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

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]

combinators.nim

@@ -1,5 +1,5 @@
 import algorithm, random, sugar
-import faststack, fixedseq, game
+import fixedseq, game
 
 
 proc nextPermutation(x: var FixedSeq): bool =

config.nims

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

faststack.nim

@@ -1,204 +0,0 @@
-import bitops, strutils, random
-
-
-proc show(i: SomeInteger, bitlength = 16) =
-  echo BiggestInt(i).toBin(bitlength)
-
-
-type
-  Color* = enum
-    cRed, cGreen, cBlue, cYellow, cPurple
-
-  ColorStack* = object
-    data: uint16
-    len*: uint8
-
-
-const
-  masks = [
-    0'u16, # dummy value just to get the indices right
-    0b0_000_000_000_000_111,
-    0b0_000_000_000_111_111,
-    0b0_000_000_111_111_111,
-    0b0_000_111_111_111_111,
-    0b0_111_111_111_111_111,
-  ]
-  allColors* = ColorStack(len: 5, data: 0b0_000_001_010_011_100)
-
-
-template offset(s: ColorStack, idx: Natural): uint8 =
-  # Compute the bit offset for a given index. 
-  # Dependent on the stack's length.
-  (s.len - 1 - idx.uint8) * 3
-  # items are stored from left to right but right-aligned, so we
-  # need to shift right to access anything other than the last
-
-
-template offset(s: ColorStack, idx: BackwardsIndex): uint8 =
-  # for backwards index, we are still shifting right but
-  # the lower the index the less we have to shift
-  (idx.uint8 - 1) * 3
-
-
-proc add*(s: var ColorStack, c: Color) =
-  # e.g. if stack is 0b0000000000000100:
-  # and color is 0b00000011
-  # shift: 0b0000000000100000
-  # bitor: 0b0000000000100000 and 0b00000011
-  # results in 0b0000000000100011
-  s.data = (s.data shl 3).bitor(cast[uint8](c))
-  inc s.len
-
-
-proc high*(s: ColorStack): uint8 = s.len - 1
-
-proc low*(s: ColorStack): uint8 = 0 # just... always 0, I guess
-
-
-proc `[]`*(s: ColorStack, i: uint8 | BackwardsIndex): Color =
-  # shift, then mask everything but the three rightmost bits
-  result = Color(
-    (s.data shr s.offset(i)) and masks[1]
-  )
-
-
-proc `[]=`*(s: var ColorStack, i: uint8 | BackwardsIndex, c: Color) =
-  let offset = s.offset(i)
-  s.data = (s.data and bitnot(masks[1] shl offset)) or (c.uint16 shl offset)
-
-
-iterator items*(s: ColorStack): Color =
-  # s.len is unsigned so it will wrap around if we do s.len - 1 in that case
-  if s.len != 0:
-    for i in countdown(s.len - 1, 0'u8):
-      yield Color((s.data shr (i * 3)) and masks[1])
-
-
-iterator pairs*(s: ColorStack): (uint8, Color) =
-  var count = 0'u8
-  for color in s:
-    yield (count, color)
-    inc count
-
-
-proc find*(s: ColorStack, needle: Color): int8 =
-  for i in 0'u8 .. s.high:
-    if s[i] == needle:
-      return i.int8
-  return -1
-
-
-proc moveSubstack*(src, dst: var ColorStack, startIdx: uint8) =
-  if startIdx >= src.len:
-    raise newException(IndexDefect, "index " & $startIdx & " is out of bounds.")
-  # Moves a sub-stack from the top of src to the top of dst
-  # shift the dst stack by the length of the substack to make room
-  let nToMove = src.len - startIdx
-  let shift = nToMove * 3
-  dst.data = dst.data shl shift
-  # then we mask the source data to present only the items 
-  # being moved, and OR that with the shifted dst data
-  dst.data = dst.data or (src.data and masks[nToMove])
-  dst.len += nToMove
-  # then we shift the source to get rid of the moved items
-  src.data = src.data shr shift
-  src.len -= nToMove
-
-
-proc moveSubstackPre*(src, dst: var ColorStack, startIdx: uint8) =
-  if startIdx >= src.len:
-    raise newException(IndexDefect, "index " & $startIdx & " is out of bounds.")
-  # Moves a sub-stack from the top of src to the bottom of dst
-  let nToMove = src.len - startIdx
-  # shift src to position the substack above its destination,
-  # get rid of everything to the left of the substack,
-  # and OR that with the existing dst data
-  let newLen = dst.len + nToMove
-  dst.data = dst.data or ( (src.data shl (dst.len * 3)) and masks[newLen] )
-  dst.len = newLen
-  # get rid of the substack we just moved
-  src.data = src.data shr (nToMove * 3)
-  src.len -= nToMove
-
-
-proc swap*(s: var ColorStack, i1, i2: uint8) =
-  # Swap the values at two indices in the stack
-  if i1 == i2: return
-
-  # i1 and i2 are unsigned, so we have to watch out for underflows
-  let diff = if i1 > i2:
-    (i1 - i2) * 3
-  else:
-    (i2 - i1) * 3
-
-  # take masks[1] from above (rightmost position) and shift to position of i1.
-  # then do the same for i2, and OR them together.
-  let mask = (masks[1] shl s.offset(i1)) or (masks[1] shl s.offset(i2))
-  # get rid of everything but the two values we're swapping
-  let masked = s.data and mask
-  # shift by the distance between values in both directions, combine, then mask
-  let swapped = ((masked shl diff) or (masked shr diff)) and mask
-  # finally, AND with the inverse of mask so that only the values being 
-  # swapped are erased, and combine that with the swapped values
-  s.data = (s.data and mask.bitnot) or swapped
-
-
-proc shuffle*(r: var Rand, s: var ColorStack) =
-  # Fisher-Yates shuffle
-  for i in countdown(s.high, 1'u8):
-    let j = r.rand(i).uint8
-    if j != i:
-      s.swap(i, j)
-
-
-proc reverse*(s: var ColorStack, first, last: uint8) =
-  var x = first
-  var y = last
-  while x < y:
-    s.swap(x, y)
-    inc x
-    dec y
-
-
-iterator asInt*(s: ColorStack): int8 =
-  for i in 0'u8 .. s.high:
-    yield int8(s[i]) # now we do have to convert
-
-
-proc `$`*(s: ColorStack): string =
-  result = "St@["
-  for c in s:
-    if result[^1] != '[':
-      result.add(", ")
-    result.add($c)
-  result.add("]")
-
-
-proc check(s: ColorStack) =
-  # ensure length is accurate
-  var d = s.data
-  for i in 0'u8 .. 4'u8:
-    if (d and masks[1]) > 4:
-      raise newException(RangeDefect, "Value out of range.")
-    if d > 0 and i >= s.len:
-      raise newException(RangeDefect, "Invalid length.")
-    else:
-      d = d shr 3
-
-
-when isMainModule:
-  var one: ColorStack
-  one.add(cRed)
-  one.add(cGreen)
-  one.add(cBlue)
-  one.add(cYellow)
-  one.add(cPurple)
-
-  var two: ColorStack
-
-  one.moveSubstack(two, 2)
-
-
-  echo one, " ", one.len
-  echo two, " ", two.len
-  echo two.find(cRed)

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

@@ -1,40 +1,17 @@
 import hashes, options
-import fixedseq, faststack
+import fixedseq, colors
-
+export colors
-export faststack.Color, faststack.ColorStack, faststack.allColors
 
 
-# type
+type
-#   Color* = enum
+  ColorStack* = FixedSeq[5, Color, int8]
-#     cRed, cGreen, cBlue, cYellow, cPurple
-
-#   ColorStack* = FixedSeq[5, Color, int8]
 
 
-# proc initColorStack*: ColorStack =
+proc initColorStack*: ColorStack =
-#   result.initFixedSeq
+  result.initFixedSeq
 
 
-# proc getAllColors: ColorStack = 
+proc `$`*[T](s: FixedSeq[T, Color, int8]): string =
-#   var i = 0'u8
-#   for c in Color.low .. Color.high:
-#     result[i] = c
-
-const
-  colorNames: array[Color, string] =
-    ["Red", "Green", "Blue", "Yellow", "Purple"]
-  colorAbbrevs: array[Color, char] = ['R', 'G', 'B', 'Y', 'P']
-
-
-proc `$`*(c: Color): string =
-  result = colorNames[c]
-
-
-proc abbrev*(c: Color): char =
-  result = colorAbbrevs[c]
-
-
-proc `$`*(s: ColorStack): string =
   result.add("St@[")
   for i, color in s:
     result.add($color)
@@ -51,7 +28,7 @@ type
     tForward = 1
 
   Square* = object
-    camels*: ColorStack
+    camels*: ShiftStack
     tile*: Option[Tile]
 
   Board* = object
@@ -83,8 +60,8 @@ proc hash*(b: Board): Hash =
 
 
 proc init*(b: var Board) =
-  # for sq in b.squares.mitems:
+  for sq in b.squares.mitems:
-  #   sq.camels.initFixedSeq
+    sq.camels.initFixedSeq
   b.initialized = true
 
 
@@ -113,7 +90,7 @@ proc setState*(b: var Board;
   b.leader = some(leadCamel)
 
 
-proc diceRemaining*(b: Board): FixedSeq[5, Color, int8] =
+proc diceRemaining*(b: Board): ColorStack =
   result.initFixedSeq
   for color, isRolled in b.diceRolled:
     if not isRolled: result.add(color)
@@ -141,11 +118,11 @@ proc advance*(b: var Board, die: Die) =
     endPos += int(t)
     if t == tBackward: prepend = true
 
-  let stackStart = b[startPos].camels.find(color).uint8
+  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'u8 ..< stackLen:
+    for i in 0 ..< 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]] = endPos
   else:
@@ -159,4 +136,4 @@ proc advance*(b: var Board, die: Die) =
   if endPos >= b.camels[b.leader.get]:
     b.leader = some(b[endPos].camels[^1])
   
-  b.diceRolled[color] = true
+  b.diceRolled[color] = true

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

@@ -1,5 +1,5 @@
 import cpuinfo, math, options, random, tables
-import combinators, game, faststack, fixedseq
+import combinators, game, fixedseq
 
 
 type
@@ -38,7 +38,7 @@ proc percents*(scores: ScoreSet): WinPercents =
 # ======================
 
 iterator legEndStates(b: Board): Board =
-  var diceRemaining: FixedSeq[5, Color, int8]
+  var diceRemaining: ColorStack
   diceRemaining.initFixedSeq
   for i, c in b.diceRolled:
     if not c: diceRemaining.add(i)
@@ -59,39 +59,6 @@ proc getLegScores*(b: Board): ScoreSet =
 # Full-game simulations
 # =====================
 
-# get rid of this later
-import strutils
-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")
-# get rid of this later
-
 proc randomGame*(b: Board, r: var Rand): Color =
   var projection = b
   while true:

test.nim

@@ -1,32 +1,7 @@
-import math, random, strformat, times, std/monotimes
+import math, random, strformat, times
 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)
@@ -43,15 +18,18 @@ proc newRandomGame(r: var Rand): Board =
   result.setState(dice, [])
 
 
-proc games(nTests, nSamples: SomeInteger, parallel = true): TestResults =
+proc testGames(n: SomeInteger = 100): auto =
-  var r = getRand()
+  var r = initRand(rand(int64))
-  var scores: ScoreSet
+  let dice = randomDice(r)
-  for i in 1 .. nTests:
+  var b: Board
-    let b = newRandomGame(r)
+  b.init
-    let dur = executionTime:
+  b.setState(dice, [])
-        let s = b.randomGames(nSamples, parallel = parallel)
+  b.display(1, 5)
-    result.ops += s.sum()
+
-    result.time += dur
+  let startTime = cpuTime()
+  let scores = b.randomGames(n, parallel = true)
+  result = cpuTime() - startTime
+  scores.display()
 
 
 proc testLegs(n: Natural = 100): auto =
@@ -94,4 +72,24 @@ proc testSpread(nTests, nSamples: Natural) =
 
 
 when isMainModule:
-  games(10, 10_000_000).summarize()
+  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 ""
+
+  # testSpread(100, 1_000_000)

ui.nim

@@ -1,5 +1,5 @@
 import os, math, strutils, strformat
-import faststack, fixedseq, game, simulation
+import fixedseq, game, simulation
 
 
 const help =