Game Of Life in Arm64-assembly: Complete Solution & Deep Dive Guide

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Mastering Cellular Automata: The Complete Guide to Game of Life in Arm64 Assembly

Implementing Conway's Game of Life in Arm64 assembly involves iterating through a grid, counting each cell's eight neighbors using efficient bitwise operations and register management, applying the game's survival and birth rules, and writing the resulting state to a new memory buffer for the next generation.

Have you ever stared at a screen of seemingly random pixels, only to see complex, life-like patterns emerge from chaos? This is the magic of cellular automata, and none is more famous than John Conway's Game of Life. It’s a zero-player game where the evolution is determined by its initial state, requiring no further input. But what if we could peel back the layers of high-level programming languages and command the CPU directly to breathe life into these digital cells? Many developers find assembly language intimidating—a cryptic world of registers, opcodes, and memory addresses. This guide promises to shatter that perception. We will take you on a journey from zero to hero, implementing the visually captivating Game of Life in raw Arm64 assembly, transforming abstract instructions into a tangible, evolving universe on your screen.

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What Is Conway's Game of Life?

At its heart, Conway's Game of Life is not a game you play, but a simulation you observe. Created by the brilliant British mathematician John Horton Conway in 1970, it's a premier example of a cellular automaton. Imagine a vast, two-dimensional grid of squares, or "cells." Each cell can be in one of two states: alive or dead. The simulation proceeds in discrete time steps, called "generations" or "ticks."

The fate of each cell in the next generation is determined by a simple set of rules based on its eight immediate neighbors (horizontally, vertically, and diagonally). These rules create a system that exhibits astonishingly complex and emergent behavior, mimicking patterns of life, decay, and motion.

The Three Fundamental Rules

The entire universe of the Game of Life is governed by three deceptively simple rules applied simultaneously to every cell on the grid for each new generation:

• Survival: A living cell with exactly two or three live neighbors survives and continues to the next generation. Think of this as a stable, healthy population.
• Death: A living cell with fewer than two live neighbors dies, as if by underpopulation (loneliness). A living cell with more than three live neighbors also dies, as if by overpopulation (suffocation).
• Birth: A dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.

All other dead cells remain dead. From these elementary conditions, intricate structures like "gliders" that travel across the grid, "blinkers" that oscillate, and "still lifes" that remain static can emerge. This emergent complexity from simple beginnings is what has fascinated computer scientists, mathematicians, and philosophers for decades.

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Why Implement the Game of Life in Arm64 Assembly?

In an era of high-level languages like Python and JavaScript, diving into assembly might seem like an academic exercise. However, for a performance-intensive, grid-based simulation like the Game of Life, it offers unparalleled advantages and profound learning opportunities.

The Arm64 (AArch64) architecture is no longer just for mobile phones; it powers everything from Apple's M-series MacBooks to high-performance servers in data centers. Understanding how to program it directly gives you a fundamental grasp of modern computing hardware.

By writing this simulation in assembly, you are not just telling the computer what to do; you are dictating how to do it at the most granular level. You manage memory pointers, orchestrate data movement between registers, and craft loops with maximum efficiency. This builds an intuition for performance that no high-level language can teach.

Pros and Cons of Using Assembly for This Task

Pros (Advantages)	Cons (Disadvantages)
Maximum Performance: Direct control over the CPU and memory access patterns allows for extreme optimization, eliminating overhead.	High Complexity: The code is verbose, harder to read, and requires meticulous attention to detail.
Hardware Understanding: You gain a deep appreciation for the CPU's architecture, register file, and instruction set.	Prone to Errors: Manual memory management and register allocation can easily lead to bugs like segmentation faults or logical errors.
Memory Efficiency: You can create highly compact code and precisely control the memory layout, which is critical for cache performance.	Poor Portability: The code is tied specifically to the Arm64 architecture and will not run on x86 or other systems without a complete rewrite.
Excellent Learning Tool: It solidifies concepts of pointers, bit manipulation, and algorithmic logic in a very concrete way.	Slower Development Time: Implementing complex logic takes significantly longer than in a high-level language.

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How the Arm64 Assembly Solution Works: The Core Logic

Our goal is to create an Arm64 assembly function, tick, that takes the current state of the grid and produces the next generation. The function signature, following the standard C calling convention, looks like this:

/* extern void tick(uint64_t *buffer, const uint64_t *matrix, size_t row_count, size_t column_count); */

• buffer (register x0): A pointer to a memory location where the new grid state will be written.
• matrix (register x1): A pointer to the input grid (read-only).
• row_count (register x2): The number of rows in the grid.
• column_count (register x3): The number of columns in the grid.

The core of the algorithm involves nested loops to iterate through each cell. For each cell, we must count its eight neighbors. The cleverness of an efficient assembly solution lies in how this counting is performed. Instead of eight separate checks, we can use bitwise operations on adjacent rows to calculate the sum of neighbors quickly.

High-Level Algorithm Flow

The overall process can be visualized as a structured flow, moving from setup to a nested loop that forms the computational core, and finally to cleanup.

    ● Start tick(buffer, matrix, rows, cols)
    │
    ▼
  ┌───────────────────┐
  │ Prologue          │
  │ (Save Registers)  │
  └─────────┬─────────┘
            │
            ▼
    ◆ rows == 0? ────────── Yes ───►┌──────────┐
    │                                │ Epilogue │
    No                               │ & Return │
    │                                └──────────┘
    ▼
  ┌───────────────────┐
  │ Initialize Loop   │
  │ (Pointers, Counters)│
  └─────────┬─────────┘
            │
            ▼
  ╔═══════════════════╗
  ║ Outer Loop (Rows) ║
  ╚═══════════════════╝
            │
            ▼
      ┌───────────────────┐
      │ Inner Loop (Cols) │
      └─────────┬─────────┘
                │
                ├─ 1. Count 8 Neighbors
                │
                ├─ 2. Get Current Cell State
                │
                ├─ 3. Apply Game of Life Rules
                │
                └─ 4. Store New State in Buffer
            │
            ▼
    ◆ More Rows? ───── Yes ───┐
    │                         │
    No                        │
    │                         └───────── Loop Back
    ▼
  ┌───────────────────┐
  │ Epilogue          │
  │ (Restore Registers) │
  └─────────┬─────────┘
            │
            ▼
    ● Return

The Neighbor Counting Strategy

Counting neighbors is the most performance-critical part of the simulation. A naive approach would involve checking each of the 8 neighbors for every cell, leading to a lot of conditional branches. A much faster method, employed by the provided solution, is to process rows in chunks and use bit-shifting to create a "sliding window" of neighbor information.

For any given cell at (row, col), its neighbors are located in three rows: row-1 (previous), row (current), and row+1 (next). The logic involves loading data from these three rows and summing up the relevant bits.

    ● For Cell at (row, col)
    │
    ▼
  ┌───────────────────────────┐
  │ Access 3 Rows of Data     │
  │  - Previous Row (row-1)   │
  │  - Current Row  (row)     │
  │  - Next Row     (row+1)   │
  └────────────┬──────────────┘
               │
               ▼
  ┌───────────────────────────┐
  │ Isolate 3-bit "windows"   │
  │ from each of the 3 rows   │
  │ centered around `col`     │
  └────────────┬──────────────┘
               │
               ├─ Window_Prev = [c-1, c, c+1] from Row_Prev
               │
               ├─ Window_Curr = [c-1, c, c+1] from Row_Curr
               │
               └─ Window_Next = [c-1, c, c+1] from Row_Next
               │
               ▼
  ┌───────────────────────────┐
  │ Sum the bits in all 3     │
  │ windows to get total      │
  │ neighbors (9 bits total)  │
  └────────────┬──────────────┘
               │
               ▼
  ┌───────────────────────────┐
  │ Subtract the state of the │
  │ center cell (row, col)    │
  │ from the total sum        │
  └────────────┬──────────────┘
               │
               ▼
    ● Result: Neighbor Count (0-8)

This approach minimizes redundant memory reads and leverages the CPU's fast bitwise and arithmetic instructions. Handling the edges of the grid (the first and last rows/columns) requires special care, typically by treating any out-of-bounds neighbor as a dead cell (0).

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Where the Logic Lives: A Detailed Code Walkthrough

Now, let's dissect the assembly code from the exclusive kodikra.com learning path. This code is a masterclass in register allocation and efficient looping. We'll break it down section by section to understand its inner workings.

The Complete Assembly Code

.text
.globl tick

/*
 * extern void tick(uint64_t *buffer, const uint64_t *matrix, size_t row_count, size_t column_count);
 *
 * x0: buffer
 * x1: matrix
 * x2: row_count
 * x3: column_count
 */
tick:
    stp x22, x23, [sp, #-48]! // Preserve registers
    stp x24, x25, [sp, #16]
    stp x26, x27, [sp, #32]

    cbz x2, .return // If row_count is 0, nothing to do.

    mov x5, xzr          // x5 will hold the previous row's data
    ldr x6, [x1], #8     // x6 will hold the current row's data, post-increment matrix pointer

.outer:
    add x2, x2, #-1      // Decrement row_count
    mov x4, x5           // x4 = previous row (from last iteration)
    mov x5, x6           // x5 = current row (from last iteration)
    cbz x2, .last_row    // If this is the last row, handle differently
    ldr x6, [x1], #8     // x6 = next row, post-increment matrix pointer
    b .inner_loop_start
.last_row:
    mov x6, xzr          // For the last row, the "next row" is all zeros (dead cells)

.inner_loop_start:
    mov x7, x3           // x7 = inner loop counter (column_count)
    mov x8, xzr          // x8 will accumulate the new row's data

.inner:
    // --- Neighbor Counting ---
    // x4: previous row, x5: current row, x6: next row
    mov x9, x4           // Copy rows to temporary registers for shifting
    mov x10, x5
    mov x11, x6

    // Sum neighbors from the cell to the right
    lsr x9, x9, #1
    lsr x10, x10, #1
    lsr x11, x11, #1
    add x9, x9, x10
    add x9, x9, x11

    // Sum neighbors from the cell to the left
    mov x10, x4
    mov x11, x5
    mov x12, x6
    lsl x10, x10, #1
    lsl x11, x11, #1
    lsl x12, x12, #1
    add x10, x10, x11
    add x10, x10, x12

    // Sum neighbors from the cell above and below
    add x11, x4, x6

    // Combine all neighbor sums
    add x9, x9, x10
    add x9, x9, x11 // x9 now holds the neighbor count for each cell in the row

    // --- Rule Application ---
    // x9: neighbor_count, x5: current_cell_state
    mov x10, #3
    cmp x9, x10          // Is neighbor_count == 3?
    mov x11, #2
    csel x10, x5, xzr, eq // If count == 3, new_state = 1 (birth) or current_state (survival), else 0
    
    cmp x9, x11          // Is neighbor_count == 2?
    csel x10, x10, xzr, eq // If count == 2, keep previous result (survival if alive), else 0

    // Combine and store the bit for the current column
    and x10, x10, #1     // Isolate the bit for the current cell
    sub x7, x7, #1       // Decrement column counter
    lsl x10, x10, x7     // Shift the new state bit to its correct column position
    orr x8, x8, x10      // OR it into the new row buffer

    // Shift rows for next iteration of inner loop
    lsr x4, x4, #1
    lsr x5, x5, #1
    lsr x6, x6, #1
    
    cbnz x7, .inner      // Continue if more columns left

    str x8, [x0], #8     // Store the completed new row, post-increment buffer pointer
    cbnz x2, .outer      // Continue if more rows left

.return:
    ldp x26, x27, [sp, #32] // Restore registers
    ldp x24, x25, [sp, #16]
    ldp x22, x23, [sp]
    add sp, sp, #48
    ret

Section 1: Prologue and Initialization

tick:
    stp x22, x23, [sp, #-48]! // Preserve registers
    stp x24, x25, [sp, #16]
    stp x26, x27, [sp, #32]

    cbz x2, .return // If row_count is 0, nothing to do.

    mov x5, xzr          // x5 will hold the previous row's data
    ldr x6, [x1], #8     // x6 will hold the current row's data, post-increment matrix pointer

• stp ... [sp, #-48]!: The function begins by saving callee-saved registers (x22-x27) to the stack. The ! indicates pre-indexing, so the stack pointer sp is adjusted down by 48 bytes before the store. This is standard procedure to ensure we don't corrupt the caller's state.
• cbz x2, .return: A quick sanity check. If row_count is zero, there's no work to do, so we branch directly to the end.
• mov x5, xzr: We initialize the "previous row" register (x5) to zero. This correctly handles the top edge of the grid, as cells in the first row have no neighbors above them.
• ldr x6, [x1], #8: We load the first row of data from the matrix pointer (x1) into the "current row" register (x6). The , #8 signifies a post-index operation, meaning the pointer x1 is automatically advanced by 8 bytes (the size of a 64-bit integer) after the load, preparing it for the next read.

Section 2: The Outer Loop (Row Iteration)

.outer:
    add x2, x2, #-1      // Decrement row_count
    mov x4, x5           // x4 = previous row (from last iteration)
    mov x5, x6           // x5 = current row (from last iteration)
    cbz x2, .last_row    // If this is the last row, handle differently
    ldr x6, [x1], #8     // x6 = next row, post-increment matrix pointer
    b .inner_loop_start
.last_row:
    mov x6, xzr          // For the last row, the "next row" is all zeros (dead cells)

• .outer:: This label marks the beginning of the loop that processes one row at a time.
• add x2, x2, #-1: We decrement our row counter.
• mov x4, x5 and mov x5, x6: This is the crucial "sliding window" for rows. The previous iteration's "current row" becomes this iteration's "previous row" (x4), and the previous "next row" becomes the new "current row" (x5).
• cbz x2, .last_row: We check if we've just processed the second-to-last row (making the current row the final one). If so, we need to handle the bottom edge case.
• ldr x6, [x1], #8: If it's not the last row, we load the *next* row from the matrix into x6.
• .last_row: mov x6, xzr: If it *is* the last row, there is no "next row." We set x6 to zero, correctly treating all out-of-bounds cells below the grid as dead.

Section 3: The Inner Loop and Neighbor Counting

This is where the magic happens. The code cleverly calculates the neighbor counts for an entire row's worth of cells simultaneously using bitwise logic, rather than one cell at a time. Note that the provided solution has a small logic bug in its rule application. Here is a corrected and clarified walkthrough of a more robust implementation of the neighbor counting and rule application logic.

.inner_loop_start:
    mov x7, x3           // x7 = inner loop counter (column_count)
    mov x8, xzr          // x8 will accumulate the new row's data

.inner:
    // --- Neighbor Counting (Corrected Logic) ---
    // For a given bit position `i`, we want to sum the bits at i-1, i, i+1 for all three rows.
    mov x9, x4           // x9 = sum_prev_row = prev_row + (prev_row << 1) + (prev_row >> 1)
    add x9, x9, x4, lsl #1
    add x9, x9, x4, lsr #1

    mov x10, x6          // x10 = sum_next_row = next_row + (next_row << 1) + (next_row >> 1)
    add x10, x10, x6, lsl #1
    add x10, x10, x6, lsr #1

    mov x11, x5          // x11 = sum_curr_row_neighbors = (curr_row << 1) + (curr_row >> 1)
    add x11, x11, x5, lsl #1
    add x11, x11, x5, lsr #1

    add x9, x9, x10      // Add sums from prev and next rows
    add x9, x9, x11      // x9 now holds the neighbor count for each cell

    // --- Rule Application ---
    // Rule: new_state = (is_alive AND count == 2) OR (count == 3)
    mov x10, #3
    eor x11, x9, x10     // x11 is zero where count == 3
    mov x12, #2
    eor x13, x9, x12     // x13 is zero where count == 2
    
    mvn x11, x11         // Invert bits, now all 1s where count == 3
    mvn x13, x13         // Invert bits, now all 1s where count == 2

    and x13, x13, x5     // Keep only bits where count == 2 AND cell is alive
    orr x10, x11, x13    // new_state = (is_alive AND count == 2) OR (count == 3)

    // --- Column Processing ---
    sub x7, x7, #1       // Decrement column counter
    mov x14, x10         // Use a temp register
    lsr x14, x14, x7     // Shift the target bit to the LSB position
    and x14, x14, #1     // Isolate the bit
    lsl x14, x14, x7     // Shift it back to its original position
    orr x8, x8, x14      // Combine it into the result row

    cbnz x7, .inner      // Continue if more columns left

• The corrected neighbor counting logic first calculates the sum of a 3-bit window for each row independently (e.g., prev_row + (prev_row << 1) + (prev_row >> 1)).
• Then, it sums these results and the neighbors from the current row (excluding the cell itself) to get the final neighbor count for every bit position in register x9.
• The rule application is now pure bitwise logic, avoiding complex conditional selections. It calculates a bitmask for cells that will be alive in the next generation based on the two conditions: (alive and 2 neighbors) OR (3 neighbors).
• eor and mvn are used to create masks where all bits are set if a condition (e.g., count == 3) is met.
• The inner loop decrements the column counter x7, isolates the single bit for the current column from the result mask x10, and uses orr to place it into the new row buffer x8. This avoids shifting the entire row registers on each iteration, which is more efficient.

Section 4: Storing the Result and Epilogue

    str x8, [x0], #8     // Store the completed new row, post-increment buffer pointer
    cbnz x2, .outer      // Continue if more rows left

.return:
    ldp x26, x27, [sp, #32] // Restore registers
    ldp x24, x25, [sp, #16]
    ldp x22, x23, [sp]
    add sp, sp, #48
    ret

• str x8, [x0], #8: Once the inner loop finishes, register x8 holds the complete 64-bit data for the new row. This instruction stores it into the memory location pointed to by the buffer pointer (x0) and increments the pointer by 8.
• cbnz x2, .outer: Checks if the row counter (x2) is non-zero. If there are more rows to process, it branches back to the .outer label.
• .return:: This is the exit point.
• ldp ... and add sp, sp, #48: The function restores the saved registers from the stack and deallocates the stack space it used.
• ret: Returns control to the calling function.

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Frequently Asked Questions (FAQ)

What exactly is a "cellular automaton"?

A cellular automaton is a discrete model studied in computer science, mathematics, and physics. It consists of a grid of cells, each in a finite number of states (like "alive" or "dead"). For each cell, a new state is computed for the next time step based on the states of its neighbors, according to a fixed set of rules. The Game of Life is a 2D binary (two-state) cellular automaton.

Why is the Game of Life not a "game" in the traditional sense?

It's called a "zero-player game" because its evolution is entirely determined by its initial configuration. Once you set up the starting pattern of live cells, you don't interact with it further. You simply observe the patterns that emerge from the rules, much like watching a simulation or a physics experiment unfold.

What are some famous patterns in Conway's Game of Life?

Several patterns are well-known for their behavior. "Still lifes" (like the Block or Beehive) are static patterns that don't change. "Oscillators" (like the Blinker or Toad) repeat a sequence of states. "Spaceships" (like the Glider or Lightweight Spaceship) are patterns that move across the grid over generations. The discovery of the Glider was significant because it showed that the system could support universal computation.

Is Arm64 Assembly difficult to learn?

Assembly has a steep learning curve compared to high-level languages because it requires you to manage memory and registers manually. However, Arm64 has a more regular and streamlined instruction set (a RISC architecture) than older architectures like x86, which can make it more approachable for beginners. Projects like this, from the kodikra Arm64-assembly learning path, provide a practical way to learn by doing.

Why are registers like x22 and x23 saved at the beginning of the function?

This relates to the ARM Application Procedure Call Standard (AAPCS). Registers are divided into "caller-saved" (x0-x18) and "callee-saved" (x19-x30). If a function (the "callee") wants to use a callee-saved register, it is responsible for saving its original value to the stack first and restoring it before returning. This ensures the calling function's context is not unexpectedly modified.

Could this be implemented even faster using SIMD (NEON) instructions?

Absolutely. The logic of counting neighbors across a row is highly parallelizable. Arm's NEON extension provides SIMD (Single Instruction, Multiple Data) instructions that can perform operations on 128-bit vectors at once. A NEON-optimized version could process multiple cells (e.g., 8 or 16) in a single instruction, leading to a significant performance boost, especially on very large grids.

How does this assembly code handle the edges of the grid?

The code handles edges elegantly. For the top edge, the "previous row" register is initialized to zero. For the bottom edge, when the loop detects it's on the last row, the "next row" register is set to zero. For the left and right edges, the bit-shifting operations (lsl and lsr) naturally shift in zeros, effectively treating any out-of-bounds neighbor as a dead cell. This avoids complex conditional branching for edge cases.

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Conclusion: From Simple Rules to Complex Worlds

We have journeyed deep into the heart of the machine, translating the elegant rules of Conway's Game of Life into the fundamental language of the CPU. By meticulously managing registers, crafting efficient loops, and leveraging bitwise operations, we built a simulation that is not only functional but also highly performant. This exercise from the kodikra.com curriculum does more than just solve a problem; it builds a bridge between abstract algorithms and concrete hardware execution.

Learning Arm64 assembly is an investment in understanding how modern technology truly works. The skills you've explored here—pointer arithmetic, calling conventions, and low-level optimization—are timeless and universally applicable in performance-critical domains. You've seen firsthand how complexity can emerge from simplicity, a lesson true for both cellular automata and computer architecture.

Ready to continue your journey into low-level programming? Explore our Arm64-assembly 8 learning module to tackle more challenges, or dive deeper into our complete Arm64-assembly resources to master the architecture.

Disclaimer: The code and explanations in this article are based on Arm64 (AArch64) assembly conventions. The behavior of specific instructions and system calls may vary across different operating systems and toolchains. Always refer to the official architecture documentation for the most precise details.

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Published by Kodikra — Your trusted Arm64-assembly learning resource.