store camel stack positions (also slower apparently)

.gitignore

@@ -1,2 +1,2 @@
-/target
-*.etl*
+*.exe
+profile_results.txt

Cargo.lock

@@ -1,90 +0,0 @@
-# This file is automatically @generated by Cargo.
-# It is not intended for manual editing.
-version = 3
-
-[[package]]
-name = "cfg-if"
-version = "1.0.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "baf1de4339761588bc0619e3cbc0120ee582ebb74b53b4efbf79117bd2da40fd"
-
-[[package]]
-name = "cup"
-version = "0.1.0"
-dependencies = [
- "enum-map",
- "fastrand",
-]
-
-[[package]]
-name = "enum-map"
-version = "2.4.2"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "50c25992259941eb7e57b936157961b217a4fc8597829ddef0596d6c3cd86e1a"
-dependencies = [
- "enum-map-derive",
-]
-
-[[package]]
-name = "enum-map-derive"
-version = "0.11.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "2a4da76b3b6116d758c7ba93f7ec6a35d2e2cf24feda76c6e38a375f4d5c59f2"
-dependencies = [
- "proc-macro2",
- "quote",
- "syn",
-]
-
-[[package]]
-name = "fastrand"
-version = "1.8.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "a7a407cfaa3385c4ae6b23e84623d48c2798d06e3e6a1878f7f59f17b3f86499"
-dependencies = [
- "instant",
-]
-
-[[package]]
-name = "instant"
-version = "0.1.12"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "7a5bbe824c507c5da5956355e86a746d82e0e1464f65d862cc5e71da70e94b2c"
-dependencies = [
- "cfg-if",
-]
-
-[[package]]
-name = "proc-macro2"
-version = "1.0.49"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "57a8eca9f9c4ffde41714334dee777596264c7825420f521abc92b5b5deb63a5"
-dependencies = [
- "unicode-ident",
-]
-
-[[package]]
-name = "quote"
-version = "1.0.23"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "8856d8364d252a14d474036ea1358d63c9e6965c8e5c1885c18f73d70bff9c7b"
-dependencies = [
- "proc-macro2",
-]
-
-[[package]]
-name = "syn"
-version = "1.0.107"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1f4064b5b16e03ae50984a5a8ed5d4f8803e6bc1fd170a3cda91a1be4b18e3f5"
-dependencies = [
- "proc-macro2",
- "quote",
- "unicode-ident",
-]
-
-[[package]]
-name = "unicode-ident"
-version = "1.0.6"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "84a22b9f218b40614adcb3f4ff08b703773ad44fa9423e4e0d346d5db86e4ebc"

Cargo.toml

@@ -1,17 +0,0 @@
-[package]
-name = "cup"
-version = "0.1.0"
-edition = "2021"
-
-# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
-
-[dependencies]
-enum-map = "2.4.2"
-fastrand = "1.8.0"
-
-# [profile.release]
-# lto = true
-
-[profile.perf]
-inherits = "release"
-debug = true

README.md

@@ -1,12 +1,10 @@
 # `cup` - CamelUp probability calculator
 
-This tool calculates probable outcomes for the board game CamelUp. It can
-calculate all possible outcomes for a single game leg in about 5ms, so
-effectively instantaneously. Full-game calculations take a little bit longer
-and are not exact (since it isn't practical to simulate all possible full
-game states.) However it can easily simulate a million random games in about
-80ms in the worst case, which should provide estimates accurate to within
-about 0.2%. (Numbers from running on a Ryzen 3700X.)
+This tool calculates probable outcomes for the board game CamelUp.
+It can calculate all possible outcomes for a single game leg in about 5ms, so effectively instantaneously.
+Full-game calculations take a little bit longer and are not exact (since it isn't practical to simulate all possible full game states.)
+However it can easily simulate a million random games in about 80ms in the worst case, which should provide estimates accurate to within about 0.2%.
+(Numbers from running on a Ryzen 3700X.)
 
 ```
 Usage: 

combinators.nim

@@ -0,0 +1,96 @@
+import algorithm, random, sugar
+import fixedseq, game
+
+
+proc nextPermutation(x: var FixedSeq): bool =
+  # copied shamelessly from std/algorithm.nim
+  if x.len < 2:
+    return false
+
+  var i = x.high
+  while i > 0 and x[i - 1] >= x[i]:
+    dec i
+
+  if i == 0:
+    return false
+
+  var j = x.high
+  while j >= i and x[j] <= x[i - 1]:
+    dec j
+
+  swap x[j], x[i - 1]
+  x.reverse(i, x.high)
+  
+  result = true
+
+
+proc prevPermutation(x: var FixedSeq): bool =
+  # copied shamelessly from std/algorithm.nim
+  if x.len < 2:
+    return false
+
+  var i = x.high
+  while i > 0 and x[i - 1] <= x[i]:
+    dec i
+
+  if i == 0:
+    return false
+
+  x.reverse(i, x.high)
+
+  var j = x.high
+  while j >= i and x[j - 1] < x[i - 1]:
+    dec j
+
+  swap x[i - 1], x[j]
+
+  result = true
+
+
+iterator allPermutations*(x: FixedSeq): FixedSeq =
+  # returns all permutations of a given seq. Order is wonky but we don't care.
+  var workingCopy = x
+  yield workingCopy
+  while workingCopy.nextPermutation: # this mutates workingCopy
+    yield workingCopy
+  workingCopy = x
+  while workingCopy.prevPermutation:
+    yield workingCopy
+
+
+iterator allDigits*(lo, hi, size: Natural): auto =
+  if size > 0: # otherwise we get an infinite loop
+    var digits: FixedSeq[5, int, int8]
+    digits.initFixedSeq
+    for i in 0 ..< size:
+      digits.add(lo)
+
+    var complete = false
+    while not complete:
+      yield digits
+      for i in countdown(digits.high, 0):
+        if digits[i] < hi:
+          inc digits[i]
+          break
+        elif i == 0: # since this is the last digit to be incremented, we must be done
+          complete = true
+        else:
+          digits[i] = lo
+
+
+iterator possibleFutures*(dice: FixedSeq): auto =
+  # iterate over all possible sequences of die rolls. Each outcome
+  # is returned as a 5-sequence of (color, number) tuples.
+  for perm in dice.allPermutations:
+    for digits in allDigits(1, 3, dice.len):
+      var f = initFixedSeq(5, Die, int8)
+      for i in 0 .. dice.high:
+        f.add((perm[i], digits[i]))
+      yield f
+
+
+proc randomFuture*(dice: FixedSeq, r: var Rand): FixedSeq[5, Die, int8] =
+  result.initFixedSeq
+  let order = dice.dup(shuffle(r))
+  for i, color in order:
+    result.add((color, r.rand(1..3)))

config.nims

@@ -0,0 +1,5 @@
+--threads: on
+--d: release
+--opt: speed
+--passC: -flto
+--passL: -flto

cup.nim

@@ -0,0 +1,17 @@
+import game, simulation, ui
+
+
+when isMainModule:
+  let config = parseArgs()
+  var b: Board
+  b.init
+  b.setState(config.state, [])
+  b.diceRolled = config.diceRolled
+  echo b.showSpaces(1, 16)
+  let legScores = b.getLegScores
+  echo "\nCurrent leg probabilities:"
+  echo legScores.showPercents()
+  
+  let gameScores = b.randomGames(1_000_000)
+  echo "\nFull game probabilities (1M simulations):"
+  echo gameScores.showPercents()

fixedseq.nim

@@ -0,0 +1,146 @@
+import random
+
+
+type
+  FixedSeq*[Idx: static int; Contents; Pointer: SomeSignedInt] = object
+    data: array[Idx, Contents]
+    last: Pointer
+
+
+proc initFixedSeq*(size: static Natural; cType: typedesc; pType: typedesc[SomeSignedInt]): auto =
+  var s: FixedSeq[size, cType, pType]
+  s.last = -1
+  result = s
+
+proc initFixedSeq*(s: var FixedSeq) =
+  s.last = -1
+
+
+proc `$`*(s: FixedSeq): string =
+  result.add("FixedSeq[")
+  for i, item in s:
+    if i != 0:
+      result.add(", ")
+    result.add($item)
+  result.add("]")
+
+
+proc `[]`*(s: FixedSeq, i: Natural): FixedSeq.Contents =
+  if i > s.last:
+    raise newException(IndexDefect, "index " & $i & " is out of bounds.")
+  s.data[i]
+
+
+proc `[]`*(s: var FixedSeq, i: Natural): var FixedSeq.Contents =
+  if i > s.last:
+    raise newException(IndexDefect, "index " & $i & " is out of bounds.")
+  s.data[i]
+
+
+proc `[]`*(s: FixedSeq, i: BackwardsIndex): auto =
+  if s.last == -1:
+    raise newException(IndexDefect, "index out of bounds, the container is empty.") # matching stdlib again
+  s.data[s.last - typeof(s.last)(i) + 1]
+
+
+proc `[]=`*(s: var FixedSeq, i: Natural, v: FixedSeq.Contents) =
+  if i > s.last:
+    raise newException(IndexDefect, "index " & $i & " is out of bounds.")
+  s.data[i] = v
+
+
+proc high*(s: FixedSeq): auto =
+  result = s.last
+
+
+proc low*(s: FixedSeq): auto =
+  result = case s.last
+  of -1: 0 # a bit weird but it's how the stdlib seq works
+  else: s.last
+
+
+proc len*(s: FixedSeq): auto =
+  result = s.last + 1
+
+
+iterator items*(s: FixedSeq): auto =
+  for i in 0 .. s.last:
+    yield s.data[i]
+
+
+iterator asInt*(s: FixedSeq): int8 =
+  for i in 0 .. s.last:
+    yield int8(s.data[i]) # now we do have to convert
+
+
+iterator pairs*(s: FixedSeq): auto =
+  var count = 0
+  for c in s:
+    yield (count, c)
+    inc count
+
+
+proc add*(s: var FixedSeq, v: FixedSeq.Contents) =
+  let i = s.last + 1
+  s.data[i] = v # will raise exception if out of bounds
+  s.last = i
+
+
+proc insert*(s: var FixedSeq, v: FixedSeq.Contents, idx: Natural = 0) =
+  for i in countdown(s.last, typeof(s.last)(idx)):
+    swap(s.data[i], s.data[i + 1]) # will also raise exception if out of bounds
+  s.data[idx] = v
+  inc s.last
+
+
+proc delete*(s: var FixedSeq, idx: Natural) =
+  if idx > s.last:
+    raise newException(IndexDefect, "index " & $idx & " is out of bounds.")
+  s.data[idx] = -1
+  dec s.last
+  for i in typeof(s.last)(idx) .. s.last:
+    swap(s.data[i], s.data[i + 1])
+
+
+proc find*(s: FixedSeq, needle: FixedSeq.Contents): FixedSeq.Pointer =
+  for i, v in s.data:
+    if v == needle:
+      return i
+  return -1
+
+
+proc reverse*(s: var FixedSeq; first, last: Natural) =
+  # copied shamelessly from std/algorithm.nim
+  var x = first
+  var y = last
+  while x < y:
+    swap(s[x], s[y])
+    inc x
+    dec y 
+
+
+proc shuffle*(s: var FixedSeq, r: var Rand) =
+  r.shuffle(s.data)
+
+
+proc moveSubstack*(src, dst: var FixedSeq; start: Natural) =
+  var count: typeof(src.last) = 0 # have to track this separately apparently
+  for idx in start .. src.last:
+    swap(src.data[idx], dst.data[dst.last + 1 + count])
+    inc count
+  dst.last += count
+  src.last -= count
+
+
+proc moveSubstackPre*(src, dst: var FixedSeq; start: Natural) =
+  let ssLen = typeof(src.last)(src.last - start + 1) # length of substack
+  for i in countdown(dst.last, 0):
+    swap(dst.data[i], dst.data[i + ssLen])
+
+  var count = 0
+  for i in start .. src.last:
+    swap(src.data[i], dst.data[count])
+    inc count
+
+  dst.last += ssLen
+  src.last -= ssLen

game.nim

@@ -0,0 +1,169 @@
+import hashes, options
+import fixedseq
+
+
+type
+  Color* = enum
+    cRed, cGreen, cBlue, cYellow, cPurple
+
+  ColorStack* = FixedSeq[5, Color, int8]
+
+
+proc initColorStack*: ColorStack =
+  result.initFixedSeq
+
+
+proc getAllColors: ColorStack = 
+  var i = 0
+  for c in Color.low .. Color.high:
+    result[i] = c
+
+const 
+  allColors* = getAllColors()
+  colorNames: array[Color, string] =
+    ["Red", "Green", "Blue", "Yellow", "Purple"]
+  colorAbbrevs: array[Color, char] = ['R', 'G', 'B', 'Y', 'P']
+
+
+proc `$`*(c: Color): string =
+  result = colorNames[c]
+
+
+proc abbrev*(c: Color): char =
+  result = colorAbbrevs[c]
+
+
+proc `$`*(s: ColorStack): string =
+  result.add("St@[")
+  for i, color in s:
+    result.add($color)
+    if i < s.high:
+      result.add(", ")
+  result.add("]")
+
+
+type
+  Die* = tuple[color: Color, value: int]
+
+  Tile* = enum
+    tBackward = -1,
+    tForward = 1
+
+  Square* = object
+    camels*: ColorStack
+    tile*: Option[Tile]
+
+  CamelPos* = object
+    square*: range[1..16]
+    stackIdx*: int8
+
+  Board* = object
+    squares*: array[1..16, Square]
+    camels*: array[Color, CamelPos]
+    diceRolled*: array[Color, bool]
+    leader*: Option[Color]
+    gameOver*: bool
+    initialized: bool
+
+
+# use a template here for better inlining
+template `[]`*[T](b: var Board, idx: T): var Square =
+  b.squares[idx]
+
+
+proc hash*(b: Board): Hash =
+  var h: Hash = 0
+  # there could be a tile anywhere so we have to check all squares
+  for i, sq in b.squares:
+    if sq.camels.len > 0 or sq.tile.isSome:
+      h = h !& i
+      if sq.tile.isSome:
+        h = h !& int(sq.tile.get) * 10 # so it isn't confused with a camel
+      else:
+        for c in sq.camels.asInt:
+          h = h !& c
+  result = !$h
+
+
+proc init*(b: var Board) =
+  for sq in b.squares.mitems:
+    sq.camels.initFixedSeq
+  b.initialized = true
+
+
+proc display*(b: Board, start, stop: int) =
+  for i in start..stop:
+    let sq = b.squares[i]
+    let lead = $i & ": "
+    if sq.tile.isSome:
+      stdout.writeLine($lead & $sq.tile.get)
+    else:
+      stdout.writeLine($lead & $sq.camels)
+  echo ""
+
+
+proc setState*(b: var Board; 
+               camels: openArray[tuple[c: Color, p: int]];
+               tiles: openArray[tuple[t: Tile, p: int]]) =
+  for (color, dest) in camels: # note that `camels` is ordered, as this determines stacking
+    b[dest].camels.add(color)
+    let height = b[dest].camels.high
+    b.camels[color] = CamelPos(square: dest, stackIdx: height)
+
+  for (tile, dest) in tiles:
+    b[dest].tile = some(tile)
+
+  for sq in b.squares:
+    if sq.camels.len > 0:
+      let squareLeader = sq.camels[^1]
+      if b.leader.isNone or b.leader.get != squareLeader:
+        b.leader = some(squareLeader)
+
+
+proc diceRemaining*(b: Board): ColorStack =
+  result.initFixedSeq
+  for color, isRolled in b.diceRolled:
+    if not isRolled: result.add(color)
+
+
+proc resetDice*(b: var Board) =
+  for c, rolled in b.diceRolled:
+    b.diceRolled[c] = false
+
+
+proc advance*(b: var Board, die: Die) =
+  let
+    (color, roll) = die
+    startPos = b.camels[color].square
+  var endPos = startPos + roll
+  
+  if endPos > 16: # camel has passed the finish line
+    b.leader = some(b[startPos].camels[^1])
+    b.gameOver = true
+    return
+
+  var prepend = false
+  if b[endPos].tile.isSome: # adjust position (and possibly stacking) to account for tile
+    let t = b[endPos].tile.get
+    endPos += int(t)
+    if t == tBackward: prepend = true
+
+  let stackStart = b[startPos].camels.find(color)
+  if prepend:
+    b[startPos].camels.moveSubstackPre(b[endPos].camels, stackStart)
+    let stackLen = b[startPos].camels.len - stackStart
+    for i in 0'i8 ..< stackLen:
+      # we know how many camels we added to the bottom, so set the position for each of those
+      b.camels[b[endPos].camels[i]] = CamelPos(square: endPos, stackIdx: i) # replace with cast later?
+  else:
+    let dstPrevHigh = b[endPos].camels.high
+    b[startPos].camels.moveSubstack(b[endPos].camels, stackStart)
+    # the camels that have moved start immediately after the previous high camel
+    for i in (dstPrevHigh + 1) .. b[endPos].camels.high:
+      b.camels[b[endPos].camels[i]] = CamelPos(square: endPos, stackIdx: i)
+  
+  # if we are stacking on or moving past the previous leader
+  if endPos >= b.camels[b.leader.get].square:
+    b.leader = some(b[endPos].camels[^1])
+  
+  b.diceRolled[color] = true

simulation.nim

@@ -0,0 +1,138 @@
+import cpuinfo, math, options, random, tables
+import combinators, game, fixedseq
+
+
+type
+  ScoreSet* = array[Color, int]
+  WinPercents* = array[Color, float]
+
+  ScoreSpread = object
+    lo*: array[Color, float]
+    hi*: array[Color, float]
+
+  LegResults* = tuple[scores: ScoreSet, endStates: CountTable[Board]]
+
+
+proc update*(scores: var ScoreSet, toAdd: ScoreSet) =
+  for i, s in toAdd:
+    scores[i] += s
+
+
+proc display*(scores: ScoreSet) =
+  let total = scores.sum
+  for color, score in scores:
+    let line = $color & ": " & $round(100 * scores[color] / total, 2) & '%'
+    stdout.writeLine(line)
+    stdout.flushFile()
+    # echo color, ": ", round(100 * scores[color] / total, 2), '%'
+
+
+proc percents*(scores: ScoreSet): WinPercents =
+  let total = scores.sum
+  for c, score in scores:
+    result[c] = score / total
+
+
+# ======================
+# Single-leg simulations
+# ======================
+
+iterator legEndStates(b: Board): Board =
+  var diceRemaining: ColorStack
+  diceRemaining.initFixedSeq
+  for i, c in b.diceRolled:
+    if not c: diceRemaining.add(i)
+
+  for future in possibleFutures(diceRemaining):
+    var prediction = b # make a copy so we can mutate
+    for dieRoll in future:
+      prediction.advance(dieRoll)
+    yield prediction
+
+
+proc getLegScores*(b: Board): ScoreSet =
+  for prediction in b.legEndStates:
+    inc result[prediction.leader.get]
+
+
+# =====================
+# Full-game simulations
+# =====================
+
+proc randomGame*(b: Board, r: var Rand): Color =
+  var projection = b
+  while true:
+    for roll in randomFuture(projection.diceRemaining, r):
+      projection.advance(roll)
+      if projection.gameOver:
+        return projection.leader.get
+    projection.resetDice()
+
+
+proc randomGamesWorker(b: Board, count: Natural, r: var Rand): ScoreSet =
+  for i in 1 .. count:
+    let winner = b.randomGame(r)
+    inc result[winner]
+
+
+# =======================
+# Multithreading nonsense
+# =======================
+
+type WorkerArgs = object
+  board: Board
+  count: Natural
+  seed: int64
+
+
+# have to do this at the module level so it can be shared
+var gamesChannel: Channel[ScoreSet]
+gamesChannel.open()
+
+
+proc randomGamesThread(args: WorkerArgs) =
+  var r = initRand(args.seed)
+  let scores = randomGamesWorker(args.board, args.count, r)
+  gamesChannel.send(scores)
+
+
+proc randomGames*(b: Board, count: Natural, parallel = true, numThreads = 0): ScoreSet =
+  randomize()
+
+  if not parallel:
+    var r = initRand(rand(int64))
+    return randomGamesWorker(b, count, r)
+
+  let numThreads =
+    if numThreads == 0:
+      countProcessors()
+    else:
+      numThreads
+
+  var workers = newSeq[Thread[WorkerArgs]](numThreads)
+  for i, w in workers.mpairs:
+    var numGames = int(floor(count / numThreads))
+    if i < (count mod numThreads):
+      numGames += 1
+    let args = WorkerArgs(board: b, count: numGames, seed: rand(int64))
+
+    createThread(w, randomGamesThread, args)
+
+  for i in 1 .. numThreads:
+    let scores = gamesChannel.recv()
+    result.update(scores)
+
+
+proc randomSpread*(b: Board; nTests, nSamples: Natural): ScoreSpread =
+  for s in result.lo.mitems:
+    s = 1
+
+  for i in 0 ..< nTests:
+    let scores = b.randomGames(nSamples)
+    let total = scores.sum
+    for color, score in scores:
+      let pct = score / total
+      if pct < result.lo[color]:
+        result.lo[color] = pct
+      if pct > result.hi[color]:
+        result.hi[color] = pct

src/game.rs

@@ -1,375 +0,0 @@
-use enum_map::{Enum, EnumMap};
-use fastrand::Rng;
-
-use crate::stack::Stack;
-
-
-#[derive(Debug, Copy, Clone, Eq, PartialEq, Default, Enum)]
-pub enum Color {
-    #[default] Red, Green, Blue, Yellow, Purple,
-}
-
-// const COLORS: Stack<Color, 5> = Stack::from_array([
-//     Color::Red,
-//     Color::Green,
-//     Color::Blue,
-//     Color::Yellow,
-//     Color::Purple,
-// ]);
-
-const COLORS: [Color; 5] = [
-    Color::Red,
-    Color::Green,
-    Color::Blue,
-    Color::Yellow,
-    Color::Purple,
-];
-
-
-type ColorStack = Stack<Color, 5>;
-
-
-#[derive(Debug, Copy, Clone)]
-pub enum Tile {
-    Forward,
-    Backward,
-}
-
-
-#[derive(Debug, Copy, Clone)]
-pub enum Square {
-    Camels(ColorStack),
-    Tile(Tile),
-}
-
-impl Square {
-    fn assume_stack(&self) -> &ColorStack {
-        match self {
-            Square::Camels(stack) => stack,
-            _ => panic!("Attempted to use the stack from a non-stack square"),
-        }
-    }
-
-    fn assume_stack_mut(&mut self) -> &mut ColorStack {
-        match self {
-            Square::Camels(stack) => stack,
-            _ => panic!("Attempted to use the stack from a non-stack square"),
-        }
-    }
-}
-
-impl Default for Square {
-    fn default() -> Self {
-        Square::Camels(ColorStack::new())
-    }
-}
-
-
-#[derive(Debug, Default, Copy, Clone)]
-pub struct Game {
-    squares: [Square; 16],
-    dice: EnumMap<Color, bool>,
-    camels: EnumMap<Color, usize>,
-}
-
-impl Game {
-    pub fn new() -> Self {
-        Self::default()
-    }
-
-    // new game with random starting positions
-    pub fn new_random() -> Self {
-        let mut game = Self::default();
-        let rng = Rng::new();
-        let mut dice = *&COLORS;
-        rng.shuffle(&mut dice);
-        for color in dice {
-            let roll = rng.usize(1..=3);
-            game.squares[roll - 1].assume_stack_mut().push(color);
-            game.camels[color] = roll - 1;
-        }
-        game
-    }
-
-    pub fn set_state(&mut self, camels: &[(Color, usize); 5], dice: &EnumMap<Color, bool>) {
-        for i in 0..16 {
-            self.squares[i] = match self.squares[i] {
-                Square::Camels(mut stack) => {
-                    stack.clear();
-                    Square::Camels(stack)
-                },
-                _ => Square::Camels(Stack::new())
-            };
-        }
-
-        for square in self.squares {
-            assert_eq!(square.assume_stack().len(), 0)
-        }
-
-        self.dice = *dice;
-        for &(color, sq) in camels {
-            self.squares[sq].assume_stack_mut().push(color);
-            self.camels[color] = sq;
-        }
-    }
-
-    pub fn get_state(&self) -> ([(Color, usize); 5], EnumMap<Color, bool>) {
-        let mut state = [(Color::Red, 0); 5];
-
-        let mut j = 0;
-        for (sq_idx, square) in self.squares.iter().enumerate() {
-            if let Square::Camels(stack) = square {
-                for camel in stack.iter() {
-                    state[j] = (*camel, sq_idx);
-                    j += 1;
-                }
-            }
-        }
-
-        (state, self.dice)
-    }
-
-    // returns winner if there is one
-    pub fn advance(&mut self, die: Color, roll: usize) -> Option<Color> {
-        let src_sq = self.camels[die];
-        let dst_sq = src_sq + roll;
-        if dst_sq >= 16 {
-            self.dice[die] = true;
-            return self.squares[src_sq].assume_stack().last().copied();
-        }
-
-        // special case when the destination square is the same as the source square
-        if let Square::Tile(Tile::Backward) = self.squares[dst_sq] {
-            if roll == 1 {
-                let src_stack = self.squares[src_sq].assume_stack_mut();
-                let slice_start = src_stack.iter().position(|&c| c == die).unwrap();
-                src_stack.shift_slice_under(slice_start);
-            }
-        }
-        else {
-            // we have to split self.squares into two slices using split_at_mut, otherwise
-            // rustc complains that we're trying to use two mutable references to the same value
-            let (left, right) = self.squares.split_at_mut(src_sq + 1);
-            let src_stack = left[src_sq].assume_stack_mut();
-            let slice_start = src_stack.iter().position(|&c| c == die).unwrap();
-
-            // since `right` starts immediately after the source square, the index of the 
-            // destination square will be roll - 1 (e.g. if roll is 1, dst will be right[0])
-            let (dst_rel_idx, prepend) = match right[roll - 1] {
-                Square::Tile(Tile::Forward) => (roll, false), // roll - 1 + 1
-                Square::Tile(Tile::Backward) => (roll - 2, true), // roll is guaranteed to be >= 2 since we already handled roll == 1
-                _ => (roll - 1, false),
-            };
-            let dst_stack = right[dst_rel_idx].assume_stack_mut();
-            let dst_true_idx = src_sq + 1 + dst_rel_idx; // src_sq + 1 was the original split boundary, so add the relative index to that to get the true index
-
-            if prepend {
-                let slice_len = src_stack.len() - slice_start;
-                src_stack.move_slice_under(dst_stack, slice_start);
-                for i in 0..slice_len {
-                    self.camels[dst_stack[i]] = dst_true_idx;
-                }
-            }
-            else {
-                let dst_prev_len = dst_stack.len();
-                src_stack.move_slice(dst_stack, slice_start);
-                for i in dst_prev_len..dst_stack.len() {
-                    self.camels[dst_stack[i]] = dst_true_idx;
-                }
-            }
-        }
-
-        self.dice[die] = true;
-        None
-    }
-
-    fn finish_leg_random(&mut self, rng: &Rng) -> Option<Color> {
-        let mut leg_dice: Stack<Color, 5> = Stack::new();
-        for (color, rolled) in self.dice {
-            if !rolled {
-                leg_dice.push(color);
-            }
-        }
-
-        rng.shuffle(&mut leg_dice[..]);
-        for color in leg_dice.iter() {
-            let roll = rng.usize(1..=3);
-            if let Some(winner) = self.advance(*color, roll) {
-                return Some(winner);
-            }
-        }
-        None
-    }
-
-    fn finish_game_random(&mut self, rng: &Rng) -> Color {
-        if let Some(winner) = self.finish_leg_random(rng) {
-            return winner;
-        }
-
-        let mut dice = COLORS; // makes a copy of the constant
-        // we are now guaranteed to be at the start of a new leg,
-        // so we don't need to check the dice state
-        loop {
-            // easiest if we shuffle at the start of the leg
-            rng.shuffle(&mut dice);
-            for i in 0..5 {
-                let roll = rng.usize(1..=3);
-                if let Some(winner) = self.advance(dice[i], roll) {
-                    return winner;
-                }
-            }
-        }
-    }
-
-    pub fn project_outcomes(&self, count: usize) -> EnumMap<Color, usize> {
-        let (orig_camels, orig_dice) = self.get_state();
-        let mut projection = *self;
-
-        let mut scores: EnumMap<Color, usize> = EnumMap::default();
-        let rng = Rng::new();
-        for i in 0..count {
-            let winner = projection.finish_game_random(&rng);
-            scores[winner] += 1;
-            projection.set_state(&orig_camels, &orig_dice);
-        }
-
-        scores
-    }
-}
-
-
-#[cfg(test)]
-mod test {
-    use super::*;
-    use Color::*;
-
-    #[test]
-    fn test_advance() {
-        let mut game = Game::new();
-        // all dice are false (not rolled) to start with
-        assert_eq!(game.dice.values().any(|&v| v), false);
-
-        let camel_state = [
-            (Blue, 0),
-            (Yellow, 0),
-            (Red, 1),
-            (Green, 2),
-            (Purple, 2),
-        ];
-        game.set_state(&camel_state, &Default::default());
-        assert_eq!(game.squares[0].assume_stack(), &Stack::from([Blue, Yellow]));
-        assert_eq!(game.camels[Blue], 0);
-        assert_eq!(game.camels[Yellow], 0);
-        assert_eq!(game.squares[1].assume_stack(), &Stack::from([Red]));
-        assert_eq!(game.camels[Red], 1);
-        assert_eq!(game.squares[2].assume_stack(), &Stack::from([Green, Purple]));
-        assert_eq!(game.camels[Green], 2);
-        assert_eq!(game.camels[Purple], 2);
-        //  BY, R, GP
-
-        game.advance(Yellow, 2);
-        assert_eq!(game.dice[Yellow], true);
-        assert_eq!(game.camels[Yellow], 2);
-        assert_eq!(game.squares[2].assume_stack(), &Stack::from([Green, Purple, Yellow]));
-        // B, R, GPY
-
-        game.advance(Red, 2);
-        assert_eq!(game.dice[Red], true);
-        assert_eq!(game.camels[Red], 3);
-        // B, _, GPY, R
-        
-        game.advance(Purple, 1);
-        assert_eq!(game.dice[Purple], true);
-        assert_eq!(game.squares[3].assume_stack(), &Stack::from([Red, Purple, Yellow]));
-        // B, _, G, RPY
-    }
-
-    #[test]
-    fn test_new_random() {
-        for _ in 0..100 {
-            let game = Game::new_random();
-            for (camel, i) in game.camels {
-                assert!(i < 3); // since we've only rolled the die once for each camel
-                let stack = game.squares[i].assume_stack();
-                assert!(stack[..].contains(&camel));
-            }
-        }
-    }
-
-    #[test]
-    fn test_finish_leg() {
-        let mut game = Game::new();
-        let camel_state = [
-            (Purple, 0),
-            (Blue, 0),
-            (Green, 1),
-            (Red, 1),
-            (Yellow, 2),
-        ];
-        game.set_state(&camel_state, &Default::default());
-        // PB, G, RY
-        game.advance(Green, 2);
-        // PB, _, RY, G
-        game.advance(Purple, 1);
-        // _, PB, RY, G
-
-        // since this is randomized, we should do it a bunch of times to make sure
-        for _ in 0..100 {
-            let mut projection = game; // copy?
-            assert_eq!(projection.squares[1].assume_stack(), &Stack::from([Purple, Blue]));
-            let rng = Rng::new();
-            projection.finish_leg_random(&rng);
-            // since we already rolled Green, it can't have moved
-            assert_eq!(projection.camels[Green], 3);
-            // likewise purple
-            assert_eq!(projection.camels[Purple], 1);
-            // blue, red,and yellow, on the other hand, *must* have moved
-            assert_ne!(projection.camels[Blue], 1);
-            assert_ne!(projection.camels[Red], 2);
-            assert_ne!(projection.camels[Yellow], 2);
-        }
-    }
-
-    #[test]
-    fn test_finish_leg_winner() {
-        let mut game = Game::new();
-        let camel_state = [
-            (Green, 13),
-            (Red, 14),
-            (Purple, 14),
-            (Blue, 15),
-            (Yellow, 15),
-        ];
-        game.set_state(&camel_state, &Default::default());
-
-        // since there are no tiles involved, and multiple camels are on 15, there must be a winner
-        let rng = Rng::new();
-        assert!(matches!(game.finish_leg_random(&rng), Some(_)));
-    }
-
-    #[test]
-    fn test_project_outcomes() {
-        let mut game = Game::new();
-        let camel_state = [
-            (Blue, 1),
-            (Green, 2),
-            (Yellow, 2),
-            (Purple, 4),
-            (Red, 10),
-        ];
-        game.set_state(&camel_state, &Default::default());
-        // _, B, GY, _, P, _, _, _, _, _, R
-
-        let scores = game.project_outcomes(10_000);
-        let mut max = 0;
-        let mut winner = Blue; // just "anything that's not red"
-        for (color, score) in scores {
-            if score > max {
-                max = score;
-                winner = color;
-            }
-        }
-
-        assert_eq!(winner, Red);
-    }
-}

src/main.rs

@@ -1,40 +0,0 @@
-use std::time::Instant;
-
-mod stack;
-mod game;
-
-use game::{Game, Color::*};
-
-
-fn main() {
-    let n_games = 200_000;
-
-    let game = Game::new_random();
-    // let mut game = Game::new();
-    // let camel_state = [
-    //     (Blue, 5),
-    //     (Purple, 5),
-    //     (Red, 7),
-    //     (Yellow, 8),
-    //     (Green, 10),
-    // ];
-    // game.set_state(&camel_state, &Default::default());
-    let start = Instant::now();
-    let scores = game.project_outcomes(n_games);
-    let end = Instant::now();
-
-    let elapsed = end.duration_since(start);
-    let secs = (elapsed.as_secs_f64() * 100f64).round() / 100f64;
-    let rate = (n_games as f64) / elapsed.as_secs_f64();
-
-    println!("Test completed:");
-    println!("{n_games} in {secs} seconds", );
-    println!("Games per second: {rate}\n");
-
-    let total = scores.values().sum::<usize>() as f64;
-    for (color, score) in scores {
-        let fract = (score as f64) / total;
-        let pct = (fract * 10_000f64).round() / 100f64;
-        println!("{color:?}: {pct}%");
-    }
-}

src/stack.rs

@@ -1,265 +0,0 @@
-use std::ops::{Index, IndexMut, RangeFull};
-use std::iter::IntoIterator;
-
-
-#[derive(Debug, Copy, Clone, Eq, PartialEq)]
-pub struct Stack<T, const S: usize> {
-    data: [T; S],
-    len: usize // we can experiment with using u8 some other time
-}
-
-
-impl<T, const S: usize> Stack<T, S> {
-    pub fn push(&mut self, v: T) {
-        self.data[self.len] = v;
-        self.len += 1;
-    }
-
-    pub fn len(&self) -> usize {
-        self.len
-    }
-
-    pub fn clear(&mut self) {
-        self.len = 0;
-    }
-
-    pub fn last(&self) -> Option<&T> {
-        if self.len == 0 {
-            None
-        }
-        else {
-            Some(&self.data[self.len - 1])
-        }
-    }
-
-    pub fn iter(&self) -> impl Iterator<Item = &T> {
-        self.data.iter().take(self.len)
-    }
-
-    pub const fn from_array(array: [T; S]) -> Self {
-        Stack {
-            data: array,
-            len: S,
-        }
-    }
-
-    pub fn into_inner(self) -> [T; S] {
-        self.data
-    }
-}
-
-
-impl<T, const S: usize> Stack<T, S>
-where T: Copy + Default
-{
-    pub fn new() -> Self {
-        Stack {
-            data: [Default::default(); S],
-            len: 0,
-        }
-    }
-
-    pub fn move_slice(&mut self, dst: &mut Self, start: usize) {
-        let slice_len = self.len - start;
-        let src_slice = &mut self.data[start..self.len];
-        let dst_slice = &mut dst.data[dst.len..(dst.len + slice_len)];
-        dst_slice.copy_from_slice(src_slice);
-
-        self.len -= slice_len;
-        dst.len += slice_len;
-    }
-
-    pub fn move_slice_under(&mut self, dst: &mut Self, start: usize) {
-        let slice_len = self.len - start;
-        let src_slice = &mut self.data[start..self.len];
-        
-        dst.data.rotate_right(slice_len);
-        let dst_slice = &mut dst.data[0..slice_len];
-
-        dst_slice.copy_from_slice(src_slice);
-
-        self.len -= slice_len;
-        dst.len += slice_len;
-    }
-
-    // like above, except source and destination are the same, i.e. reordering the stack
-    pub fn shift_slice_under(&mut self, start: usize) {
-        for mut i in start..self.len {
-            while i > 0 {
-                self.data.swap(i, i -1);
-                i -= 1;
-            }
-        }
-    }
-}
-
-
-impl<T, const S: usize> Default for Stack<T, S>
-where T: Copy + Default
-{
-    fn default() -> Self {
-        Self::new()
-    }
-}
-
-
-impl<T, const S: usize> Index<usize> for Stack<T, S> {
-    type Output = T;
-    fn index(&self, index: usize) -> &T {
-        &self.data[index]
-    }
-}
-
-impl<T, const S: usize> Index<RangeFull> for Stack<T, S> {
-    type Output = [T];
-    fn index(&self, _index: RangeFull) -> &[T] {
-        &self.data[..self.len]
-    }
-}
-
-impl<T, const S: usize> IndexMut<RangeFull> for Stack<T, S> {
-    fn index_mut(&mut self, _index: RangeFull) -> &mut [T] {
-        &mut self.data[..self.len]
-    }
-}
-
-
-impl<I, T, const S: usize> From<I> for Stack<T, S> 
-where 
-    T: Copy + Default,
-    I: IntoIterator<Item = T>
-{
-    fn from(src: I) -> Self {
-        let mut res = Self::new();
-        for (i, item) in src.into_iter().enumerate() {
-            if i >= S {
-                break;
-            }
-            res.push(item);
-        }
-        res
-    }
-}
-
-
-#[cfg(test)]
-mod test {
-    use super::*;
-
-    #[test]
-    fn test_basic() {
-        let mut stack: Stack<usize, 5> = Stack::new();
-        stack.push(1);
-        stack.push(2);
-        stack.push(3);
-
-        assert_eq!(stack.len(), 3);
-        assert_eq!(stack[0], 1);
-        assert_eq!(stack[1], 2);
-        assert_eq!(stack[2], 3);
-
-        assert_eq!(stack.last(), Some(&3));
-
-        stack.clear();
-        assert_eq!(stack.len(), 0);
-    }
-
-    #[test]
-    fn test_move_slice() {
-        let mut a: Stack<usize, 5> = Stack::new();
-        let mut b: Stack<usize, 5> = Stack::new();
-
-        a.push(1);
-        a.push(2);
-        a.push(3);
-        b.push(9);
-        b.push(8);
-
-        a.move_slice(&mut b, 1);
-        assert_eq!(b[2], 2);
-        assert_eq!(b[3], 3);
-
-        b.move_slice(&mut a, 1);
-        assert_eq!(a[1], 8);
-        assert_eq!(a[2], 2);
-        assert_eq!(a[3], 3);
-
-        a.move_slice(&mut b, 0);
-        assert_eq!(a.len(), 0);
-        assert_eq!(b[0], 9);
-        assert_eq!(b.last(), Some(&3));
-    }
-
-    #[test]
-    fn test_move_slice_under() {
-        let mut a: Stack<usize, 5> = Stack::new();
-        let mut b: Stack<usize, 5> = Stack::new();
-
-        a.push(1);
-        a.push(2);
-        a.push(3);
-        b.push(9);
-        b.push(8);
-
-        a.move_slice_under(&mut b, 1);
-        assert_eq!(a.len(), 1);
-        assert_eq!(a[0], 1);
-        
-        assert_eq!(b.len(), 4);
-        assert_eq!(b[0], 2);
-        assert_eq!(b[3], 8);
-
-        b.move_slice_under(&mut a, 0);
-        assert_eq!(b.len(), 0);
-        assert_eq!(a[0], 2);
-        assert_eq!(a[4], 1);
-    }
-
-    fn test_shift_slice_under() {
-        let mut a: Stack<usize, 5> = Stack::from([1, 2, 3, 4, 5]);
-        a.shift_slice_under(3);
-        assert_eq!(a[0], 4);
-        assert_eq!(a[1], 5);
-        assert_eq!(a[2], 1);
-        assert_eq!(a[3], 2);
-        assert_eq!(a[4], 3);
-    }
-
-    #[test]
-    fn test_from_iter() {
-        let s = Stack::<_, 5>::from([1, 2, 3]);
-        assert_eq!(s[0], 1);
-        assert_eq!(s[2], 3);
-
-        let s = Stack::<_, 2>::from([1, 2, 3]);
-        assert_eq!(s.len(), 2);
-        assert_eq!(s[0], 1);
-        assert_eq!(s[1], 2);
-    }
-
-    #[test]
-    fn test_iter() {
-        let s = Stack::<_, 5>::from([1, 2, 3]);
-        let mut it = s.iter();
-        assert_eq!(it.next(), Some(&1));
-        assert_eq!(it.next(), Some(&2));
-        assert_eq!(it.next(), Some(&3));
-        assert_eq!(it.next(), None);
-    }
-
-    #[test]
-    fn test_from_array() {
-        let s = Stack::from_array([1, 2, 3]);
-        assert_eq!(s[0], 1);
-        assert_eq!(s[1], 2);
-        assert_eq!(s[2], 3);
-        assert_eq!(s.len(), 3);
-    }
-
-    #[test]
-    fn test_slice_index() {
-        let mut s = Stack::<_, 5>::from([3, 4, 5]);
-        assert_eq!(s[..], [3, 4, 5]);
-        assert_eq!(&mut s[..], &mut [3, 4, 5]);
-    }
-}

test.nim

@@ -0,0 +1,97 @@
+import math, random, strformat, times, std/monotimes
+import fixedseq, game, simulation, ui
+
+
+type
+  TestResults = object
+    ops: int
+    time: Duration
+
+
+proc summarize(tr: TestResults) =
+  let secs = tr.time.inMilliseconds.float / 1000
+  stdout.write("Test completed:\n")
+  stdout.write("  " & $tr.ops, " operations in " & $round(secs, 2) & " seconds\n")
+  stdout.write("  " & $round(tr.ops.float / secs, 2) & " operations per second")
+  stdout.flushFile()
+
+
+template executionTime(body: untyped): Duration =
+  let start = getMonoTime()
+  body
+  getMonoTime() - start
+
+
+proc getRand(): Rand =
+  randomize()
+  result = initRand(rand(int64))
+
+
+proc randomDice(r: var Rand): seq[tuple[c: Color, p: int]] = 
+  for c in Color:
+    let v = r.rand(1..3)
+    result.add((c, v))
+  result.shuffle
+
+
+proc newRandomGame(r: var Rand): Board =
+  var dice: array[5, tuple[c: Color, p: int]]
+  for i in 0 .. 4:
+    dice[i] = (Color(i), r.rand(1..3))
+
+  result.init
+  result.setState(dice, [])
+
+
+proc games(nTests, nSamples: SomeInteger, parallel = true): TestResults =
+  var r = getRand()
+  var scores: ScoreSet
+  for i in 1 .. nTests:
+    let b = newRandomGame(r)
+    let dur = executionTime:
+        let s = b.randomGames(nSamples, parallel = parallel)
+    result.ops += s.sum()
+    result.time += dur
+
+
+proc testLegs(n: Natural = 100): auto =
+  var boards: seq[Board]
+  var r = initRand(rand(int64))
+  for i in 1 .. n:
+    var b: Board
+    b.init
+    let dice = randomDice(r)
+    b.setState(dice, [])
+    boards.add(b)
+    stdout.write("Constructed: " & $i & "\r")
+  echo ""
+  
+  echo "Running..."
+  let start = cpuTime()
+  for b in boards:
+    discard b.getLegScores
+  result = cpuTime() - start
+
+
+proc testSpread(nTests, nSamples: Natural) =
+  var b: Board
+  b.init
+  var r = initRand(rand(int64))
+  let dice = randomDice(r)
+  b.setState(dice, [])
+  b.display(1, 5)
+  let spread = randomSpread(b, nTests, nSamples)
+
+  stdout.writeLine("Variance:")
+  for c in Color:
+    let variance = 100 * (spread.hi[c] - spread.lo[c])
+    stdout.writeLine(fmt"{c}: {round(variance, 2):.2f}%")
+  
+  let diff = 100 * (max(spread.hi) - min(spread.lo))
+  stdout.writeLine(fmt"Win percentage differential: {round(diff, 2):.2f}%")
+
+  stdout.flushFile()
+
+
+when isMainModule:
+  games(10, 10_000_000).summarize()

ui.nim

@@ -0,0 +1,120 @@
+import os, math, strutils, strformat
+import fixedseq, game, simulation
+
+
+const help = 
+  """cup - Probability calculator for the board game CamelUp
+
+Usage: 
+  cup [-i] SPACE:STACK [...SPACE:STACK] [DICE]
+
+SPACE refers to a numbered board space (1-16).
+STACK refers to a stack of camel colors from bottom to top, e.g. 
+      YBR (Yellow, Blue, Red, with Red on top).
+DICE refers to the set of dice that have already been rolled,
+     e.g. GPR (Green, Purple, Red)
+
+Options:
+  -i      Interactive mode (currently unimplemented)
+  -h      Show this message and exit
+"""
+
+
+# =============================
+# User input parsing/validation
+# =============================
+
+type
+  CmdConfig* = object
+    state*: seq[tuple[c: Color, p: int]]
+    interactive*: bool
+    diceRolled*: array[Color, bool]
+
+
+proc parseColor(c: char): Color =
+  case c:
+  of 'R', 'r':
+    return cRed
+  of 'G', 'g':
+    return cGreen
+  of 'B', 'b':
+    return cBlue
+  of 'Y', 'y':
+    return cYellow
+  of 'P', 'p':
+    return cPurple
+  else:
+    raise newException(ValueError, "Invalid camel color specified.")
+
+
+proc parseArgs*(): CmdConfig =
+  for p in os.commandLineParams():
+    if p == "-h":
+      echo help
+      quit 0
+    elif p == "-i":
+      result.interactive = true
+    elif result.state.len < 5:
+      let splat = p.split(':')
+      
+      let sq = splat[0]
+      let square = sq.parseInt
+
+      let colors = splat[1]
+      for c in colors:
+        let color = parseColor(c)
+        result.state.add((color, square))
+    else:
+      for c in p:
+        let color = parseColor(c)
+        result.diceRolled[color] = true
+
+
+# ==========================
+# Game state representations
+# ==========================
+
+proc showSpaces*(b: Board; start, stop: Natural): string =
+  let numSpaces = stop - start + 1
+  let width = 4 * numSpaces - 1
+  var lines: array[7, string]
+  # start by building up an empty board
+  for i in 0 .. 6: # gotta initialize the strings
+    lines[i] = newString(width)
+    for c in lines[i].mitems:
+      c = ' '
+  # fill in the dividers
+  lines[5] = repeat("=== ", numSpaces - 1)
+  lines[5].add("===")
+
+  # now populate the board
+  for sp in 0 ..< numSpaces:
+    # fill in the square numbers
+    let squareNum = sp + start
+    let cellMid = 4 * sp + 1
+    for i, chr in $squareNum:
+      lines[6][cellMid + i] = chr
+
+    # fill in the camel stacks
+    for i, color in b.squares[squareNum].camels:
+      let lineNum = 4 - i # lines go to 6, but bottom 2 are reserved
+      let repr = '|' & color.abbrev & '|'
+      for j, chr in repr:
+        lines[lineNum][cellMid - 1 + j] = chr
+
+  result = lines.join("\n")
+
+
+proc showPercents*(scores: ScoreSet): string =
+  var lines: array[5, string]
+  for color, pct in scores.percents:
+    let label = align($color, 7) # e.g. " Green"
+    var bar = repeat(" ", 20)
+    let percentage = round(pct * 100, 2)
+    # populate the progress bar
+    let barFill = int(round(pct * 100 / 20))
+    for i in 0 ..< barFill:
+      bar[i] = '='
+
+    lines[int(color)] = fmt"{label}: [{bar}] {percentage}%"
+    result = lines.join("\n")