switch to bitshifting operations (turns out to be slower, oh well)

README.md

@@ -0,0 +1,22 @@
+# `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.)
+
+```
+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
+```

colors.nim

@@ -0,0 +1,17 @@
+type
+  Color* = enum
+    cRed, cGreen, cBlue, cYellow, cPurple
+
+
+const 
+  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]

config.nims

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

cup.nim

@@ -1,5 +1,4 @@
-import math, options, sequtils, random, sets
-import combinators, game, fixedseq, simulation, ui
+import game, simulation, ui
 
 
 when isMainModule:
@@ -8,11 +7,11 @@ when isMainModule:
   b.init
   b.setState(config.state, [])
   b.diceRolled = config.diceRolled
-  b.display(1, 5)
+  echo b.showSpaces(1, 16)
   let legScores = b.getLegScores
-  echo "Current leg probabilities:"
-  legScores.display
+  echo "\nCurrent leg probabilities:"
+  echo legScores.showPercents()
   
   let gameScores = b.randomGames(1_000_000)
   echo "\nFull game probabilities (1M simulations):"
-  gameScores.display
+  echo gameScores.showPercents()

fixedseq.nim

@@ -25,6 +25,16 @@ proc `$`*(s: FixedSeq): string =
   result.add("]")
 
 
+proc `==`*[T1: FixedSeq, T2: FixedSeq](a: T1, b: T2): bool =
+  # generics are so that we can compare ShiftStack vs regular FixedSeq
+  if a.len != b.len:
+    return false
+  for i in 0 ..< a.len:
+    if a.data[i] != b.data[i]:
+      return false
+  return true
+
+
 proc `[]`*(s: FixedSeq, i: Natural): FixedSeq.Contents =
   if i > s.last:
     raise newException(IndexDefect, "index " & $i & " is out of bounds.")
@@ -124,7 +134,7 @@ proc shuffle*(s: var FixedSeq, r: var Rand) =
 
 
 proc moveSubstack*(src, dst: var FixedSeq; start: Natural) =
-  var count: typeof(src.last) = 0 # have to track this separately apparently
+  var count: FixedSeq.Pointer = 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
@@ -133,7 +143,7 @@ proc moveSubstack*(src, dst: var FixedSeq; start: Natural) =
 
 
 proc moveSubstackPre*(src, dst: var FixedSeq; start: Natural) =
-  let ssLen = typeof(src.last)(src.last - start + 1) # length of substack
+  let ssLen = FixedSeq.Pointer(src.last - start + 1) # length of substack
   for i in countdown(dst.last, 0):
     swap(dst.data[i], dst.data[i + ssLen])
 
@@ -144,3 +154,5 @@ proc moveSubstackPre*(src, dst: var FixedSeq; start: Natural) =
 
   dst.last += ssLen
   src.last -= ssLen
+
+include shiftstack

game.nim

@@ -1,11 +1,9 @@
 import hashes, options
-import fixedseq
+import fixedseq, colors
+export colors
 
 
 type
-  Color* = enum
-    cRed, cGreen, cBlue, cYellow, cPurple
-
   ColorStack* = FixedSeq[5, Color, int8]
 
 
@@ -13,21 +11,7 @@ proc initColorStack*: ColorStack =
   result.initFixedSeq
 
 
-proc getAllColors: ColorStack = 
-  var i = 0
-  for c in Color.low .. Color.high:
-    result[i] = c
-
-const allColors* = getAllColors()
-const colorNames: array[Color, string] =
-  ["Red", "Green", "Blue", "Yellow", "Purple"]
-
-
-proc `$`*(c: Color): string =
-  result = colorNames[c]
-
-
-proc `$`*(s: ColorStack): string =
+proc `$`*[T](s: FixedSeq[T, Color, int8]): string =
   result.add("St@[")
   for i, color in s:
     result.add($color)
@@ -44,8 +28,8 @@ type
     tForward = 1
 
   Square* = object
-    camels: ColorStack
-    tile: Option[Tile]
+    camels*: ShiftStack
+    tile*: Option[Tile]
 
   Board* = object
     squares*: array[1..16, Square]

shiftstack.nim

@@ -0,0 +1,191 @@
+# optimized bit-shifting versions of the FixedSequence substack operations
+import bitops, macros
+import colors
+
+
+macro show(expr: untyped) =
+  let node = expr.toStrLit
+  quote do:
+    echo `node`, " => ", `expr`
+
+
+proc getMasks(): (array[9, uint64], array[9, uint64]) =
+  # on little-endian architectures, casting an array[8, Color] to uint64 effectively
+  # reverses it. So we switch these masks so that we can refer to them consistently.
+  let 
+    left = [
+      0'u64,
+      0xff_00_00_00_00_00_00_00'u64,
+      0xff_ff_00_00_00_00_00_00'u64,
+      0xff_ff_ff_00_00_00_00_00'u64,
+      0xff_ff_ff_ff_00_00_00_00'u64,
+      0xff_ff_ff_ff_ff_00_00_00'u64,
+      0xff_ff_ff_ff_ff_ff_00_00'u64,
+      0xff_ff_ff_ff_ff_ff_ff_00'u64,
+      0xff_ff_ff_ff_ff_ff_ff_ff'u64,
+    ]
+    right = [
+      0'u64,
+      0x00_00_00_00_00_00_00_ff'u64,
+      0x00_00_00_00_00_00_ff_ff'u64,
+      0x00_00_00_00_00_ff_ff_ff'u64,
+      0x00_00_00_00_ff_ff_ff_ff'u64,
+      0x00_00_00_ff_ff_ff_ff_ff'u64,
+      0x00_00_ff_ff_ff_ff_ff_ff'u64,
+      0x00_ff_ff_ff_ff_ff_ff_ff'u64,
+      0xff_ff_ff_ff_ff_ff_ff_ff'u64,
+    ]
+  when cpuEndian == bigEndian:
+    result = (left, right)
+  when cpuEndian == littleEndian:
+    result = (right, left)
+
+
+type ShiftStack* = FixedSeq[8, Color, int8]
+const (masksLeft, masksRight) = getMasks()
+
+
+template `shl`(a: array[8, Color], offset: Natural): array[8, Color] =
+  when cpuEndian == bigEndian:
+    cast[array[8, Color]](cast[uint64](a) shl (offset * 8))
+  when cpuEndian == littleEndian: # direction is reversed
+    cast[array[8, Color]](cast[uint64](a) shr (offset * 8))
+
+
+template `shr`(a: array[8, Color], offset: Natural): array[8, Color] =
+  when cpuEndian == bigEndian:
+    cast[array[8, Color]](cast[uint64](a) shr (offset * 8))
+  when cpuEndian == littleEndian:
+    cast[array[8, Color]](cast[uint64](a) shl (offset * 8))
+
+
+template `and`(a: array[8, Color], mask: uint64): array[8, Color] =
+  cast[array[8, Color]](cast[uint64](a) and mask)
+
+
+template `or`(a: array[8, Color], mask: uint64): array[8, Color] =
+  cast[array[8, Color]](cast[uint64](a) or mask)
+
+
+template `or`(a: array[8, Color], mask: array[8, Color]): array[8, Color] =
+  cast[array[8, Color]](cast[uint64](a) or cast[uint64](mask))
+
+
+import strutils # remove later
+proc moveSubstack*(src, dst: var ShiftStack; start: Natural) =
+  # shift the source stack to position the substack above its final resting place
+  # offset is the length of the destination stack, minus the number of items NOT being moved
+  # number of items not being moved is the same as the start index
+  var substack: array[8, Color] 
+  if dst.len == start: # no shift necessary in this case
+    substack = src.data
+  elif dst.len > start:
+    substack = src.data shr (dst.len - start)
+  elif dst.len < start:
+    substack = src.data shl (start - dst.len)
+  # next, mask the source data to present only the items being moved
+  # dst.len of 0 corresponds to last mask in masksRight, aka masksRight[^1]
+  substack = substack and masksRight[^(dst.len + 1)]
+  # then combine
+  dst.data = dst.data or substack
+  # then git rid of the moved items from the source stack
+  src.data = src.data and masksLeft[start]
+  # a little bookkeeping
+  let ssLen = int8(src.len - start)
+  src.last -= ssLen
+  dst.last += ssLen
+
+
+proc moveSubstackPre*(src, dst: var ShiftStack; start: Natural) =
+  let ssLen = int8(src.len - start)
+  # shift the destination stack to make room for the new items
+  dst.data = dst.data shr ssLen
+  # shift source stack to line up the substack with its final resting place
+  let substack = src.data shl start
+  # combine
+  dst.data = dst.data or substack
+  # get rid of the moved items
+  src.data = src.data and masksLeft[start]
+  # more bookkeeping
+  src.last -= ssLen
+  dst.last += ssLen
+
+
+proc testMove[T1, T2: FixedSeq](a1, a2: var T1; b1, b2: var T2; i: Natural): bool =
+  let (orig_a1, orig_a2) = (a1, a2)
+  let (orig_b1, orig_b2) = (b1, b2)
+  a1.moveSubstack(a2, i)
+  b1.moveSubstack(b2, i)
+  if a1 != b1 or a2 != b2:
+    echo "Failed!"
+    show orig_b1
+    show orig_b2
+    echo "<<move ", i, ">>"
+    show b1
+    show b2
+    return false
+  return true
+
+
+when isMainModule:
+  var c1 = initFixedSeq(5, Color, int8)
+  var c2 = initFixedSeq(5, Color, int8)
+
+  var s1: ShiftStack
+  s1.initFixedSeq
+  var s2: ShiftStack
+  s2.initFixedSeq
+
+  c1.add(cPurple)
+  c1.add(cRed)
+  c1.add(cYellow)
+  c1.add(cBlue)
+  c1.add(cGreen)
+
+  s1.add(cPurple)
+  s1.add(cRed)
+  s1.add(cYellow)
+  s1.add(cBlue)
+  s1.add(cGreen)
+
+  # show s1
+  # show s2
+  # echo "<<move 2>>"
+  # s1.moveSubstack(s2, 2)
+  # show s1
+  # show s2
+
+  import random
+  randomize()
+  var r = initRand(rand(int64))
+  var success = true
+
+  for n in 1 .. 1_000_000:
+    var ranFirst, ranSecond: bool
+
+    if c1.len > 0:
+      let i = r.rand(c1.high)
+      ranFirst = true
+      if not testMove(c1, c2, s1, s2, i):
+        success = false
+        echo "Failed after ", n, " iterations."
+        break
+    else:
+      ranFirst = false
+
+    if c2.len > 0:
+      let j = r.rand(c2.high)
+      ranSecond = true
+      if not testMove(c2, c1, s2, s1, j):
+        success = false
+        echo "Failed after ", n, " iterations."
+        break
+    else:
+      ranSecond = false
+
+    if (not ranFirst) and (not ranSecond):
+      echo "Ran neither first nor second move."
+      break
+
+  if success:
+    echo "Success."

simulation.nim

@@ -4,6 +4,7 @@ import combinators, game, fixedseq
 
 type
   ScoreSet* = array[Color, int]
+  WinPercents* = array[Color, float]
 
   ScoreSpread = object
     lo*: array[Color, float]
@@ -26,6 +27,12 @@ proc display*(scores: ScoreSet) =
     # 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
 # ======================

test.nim

@@ -1,5 +1,5 @@
 import math, random, strformat, times
-import fixedseq, game, simulation
+import fixedseq, game, simulation, ui
 
 
 proc randomDice(r: var Rand): seq[tuple[c: Color, p: int]] = 
@@ -9,6 +9,15 @@ proc randomDice(r: var Rand): seq[tuple[c: Color, p: int]] =
   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 testGames(n: SomeInteger = 100): auto =
   var r = initRand(rand(int64))
   let dice = randomDice(r)
@@ -18,7 +27,7 @@ proc testGames(n: SomeInteger = 100): auto =
   b.display(1, 5)
 
   let startTime = cpuTime()
-  let scores = b.randomGames(n)
+  let scores = b.randomGames(n, parallel = true)
   result = cpuTime() - startTime
   scores.display()
 
@@ -64,16 +73,23 @@ proc testSpread(nTests, nSamples: Natural) =
 
 when isMainModule:
   randomize()
+  # var r = initRand(rand(int64))
+  # let b = newRandomGame(r)
+  # b.display(1, 5)
+  # echo b.showSpaces(1, 16)
+
+  # let scores = b.getLegScores
+  # echo scores.showPercents
   # let start_states = 2_000
   # let executionTime = testLegs(start_states)
   # echo "Execution time: ", executionTime
   # echo "Leg simulations per second: ", float(start_states * 29_160) / executionTime
 
-  # for i in 1 .. 1:
-  #   let num_games = 100_000_005
-  #   let executionTime = testGames(num_games)
-  #   echo "Execution time: ", executionTime
-  #   echo "Full-game simulations per second: ", float(num_games) / executionTime
-  #   echo ""
+  for i in 1 .. 1:
+    let num_games = 100_000_005
+    let executionTime = testGames(num_games)
+    echo "Execution time: ", executionTime
+    echo "Full-game simulations per second: ", float(num_games) / executionTime
+    echo ""
 
-  testSpread(100, 1_000_000)
+  # testSpread(100, 1_000_000)

ui.nim

@@ -1,5 +1,5 @@
-import os, strutils
-import game
+import os, math, strutils, strformat
+import fixedseq, game, simulation
 
 
 const help = 
@@ -19,6 +19,11 @@ Options:
   -h      Show this message and exit
 """
 
+
+# =============================
+# User input parsing/validation
+# =============================
+
 type
   CmdConfig* = object
     state*: seq[tuple[c: Color, p: int]]
@@ -63,3 +68,53 @@ proc parseArgs*(): CmdConfig =
       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")