Put lengths, padding, gaps and alignment on the grid too

`Len` is `Px` beside `Rel` beside `Weight`, so the seam `4e28f10` left in
`Span` -- a float length added to a fixed-point cursor -- is gone, and the
sum a span compares against its box is exact.

`Weight` is its own scale, `Fixed<16>`, because a share of what is left over
is not a fraction of anything: a list divides its room by the total of them,
so the range has to hold a whole list's worth while the precision only has to
tell two weights apart. `Rel::ratio` turns two weights into a share on the
finer grid, which is what a span needs and what dividing them on their own
grid would round away.

`AxisAlign` holds a `Rel` rather than a float, which is what the layout was
reading out of it anyway. `Padding` and `Span::gap` hold `Px`, converted
where they are built instead of on every frame. `RegionAlign::rel` is gone;
its one caller wanted a position, and now builds one.

`Fixed` gains `from_num` for a number as it is written in source, `mul_int`
for a length repeated a whole number of times, and `ratio`.

Checked: fmt, clippy, 101 tests, 100 generated seeds in 86 s, all five
shrinker cases at 300 seeds, and all five examples byte-identical at
1920x1200 against `4e28f10`.

With the fuzzer comparing for equality rather than within 0.05 px, four of
the five cases now pass 100 seeds -- `resize-repaint` joins the other three.
`reorder` still fails one seed by one step, so the last of it is in what a
box is measured *in*: `px_len` and the window are still floats.

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

core/src/fixed.rs

@@ -1,3 +1,4 @@
+use crate::UiNum;
 use std::{
     fmt::{Debug, Display, Formatter},
     ops::{Add, AddAssign, Div, Mul, Neg, Sub, SubAssign},
@@ -28,6 +29,12 @@ pub struct Fixed<const SHIFT: u32>(i32);
 /// the same number reach the GPU.
 pub type Px = Fixed<6>;
 
+/// 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
@@ -86,6 +93,12 @@ impl<const SHIFT: u32> Fixed<SHIFT> {
         })
     }
 
+    /// 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
     }
@@ -117,6 +130,11 @@ impl<const SHIFT: u32> Fixed<SHIFT> {
         Self(narrow(shift_round(self.0 as i64 * by.0 as i64, BY)))
     }
 
+    /// Repeated a whole number of times, which no grid rounds.
+    pub const fn mul_int(self, by: i32) -> Self {
+        Self(narrow(self.0 as i64 * by as i64))
+    }
+
     /// 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 saturates so that a
     /// release build lays out something absurd rather than dying.
@@ -131,6 +149,16 @@ impl<const SHIFT: u32> Fixed<SHIFT> {
         Self(narrow(div_round((self.0 as i64) << BY, by.0 as i64)))
     }
 
+    /// `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(narrow(div_round((num.0 as i64) << SHIFT, den.0 as i64)))
+    }
+
     /// `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> {
@@ -347,6 +375,15 @@ mod tests {
         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);