image-builder: makeExt4: implements minimal resizing

The algorithms inside `make_ext4fs` can be followed, but it ends up
being a bit complex. I did not figure out all variables, but the amount
of them made me reluctant to implement it as a complte formula.

Instead, I looked at the actual usable space using `df` and mapped it in
a spreadsheet. With the knowledge from actively looking at the source
code, and other data, it is known that the lookup table will work, while
not be ideal.

The fudge factor starting at 256MiB is about stable, but there is a
slight downward deviation at 512MiB, which is why 512MiB was used. The
downward deviation was not observed in other values.

Here's the table as computed.

```
MIB	Fudge
5	0.84609375
8	0.5419921875
16	0.288818359375
32	0.1622314453125
64	0.09893798828125
128	0.067291259765625
256	0.0518646240234375
512	0.05208587646484375
1024	0.048187255859375
2048	0.04060554504394531
4096	0.03718090057373047
```

The difference from .52% to .37% is negligible for 0.5 vs. 4 GiB is
annoying me. The lookup table could be changed to include all known
values instead, I guess.

lib/image-builder/makeExt4.nix

@@ -1,9 +1,43 @@
-{ imageBuilder, libfaketime, e2fsprogs, make_ext4fs }:
+{ lib, imageBuilder, libfaketime, e2fsprogs, make_ext4fs }:
 
 /*  */ let scope = { "fileSystem.makeExt4" =
 
 let
+  inherit (lib.strings) splitString;
   inherit (imageBuilder) makeFilesystem;
+
+  # Bash doesn't do floating point representations. Multiplications and divisions
+  # are handled with enough precision that we can multiply and divide to get a precision.
+  precision = 1000;
+
+  first = list: lib.lists.last (lib.lists.reverseList list);
+  chopDecimal = f: first (splitString "." (toString f));
+  makeFudge = f: toString (chopDecimal (f * precision));
+
+  # This applies only to 256MiB and greater.
+  # For smaller than 256MiB images the overhead from the FS is much greater.
+  # This will also let *some* slack space at the end at greater sizes.
+  # This is the value at 512MiB where it goes slightly down compared to 256MiB.
+  fudgeFactor = makeFudge 0.05208587646484375;
+
+  # This table was built using a script that built an image with `make_ext4fs`
+  # for the given size in MiB, and recorded the available size according to `df`.
+  smallFudgeLookup = lib.strings.concatStringsSep "\n" (lib.lists.reverseList(
+    lib.attrsets.mapAttrsToList (size: factor: ''
+      elif (( size > ${toString size} )); then
+        fudgeFactor=${toString factor}
+    '') {
+    "${toString (imageBuilder.size.MiB   5)}" = makeFudge 0.84609375;
+    "${toString (imageBuilder.size.MiB   8)}" = makeFudge 0.5419921875;
+    "${toString (imageBuilder.size.MiB  16)}" = makeFudge 0.288818359375;
+    "${toString (imageBuilder.size.MiB  32)}" = makeFudge 0.1622314453125;
+    "${toString (imageBuilder.size.MiB  64)}" = makeFudge 0.09893798828125;
+    "${toString (imageBuilder.size.MiB 128)}" = makeFudge 0.067291259765625;
+    "${toString (imageBuilder.size.MiB 256)}" = makeFudge 0.0518646240234375;
+  }
+  ));
+
+  minimumSize = imageBuilder.size.MiB 5;
 in
 { partitionID
 , blockSize ? imageBuilder.size.KiB 4
@@ -11,8 +45,7 @@ in
 makeFilesystem (args // {
   filesystemType = "ext4";
 
-  inherit blockSize;
-  minimumSize = imageBuilder.size.MiB 5;
+  inherit blockSize minimumSize;
 
   nativeBuildInputs = [
     e2fsprogs
@@ -24,6 +57,40 @@ makeFilesystem (args // {
     :
   '';
 
+  computeMinimalSize = ''
+    # `local size` is in bytes.
+
+    # We don't have a static reserved factor figured out. It is rather hard with
+    # ext4fs as there are multiple factors increasing the overhead.
+    local reservedSize=0
+    local fudgeFactor=${toString fudgeFactor}
+    
+    # Instead we rely on a lookup table. See how it is built in the derivation file.
+    if (( size < ${toString (imageBuilder.size.MiB 256)} )); then
+      echo "$size is smaller than 256MiB; using the lookup table." 1>&2
+      
+      # A bit of a hack, though allows us to build the lookup table using only
+      # elifs.
+      if false; then
+        :
+      ${smallFudgeLookup}
+      else
+        # The data is smaller than 5MiB... The filesystem image size will likely
+        # not be able to accomodate... here we handle it in another way.
+        fudgeFactor=0
+        echo "Fudge factor skipped for extra small partition. Instead increasing by a fixed amount." 1>&2
+        size=$(( size + ${toString minimumSize}))
+      fi
+    fi
+
+    local reservedSize=$(( size * $fudgeFactor / ${toString precision} ))
+
+    echo "Fudge factor: $fudgeFactor / ${toString precision}" 1>&2
+    echo -n "Adding reservedSize: $size + $reservedSize = " 1>&2
+    size=$((size + reservedSize))
+    echo "$size" 1>&2
+  '';
+
   copyPhase = ''
     faketime -f "1970-01-01 00:00:00" \
       make_ext4fs \