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Chapter 18: Data Structure Implementation

Motivation

Efficient implementation of the Hologram model requires carefully designed data structures that respect conservation laws while enabling fast operations. This chapter presents production-quality implementations of the core data structures: the lattice representation, configuration buffers, and receipt structures. We optimize for both theoretical elegance and practical performance.

Lattice Representation

Memory-Efficient Lattice

#![allow(unused)]
fn main() {
use std::sync::Arc;
use parking_lot::RwLock;

/// The 12,288-site lattice with efficient memory layout
#[repr(C, align(64))]  // Cache-line aligned
pub struct Lattice {
    /// Raw data storage - exactly 12,288 bytes
    data: [u8; 12_288],

    /// Metadata for fast operations
    metadata: LatticeMetadata,

    /// Version for optimistic concurrency
    version: AtomicU64,
}

impl Lattice {
    /// Constants for lattice dimensions
    pub const PAGES: usize = 48;
    pub const BYTES_PER_PAGE: usize = 256;
    pub const TOTAL_SITES: usize = Self::PAGES * Self::BYTES_PER_PAGE;

    /// Create empty lattice
    pub fn new() -> Self {
        Self {
            data: [0; Self::TOTAL_SITES],
            metadata: LatticeMetadata::default(),
            version: AtomicU64::new(0),
        }
    }

    /// Efficient site indexing
    #[inline(always)]
    pub fn site_to_index(page: u8, byte: u8) -> usize {
        ((page as usize) % Self::PAGES) * Self::BYTES_PER_PAGE +
        ((byte as usize) % Self::BYTES_PER_PAGE)
    }

    /// Index to site conversion
    #[inline(always)]
    pub fn index_to_site(index: usize) -> (u8, u8) {
        let index = index % Self::TOTAL_SITES;
        ((index / Self::BYTES_PER_PAGE) as u8,
         (index % Self::BYTES_PER_PAGE) as u8)
    }

    /// Get value at site with bounds checking
    #[inline]
    pub fn get(&self, page: u8, byte: u8) -> u8 {
        self.data[Self::site_to_index(page, byte)]
    }

    /// Set value at site
    #[inline]
    pub fn set(&mut self, page: u8, byte: u8, value: u8) {
        let index = Self::site_to_index(page, byte);
        self.data[index] = value;
        self.version.fetch_add(1, Ordering::SeqCst);
        self.metadata.mark_dirty(index);
    }

    /// Bulk operations for efficiency
    pub fn apply_morphism(&mut self, morphism: &Morphism) {
        // Pre-compute affected sites
        let affected = morphism.affected_sites();

        // Batch updates
        for &site in &affected {
            let old_value = self.data[site];
            let new_value = morphism.apply_to_byte(old_value);
            self.data[site] = new_value;
        }

        // Single version increment
        self.version.fetch_add(1, Ordering::SeqCst);
        self.metadata.bulk_mark_dirty(&affected);
    }
}

/// Metadata for optimization
#[derive(Default)]
struct LatticeMetadata {
    /// Dirty tracking for incremental computation
    dirty_bits: BitVec,

    /// R96 histogram cache
    r96_histogram: [u32; 96],

    /// Active region bounds
    active_min: usize,
    active_max: usize,

    /// Occupancy count
    non_zero_count: usize,
}

impl LatticeMetadata {
    fn mark_dirty(&mut self, index: usize) {
        self.dirty_bits.set(index, true);
        self.active_min = self.active_min.min(index);
        self.active_max = self.active_max.max(index);
    }

    fn bulk_mark_dirty(&mut self, indices: &[usize]) {
        for &i in indices {
            self.dirty_bits.set(i, true);
        }
        // Update bounds efficiently
        if let (Some(&min), Some(&max)) = (indices.iter().min(), indices.iter().max()) {
            self.active_min = self.active_min.min(min);
            self.active_max = self.active_max.max(max);
        }
    }
}
}

SIMD-Optimized Operations

#![allow(unused)]
fn main() {
use std::arch::x86_64::*;

impl Lattice {
    /// SIMD-accelerated R96 computation
    #[target_feature(enable = "avx2")]
    unsafe fn compute_r96_simd(&self) -> [u32; 96] {
        let mut histogram = [0u32; 96];

        // Process 32 bytes at a time with AVX2
        for chunk_start in (0..Self::TOTAL_SITES).step_by(32) {
            let chunk = _mm256_loadu_si256(
                self.data[chunk_start..].as_ptr() as *const __m256i
            );

            // Compute R96 for each byte in parallel
            let r96_values = Self::simd_r96_transform(chunk);

            // Update histogram
            Self::simd_histogram_update(&mut histogram, r96_values);
        }

        histogram
    }

    #[target_feature(enable = "avx2")]
    unsafe fn simd_r96_transform(bytes: __m256i) -> __m256i {
        // R(b) = (b % 96) + floor(b/96) * 17
        let mod_96 = _mm256_set1_epi8(96);
        let factor_17 = _mm256_set1_epi8(17);

        // Compute b % 96 and b / 96
        let remainder = _mm256_rem_epi8(bytes, mod_96);
        let quotient = _mm256_div_epi8(bytes, mod_96);

        // Result = remainder + quotient * 17
        let product = _mm256_mullo_epi8(quotient, factor_17);
        _mm256_add_epi8(remainder, product)
    }
}
}

Copy-on-Write Optimization

#![allow(unused)]
fn main() {
/// Copy-on-write wrapper for efficient cloning
pub struct CowLattice {
    inner: Arc<RwLock<Lattice>>,
    /// Local modifications before committing
    local_changes: Option<HashMap<usize, u8>>,
}

impl CowLattice {
    pub fn new(lattice: Lattice) -> Self {
        Self {
            inner: Arc::new(RwLock::new(lattice)),
            local_changes: None,
        }
    }

    /// Read through to underlying lattice
    pub fn get(&self, page: u8, byte: u8) -> u8 {
        let index = Lattice::site_to_index(page, byte);

        // Check local changes first
        if let Some(ref changes) = self.local_changes {
            if let Some(&value) = changes.get(&index) {
                return value;
            }
        }

        // Read from shared lattice
        self.inner.read().get(page, byte)
    }

    /// Write triggers copy-on-write
    pub fn set(&mut self, page: u8, byte: u8, value: u8) {
        let index = Lattice::site_to_index(page, byte);

        // Initialize local changes if needed
        if self.local_changes.is_none() {
            self.local_changes = Some(HashMap::new());
        }

        self.local_changes.as_mut().unwrap().insert(index, value);
    }

    /// Commit local changes
    pub fn commit(&mut self) {
        if let Some(changes) = self.local_changes.take() {
            let mut lattice = self.inner.write();
            for (index, value) in changes {
                let (page, byte) = Lattice::index_to_site(index);
                lattice.set(page, byte, value);
            }
        }
    }
}
}

Configuration Buffers

Ring Buffer for Streaming

#![allow(unused)]
fn main() {
/// Ring buffer for streaming configurations
pub struct ConfigurationRingBuffer {
    /// Fixed-size buffer
    buffer: Vec<Configuration>,

    /// Write position
    write_pos: AtomicUsize,

    /// Read position
    read_pos: AtomicUsize,

    /// Capacity (power of 2 for fast modulo)
    capacity: usize,

    /// Mask for fast modulo (capacity - 1)
    mask: usize,
}

impl ConfigurationRingBuffer {
    pub fn new(capacity_power_of_two: usize) -> Self {
        let capacity = 1 << capacity_power_of_two;
        Self {
            buffer: vec![Configuration::default(); capacity],
            write_pos: AtomicUsize::new(0),
            read_pos: AtomicUsize::new(0),
            capacity,
            mask: capacity - 1,
        }
    }

    /// Non-blocking write
    pub fn try_write(&self, config: Configuration) -> bool {
        let write = self.write_pos.load(Ordering::Acquire);
        let read = self.read_pos.load(Ordering::Acquire);

        // Check if full
        if (write - read) >= self.capacity {
            return false;
        }

        // Write to buffer
        let index = write & self.mask;
        unsafe {
            // Safe because we checked bounds
            let slot = &self.buffer[index] as *const _ as *mut Configuration;
            slot.write(config);
        }

        // Advance write position
        self.write_pos.store(write + 1, Ordering::Release);
        true
    }

    /// Non-blocking read
    pub fn try_read(&self) -> Option<Configuration> {
        let read = self.read_pos.load(Ordering::Acquire);
        let write = self.write_pos.load(Ordering::Acquire);

        // Check if empty
        if read >= write {
            return None;
        }

        // Read from buffer
        let index = read & self.mask;
        let config = unsafe {
            // Safe because we checked bounds
            self.buffer[index].clone()
        };

        // Advance read position
        self.read_pos.store(read + 1, Ordering::Release);
        Some(config)
    }
}
}

Delta Compression

#![allow(unused)]
fn main() {
/// Delta-compressed configuration storage
pub struct DeltaConfiguration {
    /// Base configuration
    base: Arc<Configuration>,

    /// Deltas from base
    deltas: Vec<Delta>,

    /// Cached full configuration
    cached: Option<Configuration>,
}

#[derive(Clone)]
pub struct Delta {
    /// Changed sites
    sites: SmallVec<[usize; 32]>,

    /// New values
    values: SmallVec<[u8; 32]>,

    /// Receipt delta
    receipt_delta: ReceiptDelta,
}

impl DeltaConfiguration {
    /// Apply delta to configuration
    pub fn apply_delta(&mut self, delta: Delta) {
        self.deltas.push(delta);
        self.cached = None; // Invalidate cache
    }

    /// Materialize full configuration
    pub fn materialize(&mut self) -> &Configuration {
        if self.cached.is_none() {
            let mut config = (*self.base).clone();

            // Apply all deltas
            for delta in &self.deltas {
                for (i, &site) in delta.sites.iter().enumerate() {
                    config.lattice.data[site] = delta.values[i];
                }
                config.receipt = config.receipt.apply_delta(&delta.receipt_delta);
            }

            self.cached = Some(config);
        }

        self.cached.as_ref().unwrap()
    }

    /// Compact deltas when too many accumulate
    pub fn compact(&mut self) {
        if self.deltas.len() > 100 {
            let full = self.materialize().clone();
            self.base = Arc::new(full);
            self.deltas.clear();
            self.cached = None;
        }
    }
}
}

Receipt Structures

Efficient Receipt Implementation

#![allow(unused)]
fn main() {
use blake3::Hasher;

/// Optimized receipt structure
#[repr(C)]
pub struct Receipt {
    /// R96 digest (16 bytes)
    r96_digest: [u8; 16],

    /// C768 phase and fairness packed
    c768_data: u16,  // phase: 10 bits, fairness: 6 bits

    /// Φ coherence flag
    phi_coherent: bool,

    /// Budget (7 bits sufficient for 0-95)
    budget: u8,

    /// Witness hash (16 bytes)
    witness_hash: [u8; 16],
}

impl Receipt {
    /// Compute receipt from configuration
    pub fn compute(config: &Configuration) -> Self {
        // Parallel computation of components
        let r96_future = std::thread::spawn({
            let data = config.lattice.data.clone();
            move || Self::compute_r96_digest(&data)
        });

        let c768_future = std::thread::spawn({
            let timestamp = config.timestamp;
            move || Self::compute_c768_data(timestamp)
        });

        let phi_future = std::thread::spawn({
            let config = config.clone();
            move || Self::check_phi_coherence(&config)
        });

        // Wait for all components
        let r96_digest = r96_future.join().unwrap();
        let c768_data = c768_future.join().unwrap();
        let phi_coherent = phi_future.join().unwrap();

        Self {
            r96_digest,
            c768_data,
            phi_coherent,
            budget: config.budget_used.min(127) as u8,
            witness_hash: Self::compute_witness_hash(&config.witness_chain),
        }
    }

    fn compute_r96_digest(data: &[u8]) -> [u8; 16] {
        let mut histogram = [0u32; 96];

        // Build histogram
        for &byte in data {
            let r_class = Self::r96_function(byte);
            histogram[r_class as usize] += 1;
        }

        // Hash histogram
        let mut hasher = Hasher::new();
        for (i, &count) in histogram.iter().enumerate() {
            if count > 0 {
                hasher.update(&i.to_le_bytes());
                hasher.update(&count.to_le_bytes());
            }
        }

        let hash = hasher.finalize();
        let mut digest = [0u8; 16];
        digest.copy_from_slice(&hash.as_bytes()[..16]);
        digest
    }

    #[inline(always)]
    fn r96_function(byte: u8) -> u8 {
        // Fast R96 computation
        let primary = byte % 96;
        let secondary = byte / 96;
        ((primary + secondary * 17) % 96) as u8
    }
}
}

Merkle Tree for Witness Chains

#![allow(unused)]
fn main() {
/// Merkle tree for efficient witness verification
pub struct WitnessMerkleTree {
    /// Leaf nodes (witness fragments)
    leaves: Vec<WitnessFragment>,

    /// Internal nodes
    nodes: Vec<[u8; 32]>,

    /// Tree depth
    depth: usize,
}

impl WitnessMerkleTree {
    pub fn build(witnesses: Vec<WitnessFragment>) -> Self {
        let n = witnesses.len();
        let depth = (n as f64).log2().ceil() as usize;
        let padded_size = 1 << depth;

        // Pad to power of 2
        let mut leaves = witnesses;
        leaves.resize(padded_size, WitnessFragment::default());

        // Build tree bottom-up
        let mut nodes = Vec::with_capacity(padded_size - 1);
        let mut current_level: Vec<[u8; 32]> = leaves
            .iter()
            .map(|w| w.hash())
            .collect();

        while current_level.len() > 1 {
            let mut next_level = Vec::new();

            for chunk in current_level.chunks(2) {
                let hash = Self::hash_pair(&chunk[0], &chunk[1]);
                nodes.push(hash);
                next_level.push(hash);
            }

            current_level = next_level;
        }

        Self { leaves, nodes, depth }
    }

    /// Generate inclusion proof
    pub fn inclusion_proof(&self, index: usize) -> Vec<[u8; 32]> {
        let mut proof = Vec::with_capacity(self.depth);
        let mut current = index;
        let mut level_start = 0;
        let mut level_size = self.leaves.len();

        for _ in 0..self.depth {
            let sibling = current ^ 1; // Flip last bit

            if sibling < level_size {
                let sibling_hash = if level_start == 0 {
                    self.leaves[sibling].hash()
                } else {
                    self.nodes[level_start + sibling - self.leaves.len()]
                };
                proof.push(sibling_hash);
            }

            current /= 2;
            level_start += level_size;
            level_size /= 2;
        }

        proof
    }

    fn hash_pair(left: &[u8; 32], right: &[u8; 32]) -> [u8; 32] {
        let mut hasher = Hasher::new();
        hasher.update(left);
        hasher.update(right);
        hasher.finalize().into()
    }
}
}

Receipt Cache with LRU

#![allow(unused)]
fn main() {
use lru::LruCache;

/// LRU cache for receipt computation
pub struct ReceiptCache {
    /// Cache mapping configuration hash to receipt
    cache: Arc<Mutex<LruCache<[u8; 32], Receipt>>>,

    /// Statistics
    hits: AtomicU64,
    misses: AtomicU64,
}

impl ReceiptCache {
    pub fn new(capacity: usize) -> Self {
        Self {
            cache: Arc::new(Mutex::new(LruCache::new(capacity))),
            hits: AtomicU64::new(0),
            misses: AtomicU64::new(0),
        }
    }

    pub fn get_or_compute<F>(&self, key: [u8; 32], compute: F) -> Receipt
    where
        F: FnOnce() -> Receipt,
    {
        // Try cache first
        {
            let mut cache = self.cache.lock().unwrap();
            if let Some(receipt) = cache.get(&key) {
                self.hits.fetch_add(1, Ordering::Relaxed);
                return receipt.clone();
            }
        }

        // Cache miss - compute
        self.misses.fetch_add(1, Ordering::Relaxed);
        let receipt = compute();

        // Store in cache
        {
            let mut cache = self.cache.lock().unwrap();
            cache.put(key, receipt.clone());
        }

        receipt
    }

    pub fn stats(&self) -> (u64, u64) {
        (
            self.hits.load(Ordering::Relaxed),
            self.misses.load(Ordering::Relaxed),
        )
    }
}
}

Exercises

Exercise 18.1: Implement a B-tree index for content addresses.

Exercise 18.2: Design a concurrent lattice with lock-free operations.

Exercise 18.3: Optimize receipt computation for GPU acceleration.

Exercise 18.4: Implement hierarchical configuration storage.

Exercise 18.5: Create a persistent lattice with memory-mapped files.

Takeaways

  1. Cache-aligned lattice: Optimizes memory access patterns
  2. SIMD acceleration: Parallel R96 computation and histogram updates
  3. Copy-on-write: Efficient configuration cloning and modification
  4. Delta compression: Reduces storage for similar configurations
  5. Merkle witnesses: Efficient proof verification
  6. LRU caching: Avoids redundant receipt computation

These data structures form the foundation for an efficient Hologram implementation.

Next: Chapter 19 details the runtime architecture.