wireless-docs/content/tilesets-experimental.typ

= Experimental Low-Latency Tilesets

#let stylesheet = ```
.tile {
  display: inline-block;
  font-size: 1.4em;
  width: 1em;
  margin-block: -0.25em;
  aspect-ratio: 1;

  background-image: url('/wiki-schematic-sprite.png'), url('/wiki-schematic-sprite.png');
  background-color: white;
  background-size: 31.99em;
  image-rendering: pixelated;
}

.r1-l    { background-position:  -8em -5em, -0em -2em; }
.r2-l    { background-position:  -9em -5em, -0em -2em; }
.r3-l    { background-position: -10em -5em, -0em -2em; }
.r4-l    { background-position: -11em -5em, -0em -2em; }
.c-l     { background-position: -12em -7em, -0em -2em; }
.block   { background-position:  -7em -0em, -0em -2em; }
.wire-lr { background-position: -10em -2em, -0em -2em; }

```

#let tileset(file, summary: none, start: 1) = html.details(open: false)[
  #if summary != none { html.summary(summary) }

  #html.div(style: "font-size: larger", {
    show "R1": html.i(class: "tile r1-l", title: "2gt Repeater")
    show "R2": html.i(class: "tile r2-l", title: "4gt Repeater")
    show "R3": html.i(class: "tile r3-l", title: "6gt Repeater")
    show "R4": html.i(class: "tile r4-l", title: "8gt Repeater")
    show "C": html.i(class: "tile c-l", title: "Comparator")
    show "-": html.i(class: "tile wire-lr", title: "Redstone Wire (or opaque block)")
    show " ": none

    let lines = read(file).trim().split("\n").map(it => it.trim("-"))
    enum(start: start, ..lines)
  })
]

#html.style(stylesheet.text)

#link("chains.py", `chains.py`) enumerates generalized tilesets, accounting for priorities 0, -1,
and -3 with various delays. Note it does _not_ account for inverted components or pulses, so cannot
include priority -2.

Still, this means we have 3 priorities and 4 delays to work with. The number of chains with total
delay $n$ is $O(9^(n\/2))$. For example, at 8gt delay, there are 97 generalized tilesets but only
$2^4 = 16$ binary tileset.

The generalized tilesets are highly irregular, but they may be useful for static prefixes or
suffixes where latency is critical.

== Variable-length tilesets 2gt - 10gt.

I don't include them all explicitly here since the plain lists are unweildy, but at various delays
the number of general chains grows quickly:

#html.table(
  {
    html.colgroup({
      html.col(style: "width: 15ch")
      html.col(style: "width: auto")
      html.col(style: "width: 15ch")
    })
    html.thead({
      html.th[Total Delay]
      html.th[\# General]
      html.th[\# Binary]
    })
    html.tbody({
      html.tr({
        html.td[2gt]
        html.td(tileset("tileset-2-n.txt", summary: [2]))
        html.td[2]
      })
      html.tr({
        html.td[4gt]
        html.td(tileset("tileset-4-n.txt", summary: [7]))
        html.td[4]
      })
      html.tr({
        html.td[6gt]
        html.td(tileset("tileset-6-n.txt", summary: [26]))
        html.td[8]
      })
      html.tr({
        html.td[8gt]
        html.td(tileset("tileset-8-n.txt", summary: [97]))
        html.td[16]
      })
      html.tr({
        html.td[10gt]
        html.td[361]
        html.td[32]
      })
      html.tr({
        html.td[12gt]
        html.td[1343]
        html.td[64]
      })
      html.tr({
        html.td[14gt]
        html.td[4997]
        html.td[128]
      })
    })
  },
)

== Uniform subsets

The variable-length tilesets are difficult to wire, so some useful subsets are those with a fixed
number of _blocks_. These still grow faster in $n$ than the equivalent binary tilesets.

Note that the output of #link("chains.py", `chains.py`) always includes a trailing redstone wire,
since the last diode in the tileset can never be facing another diode. You must then add one to the
block count to account for this extra wire. For example, the command to generate the "10gt, 5 block"
list below is `python chains.py 10 6`, and it produces output like "`- R1 C R2 - C`" (where the
signal flows right-to-left).

#html.table(
  {
    html.colgroup({
      html.col(style: "width: 15ch")
      html.col(style: "width: auto")
      html.col(style: "width: 15ch")
    })
    html.thead({
      html.th[Total Delay]
      html.th[\# General]
      html.th[\# Binary]
    })
    html.tbody({
      html.tr({
        html.td[8gt, 4 block]
        html.td(tileset("tileset-8-4.txt", summary: [39]))
        html.td[16]
      })
      html.tr({
        html.td[10gt, 5 block]
        html.td(tileset("tileset-10-5.txt", summary: [135]))
        html.td[32]
      })
      html.tr({
        html.td[12gt, 6 block]
        html.td[481]
        html.td[64]
      })
      html.tr({
        html.td[14gt, 7 block]
        html.td[1740]
        html.td[128]
      })
    })
  },
)