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    //! Defines a stored database.

    use core::borrow::Borrow;
    use core::cell::{OnceCell, Ref, RefCell, RefMut};
    use core::hash::Hash;
    use core::num::NonZeroUsize;
    use std::collections::hash_map::{Entry as HashMapEntry};
    use uuid::Uuid;

    use crate::error::Error;
    use crate::io::{FileSystem, HashedFileIn};
    use crate::kmeans::Scalar;
    use crate::linalg::{dot, subtract};
    use crate::nbest::{NBestByKey, TakeNBestByKey};
    use crate::protos::database::{
        AttributesLog as ProtosAttributesLog,
        Database as ProtosDatabase,
        Partition as ProtosPartition,
        VectorSet as ProtosVectorSet,
    };
    use crate::protos::{Deserialize, read_message};
    use crate::slice::AsSlice;
    use crate::vector::BlockVectorSet;

    use super::{AttributeTable, AttributeValue, Attributes};

    /// Extension of a Protocol Buffers file.
    pub const PROTOBUF_EXTENSION: &str = "binpb";

    /// Capability of loading a database.
    ///
    /// Supposed to be specifalized for a specific [`Database`].
    pub trait LoadDatabase<T, FS> {
        /// Loads a database.
        fn load_database<P>(fs: FS, path: P) -> Result<Database<T, FS>, Error>
        where
            P: AsRef<str>;
    }

    /// Stored database.
    pub struct Database<T, FS> {
        fs: FS,
        vector_size: usize,
        num_partitions: usize,
        num_divisions: usize,
        num_codes: usize,
        partition_ids: Vec<String>,
        partitions: RefCell<Vec<Option<Partition<T>>>>,
        partition_centroids_id: String,
        partition_centroids: OnceCell<BlockVectorSet<T>>,
        codebook_ids: Vec<String>,
        codebooks: RefCell<Option<Vec<BlockVectorSet<T>>>>,
        attributes_log_ids: Vec<String>,
        attributes_log_load_flags: RefCell<Vec<bool>>,
        attribute_names: Vec<String>,
        attribute_table: RefCell<Option<AttributeTable>>,
    }

    impl<T, FS> Database<T, FS>
    where
        FS: FileSystem,
    {
        /// Returns the vector size.
        pub fn vector_size(&self) -> usize {
            self.vector_size
        }

        /// Returns the number of partitions.
        pub fn num_partitions(&self) -> usize {
            self.num_partitions
        }

        /// Returns the number of subvector divisions.
        pub fn num_divisions(&self) -> usize {
            self.num_divisions
        }

        /// Returns the number of codes in each codebook.
        pub fn num_codes(&self) -> usize {
            self.num_codes
        }

        /// Returns the subvector size.
        pub fn subvector_size(&self) -> usize {
            self.vector_size / self.num_divisions
        }

        /// Returns the ID of a partition.
        ///
        /// `None` if `index` ≥ `num_partitions`.
        pub fn get_partition_id(&self, index: usize) -> Option<&String> {
            self.partition_ids.get(index)
        }

        /// Returns a code vector in a specified division.
        ///
        /// `None` if `index` ≥ `num_divisons`.
        pub fn get_codebook_id(&self, index: usize) -> Option<&String> {
            self.codebook_ids.get(index)
        }
    }

    impl<T, FS> Database<T, FS>
    where
        FS: FileSystem,
        Self: LoadPartition<T>,
    {
        /// Returns an attribute value of a given vector.
        ///
        /// The first call to this function will take longer because it loads all
        /// the attributes.
        /// If you want to get attributes of your query results, please use
        /// [`QueryResult::get_attribute`] instead.
        ///
        /// `None` if the vector exists but no value is associated with `key`.
        ///
        /// Fails if no vector is associated with `vector_id`.
        pub fn get_attribute<K>(
            &self,
            vector_id: &Uuid,
            key: &K,
        ) -> Result<Option<AttributeValueRef>, Error>
        where
            String: Borrow<K>,
            K: Hash + Eq + ?Sized,
        {
            if self.attribute_table.borrow().is_none() {
                self.load_attribute_table()?;
            }
            self.get_attribute_internal(vector_id, key)
        }

        // Returns an attribute value of a given vector in a specific partition.
        fn get_attribute_in_partition<K>(
            &self,
            partition_index: usize,
            vector_id: &Uuid,
            key: &K,
        ) -> Result<Option<AttributeValueRef>, Error>
        where
            String: Borrow<K>,
            K: Hash + Eq + ?Sized,
        {
            self.load_attributes_log(partition_index)?;
            self.get_attribute_internal(vector_id, key)
        }

        fn get_attribute_internal<K>(
            &self,
            vector_id: &Uuid,
            key: &K,
        ) -> Result<Option<AttributeValueRef>, Error>
        where
            String: Borrow<K>,
            K: Hash + Eq + ?Sized,
        {
            let attribute_table = Ref::filter_map(
                self.attribute_table.borrow(),
                |tbl| tbl.as_ref(),
            ).expect("attribute table must be loaded");
            let attributes = Ref::filter_map(
                attribute_table,
                |tbl| tbl.get(vector_id),
            ).or(Err(Error::InvalidArgs(
                format!("no such vector ID: {}", vector_id),
            )))?;
            match Ref::filter_map(attributes, |attrs| attrs.get(key)) {
                Ok(value) => Ok(Some(value)),
                Err(_) => Ok(None),
            }
        }

        fn load_attribute_table(&self) -> Result<(), Error> {
            for pi in 0..self.num_partitions() {
                self.load_attributes_log(pi)?;
            }
            Ok(())
        }

        // Loads the attributes log of a specified partition if it is not loaded
        // yet.
        //
        // This function also loads the partition to list all the vector IDs in
        // the partition.
        fn load_attributes_log(&self, partition_index: usize) -> Result<(), Error> {
            if self.attributes_log_load_flags.borrow()[partition_index] {
                return Ok(());
            }
            let partition = self.get_partition(partition_index)?;
            let mut f = self.fs.open_compressed_hashed_file(format!(
                "attributes/{}.{}",
                self.attributes_log_ids[partition_index],
                PROTOBUF_EXTENSION,
            ))?;
            let attributes_log: ProtosAttributesLog = read_message(&mut f)?;
            if attributes_log.partition_id != self.partition_ids[partition_index] {
                return Err(Error::InvalidData(format!(
                    "inconsistent partition IDs: {} vs {}",
                    attributes_log.partition_id,
                    self.partition_ids[partition_index],
                )));
            }
            if self.attribute_table.borrow().is_none() {
                self.attribute_table.replace(Some(AttributeTable::new()));
            }
            let mut attribute_table = RefMut::filter_map(
                self.attribute_table.borrow_mut(),
                |tbl| tbl.as_mut(),
            ).expect("attribute table must exist");
            for (i, entry) in attributes_log.entries.into_iter().enumerate() {
                let attribute_name = self.attribute_names
                    .get(entry.name_index as usize)
                    .ok_or(Error::InvalidData(format!(
                        "attribute name index out of bounds: {}",
                        entry.name_index,
                    )))?;
                let vector_id = entry.vector_id
                    .into_option()
                    .ok_or(Error::InvalidData(format!(
                        "attributes log[{}, {}]: missing vector ID",
                        partition_index,
                        i,
                    )))?
                    .deserialize()?;
                let value = entry.value
                    .into_option()
                    .ok_or(Error::InvalidData(format!(
                        "attributes log[{}, {}]: missing value",
                        partition_index,
                        i,
                    )))?
                    .deserialize()?;
                match attribute_table.entry(vector_id) {
                    HashMapEntry::Occupied(slot) => {
                        match slot.into_mut().entry(attribute_name.clone()) {
                            HashMapEntry::Occupied(slot) => {
                                *slot.into_mut() = value;
                            },
                            HashMapEntry::Vacant(slot) => {
                                slot.insert(value);
                            },
                        };
                    },
                    HashMapEntry::Vacant(slot) => {
                        slot.insert(Attributes::from([
                            (attribute_name.clone(), value),
                        ]));
                    },
                };
            }
            // defaults to empty attributes so that
            // get_attribute won't fail for an existing vector without attributes.
            for vector_id in partition.vector_ids.iter() {
                attribute_table
                    .entry(vector_id.clone())
                    .or_insert_with(Attributes::new);
            }
            self.attributes_log_load_flags.borrow_mut()[partition_index] = true;
            Ok(())
        }

        // Obtains a specified partition.
        //
        // Lazily loads the partition if it is not loaded yet.
        //
        // Fails if:
        // - `index` exceeds the number of partitions
        // - there is any problem on the partition data
        fn get_partition(
            &self,
            index: usize,
        ) -> Result<PartitionRef<'_, T>, Error> {
            if index >= self.num_partitions() {
                return Err(Error::InvalidArgs(format!(
                    "partition index out of bounds: {}",
                    index,
                )));
            }
            if self.partitions.borrow()[index].is_none() {
                self.partitions.borrow_mut()[index] =
                    Some(self.load_partition(index)?);
            }
            let partition =
                Ref:: filter_map(
                    self.partitions.borrow(),
                    |partitions| partitions[index].as_ref(),
                )
                .or(Err(Error::InvalidData(
                    "partition must be loaded".to_string(),
                )))
                .unwrap();
            Ok(partition)
        }
    }

    // Reference type of a partition.
    type PartitionRef<'a, T> = Ref<'a, Partition<T>>;

    /// Reference type of an attribute value.
    ///
    /// You should drop this as soon as possible to avoid panics by multiple
    /// borrowing.
    pub type AttributeValueRef<'a> = Ref<'a, AttributeValue>;

    impl<T, FS> Database<T, FS>
    where
        T: Scalar,
        FS: FileSystem,
        Self: LoadPartition<T> + LoadCodebook<T> + LoadPartitionCentroids<T>,
    {
        /// Queries k-nearest neighbors (k-NN) of a given vector.
        ///
        /// The first call to this function will take longer because it lazily
        /// loads partition centroids, and codebooks.
        pub fn query<'a, V>(
            &'a self,
            v: &V,
            k: NonZeroUsize,
            nprobe: NonZeroUsize,
        ) -> Result<Vec<QueryResult<'a, T, FS>>, Error>
        where
            V: AsSlice<T> + ?Sized,
        {
            self.query_with_events(v, k, nprobe, |_| {})
        }

        /// Queries k-nearest neighbors (k-NN) of a given vector.
        ///
        /// The first call to this function will take longer because it lazily
        /// loads partition centroids, and codebooks.
        pub fn query_with_events<'a, V, EventHandler>(
            &'a self,
            v: &V,
            k: NonZeroUsize,
            nprobe: NonZeroUsize,
            mut event: EventHandler,
        ) -> Result<Vec<QueryResult<'a, T, FS>>, Error>
        where
            V: AsSlice<T> + ?Sized,
            EventHandler: FnMut(QueryEvent) -> (),
        {
            event(QueryEvent::StartingQueryInitialization);
            if self.partition_centroids.get().is_none() {
                // lazily loads partition centroids
                self.partition_centroids
                    .set(self.load_partition_centroids()?)
                    .unwrap();
            }
            if self.codebooks.borrow().is_none() {
                // loads codebooks if not loaded yet.
                let mut codebooks: Vec<BlockVectorSet<T>> =
                    Vec::with_capacity(self.num_divisions());
                for di in 0..self.num_divisions() {
                    codebooks.push(self.load_codebook(di)?);
                }
                self.codebooks.replace(Some(codebooks));
            }
            event(QueryEvent::FinishedQueryInitialization);
            event(QueryEvent::StartingPartitionSelection);
            let v = v.as_slice();
            let queries = self.query_partitions(v, k, nprobe)?;
            event(QueryEvent::FinishedPartitionSelection);
            let all_results: Vec<Vec<QueryResult<'a, T, FS>>> = queries
                .into_iter()
                .map(|query| {
                    event(QueryEvent::StartingPartitionQuery(
                        query.partition_index,
                    ));
                    let results = query.execute();
                    if results.is_ok() {
                        event(QueryEvent::FinishedPartitionQuery(
                            query.partition_index,
                        ));
                    }
                    results
                })
                .collect::<Result<Vec<_>, Error>>()?;
            event(QueryEvent::StartingResultSelection);
            let mut all_results: Vec<QueryResult<'a, T, FS>> = all_results
                .into_iter()
                .flatten()
                .n_best_by_key(k.get(), |r| r.squared_distance)
                .into();
            all_results.sort_by(|lhs, rhs| {
                lhs.squared_distance.partial_cmp(&rhs.squared_distance).unwrap()
            });
            event(QueryEvent::FinishedResultSelection);
            Ok(all_results)
        }

        // Queries partitions closest to a given vector.
        //
        // Panics if the partition centroids are not loaded.
        fn query_partitions<'a>(
            &'a self,
            v: &[T],
            k: NonZeroUsize,
            nprobe: NonZeroUsize,
        ) -> Result<Vec<PartitionQuery<'a, T, FS>>, Error> {
            let nprobe = nprobe.get();
            let k = k.get();
            let num_partitions = self.num_partitions();
            if nprobe > num_partitions {
                return Err(Error::InvalidArgs(format!(
                    "nprobe {} exceeds the number of partitions {}",
                    nprobe,
                    num_partitions,
                )));
            }
            let partition_centroids = self.partition_centroids.get()
                .expect("partition centroids must be loaded");
            // localizes vectors and calculates distances
            let mut distances: NBestByKey<(usize, Vec<T>, T), T, _> =
                NBestByKey::new(nprobe, |(_, _, distance)| *distance);
            for pi in 0..num_partitions {
                let mut localized: Vec<T> = Vec::with_capacity(self.vector_size());
                unsafe {
                    localized.set_len(self.vector_size());
                }
                let centroid = partition_centroids.get(pi);
                subtract(v, &centroid, &mut localized[..]);
                let distance = dot(&localized[..], &localized[..]);
                distances.push((pi, localized, distance));
            }
            // chooses `nprobes` shortest distances.
            distances.sort_by(|lhs, rhs| lhs.2.partial_cmp(&rhs.2).unwrap());
            // makes queries.
            let queries = distances
                .into_iter()
                .map(|(pi, localized, _)| PartitionQuery {
                    db: self,
                    codebooks: Ref::map(
                        self.codebooks.borrow(),
                        |cb| cb.as_ref().unwrap(),
                    ),
                    partition_index: pi,
                    localized,
                    k,
                })
                .collect();
            Ok(queries)
        }
    }

    /// Partition.
    ///
    /// Bears the centroid element type `T`, but the centroid is not retained
    /// because the database manages centroids.
    #[derive(Clone)]
    pub struct Partition<T> {
        _t: std::marker::PhantomData<T>,
        encoded_vectors: BlockVectorSet<u32>,
        vector_ids: Vec<Uuid>,
    }

    impl<T> Partition<T> {
        /// Returns the number of vectors in the partition.
        pub fn num_vectors(&self) -> usize {
            self.encoded_vectors.len()
        }

        /// Returns a specified encoded vector.
        ///
        /// `None` if `idnex` ≥ `num_vectors`.
        pub fn get_encoded_vector(&self, index: usize) -> Option<&[u32]> {
            if index < self.encoded_vectors.len() {
                Some(self.encoded_vectors.get(index))
            } else {
                None
            }
        }

        /// Returns the ID of a specified vector.
        ///
        /// `None` if `index` ≥ `num_vectors`.
        pub fn get_vector_id(&self, index: usize) -> Option<&Uuid> {
            self.vector_ids.get(index)
        }
    }

    /// Capability of loading a partition.
    ///
    /// Supposed to be specialized for a specific [`Database`].
    pub trait LoadPartition<T> {
        /// Loads a partition at a given index.
        ///
        /// `None` if `index` is out of the bounds.
        fn load_partition(&self, index: usize) -> Result<Partition<T>, Error>;
    }

    /// Capability of loading a codebook.
    ///
    /// Supposed to be specialized for a specific [`Database`].
    pub trait LoadCodebook<T> {
        /// Loads a codebook at a given index.
        ///
        /// Fails if `index` is out of the bounds.
        fn load_codebook(&self, index: usize) -> Result<BlockVectorSet<T>, Error>;
    }

    /// Capability of loading partition centroids.
    ///
    /// Supposed to be specialized for a specific [`Database`].
    pub trait LoadPartitionCentroids<T> {
        /// Loads partition centroids.
        ///
        /// Fails if:
        /// - vector size does not match
        /// - number of partitions does not match
        fn load_partition_centroids(&self) -> Result<BlockVectorSet<T>, Error>;
    }

    /// Events emitted while querying.
    #[derive(Debug)]
    pub enum QueryEvent {
        /// Starting to initialize a query.
        StartingQueryInitialization,
        /// Finished initializing a query.
        FinishedQueryInitialization,
        /// Starting to select partitions to query.
        StartingPartitionSelection,
        /// Finished selecting partitions to query.
        FinishedPartitionSelection,
        /// Starting to run a query on a specific partition.
        StartingPartitionQuery(usize),
        /// Finished running a query on a specific partition.
        FinishedPartitionQuery(usize),
        /// Starting to select k-nearest neighbors.
        StartingResultSelection,
        /// Finished selecting k-nearest neighbors.
        FinishedResultSelection,
    }

    /// Query in a specific partition.
    struct PartitionQuery<'a, T, FS> {
        db: &'a Database<T, FS>,
        codebooks: Ref<'a, Vec<BlockVectorSet<T>>>,
        partition_index: usize,
        localized: Vec<T>, // query vector - partition centroid
        k: usize,
    }

    impl<'a, T, FS> PartitionQuery<'a, T, FS>
    where
        T: Scalar,
        FS: FileSystem,
        Database<T, FS>: LoadPartition<T> + LoadCodebook<T>,
    {
        fn execute(&self) -> Result<Vec<QueryResult<'a, T, FS>>, Error> {
            let num_divisions = self.db.num_divisions();
            let num_codes = self.db.num_codes();
            let subvector_size = self.db.subvector_size();
            // loads the partition
            let partition = self.db.get_partition(self.partition_index)?;
            // calculates the distance table
            let mut distance_table: Vec<T> =
                Vec::with_capacity(num_divisions * num_codes);
            let mut vector_buf: Vec<T> = Vec::with_capacity(subvector_size);
            unsafe {
                vector_buf.set_len(subvector_size);
            }
            for di in 0..num_divisions {
                let from = di * subvector_size;
                let to = from + subvector_size;
                let subv = &self.localized[from..to];
                let codebook = &self.codebooks[di];
                for ci in 0..num_codes {
                    let code_vector = codebook.get(ci);
                    let d = &mut vector_buf[..];
                    subtract(subv, code_vector, d);
                    distance_table.push(dot(d, d));
                }
            }
            // approximates the squared distances to vectors in the partition
            let num_vectors = partition.num_vectors();
            let mut results: NBestByKey<QueryResult<'a, T, FS>, T, _> =
                NBestByKey::new(
                    self.k,
                    |i: &QueryResult<'a, T, FS>| i.squared_distance,
                );
            for vi in 0..num_vectors {
                let encoded_vector = partition.get_encoded_vector(vi).unwrap();
                let mut distance = T::zero();
                for di in 0..num_divisions {
                    let ci = encoded_vector[di] as usize;
                    distance += distance_table[di * num_codes + ci];
                }
                results.push(QueryResult {
                    db: self.db,
                    partition_index: self.partition_index,
                    vector_id: partition.get_vector_id(vi).unwrap().clone(),
                    vector_index: vi,
                    squared_distance: distance,
                });
            }
            Ok(results.into())
        }
    }

    /// Query result.
    #[derive(Clone)]
    pub struct QueryResult<'a, T, FS> {
        db: &'a Database<T, FS>,
        /// Partition index.
        pub partition_index: usize,
        /// Vector ID. Must be unique across the entire database.
        pub vector_id: Uuid,
        /// Vector index. Local index in the partition.
        pub vector_index: usize,
        /// Approximate squared distance.
        pub squared_distance: T,
    }

    impl<'a, T, FS> QueryResult<'a, T, FS>
    where
        T: Scalar,
        FS: FileSystem,
        Database<T, FS>:
            LoadPartition<T> + LoadCodebook<T> + LoadPartitionCentroids<T>,
    {
        /// Returns an attribute value of the vector corresponding to the result.
        ///
        /// The first call of this function on a result belonging to a partition
        /// will take longer because it will load the attributes of the partition.
        pub fn get_attribute<K>(
            &self,
            key: &K,
        ) -> Result<Option<AttributeValueRef>, Error>
        where
            String: Borrow<K>,
            K: Hash + Eq + ?Sized,
        {
            self.db.get_attribute_in_partition(
                self.partition_index,
                &self.vector_id,
                key,
            )
        }
    }

    mod f32impl {
        use super::*;

        impl<FS> LoadDatabase<f32, FS> for Database<f32, FS>
        where
            FS: FileSystem,
        {
            /// Loads a database.
            ///
            /// Fails if:
            /// - `vector_size` is zero
            /// - `num_divisions` is zero
            /// - `num_partitions` is zero
            /// - `num_codes` is zero
            /// - `vector_size` is not a multiple of `num_divisions`
            /// - `num_partitions` and `partitions_refs.len()` do not match
            /// - `vector_size` and centroid size do not match
            /// - `num_divisions` and `codebook_refs.len()` do not match
            fn load_database<P>(fs: FS, path: P) -> Result<Database<f32, FS>, Error>
            where
                P: AsRef<str>,
            {
                let mut f = fs.open_compressed_hashed_file(path)?;
                let db: ProtosDatabase = read_message(&mut f)?;
                f.verify()?;
                let vector_size = db.vector_size as usize;
                let num_partitions = db.num_partitions as usize;
                let num_divisions = db.num_divisions as usize;
                let num_codes = db.num_codes as usize;
                if vector_size == 0 {
                    return Err(Error::InvalidData(format!("vector_size is zero")));
                }
                if num_divisions == 0 {
                    return Err(Error::InvalidData(format!("num_divisions is zero")));
                }
                if num_partitions == 0 {
                    return Err(Error::InvalidData(format!("num_partitions is zero")));
                }
                if num_codes == 0 {
                    return Err(Error::InvalidData(format!("num_codes is zero")));
                }
                if vector_size % num_divisions != 0 {
                    return Err(Error::InvalidData(format!(
                        "vector_size {} is not multiple of num_divisions {}",
                        vector_size,
                        num_divisions,
                    )));
                }
                if num_partitions != db.partition_ids.len() {
                    return Err(Error::InvalidData(format!(
                        "num_partitions {} and partition_ids.len() {} do not match",
                        db.num_partitions,
                        db.partition_ids.len(),
                    )));
                }
                if num_divisions != db.codebook_ids.len() {
                    return Err(Error::InvalidData(format!(
                        "num_divisions {} and codebook_ids.len() {} do not match",
                        db.num_divisions,
                        db.codebook_ids.len(),
                    )));
                }
                let db = Database {
                    fs,
                    vector_size,
                    num_partitions,
                    num_divisions,
                    num_codes,
                    partition_ids: db.partition_ids,
                    partitions: RefCell::new(vec![None; num_partitions]),
                    partition_centroids_id: db.partition_centroids_id,
                    partition_centroids: OnceCell::new(),
                    codebook_ids: db.codebook_ids,
                    codebooks: RefCell::new(None),
                    attributes_log_ids: db.attributes_log_ids,
                    attributes_log_load_flags:
                        RefCell::new(vec![false; num_partitions]),
                    attribute_names: db.attribute_names,
                    attribute_table: RefCell::new(None),
                };
                Ok(db)
            }
        }

        impl<FS> LoadPartitionCentroids<f32> for Database<f32, FS>
        where
            FS: FileSystem,
        {
            fn load_partition_centroids(
                &self,
            ) -> Result<BlockVectorSet<f32>, Error> {
                let mut f = self.fs.open_hashed_file(format!(
                    "partitions/{}.{}",
                    self.partition_centroids_id,
                    PROTOBUF_EXTENSION,
                ))?;
                let partition_centroids: ProtosVectorSet = read_message(&mut f)?;
                let partition_centroids: BlockVectorSet<f32> =
                    partition_centroids.deserialize()?;
                if partition_centroids.vector_size() != self.vector_size() {
                    return Err(Error::InvalidData(format!(
                        "partition centroids vector size mismatch: expected {}, got {}",
                        self.vector_size(),
                        partition_centroids.vector_size(),
                    )));
                }
                if partition_centroids.len() != self.num_partitions() {
                    return Err(Error::InvalidData(format!(
                        "partition centroids data length mismatch: expected {}, got {}",
                        self.num_partitions(),
                        partition_centroids.len(),
                    )));
                }
                Ok(partition_centroids)
            }
        }

        impl<FS> LoadCodebook<f32> for Database<f32, FS>
        where
            FS: FileSystem,
        {
            /// Loads a codebook.
            ///
            /// Fails if:
            /// - `index` exceeds the number of codebooks.
            /// - codebook file cannot be loaded.
            /// - vector size does not match the subvector size of the database.
            /// - number of vectors does not match that of the database.
            fn load_codebook(
                &self,
                index: usize,
            ) -> Result<BlockVectorSet<f32>, Error>
            where
                FS: FileSystem,
            {
                if index >= self.num_divisions() {
                    return Err(Error::InvalidArgs(format!(
                        "index {} exceeds the number of codebooks {}",
                        index,
                        self.num_divisions(),
                    )));
                }
                let mut f = self.fs.open_hashed_file(format!(
                    "codebooks/{}.{}",
                    self.get_codebook_id(index).unwrap(),
                    PROTOBUF_EXTENSION,
                ))?;
                let codebook: ProtosVectorSet = read_message(&mut f)?;
                f.verify()?;
                let codebook: BlockVectorSet<f32> = codebook.deserialize()?;
                if codebook.vector_size() != self.subvector_size() {
                    return Err(Error::InvalidData(format!(
                        "vector_size is inconsistent: expected {} but got {}",
                        self.subvector_size(),
                        codebook.vector_size(),
                    )));
                }
                if codebook.len() != self.num_codes() {
                    return Err(Error::InvalidData(format!(
                        "number of codes is inconsistent: expected {} but got {}",
                        self.num_codes(),
                        codebook.len(),
                    )));
                }
                Ok(codebook)
            }
        }

        impl<FS> LoadPartition<f32> for Database<f32, FS>
        where
            FS: FileSystem,
        {
            /// Loads a partition.
            ///
            /// Loads a Protocol Buffers message (`p`) from the file system.
            ///
            /// Fails if:
            /// - `index` exceeds the number of partitions.
            /// - `self.vector_size` and `p.vector_size` do not match
            /// - `self.num_divisions` and `p.num_divisions` do not match
            /// - `p.num_vectors` and `p.encoded_vectors.len()` do not match
            /// - `p.num_vectors` and `p.vector_ids.len()` do not match
            /// - `p.num_divisions` and encoded vector length do not match
            fn load_partition(
                &self,
                index: usize,
            ) -> Result<Partition<f32>, Error> {
                if index >= self.num_partitions {
                    return Err(Error::InvalidArgs(format!(
                        "index {} exceeds the number of partitions {}",
                        index,
                        self.num_partitions,
                    )));
                }
                let mut f = self.fs.open_compressed_hashed_file(format!(
                    "partitions/{}.{}",
                    self.get_partition_id(index).unwrap(),
                    PROTOBUF_EXTENSION,
                ))?;
                let partition: ProtosPartition = read_message(&mut f)?;
                f.verify()?;
                let vector_size = partition.vector_size as usize;
                let num_divisions = partition.num_divisions as usize;
                let encoded_vectors: BlockVectorSet<u32> = partition.encoded_vectors
                    .into_option()
                    .ok_or(Error::InvalidData(
                        "missing encoded vectors".to_string(),
                    ))?
                    .deserialize()?;
                if vector_size != self.vector_size() {
                    return Err(Error::InvalidData(format!(
                        "vector_size {} and partition.vector_size {} do not match",
                        self.vector_size(),
                        vector_size,
                    )));
                }
                if num_divisions != self.num_divisions() {
                    return Err(Error::InvalidData(format!(
                        "num_divisions {} and partition.num_divisions {} do not match",
                        self.num_divisions(),
                        num_divisions,
                    )));
                }
                if encoded_vectors.len() != partition.vector_ids.len() {
                    return Err(Error::InvalidData(format!(
                        "number of vector IDs is inconsistent: exptected {} but got {}",
                        encoded_vectors.len(),
                        partition.vector_ids.len(),
                    )));
                }
                let vector_ids: Vec<Uuid> = partition.vector_ids
                    .into_iter()
                    .map(|id| id.deserialize().unwrap())
                    .collect();
                Ok(Partition {
                    _t: std::marker::PhantomData,
                    encoded_vectors,
                    vector_ids,
                })
            }
        }
    }