[derive(DefaultUiState)]
+struct State {
+    ui_state: DefaultUiState,
+}
+
+impl DefaultAppState for State {
+    fn new(mut ui_state: DefaultUiState, rsc: &mut DefaultRsc<Self>, _: Proxy<Self>) -> Self {
+        let seed = env("IRIS_SEED", 1);
+        let depth = env("IRIS_DEPTH", 4) as usize;
+        let (root, _) = iris::random::grow(rsc, seed, depth, &Edits::default());
+        ui_state.set_root(root);
+        Self { ui_state }
+    }
+}

examples/tabs/main.rs

@@ -20,22 +20,26 @@ impl DefaultAppState for Client {
         let pad_test = (
             rrect.color(Color::BLUE),
             (
+                // The square is one widget and the two shares of the row it
+                // sits centred in are another: a length is a property of a
+                // widget, so `.width` here would overwrite the `.sized`.
                 rrect
                     .color(Color::RED)
                     .sized((100, 100))
                     .center()
-                    .width(rest(2)),
+                    .wrapper()
+                    .width(leftover(2)),
                 (
                     rrect.color(Color::ORANGE),
                     rrect.color(Color::LIME).pad(10.0),
                 )
                     .span(Dir::RIGHT)
-                    .width(rest(2)),
+                    .width(leftover(2)),
                 rrect.color(Color::YELLOW),
             )
                 .span(Dir::RIGHT)
                 .pad(10)
-                .width(rest(3)),
+                .width(leftover(3)),
         )
             .span(Dir::RIGHT)
             .add(rsc);
@@ -121,11 +125,11 @@ impl DefaultAppState for Client {
             .add(rsc);
 
         let text_edit_scroll = (
-            msg_area.height(rest(1)),
+            msg_area.height(leftover(1)),
             (
                 Rect::new(Color::WHITE.darker(0.9)),
                 (
-                    add_text.width(rest(1)),
+                    add_text.width(leftover(1)),
                     Rect::new(Color::GREEN)
                         .on(CursorSense::click(), move |ctx, rsc: &mut ClientRsc| {
                             rsc.run_event::<Submit>(add_text, (), ctx.state);
@@ -143,7 +147,7 @@ impl DefaultAppState for Client {
             .span(Dir::DOWN)
             .add(rsc);
 
-        let main = WidgetPtr::new().add(rsc);
+        let main = Wrapper::new().add(rsc);
 
         let vals = Rc::new(RefCell::new((0, Vec::new())));
         let mut switch_button = |color, to: WeakWidget, label| {

examples/text.rs

@@ -26,12 +26,17 @@ impl DefaultAppState for State {
             .wrap(true)
             .text_align(Align::LEFT)
             .pad(16)
+            .width(rel(1.0))
             .background(panel());
 
+        // Each one takes the whole width, because `text_align` puts the
+        // glyphs somewhere in the box the text is given and a text that
+        // reports the width of its own glyphs is given exactly that.
+        let label = |text: &str, align| wtext(text).size(24).text_align(align).width(rel(1.0));
         let aligned = (
-            wtext("left").size(24).text_align(Align::LEFT),
-            wtext("centred").size(24).text_align(Align::CENTER),
-            wtext("right").size(24).text_align(Align::RIGHT),
+            label("left", Align::LEFT),
+            label("centred", Align::H_CENTER),
+            label("right", Align::RIGHT),
         )
             .span(Dir::DOWN)
             .gap(8)

scripts/run-headless.sh

@@ -17,6 +17,10 @@
 # custom one would otherwise inherit the other's output and quietly screenshot
 # the wrong size.
 #
+# `--resize WxH@Hz` changes the output under the app once it is up, then
+# screenshots. A resize is its own case: what it has to match is a cold start
+# at that size, byte for byte, and nothing in `cargo test` can see it.
+#
 # `--replay FILE` drives a `.touch` recording into the window through
 # `replay-touch`, which reads it with the same parser `iris::harness` uses. A
 # recording is `<ms> down|move|up <x> <y>` in the output's own pixels. With
@@ -46,6 +50,7 @@ run="${XDG_RUNTIME_DIR:-/tmp}/iris-headless"
 seconds=3
 shot=""
 replay=""
+resize=""
 example=""
 kind=example
 mode=1920x1200@60Hz
@@ -57,13 +62,14 @@ while [ $# -gt 0 ]; do
         --seconds) seconds=$2; shift 2 ;;
         --bin) kind=bin; shift ;;
         --mode) mode=$2; shift 2 ;;
+        --resize) resize=$2; shift 2 ;;
         --replay) replay=$2; shift 2 ;;
         --dir) workdir=$(cd "$2" && pwd); shift 2 ;;
         --) shift; break ;;
         *) example=$1; shift ;;
     esac
 done
-[ -n "$example" ] || { echo "usage: $0 NAME [--bin] [--dir DIR] [--mode WxH@Hz] [--replay TOUCH] [--shot PNG] [--seconds N] [-- cargo args]" >&2; exit 2; }
+[ -n "$example" ] || { echo "usage: $0 NAME [--bin] [--dir DIR] [--mode WxH@Hz] [--resize WxH@Hz] [--replay TOUCH] [--shot PNG] [--seconds N] [-- cargo args]" >&2; exit 2; }
 [ -z "$replay" ] || [ -f "$replay" ] || { echo "run-headless: no touch script at $replay" >&2; exit 2; }
 [ -z "$shot" ] || need grim "the screenshot --shot writes"
 
@@ -142,6 +148,12 @@ while [ $i -lt "$((seconds * 2))" ]; do
     i=$((i + 1)); sleep 0.5
 done
 
+if [ -n "$resize" ] && kill -0 "$pid" 2>/dev/null; then
+    swaymsg output HEADLESS-1 mode "$resize" >/dev/null
+    echo "run-headless: resized to $resize" >&2
+    sleep 2
+fi
+
 if [ -n "$replay" ] && kill -0 "$pid" 2>/dev/null; then
     if [ -n "$shot" ]; then
         grim "${shot%.png}-before.png"

src/default/attr.rs

@@ -15,8 +15,10 @@ where
             let region = ctx.data.render.window_region(&id).unwrap();
             let id_pos = region.top_left;
             let container_pos = ctx.data.render.window_region(&container).unwrap().top_left;
-            let pos = ctx.data.pos + container_pos - id_pos;
-            let size = region.size();
+            // The pointer arrives from the platform in floats; everything
+            // it is compared against is on the grid.
+            let pos = (PxVec2::from_f32(ctx.data.pos) + container_pos - id_pos).to_f32();
+            let size = region.size().to_f32();
             select(
                 rsc,
                 ctx.data.render,
@@ -70,8 +72,8 @@ fn select(
     if let Some(region) = render.window_region(&id) {
         state.window.set_ime_allowed(true);
         state.window.set_ime_cursor_area(
-            LogicalPosition::<f32>::from(region.top_left.tuple()),
-            LogicalSize::<f32>::from(region.size().tuple()),
+            LogicalPosition::<f32>::from(region.top_left.to_f32().tuple()),
+            LogicalSize::<f32>::from(region.size().to_f32().tuple()),
         );
     }
     state.focus = Some(id);

src/default/sense.rs

@@ -198,7 +198,7 @@ impl SensorUi for UiRenderState {
                 let Some(region) = region_of(id) else {
                     continue;
                 };
-                if !cursor.exists || !region.contains(cursor.pos) {
+                if !cursor.exists || !region.contains(PxVec2::from_f32(cursor.pos)) {
                     continue;
                 }
                 hovered.now.push(id);
@@ -249,8 +249,8 @@ fn deliver<Rsc: HasEvents>(
     region: PixelRegion,
 ) -> bool {
     let data = CursorData {
-        pos: cursor.pos - region.top_left,
-        size: region.bot_right - region.top_left,
+        pos: cursor.pos - region.top_left.to_f32(),
+        size: region.size().to_f32(),
         scroll_delta: cursor.scroll_delta,
         hover,
         cursor: cursor.clone(),

src/harness.rs

@@ -29,8 +29,14 @@ macro_rules! assert_corners {
         assert_eq!(
             $harness.region(&$id).expect("widget drew nothing"),
             $crate::core::PixelRegion {
-                top_left: $crate::core::util::Vec2::new($x0 as f32, $y0 as f32),
-                bot_right: $crate::core::util::Vec2::new($x1 as f32, $y1 as f32),
+                top_left: $crate::core::PxVec2::new(
+                    $crate::core::Px::from_f32($x0 as f32),
+                    $crate::core::Px::from_f32($y0 as f32),
+                ),
+                bot_right: $crate::core::PxVec2::new(
+                    $crate::core::Px::from_f32($x1 as f32),
+                    $crate::core::Px::from_f32($y1 as f32),
+                ),
             }
         );
     };
@@ -151,13 +157,20 @@ impl Harness {
     }
 
     pub fn size(&self) -> Vec2 {
-        self.render.output_size()
+        self.render.output_size().to_f32()
     }
 
     pub fn resize(&mut self, size: impl Into<Vec2>) {
         self.render.resize(size);
     }
 
+    /// Changes a length rule after the fact, the way `.width()` sets one.
+    pub fn set_len(&mut self, id: impl IdLike, axis: Axis, len: impl Into<LayoutLen>) {
+        self.rsc
+            .widgets_mut()
+            .set_size_rule(id, axis, SizeRule::Exact(len.into()));
+    }
+
     /// Sets the root and lays it out, so a pointer event has something to hit.
     pub fn set_root<T>(&mut self, widget: impl WidgetLike<DefaultRsc<HarnessState>, T>) {
         widget.set_root(&mut self.rsc, &mut self.state);

src/lib.rs

@@ -8,6 +8,7 @@
 pub mod default;
 pub mod event;
 pub mod harness;
+pub mod random;
 pub mod widget;
 
 pub use iris_core as core;

src/random.rs

@@ -0,0 +1,915 @@
+//! A seeded random widget tree, for tests and for looking at.
+//!
+//! One seed is one tree, on any machine and after any upgrade, so a test can
+//! grow the same tree twice and a failing seed is reproduced by its number.
+//! `examples/random.rs` draws one; `tests/generated.rs` checks that laying one
+//! out again lands where growing it from scratch would.
+
+use crate::prelude::*;
+use std::collections::HashMap;
+
+/// The declared lengths of one widget carrying a size rule, by axis.
+pub type Lens = [Option<LayoutLen>; 2];
+
+/// Where one widget carrying an alignment sits, by axis. `None` uses the
+/// centered default.
+pub type Aligns = [Option<AxisAlign>; 2];
+
+/// What a test changes between two trees grown from the same seed, so the
+/// warm one can be mutated and the cold one grown that way to begin with.
+#[derive(Default)]
+pub struct Edits {
+    /// Declared sizes, by the order the rules were put on.
+    pub sizes: HashMap<usize, Lens>,
+    /// Which children a span has, by the order the spans were made.
+    pub spans: HashMap<usize, SpanEdit>,
+    /// Alignments, by the order they were put on.
+    pub aligns: HashMap<usize, Aligns>,
+    /// Which widgets own a movable region, by the order they were offered
+    /// one. Region nodes change what a move writes and how deep a primitive's
+    /// chain is, so a tree that never grows one leaves both untested.
+    pub nodes: HashMap<usize, bool>,
+    /// Whether a [`Branch`] takes the side it would take at any measurement,
+    /// rather than the side the one it made says. The oracle wants the
+    /// measured side -- that is the whole point of a branch, and how a widget
+    /// believing a measurement a cold start would not have given it becomes a
+    /// different tree. A rig measuring cost wants this instead: a fixture
+    /// whose shape moves with the thing being measured cannot be compared
+    /// with itself across a change to it, and seed 1 at depth 8 went from 88
+    /// drawn widgets and 2,298 primitive writes a frame to 115 and 8,209
+    /// across fixed point, which is three and a half times the work behind a
+    /// number read as three and a half times the cost.
+    pub fixed_branches: bool,
+}
+
+#[derive(Default, Clone)]
+pub struct SpanEdit {
+    /// Children to leave out, by index among the ones grown.
+    pub detach: Vec<usize>,
+    /// How many of the span's spares are in it, appended in order.
+    pub attach: usize,
+}
+
+/// xorshift64, written out rather than taken from a crate so that a seed
+/// keeps meaning the same tree.
+pub struct Rng(u64);
+
+impl Rng {
+    pub fn new(seed: u64) -> Self {
+        Self(seed | 1)
+    }
+
+    pub fn bits(&mut self) -> u64 {
+        self.0 ^= self.0 << 13;
+        self.0 ^= self.0 >> 7;
+        self.0 ^= self.0 << 17;
+        self.0
+    }
+
+    pub fn below(&mut self, n: usize) -> usize {
+        (self.bits() % n as u64) as usize
+    }
+
+    pub fn chance(&mut self) -> bool {
+        self.bits() & 1 == 0
+    }
+}
+
+const COLORS: [UiColor; 6] = [
+    UiColor::RED,
+    UiColor::GREEN,
+    UiColor::BLUE,
+    UiColor::YELLOW,
+    UiColor::CYAN,
+    UiColor::MAGENTA,
+];
+
+/// Leaves grown beside every span, for a test to put into it.
+const SPARES: usize = 3;
+
+const WORDS: &str = "Wrapping shapes one source into as many lines as the box \
+    leaves room for, so a paragraph's height is an answer and not a setting.";
+
+/// What growing a tree gives back: every widget in creation order, so two
+/// trees from one seed line up index for index, and the declared sizes, which
+/// are what a test changes to watch the change propagate.
+#[derive(Default)]
+pub struct Tree {
+    pub ids: Vec<WidgetId>,
+    pub sized: Vec<WidgetId>,
+    pub aligned: Vec<WidgetId>,
+    pub nodes: Vec<WidgetId>,
+    pub spans: Vec<Spanned>,
+    pub scrolls: Vec<WeakWidget<Scroll>>,
+}
+
+/// Branches on a child's measured length. Comparing boxes catches a widget
+/// that moved; this catches one that believed a measurement a cold start
+/// would not have given it, by turning that into a different tree. Its own
+/// configuration never changes, so which side draws is a property of the
+/// layout alone.
+pub struct Branch {
+    pub probe: StrongWidget,
+    pub wide: StrongWidget,
+    pub narrow: StrongWidget,
+    pub threshold: f32,
+}
+
+impl Widget for Branch {
+    fn draw(&mut self, painter: &mut Painter) -> Size {
+        let mut top = UiRegion::FULL;
+        top.y.end = top.y.start.offset(Px::from_int(40));
+        let measured = painter.widget_within(&self.probe, top).len(Axis::X);
+        let px = measured.apply_leftover().to_px(painter.px_len(Axis::X));
+
+        let mut below = UiRegion::FULL;
+        below.y.start = below.y.start.offset(Px::from_int(40));
+        match px > Px::from_f32(self.threshold) {
+            true => painter.widget_within(&self.wide, below),
+            false => painter.widget_within(&self.narrow, below),
+        };
+        Size::LEFTOVER
+    }
+}
+
+pub struct Spanned {
+    pub id: WeakWidget<Span>,
+    /// Everything made for this span that it does not hold -- spares never
+    /// attached and children detached alike. A widget belongs to one parent,
+    /// and one that belongs to nobody still has to be held here: dropping
+    /// the last share of it frees its id for the next widget to be given,
+    /// which puts two trees out of step.
+    pub spares: Vec<StrongWidget>,
+    /// How many children it was grown with, before any edit.
+    pub grown: usize,
+}
+
+/// A tree described rather than built: [`plan`] turns a seed into one of
+/// these and [`build`] turns it into widgets, where growing did both at once.
+///
+/// The split is what makes a counterexample readable. A failing seed used to
+/// be the entire record of one, because a grower that makes widgets as it
+/// draws leaves nothing to take apart -- a shrinker could only grow its own
+/// trees and hope to meet the same shape, which in practice it does not. A
+/// plan is reduced by [`Plan::smaller`] and built again, so any seed that
+/// fails can be cut down until what is left is small enough to read.
+#[derive(Clone, Debug, PartialEq)]
+pub struct Plan {
+    pub kind: Kind,
+    /// The declared size this widget carries. Whoever grows a widget offers
+    /// it one and the offer is taken or declined; a second offer to the same
+    /// widget is dropped, because two rules on one widget would settle in the
+    /// order they were applied rather than in grow order.
+    pub size: Option<Lens>,
+    /// The alignment it carries, under the same one-offer rule.
+    pub align: Option<Aligns>,
+    /// Whether it was offered a movable region of its own and what it
+    /// answered. `Some(false)` is an offer declined, which still uses up the
+    /// one offer, where `None` is an offer never made.
+    pub region_node: Option<bool>,
+}
+
+#[derive(Clone, Debug, PartialEq)]
+pub enum Kind {
+    /// Wrapped and unwrapped text, because only one of them reads the width
+    /// it is given and so only one has to be drawn again for a new one.
+    Wrapped,
+    OneLine,
+    Rect {
+        color: usize,
+        alpha: u8,
+    },
+    /// Scrolling reads the pixel length of its box, which nothing else here
+    /// does, and gives its child a box longer than its own.
+    Scroll {
+        axis: Axis,
+        inner: Box<Plan>,
+    },
+    /// All three sides are grown either way, so a tree that draws one has the
+    /// same ids as a tree that draws another.
+    Branch {
+        probe: Box<Plan>,
+        wide: Box<Plan>,
+        narrow: Box<Plan>,
+        threshold: f32,
+    },
+    /// Each side its own, since a padding that is the same all round hides
+    /// anything that treats one edge differently from another.
+    Pad {
+        padding: [i32; 4],
+        inner: Box<Plan>,
+    },
+    Stack {
+        children: Vec<Plan>,
+    },
+    Span {
+        dir: usize,
+        gap: i32,
+        /// Grown for this span, in the order they are made.
+        children: Vec<Plan>,
+        /// Grown beside it whether or not they end up in it, so the widget
+        /// after them has the same id in a tree that leaves them out as in
+        /// one that puts them in.
+        spares: Vec<Plan>,
+        /// Which of `children` then `spares` are actually in the span, and
+        /// in what order -- kept apart from the two lists above so that a
+        /// tree which detaches, attaches or reorders its children still
+        /// makes the same widgets in the same order, and two builds line up
+        /// index for index. Anything not named here is built and held
+        /// rather than dropped, since freeing an id hands it to the next
+        /// widget and puts two trees out of step.
+        order: Vec<usize>,
+    },
+}
+
+impl Plan {
+    /// A widget carrying nothing anybody has offered it yet.
+    fn bare(kind: Kind) -> Self {
+        Self {
+            kind,
+            size: None,
+            align: None,
+            region_node: None,
+        }
+    }
+
+    /// How many widgets building it makes, spares and detached children
+    /// included, since those are made either way.
+    pub fn size(&self) -> usize {
+        1 + match &self.kind {
+            Kind::Scroll { inner, .. } | Kind::Pad { inner, .. } => inner.size(),
+            Kind::Branch {
+                probe,
+                wide,
+                narrow,
+                ..
+            } => probe.size() + wide.size() + narrow.size(),
+            Kind::Stack { children } => children.iter().map(Plan::size).sum(),
+            Kind::Span {
+                children, spares, ..
+            } => children.iter().chain(spares).map(Plan::size).sum(),
+            _ => 0,
+        }
+    }
+
+    /// The trees to try instead of this one when reducing a counterexample,
+    /// biggest cut first: a shrinker takes the first that still fails, so
+    /// offering "this subtree alone" before "this subtree with one child
+    /// fewer" is what gets from six hundred widgets to six rather than to
+    /// five hundred and ninety.
+    ///
+    /// Every one of these is a tree the generator could have grown, so a
+    /// reduced plan is a counterexample in its own right rather than a
+    /// special case only the shrinker can make.
+    pub fn smaller(&self) -> Vec<Plan> {
+        let mut out = Vec::new();
+        // Standing in for the whole of it, which is the largest cut there is.
+        for kid in self.kids() {
+            out.push(kid.clone());
+        }
+        // Then what it carries, which costs nothing to put back if it was
+        // not the thing that mattered.
+        for dropped in [
+            self.region_node.map(|_| Plan {
+                region_node: None,
+                ..self.clone()
+            }),
+            self.align.map(|_| Plan {
+                align: None,
+                ..self.clone()
+            }),
+            self.size.map(|_| Plan {
+                size: None,
+                ..self.clone()
+            }),
+        ]
+        .into_iter()
+        .flatten()
+        {
+            out.push(dropped);
+        }
+        out.extend(self.kind.smaller().into_iter().map(|kind| Plan {
+            kind,
+            ..self.clone()
+        }));
+        out
+    }
+
+    /// Visits every widget in the order [`build`] makes them, so a count
+    /// kept by the visitor indexes the same widget as the matching [`Tree`]
+    /// vector does.
+    pub fn walk_mut(&mut self, at: &mut impl FnMut(&mut Plan)) {
+        match &mut self.kind {
+            Kind::Scroll { inner, .. } | Kind::Pad { inner, .. } => inner.walk_mut(at),
+            Kind::Branch {
+                probe,
+                wide,
+                narrow,
+                ..
+            } => {
+                probe.walk_mut(at);
+                wide.walk_mut(at);
+                narrow.walk_mut(at);
+            }
+            Kind::Stack { children } => {
+                for child in children {
+                    child.walk_mut(at);
+                }
+            }
+            Kind::Span {
+                children, spares, ..
+            } => {
+                for child in children.iter_mut().chain(spares) {
+                    child.walk_mut(at);
+                }
+            }
+            _ => {}
+        }
+        at(self);
+    }
+
+    /// The same tree with `edits` applied, by the indices the generator would
+    /// have used for them.
+    ///
+    /// [`plan`] resolves edits while drawing, which needs a seed. A scenario
+    /// needs them applied to a tree that already exists -- one it has built,
+    /// and one a shrinker may already have cut down, where no seed grows it
+    /// any more. Both routes take the same [`Edits`], so a case written
+    /// against one reads the same against the other.
+    pub fn edited(&self, edits: &Edits) -> Plan {
+        let mut out = self.clone();
+        let (mut sized, mut aligned, mut nodes, mut spans) = (0, 0, 0, 0);
+        out.walk_mut(&mut |plan| {
+            if let Kind::Span {
+                children,
+                spares,
+                order,
+                ..
+            } = &mut plan.kind
+            {
+                if let Some(edit) = edits.spans.get(&spans) {
+                    *order = span_edited(order, children.len(), spares.len(), edit);
+                }
+                spans += 1;
+            }
+            if let Kind::Branch { threshold, .. } = &mut plan.kind
+                && edits.fixed_branches
+            {
+                *threshold = f32::MIN;
+            }
+            if plan.size.is_some() {
+                if let Some(lens) = edits.sizes.get(&sized) {
+                    plan.size = Some(*lens);
+                }
+                sized += 1;
+            }
+            if plan.align.is_some() {
+                if let Some(align) = edits.aligns.get(&aligned) {
+                    plan.align = Some(*align);
+                }
+                aligned += 1;
+            }
+            if plan.region_node.is_some() {
+                if let Some(take) = edits.nodes.get(&nodes) {
+                    plan.region_node = Some(*take);
+                }
+                nodes += 1;
+            }
+        });
+        out
+    }
+
+    fn kids(&self) -> Vec<&Plan> {
+        match &self.kind {
+            Kind::Scroll { inner, .. } | Kind::Pad { inner, .. } => vec![inner],
+            Kind::Branch {
+                probe,
+                wide,
+                narrow,
+                ..
+            } => vec![probe, wide, narrow],
+            Kind::Stack { children } => children.iter().collect(),
+            Kind::Span { children, .. } => children.iter().collect(),
+            _ => Vec::new(),
+        }
+    }
+}
+
+impl Kind {
+    /// Simplifications of the shape alone, leaving what the widget carries to
+    /// [`Plan::smaller`]. Replacing a node with one of its children is there
+    /// rather than here, since it answers with a whole `Plan`.
+    fn smaller(&self) -> Vec<Kind> {
+        let mut out = Vec::new();
+        /// One child reduced at a time, rebuilt into the same shape. Every
+        /// answer has the same number of children as it was given, so it is
+        /// for the shapes whose child count is part of what they are.
+        fn reduced(kids: &[Plan], rebuild: &dyn Fn(Vec<Plan>) -> Kind) -> Vec<Kind> {
+            let mut out = Vec::new();
+            for (i, kid) in kids.iter().enumerate() {
+                for small in kid.smaller() {
+                    let mut next = kids.to_vec();
+                    next[i] = small;
+                    out.push(rebuild(next));
+                }
+            }
+            out
+        }
+
+        /// One child dropped, then [`reduced`]. For the shapes that hold any
+        /// number of children, where dropping one is the cut that matters.
+        fn each(kids: &[Plan], rebuild: &dyn Fn(Vec<Plan>) -> Kind) -> Vec<Kind> {
+            let mut out = Vec::new();
+            for i in 0..kids.len() {
+                if kids.len() > 1 {
+                    let mut less = kids.to_vec();
+                    less.remove(i);
+                    out.push(rebuild(less));
+                }
+            }
+            out.extend(reduced(kids, rebuild));
+            out
+        }
+        match self {
+            // The one leaf that reads the width it is given, then the one
+            // that does not, then the one that measures nothing at all.
+            Kind::Wrapped => out.push(Kind::OneLine),
+            Kind::OneLine => out.push(Kind::Rect {
+                color: 0,
+                alpha: 255,
+            }),
+            Kind::Rect { .. } => {}
+            Kind::Scroll { axis, inner } => {
+                let axis = *axis;
+                out.extend(each(std::slice::from_ref(inner), &|mut k| Kind::Scroll {
+                    axis,
+                    inner: Box::new(k.remove(0)),
+                }));
+            }
+            Kind::Branch {
+                probe,
+                wide,
+                narrow,
+                threshold,
+            } => {
+                let threshold = *threshold;
+                // All three sides stay: a branch is the widget that draws
+                // one of two on a measurement, and one with a side missing
+                // is a different widget rather than a smaller one. Dropping
+                // the branch for a side is offered by `Plan::smaller`.
+                let sides = [(**probe).clone(), (**wide).clone(), (**narrow).clone()];
+                out.extend(reduced(&sides, &|k| Kind::Branch {
+                    probe: Box::new(k[0].clone()),
+                    wide: Box::new(k[1].clone()),
+                    narrow: Box::new(k[2].clone()),
+                    threshold,
+                }));
+            }
+            Kind::Pad { padding, inner } => {
+                let padding = *padding;
+                if padding != [0; 4] {
+                    out.push(Kind::Pad {
+                        padding: [0; 4],
+                        inner: inner.clone(),
+                    });
+                }
+                out.extend(each(std::slice::from_ref(inner), &|mut k| Kind::Pad {
+                    padding,
+                    inner: Box::new(k.remove(0)),
+                }));
+            }
+            Kind::Stack { children } => {
+                out.extend(each(children, &|children| Kind::Stack { children }))
+            }
+            Kind::Span {
+                dir,
+                gap,
+                children,
+                spares,
+                order,
+            } => {
+                let (dir, gap, n) = (*dir, *gap, children.len());
+                let span = |children: Vec<Plan>, spares: Vec<Plan>, order: Vec<usize>| Kind::Span {
+                    dir,
+                    gap,
+                    children,
+                    spares,
+                    order,
+                };
+                let identity: Vec<usize> = (0..n).collect();
+                // An order the generator did not choose is part of the tree,
+                // so take that off before taking the tree apart.
+                if *order != identity {
+                    out.push(span(children.clone(), spares.clone(), identity));
+                }
+                // Spares exist to be attached; with none attached they are
+                // widgets the span never holds.
+                if !spares.is_empty() && order.iter().all(|&i| i < n) {
+                    out.push(span(children.clone(), Vec::new(), order.clone()));
+                }
+                if gap != 0 {
+                    out.push(Kind::Span {
+                        dir,
+                        gap: 0,
+                        children: children.clone(),
+                        spares: spares.clone(),
+                        order: order.clone(),
+                    });
+                }
+                for k in 0..n {
+                    if n > 1 {
+                        let mut less = children.clone();
+                        less.remove(k);
+                        // Everything after it shifts down, spares included,
+                        // since they are indexed past the children.
+                        let order = order
+                            .iter()
+                            .filter(|&&i| i != k)
+                            .map(|&i| if i > k { i - 1 } else { i })
+                            .collect();
+                        out.push(span(less, spares.clone(), order));
+                    }
+                }
+                for (i, kid) in children.iter().enumerate() {
+                    for small in kid.smaller() {
+                        let mut next = children.clone();
+                        next[i] = small;
+                        out.push(span(next, spares.clone(), order.clone()));
+                    }
+                }
+            }
+        }
+        out
+    }
+}
+
+/// A [`SpanEdit`] applied to the order a span already holds its children in.
+///
+/// `detach` names positions in that order and `attach` takes from the front
+/// of what the span is not holding, both of which is what a test changing a
+/// live span does -- so an edit means the same thing said to a tree and said
+/// to the plan it was built from. On a span nobody has edited the order is
+/// the children in the order they were grown, and this is then "leave these
+/// out and put that many spares on the end".
+fn span_edited(order: &[usize], children: usize, spares: usize, edit: &SpanEdit) -> Vec<usize> {
+    let mut detach = edit.detach.clone();
+    detach.sort_unstable();
+    detach.dedup();
+    let mut next: Vec<usize> = order
+        .iter()
+        .enumerate()
+        .filter(|(at, _)| !detach.contains(at))
+        .map(|(_, &which)| which)
+        .collect();
+    // What the span is not holding, in the order it hands them back: what it
+    // was already not holding first, in the order the widgets were made, and
+    // what this edit takes out after that, highest position first. A child
+    // just detached goes to the back rather than straight back in, which is
+    // what makes detaching one and attaching one a trade.
+    let mut free: Vec<usize> = (0..children + spares)
+        .filter(|i| !order.contains(i))
+        .collect();
+    free.extend(detach.iter().rev().filter_map(|&at| order.get(at).copied()));
+    next.extend(free.into_iter().take(edit.attach));
+    next
+}
+
+/// Plans the tree `seed` describes, `edits` replacing what it would otherwise
+/// have given the widgets that carry them.
+///
+/// The edits are resolved here rather than at build time, so that a plan is
+/// the whole of what a tree is and building one has nothing left to decide.
+pub fn plan(seed: u64, depth: usize, edits: &Edits) -> Plan {
+    let mut sow = Sow {
+        rng: Rng::new(seed),
+        edits,
+        sized: 0,
+        aligned: 0,
+        nodes: 0,
+        spans: 0,
+    };
+    sow.node(depth)
+}
+
+/// Grows the tree `seed` describes, `edits` replacing the declared sizes it
+/// would otherwise have given those wrappers.
+pub fn grow<Rsc: UiRsc + 'static>(
+    rsc: &mut Rsc,
+    seed: u64,
+    depth: usize,
+    edits: &Edits,
+) -> (StrongWidget, Tree) {
+    build(rsc, &plan(seed, depth, edits))
+}
+
+/// Draws a plan out of the random stream. Every draw happens in the order it
+/// always has and before the decision it feeds, including the decisions that
+/// are then dropped, because a seed has to keep meaning the same tree.
+struct Sow<'a> {
+    rng: Rng,
+    edits: &'a Edits,
+    sized: usize,
+    aligned: usize,
+    nodes: usize,
+    spans: usize,
+}
+
+impl Sow<'_> {
+    fn leaf(&mut self) -> Plan {
+        Plan::bare(match self.rng.below(4) {
+            0 => Kind::Wrapped,
+            1 => Kind::OneLine,
+            _ => {
+                let color = self.rng.below(COLORS.len());
+                let alpha = (self.rng.below(5) * 63) as u8;
+                Kind::Rect { color, alpha }
+            }
+        })
+    }
+
+    fn len(&mut self) -> Option<LayoutLen> {
+        match self.rng.below(4) {
+            0 => Some(LayoutLen::px(20.0 + self.rng.below(180) as f32)),
+            1 => Some(LayoutLen::LEFTOVER),
+            _ => None,
+        }
+    }
+
+    fn align(&mut self) -> Aligns {
+        let axis = |s: &mut Self| match s.rng.below(4) {
+            0 => None,
+            1 => Some(AxisAlign::NEG),
+            2 => Some(AxisAlign::CENTER),
+            _ => Some(AxisAlign::POS),
+        };
+        let (x, y) = (axis(self), axis(self));
+        // Aligning on neither axis leaves the branch unexercised.
+        match x.is_none() && y.is_none() {
+            true => [Some(AxisAlign::CENTER), y],
+            false => [x, y],
+        }
+    }
+
+    /// A declared size over half the tree, kept where a test can change it.
+    fn sized(&mut self, inner: &mut Plan) {
+        let take = self.rng.chance();
+        let lens = [self.len(), self.len()];
+        if !take || inner.size.is_some() {
+            return;
+        }
+        let idx = self.sized;
+        self.sized += 1;
+        inner.size = Some(self.edits.sizes.get(&idx).copied().unwrap_or(lens));
+    }
+
+    /// An alignment over some of the tree, kept where a test can change it.
+    fn aligned(&mut self, inner: &mut Plan) {
+        let align = self.align();
+        if inner.align.is_some() {
+            return;
+        }
+        let idx = self.aligned;
+        self.aligned += 1;
+        inner.align = Some(self.edits.aligns.get(&idx).copied().unwrap_or(align));
+    }
+
+    /// A movable region of its own over some of the tree. What it changes is
+    /// how a move is written and how long a primitive's chain is, neither of
+    /// which any other branch here varies.
+    fn noded(&mut self, inner: &mut Plan) {
+        let take = self.rng.below(4) == 0;
+        if inner.region_node.is_some() {
+            return;
+        }
+        let idx = self.nodes;
+        self.nodes += 1;
+        inner.region_node = Some(self.edits.nodes.get(&idx).copied().unwrap_or(take));
+    }
+
+    fn offered(&mut self, inner: &mut Plan) {
+        self.sized(inner);
+        self.noded(inner);
+    }
+
+    fn node(&mut self, depth: usize) -> Plan {
+        if depth == 0 {
+            return self.leaf();
+        }
+        let positioned = self.rng.below(6);
+        if positioned == 0 {
+            let mut inner = self.node(depth - 1);
+            self.offered(&mut inner);
+            let axis = if self.rng.chance() { Axis::X } else { Axis::Y };
+            return Plan::bare(Kind::Scroll {
+                axis,
+                inner: Box::new(inner),
+            });
+        }
+        if positioned == 2 {
+            let probe = self.node(depth - 1);
+            let wide = self.node(depth - 1);
+            let narrow = self.node(depth - 1);
+            // Drawn either way, so the side a fixed branch takes is still a
+            // side the generator chose -- and it consumes the same randomness
+            // as a measured one, so the two grow the same ids.
+            let measured = self.rng.below(500) as f32;
+            let threshold = match self.edits.fixed_branches {
+                true => f32::MIN,
+                false => measured,
+            };
+            return Plan::bare(Kind::Branch {
+                probe: Box::new(probe),
+                wide: Box::new(wide),
+                narrow: Box::new(narrow),
+                threshold,
+            });
+        }
+        if positioned == 1 {
+            // Carries an alignment and makes no widget of its own, so the
+            // plan for it is the child it aligned.
+            let mut inner = self.node(depth - 1);
+            self.offered(&mut inner);
+            self.aligned(&mut inner);
+            return inner;
+        }
+        if self.rng.below(4) == 0 {
+            let mut inner = self.node(depth - 1);
+            self.offered(&mut inner);
+            let side = |s: &mut Self| s.rng.below(24) as i32;
+            let padding = [side(self), side(self), side(self), side(self)];
+            return Plan::bare(Kind::Pad {
+                padding,
+                inner: Box::new(inner),
+            });
+        }
+        let grown = 2 + self.rng.below(3);
+        let mut children = Vec::with_capacity(grown);
+        for _ in 0..grown {
+            let mut child = self.node(depth - 1);
+            self.offered(&mut child);
+            children.push(child);
+        }
+        if self.rng.chance() {
+            return Plan::bare(Kind::Stack { children });
+        }
+        let spares: Vec<Plan> = (0..SPARES).map(|_| self.leaf()).collect();
+        let idx = self.spans;
+        self.spans += 1;
+        let edit = self.edits.spans.get(&idx).cloned().unwrap_or_default();
+        let dir = self.rng.below(4);
+        // A row takes the height it is given rather than its tallest child,
+        // which is a rule beside it. Derived from an existing choice and
+        // consuming no randomness: a seed must keep growing the same tree
+        // when the generator gains another configuration.
+        let gap = self.rng.below(3) as i32 * 4;
+        let grown: Vec<usize> = (0..children.len()).collect();
+        let order = span_edited(&grown, children.len(), spares.len(), &edit);
+        Plan::bare(Kind::Span {
+            dir,
+            gap,
+            children,
+            spares,
+            order,
+        })
+    }
+}
+
+/// Builds a plan's widgets in the order it describes them, so two builds of
+/// one plan line up index for index and their boxes can be compared.
+pub fn build<Rsc: UiRsc + 'static>(rsc: &mut Rsc, plan: &Plan) -> (StrongWidget, Tree) {
+    let mut build = Build {
+        rsc,
+        tree: Tree::default(),
+    };
+    let root = build.node(plan);
+    (root, build.tree)
+}
+
+struct Build<'a, Rsc> {
+    rsc: &'a mut Rsc,
+    tree: Tree,
+}
+
+impl<Rsc: UiRsc + 'static> Build<'_, Rsc> {
+    fn node(&mut self, plan: &Plan) -> StrongWidget {
+        let built = self.kind(&plan.kind);
+        let id = built.id();
+        if let Some(lens) = plan.size {
+            self.rsc
+                .ui_mut()
+                .widgets
+                .set_size_rules(id, lens[0], lens[1]);
+            self.tree.sized.push(id);
+        }
+        if let Some(align) = plan.align {
+            let widgets = &mut self.rsc.ui_mut().widgets;
+            for (axis, align) in [Axis::X, Axis::Y].into_iter().zip(align) {
+                widgets.set_alignment(id, axis, align.unwrap_or_default());
+            }
+            self.tree.aligned.push(id);
+        }
+        if let Some(take) = plan.region_node {
+            self.rsc.ui_mut().widgets.set_region_node(id, take);
+            self.tree.nodes.push(id);
+        }
+        built
+    }
+
+    fn kind(&mut self, kind: &Kind) -> StrongWidget {
+        let id: StrongWidget = match kind {
+            Kind::Wrapped => wtext(WORDS).size(16).wrap(true).add_strong(self.rsc),
+            Kind::OneLine => wtext("one line, overflowing whatever it is given")
+                .size(16)
+                .wrap(false)
+                .add_strong(self.rsc),
+            Kind::Rect { color, alpha } => rect(COLORS[*color].alpha(*alpha)).add_strong(self.rsc),
+            Kind::Scroll { axis, inner } => {
+                let inner = self.node(inner);
+                let id = Scroll::new(inner, *axis).add(self.rsc);
+                self.tree.scrolls.push(id);
+                self.tree.ids.push(id.id());
+                return id.add_strong(self.rsc);
+            }
+            Kind::Branch {
+                probe,
+                wide,
+                narrow,
+                threshold,
+            } => {
+                let probe = self.node(probe);
+                let wide = self.node(wide);
+                let narrow = self.node(narrow);
+                let id = Branch {
+                    probe,
+                    wide,
+                    narrow,
+                    threshold: *threshold,
+                }
+                .add(self.rsc);
+                self.tree.ids.push(id.id());
+                return id.add_strong(self.rsc);
+            }
+            Kind::Pad { padding, inner } => {
+                let inner = self.node(inner);
+                let [left, right, top, bottom] = padding.map(Px::from_int);
+                let padding = Padding {
+                    left,
+                    right,
+                    top,
+                    bottom,
+                };
+                Pad { padding, inner }.add_strong(self.rsc)
+            }
+            Kind::Stack { children } => {
+                let children = children.iter().map(|c| self.node(c)).collect();
+                Stack {
+                    children,
+                    size: StackSize::Child(0),
+                }
+                .add_strong(self.rsc)
+            }
+            Kind::Span {
+                dir,
+                gap,
+                children,
+                spares,
+                order,
+            } => {
+                let grown = children.len();
+                // Every one of them is made, in this order, whether or not
+                // the span ends up holding it.
+                let made: Vec<StrongWidget> = children
+                    .iter()
+                    .chain(spares)
+                    .map(|c| self.node(c))
+                    .collect();
+                let mut left: Vec<Option<StrongWidget>> = made.into_iter().map(Some).collect();
+                let children: Vec<StrongWidget> = order
+                    .iter()
+                    .filter_map(|&i| left.get_mut(i).and_then(Option::take))
+                    .collect();
+                // What the span does not hold is still held here: dropping
+                // the last share of a widget frees its id for the next one
+                // to be given, which puts two trees out of step.
+                let spares: Vec<StrongWidget> = left.into_iter().flatten().collect();
+                let dir = [Dir::RIGHT, Dir::DOWN, Dir::LEFT, Dir::UP][*dir % 4];
+                let id = Span {
+                    children,
+                    dir,
+                    gap: Px::from_int(*gap),
+                }
+                .add(self.rsc);
+                if dir.axis == Axis::X {
+                    self.rsc
+                        .widgets_mut()
+                        .set_size_rules(id, None, Some(LayoutLen::rel(1.0)));
+                }
+                self.tree.ids.push(id.id());
+                self.tree.spans.push(Spanned { id, spares, grown });
+                return id.add_strong(self.rsc);
+            }
+        };
+        self.tree.ids.push(id.id());
+        id
+    }
+}

src/widget/image.rs

@@ -8,15 +8,11 @@ pub struct Image {
 impl Widget for Image {
     fn draw(&mut self, painter: &mut Painter) -> Size {
         painter.primitive(&self.handle);
-        Size::abs(self.handle.size())
+        Size::px(self.handle.size())
     }
 
-    fn size_hint(&self, axis: Axis) -> Option<Len> {
-        Some(Len::abs(self.handle.size().axis(axis)))
-    }
-
-    fn on_resize(&self, _: Axis) -> OnResize {
-        OnResize::Scale
+    fn size_hint(&self, axis: Axis) -> Option<LayoutLen> {
+        Some(LayoutLen::px(self.handle.size().axis(axis)))
     }
 }
 

src/widget/mask.rs

@@ -7,11 +7,12 @@ pub struct Masked {
 impl Widget for Masked {
     fn draw(&mut self, painter: &mut Painter) -> Size {
         painter.set_mask(painter.region());
-        painter.widget(&self.inner).size()
-    }
-
-    /// It clips to the box it was given, not to the part its child used.
-    fn on_resize(&self, _: Axis) -> OnResize {
-        OnResize::Redraw
+        painter.widget(&self.inner);
+        // What it occupies is its box, on both axes, for the reason `Scroll`
+        // reports the same: it clips what is inside to that box, so it can
+        // neither take less of one nor honestly ask for more. Passing the
+        // inner size up instead asks to be placed at a length it does not
+        // draw, and the framework would place the drawing it clipped away.
+        Size::LEFTOVER
     }
 }

src/widget/mod.rs

@@ -1,15 +1,15 @@
 mod image;
 mod mask;
 mod position;
-mod ptr;
 mod rect;
 mod text;
 mod trait_fns;
+mod wrapper;
 
 pub use image::*;
 pub use mask::*;
 pub use position::*;
-pub use ptr::*;
 pub use rect::*;
 pub use text::*;
 pub use trait_fns::*;
+pub use wrapper::*;

src/widget/position/align.rs

@@ -1,22 +0,0 @@
-use crate::prelude::*;
-
-pub struct Aligned {
-    pub inner: StrongWidget,
-    pub align: Align,
-}
-
-impl Widget for Aligned {
-    fn draw(&mut self, painter: &mut Painter) -> Size {
-        // Drawn where it may be too big, then given its aligned box once its
-        // size is known.
-        let size = painter.widget(&self.inner).size();
-        let region = match self.align.tuple() {
-            (Some(x), Some(y)) => size.to_uivec2().align(RegionAlign { x, y }),
-            (Some(x), None) => UiRegion::new(size.x.apply_rest().align(x), UiSpan::FULL),
-            (None, Some(y)) => UiRegion::new(UiSpan::FULL, size.y.apply_rest().align(y)),
-            (None, None) => UiRegion::FULL,
-        };
-        painter.widget_within(&self.inner, region);
-        size
-    }
-}

src/widget/position/max_size.rs

@@ -1,25 +0,0 @@
-use crate::prelude::*;
-
-pub struct MaxSize {
-    pub inner: StrongWidget,
-    pub x: Option<Len>,
-    pub y: Option<Len>,
-}
-
-impl Widget for MaxSize {
-    fn draw(&mut self, painter: &mut Painter) -> Size {
-        let child = painter.widget(&self.inner).size();
-        let output = painter.output_size();
-        Size {
-            x: capped(child.x, self.x, output.x),
-            y: capped(child.y, self.y, output.y),
-        }
-    }
-}
-
-fn capped(len: Len, max: Option<Len>, output: f32) -> Len {
-    match max {
-        Some(max) if len.apply_rest().to_abs(output) > max.apply_rest().to_abs(output) => max,
-        _ => len,
-    }
-}

src/widget/position/mod.rs

@@ -1,19 +1,13 @@
-mod align;
 mod layer;
-mod max_size;
 mod offset;
 mod pad;
 mod scroll;
-mod set_size;
 mod span;
 mod stack;
 
-pub use align::*;
 pub use layer::*;
-pub use max_size::*;
 pub use offset::*;
 pub use pad::*;
 pub use scroll::*;
-pub use set_size::*;
 pub use span::*;
 pub use stack::*;

src/widget/position/pad.rs

@@ -7,16 +7,22 @@ pub struct Pad {
 
 impl Widget for Pad {
     fn draw(&mut self, painter: &mut Painter) -> Size {
+        // The inner's own alignment, not the near edge. This reports the
+        // inner's size plus the padding, so where the box is that answer the
+        // inset box is exactly the inner and alignment has no room to move
+        // it; where the box is bigger -- a share of a row, a rule over this
+        // widget -- the slack is the inner's to sit in, and forcing the near
+        // edge pinned it to a corner it had not asked for.
         let inner = painter
             .widget_within(&self.inner, self.padding.region())
             .size();
         Size {
-            x: Len {
-                abs: inner.x.abs + self.padding.left + self.padding.right,
+            x: LayoutLen {
+                px: inner.x.px + self.padding.left + self.padding.right,
                 ..inner.x
             },
-            y: Len {
-                abs: inner.y.abs + self.padding.top + self.padding.bottom,
+            y: LayoutLen {
+                px: inner.y.px + self.padding.top + self.padding.bottom,
                 ..inner.y
             },
         }
@@ -24,22 +30,22 @@ impl Widget for Pad {
 }
 
 pub struct Padding {
-    pub left: f32,
-    pub right: f32,
-    pub top: f32,
-    pub bottom: f32,
+    pub left: Px,
+    pub right: Px,
+    pub top: Px,
+    pub bottom: Px,
 }
 
 impl Padding {
     pub const ZERO: Self = Self {
-        left: 0.0,
-        right: 0.0,
-        top: 0.0,
-        bottom: 0.0,
+        left: Px::ZERO,
+        right: Px::ZERO,
+        top: Px::ZERO,
+        bottom: Px::ZERO,
     };
 
     pub fn uniform(amt: impl UiNum) -> Self {
-        let amt = amt.to_f32();
+        let amt = Px::from_num(amt);
         Self {
             left: amt,
             right: amt,
@@ -49,78 +55,76 @@ impl Padding {
     }
     pub fn region(&self) -> UiRegion {
         let mut region = UiRegion::FULL;
-        region.x.start.abs += self.left;
-        region.y.start.abs += self.top;
-        region.x.end.abs -= self.right;
-        region.y.end.abs -= self.bottom;
+        region.x.start.px += self.left;
+        region.y.start.px += self.top;
+        region.x.end.px -= self.right;
+        region.y.end.px -= self.bottom;
         region
     }
     pub fn x(amt: impl UiNum) -> Self {
-        let amt = amt.to_f32();
+        let amt = Px::from_num(amt);
         Self {
             left: amt,
             right: amt,
-            top: 0.0,
-            bottom: 0.0,
+            ..Self::ZERO
         }
     }
     pub fn y(amt: impl UiNum) -> Self {
-        let amt = amt.to_f32();
+        let amt = Px::from_num(amt);
         Self {
-            left: 0.0,
-            right: 0.0,
             top: amt,
             bottom: amt,
+            ..Self::ZERO
         }
     }
 
     pub fn top(amt: impl UiNum) -> Self {
         let mut s = Self::ZERO;
-        s.top = amt.to_f32();
+        s.top = Px::from_num(amt);
         s
     }
 
     pub fn bottom(amt: impl UiNum) -> Self {
         let mut s = Self::ZERO;
-        s.bottom = amt.to_f32();
+        s.bottom = Px::from_num(amt);
         s
     }
 
     pub fn left(amt: impl UiNum) -> Self {
         let mut s = Self::ZERO;
-        s.left = amt.to_f32();
+        s.left = Px::from_num(amt);
         s
     }
 
     pub fn right(amt: impl UiNum) -> Self {
         let mut s = Self::ZERO;
-        s.right = amt.to_f32();
+        s.right = Px::from_num(amt);
         s
     }
 
     pub fn with_top(mut self, amt: impl UiNum) -> Self {
-        self.top = amt.to_f32();
+        self.top = Px::from_num(amt);
         self
     }
 
     pub fn with_bottom(mut self, amt: impl UiNum) -> Self {
-        self.bottom = amt.to_f32();
+        self.bottom = Px::from_num(amt);
         self
     }
 
     pub fn with_left(mut self, amt: impl UiNum) -> Self {
-        self.left = amt.to_f32();
+        self.left = Px::from_num(amt);
         self
     }
 
     pub fn with_right(mut self, amt: impl UiNum) -> Self {
-        self.right = amt.to_f32();
+        self.right = Px::from_num(amt);
         self
     }
 }
 
 impl<T: UiNum> From<T> for Padding {
     fn from(amt: T) -> Self {
-        Self::uniform(amt.to_f32())
+        Self::uniform(amt)
     }
 }

src/widget/position/scroll.rs

@@ -3,36 +3,73 @@ use crate::prelude::*;
 pub struct Scroll {
     inner: StrongWidget,
     axis: Axis,
-    amt: f32,
+    amt: Px,
     snap_end: bool,
-    container_len: f32,
-    content_len: f32,
+    container_len: Px,
+    content_len: Px,
 }
 
 impl Widget for Scroll {
     fn draw(&mut self, painter: &mut Painter) -> Size {
-        let output_len = painter.output_size().axis(self.axis);
-        let container_len = painter.region().axis(self.axis).len();
-        // Drawn in the whole container to learn its length, then placed at
-        // the scrolled offset.
-        let child = painter.widget(&self.inner).size();
-        let content_len = child
-            .axis(self.axis)
-            .apply_rest()
-            .within_len(container_len)
-            .to_abs(output_len);
-        self.container_len = container_len.to_abs(output_len);
-        self.content_len = content_len;
+        let container_len = painter.px_len(self.axis);
+        // Draw in the whole container only when its scrolling-axis length is
+        // not already known, then draw it at the scrolled offset.
+        let whole = UiRegion::FULL;
+        let answer_len = match painter.known_len(&self.inner, self.axis, whole, whole.size()) {
+            Some(len) => len,
+            None => painter.widget(&self.inner).size().axis(self.axis),
+        };
+        let content = answer_len.apply_leftover();
+        self.container_len = container_len;
+        self.content_len = content.to_px(container_len);
 
         if self.snap_end {
             self.amt = self.content_len - self.container_len;
         }
         self.update_amt();
+        let align = painter.alignment().axis(self.axis);
+        // Content of a fixed length that fits sits at the start of any box it
+        // fits in -- but only anchored there. Anywhere else it is a part of
+        // the room left over, so it moves with every length the box takes and
+        // the drawing holds for that length alone. One scrolled part way sits
+        // where it is until the box shrinks past what is left of it. Kept to
+        // the end, it moves with every length.
+        let fixed_len = content.rel == Rel::ZERO;
+        if fixed_len && self.content_len <= self.container_len && align == AxisAlign::NEG {
+            painter.holds(self.axis, self.content_len..=Px::MAX);
+        } else if fixed_len && !self.snap_end {
+            let left = self.content_len - self.amt;
+            painter.holds(self.axis, Px::MIN..=left);
+        }
 
-        let mut region = UiRegion::FULL.offset(Vec2::from_axis(self.axis, -self.amt, 0.0));
-        region.axis_mut(self.axis).end = region.axis(self.axis).start.offset(self.content_len);
-        painter.widget_within(&self.inner, region);
-        child
+        // Content shorter than the viewport has room to sit in, and where it
+        // sits is this widget's own alignment -- the same property that would
+        // have placed the whole scroll in a box longer than it.
+        let slack = (self.container_len - self.content_len).max(Px::ZERO);
+        let anchor = slack.mul(align.rel());
+        let mut region = UiRegion::FULL;
+        // Content that fills the viewport and has not been scrolled is the
+        // viewport, and is handed back as it came. Writing the same box as
+        // its own length in pixels is the same box in another form, and the
+        // two do not round alike: a part centred in `rel 1` lands a step from
+        // one centred in `px 900`, since halving a difference is not halving
+        // each part of it.
+        let moved = anchor != Px::ZERO || self.amt != Px::ZERO;
+        if moved || self.content_len != self.container_len {
+            let offset = UiVec2::from_axis(
+                self.axis,
+                Len::from_parts(Rel::ZERO, anchor - self.amt),
+                Len::ZERO,
+            );
+            region = region.offset(offset);
+            region.axis_mut(self.axis).end = region.axis(self.axis).start.offset(self.content_len);
+        }
+        painter.widget_at(&self.inner, region, region.size(), [true; 2]);
+        // What it occupies is its box, on both axes: it clips its content to
+        // that box, so it can neither take less of one nor honestly ask for
+        // more. The content's length is what it scrolls through, not what it
+        // is.
+        Size::LEFTOVER
     }
 }
 
@@ -41,22 +78,24 @@ impl Scroll {
         Self {
             inner,
             axis,
-            amt: 0.0,
+            amt: Px::ZERO,
             snap_end: true,
-            container_len: 0.0,
-            content_len: 0.0,
+            container_len: Px::ZERO,
+            content_len: Px::ZERO,
         }
     }
 
     pub fn update_amt(&mut self) {
-        self.amt = self.amt.max(0.0);
-        let len = (self.content_len - self.container_len).max(0.0);
+        self.amt = self.amt.max(Px::ZERO);
+        let len = (self.content_len - self.container_len).max(Px::ZERO);
         self.amt = self.amt.min(len);
         self.snap_end = self.amt == len;
     }
 
+    /// Scrolled by a distance the platform measures, which is the last place
+    /// a wheel notch or a finger is a float.
     pub fn scroll(&mut self, amt: f32) {
-        self.amt -= amt;
+        self.amt -= Px::from_f32(amt);
         self.update_amt();
     }
 }

src/widget/position/set_size.rs

@@ -1,26 +0,0 @@
-use crate::prelude::*;
-
-pub struct SetSize {
-    pub inner: StrongWidget,
-    pub x: Option<Len>,
-    pub y: Option<Len>,
-}
-
-impl Widget for SetSize {
-    fn draw(&mut self, painter: &mut Painter) -> Size {
-        let child = painter.widget(&self.inner).size();
-        Size {
-            x: self.x.unwrap_or(child.x),
-            y: self.y.unwrap_or(child.y),
-        }
-    }
-
-    /// A declared axis is known without looking at the child, which is what
-    /// lets a span lay out around `.height(rest(1))` without drawing it.
-    fn size_hint(&self, axis: Axis) -> Option<Len> {
-        match axis {
-            Axis::X => self.x,
-            Axis::Y => self.y,
-        }
-    }
-}

src/widget/position/span.rs

@@ -4,73 +4,189 @@ use std::marker::PhantomData;
 pub struct Span {
     pub children: Vec<StrongWidget>,
     pub dir: Dir,
-    pub gap: f32,
+    pub gap: Px,
 }
 
 impl Widget for Span {
     fn draw(&mut self, painter: &mut Painter) -> Size {
         let axis = self.dir.axis;
-        // A length for every child before any is placed: from its own hint
-        // where it has one, and from drawing it where it does not.
-        let lens: Vec<Len> = self
-            .children
-            .iter()
-            .map(|child| match painter.size_hint(child, axis) {
+        // A length for every child before their final boxes are chosen: from
+        // a hint where one exists, and from drawing otherwise.
+        let mut cursor = Len::rel_min();
+        let mut lens = Vec::with_capacity(self.children.len());
+        for child in &self.children {
+            let mut span = UiSpan::new(cursor, Len::rel_max());
+            if self.dir.sign == Sign::Neg {
+                span.flip();
+            }
+            let region = UiRegion::from_axis(axis, span, UiSpan::FULL);
+            // Offered the room left from the cursor, because a text has to
+            // wrap at the width actually there, but reporting a fraction of
+            // the whole row: `rel(0.5)` is half the span whatever else is in
+            // it and wherever this child sits among them.
+            let len = match painter.known_len(child, axis, region, UiVec2::FULL_SIZE) {
                 Some(len) => len,
-                None => painter.widget(child).len(axis),
-            })
-            .collect();
+                None => painter
+                    .widget_at(child, region, UiVec2::FULL_SIZE, [false; 2])
+                    .len(axis),
+            };
+            cursor.px += len.px + self.gap;
+            cursor.rel += len.rel;
+            lens.push(len);
+        }
 
-        let gap = self.gap * self.children.len().saturating_sub(1) as f32;
-        let total = lens.iter().fold(Len::abs(gap), |sum, len| sum + *len);
+        let gaps = self
+            .gap
+            .mul_int(self.children.len().saturating_sub(1) as i32);
+        let total = lens.iter().fold(
+            LayoutLen {
+                px: gaps,
+                ..LayoutLen::ZERO
+            },
+            |sum, len| sum + *len,
+        );
 
-        let mut start = UiScalar::rel_min();
-        let mut ortho = Len::ZERO;
+        // Whether anything is left over is a question in pixels: `rel(0.5)`
+        // beside 300 px is full at 600 and overfull at 400. The room to
+        // divide is `len * fixed - total.px`, and the length where it runs
+        // out is exactly the box a parent sizing itself from this answer
+        // hands back -- which is why this used to need a margin either side
+        // of the boundary, and why it does not now: that box and this sum are
+        // whole counts of the same step, and both routes to it land on the
+        // same count. What the generated oracle checks is the consequence,
+        // since which children exist at all turns on this.
+        let fixed = Rel::ONE - total.rel;
+        let mut shares = false;
+        if total.leftover > Weight::ZERO {
+            let current = painter.px_len(axis);
+            let holds = if fixed > Rel::ZERO {
+                // The box length the fixed parts alone fill.
+                let full = total.px.div(fixed);
+                shares = current > full;
+                match shares {
+                    true => Holds::from(full.next_up()..=Px::MAX),
+                    false => Holds::from(Px::MIN..=full),
+                }
+            } else if fixed < Rel::ZERO {
+                // The relative parts grow faster than the box does, so here
+                // a shorter box is the one that leaves room.
+                let full = total.px.div(fixed);
+                shares = current < full;
+                match shares {
+                    true => Holds::from(Px::MIN..=full.next_down()),
+                    false => Holds::from(full..=Px::MAX),
+                }
+            } else {
+                // The relative parts take exactly the box, whatever it is, so
+                // the only room is what negative pixels leave.
+                shares = total.px < Px::ZERO;
+                Holds::ANY
+            };
+            painter.holds(axis, holds);
+        }
+
+        // Across itself a span is as long as its longest child -- unless a
+        // rule beside it gives that length outright, and then reading them
+        // answers nothing and makes its size depend on theirs for it. A rule
+        // that only bounds the length does not count: the answer is still
+        // this span's to give.
+        let shrinks = !painter.has_exact_size(!axis);
+        // What the fixed parts and the gaps before here take, which is a sum
+        // of lengths and exact, and how much of the leftover weight is
+        // spoken for. A position is one from the other rather than a step
+        // from the last child: the share of the room is rounded, and taking
+        // each from the one before it would carry every rounding along the
+        // row.
+        let mut fixed = Len::rel_min();
+        let mut taken = Weight::ZERO;
+        let room = Len::rel_max() - Len::from_parts(total.rel, total.px);
+        let mut start = Len::rel_min();
+        let mut ortho = LayoutLen::ZERO;
         for (child, len) in self.children.iter().zip(&lens) {
+            // A child asking for nothing but a part of what is left over,
+            // when nothing is, is not drawn at all. One that also asked for
+            // pixels or a fraction keeps those and overflows.
+            if len.leftover > Weight::ZERO && len.px == Px::ZERO && len.rel == Rel::ZERO && !shares
+            {
+                painter.undraw(child);
+                fixed.px += self.gap;
+                continue;
+            }
             let mut span = UiSpan::FULL;
             span.start = start;
-            if len.rest > 0.0 {
-                let offset = UiScalar::new(total.rel, total.abs);
-                let rel_end = UiScalar::rel(len.rest / total.rest);
-                let end = (UiScalar::rel_max() + start) - offset;
-                start = rel_end.within(&start.to(end));
+            if len.leftover > Weight::ZERO && shares {
+                taken += len.leftover;
             }
-            start.abs += len.abs;
-            start.rel += len.rel;
+            fixed.px += len.px;
+            fixed.rel += len.rel;
+            start = shared(fixed, taken, total.leftover, room);
             span.end = start;
             let mut region = UiRegion::from_axis(axis, span, UiSpan::FULL);
             if self.dir.sign == Sign::Neg {
                 region.flip(axis);
             }
-            let used = painter.widget_within(child, region).size().axis(!axis);
-            // TODO: rel shouldn't do this, but no easy way before actually calculating pixels
-            if used.rel > 0.0 || used.rest > 0.0 {
-                ortho = Len::REST;
-            } else if ortho.rest == 0.0 {
-                ortho.abs = ortho.abs.max(used.abs);
+            // Along the row this box is the child's own answer, so the answer
+            // is not placed in it again; across it the child sits where its
+            // alignment says.
+            let placed = painter.widget_at(
+                child,
+                region,
+                UiVec2::FULL_SIZE,
+                [axis == Axis::X, axis == Axis::Y],
+            );
+            if shrinks {
+                let used = placed.len(!axis);
+                // Choosing between a fixed and a relative length from the
+                // span's own eventual width admits multiple fixed points.
+                // A scalable child therefore makes Children scalable too;
+                // only fixed children are compared with one another.
+                if used.rel != Rel::ZERO || used.leftover != Weight::ZERO {
+                    ortho = LayoutLen::LEFTOVER;
+                } else if ortho.leftover == Weight::ZERO {
+                    ortho.px = ortho.px.max(used.px);
+                }
             }
-            start.abs += self.gap;
+            fixed.px += self.gap;
+            start = shared(fixed, taken, total.leftover, room);
         }
 
-        let along = match total.rest == 0.0 && total.rel == 0.0 {
-            true => total,
-            false => Len::default(),
+        // Carried whole rather than collapsed to one share: a span that sizes
+        // from its children does not resolve `leftover`, it passes the weight up,
+        // so nesting spans divides the same space rather than re-dividing a
+        // share of it. Four `leftover(1)` children under two spans under one span
+        // get a quarter each, which collapsing to `leftover(1)` per level does
+        // not give. Resolution happens at the nearest ancestor with a length,
+        // and the root always has one.
+        let along = total;
+        let ortho = match shrinks {
+            true => ortho,
+            false => LayoutLen::rel(1.0),
         };
         Size::from_axis(axis, along, ortho)
     }
 }
 
+/// Where a row has reached: everything fixed before this point, which is a
+/// sum and exact, plus the share of the room the weights so far are worth,
+/// which is one rounding wherever it is asked for.
+fn shared(fixed: Len, taken: Weight, weight: Weight, room: Len) -> Len {
+    if taken == Weight::ZERO {
+        return fixed;
+    }
+    fixed + room.scale(Rel::ratio(taken, weight))
+}
+
 impl Span {
     pub fn empty(dir: Dir) -> Self {
         Self {
             children: Vec::new(),
             dir,
-            gap: 0.0,
+            gap: Px::ZERO,
         }
     }
 
     pub fn gap(mut self, gap: impl UiNum) -> Self {
-        self.gap = gap.to_f32();
+        self.gap = Px::from_num(gap);
         self
     }
 
@@ -86,7 +202,7 @@ impl Span {
 pub struct SpanBuilder<State, const LEN: usize, Wa: WidgetArrLike<State, LEN, Tag>, Tag> {
     pub children: Wa,
     pub dir: Dir,
-    pub gap: f32,
+    pub gap: Px,
     _pd: PhantomData<(State, Tag)>,
 }
 
@@ -112,13 +228,13 @@ impl<State, const LEN: usize, Wa: WidgetArrLike<State, LEN, Tag>, Tag>
         Self {
             children,
             dir,
-            gap: 0.0,
+            gap: Px::ZERO,
             _pd: PhantomData,
         }
     }
 
     pub fn gap(mut self, gap: impl UiNum) -> Self {
-        self.gap = gap.to_f32();
+        self.gap = Px::from_num(gap);
         self
     }
 }

src/widget/position/stack.rs

@@ -13,18 +13,42 @@ impl Widget for Stack {
             StackSize::Default => None,
             StackSize::Child(i) => Some(i),
         };
-        let mut size = Size::default();
+        // Every child gets the whole of this stack's box, the sizing one
+        // included, and the stack is then handed a box of the length that
+        // child asked for. Not the part of the box that length takes: the
+        // stack's own box becomes that length, and taking the fraction of it
+        // again is the fraction twice -- a child asking for half of a stack
+        // that is already half a row would have a quarter of the row.
+        //
+        // It cannot be told apart by asking whether this box is the answer
+        // yet, either. A drawing has to be a function of the box alone, since
+        // moving the stack into the box it asked for reuses the drawing by
+        // scaling it, and a drawing made a fraction of one box is right in
+        // any other. So: fractions of this box throughout, and the move is
+        // the whole of the difference.
+        let region = UiRegion::FULL;
+        // Whichever child sizes the stack is asked here and not again below,
+        // on the layer it ends up on: a retained drawing belongs to the layer
+        // it was made on, so measuring it anywhere else costs a second
+        // drawing of it. Its box is its own answer, so the answer is not
+        // placed inside it again.
+        let size = match sizing.and_then(|i| self.children.get(i).map(|c| (i, c))) {
+            Some((i, child)) => {
+                painter.child_layer_at(i);
+                painter
+                    .widget_at(child, region, region.size(), [true; 2])
+                    .size()
+            }
+            None => Size::LEFTOVER,
+        };
         for (i, child) in self.children.iter().enumerate() {
-            match i {
-                0 => painter.child_layer(),
-                _ => painter.next_layer(),
-            }
-            let drawn = painter.widget(child);
-            // Only the child that sizes the stack is read, so the others
-            // changing size does not redraw it.
             if sizing == Some(i) {
-                size = drawn.size();
+                continue;
             }
+            painter.child_layer_at(i);
+            // A box that owes nothing to this child's own answer: where it
+            // sits in one bigger than itself is its own business.
+            painter.widget_within(child, region);
         }
         size
     }

src/widget/rect.rs

@@ -35,16 +35,11 @@ impl Widget for Rect {
             thickness: self.thickness,
             inner_radius: self.inner_radius,
         });
-        Size::REST
+        Size::LEFTOVER
     }
 
-    fn size_hint(&self, _: Axis) -> Option<Len> {
-        Some(Len::REST)
-    }
-
-    /// Its box is its primitive's own region, so a new one is written there.
-    fn on_resize(&self, _: Axis) -> OnResize {
-        OnResize::Scale
+    fn size_hint(&self, _: Axis) -> Option<LayoutLen> {
+        Some(LayoutLen::LEFTOVER)
     }
 }
 

src/widget/text/edit.rs

@@ -93,10 +93,6 @@ impl Widget for TextEdit {
         );
         size
     }
-
-    fn on_resize(&self, axis: Axis) -> OnResize {
-        self.view.on_resize(axis)
-    }
 }
 
 const CARET_WIDTH: f32 = 1.0;
@@ -130,7 +126,6 @@ impl<'a> TextEditCtx<'a> {
     pub fn set(&mut self, text: &str) {
         let text = self.string(text);
         self.text.view.buf.set_text(text);
-        self.text.view.buf.changed = true;
         self.text.selection = None;
     }
 
@@ -177,7 +172,6 @@ impl<'a> TextEditCtx<'a> {
         };
         let at = at.min(self.text.view.buf.text().len());
         self.text.view.buf.edit().insert_str(at, text);
-        self.text.view.buf.changed = true;
         self.set_caret(at + text.len());
     }
 
@@ -190,7 +184,6 @@ impl<'a> TextEditCtx<'a> {
         }
         let range = sel.text_range();
         self.text.view.buf.edit().replace_range(range.clone(), "");
-        self.text.view.buf.changed = true;
         self.set_caret(range.start);
         true
     }
@@ -268,7 +261,6 @@ impl<'a> TextEditCtx<'a> {
 
     fn delete_range(&mut self, start: usize, end: usize) {
         self.text.view.buf.edit().replace_range(start..end, "");
-        self.text.view.buf.changed = true;
         self.set_caret(start);
     }
 
@@ -284,7 +276,13 @@ impl<'a> TextEditCtx<'a> {
     }
 
     pub fn select(&mut self, pos: Vec2, size: Vec2, drag: bool, recent: bool) {
-        let pos = pos - self.text.region().top_left().to_abs(size);
+        let pos = pos
+            - self
+                .text
+                .region()
+                .top_left()
+                .to_px(PxVec2::from_f32(size))
+                .to_f32();
         let prev_sel = self.text.selection;
         let prev_hit = self.text.double_hit;
 

src/widget/text/mod.rs

@@ -14,11 +14,8 @@ pub struct Text {
 }
 
 pub struct TextView {
-    pub attrs: MutDetect<TextAttrs>,
-    pub buf: MutDetect<TextBuffer>,
-    // cache
-    tex: Option<RenderedText>,
-    width: Option<f32>,
+    pub attrs: TextAttrs,
+    pub buf: TextBuffer,
     pub hint: Option<StrongWidget>,
 }
 
@@ -28,19 +25,13 @@ impl TextView {
     }
 
     pub fn wrap_width(&self) -> Option<f32> {
-        self.width
+        self.buf.wrap_width()
     }
 }
 
 impl TextView {
     pub fn new(buf: TextBuffer, attrs: TextAttrs, hint: Option<StrongWidget>) -> Self {
-        Self {
-            attrs: attrs.into(),
-            buf: buf.into(),
-            tex: None,
-            width: None,
-            hint,
-        }
+        Self { attrs, buf, hint }
     }
 
     /// region where the text should be draw
@@ -52,22 +43,31 @@ impl TextView {
             .align(self.align)
     }
 
+    /// The text shaped for the width it is drawn in. The buffer keeps its
+    /// answers under the attrs too, so changing those asks a new question
+    /// rather than invalidating anything.
     fn render(&mut self, painter: &mut Painter) -> &RenderedText {
-        let width = if self.attrs.wrap {
-            Some(painter.px_size().x)
-        } else {
-            None
-        };
-        if width != self.width || self.tex.is_none() || self.attrs.changed || self.buf.changed {
-            self.width = width;
-            self.tex = Some(painter.render_text(&mut self.buf, &self.attrs, width));
-            self.attrs.changed = false;
-            self.buf.changed = false;
+        let width = self.attrs.wrap.then(|| painter.px_len(Axis::X));
+        // The shaper measures in floats, which is where a glyph advance comes
+        // from; what it answers goes back on the grid.
+        let text = painter.render_text(&mut self.buf, &self.attrs, width.map(Px::to_f32));
+        // A greedy break is the same break at every width from its longest
+        // line up to the one it was made at: each line still fits, and none
+        // could take a word that did not fit in the wider box. A line too
+        // long to fit at all says nothing about narrower boxes.
+        //
+        // The step at or above that longest line rather than the nearest
+        // one, since the shaper measures in floats: the nearest step is
+        // under the line half the time, and a range starting there admits a
+        // box the line does not fit in, where the break is not this one.
+        if let Some(width) = width {
+            painter.holds(Axis::X, Px::ceil_from_f32(text.size.x).min(width)..=width);
         }
-        self.tex.as_ref().unwrap()
+        text
     }
+
     pub fn tex(&self) -> Option<&RenderedText> {
-        self.tex.as_ref()
+        self.buf.rendered()
     }
     /// Draws the text, and says where the glyphs went and what they use.
     pub fn draw(&mut self, painter: &mut Painter) -> (UiRegion, Size) {
@@ -83,28 +83,17 @@ impl TextView {
 
         let tex = self.render(painter);
         let region = tex.size.align(align);
-        let size = Size::abs(tex.size);
+        // The step at or above what the shaper measured, so a parent that
+        // hands back the length this reports hands back a box the longest
+        // line fits in. Rounded to the nearest step it is half the time a
+        // hair under that line, and the break made in it is not the break a
+        // cold layout makes there.
+        let size = Size::from_px(PxVec2::ceil_from_f32(tex.size));
         let within = region.within(&painter.region());
         painter.glyphs(tex, within);
         (region, size)
     }
 
-    /// Wrapping reads the width it is offered, so a wider box reshapes it and
-    /// a taller one does not. Alignment matters too, and separately: glyphs
-    /// anchored to the start of an axis stay put when that extent changes,
-    /// but centred or end-aligned ones move even though the shaping stands.
-    pub fn on_resize(&self, axis: Axis) -> OnResize {
-        let reshapes = axis == Axis::X && self.attrs.wrap;
-        let anchored = match axis {
-            Axis::X => self.align.x,
-            Axis::Y => self.align.y,
-        } == AxisAlign::Neg;
-        match reshapes || !anchored {
-            true => OnResize::Redraw,
-            false => OnResize::Translate,
-        }
-    }
-
     pub fn content(&self) -> String {
         self.buf.text().to_string()
     }
@@ -131,10 +120,6 @@ impl Widget for Text {
         self.update_buf();
         self.view.draw(painter).1
     }
-
-    fn on_resize(&self, axis: Axis) -> OnResize {
-        self.view.on_resize(axis)
-    }
 }
 
 impl Deref for Text {

src/widget/trait_fns.rs

@@ -12,14 +12,23 @@ widget_trait! {
         }
     }
 
-    fn align(self, align: impl Into<Align>) -> impl WidgetFn<Rsc, Aligned> {
-        move |state| Aligned {
-            inner: self.add_strong(state),
-            align: align.into(),
+    fn align(self, align: impl Into<Align>) -> impl WidgetIdFn<Rsc, WL::Widget> {
+        // An axis left out keeps whatever it had, which is centered unless
+        // something else set it.
+        let align = align.into();
+        move |state| {
+            let id = self.add(state);
+            let widgets = &mut state.ui_mut().widgets;
+            for (axis, align) in [(Axis::X, align.x), (Axis::Y, align.y)] {
+                if let Some(align) = align {
+                    widgets.set_alignment(id, axis, align);
+                }
+            }
+            id
         }
     }
 
-    fn center(self) -> impl WidgetFn<Rsc, Aligned> {
+    fn center(self) -> impl WidgetIdFn<Rsc, WL::Widget> {
         self.align(Align::CENTER)
     }
 
@@ -31,48 +40,46 @@ widget_trait! {
         }
     }
 
-    fn sized(self, size: impl Into<Size>) -> impl WidgetFn<Rsc, SetSize> {
+    fn region_node(self) -> impl WidgetIdFn<Rsc, WL::Widget> {
+        |state| {
+            let id = self.add(state);
+            state.ui_mut().widgets.set_region_node(id, true);
+            id
+        }
+    }
+
+    fn sized(self, size: impl Into<Size>) -> impl WidgetIdFn<Rsc, WL::Widget> {
         let size = size.into();
-        move |state| SetSize {
-            inner: self.add_strong(state),
-            x: Some(size.x),
-            y: Some(size.y),
+        move |state| {
+            let id = self.add(state);
+            let widgets = &mut state.ui_mut().widgets;
+            widgets.set_size_rule(id, Axis::X, SizeRule::Exact(size.x));
+            widgets.set_size_rule(id, Axis::Y, SizeRule::Exact(size.y));
+            id
         }
     }
 
-    fn max_width(self, len: impl Into<Len>) -> impl WidgetFn<Rsc, MaxSize> {
+    fn width(self, len: impl Into<LayoutLen>) -> impl WidgetIdFn<Rsc, WL::Widget> {
         let len = len.into();
-        move |state| MaxSize {
-            inner: self.add_strong(state),
-            x: Some(len),
-            y: None,
+        move |state| {
+            let id = self.add(state);
+            state
+                .ui_mut()
+                .widgets
+                .set_size_rule(id, Axis::X, SizeRule::Exact(len));
+            id
         }
     }
 
-    fn max_height(self, len: impl Into<Len>) -> impl WidgetFn<Rsc, MaxSize> {
+    fn height(self, len: impl Into<LayoutLen>) -> impl WidgetIdFn<Rsc, WL::Widget> {
         let len = len.into();
-        move |state| MaxSize {
-            inner: self.add_strong(state),
-            x: None,
-            y: Some(len),
-        }
-    }
-
-    fn width(self, len: impl Into<Len>) -> impl WidgetFn<Rsc, SetSize> {
-        let len = len.into();
-        move |state| SetSize {
-            inner: self.add_strong(state),
-            x: Some(len),
-            y: None,
-        }
-    }
-
-    fn height(self, len: impl Into<Len>) -> impl WidgetFn<Rsc, SetSize> {
-        let len = len.into();
-        move |state| SetSize {
-            inner: self.add_strong(state),
-            x: None,
-            y: Some(len),
+        move |state| {
+            let id = self.add(state);
+            state
+                .ui_mut()
+                .widgets
+                .set_size_rule(id, Axis::Y, SizeRule::Exact(len));
+            id
         }
     }
 
@@ -85,7 +92,9 @@ widget_trait! {
 
     fn scrollable(self) -> impl WidgetIdFn<Rsc, Scroll> where Rsc: HasEvents {
         move |state| {
-            Scroll::new(self.add_strong(state), Axis::Y)
+            let inner = self.add(state);
+            state.ui_mut().widgets.set_region_node(inner, true);
+            Scroll::new(inner.upgrade(state), Axis::Y)
                 .on(CursorSense::Scroll, |ctx, rsc| {
                     let delta = ctx.data.scroll_delta.y * 50.0;
                     ctx.widget(rsc).scroll(delta);
@@ -125,9 +134,13 @@ widget_trait! {
         |state| self.add(state)
     }
 
-    fn set_ptr(self, ptr: WeakWidget<WidgetPtr>, state: &mut Rsc) {
-        let id = self.add_strong(state);
-        state.ui_mut().widgets[ptr].inner = Some(id);
+    // Named for the type it makes rather than as `wrapped`, which would read
+    // as the text setting. `widget_trait!` takes no attributes, so what it is
+    // for is on `Wrapper` itself.
+    fn wrapper(self) -> impl WidgetFn<Rsc, Wrapper> {
+        |state| Wrapper {
+            inner: Some(self.add_strong(state)),
+        }
     }
 }
 

src/widget/wrapper.rs

@@ -1,11 +1,19 @@
 use crate::prelude::*;
 use std::marker::Unsize;
 
-pub struct WidgetPtr {
+/// One widget in a box of its own, doing as little as possible on the way:
+/// it draws its child in the whole of its box and reports back what the child
+/// said. It exists because a length and an alignment are properties of one
+/// widget, so a widget cannot both be 100 wide and take two shares of a row
+/// -- the two lengths need two widgets, and this is the smaller one.
+///
+/// Its child is optional so it can also be the swappable slot a tab bar
+/// needs, which is what it was written for.
+pub struct Wrapper {
     pub inner: Option<StrongWidget>,
 }
 
-impl Widget for WidgetPtr {
+impl Widget for Wrapper {
     fn draw(&mut self, painter: &mut Painter) -> Size {
         match &self.inner {
             Some(id) => painter.widget(id).size(),
@@ -14,7 +22,7 @@ impl Widget for WidgetPtr {
     }
 }
 
-impl WidgetPtr {
+impl Wrapper {
     pub fn new() -> Self {
         Self::default()
     }
@@ -35,7 +43,7 @@ impl WidgetPtr {
     }
 }
 
-impl Default for WidgetPtr {
+impl Default for Wrapper {
     fn default() -> Self {
         Self::empty()
     }

tests/cases/determinism.rs

@@ -0,0 +1,101 @@
+//! A measurement that decides control flow.
+//!
+//! Comparing boxes catches a widget that moved. It does not catch a widget
+//! that measured a child, believed a different answer from the one a cold
+//! start would give, and took the other branch -- which is the same defect
+//! arriving somewhere it cannot be ignored. A widget here branches on what it
+//! measured, so a disagreement shows up as a different tree.
+
+use iris::harness::Harness;
+use iris::prelude::*;
+
+/// Measures `probe` across `axis` and draws one of two children on the
+/// answer. Its own configuration never changes, so which child is drawn is a
+/// property of the layout alone.
+struct BranchesOnMeasurement {
+    probe: StrongWidget,
+    wide: StrongWidget,
+    narrow: StrongWidget,
+    threshold: f32,
+}
+
+impl Widget for BranchesOnMeasurement {
+    fn draw(&mut self, painter: &mut Painter) -> Size {
+        let mut top = UiRegion::FULL;
+        top.y.end = top.y.start.offset(Px::from_int(40));
+        let measured = painter.widget_within(&self.probe, top).len(Axis::X);
+        let px = measured.apply_leftover().to_px(painter.px_len(Axis::X));
+
+        let mut below = UiRegion::FULL;
+        below.y.start = below.y.start.offset(Px::from_int(40));
+        match px > Px::from_f32(self.threshold) {
+            true => painter.widget_within(&self.wide, below),
+            false => painter.widget_within(&self.narrow, below),
+        };
+        Size::LEFTOVER
+    }
+}
+
+fn plant(h: &mut Harness, threshold: f32) -> (WidgetId, WidgetId) {
+    let words = "the quick brown fox jumps over the lazy dog and keeps running";
+    let probe = wtext(words).size(16).wrap(true).add(&mut h.rsc);
+    let wide = rect(Color::RED).add(&mut h.rsc);
+    let narrow = rect(Color::BLUE).add(&mut h.rsc);
+    let branch = BranchesOnMeasurement {
+        probe: probe.add_strong(&mut h.rsc),
+        wide: wide.add_strong(&mut h.rsc),
+        narrow: narrow.add_strong(&mut h.rsc),
+        threshold,
+    }
+    .add(&mut h.rsc);
+    let side = rect(Color::GREEN).width(120).add(&mut h.rsc);
+    h.set_root((side, branch).span(Dir::RIGHT));
+    (wide.id(), narrow.id())
+}
+
+/// Which of the two branches drew, as a pair a test can compare.
+fn taken(h: &Harness, wide: WidgetId, narrow: WidgetId) -> (bool, bool) {
+    (h.region(&wide).is_some(), h.region(&narrow).is_some())
+}
+
+#[test]
+fn a_branch_taken_on_a_measurement_holds_across_repaints() {
+    for threshold in [0.0, 200.0, 400.0, 600.0, 779.0, 780.0, 781.0, 2000.0] {
+        let mut h = Harness::new((900, 600));
+        let (wide, narrow) = plant(&mut h, threshold);
+        let first = taken(&h, wide, narrow);
+        assert_ne!(first, (false, false), "threshold {threshold}: neither drew");
+
+        for frame in 0..4 {
+            h.rsc.widgets_mut().get_dyn_mut(wide);
+            h.rsc.widgets_mut().get_dyn_mut(narrow);
+            h.frame();
+            assert_eq!(
+                taken(&h, wide, narrow),
+                first,
+                "threshold {threshold}, repaint {frame}: the branch moved when nothing did"
+            );
+        }
+    }
+}
+
+#[test]
+fn a_branch_taken_on_a_measurement_is_the_one_a_cold_start_takes() {
+    for threshold in [0.0, 200.0, 400.0, 600.0, 779.0, 780.0, 781.0, 2000.0] {
+        let mut warm = Harness::new((900, 600));
+        let (wide, narrow) = plant(&mut warm, threshold);
+        warm.resize((640, 480));
+        warm.frame();
+        warm.rsc.widgets_mut().get_dyn_mut(wide);
+        warm.frame();
+
+        let mut cold = Harness::new((640, 480));
+        let (cwide, cnarrow) = plant(&mut cold, threshold);
+
+        assert_eq!(
+            taken(&warm, wide, narrow),
+            taken(&cold, cwide, cnarrow),
+            "threshold {threshold}: warm and cold took different branches"
+        );
+    }
+}

tests/cases/drift.rs

@@ -0,0 +1,45 @@
+//! What a retained drawing costs in accuracy when it is moved instead of made
+//! again. A subtree's stored regions are the only record of where it is, so a
+//! move that works from the last answer rather than from the box it is now in
+//! integrates its own rounding, and nothing later recomputes it. Re-expressing
+//! each part as the same fraction of the new box is what keeps a long-lived
+//! layout on the one a cold start produces.
+
+use iris::harness::Harness;
+use iris::prelude::*;
+
+/// A row of a fixed height under a bar, so changing the bar's height moves the
+/// row without changing the box it is given: the move path, repeatedly.
+fn plant(h: &mut Harness, bar_height: f32) -> (WeakWidget<Rect>, WeakWidget<Rect>) {
+    let bar = rect(Color::RED).height(bar_height).add(&mut h.rsc);
+    let inner = rect(Color::BLUE).add(&mut h.rsc);
+    let row = (inner, rect(Color::GREEN)).span(Dir::RIGHT).height(100);
+    h.set_root((bar, row).span(Dir::DOWN));
+    (bar, inner)
+}
+
+/// Enough moves to pass the 0.05 physical pixels layout treats as the same
+/// place, for a move that adds an offset to the last answer. Measured on this
+/// fixture on 2026-09-15: adding the offset to both ends of a span shortened
+/// the row by 0.071 over this many moves and by 0.712 over ten times as many,
+/// growing with the count rather than settling. Placing the far end from the
+/// near one instead left 0.069, because the length is re-derived either way.
+const MOVES: usize = 20_000;
+
+#[test]
+fn a_subtree_moved_many_times_stays_where_a_cold_layout_puts_it() {
+    let mut warm = Harness::new((640, 900));
+    let (bar, inner) = plant(&mut warm, 40.0);
+    let mut height = 40.0;
+    for step in 0..MOVES {
+        height = 40.0 + (step % 300) as f32 * 0.37;
+        warm.set_len(bar, Axis::Y, height);
+        warm.frame();
+    }
+
+    let mut cold = Harness::new((640, 900));
+    let (_, cold_inner) = plant(&mut cold, height);
+    cold.frame();
+
+    assert_eq!(warm.region(&inner), cold.region(&cold_inner));
+}

tests/cases/idempotence.rs

@@ -0,0 +1,29 @@
+//! Whether measuring a widget and then giving it the length it reported is a
+//! fixed point, which is what a span that sizes to its children needs.
+
+use iris::harness::Harness;
+use iris::prelude::*;
+
+#[test]
+fn a_wrapping_text_in_a_span_settles_on_one_width() {
+    let mut h = Harness::new((900, 600));
+    let words = "the quick brown fox jumps over the lazy dog and keeps on running \
+                 until it reaches the end of a rather long line of text";
+    let t = wtext(words).size(16).wrap(true).add(&mut h.rsc);
+    let filler = rect(Color::BLUE).add(&mut h.rsc);
+    h.set_root((t, filler).span(Dir::RIGHT));
+
+    let mut widths = Vec::new();
+    for _ in 0..6 {
+        let r = h.region(&t.id()).unwrap();
+        widths.push(r.bot_right.x - r.top_left.x);
+        // Redrawing it changes nothing about the state, so nothing may move.
+        h.rsc.widgets_mut().get_dyn_mut(t.id());
+        h.frame();
+    }
+    println!("widths over six frames: {widths:?}");
+    assert!(
+        widths.windows(2).all(|w| w[0] == w[1]),
+        "a repaint that changed nothing moved it: {widths:?}"
+    );
+}

tests/cases/layout.rs

@@ -0,0 +1,725 @@
+//! Where a frame puts things, with no window to put them in.
+
+use iris::harness::{Harness, assert_corners};
+use iris::prelude::*;
+
+/// A fixed 100 wide, and the rest of the 400 to its neighbour.
+fn two_rects(h: &mut Harness) -> (WidgetId, WidgetId) {
+    let left = rect(Color::RED).width(100).add(&mut h.rsc);
+    let right = rect(Color::BLUE).add(&mut h.rsc);
+    h.set_root((left, right).span(Dir::RIGHT));
+    (left.id(), right.id())
+}
+
+#[test]
+fn a_span_gives_each_child_the_width_it_asked_for() {
+    let mut h = Harness::new((400, 200));
+    let (left, right) = two_rects(&mut h);
+
+    assert_corners!(h, left, (0, 0), (100, 200));
+    assert_corners!(h, right, (100, 0), (400, 200));
+}
+
+/// A span offers each child the room left after the one before, because a
+/// text has to wrap at the width actually there, but reads what the child
+/// reports as a fraction of the whole row. So two children asking for half
+/// each take the whole row between them, however much of it was left when
+/// each was asked, and a third overflows.
+#[test]
+fn a_span_reads_a_child_report_as_a_fraction_of_the_row() {
+    let mut h = Harness::new((400, 100));
+    let half = rect(Color::RED).width(rel(0.5)).add(&mut h.rsc);
+    let inner = rect(Color::GREEN).width(rel(0.5)).add(&mut h.rsc);
+    let nested = (inner,).span(Dir::RIGHT).add(&mut h.rsc);
+    let tail = rect(Color::BLUE).width(100).add(&mut h.rsc);
+    h.set_root((half, nested, tail).span(Dir::RIGHT).width(rel(1.0)));
+
+    // The nested span is placed at the length it reported and drawn there
+    // once more; half of that final box is what its own child takes.
+    assert_corners!(h, nested, (200, 0), (400, 100));
+    assert_corners!(h, inner, (200, 0), (300, 100));
+    assert_corners!(h, tail, (400, 0), (500, 100));
+}
+
+/// The same fraction either way round: after a 100 px child in a 400 px row,
+/// `rel(0.5)` is 100 to 300 whether the child's own rule says so or the child
+/// drew half of what it was offered and reported that. Half the row, not half
+/// of the 300 px left of it.
+#[test]
+fn a_reported_fraction_is_of_the_row_like_a_declared_one() {
+    let mut declaring = Harness::new((400, 100));
+    let head = rect(Color::RED).width(100).add(&mut declaring.rsc);
+    let declared = rect(Color::GREEN).width(rel(0.5)).add(&mut declaring.rsc);
+    declaring.set_root((head, declared).span(Dir::RIGHT).width(rel(1.0)));
+    assert_corners!(declaring, declared, (100, 0), (300, 100));
+
+    let mut reporting = Harness::new((400, 100));
+    let head = rect(Color::RED).width(100).add(&mut reporting.rsc);
+    let inner = rect(Color::GREEN).width(rel(0.5)).add(&mut reporting.rsc);
+    let reported = (inner,).span(Dir::RIGHT).add(&mut reporting.rsc);
+    reporting.set_root((head, reported).span(Dir::RIGHT).width(rel(1.0)));
+    assert_corners!(reporting, reported, (100, 0), (300, 100));
+}
+
+/// What the fraction a child reports is of and what box it is offered are
+/// two different lengths, and only the first is the whole row: a text still
+/// wraps at the room actually left after its neighbour, so the same
+/// paragraph is taller where less of the row is left for it.
+#[test]
+fn a_text_in_a_span_wraps_at_the_room_left_rather_than_the_whole_row() {
+    let paragraph = "Wrapping shapes one source into as many lines as the box \
+                     leaves room for, so a paragraph's height is an answer.";
+    let height_after = |head_width: i32| {
+        let mut h = Harness::new((400, 400));
+        let head = rect(Color::RED).width(head_width).add(&mut h.rsc);
+        let text = wtext(paragraph).size(16).wrap(true).add(&mut h.rsc);
+        h.set_root((head, text).span(Dir::RIGHT).width(rel(1.0)));
+        let region = h.region(&text).unwrap();
+        (region.bot_right.y - region.top_left.y).to_f32()
+    };
+
+    let (crowded, whole_row) = (height_after(300), height_after(0));
+    assert!(crowded > whole_row, "{crowded} against {whole_row}");
+}
+
+/// A stack takes its size from one child and gives every child that size, so
+/// a child asking for half of it is asking for half of what it is itself the
+/// size of. Once the stack has been placed at the length it reported that
+/// length is the box, and taking the fraction of it again takes it twice:
+/// half a row became a quarter, and a further stack around it a further half.
+/// Nothing pinned it because a pixel is the same length wherever it is taken
+/// from, so only a share ever shrank -- and warm and cold shrink alike, so no
+/// oracle saw it either.
+#[test]
+fn a_stack_sized_by_a_child_does_not_take_that_childs_fraction_twice() {
+    let mut h = Harness::new((400, 200));
+    let half = rect(Color::RED).width(rel(0.5)).add(&mut h.rsc);
+    let behind = rect(Color::BLUE).add(&mut h.rsc);
+    let stack = Stack {
+        children: vec![behind.add_strong(&mut h.rsc), half.add_strong(&mut h.rsc)],
+        size: StackSize::Child(1),
+    }
+    .add(&mut h.rsc);
+    h.set_root((stack,).span(Dir::RIGHT).width(rel(1.0)));
+
+    assert_corners!(h, stack, (0, 0), (200, 200));
+    assert_corners!(h, half, (0, 0), (200, 200));
+    assert_corners!(h, behind, (0, 0), (200, 200));
+}
+
+/// The same reading through a pad: its inset is the whole box less the
+/// padding, so half of the inset plus the padding is half the box plus one
+/// padding, not two.
+#[test]
+fn a_pad_reports_a_fraction_of_its_inset_as_a_fraction_of_its_box() {
+    let mut h = Harness::new((400, 100));
+    let inner = rect(Color::GREEN).width(rel(0.5)).add(&mut h.rsc);
+    let padded = (inner,).span(Dir::RIGHT).pad(10).add(&mut h.rsc);
+    let tail = rect(Color::BLUE).width(100).add(&mut h.rsc);
+    // Ruled to the window: a root reporting a fraction of it is otherwise
+    // placed inside it by its own alignment, which is not what is under test.
+    h.set_root((padded, tail).span(Dir::RIGHT).width(rel(1.0)));
+
+    assert_corners!(h, padded, (0, 0), (210, 100));
+    assert_corners!(h, tail, (210, 0), (310, 100));
+}
+
+#[test]
+fn a_span_ruled_across_itself_does_not_measure_its_children_there() {
+    let mut h = Harness::new((400, 200));
+    let child = rect(Color::RED).height(40).add(&mut h.rsc);
+    let span = (child,).span(Dir::RIGHT).height(rel(1.0)).add(&mut h.rsc);
+    h.set_root(span);
+
+    assert_eq!(h.render.active[&span.id()].size.y, LayoutLen::rel(1.0));
+}
+
+#[test]
+fn a_span_reports_its_tallest_fixed_child() {
+    let mut h = Harness::new((400, 200));
+    let short = rect(Color::RED).height(40).add(&mut h.rsc);
+    let tall = rect(Color::BLUE).height(70).add(&mut h.rsc);
+    let span = (short, tall).span(Dir::RIGHT).add(&mut h.rsc);
+    h.set_root(span);
+
+    assert_eq!(h.render.active[&span.id()].size.y, LayoutLen::px(70.0));
+}
+
+#[test]
+fn resizing_relays_out_against_the_new_output() {
+    let mut h = Harness::new((400, 200));
+    let (left, right) = two_rects(&mut h);
+
+    h.resize((800, 100));
+    assert!(h.needs_redraw());
+    h.frame();
+
+    assert_corners!(h, left, (0, 0), (100, 100));
+    assert_corners!(h, right, (100, 0), (800, 100));
+}
+
+#[test]
+fn an_empty_widget_takes_a_share_of_a_span() {
+    let mut h = Harness::new((400, 200));
+    let gap = ().add(&mut h.rsc);
+    let right = rect(Color::BLUE).width(100).add(&mut h.rsc);
+    h.set_root((gap, right).span(Dir::RIGHT));
+
+    assert_corners!(h, gap, (0, 0), (300, 200));
+    assert_corners!(h, right, (300, 0), (400, 200));
+}
+
+#[test]
+fn a_child_drawn_twice_moves_once() {
+    let mut h = Harness::new((400, 200));
+    // The span measures a child and then places it; listing it twice would
+    // move it twice. The span's own fixed total is shorter than the window,
+    // so the span is centred in it and everything under it carries that.
+    let inner = rect(Color::BLUE).add(&mut h.rsc);
+    let centered = inner.center().width(200).add(&mut h.rsc);
+    let left = rect(Color::RED).width(100).add(&mut h.rsc);
+    h.set_root((left, centered).span(Dir::RIGHT));
+    assert_corners!(h, inner, (150, 0), (350, 200));
+
+    h.set_len(left, Axis::X, 150);
+    h.frame();
+
+    assert_corners!(h, inner, (175, 0), (375, 200));
+}
+
+#[test]
+fn alignment_accepts_an_arbitrary_fraction_and_changes_at_runtime() {
+    let mut h = Harness::new((400, 200));
+    let fixed = rect(Color::BLUE).sized((100, 100)).add(&mut h.rsc);
+    h.rsc
+        .widgets_mut()
+        .set_alignment(fixed, Axis::X, AxisAlign::new(0.25));
+    h.rsc
+        .widgets_mut()
+        .set_alignment(fixed, Axis::Y, AxisAlign::NEG);
+    h.set_root(fixed);
+    assert_corners!(h, fixed, (75, 0), (175, 100));
+
+    h.rsc
+        .widgets_mut()
+        .set_alignment(fixed, Axis::X, AxisAlign::new(0.75));
+    h.frame();
+    assert_corners!(h, fixed, (225, 0), (325, 100));
+}
+
+#[test]
+fn a_resize_lands_where_a_cold_start_would() {
+    let build = |h: &mut Harness| {
+        let para = wtext(
+            "Wrapping shapes one source into as many lines as its container leaves room \
+             for, so the height of a paragraph is an answer rather than a setting.",
+        )
+        .size(20)
+        .wrap(true)
+        .pad(16)
+        .add(&mut h.rsc);
+        let below = rect(Color::RED).add(&mut h.rsc);
+        let root = (para, below).span(Dir::DOWN).pad(12);
+        h.set_root(root);
+        (para, below)
+    };
+
+    let mut cold = Harness::new((900, 1200));
+    let (cold_para, cold_below) = build(&mut cold);
+
+    let mut resized = Harness::new((1920, 1200));
+    let (para, below) = build(&mut resized);
+    resized.resize((900, 1200));
+    resized.frame();
+
+    assert_eq!(resized.region(&para), cold.region(&cold_para), "paragraph");
+    assert_eq!(resized.region(&below), cold.region(&cold_below), "below");
+}
+
+#[test]
+fn a_fixed_box_is_drawn_again_rather_than_stretched() {
+    let mut h = Harness::new((400, 400));
+    // The panel fills a stack sized by its sibling, so it is first asked in
+    // the whole box and then given the shorter one. Reusing it in that fixed
+    // box afterwards would leave it whatever height it happened to have.
+    let panel = rect(Color::BLUE).add(&mut h.rsc);
+    let leaf = rect(Color::RED).height(100).add(&mut h.rsc);
+    let stack = (panel, leaf)
+        .stack()
+        .size(StackSize::Child(1))
+        .add(&mut h.rsc);
+    h.set_root(stack.align(Align::TOP));
+    assert_corners!(h, panel, (0, 0), (400, 100));
+
+    h.set_len(leaf, Axis::Y, 250);
+    h.frame();
+
+    assert_corners!(h, panel, (0, 0), (400, 250));
+}
+
+#[test]
+fn a_moved_subtree_takes_its_children_with_it() {
+    let mut h = Harness::new((400, 400));
+    let first = rect(Color::RED).height(40).add(&mut h.rsc);
+    let inner = rect(Color::BLUE).add(&mut h.rsc);
+    let row = inner.pad(10).height(40).region_node().add(&mut h.rsc);
+    // 80 of fixed rows in a 400 window, so the span takes 80 and sits in the
+    // middle of what it was given.
+    h.set_root((first, row).span(Dir::DOWN));
+    assert_corners!(h, inner, (10, 210), (390, 230));
+
+    h.set_len(first, Axis::Y, 80);
+    h.frame();
+
+    // The row opted into one movable region, so its descendants follow one
+    // entry rather than having their primitive regions rewritten.
+    assert_corners!(h, inner, (10, 230), (390, 250));
+}
+
+#[test]
+fn a_fixed_length_child_keeps_it_when_the_box_around_it_grows() {
+    let mut h = Harness::new((400, 200));
+    let fixed = rect(Color::BLUE).width(50).add(&mut h.rsc);
+    let leftover = rect(Color::GREEN).add(&mut h.rsc);
+    let panel = (fixed, leftover).span(Dir::RIGHT).add(&mut h.rsc);
+    // Changing the bar's width is the only thing that changes the box the
+    // panel and everything under it was drawn for.
+    let bar = rect(Color::RED).width(100).add(&mut h.rsc);
+    h.set_root((bar, panel).span(Dir::RIGHT));
+    assert_corners!(h, fixed, (100, 0), (150, 200));
+    assert_corners!(h, leftover, (150, 0), (400, 200));
+
+    h.set_len(bar, Axis::X, 200);
+    h.frame();
+
+    // The panel's box is 100 shorter, so the fixed child is the same 50 wide
+    // against its new start and the one taking what is left absorbs the change.
+    assert_corners!(h, fixed, (200, 0), (250, 200));
+    assert_corners!(h, leftover, (250, 0), (400, 200));
+}
+
+#[test]
+fn a_box_with_a_fixed_length_can_be_stretched_on_its_other_axis() {
+    let mut h = Harness::new((400, 200));
+    // The row is 40 tall whatever happens, which used to make its drawing
+    // impossible to take out of: recovering a fraction of a box needs a
+    // relative extent, and it has none on that axis.
+    let inner = rect(Color::BLUE).add(&mut h.rsc);
+    let row = inner.pad(10).height(40).add(&mut h.rsc);
+    let filler = rect(Color::GREEN).add(&mut h.rsc);
+    // This column is an item in a row, so it takes the width left for it
+    // rather than asking for a full row-width in addition to the bar.
+    let column = (row, filler).span(Dir::DOWN).add(&mut h.rsc);
+    let bar = rect(Color::RED).width(100).add(&mut h.rsc);
+    h.set_root((bar, column).span(Dir::RIGHT));
+    assert_corners!(h, inner, (110, 10), (390, 30));
+
+    h.set_len(bar, Axis::X, 200);
+    h.frame();
+
+    assert_corners!(h, inner, (210, 10), (390, 30));
+}
+
+#[test]
+fn only_a_region_node_lengthens_the_chain_and_it_can_be_removed() {
+    let mut h = Harness::new((400, 200));
+    let leaf = rect(Color::BLUE).add(&mut h.rsc);
+    let buried = leaf.pad(4).pad(4).pad(4).pad(4).add(&mut h.rsc);
+    let bar = rect(Color::RED).width(100).add(&mut h.rsc);
+    h.set_root((bar, buried).span(Dir::RIGHT));
+
+    let move_idx = h.render.active[&leaf.id()].parent_move;
+    assert_eq!(h.render.moves.depth(move_idx), 0, "the window is no entry");
+
+    h.rsc.widgets_mut().set_region_node(buried, true);
+    h.frame();
+    let move_idx = h.render.active[&leaf.id()].parent_move;
+    assert_eq!(
+        h.render.moves.depth(move_idx),
+        1,
+        "the opted-in widget's region alone"
+    );
+
+    h.rsc.widgets_mut().set_region_node(buried, false);
+    h.frame();
+    let move_idx = h.render.active[&leaf.id()].parent_move;
+    assert_eq!(h.render.moves.depth(move_idx), 0);
+}
+
+/// A span that sizes from its children passes their `leftover` weight up
+/// than collapsing it to one share, so nesting divides the same space instead
+/// of re-dividing a share of it.
+#[test]
+fn nested_spans_divide_the_space_once_however_deep_the_nesting_is() {
+    let mut h = Harness::new((400, 200));
+    let (a, b, c, d) = (
+        rect(Color::RED).add(&mut h.rsc),
+        rect(Color::BLUE).add(&mut h.rsc),
+        rect(Color::GREEN).add(&mut h.rsc),
+        rect(Color::WHITE).add(&mut h.rsc),
+    );
+    let left = (a, b).span(Dir::RIGHT).add(&mut h.rsc);
+    let right = (c, d).span(Dir::RIGHT).add(&mut h.rsc);
+    h.set_root((left, right).span(Dir::RIGHT));
+
+    for (i, id) in [a, b, c, d].into_iter().enumerate() {
+        let x = i as f32 * 100.0;
+        assert_corners!(h, id, (x, 0), (x + 100.0, 200));
+    }
+}
+
+/// The same space, unevenly nested: weights carried up mean a share is a
+/// share of the whole, not of whatever branch a widget happens to sit in.
+///
+/// Each edge lands on the even division or one step below it, since a share
+/// is a fraction of the room and a truncating multiply gives up what that
+/// fraction does not divide. What stays exact is that each share starts
+/// where the last one ended and the row ends at its own edge.
+#[test]
+fn an_uneven_nesting_still_gives_every_share_the_same_length() {
+    let mut h = Harness::new((400, 200));
+    let (a, b, c, d) = (
+        rect(Color::RED).add(&mut h.rsc),
+        rect(Color::BLUE).add(&mut h.rsc),
+        rect(Color::GREEN).add(&mut h.rsc),
+        rect(Color::WHITE).add(&mut h.rsc),
+    );
+    let one = (a,).span(Dir::RIGHT).add(&mut h.rsc);
+    let three = (b, c, d).span(Dir::RIGHT).add(&mut h.rsc);
+    h.set_root((one, three).span(Dir::RIGHT));
+
+    let mut start = Px::ZERO;
+    for (i, id) in [a, b, c, d].into_iter().enumerate() {
+        let got = h.region(&id).expect("widget drew nothing");
+        let even = Px::from_int((i as i32 + 1) * 100);
+        assert_eq!(got.top_left, PxVec2::new(start, Px::ZERO), "share {i}");
+        assert_eq!(got.bot_right.y, Px::from_int(200), "share {i}");
+        assert!(
+            got.bot_right.x == even || got.bot_right.x == even.next_down(),
+            "share {i} ends at {:?}, not {even:?}",
+            got.bot_right.x
+        );
+        start = got.bot_right.x;
+    }
+    assert_eq!(
+        start,
+        Px::from_int(400),
+        "the row stopped short of its edge"
+    );
+}
+
+/// However many ways a row is divided, the shares add up to the row: each
+/// one is the fixed parts before it plus a share of the room, rather than a
+/// step from where the last one ended, so the roundings do not accumulate
+/// along it. Chained, two hundred of them ended a step short of the edge.
+#[test]
+fn a_row_of_equal_shares_fills_it_exactly() {
+    for n in [2usize, 3, 7, 64, 200] {
+        let mut h = Harness::new((1000, 100));
+        let mut ids = Vec::new();
+        let mut kids: Vec<StrongWidget> = Vec::new();
+        for _ in 0..n {
+            let kid = rect(Color::RED).add(&mut h.rsc);
+            ids.push(kid.id());
+            kids.push(kid.add_strong(&mut h.rsc));
+        }
+        let span = Span {
+            children: kids,
+            dir: Dir::RIGHT,
+            gap: Px::ZERO,
+        }
+        .add(&mut h.rsc);
+        h.set_root(span);
+        h.frame();
+
+        for (i, id) in ids.iter().enumerate() {
+            let at = h.region(id).expect("a share drew nothing").top_left.x;
+            let want = Px::from_f32(1000.0 * (i as f32) / (n as f32));
+            assert!(
+                (at - want).abs() <= Px::STEP,
+                "{n} shares: the {i}th starts at {at:?}, not {want:?}"
+            );
+        }
+        let end = h.region(ids.last().unwrap()).unwrap().bot_right.x;
+        assert_eq!(end, Px::from_int(1000), "{n} shares do not reach the edge");
+    }
+}
+
+/// Where the shader puts an edge: the fraction resolved against the window
+/// plus the pixel offset, taken to the boundary it composes to within half
+/// a step of. Kept in step with `snap_floor` in `prelude.wgsl`.
+fn drawn_edges(h: &Harness, id: WidgetId, axis: Axis) -> (f32, f32) {
+    let active = &h.render.active[&id];
+    let region = h.render.moves.resolve(active.parent_move, active.region);
+    let dim = h.size().axis(axis);
+    let snap = |v: f32| (v + Px::STEP.to_f32() * 0.5).floor();
+    let edge = |s: Len| snap(s.rel.to_f32() * dim + s.px.to_f32());
+    let span = region.axis(axis);
+    (edge(span.start), edge(span.end))
+}
+
+fn hairline(h: &mut Harness, marks: &mut Vec<WidgetId>) -> StrongWidget {
+    let mark = rect(Color::RED).width(1).add_strong(&mut h.rsc);
+    marks.push(mark.id());
+    mark
+}
+
+fn share(h: &mut Harness, inner: StrongWidget, ratio: f32) -> StrongWidget {
+    h.set_len(&inner, Axis::X, LayoutLen::leftover(ratio));
+    inner
+}
+
+/// Shares in weights no binary fraction lands on, a padding on one branch
+/// and not the other, so an edge falls near an integer as often as it can.
+fn hairlines(h: &mut Harness, depth: usize, marks: &mut Vec<WidgetId>) -> StrongWidget {
+    let mut span = Span::empty(Dir::RIGHT);
+    if depth == 0 {
+        let left = rect(Color::BLUE).add_strong(&mut h.rsc);
+        let left = share(h, left, 3.0);
+        span.push(left);
+        let mark = hairline(h, marks);
+        span.push(mark);
+        let right = rect(Color::BLUE).add_strong(&mut h.rsc);
+        let right = share(h, right, 7.0);
+        span.push(right);
+        return span.add_strong(&mut h.rsc);
+    }
+    let first = hairlines(h, depth - 1, marks);
+    let first = share(h, first, 3.0);
+    span.push(first);
+    let second = hairlines(h, depth - 1, marks);
+    let second = Pad {
+        padding: Padding {
+            left: Px::from_int(3),
+            right: Px::from_int(7),
+            top: Px::ZERO,
+            bottom: Px::ZERO,
+        },
+        inner: second,
+    }
+    .add_strong(&mut h.rsc);
+    let second = share(h, second, 5.0);
+    span.push(second);
+    span.add_strong(&mut h.rsc)
+}
+
+/// A one-pixel line is a pixel wherever it is drawn. Both edges of a fixed
+/// length share their box's fraction, so composing the chain moves them
+/// together and the shader's `floor` cannot round the pixel between them
+/// away -- only shift it. A separator that disappeared at one window size
+/// would be a defect no size comparison catches.
+#[test]
+fn a_one_pixel_line_keeps_its_pixel_through_a_chain() {
+    let mut h = Harness::new((1920, 1200));
+    let mut marks = Vec::new();
+    let root = hairlines(&mut h, 4, &mut marks);
+    h.state.set_root(root);
+    h.frame();
+    assert_eq!(marks.len(), 16);
+
+    for size in [(1920, 1200), (1919, 1201), (997, 1003), (1367, 733)] {
+        h.resize(size);
+        h.frame();
+        for mark in &marks {
+            let (start, end) = drawn_edges(&h, *mark, Axis::X);
+            assert_eq!(end - start, 1.0, "at {size:?}, mark {mark:?}");
+        }
+    }
+}
+
+/// A span short of room takes it from its shares, which go to nothing and
+/// then to nothing wider; the fixed lengths between them keep their pixels.
+/// Collapsing those to make room would delete a separator the caller asked
+/// for, which is worse than overflowing.
+#[test]
+fn a_span_out_of_room_shrinks_its_shares_and_not_its_fixed_lengths() {
+    let mut h = Harness::new((400, 20));
+    let mut marks = Vec::new();
+    let mut span = Span::empty(Dir::RIGHT);
+    for _ in 0..3 {
+        let share_of = rect(Color::BLUE).add_strong(&mut h.rsc);
+        let share_of = share(&mut h, share_of, 1.0);
+        span.push(share_of);
+        let mark = hairline(&mut h, &mut marks);
+        span.push(mark);
+    }
+    let root = span.add_strong(&mut h.rsc);
+    h.state.set_root(root);
+    h.frame();
+
+    for width in [400, 10, 3, 1] {
+        h.resize((width, 20));
+        h.frame();
+        for mark in &marks {
+            let (start, end) = drawn_edges(&h, *mark, Axis::X);
+            assert_eq!(end - start, 1.0, "at {width} wide, mark {mark:?}");
+        }
+    }
+}
+
+#[test]
+fn only_a_pure_leftover_child_disappears_when_nothing_is_left() {
+    let mut h = Harness::new((100, 20));
+    let fixed = rect(Color::RED).width(100).add(&mut h.rsc);
+    let leftover = rect(Color::BLUE).add(&mut h.rsc);
+    h.set_root((fixed, leftover).span(Dir::RIGHT));
+
+    assert_corners!(h, fixed, (0, 0), (100, 20));
+    assert_eq!(h.region(&leftover), None);
+
+    // An undrawn child remains a dependency of the span, so making room for
+    // it draws it without rebuilding the tree.
+    h.set_len(fixed, Axis::X, 60);
+    h.frame();
+    assert_corners!(h, leftover, (60, 0), (100, 20));
+
+    let mut h = Harness::new((100, 20));
+    let fixed = rect(Color::RED).width(100).add(&mut h.rsc);
+    let mixed = rect(Color::BLUE)
+        .width(LayoutLen::px(20) + LayoutLen::LEFTOVER)
+        .add(&mut h.rsc);
+    h.set_root((fixed, mixed).span(Dir::RIGHT));
+
+    // Pixels and fractions still overflow; only a child whose entire length
+    // is leftover is omitted.
+    assert_corners!(h, mixed, (100, 0), (120, 20));
+}
+
+#[test]
+fn leftover_children_disappear_at_the_exact_fixed_content_boundary() {
+    let mut h = Harness::new((100, 100));
+    let first = rect(Color::RED).height(90).add(&mut h.rsc);
+    let a = rect(Color::GREEN).add(&mut h.rsc);
+    let b = rect(Color::BLUE).add(&mut h.rsc);
+    let inner = (a, b).span(Dir::DOWN).gap(4).add(&mut h.rsc);
+    h.set_root((first, inner).span(Dir::DOWN));
+    assert!(h.region(&a).is_some());
+    assert!(h.region(&b).is_some());
+
+    h.set_len(first, Axis::Y, 96.0);
+    h.frame();
+
+    assert!(h.region(&a).is_none());
+    assert!(h.region(&b).is_none());
+}
+
+/// **A stack child smaller than the stack sits where its own alignment
+/// says.** `Stack` gives every child the box its sizing child defines and
+/// used to force the near edge on all of them; that override is owed only to
+/// the sizing child, which has already placed its own content in the box the
+/// stack derived from its answer. Every other child is handed a box that owes
+/// nothing to it, so where it sits in one bigger than itself is its own
+/// business -- and with the override it could not be aligned at all, which is
+/// what moved the `tabs` example's counters to the wrong corner.
+#[test]
+fn a_stack_child_smaller_than_the_stack_keeps_its_own_alignment() {
+    let mut h = Harness::new((400, 200));
+    let big = rect(Color::BLUE).add(&mut h.rsc);
+    let small = rect(Color::RED).sized((50, 50)).add(&mut h.rsc);
+    h.rsc
+        .widgets_mut()
+        .set_alignment(small.id(), Axis::X, AxisAlign::POS);
+    let (a, b) = (big.add_strong(&mut h.rsc), small.add_strong(&mut h.rsc));
+    let children: Vec<StrongWidget> = vec![a, b];
+    h.set_root(Stack {
+        children,
+        size: StackSize::Default,
+    });
+
+    assert_corners!(h, big, (0, 0), (400, 200));
+    // The far edge on X because it asked for it, the middle on Y because
+    // that is the default.
+    assert_corners!(h, small, (350, 75), (400, 125));
+}
+/// Five children of one span, buried under three containers that are each a
+/// fraction of their parent so no length reaches the window without being
+/// composed and rounded on the way. Returns each child's drawn width and
+/// each gap between them, in pixels.
+fn row_under_fractions(kid: Option<LayoutLen>, gap: f32, box_w: f32) -> (Vec<Px>, Vec<Px>) {
+    let mut h = Harness::new((box_w, 400.0));
+    let mut ids = Vec::new();
+    let mut kids: Vec<StrongWidget> = Vec::new();
+    for _ in 0..5 {
+        let r = rect(Color::RED).add(&mut h.rsc);
+        if let Some(len) = kid {
+            h.rsc
+                .widgets_mut()
+                .set_size_rule(r.id(), Axis::X, SizeRule::Exact(len));
+        }
+        ids.push(r.id());
+        kids.push(r.add_strong(&mut h.rsc));
+    }
+    let span = Span {
+        children: kids,
+        dir: Dir::RIGHT,
+        gap: Px::from_f32(gap),
+    }
+    .add(&mut h.rsc);
+    let a = (span.width(rel(0.9)),).span(Dir::RIGHT).add(&mut h.rsc);
+    let b = (a.width(rel(0.8)),).span(Dir::RIGHT).add(&mut h.rsc);
+    h.set_root((b.width(rel(0.7)),).span(Dir::RIGHT));
+    let boxes: Vec<_> = ids
+        .iter()
+        .map(|id| h.region(id).expect("a child drew nothing"))
+        .collect();
+    (
+        boxes.iter().map(|b| b.bot_right.x - b.top_left.x).collect(),
+        boxes
+            .windows(2)
+            .map(|p| p[1].top_left.x - p[0].bot_right.x)
+            .collect(),
+    )
+}
+
+/// **A length given in pixels is that many pixels, wherever it ends up.** A
+/// gap and a declared width compose additively -- `Len::within` adds a part's
+/// own pixels rather than scaling them, and both ends of a gap carry the same
+/// fraction, so the multiply that rounds is the same on each -- which is why
+/// nesting the row inside fractions of fractions cannot move them. Swept over
+/// 2,100 box widths when this was written and exact at every one; five here,
+/// including widths that divide badly by five.
+#[test]
+fn a_length_in_pixels_is_that_many_pixels_however_it_is_nested() {
+    for box_w in [300.0, 1000.0, 1001.0, 1003.0, 1920.0] {
+        let want = Px::from_int(7);
+        let (_, gaps) = row_under_fractions(None, 7.0, box_w);
+        assert!(
+            gaps.iter().all(|g| *g == want),
+            "box {box_w}: gaps between leftover children are {gaps:?}"
+        );
+        let (widths, gaps) = row_under_fractions(Some(LayoutLen::px(100.0)), 7.0, box_w);
+        assert!(
+            gaps.iter().all(|g| *g == want),
+            "box {box_w}: gaps between fixed children are {gaps:?}"
+        );
+        assert!(
+            widths.iter().all(|w| *w == Px::from_int(100)),
+            "box {box_w}: declared widths came out {widths:?}"
+        );
+    }
+}
+
+/// **Children asking for the same share of a row are not the same length**,
+/// and this pins by how much rather than claiming they are equal. A position
+/// is the quantity that gets rounded, so the row fills exactly and no two
+/// children leave a seam; what that costs is a step or two between lengths
+/// that were asked for identically. Exact composition would shrink the
+/// spread, not remove it: five equal lengths cannot fill a row whose step
+/// count is not a multiple of five.
+#[test]
+fn equal_shares_differ_by_at_most_two_steps_and_fill_the_row() {
+    for kid in [None, Some(LayoutLen::rel(0.2))] {
+        for box_w in [300.0, 1000.0, 1001.0, 1003.0, 1920.0] {
+            let (widths, gaps) = row_under_fractions(kid, 0.0, box_w);
+            let spread = *widths.iter().max().unwrap() - *widths.iter().min().unwrap();
+            assert!(
+                spread <= Px::from_raw(2),
+                "box {box_w}, {kid:?}: widths {widths:?} spread {spread:?}"
+            );
+            assert!(
+                gaps.iter().all(|g| *g == Px::ZERO),
+                "box {box_w}, {kid:?}: children left seams {gaps:?}"
+            );
+        }
+    }
+}

tests/cases/plan.rs

@@ -0,0 +1,121 @@
+//! The tree a seed describes, as a value rather than as widgets.
+//!
+//! Two things have to hold for a plan to be worth having. Editing a plan has
+//! to mean what growing with those edits means, or a scenario reads one thing
+//! and the oracle another. And reducing a plan has to end, or a shrinker
+//! searching for the smallest counterexample never returns.
+
+use iris::random::{Edits, Kind, Plan, Rng, SpanEdit, plan};
+use std::collections::HashMap;
+
+fn some_edits(seed: u64, of: &Plan) -> Edits {
+    let mut rng = Rng::new(seed);
+    let (mut sized, mut aligned, mut nodes, mut spans) = (0, 0, 0, 0);
+    let mut of = of.clone();
+    of.walk_mut(&mut |p| {
+        if matches!(p.kind, Kind::Span { .. }) {
+            spans += 1;
+        }
+        sized += p.size.is_some() as usize;
+        aligned += p.align.is_some() as usize;
+        nodes += p.region_node.is_some() as usize;
+    });
+    let pick =
+        |n: usize, rng: &mut Rng| -> Vec<usize> { (0..n).filter(|_| rng.chance()).collect() };
+    Edits {
+        sizes: pick(sized, &mut rng)
+            .into_iter()
+            .map(|i| (i, [Some(LayoutLen::LEFTOVER), None]))
+            .collect(),
+        aligns: pick(aligned, &mut rng)
+            .into_iter()
+            .map(|i| (i, [Some(AxisAlign::POS), None]))
+            .collect(),
+        nodes: pick(nodes, &mut rng)
+            .into_iter()
+            .map(|i| (i, true))
+            .collect(),
+        spans: pick(spans, &mut rng)
+            .into_iter()
+            .map(|i| {
+                (
+                    i,
+                    SpanEdit {
+                        detach: vec![0],
+                        attach: 2,
+                    },
+                )
+            })
+            .collect::<HashMap<_, _>>(),
+        fixed_branches: false,
+    }
+}
+
+use iris::prelude::*;
+
+/// The two routes to an edited tree are one tree. `plan` resolves edits out
+/// of the random stream as it draws; `edited` puts them on a tree that
+/// already exists, which is the only route a shrunk plan has, since no seed
+/// grows one. A scenario written against either has to read the same.
+#[test]
+fn editing_a_plan_is_growing_one_with_those_edits() {
+    for seed in 1..=60 {
+        let bare = plan(seed, 5, &Edits::default());
+        let edits = some_edits(seed, &bare);
+        assert_eq!(
+            bare.edited(&edits),
+            plan(seed, 5, &edits),
+            "seed {seed}: edited and grown-with-edits disagree"
+        );
+    }
+}
+
+/// Every simplification is strictly smaller, so taking them in turn reaches a
+/// fixed point instead of circling. A shrinker that can return to a tree it
+/// has already tried does not stop.
+#[test]
+fn every_simplification_of_a_plan_is_smaller_than_it() {
+    for seed in 1..=60 {
+        let tree = plan(seed, 4, &Edits::default());
+        let mut queue = vec![tree];
+        let mut seen = 0;
+        while let Some(node) = queue.pop() {
+            seen += 1;
+            if seen > 400 {
+                break;
+            }
+            for small in node.smaller() {
+                assert!(
+                    small.size() <= node.size(),
+                    "seed {seed}: a simplification grew from {} to {}",
+                    node.size(),
+                    small.size()
+                );
+                if small.size() < node.size() {
+                    queue.push(small);
+                }
+            }
+        }
+    }
+}
+
+/// Reducing until nothing reduces ends, and ends at something small enough to
+/// read rather than at the tree it started from.
+#[test]
+fn reducing_a_plan_all_the_way_ends() {
+    for seed in 1..=30 {
+        let mut node = plan(seed, 5, &Edits::default());
+        let grown = node.size();
+        let mut steps = 0;
+        while let Some(next) = node.smaller().into_iter().next() {
+            node = next;
+            steps += 1;
+            assert!(steps < 10_000, "seed {seed}: reducing did not end");
+        }
+        assert!(
+            node.size() < grown.max(2),
+            "seed {seed}: reduced {grown} widgets to {}",
+            node.size()
+        );
+    }
+}

tests/cases/retained.rs

@@ -0,0 +1,630 @@
+//! What a second frame draws again, and what it keeps.
+
+use std::{cell::Cell, rc::Rc};
+
+use iris::harness::{Harness, assert_corners};
+use iris::prelude::*;
+
+/// A leaf that counts its draws and reports whatever size it is given, so a
+/// test can see what the retained path skipped. One that reads its box in
+/// pixels has a drawing that holds for that box alone.
+struct Counted {
+    draws: Rc<Cell<usize>>,
+    size: Size,
+    reads_box: bool,
+}
+
+impl Widget for Counted {
+    fn draw(&mut self, painter: &mut Painter) -> Size {
+        self.draws.set(self.draws.get() + 1);
+        if self.reads_box {
+            painter.px_size();
+        }
+        self.size
+    }
+}
+
+struct Counts(Rc<Cell<usize>>);
+
+impl Counts {
+    fn get(&self) -> usize {
+        self.0.get()
+    }
+}
+
+fn counted(h: &mut Harness, size: Size, reads_box: bool) -> (WeakWidget<Counted>, Counts) {
+    let draws = Rc::new(Cell::new(0));
+    let id = Counted {
+        draws: draws.clone(),
+        size,
+        reads_box,
+    }
+    .add(&mut h.rsc);
+    (id, Counts(draws))
+}
+
+struct Layered {
+    children: [StrongWidget<Rect>; 2],
+    _revision: usize,
+}
+
+impl Widget for Layered {
+    fn draw(&mut self, painter: &mut Painter) -> Size {
+        painter.child_layer();
+        painter.widget(&self.children[0]);
+        painter.next_layer();
+        painter.widget(&self.children[1]);
+        Size::default()
+    }
+}
+
+#[test]
+fn a_redrawn_layered_widget_keeps_the_layer_it_was_entered_on() {
+    let mut h = Harness::new((400, 200));
+    let children = [
+        rect(Color::RED).add_strong(&mut h.rsc),
+        rect(Color::BLUE).add_strong(&mut h.rsc),
+    ];
+    let root = Layered {
+        children,
+        _revision: 0,
+    }
+    .add(&mut h.rsc);
+    h.set_root(root);
+
+    h.rsc[root]._revision += 1;
+    h.frame();
+
+    let label = h.rsc.widgets().label(root.id());
+    let active = h
+        .render
+        .debug(h.rsc.widgets(), label)
+        .find(|active| active.id == root.id())
+        .unwrap();
+    assert_eq!(active.layer, 0);
+}
+
+/// A fixed-width leaf beside one that takes what is left over, so changing
+/// the first hands the second a different box without the output changing.
+fn pair(h: &mut Harness, reads_box: bool) -> (WeakWidget<Counted>, Counts, WidgetId) {
+    let (first, _) = counted(h, Size::from((100, 200)), false);
+    let (second, draws) = counted(h, Size::LEFTOVER, reads_box);
+    h.set_root((first, second).span(Dir::RIGHT));
+    (first, draws, second.id())
+}
+
+#[test]
+fn a_leaf_that_ignores_its_box_is_not_drawn_again_when_the_box_changes() {
+    let mut h = Harness::new((400, 200));
+    let (first, draws, second) = pair(&mut h, false);
+    let settled = draws.get();
+    assert_corners!(h, second, (100, 0), (400, 200));
+
+    h.rsc[first].size = Size::from((150, 200));
+    h.frame();
+
+    assert_eq!(
+        draws.get(),
+        settled,
+        "its box is a field to write, not a reason to draw"
+    );
+    assert_corners!(h, second, (150, 0), (400, 200));
+}
+
+#[test]
+fn moving_an_ordinary_subtree_remaps_its_mask() {
+    let mut h = Harness::new((400, 200));
+    let (first, _) = counted(&mut h, Size::from((100, 200)), false);
+    let inner = rect(Color::BLUE).add(&mut h.rsc);
+    let masked = inner.masked().add(&mut h.rsc);
+    h.set_root((first, masked).span(Dir::RIGHT));
+
+    h.rsc[first].size = Size::from((150, 200));
+    h.frame();
+
+    let active = &h.render.active[&masked.id()];
+    assert_eq!(
+        h.rsc.ui().masks[active.mask.idx()].region,
+        UiRegion::new(UiSpan::new(Len::px(150.0), Len::rel_max()), UiSpan::FULL,)
+    );
+    assert_corners!(h, inner, (150, 0), (400, 200));
+}
+
+#[test]
+fn a_leaf_that_depends_on_its_box_is_drawn_again_when_the_box_changes() {
+    let mut h = Harness::new((400, 200));
+    let (first, draws, second) = pair(&mut h, true);
+    let settled = draws.get();
+
+    h.rsc[first].size = Size::from((150, 200));
+    h.frame();
+
+    // The preceding fixed child makes the remaining box this child's real
+    // box, so measuring it also draws it in its final box.
+    assert_eq!(draws.get(), settled + 1);
+    assert_corners!(h, second, (150, 0), (400, 200));
+}
+
+#[test]
+fn a_span_child_that_declares_its_length_is_drawn_once() {
+    let mut h = Harness::new((400, 200));
+    let (told, told_draws) = counted(&mut h, Size::from((100, 200)), false);
+    let (asked, asked_draws) = counted(&mut h, Size::from((100, 200)), true);
+    // The span takes one child's length from its hint and has to draw the
+    // other to find out, so only the second is drawn before its final box.
+    let hinted = told.width(100).add(&mut h.rsc);
+    h.set_root((hinted, asked).span(Dir::RIGHT));
+
+    assert_eq!(told_draws.get(), 1);
+    // Reading its box makes its drawing hold for the measuring box alone,
+    // and it reports less than that box: so it is drawn again in the box its
+    // answer places it in, and once more in the final box the span chooses.
+    // A widget that says what it holds for, as text does, skips the middle
+    // one.
+    assert_eq!(
+        asked_draws.get(),
+        3,
+        "drawn to be measured, in its placed box, then in its final box"
+    );
+}
+
+#[test]
+fn a_span_relays_out_when_a_child_it_measured_changes() {
+    let mut h = Harness::new((400, 200));
+    let (first, _, second) = pair(&mut h, false);
+
+    h.rsc[first].size = Size::from((250, 200));
+    h.frame();
+
+    assert_corners!(h, first, (0, 0), (250, 200));
+    assert_corners!(h, second, (250, 0), (400, 200));
+}
+
+#[test]
+fn a_repaint_that_keeps_its_size_does_not_relay_out() {
+    let mut h = Harness::new((400, 200));
+    let (first, draws) = counted(&mut h, Size::from((100, 200)), false);
+    let (second, _) = counted(&mut h, Size::LEFTOVER, false);
+    h.set_root((first, second).span(Dir::RIGHT));
+    let settled = draws.get();
+
+    // Taking mutable access is the ordinary content-change signal. This
+    // widget returns the same size, so the parent has nothing to lay out.
+    let _ = h.rsc.widgets_mut().get_dyn_mut(first.id());
+    h.frame();
+
+    assert_eq!(draws.get(), settled + 1);
+}
+
+#[test]
+fn a_span_child_survives_the_next_frame() {
+    let mut h = Harness::new((400, 200));
+    // Both children declare a length, so the span chooses their boxes from
+    // hints rather than drawing them to find out.
+    let top = rect(Color::RED).height(80).add(&mut h.rsc);
+    let bottom = rect(Color::BLUE).height(120).add(&mut h.rsc);
+    h.set_root((top, bottom).span(Dir::DOWN));
+
+    h.rsc.widgets_mut().get_dyn_mut(top.id());
+    h.frame();
+
+    assert_corners!(h, top, (0, 0), (400, 80));
+    assert_corners!(h, bottom, (0, 80), (400, 200));
+}
+
+/// Lays its child out from the hint alone, never reading what it drew.
+struct FromHint {
+    inner: StrongWidget,
+}
+
+impl Widget for FromHint {
+    fn draw(&mut self, painter: &mut Painter) -> Size {
+        let len = painter.size_hint(&self.inner, Axis::Y).unwrap();
+        let mut region = UiRegion::FULL;
+        region.y.end = region.y.start.offset(len.px);
+        painter.widget_within(&self.inner, region);
+        Size::LEFTOVER
+    }
+}
+
+#[test]
+fn a_parent_that_only_read_a_hint_relays_out_when_the_hint_changes() {
+    let mut h = Harness::new((400, 200));
+    let inner = rect(Color::RED).height(80).add(&mut h.rsc);
+    let parent = FromHint {
+        inner: inner.add_strong(&mut h.rsc),
+    }
+    .add(&mut h.rsc);
+    h.set_root(parent);
+    assert_corners!(h, inner, (0, 0), (400, 80));
+
+    h.set_len(inner, Axis::Y, 120);
+    h.frame();
+
+    assert_corners!(h, inner, (0, 0), (400, 120));
+}
+
+/// Reads its box's size, which nothing but its own draw can put right.
+struct ReadsBox {
+    draws: Rc<Cell<usize>>,
+}
+
+impl Widget for ReadsBox {
+    fn draw(&mut self, painter: &mut Painter) -> Size {
+        self.draws.set(self.draws.get() + 1);
+        Size::from_px(painter.px_size().div_int(4))
+    }
+}
+
+/// Reads its box across one axis only, so its drawing holds for a taller
+/// box on its own and only a wider one is worth a draw.
+///
+/// Both of these report a quarter of what they read, without saying that the
+/// drawing holds there too, so each length they are asked at costs two draws:
+/// one to answer, and one in the quarter-sized box that answer places them
+/// in. The counts below are in those pairs.
+struct ReadsWidth {
+    draws: Rc<Cell<usize>>,
+}
+
+impl Widget for ReadsWidth {
+    fn draw(&mut self, painter: &mut Painter) -> Size {
+        self.draws.set(self.draws.get() + 1);
+        Size::from_px(PxVec2::new(
+            painter.px_len(Axis::X).div_int(4),
+            Px::from_int(20),
+        ))
+    }
+}
+
+#[test]
+fn a_resize_does_not_redraw_what_the_shader_can_move() {
+    let mut h = Harness::new((400, 200));
+    let (leaf, draws) = counted(&mut h, Size::LEFTOVER, false);
+    h.set_root(leaf);
+    let settled = draws.get();
+
+    h.resize((800, 100));
+    assert!(h.needs_redraw());
+    h.frame();
+
+    assert_eq!(
+        draws.get(),
+        settled,
+        "a scaling drawing follows its box, and the output is one"
+    );
+    assert_corners!(h, leaf, (0, 0), (800, 100));
+}
+
+#[test]
+fn a_span_ruled_across_itself_moves_its_child_without_redrawing_it() {
+    let mut h = Harness::new((400, 200));
+    let (leaf, draws) = counted(&mut h, Size::LEFTOVER, false);
+    let span = (leaf,).span(Dir::RIGHT).height(rel(1.0)).add(&mut h.rsc);
+    h.set_root(span);
+    let settled = draws.get();
+
+    h.resize((400, 100));
+    h.frame();
+
+    assert_eq!(draws.get(), settled);
+    assert_corners!(h, leaf, (0, 0), (400, 100));
+    assert_eq!(h.render.active[&span.id()].size.y, LayoutLen::rel(1.0));
+}
+
+/// The output is the root of the box chain, so a resize is a box that changed
+/// length like any other -- there is not a second rule for the window. A
+/// drawing that holds for one length is drawn again whichever box moved.
+#[test]
+fn a_resize_redraws_what_does_not_scale() {
+    let mut h = Harness::new((400, 200));
+    let (leaf, draws) = counted(&mut h, Size::LEFTOVER, true);
+    h.set_root(leaf);
+    let settled = draws.get();
+
+    h.resize((800, 100));
+    h.frame();
+
+    assert_eq!(draws.get(), settled + 1, "its box is a different length");
+    assert_corners!(h, leaf, (0, 0), (800, 100));
+}
+
+#[test]
+fn a_resize_redraws_what_read_its_box() {
+    let mut h = Harness::new((400, 200));
+    let draws = Rc::new(Cell::new(0));
+    let leaf = ReadsBox {
+        draws: draws.clone(),
+    }
+    .add(&mut h.rsc);
+    h.set_root(leaf);
+    let settled = draws.get();
+
+    h.resize((800, 100));
+    h.frame();
+
+    assert_eq!(draws.get(), settled + 2);
+}
+
+#[test]
+fn a_resize_only_redraws_read_axes() {
+    let mut h = Harness::new((400, 200));
+    let draws = Rc::new(Cell::new(0));
+    let leaf = ReadsWidth {
+        draws: draws.clone(),
+    }
+    .add(&mut h.rsc);
+    h.set_root(leaf);
+    let settled = draws.get();
+
+    h.resize((400, 300));
+    h.frame();
+    assert_eq!(draws.get(), settled, "height was never read");
+
+    h.resize((800, 300));
+    h.frame();
+    assert_eq!(draws.get(), settled + 2, "width changes its answer");
+}
+
+/// A window is measured onto the grid like everything else, so a resize too
+/// small to reach the next step is not a resize at all -- and one that does
+/// reach it is, however little of a pixel it is worth.
+#[test]
+fn a_resize_within_one_step_is_not_a_resize() {
+    let mut h = Harness::new((400, 200));
+    let draws = Rc::new(Cell::new(0));
+    let leaf = ReadsWidth {
+        draws: draws.clone(),
+    }
+    .add(&mut h.rsc);
+    h.set_root(leaf);
+    let settled = draws.get();
+
+    // All of these are 400 px to the nearest step.
+    let step = Px::STEP.to_f32();
+    for part in [0.1, 0.2, 0.3] {
+        h.resize((400.0 + step * part, 200.0));
+        h.frame();
+        assert_eq!(draws.get(), settled);
+    }
+
+    h.resize((400.0 + step, 200.0));
+    h.frame();
+    assert_eq!(draws.get(), settled + 2);
+}
+
+/// The same for a box that changes because a sibling did: what is compared
+/// is the length on the grid, and three lengths that land on one step are
+/// one length.
+#[test]
+fn a_box_change_within_one_step_is_not_a_change() {
+    let mut h = Harness::new((400, 200));
+    let (first, draws, _) = pair(&mut h, true);
+    let settled = draws.get();
+
+    let step = Px::STEP.to_f32();
+    for part in [0.1, 0.2, 0.3] {
+        h.rsc[first].size.x = LayoutLen::px(100.0 + step * part);
+        h.frame();
+        assert_eq!(draws.get(), settled);
+    }
+
+    h.rsc[first].size.x = LayoutLen::px(100.0 + step);
+    h.frame();
+    assert_eq!(draws.get(), settled + 1);
+}
+
+#[test]
+fn reporting_the_same_output_size_does_not_start_a_resize() {
+    let mut h = Harness::new((400, 200));
+    let draws = Rc::new(Cell::new(0));
+    let leaf = ReadsBox {
+        draws: draws.clone(),
+    }
+    .add(&mut h.rsc);
+    h.set_root(leaf);
+    let settled = draws.get();
+
+    h.resize((400, 200));
+
+    assert!(!h.needs_redraw());
+    h.frame();
+    assert_eq!(draws.get(), settled);
+}
+
+#[test]
+fn narrowing_the_output_reflows_text_and_relays_out_around_it() {
+    let mut h = Harness::new((600, 400));
+    let para = wtext(
+        "Wrapping shapes one source into as many lines as its container leaves \
+        room for, so the height of a paragraph is an answer rather than a setting.",
+    )
+    .size(20)
+    .wrap(true)
+    .add(&mut h.rsc);
+    let below = rect(Color::RED).add(&mut h.rsc);
+    h.set_root((para, below).span(Dir::DOWN));
+    let top = h.region(&below).expect("drew nothing").top_left.y;
+
+    h.resize((300, 400));
+    h.frame();
+
+    let lower = h.region(&below).expect("drew nothing").top_left.y;
+    assert!(lower > top, "same words, half the width: {top} -> {lower}");
+}
+
+#[test]
+fn a_change_two_levels_under_its_reader_still_reaches_it() {
+    let mut h = Harness::new((400, 400));
+    // Every wrapper up to the outer pad read the size below it, so the outer
+    // pad is what draws again -- and the span it hands the box to is the same
+    // size as before, which is what lets a draw reuse its way past the leaf.
+    let (leaf, _) = counted(&mut h, Size::px((100, 100).into()), true);
+    let padded = leaf.pad(10).add(&mut h.rsc);
+    let below = rect(Color::RED).add(&mut h.rsc);
+    h.set_root((padded, below).span(Dir::DOWN).pad(12));
+    assert_corners!(h, below, (12, 132), (388, 388));
+
+    h.rsc[leaf].size = Size::px((100, 200).into());
+    h.frame();
+
+    assert_corners!(h, below, (12, 232), (388, 388));
+}
+
+/// Reads nothing of its box, so its drawing holds for any length, and has a
+/// child so that whatever asks about the subtree has one to reach.
+struct Stretchy {
+    inner: StrongWidget,
+    draws: Rc<Cell<usize>>,
+}
+
+impl Widget for Stretchy {
+    fn draw(&mut self, painter: &mut Painter) -> Size {
+        self.draws.set(self.draws.get() + 1);
+        painter.widget(&self.inner).size()
+    }
+}
+
+#[test]
+fn stretching_a_subtree_carries_the_children_in_it() {
+    let mut h = Harness::new((400, 400));
+    let first = rect(Color::RED).height(40).add(&mut h.rsc);
+    let inner = rect(Color::BLUE).add(&mut h.rsc);
+    let draws = Rc::new(Cell::new(0));
+    let outer = Stretchy {
+        inner: inner.add_strong(&mut h.rsc),
+        draws: draws.clone(),
+    }
+    .add(&mut h.rsc);
+    h.set_root((first, outer).span(Dir::DOWN));
+    let settled = draws.get();
+    assert_corners!(h, inner, (0, 40), (400, 400));
+
+    h.set_len(first, Axis::Y, 80);
+    h.frame();
+
+    assert_eq!(
+        draws.get(),
+        settled,
+        "its drawing follows its box, rather than being made again"
+    );
+    assert_corners!(h, outer, (0, 80), (400, 400));
+    assert_corners!(h, inner, (0, 80), (400, 400));
+}
+
+#[test]
+fn a_widened_row_redraws_what_reads_its_length_and_nothing_else() {
+    let mut h = Harness::new((400, 200));
+    // What a transcript row is: something whose shaping depends on the width
+    // it is given, beside something that only has to be the right shape.
+    let (wraps, wrap_draws) = counted(&mut h, Size::LEFTOVER, true);
+    let (backing, back_draws) = counted(&mut h, Size::LEFTOVER, false);
+    let row = (backing, wraps).span(Dir::RIGHT).add(&mut h.rsc);
+    let bar = rect(Color::RED).width(100).add(&mut h.rsc);
+    h.set_root((bar, row).span(Dir::RIGHT));
+    let (settled_wrap, settled_back) = (wrap_draws.get(), back_draws.get());
+
+    h.set_len(bar, Axis::X, 200);
+    h.frame();
+
+    // The span reads every child's size, so redrawing one takes the span
+    // with it -- and the span then measures and places the redrawn child.
+    assert!(wrap_draws.get() > settled_wrap, "reads the width it got");
+    assert_eq!(back_draws.get(), settled_back, "only has to be the shape");
+    assert_corners!(h, backing, (200, 0), (300, 200));
+    assert_corners!(h, wraps, (300, 0), (400, 200));
+}
+
+#[test]
+fn a_declared_length_child_is_not_redrawn_when_the_box_around_it_grows() {
+    let mut h = Harness::new((400, 200));
+    // Its box is a fixed 80 wherever the row's edges end up, so drawing it
+    // again would be for a width it does not have. The declared width is what
+    // lets the span say that without drawing it: a width the span learnt by
+    // drawing the child in its own box is only an answer for that box.
+    let (counter, draws) = counted(&mut h, Size::from((80, 200)), true);
+    let fixed = counter.width(80).add(&mut h.rsc);
+    let (leftover, _) = counted(&mut h, Size::LEFTOVER, false);
+    let row = (fixed, leftover).span(Dir::RIGHT).add(&mut h.rsc);
+    let bar = rect(Color::RED).width(100).add(&mut h.rsc);
+    h.set_root((bar, row).span(Dir::RIGHT));
+    let settled = draws.get();
+
+    h.set_len(bar, Axis::X, 200);
+    h.frame();
+
+    assert_eq!(draws.get(), settled, "its own length did not change");
+    assert_corners!(h, fixed, (200, 0), (280, 200));
+}
+
+/// A retained drawing belongs to the layer it was made on: asked for again
+/// on another one it has to be drawn there, since nothing about its geometry
+/// says it is in a list that paints at a different moment.
+#[test]
+fn a_widget_asked_again_on_another_layer_is_drawn_there() {
+    /// Draws its child on its own layer, then again one layer in -- which is
+    /// what a container measuring a child by drawing it used to do.
+    struct Twice(StrongWidget);
+
+    impl Widget for Twice {
+        fn draw(&mut self, painter: &mut Painter) -> Size {
+            let size = painter.widget(&self.0).size();
+            painter.child_layer();
+            painter.widget(&self.0);
+            size
+        }
+    }
+
+    let mut h = Harness::new((400, 200));
+    let (front, draws) = counted(&mut h, Size::from((100, 50)), false);
+    let outer = Twice(front.add_strong(&mut h.rsc)).add(&mut h.rsc);
+    h.set_root(outer);
+    h.frame();
+
+    assert_ne!(
+        h.render.active[&front.id()].layer,
+        h.render.active[&outer.id()].layer,
+        "the first drawing was kept, on the layer it was measured on"
+    );
+    assert_eq!(draws.get(), 2, "the second ask could not reuse the first");
+}
+
+/// Which is why `Stack` measures the child that sizes it on the layer that
+/// child draws on: one drawing, above the background it stacks over, rather
+/// than one on each layer and the wrong one kept.
+#[test]
+fn a_stacks_sizing_child_is_drawn_once_where_it_belongs() {
+    let mut h = Harness::new((400, 200));
+    let background = rect(Color::RED).add(&mut h.rsc);
+    let (front, draws) = counted(&mut h, Size::from((100, 50)), false);
+    let stack = Stack {
+        children: vec![
+            background.add_strong(&mut h.rsc),
+            front.add_strong(&mut h.rsc),
+        ],
+        size: StackSize::Child(1),
+    }
+    .add(&mut h.rsc);
+    h.set_root(stack);
+    h.frame();
+
+    let layer = |id| h.render.active[&id].layer;
+    assert_ne!(layer(front.id()), layer(stack.id()));
+    assert_ne!(layer(front.id()), layer(background.id()));
+    assert_eq!(draws.get(), 1);
+}
+
+/// A widget's own mask is not the one it inherited, and a redraw of it
+/// inherits the second: handing back the first is handing it its own mask to
+/// set a second time, which `set_mask` asserts against.
+#[test]
+fn a_masked_widget_redrawn_on_its_own_sets_its_mask_again() {
+    let mut h = Harness::new((400, 200));
+    let inner = rect(Color::BLUE).add(&mut h.rsc);
+    let masked = inner.masked().add(&mut h.rsc);
+    let other = rect(Color::RED).width(100).add(&mut h.rsc);
+    h.set_root((other, masked).span(Dir::RIGHT));
+    h.rsc.widgets_mut().get_dyn_mut(masked.id());
+    h.frame();
+    assert_corners!(h, inner, (100, 0), (400, 200));
+}

tests/cases/scroll.rs

@@ -0,0 +1,84 @@
+//! Scrolling moves content and stops at its ends.
+
+use iris::harness::{Harness, assert_corners};
+use iris::prelude::*;
+
+#[test]
+fn scrollable_enables_a_region_node_but_raw_scroll_does_not() {
+    let mut h = Harness::new((100, 100));
+    let default_child = ().add(&mut h.rsc);
+    let _default = default_child.scrollable().add(&mut h.rsc);
+    assert!(h.rsc.widgets().is_region_node(default_child));
+    h.rsc.widgets_mut().set_region_node(default_child, false);
+    assert!(!h.rsc.widgets().is_region_node(default_child));
+
+    let raw_child = ().add(&mut h.rsc);
+    let _raw = Scroll::new(raw_child.add_strong(&mut h.rsc), Axis::Y).add(&mut h.rsc);
+    assert!(!h.rsc.widgets().is_region_node(raw_child));
+
+    let explicit = ().region_node().add(&mut h.rsc);
+    assert!(h.rsc.widgets().is_region_node(explicit));
+}
+
+#[test]
+fn a_scrollable_child_can_drop_its_region_node() {
+    let mut h = Harness::new((400, 200));
+    let top = rect(Color::RED).height(200).add(&mut h.rsc);
+    let bottom = rect(Color::BLUE).height(200).add(&mut h.rsc);
+    let content = (top, bottom).span(Dir::DOWN).add(&mut h.rsc);
+    h.set_root(content.scrollable());
+    h.rsc.widgets_mut().set_region_node(content, false);
+    h.frame();
+
+    h.move_to((200, 100));
+    h.scroll((0, 1));
+    h.frame();
+
+    assert!(!h.rsc.widgets().is_region_node(content));
+    assert_corners!(h, top, (0, -150), (400, 50));
+}
+
+#[test]
+fn a_wheel_scrolls_the_content_and_stops_at_its_end() {
+    let mut h = Harness::new((400, 200));
+    // Twice the window's height, so there is 200 to scroll.
+    let top = rect(Color::RED).height(200).add(&mut h.rsc);
+    let bottom = rect(Color::BLUE).height(200).add(&mut h.rsc);
+    h.set_root((top, bottom).span(Dir::DOWN).scrollable());
+    h.move_to((200, 100));
+
+    // `Scroll` starts snapped to the end.
+    assert_corners!(h, top, (0, -200), (400, 0));
+
+    // The handler scales a wheel line by 50.
+    h.scroll((0, 1));
+    h.frame();
+    assert_corners!(h, top, (0, -150), (400, 50));
+
+    h.scroll((0, 10));
+    h.frame();
+    assert_corners!(h, top, (0, 0), (400, 200));
+}
+
+/// A widget that clips to its box may not report more than the box: its
+/// parent would place the part it cut off, and the framework would put a
+/// drawing longer than its box somewhere. `Masked` is the second of these
+/// after `Scroll`, and the assertion in `draw_at` is what says so.
+#[test]
+#[should_panic = "clips to"]
+fn a_clipping_widget_reporting_more_than_its_box_is_caught() {
+    struct Clipper(StrongWidget);
+
+    impl Widget for Clipper {
+        fn draw(&mut self, painter: &mut Painter) -> Size {
+            painter.set_mask(painter.region());
+            painter.widget(&self.0).size()
+        }
+    }
+
+    let mut h = Harness::new((100, 100));
+    let tall = rect(Color::RED).height(400).add_strong(&mut h.rsc);
+    let clipper = Clipper(tall).add(&mut h.rsc);
+    h.set_root(clipper);
+    h.frame();
+}

tests/cases/unsettled.rs

@@ -0,0 +1,616 @@
+//! The smallest trees that laid out differently warm than cold, each shrunk
+//! by `tests/shrink.rs` from hundreds of widgets. The first two are a cold
+//! frame that had not settled: a wrapping text shaped at a width it was
+//! measured in rather than the one it was given. The rest are a widget
+//! measured again in a box its own answer had decided, where the old answer
+//! is a fixed point whatever the content now says. The last three are
+//! neither: one box length, composed two ways, landing either side of the
+//! boundary that decided whether a child was drawn at all, and two boxes
+//! reached through a region node's own entry rather than through the offer
+//! that node was given. The last is a wrapping text handed back the width
+//! it measured, rounded to a step below the line it measured there.
+
+use iris::harness::Harness;
+use iris::prelude::*;
+use iris::random::Branch;
+
+/// Six widgets, shrunk from a 402-widget tree the fuzzer found. Nothing about
+/// the tree changes -- every widget is marked for redraw and the frame is
+/// taken again -- so no box may move, and a warm frame has to land where a
+/// cold one does.
+fn plant(h: &mut Harness) -> Vec<WidgetId> {
+    let plain = wtext("Wrapping").size(16).wrap(false).add(&mut h.rsc);
+    let wrapped = wtext("Wrapping shapes").size(16).wrap(true).add(&mut h.rsc);
+    let sized = wrapped.width(76).add(&mut h.rsc);
+    let aligned = sized;
+    h.rsc
+        .widgets_mut()
+        .set_alignment(sized, Axis::X, AxisAlign::POS);
+    h.rsc
+        .widgets_mut()
+        .set_alignment(sized, Axis::Y, AxisAlign::POS);
+    let stack = Stack {
+        children: vec![plain.add_strong(&mut h.rsc), aligned.add_strong(&mut h.rsc)],
+        size: StackSize::Child(0),
+    }
+    .add(&mut h.rsc);
+    let root = (stack,).span(Dir::RIGHT).add(&mut h.rsc);
+    h.set_root(root);
+    vec![
+        plain.id(),
+        wrapped.id(),
+        sized.id(),
+        aligned.id(),
+        stack.id(),
+        root.id(),
+    ]
+}
+
+/// The first frame does not reach the layout a second one does, so "cold" is
+/// not a fixed point and comparing against it compares against a tree that
+/// has not settled.
+#[test]
+fn one_frame_is_enough() {
+    let mut h = Harness::new((640, 900));
+    let ids = plant(&mut h);
+    let first = h.region(&ids[1]).unwrap();
+    for _ in 0..3 {
+        for &id in &ids {
+            h.rsc.widgets_mut().get_dyn_mut(id);
+        }
+        h.frame();
+    }
+    let settled = h.region(&ids[1]).unwrap();
+    println!(
+        "first frame {} tall, settled {} tall",
+        first.bot_right.y - first.top_left.y,
+        settled.bot_right.y - settled.top_left.y
+    );
+    assert_eq!(
+        first.bot_right.y - first.top_left.y,
+        settled.bot_right.y - settled.top_left.y,
+        "the first frame had not finished laying out"
+    );
+}
+
+#[test]
+fn repainting_everything_moves_nothing() {
+    let mut warm = Harness::new((640, 900));
+    let ids = plant(&mut warm);
+    for &id in &ids {
+        warm.rsc.widgets_mut().get_dyn_mut(id);
+    }
+    warm.frame();
+
+    let mut cold = Harness::new((640, 900));
+    let cold_ids = plant(&mut cold);
+
+    let mut wrong = Vec::new();
+    for (i, (&w, &c)) in ids.iter().zip(&cold_ids).enumerate() {
+        let (got, want) = (warm.region(&w), cold.region(&c));
+        if got != want {
+            wrong.push(format!("widget {i}: warm {got:?} cold {want:?}"));
+        }
+    }
+    assert!(wrong.is_empty(), "{}", wrong.join("\n"));
+}
+
+/// Six widgets, shrunk from 905. Everything inside the declared 189x176 box
+/// is the same size whatever the output is, so a resize may not change any of
+/// it -- but the text comes out 3.92px narrower warm than cold.
+fn plant_fixed(h: &mut Harness) -> Vec<WidgetId> {
+    let words = "Wrapping shapes one source into as many lines as the box leaves";
+    let text = wtext(words).size(16).wrap(true).add(&mut h.rsc);
+    let aligned = text;
+    h.rsc
+        .widgets_mut()
+        .set_alignment(text, Axis::X, AxisAlign::NEG);
+    let inner = (aligned,).span(Dir::RIGHT).add(&mut h.rsc);
+    let sized = inner.sized((189, 176)).add(&mut h.rsc);
+    let filler = rect(Color::RED).add(&mut h.rsc);
+    let root = (filler, sized).span(Dir::RIGHT).add(&mut h.rsc);
+    h.state.root = Some(root.add_strong(&mut h.rsc));
+    vec![
+        text.id(),
+        aligned.id(),
+        inner.id(),
+        sized.id(),
+        filler.id(),
+        root.id(),
+    ]
+}
+
+#[test]
+fn a_resize_does_not_reach_inside_a_box_of_declared_pixels() {
+    let mut warm = Harness::new((1920, 1200));
+    let ids = plant_fixed(&mut warm);
+    warm.frame();
+    warm.resize((640, 900));
+    warm.frame();
+
+    let mut cold = Harness::new((640, 900));
+    let cold_ids = plant_fixed(&mut cold);
+    cold.frame();
+
+    let mut wrong = Vec::new();
+    for (i, (&w, &c)) in ids.iter().zip(&cold_ids).enumerate() {
+        let (got, want) = (warm.region(&w), cold.region(&c));
+        if got != want {
+            wrong.push(format!("widget {i}: warm {got:?} cold {want:?}"));
+        }
+    }
+    assert!(wrong.is_empty(), "{}", wrong.join("\n"));
+}
+
+/// Four widgets, shrunk from 486. A span's two children are swapped: warm by
+/// moving them, cold by growing them that way. Same widgets, same sizes, one
+/// ends up 29.9px from where the other does.
+fn plant_pair(h: &mut Harness, swapped: bool) -> (Vec<WidgetId>, WeakWidget<Span>) {
+    let wrapped = wtext("Wrapping shapes one source into as many lines")
+        .size(16)
+        .wrap(true)
+        .add(&mut h.rsc);
+    let plain = wtext("one line, overflowing whatever it is given")
+        .size(16)
+        .wrap(false)
+        .add(&mut h.rsc);
+    let first: StrongWidget = wrapped.add_strong(&mut h.rsc);
+    let second: StrongWidget = plain.add_strong(&mut h.rsc);
+    let children = match swapped {
+        true => vec![second, first],
+        false => vec![first, second],
+    };
+    let span = Span {
+        children,
+        dir: Dir::RIGHT,
+        gap: Px::ZERO,
+    }
+    .add(&mut h.rsc);
+    let span_handle = span;
+    let aligned = span;
+    h.rsc
+        .widgets_mut()
+        .set_alignment(span, Axis::X, AxisAlign::CENTER);
+    h.state.root = Some(aligned.add_strong(&mut h.rsc));
+    (
+        vec![wrapped.id(), plain.id(), span.id(), aligned.id()],
+        span_handle,
+    )
+}
+
+#[test]
+fn swapping_two_children_lands_where_growing_them_that_way_does() {
+    let mut warm = Harness::new((640, 900));
+    let (ids, span) = plant_pair(&mut warm, false);
+    warm.frame();
+    warm.rsc[span].children.rotate_left(1);
+    warm.frame();
+
+    let mut cold = Harness::new((640, 900));
+    let (cold_ids, _) = plant_pair(&mut cold, true);
+    cold.frame();
+
+    let mut wrong = Vec::new();
+    for (i, (&w, &c)) in ids.iter().zip(&cold_ids).enumerate() {
+        let (got, want) = (warm.region(&w), cold.region(&c));
+        if got != want {
+            wrong.push(format!("widget {i}: warm {got:?} cold {want:?}"));
+        }
+    }
+    assert!(wrong.is_empty(), "{}", wrong.join("\n"));
+}
+
+/// Eight widgets, shrunk from 80. The scroll decides how wide to make its
+/// content from what the content says, and hands that box down through a
+/// pass-through; the span under it was given that box once, so nothing at its
+/// own edge says the box was its own answer.
+fn plant_scrolled(h: &mut Harness, swapped: bool) -> (Vec<WidgetId>, [WeakWidget<Span>; 2]) {
+    let words = "Wrapping shapes one source into as many lines as the box leaves room for,";
+    let text = wtext(words).size(16).wrap(true).add(&mut h.rsc);
+    let filler = rect(Color::RED).add(&mut h.rsc);
+    let mut inner_children: Vec<StrongWidget> =
+        vec![text.add_strong(&mut h.rsc), filler.add_strong(&mut h.rsc)];
+    if swapped {
+        inner_children.rotate_left(1);
+    }
+    let inner = Span {
+        children: inner_children,
+        dir: Dir::RIGHT,
+        gap: Px::ZERO,
+    }
+    .add(&mut h.rsc);
+    let block = rect(Color::RED).add(&mut h.rsc);
+    let fixed = block.width(87).add(&mut h.rsc);
+    let mut outer_children: Vec<StrongWidget> =
+        vec![fixed.add_strong(&mut h.rsc), inner.add_strong(&mut h.rsc)];
+    if swapped {
+        outer_children.rotate_left(1);
+    }
+    let outer = Span {
+        children: outer_children,
+        dir: Dir::RIGHT,
+        gap: Px::ZERO,
+    }
+    .add(&mut h.rsc);
+    // Carried no rule even before rules were a property: it is here to be a
+    // widget between the span and the scroll, not to declare anything.
+    let through = (outer,).span(Dir::RIGHT).add(&mut h.rsc);
+    let scroll = Scroll::new(through.add_strong(&mut h.rsc), Axis::X).add(&mut h.rsc);
+    h.state.root = Some(scroll.add_strong(&mut h.rsc));
+    (
+        vec![
+            text.id(),
+            filler.id(),
+            inner.id(),
+            block.id(),
+            fixed.id(),
+            outer.id(),
+            through.id(),
+            scroll.id(),
+        ],
+        [inner, outer],
+    )
+}
+
+#[test]
+fn a_span_given_the_box_its_answer_decided_matches_a_cold_layout() {
+    let mut warm = Harness::new((640, 900));
+    let (ids, spans) = plant_scrolled(&mut warm, false);
+    warm.frame();
+    for span in spans {
+        warm.rsc[span].children.rotate_left(1);
+    }
+    warm.frame();
+
+    let mut cold = Harness::new((640, 900));
+    let (cold_ids, _) = plant_scrolled(&mut cold, true);
+    cold.frame();
+
+    let mut wrong = Vec::new();
+    for (i, (&w, &c)) in ids.iter().zip(&cold_ids).enumerate() {
+        let (got, want) = (warm.region(&w), cold.region(&c));
+        if got != want {
+            wrong.push(format!("widget {i}: warm {got:?} cold {want:?}"));
+        }
+    }
+    assert!(wrong.is_empty(), "{}", wrong.join("\n"));
+}
+
+/// Reports a width derived from the box it is asked in. Reading through the
+/// painter is its declaration that the answer holds for that width only.
+struct Wider {
+    extra: f32,
+}
+
+impl Widget for Wider {
+    fn draw(&mut self, painter: &mut Painter) -> Size {
+        Size {
+            x: LayoutLen {
+                px: painter.px_len(Axis::X) + Px::from_f32(self.extra),
+                ..LayoutLen::ZERO
+            },
+            y: LayoutLen::LEFTOVER,
+        }
+    }
+}
+
+fn plant_wider(h: &mut Harness, extra: f32) -> (WeakWidget<Wider>, WidgetId) {
+    let content = Wider { extra }.add(&mut h.rsc);
+    let scroll = Scroll::new(content.add_strong(&mut h.rsc), Axis::X).add(&mut h.rsc);
+    let root = scroll;
+    h.rsc
+        .widgets_mut()
+        .set_alignment(scroll, Axis::X, AxisAlign::NEG);
+    h.set_root(root);
+    (content, scroll.id())
+}
+
+#[test]
+fn a_scrolls_retained_answer_is_the_one_a_cold_layout_asks_for() {
+    let mut warm = Harness::new((100, 100));
+    let (content, scroll) = plant_wider(&mut warm, 50.0);
+    warm.rsc[content].extra = 70.0;
+    warm.frame();
+
+    let mut cold = Harness::new((100, 100));
+    let (_, cold_scroll) = plant_wider(&mut cold, 70.0);
+
+    assert_eq!(warm.region(&scroll), cold.region(&cold_scroll));
+}
+
+/// Six widgets, shrunk from 266. `measured`'s box is exactly the height of its
+/// one fixed child, which is the box a parent sizing itself from that answer
+/// hands back -- so whether its leftover-only child was drawn at all came down
+/// to the 0.00003 px the composed length differs by, one way warm and the
+/// other cold.
+fn plant_boundary(h: &mut Harness, swapped: bool) -> (Vec<WidgetId>, [WeakWidget<Span>; 2]) {
+    let filler = rect(Color::RED).add(&mut h.rsc);
+    let plain = wtext("one line, overflowing whatever it is given")
+        .size(16)
+        .wrap(false)
+        .add(&mut h.rsc);
+    let mut pair: Vec<StrongWidget> =
+        vec![filler.add_strong(&mut h.rsc), plain.add_strong(&mut h.rsc)];
+    if swapped {
+        pair.rotate_left(1);
+    }
+    let measured = Span {
+        children: pair,
+        dir: Dir::DOWN,
+        gap: Px::ZERO,
+    }
+    .add(&mut h.rsc);
+    // Takes the whole box on its own, so the span above has nothing left to
+    // divide and `measured` is given exactly the text's height.
+    let whole = rect(Color::RED).add(&mut h.rsc);
+    h.rsc
+        .widgets_mut()
+        .set_size_rules(whole, None, Some(LayoutLen::rel(1.0)));
+    let mut inner_children: Vec<StrongWidget> = vec![
+        measured.add_strong(&mut h.rsc),
+        whole.add_strong(&mut h.rsc),
+    ];
+    if swapped {
+        inner_children.rotate_left(1);
+    }
+    let inner = Span {
+        children: inner_children,
+        dir: Dir::DOWN,
+        gap: Px::ZERO,
+    }
+    .add(&mut h.rsc);
+    h.rsc
+        .widgets_mut()
+        .set_size_rules(inner, None, Some(LayoutLen::px(198.0)));
+    // One more span above it: without a box composed through it, both trees
+    // round the same way and the boundary is never crossed.
+    let outer = (inner,).span(Dir::DOWN).add(&mut h.rsc);
+    h.set_root(outer);
+    (
+        vec![
+            filler.id(),
+            plain.id(),
+            measured.id(),
+            whole.id(),
+            inner.id(),
+            outer.id(),
+        ],
+        [measured, inner],
+    )
+}
+
+#[test]
+fn a_box_that_only_rounds_past_its_fixed_children_leaves_nothing_over() {
+    let mut warm = Harness::new((640, 900));
+    let (ids, spans) = plant_boundary(&mut warm, false);
+    warm.frame();
+    for span in spans {
+        warm.rsc[span].children.rotate_left(1);
+    }
+    warm.frame();
+
+    let mut cold = Harness::new((640, 900));
+    let (cold_ids, _) = plant_boundary(&mut cold, true);
+    cold.frame();
+
+    let mut wrong = Vec::new();
+    for (i, (&w, &c)) in ids.iter().zip(&cold_ids).enumerate() {
+        let (got, want) = (warm.region(&w), cold.region(&c));
+        if got != want {
+            wrong.push(format!("widget {i}: warm {got:?} cold {want:?}"));
+        }
+    }
+    assert!(wrong.is_empty(), "{}", wrong.join("\n"));
+}
+
+/// Five widgets, shrunk by `tests/shrink.rs` from the 277 the oracle's seed
+/// 18 grows at depth 6. A scroll inside a scroll, the inner one owning a
+/// movable region of its own, and only its text marked for redraw. Nothing
+/// about the tree changes, so no box may.
+fn plant_nested_scrolls(h: &mut Harness) -> Vec<WidgetId> {
+    let text = wtext("one line, overflowing whatever it is given")
+        .size(16)
+        .wrap(false)
+        .add(&mut h.rsc);
+    let inner = Scroll::new(text.add_strong(&mut h.rsc), Axis::X).add(&mut h.rsc);
+    h.rsc.widgets_mut().set_region_node(inner.id(), true);
+    let filler = rect(Color::RED).add(&mut h.rsc);
+    h.rsc.widgets_mut().set_size_rules(
+        filler.id(),
+        Some(LayoutLen::px(87.0)),
+        Some(LayoutLen::px(24.0)),
+    );
+    let span = Span {
+        children: vec![inner.add_strong(&mut h.rsc), filler.add_strong(&mut h.rsc)],
+        dir: Dir::DOWN,
+        gap: Px::ZERO,
+    }
+    .add(&mut h.rsc);
+    let root = Scroll::new(span.add_strong(&mut h.rsc), Axis::Y).add(&mut h.rsc);
+    h.set_root(root);
+    vec![text.id(), inner.id(), filler.id(), span.id(), root.id()]
+}
+
+/// A local redraw asks a dirty widget in the box its parent gave it, and only
+/// where that box is as long as the one it was offered; anything else is a
+/// question its parent has to ask. This inner scroll's offer is the outer
+/// scroll's whole viewport and the box it was given is 24px shorter -- the
+/// height of the sized child the outer scroll snaps to the end of -- so what
+/// it must not do is settle itself. It was drawn at its offer once, and the
+/// inner scroll and its text stayed 24px too low.
+#[test]
+fn redrawing_one_widget_does_not_move_what_scrolls_around_it() {
+    let mut warm = Harness::new((900, 1200));
+    let ids = plant_nested_scrolls(&mut warm);
+    warm.rsc.widgets_mut().get_dyn_mut(ids[0]);
+    warm.frame();
+
+    let mut cold = Harness::new((900, 1200));
+    let cold_ids = plant_nested_scrolls(&mut cold);
+
+    let mut wrong = Vec::new();
+    for (i, (&w, &c)) in ids.iter().zip(&cold_ids).enumerate() {
+        let (got, want) = (warm.region(&w), cold.region(&c));
+        if got != want {
+            wrong.push(format!("widget {i}: warm {got:?} cold {want:?}"));
+        }
+    }
+    assert!(wrong.is_empty(), "{}", wrong.join("\n"));
+}
+
+/// Ten widgets, of the shape `tests/shrink.rs` reduces the oracle's seed 220
+/// to. The pad owns a movable region and is the scroll's content, so the box
+/// the scroll places it in is as long as that content while the box it was
+/// offered is the viewport -- and with no padding to tell those two apart,
+/// the span inside it looked like it was still at its offer. So everything
+/// under the pad was asked again in the *placed* box, the offer resolving
+/// against the node's own entry, which holds that box: the texts kept the
+/// widths they had, the content stayed the length those widths make, and the
+/// old answer confirmed itself. What the branch adds is a tree that differs
+/// rather than a box that moved, since a probe measured at the wrong width
+/// takes the other side.
+fn plant_under_a_node(h: &mut Harness, swapped: bool) -> (Vec<WidgetId>, [WeakWidget<Span>; 2]) {
+    let probe = rect(Color::RED).add(&mut h.rsc);
+    let wide = rect(Color::GREEN).add(&mut h.rsc);
+    let narrow = rect(Color::BLUE).add(&mut h.rsc);
+    let branch = Branch {
+        probe: probe.add_strong(&mut h.rsc),
+        wide: wide.add_strong(&mut h.rsc),
+        narrow: narrow.add_strong(&mut h.rsc),
+        threshold: 213.0,
+    }
+    .add(&mut h.rsc);
+    let wrapped = wtext(
+        "Wrapping shapes one source into as many lines as the box \
+         leaves room for, so a paragraph's height is an answer and not a setting.",
+    )
+    .size(16)
+    .wrap(true)
+    .add(&mut h.rsc);
+    let plain = wtext("one line, overflowing whatever it is given")
+        .size(16)
+        .wrap(false)
+        .add(&mut h.rsc);
+    let row = |h: &mut Harness, mut children: Vec<StrongWidget>| {
+        if swapped {
+            children.rotate_left(1);
+        }
+        Span {
+            children,
+            dir: Dir::RIGHT,
+            gap: Px::ZERO,
+        }
+        .add(&mut h.rsc)
+    };
+    let texts: Vec<StrongWidget> =
+        vec![wrapped.add_strong(&mut h.rsc), plain.add_strong(&mut h.rsc)];
+    let inner = row(h, texts);
+    let pair: Vec<StrongWidget> = vec![branch.add_strong(&mut h.rsc), inner.add_strong(&mut h.rsc)];
+    let outer = row(h, pair);
+    let pad = Pad {
+        padding: Padding::ZERO,
+        inner: outer.add_strong(&mut h.rsc),
+    }
+    .add(&mut h.rsc);
+    h.rsc.widgets_mut().set_region_node(pad.id(), true);
+    let root = Scroll::new(pad.add_strong(&mut h.rsc), Axis::X).add(&mut h.rsc);
+    h.set_root(root);
+    (
+        vec![
+            probe.id(),
+            wide.id(),
+            narrow.id(),
+            branch.id(),
+            wrapped.id(),
+            plain.id(),
+            inner.id(),
+            outer.id(),
+            pad.id(),
+            root.id(),
+        ],
+        [outer, inner],
+    )
+}
+
+#[test]
+fn a_widget_under_a_region_node_is_asked_in_the_box_that_node_was_offered() {
+    let mut warm = Harness::new((900, 1200));
+    let (ids, spans) = plant_under_a_node(&mut warm, false);
+    warm.frame();
+    for span in spans {
+        warm.rsc[span].children.rotate_left(1);
+    }
+    warm.frame();
+
+    let mut cold = Harness::new((900, 1200));
+    let (cold_ids, _) = plant_under_a_node(&mut cold, true);
+    cold.frame();
+
+    let mut wrong = Vec::new();
+    for (i, (&w, &c)) in ids.iter().zip(&cold_ids).enumerate() {
+        let (got, want) = (warm.region(&w), cold.region(&c));
+        if got != want {
+            wrong.push(format!("widget {i}: warm {got:?} cold {want:?}"));
+        }
+    }
+    assert!(wrong.is_empty(), "{}", wrong.join("\n"));
+}
+
+const PARAGRAPH: &str = "Wrapping shapes one source into as many lines as the \
+    box leaves room for, so a paragraph's height is an answer and not a setting.";
+
+/// Eight widgets, shrunk from a 118-widget tree (seed 1121, depth 4,
+/// `shuffle-swap-for-three`). The stack takes its size from the span above,
+/// the span takes its width from the longest line of the texts in it, and
+/// the text below the span is then wrapped at that width -- so a width the
+/// shaper measured comes back to it as the box to break in.
+fn plant_a_measured_width(h: &mut Harness, swapped: bool) -> (WeakWidget<Span>, WidgetId) {
+    let first: StrongWidget = rect(Color::YELLOW).add_strong(&mut h.rsc);
+    let mut inner = Span::empty(Dir::UP);
+    inner.children = match swapped {
+        true => swapped_in(h),
+        false => vec![first],
+    };
+    let inner = inner.height(142).add(&mut h.rsc);
+    let text = wtext(PARAGRAPH).size(16).wrap(true).add(&mut h.rsc);
+    let stack = Stack {
+        children: vec![inner.add_strong(&mut h.rsc), text.add_strong(&mut h.rsc)],
+        size: StackSize::Child(0),
+    }
+    .add(&mut h.rsc);
+    h.set_root((stack,).span(Dir::DOWN).width(195));
+    (inner, text.id())
+}
+
+/// What the span holds once its children have been swapped, which is what
+/// the warm tree is changed to and what the cold one is grown with.
+fn swapped_in(h: &mut Harness) -> Vec<StrongWidget> {
+    let paragraph = |h: &mut Harness| -> StrongWidget {
+        wtext(PARAGRAPH).size(16).wrap(true).add_strong(&mut h.rsc)
+    };
+    vec![
+        paragraph(h),
+        rect(Color::YELLOW).add_strong(&mut h.rsc),
+        paragraph(h),
+    ]
+}
+
+/// A text handed back the width it measured breaks there the way it broke
+/// when it measured it. The width the shaper answers is not on the grid, and
+/// a report rounded to the nearest step is under the longest line half the
+/// time: a warm tree then keeps a break made in a wider box while a cold one
+/// makes a narrower break in the same box, and the paragraph gains a line.
+#[test]
+fn a_text_is_given_back_a_box_the_line_it_measured_fits_in() {
+    let mut warm = Harness::new((900, 1200));
+    let (inner, text) = plant_a_measured_width(&mut warm, false);
+    warm.frame();
+    warm.rsc[inner].children = swapped_in(&mut warm);
+    warm.frame();
+
+    let mut cold = Harness::new((900, 1200));
+    let (_, cold_text) = plant_a_measured_width(&mut cold, true);
+    cold.frame();
+
+    assert_eq!(warm.region(&text), cold.region(&cold_text));
+}

tests/chain_cost.rs

@@ -0,0 +1,223 @@
+//! What the vertex shader's move-chain walk costs, against how many nested
+//! region nodes a primitive resolves through.
+//!
+//!     cargo test --release --test chain_cost -- --ignored --nocapture
+//!
+//! Timed on the GPU with timestamp queries rather than by the clock: wall time
+//! here varied by 2x between runs of one unchanged binary. The pass is
+//! submitted and waited on, so this is the GPU's cost and not the recording
+//! loop's -- which is what `draw_cost.rs` measures instead.
+//!
+//! The instances are two pixels wide so that vertex work dominates; a chain
+//! walk that does not show up against small quads will not show up against
+//! anything.
+//!
+//! The instance is leaked deliberately, for the reason `draw_cost.rs` gives.
+
+use iris::prelude::*;
+use iris_core::{
+    Len, MaskIdx, MoveIdx, PrimitiveInst, RectPrimitive, UiData, UiRegion, UiRenderNode,
+    UiRenderState, UiSpan,
+};
+use wgpu::{Color as GpuColor, *};
+
+const SIZE: u32 = 1024;
+const INSTANCES: usize = 200_000;
+const FRAMES: u32 = 20;
+/// Reported as the best of this many batches, since the mean moves by more
+/// than the thing being measured.
+const BATCHES: u32 = 8;
+
+fn gpu() -> Option<(Device, Queue, f32)> {
+    let all = Instance::new(InstanceDescriptor::new_without_display_handle());
+    let instance = match pollster::block_on(all.request_adapter(&RequestAdapterOptions::default()))
+    {
+        Ok(_) => all,
+        Err(_) => Instance::new(InstanceDescriptor {
+            backends: Backends::GL,
+            ..InstanceDescriptor::new_without_display_handle()
+        }),
+    };
+    let instance: &'static Instance = Box::leak(Box::new(instance));
+    let adapter =
+        pollster::block_on(instance.request_adapter(&RequestAdapterOptions::default())).ok()?;
+    if !adapter.features().contains(Features::TIMESTAMP_QUERY) {
+        println!("no timestamp queries on {:?}", adapter.get_info().name);
+        return None;
+    }
+    println!("adapter: {:?}", adapter.get_info().name);
+    let (device, queue) = pollster::block_on(adapter.request_device(&DeviceDescriptor {
+        required_features: Features::TIMESTAMP_QUERY,
+        ..Default::default()
+    }))
+    .ok()?;
+    let period = queue.get_timestamp_period();
+    Some((device, queue, period))
+}
+
+fn config(format: TextureFormat) -> SurfaceConfiguration {
+    SurfaceConfiguration {
+        usage: TextureUsages::RENDER_ATTACHMENT,
+        format,
+        color_space: SurfaceColorSpace::Auto,
+        width: SIZE,
+        height: SIZE,
+        present_mode: PresentMode::Fifo,
+        desired_maximum_frame_latency: 2,
+        alpha_mode: CompositeAlphaMode::Auto,
+        view_formats: vec![],
+    }
+}
+
+/// A chain `depth` slots long, and instances that all resolve through its end.
+fn fill(ui: &mut UiData, render: &mut UiRenderState, depth: usize) {
+    let kind = ui.primitives.kind::<RectPrimitive>();
+    let id = ui.widgets.add_strong(Rect::new(UiColor::WHITE)).id();
+
+    let mut slot = MoveIdx::NONE;
+    for _ in 0..depth {
+        slot = render.moves.push(slot, UiRegion::FULL);
+    }
+
+    let px = |v: f32| Len::px(v);
+    for i in 0..INSTANCES {
+        let x = (i % (SIZE as usize / 2)) as f32 * 2.0;
+        let y = (i / (SIZE as usize / 2)) as f32;
+        render.layers.write(
+            0,
+            PrimitiveInst {
+                kind,
+                id,
+                primitive: RectPrimitive::color(UiColor::WHITE),
+                region: UiRegion::new(
+                    UiSpan::new(px(x), px(x + 2.0)),
+                    UiSpan::new(px(y), px(y + 1.0)),
+                ),
+                mask_idx: MaskIdx::NONE,
+                move_idx: slot,
+            },
+        );
+    }
+}
+
+/// Nanoseconds the pass took on the GPU, best of `BATCHES`.
+fn pass_cost(device: &Device, queue: &Queue, period: f32, depth: usize) -> f64 {
+    let format = TextureFormat::Bgra8Unorm;
+    let mut node = UiRenderNode::new(device, &config(format));
+    let mut ui = UiData::default();
+    let mut render = UiRenderState::new();
+    fill(&mut ui, &mut render, depth);
+    node.update(device, queue, &mut ui, &mut render);
+
+    let target = device.create_texture(&TextureDescriptor {
+        label: Some("chain cost"),
+        size: Extent3d {
+            width: SIZE,
+            height: SIZE,
+            depth_or_array_layers: 1,
+        },
+        mip_level_count: 1,
+        sample_count: 1,
+        dimension: TextureDimension::D2,
+        format,
+        usage: TextureUsages::RENDER_ATTACHMENT,
+        view_formats: &[],
+    });
+    let view = target.create_view(&TextureViewDescriptor::default());
+
+    let queries = device.create_query_set(&QuerySetDescriptor {
+        label: Some("chain cost"),
+        ty: QueryType::Timestamp,
+        count: 2,
+    });
+    let resolved = device.create_buffer(&BufferDescriptor {
+        label: Some("resolved"),
+        size: 16,
+        usage: BufferUsages::QUERY_RESOLVE | BufferUsages::COPY_SRC,
+        mapped_at_creation: false,
+    });
+    let readback = device.create_buffer(&BufferDescriptor {
+        label: Some("readback"),
+        size: 16,
+        usage: BufferUsages::MAP_READ | BufferUsages::COPY_DST,
+        mapped_at_creation: false,
+    });
+
+    let frame = || {
+        let mut encoder = device.create_command_encoder(&CommandEncoderDescriptor::default());
+        {
+            let pass = &mut encoder.begin_render_pass(&RenderPassDescriptor {
+                label: None,
+                color_attachments: &[Some(RenderPassColorAttachment {
+                    view: &view,
+                    resolve_target: None,
+                    ops: Operations {
+                        load: LoadOp::Clear(GpuColor::BLACK),
+                        store: StoreOp::Store,
+                    },
+                    depth_slice: None,
+                })],
+                depth_stencil_attachment: None,
+                timestamp_writes: Some(RenderPassTimestampWrites {
+                    query_set: &queries,
+                    beginning_of_pass_write_index: Some(0),
+                    end_of_pass_write_index: Some(1),
+                }),
+                occlusion_query_set: None,
+                multiview_mask: None,
+            });
+            node.draw(pass);
+        }
+        encoder.resolve_query_set(&queries, 0..2, &resolved, 0);
+        encoder.copy_buffer_to_buffer(&resolved, 0, &readback, 0, 16);
+        queue.submit(Some(encoder.finish()));
+
+        let slice = readback.slice(..);
+        slice.map_async(MapMode::Read, |_| {});
+        let _ = device.poll(PollType::Wait {
+            submission_index: None,
+            timeout: None,
+        });
+        let ns = {
+            let view = slice.get_mapped_range().expect("timestamps did not map");
+            let stamps: [u64; 2] = [
+                u64::from_le_bytes(view[..8].try_into().unwrap()),
+                u64::from_le_bytes(view[8..16].try_into().unwrap()),
+            ];
+            (stamps[1].saturating_sub(stamps[0])) as f64 * period as f64
+        };
+        readback.unmap();
+        ns
+    };
+
+    frame();
+    let mut best = f64::MAX;
+    for _ in 0..BATCHES {
+        let mut total = 0.0;
+        for _ in 0..FRAMES {
+            total += frame();
+        }
+        best = best.min(total / FRAMES as f64);
+    }
+    best
+}
+
+#[test]
+#[ignore = "measurement, not a check"]
+fn chain_cost_by_depth() {
+    let Some((device, queue, period)) = gpu() else {
+        println!("no gpu with timestamps; nothing measured");
+        return;
+    };
+    println!("{INSTANCES} instances, {SIZE}x{SIZE}, best of {BATCHES} batches");
+    let mut base = None;
+    for depth in [1, 2, 4, 8, 16, 32, 64] {
+        let ns = pass_cost(&device, &queue, period, depth);
+        let base = *base.get_or_insert(ns);
+        println!(
+            "depth {depth:>3}: {:>9.1} us   {:+6.1}% against depth 1",
+            ns / 1000.0,
+            (ns - base) / base * 100.0
+        );
+    }
+}

tests/draw_cost.rs

@@ -22,8 +22,8 @@ use std::time::Instant;
 
 use iris::prelude::*;
 use iris_core::{
-    GlyphPrimitive, MaskIdx, PrimitiveInst, RectPrimitive, TextureHandle, TexturePrimitive, UiData,
-    UiRegion, UiRenderNode, UiRenderState,
+    GlyphPrimitive, MaskIdx, MoveIdx, PrimitiveInst, RectPrimitive, TextureHandle,
+    TexturePrimitive, UiData, UiRegion, UiRenderNode, UiRenderState,
 };
 use wgpu::{Color as GpuColor, *};
 
@@ -95,6 +95,7 @@ fn fill(
                     primitive: RectPrimitive::color(UiColor::WHITE),
                     region: UiRegion::FULL,
                     mask_idx: MaskIdx::NONE,
+                    move_idx: MoveIdx::NONE,
                 },
             );
             render.layers.write(
@@ -111,6 +112,7 @@ fn fill(
                     },
                     region: UiRegion::FULL,
                     mask_idx: MaskIdx::NONE,
+                    move_idx: MoveIdx::NONE,
                 },
             );
         }
@@ -123,6 +125,7 @@ fn fill(
                     primitive: TexturePrimitive::from(h),
                     region: UiRegion::FULL,
                     mask_idx: MaskIdx::NONE,
+                    move_idx: MoveIdx::NONE,
                 },
             );
         }

tests/generated.rs

@@ -0,0 +1,126 @@
+//! Laying a tree out again has to land where growing it that way would.
+//!
+//! Every case is one of `scenario`'s, over the trees `iris::random` grows
+//! from a seed. The fast test takes a handful of seeds and the ignored one
+//! takes as many as it is asked for; both run the same cases the shrinker
+//! does over the same trees, so a seed that fails here is reduced by
+//!
+//!     SHRINK_SEED=<seed> SHRINK_DEPTH=<depth> SHRINK_CASE=<case> \
+//!       cargo test --release --test shrink -- --ignored --nocapture
+//!
+//! `IRIS_GENERATED_SEED`, `IRIS_GENERATED_SEEDS` and `IRIS_GENERATED_DEPTH`
+//! select what the long run covers.
+
+#[path = "scenario/mod.rs"]
+mod scenario;
+
+use iris::random::{Edits, plan};
+use scenario::{ALL, Case, diverges, env, over_seeds};
+
+/// How deep the generator branches. The generator widens two to four ways per
+/// level, so depth is exponential in width and a deep narrow tree is not
+/// reachable by raising this -- it buys more overlap between dependency
+/// paths, not more ancestry.
+fn depth() -> usize {
+    env("IRIS_GENERATED_DEPTH", 4)
+}
+
+/// The seeds the ordinary tests take. Seven that have never failed; 86,
+/// which a `Scroll` fixed point once settled differently on; and 20, which
+/// caught a locally redrawn widget being placed twice in the box its parent
+/// had already placed it in.
+const SEEDS: [u64; 10] = [1, 2, 3, 5, 8, 10, 13, 20, 86, 98];
+
+fn check(seed: u64, depth: usize, case: Case) {
+    let grown = plan(seed, depth, &Edits::default());
+    if let Some(how) = diverges(&grown, case, seed) {
+        panic!(
+            "seed {seed} at depth {depth} differs after {}: {how}\n\
+             reduce it with SHRINK_SEED={seed} SHRINK_DEPTH={depth} \
+             SHRINK_CASE={} cargo test --release --test shrink -- --ignored --nocapture",
+            case.name(),
+            case.name(),
+        );
+    }
+}
+
+macro_rules! case {
+    ($name:ident, $case:expr) => {
+        #[test]
+        fn $name() {
+            for seed in SEEDS {
+                check(seed, depth(), $case);
+            }
+        }
+    };
+}
+
+case!(
+    many_widgets_redrawing_at_once_leaves_every_box_where_it_was,
+    Case::RepaintSome
+);
+case!(
+    everything_redrawing_at_once_leaves_every_box_where_it_was,
+    Case::Repaint
+);
+case!(
+    a_resize_lands_where_starting_at_that_size_would,
+    Case::Resize
+);
+case!(
+    a_resize_and_a_repaint_land_where_starting_that_way_would,
+    Case::ResizeRepaint
+);
+case!(
+    a_size_change_after_a_resize_lands_the_same_way,
+    Case::ResizeSize
+);
+case!(
+    a_size_change_lands_where_growing_it_that_way_would,
+    Case::Size
+);
+case!(
+    every_size_changing_at_once_lands_where_growing_it_that_way_would,
+    Case::EverySize
+);
+case!(
+    an_alignment_change_lands_where_growing_it_that_way_would,
+    Case::Align
+);
+case!(
+    giving_and_taking_a_movable_region_rebuilds_what_resolves_it,
+    Case::RegionNode
+);
+case!(
+    reordering_a_span_lands_where_growing_it_that_way_would,
+    Case::Reorder
+);
+
+#[test]
+fn adding_and_removing_span_children_lands_where_growing_it_that_way_would() {
+    for case in ALL {
+        if matches!(case, Case::Shuffle(_)) {
+            for seed in SEEDS {
+                check(seed, depth(), case);
+            }
+        }
+    }
+}
+
+#[test]
+#[ignore = "as many seeds as it is asked for, rather than the nine the others check"]
+fn a_long_run_of_seeds_agrees() {
+    let depth = depth();
+    let seeds: Vec<u64> = match std::env::var("IRIS_GENERATED_SEED")
+        .ok()
+        .and_then(|v| v.parse().ok())
+    {
+        Some(seed) => vec![seed],
+        None => (1..=env("IRIS_GENERATED_SEEDS", 100_u64)).collect(),
+    };
+    over_seeds(seeds, |seed| {
+        for case in ALL {
+            check(seed, depth, case);
+        }
+    });
+}

tests/layout.rs

@@ -1,111 +0,0 @@
-//! Where a frame puts things, with no window to put them in.
-
-use iris::harness::{Harness, assert_corners};
-use iris::prelude::*;
-
-/// A fixed 100 wide, and the rest of the 400 to its neighbour.
-fn two_rects(h: &mut Harness) -> (WidgetId, WidgetId) {
-    let left = rect(Color::RED).width(100).add(&mut h.rsc);
-    let right = rect(Color::BLUE).add(&mut h.rsc);
-    h.set_root((left, right).span(Dir::RIGHT));
-    (left.id(), right.id())
-}
-
-#[test]
-fn a_span_gives_each_child_the_width_it_asked_for() {
-    let mut h = Harness::new((400, 200));
-    let (left, right) = two_rects(&mut h);
-
-    assert_corners!(h, left, (0, 0), (100, 200));
-    assert_corners!(h, right, (100, 0), (400, 200));
-}
-
-#[test]
-fn resizing_relays_out_against_the_new_output() {
-    let mut h = Harness::new((400, 200));
-    let (left, right) = two_rects(&mut h);
-
-    h.resize((800, 100));
-    assert!(h.needs_redraw());
-    h.frame();
-
-    assert_corners!(h, left, (0, 0), (100, 100));
-    assert_corners!(h, right, (100, 0), (800, 100));
-}
-
-#[test]
-fn an_empty_widget_takes_a_share_of_a_span() {
-    let mut h = Harness::new((400, 200));
-    let gap = ().add(&mut h.rsc);
-    let right = rect(Color::BLUE).width(100).add(&mut h.rsc);
-    h.set_root((gap, right).span(Dir::RIGHT));
-
-    assert_corners!(h, gap, (0, 0), (300, 200));
-    assert_corners!(h, right, (300, 0), (400, 200));
-}
-
-#[test]
-fn a_child_drawn_twice_moves_once() {
-    let mut h = Harness::new((400, 200));
-    // `Aligned` draws its child twice; listing it twice would move it twice.
-    let inner = rect(Color::BLUE).add(&mut h.rsc);
-    let centered = inner.center().width(200).add(&mut h.rsc);
-    let left = rect(Color::RED).width(100).add(&mut h.rsc);
-    h.set_root((left, centered).span(Dir::RIGHT));
-    assert_corners!(h, inner, (100, 0), (300, 200));
-
-    h.rsc[left].x = Some(Len::abs(150));
-    h.frame();
-
-    assert_corners!(h, inner, (150, 0), (350, 200));
-}
-
-#[test]
-fn a_resize_lands_where_a_cold_start_would() {
-    let build = |h: &mut Harness| {
-        let para = wtext(
-            "Wrapping shapes one source into as many lines as its container leaves room \
-             for, so the height of a paragraph is an answer rather than a setting.",
-        )
-        .size(20)
-        .wrap(true)
-        .pad(16)
-        .add(&mut h.rsc);
-        let below = rect(Color::RED).add(&mut h.rsc);
-        let root = (para, below).span(Dir::DOWN).pad(12);
-        h.set_root(root);
-        (para, below)
-    };
-
-    let mut cold = Harness::new((900, 1200));
-    let (cold_para, cold_below) = build(&mut cold);
-
-    let mut resized = Harness::new((1920, 1200));
-    let (para, below) = build(&mut resized);
-    resized.resize((900, 1200));
-    resized.frame();
-
-    assert_eq!(resized.region(&para), cold.region(&cold_para), "paragraph");
-    assert_eq!(resized.region(&below), cold.region(&cold_below), "below");
-}
-
-#[test]
-fn a_fixed_box_is_drawn_again_rather_than_stretched() {
-    let mut h = Harness::new((400, 400));
-    // The panel fills a stack sized by its sibling, so it is drawn in the
-    // whole box and then placed in the shorter one. Reusing it in that fixed
-    // box afterwards would leave it whatever height it happened to have.
-    let panel = rect(Color::BLUE).add(&mut h.rsc);
-    let leaf = rect(Color::RED).height(100).add(&mut h.rsc);
-    let stack = (panel, leaf)
-        .stack()
-        .size(StackSize::Child(1))
-        .add(&mut h.rsc);
-    h.set_root(stack.align(Align::TOP));
-    assert_corners!(h, panel, (0, 0), (400, 100));
-
-    h.rsc[leaf].y = Some(Len::abs(250));
-    h.frame();
-
-    assert_corners!(h, panel, (0, 0), (400, 250));
-}

tests/layout_diagnostics.rs

@@ -0,0 +1,253 @@
+//! Retained CPU-layout diagnostics on one reproducible random tree.
+//!
+//! Counters and phase timers:
+//!
+//!     cargo test --release --features layout-diagnostics \
+//!       --test layout_diagnostics -- --ignored --nocapture
+//!
+//! Uninstrumented hardware totals for one phase:
+//!
+//!     IRIS_PHASE=resize IRIS_FRAMES=1000 perf stat \
+//!       -e cycles:u,instructions:u cargo test --release \
+//!       --test layout_diagnostics -- --ignored --nocapture
+//!
+//! `IRIS_PHASE` is `cold`, `repaint`, `many`, `size`, `scroll`, `resize`, or
+//! `all`. `IRIS_SEED`, `IRIS_DEPTH`, and `IRIS_FRAMES` select the load, and
+//! `IRIS_DIRTY` how many widgets `many` marks at once.
+
+use iris::harness::Harness;
+use iris::prelude::*;
+use iris::random::{Edits, Tree, grow};
+use std::time::Instant;
+
+const OUTPUT: (f32, f32) = (1920.0, 1200.0);
+
+#[cfg(feature = "layout-diagnostics")]
+#[test]
+fn a_selected_widget_retains_its_layout_events() {
+    use iris::core::layout_diagnostics::{self as diagnostics, TraceEvent};
+
+    diagnostics::clear_traced_widgets();
+    let _ = diagnostics::take();
+    let mut harness = Harness::new((400, 200));
+    let leaf = rect(Color::RED).region_node().add(&mut harness.rsc);
+    let other = rect(Color::BLUE).add(&mut harness.rsc);
+    let root = (leaf, other).span(Dir::RIGHT).add(&mut harness.rsc);
+    harness.set_root(root);
+    diagnostics::trace_widget(leaf.id());
+    let _ = diagnostics::take();
+
+    let _ = harness.rsc.widgets_mut().get_dyn_mut(root.id());
+    let _ = harness.rsc.widgets_mut().get_dyn_mut(leaf.id());
+    harness.frame();
+
+    let report = diagnostics::take();
+    assert!(
+        report
+            .traces()
+            .iter()
+            .any(|event| matches!(event, TraceEvent::RegionNode { id, .. } if *id == leaf.id()))
+    );
+    assert!(
+        report
+            .traces()
+            .iter()
+            .any(|event| matches!(event, TraceEvent::DrawRequest { id, .. } if *id == leaf.id()))
+    );
+    assert!(
+        report
+            .traces()
+            .iter()
+            .any(|event| matches!(event, TraceEvent::SizeRead { id, .. } if *id == leaf.id()))
+    );
+    assert!(
+        report
+            .traces()
+            .iter()
+            .any(|event| matches!(event, TraceEvent::SizeReported { id, .. } if *id == leaf.id()))
+    );
+    diagnostics::clear_traced_widgets();
+}
+
+fn env<T: std::str::FromStr>(name: &str, fallback: T) -> T {
+    std::env::var(name)
+        .ok()
+        .and_then(|value| value.parse().ok())
+        .unwrap_or(fallback)
+}
+
+#[cfg(feature = "layout-diagnostics")]
+fn trace_selected(tree: &Tree) {
+    let Ok(value) = std::env::var("IRIS_TRACE_INDEX") else {
+        return;
+    };
+    let index = value
+        .parse::<usize>()
+        .expect("IRIS_TRACE_INDEX must be a tree.ids index");
+    let id = tree.ids[index];
+    iris::core::layout_diagnostics::trace_widget(id);
+    println!("tracing tree.ids[{index}] = {id:?}");
+}
+
+#[cfg(not(feature = "layout-diagnostics"))]
+fn trace_selected(_: &Tree) {}
+
+/// The shape a cost is measured on must not depend on what layout measured,
+/// or two commits are compared on two different trees. See `Edits`.
+fn rig_edits() -> Edits {
+    Edits {
+        fixed_branches: true,
+        ..Default::default()
+    }
+}
+
+fn warm(seed: u64, depth: usize) -> (Harness, Tree) {
+    let mut harness = Harness::new(OUTPUT);
+    let (root, tree) = grow(&mut harness.rsc, seed, depth, &rig_edits());
+    harness.state.root = Some(root);
+    harness.frame();
+    println!(
+        "fixture: seed {seed}, depth {depth}, {} widgets, {} active",
+        tree.ids.len(),
+        harness.render.active_widgets()
+    );
+    #[cfg(feature = "layout-diagnostics")]
+    let _ = iris::core::layout_diagnostics::take();
+    (harness, tree)
+}
+
+fn report(label: &str, mut elapsed: Vec<f64>, _harness: &Harness) {
+    elapsed.sort_by(|a, b| a.partial_cmp(b).unwrap());
+    let frames = elapsed.len();
+    // The worst frame is the stutter somebody sees, so it goes beside the
+    // median; p99 says whether it is the load or a single interruption.
+    println!(
+        "{label}: {frames} frame(s), min {:.3} ms, median {:.3} ms, p99 {:.3} ms, \
+         max {:.3} ms, total {:.1} ms",
+        elapsed[0],
+        elapsed[frames / 2],
+        elapsed[frames * 99 / 100],
+        elapsed[frames - 1],
+        elapsed.iter().sum::<f64>(),
+    );
+    #[cfg(feature = "layout-diagnostics")]
+    {
+        let diagnostics = iris::core::layout_diagnostics::take();
+        print!("{}", diagnostics.per_frame(frames));
+        for callsite in diagnostics.hot_text().iter().take(3) {
+            let mut ancestry = Vec::new();
+            let mut id = Some(callsite.id);
+            while let Some(widget) = id {
+                ancestry.push(_harness.rsc.widgets().label(widget).as_str());
+                id = _harness
+                    .render
+                    .active
+                    .get(&widget)
+                    .and_then(|active| active.parent);
+            }
+            println!("    text ancestry: {}", ancestry.join(" < "));
+        }
+    }
+}
+
+fn run(
+    label: &str,
+    frames: usize,
+    harness: &mut Harness,
+    mut change: impl FnMut(&mut Harness, usize),
+) {
+    let mut elapsed = Vec::with_capacity(frames);
+    for frame in 0..frames {
+        change(harness, frame);
+        let start = Instant::now();
+        harness.frame();
+        elapsed.push(start.elapsed().as_secs_f64() * 1_000.0);
+    }
+    report(label, elapsed, harness);
+}
+
+#[test]
+#[ignore = "measurement, not a check"]
+fn layout_cost() {
+    let seed = env("IRIS_SEED", 1_u64);
+    let depth = env("IRIS_DEPTH", 7_usize);
+    let frames = env("IRIS_FRAMES", 100_usize);
+    assert!(frames > 0, "IRIS_FRAMES must be greater than zero");
+    let phase = env("IRIS_PHASE", String::from("all"));
+    assert!(
+        ["all", "cold", "repaint", "many", "size", "scroll", "resize"].contains(&phase.as_str()),
+        "unknown IRIS_PHASE {phase:?}"
+    );
+    let selected = |name| phase == "all" || phase == name;
+
+    if selected("cold") {
+        let mut harness = Harness::new(OUTPUT);
+        let (root, tree) = grow(&mut harness.rsc, seed, depth, &rig_edits());
+        harness.state.root = Some(root);
+        println!(
+            "fixture: seed {seed}, depth {depth}, {} widgets",
+            tree.ids.len()
+        );
+        trace_selected(&tree);
+        #[cfg(feature = "layout-diagnostics")]
+        let _ = iris::core::layout_diagnostics::take();
+        run("cold", 1, &mut harness, |_, _| {});
+        drop(tree);
+    }
+
+    if selected("repaint") {
+        let (mut harness, tree) = warm(seed, depth);
+        trace_selected(&tree);
+        let leaf = tree.ids[0];
+        run("repaint", frames, &mut harness, move |harness, _| {
+            let _ = harness.rsc.widgets_mut().get_dyn_mut(leaf);
+        });
+    }
+
+    if selected("many") {
+        let (mut harness, tree) = warm(seed, depth);
+        trace_selected(&tree);
+        // Spread through the tree rather than taken from one subtree, so the
+        // dependency paths the frame settles overlap.
+        let wanted = env("IRIS_DIRTY", 32_usize).max(1);
+        let step = (tree.ids.len() / wanted).max(1);
+        let dirty: Vec<_> = tree.ids.iter().copied().step_by(step).collect();
+        println!("marking {} of {} widgets", dirty.len(), tree.ids.len());
+        run("many", frames, &mut harness, move |harness, _| {
+            for &id in &dirty {
+                harness.rsc.widgets_mut().get_dyn_mut(id);
+            }
+        });
+    }
+
+    if selected("size") {
+        let (mut harness, tree) = warm(seed, depth);
+        trace_selected(&tree);
+        let sized = tree.sized[0];
+        run("size", frames, &mut harness, move |harness, frame| {
+            let len = LayoutLen::px(100.0 + (frame % 2) as f32 * 40.0);
+            harness
+                .rsc
+                .widgets_mut()
+                .set_size_rule(sized, Axis::X, SizeRule::Exact(len));
+        });
+    }
+
+    if selected("scroll") {
+        let (mut harness, tree) = warm(seed, depth);
+        trace_selected(&tree);
+        let scroll = tree.scrolls[0];
+        run("scroll", frames, &mut harness, move |harness, frame| {
+            harness.rsc[scroll].scroll(if frame % 2 == 0 { 12.0 } else { -12.0 });
+        });
+    }
+
+    if selected("resize") {
+        let (mut harness, tree) = warm(seed, depth);
+        trace_selected(&tree);
+        run("resize", frames, &mut harness, |harness, frame| {
+            harness.resize((OUTPUT.0 - ((frame + 1) % 2) as f32 * 8.0, OUTPUT.1));
+        });
+        drop(tree);
+    }
+}

tests/remap.rs

@@ -1,27 +0,0 @@
-//! What a drawing can be taken out of, and what it cannot.
-
-use iris::core::{Remap, UiRegion, UiScalar, UiSpan};
-
-/// A box `size` tall whose top is `rel` of the way down the window.
-fn fixed(rel: f32, size: f32) -> UiRegion {
-    UiRegion::new(
-        UiSpan::FULL,
-        UiSpan::new(UiScalar { rel, abs: 0.0 }, UiScalar { rel, abs: size }),
-    )
-}
-
-#[test]
-fn a_fixed_box_can_be_carried_but_not_stretched() {
-    let from = fixed(0.0, 164.0);
-    assert!(Remap::new(from, UiRegion::FULL).is_none());
-    assert!(Remap::new(from, fixed(0.5, 164.0)).is_some());
-    assert!(Remap::new(from, fixed(0.0, 98.0)).is_none());
-}
-
-#[test]
-fn a_relative_box_can_be_stretched_to_any_other() {
-    let remap = Remap::new(UiRegion::FULL, fixed(0.0, 98.0)).expect("relative boxes remap");
-    // A part that filled the window keeps filling what replaced it, which is
-    // exactly what `outside` could not say for a box of a fixed length.
-    assert_eq!(remap.apply(UiRegion::FULL), fixed(0.0, 98.0));
-}

tests/replace_cost.rs

@@ -0,0 +1,41 @@
+//! What remapping a subtree costs per frame, as a load for a counter rather
+//! than a check. A span of 200 fixed-height rows, five primitives each, with
+//! the row above them changing height every frame, so every row below is
+//! offered a box the same shape somewhere else.
+//!
+//!     cargo test --release --test replace_cost -- --ignored
+//!     perf stat -e instructions:u target/release/.../replace_cost-* --ignored
+//!
+//! Wall time is the wrong number here; see `draw_cost.rs`.
+
+use iris::harness::Harness;
+use iris::prelude::*;
+
+const ROWS: usize = 200;
+const FRAMES: usize = 200;
+
+#[test]
+#[ignore = "measurement, not a check"]
+fn remapping_rows_every_frame() {
+    let mut h = Harness::new((1920, 1200));
+    let first = rect(Color::RED).height(40).add(&mut h.rsc);
+    let mut span = Span::empty(Dir::DOWN);
+    span.push(first.add_strong(&mut h.rsc));
+    for i in 0..ROWS {
+        let row = (
+            rect(Color::BLUE.darker(i as f32 / (ROWS * 2) as f32)),
+            rect(Color::GREEN).pad(2),
+            wtext("row").size(16).pad(2),
+        )
+            .span(Dir::RIGHT)
+            .pad(4)
+            .height(40)
+            .add(&mut h.rsc);
+        span.push(row.add_strong(&mut h.rsc));
+    }
+    h.set_root(span);
+    for i in 0..FRAMES {
+        h.set_len(first, Axis::Y, 40.0 + (i % 2) as f32);
+        h.frame();
+    }
+}

tests/retained.rs

@@ -1,252 +0,0 @@
-//! What a second frame draws again, and what it keeps.
-
-use std::{cell::Cell, rc::Rc};
-
-use iris::harness::{Harness, assert_corners};
-use iris::prelude::*;
-
-/// A leaf that counts its draws and reports whatever size it is given, so a
-/// test can see what the retained path skipped.
-struct Counted {
-    draws: Rc<Cell<usize>>,
-    size: Size,
-    dependence: OnResize,
-}
-
-impl Widget for Counted {
-    fn draw(&mut self, _: &mut Painter) -> Size {
-        self.draws.set(self.draws.get() + 1);
-        self.size
-    }
-
-    fn on_resize(&self, _: Axis) -> OnResize {
-        self.dependence
-    }
-}
-
-struct Counts(Rc<Cell<usize>>);
-
-impl Counts {
-    fn get(&self) -> usize {
-        self.0.get()
-    }
-}
-
-fn counted(h: &mut Harness, size: Size, dependence: OnResize) -> (WeakWidget<Counted>, Counts) {
-    let draws = Rc::new(Cell::new(0));
-    let id = Counted {
-        draws: draws.clone(),
-        size,
-        dependence,
-    }
-    .add(&mut h.rsc);
-    (id, Counts(draws))
-}
-
-/// A fixed-width leaf beside one that takes the rest, so changing the first
-/// hands the second a different box without the output changing.
-fn pair(h: &mut Harness, rest: OnResize) -> (WeakWidget<Counted>, Counts, WidgetId) {
-    let (first, _) = counted(h, Size::from((100, 200)), OnResize::Translate);
-    let (second, draws) = counted(h, Size::REST, rest);
-    h.set_root((first, second).span(Dir::RIGHT));
-    (first, draws, second.id())
-}
-
-#[test]
-fn a_leaf_that_ignores_its_box_is_not_drawn_again_when_the_box_changes() {
-    let mut h = Harness::new((400, 200));
-    let (first, draws, second) = pair(&mut h, OnResize::Scale);
-    let settled = draws.get();
-    assert_corners!(h, second, (100, 0), (400, 200));
-
-    h.rsc[first].size = Size::from((150, 200));
-    h.frame();
-
-    assert_eq!(
-        draws.get(),
-        settled,
-        "its box is a field to write, not a reason to draw"
-    );
-    assert_corners!(h, second, (150, 0), (400, 200));
-}
-
-#[test]
-fn a_leaf_that_depends_on_its_box_is_drawn_again_when_the_box_changes() {
-    let mut h = Harness::new((400, 200));
-    let (first, draws, second) = pair(&mut h, OnResize::Redraw);
-    let settled = draws.get();
-
-    h.rsc[first].size = Size::from((150, 200));
-    h.frame();
-
-    // Twice: once for the span to measure it, once for its real box. A child
-    // that can hint its length is spared the first, and a smaller number here
-    // means someone has made that cheaper rather than broken it.
-    assert_eq!(draws.get(), settled + 2);
-    assert_corners!(h, second, (150, 0), (400, 200));
-}
-
-#[test]
-fn a_span_child_that_declares_its_length_is_drawn_once() {
-    let mut h = Harness::new((400, 200));
-    let (told, told_draws) = counted(&mut h, Size::from((100, 200)), OnResize::Translate);
-    let (asked, asked_draws) = counted(&mut h, Size::from((100, 200)), OnResize::Translate);
-    // The span takes one child's length from its hint and has to draw the
-    // other to find out, so only the second is drawn before it is placed.
-    let hinted = told.width(100).add(&mut h.rsc);
-    h.set_root((hinted, asked).span(Dir::RIGHT));
-
-    assert_eq!(told_draws.get(), 1);
-    assert_eq!(
-        asked_draws.get(),
-        2,
-        "drawn to be measured, then again to be placed"
-    );
-}
-
-#[test]
-fn a_span_relays_out_when_a_child_it_measured_changes() {
-    let mut h = Harness::new((400, 200));
-    let (first, _, second) = pair(&mut h, OnResize::Translate);
-
-    h.rsc[first].size = Size::from((250, 200));
-    h.frame();
-
-    assert_corners!(h, first, (0, 0), (250, 200));
-    assert_corners!(h, second, (250, 0), (400, 200));
-}
-
-#[test]
-fn a_placed_child_survives_the_next_frame() {
-    let mut h = Harness::new((400, 200));
-    // Both children declare a length, so the span places them from their hints
-    // rather than drawing them to find out.
-    let top = rect(Color::RED).height(80).add(&mut h.rsc);
-    let bottom = rect(Color::BLUE).height(120).add(&mut h.rsc);
-    h.set_root((top, bottom).span(Dir::DOWN));
-
-    h.rsc.widgets_mut().get_dyn_mut(top.id());
-    h.frame();
-
-    assert_corners!(h, top, (0, 0), (400, 80));
-    assert_corners!(h, bottom, (0, 80), (400, 200));
-}
-
-/// Lays its child out from the hint alone, never reading what it drew.
-struct FromHint {
-    inner: StrongWidget,
-}
-
-impl Widget for FromHint {
-    fn draw(&mut self, painter: &mut Painter) -> Size {
-        let len = painter.size_hint(&self.inner, Axis::Y).unwrap();
-        let mut region = UiRegion::FULL;
-        region.y.end = region.y.start.offset(len.abs);
-        painter.widget_within(&self.inner, region);
-        Size::REST
-    }
-}
-
-#[test]
-fn a_parent_that_only_read_a_hint_relays_out_when_the_hint_changes() {
-    let mut h = Harness::new((400, 200));
-    let inner = rect(Color::RED).height(80).add(&mut h.rsc);
-    let parent = FromHint {
-        inner: inner.add_strong(&mut h.rsc),
-    }
-    .add(&mut h.rsc);
-    h.set_root(parent);
-    assert_corners!(h, inner, (0, 0), (400, 80));
-
-    h.rsc[inner].y = Some(Len::abs(120));
-    h.frame();
-
-    assert_corners!(h, inner, (0, 0), (400, 120));
-}
-
-/// Reads the output's size, which nothing but its own draw can put right.
-struct ReadsOutput {
-    draws: Rc<Cell<usize>>,
-}
-
-impl Widget for ReadsOutput {
-    fn draw(&mut self, painter: &mut Painter) -> Size {
-        self.draws.set(self.draws.get() + 1);
-        Size::abs(painter.output_size() / 4.0)
-    }
-}
-
-#[test]
-fn a_resize_does_not_redraw_what_the_shader_can_move() {
-    let mut h = Harness::new((400, 200));
-    let (leaf, draws) = counted(&mut h, Size::REST, OnResize::Redraw);
-    h.set_root(leaf);
-    let settled = draws.get();
-
-    h.resize((800, 100));
-    assert!(h.needs_redraw());
-    h.frame();
-
-    assert_eq!(
-        draws.get(),
-        settled,
-        "its box is the same fraction of a different output"
-    );
-    assert_corners!(h, leaf, (0, 0), (800, 100));
-}
-
-#[test]
-fn a_resize_redraws_what_read_the_output() {
-    let mut h = Harness::new((400, 200));
-    let draws = Rc::new(Cell::new(0));
-    let leaf = ReadsOutput {
-        draws: draws.clone(),
-    }
-    .add(&mut h.rsc);
-    h.set_root(leaf);
-    let settled = draws.get();
-
-    h.resize((800, 100));
-    h.frame();
-
-    assert_eq!(draws.get(), settled + 1);
-}
-
-#[test]
-fn narrowing_the_output_reflows_text_and_relays_out_around_it() {
-    let mut h = Harness::new((600, 400));
-    let para = wtext(
-        "Wrapping shapes one source into as many lines as its container leaves \
-        room for, so the height of a paragraph is an answer rather than a setting.",
-    )
-    .size(20)
-    .wrap(true)
-    .add(&mut h.rsc);
-    let below = rect(Color::RED).add(&mut h.rsc);
-    h.set_root((para, below).span(Dir::DOWN));
-    let top = h.region(&below).expect("drew nothing").top_left.y;
-
-    h.resize((300, 400));
-    h.frame();
-
-    let lower = h.region(&below).expect("drew nothing").top_left.y;
-    assert!(lower > top, "same words, half the width: {top} -> {lower}");
-}
-
-#[test]
-fn a_change_two_levels_under_its_reader_still_reaches_it() {
-    let mut h = Harness::new((400, 400));
-    // Every wrapper up to the outer pad read the size below it, so the outer
-    // pad is what draws again -- and the span it hands the box to is the same
-    // size as before, which is what lets a draw reuse its way past the leaf.
-    let (leaf, _) = counted(&mut h, Size::abs((100, 100).into()), OnResize::Redraw);
-    let padded = leaf.pad(10).add(&mut h.rsc);
-    let below = rect(Color::RED).add(&mut h.rsc);
-    h.set_root((padded, below).span(Dir::DOWN).pad(12));
-    assert_corners!(h, below, (12, 132), (388, 388));
-
-    h.rsc[leaf].size = Size::abs((100, 200).into());
-    h.frame();
-
-    assert_corners!(h, below, (12, 232), (388, 388));
-}

tests/revision_cost.rs

@@ -0,0 +1,203 @@
+//! What a resize frame costs and what it holds, on a tree the revision before
+//! #16 also builds.
+//!
+//! Deliberately written in the API subset `43ce8c7` and this branch share, so
+//! the same source can be dropped into an old worktree and measured there:
+//! that is the only like-for-like comparison with the code the retained
+//! layout replaced. The random tree cannot carry one, because the generator
+//! itself changed with the work.
+//!
+//!     ROWS=40 FRAMES=500 cargo test --release --test revision_cost \
+//!       -- --ignored --nocapture resize_cost
+//!     ROWS=2000 cargo test --release --test revision_cost \
+//!       -- --ignored --nocapture text_memory
+//!
+//! Wall time on this machine varies with CPU frequency; take the number from
+//! `perf stat -e instructions:u` on the test binary directly.
+
+use iris::harness::Harness;
+use iris::prelude::*;
+use std::time::Instant;
+
+/// xorshift64, so one seed is one set of paragraphs on any machine.
+struct Rng(u64);
+
+impl Rng {
+    fn bits(&mut self) -> u64 {
+        self.0 ^= self.0 << 13;
+        self.0 ^= self.0 >> 7;
+        self.0 ^= self.0 << 17;
+        self.0
+    }
+
+    fn below(&mut self, n: usize) -> usize {
+        (self.bits() % n as u64) as usize
+    }
+}
+
+const WORDS: [&str; 24] = [
+    "wrapping",
+    "shapes",
+    "one",
+    "source",
+    "into",
+    "as",
+    "many",
+    "lines",
+    "as",
+    "the",
+    "box",
+    "leaves",
+    "room",
+    "for",
+    "paragraph",
+    "height",
+    "answer",
+    "setting",
+    "container",
+    "width",
+    "before",
+    "knows",
+    "measured",
+    "again",
+];
+
+/// A run of its own words, so nothing here is fast for two texts being the
+/// same string.
+fn words(rng: &mut Rng, least: usize, most: usize) -> String {
+    let words = least + rng.below(most - least);
+    let mut out = String::new();
+    for _ in 0..words {
+        if !out.is_empty() {
+            out.push(' ');
+        }
+        out.push_str(WORDS[rng.below(WORDS.len())]);
+    }
+    out
+}
+
+const OUTPUT: (f32, f32) = (900.0, 1200.0);
+
+fn env<T: std::str::FromStr>(name: &str, fallback: T) -> T {
+    std::env::var(name)
+        .ok()
+        .and_then(|value| value.parse().ok())
+        .unwrap_or(fallback)
+}
+
+/// A row of a fixed-width rect beside a column of one wrapping and one
+/// overflowing text: the shape that makes a container measure a child in a
+/// box it will not keep.
+fn build(h: &mut Harness, rows: usize) -> Vec<WidgetId> {
+    let mut rng = Rng(1);
+    let mut paragraphs = Vec::new();
+    let mut col = Span::empty(Dir::DOWN);
+    for _ in 0..rows {
+        let mut row = Span::empty(Dir::RIGHT);
+        row.push(
+            rect(Color::RED)
+                .width(LayoutLen::px(40.0))
+                .add_strong(&mut h.rsc),
+        );
+        let mut body = Span::empty(Dir::DOWN);
+        let para = wtext(words(&mut rng, 12, 52))
+            .size(16)
+            .wrap(true)
+            .add_strong(&mut h.rsc);
+        paragraphs.push(para.id());
+        body.push(para);
+        body.push(
+            // Short, or its unwrapped width decides the row and the
+            // paragraph beside it never wraps.
+            wtext(words(&mut rng, 2, 6))
+                .size(16)
+                .wrap(false)
+                .add_strong(&mut h.rsc),
+        );
+        row.push(body.add_strong(&mut h.rsc));
+        col.push(row.add_strong(&mut h.rsc));
+    }
+    let root = col.add(&mut h.rsc);
+    h.set_root(root);
+    paragraphs
+}
+
+#[test]
+#[ignore = "measurement, not a check"]
+fn resize_cost() {
+    let rows = env("ROWS", 40_usize);
+    let frames = env("FRAMES", 500_usize);
+    let mut h = Harness::new(OUTPUT);
+    let paragraphs = build(&mut h, rows);
+    // What it cost is only half the comparison: the old code is cheaper
+    // partly because it wraps at the container's whole width rather than the
+    // part left beside the rect, and draws past the edge of the output.
+    println!("output width {}", OUTPUT.0);
+    for (at, id) in paragraphs.iter().enumerate().take(3) {
+        println!("paragraph {at}: {:?}", h.region(id));
+    }
+
+    // Two widths in turn is the friendly case for anything that remembers an
+    // answer, so `SWEEP=1` never repeats one -- a drag rather than a toggle.
+    let sweep = env("SWEEP", 0_usize) != 0;
+    let mut elapsed = Vec::with_capacity(frames);
+    for frame in 0..frames {
+        let narrower = match sweep {
+            true => (frame % 256) as f32,
+            false => ((frame + 1) % 2) as f32 * 8.0,
+        };
+        h.resize((OUTPUT.0 - narrower, OUTPUT.1));
+        let start = Instant::now();
+        h.frame();
+        elapsed.push(start.elapsed().as_secs_f64() * 1000.0);
+    }
+    elapsed.sort_by(|a, b| a.partial_cmp(b).unwrap());
+    println!(
+        "resize: {frames} frames, min {:.3} ms, median {:.3} ms, p99 {:.3} ms, \
+         max {:.3} ms, total {:.1} ms",
+        elapsed[0],
+        elapsed[frames / 2],
+        elapsed[frames * 99 / 100],
+        elapsed[frames - 1],
+        elapsed.iter().sum::<f64>()
+    );
+}
+
+fn kb(field: &str) -> u64 {
+    std::fs::read_to_string("/proc/self/status")
+        .unwrap()
+        .lines()
+        .find(|line| line.starts_with(field))
+        .and_then(|line| line.split_whitespace().nth(1)?.parse().ok())
+        .unwrap()
+}
+
+fn report(label: &str) {
+    println!(
+        "{label:24} rss {:>7} kB   peak {:>7} kB",
+        kb("VmRSS:"),
+        kb("VmHWM:")
+    );
+}
+
+/// Run this one on its own: the figures are the whole process's.
+#[test]
+#[ignore = "measurement, not a check"]
+fn text_memory() {
+    let rows = env("ROWS", 2000_usize);
+    report("before");
+    let mut h = Harness::new(OUTPUT);
+    let paragraphs = build(&mut h, rows);
+    report("after cold frame");
+    for frame in 0..40 {
+        h.resize((OUTPUT.0 - ((frame + 1) % 2) as f32 * 8.0, OUTPUT.1));
+        h.frame();
+    }
+    report("after 40 resizes");
+    // Settled: the output holds still and one leaf repaints per frame.
+    for _ in 0..10 {
+        let _ = h.rsc.widgets_mut().get_dyn_mut(paragraphs[0]);
+        h.frame();
+    }
+    report("after settling");
+}

tests/scenario/mod.rs

@@ -0,0 +1,467 @@
+//! The scenarios both fuzzers run, over the tree a [`Plan`] describes.
+//!
+//! One implementation rather than two. The oracle grew its trees from a seed
+//! and the shrinker grew its own, with every scenario written out on each
+//! side, so a failure the oracle found could not be handed to the shrinker:
+//! there was no tree to pass it, only a seed, and a seed cannot be made
+//! smaller. Both take a plan now, so whatever finds a counterexample can also
+//! reduce it.
+//!
+//! Each target compiles this for itself, so what only one of them calls is
+//! dead code in the other.
+#![allow(dead_code)]
+
+use iris::harness::Harness;
+use iris::prelude::*;
+use iris::random::{Aligns, Edits, Kind, Lens, Plan, Rng, SpanEdit, Tree, build};
+use std::collections::HashMap;
+
+/// A seed per thread but one, since a seed grows, lays out and drops its tree
+/// alone. A failing seed still shrinks and panics on its own thread.
+pub fn over_seeds(seeds: Vec<u64>, run: impl Fn(u64) + Sync) {
+    let threads =
+        std::thread::available_parallelism().map_or(1, |n| n.get().saturating_sub(1).max(1));
+    let chunk = seeds.len().div_ceil(threads).max(1);
+    std::thread::scope(|scope| {
+        for part in seeds.chunks(chunk) {
+            let run = &run;
+            scope.spawn(move || part.iter().for_each(|&seed| run(seed)));
+        }
+    });
+}
+
+pub fn env<T: std::str::FromStr>(name: &str, fallback: T) -> T {
+    std::env::var(name)
+        .ok()
+        .and_then(|v| v.parse().ok())
+        .unwrap_or(fallback)
+}
+
+/// The window a tree is grown in, and the one a resize takes it to.
+const OUTER: (f32, f32) = (1920.0, 1200.0);
+const INNER: (f32, f32) = (640.0, 900.0);
+const STILL: (f32, f32) = (900.0, 1200.0);
+
+/// The same box, to two steps of the grid between the two ways of reaching
+/// it. A move, a repaint, a row of shares and every length in pixels land on
+/// the same number. What needs the slack is a position: a box centred in a
+/// fraction of its parent against the same box centred in its own pixels,
+/// and a box re-expressed as a fraction of a parent that changed length.
+/// A step is a thousandth of a pixel, where this was a twentieth of one
+/// before any of it was on a grid.
+///
+/// **One step is not enough**, tried 2026-09-17 once a length in pixels
+/// stopped being composed: it passes the 100-seed oracle and fails the
+/// 400-seed shrinker on `resize-size`, seeds 384 and 162, by 0.002 px. So
+/// what is left here is the resize path's own rounding rather than a length
+/// reached two ways.
+const AGREE_STEPS: i32 = 2;
+
+/// A way of changing what a span holds. Each is a shape worth its own case:
+/// taking a child out of the middle is not the same as emptying a span, and
+/// adding one is not the same as adding three.
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub enum Shuffle {
+    /// Every other child, so what is left is interleaved with what went.
+    EveryOther,
+    /// Everything but the first, which is the last step before empty.
+    AllButFirst,
+    /// Three more on the end at once.
+    AddThree,
+    /// The first out and three more on, so the count moves both ways.
+    SwapForThree,
+    /// One out of the middle and one on the end.
+    TradeOne,
+}
+
+impl Shuffle {
+    fn of(self, grown: usize) -> SpanEdit {
+        let all = |step: usize, from: usize| (from..grown).step_by(step).collect();
+        match self {
+            Self::EveryOther => SpanEdit {
+                detach: all(2, 0),
+                attach: 0,
+            },
+            Self::AllButFirst => SpanEdit {
+                detach: all(1, 1),
+                attach: 0,
+            },
+            Self::AddThree => SpanEdit {
+                detach: Vec::new(),
+                attach: 3,
+            },
+            Self::SwapForThree => SpanEdit {
+                detach: vec![0],
+                attach: 3,
+            },
+            Self::TradeOne => SpanEdit {
+                detach: vec![grown / 2],
+                attach: 1,
+            },
+        }
+    }
+}
+
+/// What a warm tree is put through before it is compared with a cold one
+/// grown the way it was left.
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub enum Case {
+    /// Nothing changes, so no box may either. What this exercises is the
+    /// order a frame settles a dirty set in.
+    Repaint,
+    /// Every fifth widget rather than all of them: marking all of them
+    /// redraws the whole tree, which is a cold start reached the long way,
+    /// where the mixed case leaves a redrawn subtree beside a retained one.
+    RepaintSome,
+    Resize,
+    ResizeRepaint,
+    /// A resize and then a size change, so a retained answer is asked to
+    /// survive two different kinds of invalidation in a row.
+    ResizeSize,
+    /// A few declared sizes.
+    Size,
+    /// Every declared size at once, so every reader of a size has a changed
+    /// descendant in the same frame and the whole dirty set settles together.
+    EverySize,
+    Align,
+    /// Giving a widget a movable region of its own, or taking it away, is a
+    /// structural change: every primitive under it changes which chain
+    /// resolves it.
+    RegionNode,
+    /// The same children in a different order, which moves every one of them
+    /// without changing what any of them is.
+    Reorder,
+    Shuffle(Shuffle),
+}
+
+pub const ALL: [Case; 15] = [
+    Case::Repaint,
+    Case::RepaintSome,
+    Case::Resize,
+    Case::ResizeRepaint,
+    Case::ResizeSize,
+    Case::Size,
+    Case::EverySize,
+    Case::Align,
+    Case::RegionNode,
+    Case::Reorder,
+    Case::Shuffle(Shuffle::EveryOther),
+    Case::Shuffle(Shuffle::AllButFirst),
+    Case::Shuffle(Shuffle::AddThree),
+    Case::Shuffle(Shuffle::SwapForThree),
+    Case::Shuffle(Shuffle::TradeOne),
+];
+
+impl Case {
+    /// The name `CASE` selects it by, and the one a failure prints.
+    pub fn name(self) -> &'static str {
+        match self {
+            Self::Repaint => "repaint",
+            Self::RepaintSome => "repaint-some",
+            Self::Resize => "resize",
+            Self::ResizeRepaint => "resize-repaint",
+            Self::ResizeSize => "resize-size",
+            Self::Size => "size",
+            Self::EverySize => "every-size",
+            Self::Align => "align",
+            Self::RegionNode => "region-node",
+            Self::Reorder => "reorder",
+            Self::Shuffle(Shuffle::EveryOther) => "shuffle-every-other",
+            Self::Shuffle(Shuffle::AllButFirst) => "shuffle-all-but-first",
+            Self::Shuffle(Shuffle::AddThree) => "shuffle-add-three",
+            Self::Shuffle(Shuffle::SwapForThree) => "shuffle-swap-for-three",
+            Self::Shuffle(Shuffle::TradeOne) => "shuffle-trade-one",
+        }
+    }
+
+    pub fn named(name: &str) -> Option<Self> {
+        ALL.into_iter().find(|case| case.name() == name)
+    }
+
+    /// Grown in the first, compared in the second.
+    fn window(self) -> ((f32, f32), (f32, f32)) {
+        match self {
+            Self::Resize | Self::ResizeRepaint | Self::ResizeSize => (OUTER, INNER),
+            _ => (STILL, STILL),
+        }
+    }
+}
+
+fn mark(warm: &mut Harness, tree: &Tree, step: usize) {
+    for &id in tree.ids.iter().step_by(step) {
+        warm.rsc.widgets_mut().get_dyn_mut(id);
+    }
+}
+
+fn a_len(rng: &mut Rng) -> Option<LayoutLen> {
+    Some(LayoutLen::px(20.0 + rng.below(180) as f32))
+}
+
+fn resize_one(warm: &mut Harness, tree: &Tree, idx: usize, rng: &mut Rng) -> Lens {
+    let lens = [a_len(rng), a_len(rng)];
+    warm.rsc
+        .widgets_mut()
+        .set_size_rules(tree.sized[idx], lens[0], lens[1]);
+    lens
+}
+
+fn realign_one(warm: &mut Harness, tree: &Tree, idx: usize, rng: &mut Rng) -> Aligns {
+    let side = |rng: &mut Rng| match rng.below(4) {
+        0 => None,
+        1 => Some(AxisAlign::NEG),
+        2 => Some(AxisAlign::CENTER),
+        _ => Some(AxisAlign::POS),
+    };
+    let align = [side(rng), side(rng)];
+    let id = tree.aligned[idx];
+    for (axis, align) in [Axis::X, Axis::Y].into_iter().zip(align) {
+        warm.rsc
+            .widgets_mut()
+            .set_alignment(id, axis, align.unwrap_or_default());
+    }
+    align
+}
+
+/// Every span's children in a different order, said both to the warm tree and
+/// to the plan the cold one is grown from.
+fn reorder(warm: &mut Harness, tree: &Tree, plan: &Plan) -> Plan {
+    for span in &tree.spans {
+        let children = &mut warm.rsc[span.id].children;
+        if !children.is_empty() {
+            children.rotate_left(1);
+        }
+    }
+    let mut out = plan.clone();
+    out.walk_mut(&mut |node| {
+        if let Kind::Span { order, .. } = &mut node.kind
+            && !order.is_empty()
+        {
+            order.rotate_left(1);
+        }
+    });
+    out
+}
+
+/// Applies `shuffle` to every third span. What it takes out is given back to
+/// the span's spares: the last share of a widget must outlive the comparison,
+/// or its id is handed to something else and the two trees stop lining up.
+fn reshuffle(warm: &mut Harness, tree: &mut Tree, shuffle: Shuffle) -> HashMap<usize, SpanEdit> {
+    let mut edits = HashMap::new();
+    for (idx, span) in tree.spans.iter_mut().enumerate().step_by(3) {
+        let edit = shuffle.of(span.grown);
+        let mut take = edit.detach.clone();
+        take.sort_unstable();
+        let children = &mut warm.rsc[span.id].children;
+        // Highest first, so an index means the same child however many of its
+        // neighbours are going too.
+        for j in take.into_iter().rev() {
+            if j < children.len() {
+                span.spares.push(children.remove(j));
+            }
+        }
+        let attach = edit.attach.min(span.spares.len());
+        let moved: Vec<_> = span.spares.drain(..attach).collect();
+        warm.rsc[span.id].children.extend(moved);
+        edits.insert(idx, edit);
+    }
+    edits
+}
+
+/// Changes the warm tree and answers with the plan a cold tree grown that way
+/// comes from. Each arm settles its own frame, so a case that changes nothing
+/// does not get a second one that could settle what the first left.
+fn change(case: Case, warm: &mut Harness, tree: &mut Tree, plan: &Plan, rng: &mut Rng) -> Plan {
+    let some_sizes = |warm: &mut Harness, tree: &Tree, rng: &mut Rng| {
+        let mut sizes = HashMap::new();
+        for _ in 0..4 {
+            if tree.sized.is_empty() {
+                break;
+            }
+            let idx = rng.below(tree.sized.len());
+            sizes.insert(idx, resize_one(warm, tree, idx, rng));
+        }
+        sizes
+    };
+    let edits = match case {
+        Case::Resize => return plan.clone(),
+        Case::Repaint | Case::ResizeRepaint => {
+            mark(warm, tree, 1);
+            warm.frame();
+            return plan.clone();
+        }
+        Case::RepaintSome => {
+            mark(warm, tree, 5);
+            warm.frame();
+            return plan.clone();
+        }
+        Case::Reorder => {
+            let out = reorder(warm, tree, plan);
+            warm.frame();
+            return out;
+        }
+        Case::Size | Case::ResizeSize => Edits {
+            sizes: some_sizes(warm, tree, rng),
+            ..Default::default()
+        },
+        Case::EverySize => Edits {
+            sizes: (0..tree.sized.len())
+                .map(|idx| (idx, resize_one(warm, tree, idx, rng)))
+                .collect(),
+            ..Default::default()
+        },
+        Case::Align => Edits {
+            aligns: (0..tree.aligned.len())
+                .step_by(3)
+                .map(|idx| (idx, realign_one(warm, tree, idx, rng)))
+                .collect(),
+            ..Default::default()
+        },
+        Case::RegionNode => {
+            let mut nodes = HashMap::new();
+            for idx in (0..tree.nodes.len()).step_by(2) {
+                let id = tree.nodes[idx];
+                let take = !warm.rsc.widgets().is_region_node(id);
+                warm.rsc.widgets_mut().set_region_node(id, take);
+                nodes.insert(idx, take);
+            }
+            Edits {
+                nodes,
+                ..Default::default()
+            }
+        }
+        Case::Shuffle(shuffle) => Edits {
+            spans: reshuffle(warm, tree, shuffle),
+            ..Default::default()
+        },
+    };
+    warm.frame();
+    plan.edited(&edits)
+}
+
+/// What a widget was configured with, so a tree a fuzzer found can be written
+/// out by hand. A failure is a lead; the fast test that replaces it has to be
+/// buildable from what the failure printed.
+fn describe(id: WidgetId, h: &Harness) -> String {
+    let rules = h.rsc.widgets().size_rules(id);
+    let rule = |r: SizeRule| match r.exact() {
+        Some(len) => format!("{len}"),
+        None => "-".into(),
+    };
+    let align = h.rsc.widgets().alignment(id);
+    let side = |a: AxisAlign| {
+        if a == AxisAlign::NEG {
+            "neg".into()
+        } else if a == AxisAlign::CENTER {
+            "mid".into()
+        } else if a == AxisAlign::POS {
+            "pos".into()
+        } else {
+            format!("{:.2}", a.rel())
+        }
+    };
+    // A rule and an alignment are properties of whatever carries them, so
+    // they print with that widget rather than as widgets of their own.
+    let mut out = describe_widget(id, h);
+    if (rules.x, rules.y) != (SizeRule::Free, SizeRule::Free) {
+        out += &format!("[x:{},y:{}]", rule(rules.x), rule(rules.y));
+    }
+    if align != RegionAlign::default() {
+        out += &format!("@{},{}", side(align.x), side(align.y));
+    }
+    out
+}
+
+fn describe_widget(id: WidgetId, h: &Harness) -> String {
+    let label = h.rsc.widgets().label(id).to_string();
+    let Some(widget) = h.rsc.widgets().get_dyn(id) else {
+        return label;
+    };
+    let any: &dyn std::any::Any = widget;
+    if let Some(w) = any.downcast_ref::<Span>() {
+        let sign = if w.dir.sign == Sign::Neg { "-" } else { "+" };
+        return format!(
+            "Span{{dir:{:?}{sign},gap:{},n:{}}}",
+            w.dir.axis,
+            w.gap,
+            w.children.len()
+        );
+    }
+    if let Some(w) = any.downcast_ref::<Pad>() {
+        let p = &w.padding;
+        return format!(
+            "Pad{{l:{},r:{},t:{},b:{}}}",
+            p.left, p.right, p.top, p.bottom
+        );
+    }
+    if let Some(w) = any.downcast_ref::<Stack>() {
+        return format!("Stack{{n:{}}}", w.children.len());
+    }
+    label
+}
+
+fn same_region(got: Option<PixelRegion>, want: Option<PixelRegion>) -> bool {
+    match (got, want) {
+        (Some(got), Some(want)) => {
+            let same = |a: Px, b: Px| (a - b).abs() <= Px::STEP.mul_int(AGREE_STEPS);
+            same(got.top_left.x, want.top_left.x)
+                && same(got.top_left.y, want.top_left.y)
+                && same(got.bot_right.x, want.bot_right.x)
+                && same(got.bot_right.y, want.bot_right.y)
+        }
+        (None, None) => true,
+        _ => false,
+    }
+}
+
+/// Runs `case` on the tree `plan` describes, warm and cold, and says where
+/// the two disagree. `seed` chooses only the values a case picks at random,
+/// so one plan under one case is one comparison however it was reached.
+pub fn diverges(plan: &Plan, case: Case, seed: u64) -> Option<String> {
+    let (start, end) = case.window();
+    let mut warm = Harness::new(start);
+    let (root, mut tree) = build(&mut warm.rsc, plan);
+    warm.state.root = Some(root);
+    // The frame that makes it warm: without it nothing is retained and the
+    // comparison is two cold starts agreeing with each other.
+    warm.frame();
+    if start != end {
+        warm.resize(end);
+        warm.frame();
+    }
+    let cold_plan = change(case, &mut warm, &mut tree, plan, &mut Rng::new(seed));
+
+    let mut cold = Harness::new(end);
+    let (root, cold_tree) = build(&mut cold.rsc, &cold_plan);
+    cold.state.root = Some(root);
+    cold.frame();
+
+    let mut drawn = 0;
+    for (i, (&w, &c)) in tree.ids.iter().zip(&cold_tree.ids).enumerate() {
+        let (got, want) = (warm.region(&w), cold.region(&c));
+        drawn += got.is_some() as usize;
+        if same_region(got, want) {
+            continue;
+        }
+        // Where two trees disagree is rarely where the cause is, so the
+        // ancestry comes with it, marking the widgets that own a region.
+        let mut chain = Vec::new();
+        let mut at = Some(w);
+        while let Some(id) = at {
+            let active = &warm.render.active[&id];
+            let node = match active.move_idx == active.parent_move {
+                true => "",
+                false => "*",
+            };
+            chain.push(format!("{}{node}", describe(id, &warm)));
+            at = active.parent;
+        }
+        return Some(format!(
+            "widget {i}\n  warm {got:?}\n  cold {want:?}\n  {}",
+            chain.join(" < ")
+        ));
+    }
+    match drawn {
+        0 => Some("nothing was drawn".into()),
+        _ => None,
+    }
+}

tests/scroll.rs

@@ -1,26 +0,0 @@
-//! Scrolling moves content and stops at its ends.
-
-use iris::harness::{Harness, assert_corners};
-use iris::prelude::*;
-
-#[test]
-fn a_wheel_scrolls_the_content_and_stops_at_its_end() {
-    let mut h = Harness::new((400, 200));
-    // Twice the window's height, so there is 200 to scroll.
-    let top = rect(Color::RED).height(200).add(&mut h.rsc);
-    let bottom = rect(Color::BLUE).height(200).add(&mut h.rsc);
-    h.set_root((top, bottom).span(Dir::DOWN).scrollable());
-    h.move_to((200, 100));
-
-    // `Scroll` starts snapped to the end.
-    assert_corners!(h, top, (0, -200), (400, 0));
-
-    // The handler scales a wheel line by 50.
-    h.scroll((0, 1));
-    h.frame();
-    assert_corners!(h, top, (0, -150), (400, 50));
-
-    h.scroll((0, 10));
-    h.frame();
-    assert_corners!(h, top, (0, 0), (400, 200));
-}

tests/shrink.rs

@@ -0,0 +1,99 @@
+//! A fuzzer that reduces its own counterexample.
+//!
+//! A seed is not a lead anybody can read: the tree is hundreds of widgets,
+//! and reconstructing the part that matters by hand has failed every time it
+//! has been tried. This grows the trees `iris::random` describes, takes them
+//! apart, and prints the smallest one that still fails as something to write
+//! a fast test from.
+//!
+//!     cargo test --release --test shrink -- --ignored --nocapture
+//!
+//! `SHRINK_SEEDS` how many trees to try, `SHRINK_DEPTH` how deep to grow
+//! them, `SHRINK_CASE` which scenario or `all` for every one. `SHRINK_SEED`
+//! takes a single seed, which is how a failure `generated` printed is handed
+//! straight here: the two run the same cases over the same trees, so a seed
+//! that fails there fails here and is reduced.
+//!
+//! It is a fuzzer: run it once the ordinary tests pass, and turn what it
+//! finds into a test of its own rather than leaving a seed as the record.
+
+#[path = "scenario/mod.rs"]
+mod scenario;
+
+use iris::random::{Edits, Plan, plan};
+use scenario::{ALL, Case, diverges, env, over_seeds};
+
+/// Takes the first simplification that still fails, until none does. The
+/// simplifications come biggest first, so this walks down rather than
+/// nibbling: a six-hundred-widget tree reaches single figures in a few
+/// hundred builds.
+fn shrink(mut node: Plan, case: Case, seed: u64) -> Plan {
+    loop {
+        let Some(next) = node
+            .smaller()
+            .into_iter()
+            .find(|small| diverges(small, case, seed).is_some())
+        else {
+            return node;
+        };
+        node = next;
+    }
+}
+
+fn cases() -> Vec<Case> {
+    match env("SHRINK_CASE", String::from("all")).as_str() {
+        "all" => ALL.to_vec(),
+        name => match Case::named(name) {
+            Some(case) => vec![case],
+            None => panic!(
+                "unknown SHRINK_CASE {name:?}; one of all, {}",
+                ALL.map(Case::name).join(", ")
+            ),
+        },
+    }
+}
+
+#[test]
+#[ignore = "a fuzzer; run it once the ordinary tests pass"]
+fn no_grown_tree_lays_out_differently_warm_than_cold() {
+    let depth: usize = env("SHRINK_DEPTH", 5);
+    let cases = cases();
+    let seeds: Vec<u64> = match std::env::var("SHRINK_SEED")
+        .ok()
+        .and_then(|v| v.parse().ok())
+    {
+        Some(seed) => vec![seed],
+        None => (1..=env("SHRINK_SEEDS", 400_u64)).collect(),
+    };
+    let count = seeds.len();
+
+    over_seeds(seeds, |seed| {
+        let grown = plan(seed, depth, &Edits::default());
+        for &case in &cases {
+            let Some(how) = diverges(&grown, case, seed) else {
+                continue;
+            };
+            let small = shrink(grown.clone(), case, seed);
+            println!(
+                "seed {seed} case {}: {how}\ngrown {} widgets, shrank to {}\n{small:#?}",
+                case.name(),
+                grown.size(),
+                small.size()
+            );
+            panic!(
+                "seed {seed} lays out differently warm than cold after {}",
+                case.name()
+            );
+        }
+    });
+
+    let sizes: Vec<usize> = (1..=count as u64)
+        .map(|seed| plan(seed, depth, &Edits::default()).size())
+        .collect();
+    println!(
+        "{count} trees at depth {depth} agree over {} case(s): {} widgets total, largest {}",
+        cases.len(),
+        sizes.iter().sum::<usize>(),
+        sizes.iter().max().copied().unwrap_or(0)
+    );
+}

tests/suite.rs

@@ -0,0 +1,34 @@
+//! Every ordinary correctness test, as modules of one target.
+//!
+//! One binary rather than a dozen: each `tests/*.rs` links the whole
+//! dependency graph again, which is most of what `cargo test` spends its time
+//! on here. Libtest still runs the cases in parallel, and a filter still
+//! selects them -- `cargo test --test suite layout::` for one module.
+//!
+//! The rigs stay their own targets: `shrink` and `generated` are fuzzers run
+//! on their own, and the `*_cost` and `*_diagnostics` ones are measurements.
+
+#[path = "cases/determinism.rs"]
+mod determinism;
+#[path = "cases/drift.rs"]
+mod drift;
+#[path = "cases/idempotence.rs"]
+mod idempotence;
+#[path = "cases/layout.rs"]
+mod layout;
+#[path = "cases/plan.rs"]
+mod plan;
+#[path = "cases/pointer.rs"]
+mod pointer;
+#[path = "cases/pointer_routing.rs"]
+mod pointer_routing;
+#[path = "cases/retained.rs"]
+mod retained;
+#[path = "cases/scroll.rs"]
+mod scroll;
+#[path = "cases/tasks.rs"]
+mod tasks;
+#[path = "cases/text_edit.rs"]
+mod text_edit;
+#[path = "cases/unsettled.rs"]
+mod unsettled;

tests/trace_unsettled.rs

@@ -0,0 +1,140 @@
+//! Traces the six-widget tree in `unsettled.rs`, to see what box its text is
+//! actually drawn in on a first frame against a settled one.
+
+#![cfg(feature = "layout-diagnostics")]
+
+use iris::core::layout_diagnostics::{self as diag, TraceEvent};
+use iris::harness::Harness;
+use iris::prelude::*;
+
+fn plant(h: &mut Harness) -> Vec<WidgetId> {
+    let plain = wtext("Wrapping").size(16).wrap(false).add(&mut h.rsc);
+    let wrapped = wtext("Wrapping shapes").size(16).wrap(true).add(&mut h.rsc);
+    let sized = wrapped.width(76).add(&mut h.rsc);
+    let aligned = sized;
+    h.rsc
+        .widgets_mut()
+        .set_alignment(sized, Axis::X, AxisAlign::POS);
+    h.rsc
+        .widgets_mut()
+        .set_alignment(sized, Axis::Y, AxisAlign::POS);
+    let stack = Stack {
+        children: vec![plain.add_strong(&mut h.rsc), aligned.add_strong(&mut h.rsc)],
+        size: StackSize::Child(0),
+    }
+    .add(&mut h.rsc);
+    let root = (stack,).span(Dir::RIGHT).add(&mut h.rsc);
+    h.state.root = Some(root.add_strong(&mut h.rsc));
+    vec![
+        plain.id(),
+        wrapped.id(),
+        sized.id(),
+        aligned.id(),
+        stack.id(),
+        root.id(),
+    ]
+}
+
+fn dump(label: &str, report: &diag::Report, text: WidgetId) {
+    println!("--- {label} ---");
+    for event in report.traces() {
+        match event {
+            TraceEvent::DrawRequest {
+                id,
+                region,
+                pixel_size,
+                ..
+            } if *id == text => {
+                println!(
+                    "  draw in {:.2}x{:.2}  region {region:?}",
+                    pixel_size.x, pixel_size.y
+                )
+            }
+            TraceEvent::SizeReported { id, size } if *id == text => {
+                println!("  reported {size}")
+            }
+            TraceEvent::SizeRead { id, reader, size } if *id == text => {
+                println!("  size read by {reader:?}: {size}")
+            }
+            TraceEvent::RegionNode { id, parent, region } if *id == text => {
+                println!("  region node under {parent:?} at {region:?}")
+            }
+            TraceEvent::Reuse { id, outcome } if *id == text => println!("  reuse: {outcome:?}"),
+            _ => {}
+        }
+    }
+}
+
+#[test]
+#[ignore = "a diagnostic, not a check"]
+fn what_box_the_text_is_drawn_in() {
+    diag::clear_traced_widgets();
+    let _ = diag::take();
+    let mut h = Harness::new((640, 900));
+    let ids = plant(&mut h);
+    let text = ids[1];
+    diag::trace_widget(text);
+    let _ = diag::take();
+
+    h.frame();
+    dump("first frame", &diag::take(), text);
+
+    for _ in 0..2 {
+        for &id in &ids {
+            h.rsc.widgets_mut().get_dyn_mut(id);
+        }
+        let _ = diag::take();
+        h.frame();
+        dump("repaint", &diag::take(), text);
+    }
+    diag::clear_traced_widgets();
+}
+
+fn plant_fixed(h: &mut Harness) -> Vec<WidgetId> {
+    let words = "Wrapping shapes one source into as many lines as the box leaves";
+    let text = wtext(words).size(16).wrap(true).add(&mut h.rsc);
+    let aligned = text;
+    h.rsc
+        .widgets_mut()
+        .set_alignment(text, Axis::X, AxisAlign::NEG);
+    let inner = (aligned,).span(Dir::RIGHT).add(&mut h.rsc);
+    let sized = inner.sized((189, 176)).add(&mut h.rsc);
+    let filler = rect(Color::RED).add(&mut h.rsc);
+    let root = (filler, sized).span(Dir::RIGHT).add(&mut h.rsc);
+    h.state.root = Some(root.add_strong(&mut h.rsc));
+    vec![
+        text.id(),
+        aligned.id(),
+        inner.id(),
+        sized.id(),
+        filler.id(),
+        root.id(),
+    ]
+}
+
+#[test]
+#[ignore = "a diagnostic, not a check"]
+fn what_box_the_fixed_text_is_drawn_in() {
+    diag::clear_traced_widgets();
+    let _ = diag::take();
+    let mut h = Harness::new((1920, 1200));
+    let ids = plant_fixed(&mut h);
+    let text = ids[0];
+    diag::trace_widget(text);
+    let _ = diag::take();
+
+    h.frame();
+    dump("first frame at 1920", &diag::take(), text);
+    h.resize((640, 900));
+    h.frame();
+    dump("after resize to 640", &diag::take(), text);
+
+    let mut cold = Harness::new((640, 900));
+    let cids = plant_fixed(&mut cold);
+    diag::clear_traced_widgets();
+    diag::trace_widget(cids[0]);
+    let _ = diag::take();
+    cold.frame();
+    dump("cold at 640", &diag::take(), cids[0]);
+    diag::clear_traced_widgets();
+}