From 08e0b11db91eb54dd3edd846d98185f7fc0b96e9 Mon Sep 17 00:00:00 2001 From: jackjohn7 <70782491+jackjohn7@users.noreply.github.com> Date: Wed, 5 Nov 2025 21:29:08 -0600 Subject: [PATCH] use an OR in a spot where it will help some tiny amount, set up doc --- design/inc/logo.png | Bin 0 -> 163294 bytes design/othello.typ | 387 + design/references.bib | 6 + design/report.pdf | 12669 +++++++++++++++++++++++++++ design/report.typ | 431 + design/structures/bitboard-p1.yaml | 135 + flake.nix | 2 +- src/board/mod.rs | 5 +- src/game.rs | 2 +- 9 files changed, 13632 insertions(+), 5 deletions(-) create mode 100644 design/inc/logo.png create mode 100644 design/othello.typ create mode 100644 design/references.bib create mode 100644 design/report.pdf create mode 100644 design/report.typ create mode 100644 design/structures/bitboard-p1.yaml diff --git a/design/inc/logo.png b/design/inc/logo.png new file mode 100644 index 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index 0000000..962fda3 --- /dev/null +++ b/design/references.bib @@ -0,0 +1,6 @@ +@book{2020_molecular_biology_principles_of_genome_function_craig, + title={Molecular biology: principles of genome function}, + author={Craig, Nancy and Green, Rachel and Cohen-Fix, Orna and Greider, Carol and Storz, Gisela and Wolberger, Cynthia}, + year={2020}, + publisher={Oxford University Press} +} diff --git a/design/report.pdf b/design/report.pdf new file mode 100644 index 0000000..95b72a6 --- /dev/null +++ b/design/report.pdf @@ -0,0 +1,12669 @@ +%PDF-1.7 +% + +1 0 obj +<< + /Type /Pages + /Count 10 + /Kids [877 0 R 890 0 R 892 0 R 896 0 R 898 0 R 904 0 R 912 0 R 914 0 R 916 0 R 918 0 R] +>> +endobj + +2 0 obj +<< + /Type /Outlines + /First 3 0 R + /Last 7 0 R + /Count 2 +>> +endobj + +3 0 obj +<< + /Parent 2 0 R + /Next 7 0 R + /First 4 0 R + /Last 6 0 R + /Count -3 + /Title (1 Introduction) + /Dest 855 0 R +>> +endobj + +4 0 obj +<< + /Parent 3 0 R + /Next 5 0 R + /Title (1.1 A Naive Solution) + 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53 54 55 56 57 58 59 60] + /Pg 918 0 R +>> +endobj + +57 0 obj +<< + /Type /StructElem + /S /P + /P 30 0 R + /K [35 36 37 38 39 40 41 42 43 44 45 46 47 48] + /Pg 918 0 R +>> +endobj + +58 0 obj +<< + /Type /StructElem + /S /P + /P 30 0 R + /K [23 24 25 26 27 28 29 30 31 32 33 34] + /Pg 918 0 R +>> +endobj + +59 0 obj +<< + /Type /StructElem + /S /P + /P 30 0 R + /K [11 12 13 14 15 16 17 18 19 20 21 22] + /Pg 918 0 R +>> +endobj + +60 0 obj +<< + /Type /StructElem + /S /P + /P 30 0 R + /K [0 1 2 3 4 5 6 7 8 9 10] + /Pg 918 0 R +>> +endobj + +61 0 obj +<< + /Type /StructElem + /S /P + /P 30 0 R + /K [247 248 249 250 251 252 253 254 255 256 257] + /Pg 916 0 R +>> +endobj + +62 0 obj +<< + /Type /StructElem + /S /P + /P 30 0 R + /K [234 235 236 237 238 239 240 241 242 243 244 245 246] + /Pg 916 0 R +>> +endobj + +63 0 obj +<< + /Type /StructElem + /S /P + /P 30 0 R + /K [223 224 225 226 227 228 229 230 231 232 233] + /Pg 916 0 R +>> +endobj + +64 0 obj +<< + /Type /StructElem + /S /P + /P 30 0 R + /K [204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222] + /Pg 916 0 R +>> +endobj + +65 0 obj +<< + /Type /StructElem + /S /P + /P 30 0 R + /K [195 196 197 198 199 200 201 202 203] + /Pg 916 0 R +>> +endobj + +66 0 obj +<< + /Type /StructElem + /S /P + /P 30 0 R + /K [186 187 188 189 190 191 192 193 194] + /Pg 916 0 R +>> +endobj + +67 0 obj +<< + /Type /StructElem + /S /H3 + /P 26 0 R + /T (Implementation in Rust) + /K [184 185] + /Pg 916 0 R +>> +endobj + +68 0 obj +<< + /Type /StructElem + /S /Div + /P 26 0 R + /K [71 0 R 69 0 R] +>> +endobj + +69 0 obj +<< + /Type /StructElem + /S /Div + /P 68 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [70 0 R] +>> +endobj + +70 0 obj +<< + /Type /StructElem + /S /P + /P 69 0 R + /K [166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181] + /Pg 916 0 R +>> +endobj + +71 0 obj +<< + /Type /StructElem + /S /Caption + /P 68 0 R + /K [73 0 R 72 0 R] +>> +endobj + +72 0 obj +<< + /Type /StructElem 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+0000208409 00000 n +0000212677 00000 n +0000217733 00000 n +0000347351 00000 n +0000347497 00000 n +0000348680 00000 n +trailer +<< + /Size 925 + /Root 924 0 R + /Info 922 0 R + /ID [(JCWNDJ/LTCMASwoXHdTlQg==) (JCWNDJ/LTCMASwoXHdTlQg==)] +>> +startxref +348939 +%%EOF \ No newline at end of file diff --git a/design/report.typ b/design/report.typ new file mode 100644 index 0000000..e0520b4 --- /dev/null +++ b/design/report.typ @@ -0,0 +1,431 @@ +#import "@preview/efter-plugget:0.1.1" + +#import "othello.typ": position, othello, othello-legend, shift-indicator + +#import "@preview/lovelace:0.3.0": pseudocode-list + +#import "@preview/algorithmic:1.0.6" +#import algorithmic: style-algorithm, algorithm-figure + +// library for visualizing registers and memory +#import "@preview/rivet:0.3.0": schema + +// hallon is an optional library for subfigures. +#import "@preview/hallon:0.1.2": subfigure +// cellpress is an optional library for Cell Press table style. +#import "@preview/cellpress-unofficial:0.1.0" as cellpress: toprule, midrule, bottomrule +// smartaref is an optional library for handling consecutive references. +#import "@preview/smartaref:0.1.0": cref, Cref + +#show: efter-plugget.template.with( + logo: image("inc/logo.png"), + title: [Othello Done Fast], + subtitle: [Squeezing out maximum performance using better datastructures], + page-header-title: ("Othello"), + course-name: ("Artificial Intelligence"), + course-code: "CSC-4753", + authors: "Jack Branch", +) + +#show: cellpress.style-table + +#let bitarray(arr) = { + grid(columns: arr.len(), + ..arr.filter(a => a != "").map(a => rect[ + #text(str(a)) + ]) + ) +} + +// #quote( +// block: true, +// attribution: [anonymous], +// )[ +// #emph["Chemistry is all around us."] +// ] + +Some of the datastructures and algorithms in use for this assignment are a bit unintuitive, so I figured I would spend the time thoroughly explaining each. + += Introduction + +In standard Othello, you have an eight by eight board of squares. Each square can contain a disc that is either black or white. How might you represent this structure in memory? This question and the implications of its answers is what this document will explore. + +I will make references to Rust structures and types while using pseudocode for all algorithms. + +== A Naive Solution + +A common naive approach would be to represent it as an array of characters where a `b` character represents a black disc, a `w` character represents a white disc, and an empty space represents a square with no disc at all. + +```rust +struct NaiveBoard { + board: [[char; 8]; 8] // in C, char[8][8] +} +``` + +One may observe that each ordinary `char` is represented as a single byte (unsigned 8-bit integer) and thus this structure would take a total of 64 bytes in memory. While this spacial efficiency problem is egregious, I'd argue it's the least of its concerns. + +The much larger problem with this datastructure is its impact on runtime performance of algorithms in terms of pure speed. While they _technically_ have the same time complexity in Big $O$, Big $O$ does not tell the full story here. This will be explained in further detail in the next section. + +== The Optimal Solution + +One may observe that each square in our board ultimately exists in one of three states at a time. These states are _has a black disc_, _has a white disc_, and _has no disc at all_. We could encode this information in just two bits! The first bit can encode whether or not there is a black disc while the second encodes whether or not there is a white disc. Naturally, if both bits are 0, then there is no disc at all. + +So we'd have `00` for no disc, `10` for a black disc, and `01` for a white disc. `11` is not a valid state, so you would want to ensure your program cannot produce it. To create a full Othello board, you'll want to simply associate two unsigned 64-bit integers (one for black and one for white). I will hereafter refer to this structure as a _BitBoard_. An awesome thing about this representation is that we can derive certain properties using only bitwise operations. + +For example, we can compute _all_ of the empty spaces by computing the negation of the bitwise `OR` of the two boards. To do the same with the naive solution, would require that you loop through the datastructure. Since the dimensions of the structure are constant, that algorithm would have constant time complexity. They may be equivalent in a sense, but they still perform quite differently. The naive requires repeated randomly array-accessed string comparisons while our new algorithm is, depending on CPU architecture, executing only one or two instructions total. + +Perhaps that operation is too simple to be fully representative. In the following chapters, I will demonstrate that same general bitwise approach can be had for all of the required algorithms. + +#figure(caption: "Starting Position", + othello(position( + "........", + "........", + "...0....", + "..0WB...", + "...BW0..", + "....0...", + "........", + "........" + ), cell-size: 16pt)) + +#let bitboard-p1 = yaml("./structures/bitboard-p1.yaml") +#let doc = schema.load(bitboard-p1) + +At the bit level, the structure of a single sub-board is as follows: #footnote("Text is a bit small. May have to zoom.") +#figure(caption: "Layout for a single sub-board", + schema.render(doc)) + + +Now an entire game's board would simply be two of these. Ideally allocated contiguously in memory as part of one structure. My BitBoard is represented by the following rust code: +```rust +// `Board` is referred to as "sub-board" in this paper. +pub type Board = u64; +pub struct BitBoard { + pub boards: [Board; 2], +} +``` + +== A Note on Notation + +I will use boards with descending rank and ascending file with the following legend. The starting board and black's first available moves will appear as follows: + +#grid( + columns: (auto, 1fr), + gutter: 30pt, + align: (center, left), + + // Board + othello(position( + "........", + "........", + "...0....", + "..0WB...", + "...BW0..", + "....0...", + "........", + "........" + )), + + // Legend + othello-legend() +) + += Board Operations + +== Generating Moves + +In Othello, the only legal moves are ones that _flank_ your opponent. In other words, you have to place a disc that pinches one or more of your opponent's pieces. + +In simple terms, the algorithm is as follows: + +#pseudocode-list[ + + keep a running sub-board of available moves + + *for each* disc of the current player's discs + + *for each* direction + + keep a running sub-board of opponent squares in this direction + + *while* the next square in that direction is has an opponent disc + + add to running sub-board of opponent squares + + *end* + + *if* next square in direction is empty + + add next empty square to running sub-board of moves + + *end* + + *end* + + *end* +] + +=== The Optimal Solution + +To generate moves, we need to generate a sub-board (unsigned 64-bit integer) where bits are excited if and only if the current player can place a disc there. + +Now, one might scratch their head wondering how they gain anything with this datastructure if you need to go disc by disc and shift them over repeatedly to determine whether or not there is an available move. Thankfully, because of the structure of the BitBoard, we can avoid this process entirely! + +Now, since my structure happens to be Big Endian #footnote("It would be equally viable in Little Endian, but you would need to reverse directions of shifts."), to compute a sub-board with every piece moved to the right, we can shift the entire board to the left by one. Observe that in our diagram , *b1* is to the _left_ of *a1* despite it being to the _right_ in the board visually +#footnote[An advantage of a Little Endian implementation is that the shift logic would be slightly more intuitive. However, in a Big Endian structure, the sub-board containing only *a1* is defined as $1$ which just seems natural to my human brain.]. +With that in mind, we can just think of all the different values that correspond to particular adjacencies. To go up, trivially, we shift left by 8. To go up and to the right, we shift once more. To go up and to the left, we shift by one less. Going down, we mirror the shifts to go up but swap the diagonals. To go to the left, we shift to the right once. Thus, we have the following shift constants: + +#figure(caption: "Shift constants", + shift-indicator((7, 8, 9, 1, 0, -1, -9, -8, -7)) +) + +Consider a black disc on *h1*. If we shift it to the right, where does it end up? Observe what happens: + +#grid( + columns: (auto, auto), + gutter: 70pt, + align: (center, left), + + figure(caption: [*h1*], othello(cell-size: 20pt, position( + "........", + "........", + "........", + "........", + "........", + "........", + "........", + ".......B" + ))) + , + + // Board shifted once over + figure(caption: [*h1 << 1*], othello(cell-size: 20pt, position( + "........", + "........", + "........", + "........", + "........", + "........", + "B.......", + "........" + ))), +) + +Therefore, it is prudent that we prevent wrap-around when moving horizontally or diagonally. We can do this by masking out the *a* file when moving left (visually) and masking out the *h* file when moving right. + +#grid( + columns: (auto, auto, auto), + align: (center, left), + + othello(cell-size: 16pt, position( + "........", + "........", + "........", + "........", + "........", + "........", + "........", + ".......B" + )) + , + + figure(caption: [*!h*], othello(cell-size: 16pt, position( + ".......X", + ".......X", + ".......X", + ".......X", + ".......X", + ".......X", + ".......X", + ".......X" + ))) + , + + // Board shifted once over + figure(caption: [*(h1 & !h) << 1*], othello(cell-size: 16pt, position( + "........", + "........", + "........", + "........", + "........", + "........", + "........", + "........" + ))), +) + +Thus, we can associate directional shifts with masks. With those pieces in mind, let's go through the algorithm to find left-flanks in the starting position for Black +#footnote[A left flank involves placing a disc to the right of an enemy disc]. + +#grid( + columns: (auto, auto, auto), + align: (center, left), + + othello(cell-size: 14pt, position( + "........", + "........", + "........", + "...WB...", + "...BW...", + "........", + "........", + "........" + )) + , + + figure(caption: [(B & !h) << 1], othello(cell-size: 14pt, position( + ".......X", + ".......X", + ".......X", + ".....B.X", + "....B..X", + ".......X", + ".......X", + ".......X" + ))), + + figure(caption: [*((P & !h) << 1) & O* #footnote[$P$ is the current team playing, and $O$ is the opponent.]], othello(cell-size: 14pt, position( + "........", + "........", + "........", + "........", + "....W...", + "........", + "........", + "........" + ))), +) + +The result above is only the first pass when computing left flanks. You would want to run the same computation again six more times with the previous result as input instead of $B$. +However, since there are no more discs to the right, we'd end up with the next seven passes will end up being effectively no-ops. Let's call this sub-board $A_r$. + +Once we've finished looking seven squares to the right, we want to add #footnote[*XOR* is slightly faster and equivalent in this case.] empty squares to the right of the squares we've computed to our total sub-board of available moves $M$. + +#figure(caption: [*$((A_r << 1) & E)$*], othello(cell-size: 30pt, position( + "........", + "........", + "........", + "........", + ".....0..", + "........", + "........", + "........" +))), + +Thus, we have determined that our sub-board $M$ contains *f5*. Okay, with that out of the way, let's generalize the algorithm for each direction. + +#show: style-algorithm +#algorithm-figure( + "Move Generation", + vstroke: .5pt + luma(200), + { + import algorithmic: * + Comment[Define the directional shift constants] + Assign[$D$][${ 9, 8, 7, 1, -1, -7, -8, -9 }$] + Comment[Define the masks ($F_a$ includes all but $F_a$)] + Assign[$F_a$][0x7F7F7F7F7F7F7F7F] + Assign[$F_h$][0xFEFEFEFEFEFEFEFE] + Assign[all][0xFEFEFEFEFEFEFEFE] + Assign[$M$][${ + F_a, + "all", + F_h, + F_a, + F_h, + F_a, + "all", + F_h, + }$] + LineBreak + Comment[A helper function that shifts in the appropriate direction depending on the magnitude] + Procedure( + "directional_shift", + ("magnitude", "board"), + { + If($"magnitude" >= 0 $, { + Return[$"board" << "magnitude"$] + }) + Else({ + Return[$"board" >> "magnitude"$] + }) + }, + ) + LineBreak + Procedure( + "Available", + ("P", "O"), + { + Comment[Define the board of empty squares] + Assign[$E$][$!(P | O)$] + LineBreak + Assign[$"move"$][$0$] + Assign[$i$][$0$] + While( + $i < 8$, + { + Assign([d], [$D[i]$]) + Assign([m], [$M[i]$]) + Assign([$A$], FnInline[directional_shift][$(d, P amp m)$]) + Assign([$A$], FnInline[directional_shift][$(d, A amp m)$]) + Assign([$A$], FnInline[directional_shift][$(d, A amp m)$]) + Assign([$A$], FnInline[directional_shift][$(d, A amp m)$]) + Assign([$A$], FnInline[directional_shift][$(d, A amp m)$]) + Assign([$A$], FnInline[directional_shift][$(d, A amp m)$]) + Assign([$A$], FnInline[directional_shift][$(d, A amp m)$]) + Assign([$"move"$], $"move" | A$) + Assign([$i$], $i + 1$) + }, + ) + Return[$"move"$] + }, + ) + } +) + +If the algorithm is performed correctly, you will end up with the following board of legal moves: + +#figure(caption: [Starting moves for Black], othello(cell-size: 30pt, position( + "........", + "........", + "...0....", + "..0.....", + ".....0..", + "....0...", + "........", + "........" +))) + +=== Implementation in Rust + +```rust +const NOT_A_FILE: Board = 0x7F7F7F7F7F7F7F7F; +const NOT_H_FILE: Board = 0xFEFEFEFEFEFEFEFE; +const SHIFT_MASK_COMBOS: [(i8, Board); 8] = [ + (9, NOT_A_FILE), // 9 (up right) + (8, Board::MAX), // 8 (up) + (7, NOT_H_FILE), // 7 (up left) + (1, NOT_A_FILE), // 1 (right) + (-1, NOT_H_FILE), // -1 (left) + (-7, NOT_A_FILE), // -7 (down right) + (-8, Board::MAX), // -8 (down) + (-9, NOT_H_FILE), // -9 (down left) +]; + +impl BitBoard { + pub fn available(&self, current_team: Team) -> Board { + let empties = !(self.boards[0] | self.boards[1]); + let mut moves = 0; + let (team, opponent) = ( + self.boards[current_team as usize], + self.boards[current_team.next() as usize], + ); + + for (shift, mask) in SHIFT_MASK_COMBOS { + let mut sub_move = shift_in_direction(shift, team & mask) & opponent; + sub_move |= shift_in_direction(shift, sub_move & mask) & opponent; + sub_move |= shift_in_direction(shift, sub_move & mask) & opponent; + sub_move |= shift_in_direction(shift, sub_move & mask) & opponent; + sub_move |= shift_in_direction(shift, sub_move & mask) & opponent; + sub_move |= shift_in_direction(shift, sub_move & mask) & opponent; + sub_move = shift_in_direction(shift, sub_move & mask) & empties; + moves |= sub_move; + } + + moves + } +} +``` + +=== Benchmarks + +== Playing Moves + +=== Benchmarks diff --git a/design/structures/bitboard-p1.yaml b/design/structures/bitboard-p1.yaml new file mode 100644 index 0000000..7ec816c --- /dev/null +++ b/design/structures/bitboard-p1.yaml @@ -0,0 +1,135 @@ +structures: + main: + bits: 64 + ranges: + 63: + name: h8 + description: top-right corner + 62: + name: g8 + 61: + name: f8 + 60: + name: e8 + 59: + name: d8 + 58: + name: c8 + 57: + name: b8 + 56: + name: a8 + description: top-left corner + 55: + name: h7 + 54: + name: g7 + 53: + name: f7 + 52: + name: e7 + 51: + name: d7 + 50: + name: c7 + 49: + name: b7 + 48: + name: a7 + 47: + name: h6 + 46: + name: g6 + 45: + name: f6 + 44: + name: e6 + 43: + name: d6 + 42: + name: c6 + 41: + name: b6 + 40: + name: a6 + 39: + name: h5 + 38: + name: g5 + 37: + name: f5 + 36: + name: e5 + 35: + name: d5 + 34: + name: c5 + 33: + name: b5 + 32: + name: a5 + 31: + name: h4 + 30: + name: g4 + 29: + name: f4 + 28: + name: e4 + 27: + name: d4 + 26: + name: c4 + 25: + name: b4 + 24: + name: a4 + 23: + name: h3 + 22: + name: g3 + 21: + name: f3 + 20: + name: e3 + 19: + name: d3 + 18: + name: c3 + 17: + name: b3 + 16: + name: a3 + 15: + name: h2 + 14: + name: g2 + 13: + name: f2 + 12: + name: e2 + 11: + name: d2 + 10: + name: c2 + 9: + name: b2 + 8: + name: a2 + 7: + name: h1 + 6: + name: g1 + 5: + name: f1 + 4: + name: e1 + 3: + name: d1 + 2: + name: c1 + 1: + name: b1 + 0: + name: a1 + description: bottom-left corner diff --git a/flake.nix b/flake.nix index 492ff35..8bfc607 100644 --- a/flake.nix +++ b/flake.nix @@ -11,7 +11,7 @@ devShells."x86_64-linux".default = pkgs.mkShell { buildInputs = with pkgs; [ - cargo rustc rustfmt clippy rust-analyzer glibc + cargo rustc rustfmt clippy rust-analyzer glibc typst tinymist ]; nativeBuildInputs = [ pkgs.pkg-config ]; env.RUST_SRC_PATH = "${pkgs.rust.packages.stable.rustPlatform.rustLibSrc}"; diff --git a/src/board/mod.rs b/src/board/mod.rs index 92917c3..ba2d439 100644 --- a/src/board/mod.rs +++ b/src/board/mod.rs @@ -144,6 +144,7 @@ impl Display for BitBoard { } } +#[inline] fn shift_in_direction(magnitude: i8, value: Board) -> Board { if magnitude >= 0 { let (result, _) = value.overflowing_shl(magnitude.unsigned_abs() as u32); @@ -374,10 +375,8 @@ impl BitBoard { } } - self.boards[current_team_idx] += flips; + self.boards[current_team_idx] |= flips | play; self.boards[current_team.next() as usize] ^= flips; - - self.boards[current_team_idx] += play; } /// Compute the score (B, W) by counting the excited bits in each board. diff --git a/src/game.rs b/src/game.rs index e5cbb64..dc9a676 100644 --- a/src/game.rs +++ b/src/game.rs @@ -50,7 +50,7 @@ impl Game { #[cfg(test)] mod tests { use super::*; - use crate::board::{squares::*, view::View}; + use crate::board::squares::*; #[test] fn play_switches_team() { let mut game = Game::default();