wallet-core/packages/idb-bridge/src/tree/b+tree.ts

2266 lines
81 KiB
TypeScript

// B+ tree by David Piepgrass. License: MIT
import { ISortedMap, ISortedMapF } from "./interfaces.js";
export type {
IMap,
IMapF,
IMapSink,
IMapSource,
ISet,
ISetF,
ISetSink,
ISetSource,
ISortedMap,
ISortedMapF,
ISortedMapSource,
ISortedSet,
ISortedSetF,
ISortedSetSource,
} from "./interfaces.js";
export type EditRangeResult<V, R = number> = {
value?: V;
break?: R;
delete?: boolean;
};
type index = number;
// Informative microbenchmarks & stuff:
// http://www.jayconrod.com/posts/52/a-tour-of-v8-object-representation (very educational)
// https://blog.mozilla.org/luke/2012/10/02/optimizing-javascript-variable-access/ (local vars are faster than properties)
// http://benediktmeurer.de/2017/12/13/an-introduction-to-speculative-optimization-in-v8/ (other stuff)
// https://jsperf.com/js-in-operator-vs-alternatives (avoid 'in' operator; `.p!==undefined` faster than `hasOwnProperty('p')` in all browsers)
// https://jsperf.com/instanceof-vs-typeof-vs-constructor-vs-member (speed of type tests varies wildly across browsers)
// https://jsperf.com/detecting-arrays-new (a.constructor===Array is best across browsers, assuming a is an object)
// https://jsperf.com/shallow-cloning-methods (a constructor is faster than Object.create; hand-written clone faster than Object.assign)
// https://jsperf.com/ways-to-fill-an-array (slice-and-replace is fastest)
// https://jsperf.com/math-min-max-vs-ternary-vs-if (Math.min/max is slow on Edge)
// https://jsperf.com/array-vs-property-access-speed (v.x/v.y is faster than a[0]/a[1] in major browsers IF hidden class is constant)
// https://jsperf.com/detect-not-null-or-undefined (`x==null` slightly slower than `x===null||x===undefined` on all browsers)
// Overall, microbenchmarks suggest Firefox is the fastest browser for JavaScript and Edge is the slowest.
// Lessons from https://v8project.blogspot.com/2017/09/elements-kinds-in-v8.html:
// - Avoid holes in arrays. Avoid `new Array(N)`, it will be "holey" permanently.
// - Don't read outside bounds of an array (it scans prototype chain).
// - Small integer arrays are stored differently from doubles
// - Adding non-numbers to an array deoptimizes it permanently into a general array
// - Objects can be used like arrays (e.g. have length property) but are slower
// - V8 source (NewElementsCapacity in src/objects.h): arrays grow by 50% + 16 elements
/**
* Types that BTree supports by default
*/
export type DefaultComparable =
| number
| string
| Date
| boolean
| null
| undefined
| (number | string)[]
| {
valueOf: () =>
| number
| string
| Date
| boolean
| null
| undefined
| (number | string)[];
};
/**
* Compares DefaultComparables to form a strict partial ordering.
*
* Handles +/-0 and NaN like Map: NaN is equal to NaN, and -0 is equal to +0.
*
* Arrays are compared using '<' and '>', which may cause unexpected equality:
* for example [1] will be considered equal to ['1'].
*
* Two objects with equal valueOf compare the same, but compare unequal to
* primitives that have the same value.
*/
export function defaultComparator(
a: DefaultComparable,
b: DefaultComparable,
): number {
// Special case finite numbers first for performance.
// Note that the trick of using 'a - b' and checking for NaN to detect non-numbers
// does not work if the strings are numeric (ex: "5"). This would leading most
// comparison functions using that approach to fail to have transitivity.
if (Number.isFinite(a as any) && Number.isFinite(b as any)) {
return (a as number) - (b as number);
}
// The default < and > operators are not totally ordered. To allow types to be mixed
// in a single collection, compare types and order values of different types by type.
let ta = typeof a;
let tb = typeof b;
if (ta !== tb) {
return ta < tb ? -1 : 1;
}
if (ta === "object") {
// standardized JavaScript bug: null is not an object, but typeof says it is
if (a === null) return b === null ? 0 : -1;
else if (b === null) return 1;
a = a!.valueOf() as DefaultComparable;
b = b!.valueOf() as DefaultComparable;
ta = typeof a;
tb = typeof b;
// Deal with the two valueOf()s producing different types
if (ta !== tb) {
return ta < tb ? -1 : 1;
}
}
// a and b are now the same type, and will be a number, string or array
// (which we assume holds numbers or strings), or something unsupported.
if (a! < b!) return -1;
if (a! > b!) return 1;
if (a === b) return 0;
// Order NaN less than other numbers
if (Number.isNaN(a as any)) return Number.isNaN(b as any) ? 0 : -1;
else if (Number.isNaN(b as any)) return 1;
// This could be two objects (e.g. [7] and ['7']) that aren't ordered
return Array.isArray(a) ? 0 : Number.NaN;
}
/**
* Compares items using the < and > operators. This function is probably slightly
* faster than the defaultComparator for Dates and strings, but has not been benchmarked.
* Unlike defaultComparator, this comparator doesn't support mixed types correctly,
* i.e. use it with `BTree<string>` or `BTree<number>` but not `BTree<string|number>`.
*
* NaN is not supported.
*
* Note: null is treated like 0 when compared with numbers or Date, but in general
* null is not ordered with respect to strings (neither greater nor less), and
* undefined is not ordered with other types.
*/
export function simpleComparator(a: string, b: string): number;
export function simpleComparator(a: number | null, b: number | null): number;
export function simpleComparator(a: Date | null, b: Date | null): number;
export function simpleComparator(
a: (number | string)[],
b: (number | string)[],
): number;
export function simpleComparator(a: any, b: any): number {
return a > b ? 1 : a < b ? -1 : 0;
}
/**
* A reasonably fast collection of key-value pairs with a powerful API.
* Largely compatible with the standard Map. BTree is a B+ tree data structure,
* so the collection is sorted by key.
*
* B+ trees tend to use memory more efficiently than hashtables such as the
* standard Map, especially when the collection contains a large number of
* items. However, maintaining the sort order makes them modestly slower:
* O(log size) rather than O(1). This B+ tree implementation supports O(1)
* fast cloning. It also supports freeze(), which can be used to ensure that
* a BTree is not changed accidentally.
*
* Confusingly, the ES6 Map.forEach(c) method calls c(value,key) instead of
* c(key,value), in contrast to other methods such as set() and entries()
* which put the key first. I can only assume that the order was reversed on
* the theory that users would usually want to examine values and ignore keys.
* BTree's forEach() therefore works the same way, but a second method
* `.forEachPair((key,value)=>{...})` is provided which sends you the key
* first and the value second; this method is slightly faster because it is
* the "native" for-each method for this class.
*
* Out of the box, BTree supports keys that are numbers, strings, arrays of
* numbers/strings, Date, and objects that have a valueOf() method returning a
* number or string. Other data types, such as arrays of Date or custom
* objects, require a custom comparator, which you must pass as the second
* argument to the constructor (the first argument is an optional list of
* initial items). Symbols cannot be used as keys because they are unordered
* (one Symbol is never "greater" or "less" than another).
*
* @example
* Given a {name: string, age: number} object, you can create a tree sorted by
* name and then by age like this:
*
* var tree = new BTree(undefined, (a, b) => {
* if (a.name > b.name)
* return 1; // Return a number >0 when a > b
* else if (a.name < b.name)
* return -1; // Return a number <0 when a < b
* else // names are equal (or incomparable)
* return a.age - b.age; // Return >0 when a.age > b.age
* });
*
* tree.set({name:"Bill", age:17}, "happy");
* tree.set({name:"Fran", age:40}, "busy & stressed");
* tree.set({name:"Bill", age:55}, "recently laid off");
* tree.forEachPair((k, v) => {
* console.log(`Name: ${k.name} Age: ${k.age} Status: ${v}`);
* });
*
* @description
* The "range" methods (`forEach, forRange, editRange`) will return the number
* of elements that were scanned. In addition, the callback can return {break:R}
* to stop early and return R from the outer function.
*
* - TODO: Test performance of preallocating values array at max size
* - TODO: Add fast initialization when a sorted array is provided to constructor
*
* For more documentation see https://github.com/qwertie/btree-typescript
*
* Are you a C# developer? You might like the similar data structures I made for C#:
* BDictionary, BList, etc. See http://core.loyc.net/collections/
*
* @author David Piepgrass
*/
export default class BTree<K = any, V = any>
implements ISortedMapF<K, V>, ISortedMap<K, V>
{
private _root: BNode<K, V> = EmptyLeaf as BNode<K, V>;
_size: number = 0;
_maxNodeSize: number;
/**
* provides a total order over keys (and a strict partial order over the type K)
* @returns a negative value if a < b, 0 if a === b and a positive value if a > b
*/
_compare: (a: K, b: K) => number;
/**
* Initializes an empty B+ tree.
* @param compare Custom function to compare pairs of elements in the tree.
* If not specified, defaultComparator will be used which is valid as long as K extends DefaultComparable.
* @param entries A set of key-value pairs to initialize the tree
* @param maxNodeSize Branching factor (maximum items or children per node)
* Must be in range 4..256. If undefined or <4 then default is used; if >256 then 256.
*/
public constructor(
entries?: [K, V][],
compare?: (a: K, b: K) => number,
maxNodeSize?: number,
) {
this._maxNodeSize = maxNodeSize! >= 4 ? Math.min(maxNodeSize!, 256) : 32;
this._compare =
compare || (defaultComparator as any as (a: K, b: K) => number);
if (entries) this.setPairs(entries);
}
/////////////////////////////////////////////////////////////////////////////
// ES6 Map<K,V> methods /////////////////////////////////////////////////////
/** Gets the number of key-value pairs in the tree. */
get size() {
return this._size;
}
/** Gets the number of key-value pairs in the tree. */
get length() {
return this._size;
}
/** Returns true iff the tree contains no key-value pairs. */
get isEmpty() {
return this._size === 0;
}
/** Releases the tree so that its size is 0. */
clear() {
this._root = EmptyLeaf as BNode<K, V>;
this._size = 0;
}
forEach(
callback: (v: V, k: K, tree: BTree<K, V>) => void,
thisArg?: any,
): number;
/** Runs a function for each key-value pair, in order from smallest to
* largest key. For compatibility with ES6 Map, the argument order to
* the callback is backwards: value first, then key. Call forEachPair
* instead to receive the key as the first argument.
* @param thisArg If provided, this parameter is assigned as the `this`
* value for each callback.
* @returns the number of values that were sent to the callback,
* or the R value if the callback returned {break:R}. */
forEach<R = number>(
callback: (v: V, k: K, tree: BTree<K, V>) => { break?: R } | void,
thisArg?: any,
): R | number {
if (thisArg !== undefined) callback = callback.bind(thisArg);
return this.forEachPair((k, v) => callback(v, k, this));
}
/** Runs a function for each key-value pair, in order from smallest to
* largest key. The callback can return {break:R} (where R is any value
* except undefined) to stop immediately and return R from forEachPair.
* @param onFound A function that is called for each key-value pair. This
* function can return {break:R} to stop early with result R.
* The reason that you must return {break:R} instead of simply R
* itself is for consistency with editRange(), which allows
* multiple actions, not just breaking.
* @param initialCounter This is the value of the third argument of
* `onFound` the first time it is called. The counter increases
* by one each time `onFound` is called. Default value: 0
* @returns the number of pairs sent to the callback (plus initialCounter,
* if you provided one). If the callback returned {break:R} then
* the R value is returned instead. */
forEachPair<R = number>(
callback: (k: K, v: V, counter: number) => { break?: R } | void,
initialCounter?: number,
): R | number {
var low = this.minKey(),
high = this.maxKey();
return this.forRange(low!, high!, true, callback, initialCounter);
}
/**
* Finds a pair in the tree and returns the associated value.
* @param defaultValue a value to return if the key was not found.
* @returns the value, or defaultValue if the key was not found.
* @description Computational complexity: O(log size)
*/
get(key: K, defaultValue?: V): V | undefined {
return this._root.get(key, defaultValue, this);
}
/**
* Adds or overwrites a key-value pair in the B+ tree.
* @param key the key is used to determine the sort order of
* data in the tree.
* @param value data to associate with the key (optional)
* @param overwrite Whether to overwrite an existing key-value pair
* (default: true). If this is false and there is an existing
* key-value pair then this method has no effect.
* @returns true if a new key-value pair was added.
* @description Computational complexity: O(log size)
* Note: when overwriting a previous entry, the key is updated
* as well as the value. This has no effect unless the new key
* has data that does not affect its sort order.
*/
set(key: K, value: V, overwrite?: boolean): boolean {
if (this._root.isShared) this._root = this._root.clone();
var result = this._root.set(key, value, overwrite, this);
if (result === true || result === false) return result;
// Root node has split, so create a new root node.
this._root = new BNodeInternal<K, V>([this._root, result]);
return true;
}
/**
* Returns true if the key exists in the B+ tree, false if not.
* Use get() for best performance; use has() if you need to
* distinguish between "undefined value" and "key not present".
* @param key Key to detect
* @description Computational complexity: O(log size)
*/
has(key: K): boolean {
return this.forRange(key, key, true, undefined) !== 0;
}
/**
* Removes a single key-value pair from the B+ tree.
* @param key Key to find
* @returns true if a pair was found and removed, false otherwise.
* @description Computational complexity: O(log size)
*/
delete(key: K): boolean {
return this.editRange(key, key, true, DeleteRange) !== 0;
}
/////////////////////////////////////////////////////////////////////////////
// Clone-mutators ///////////////////////////////////////////////////////////
/** Returns a copy of the tree with the specified key set (the value is undefined). */
with(key: K): BTree<K, V | undefined>;
/** Returns a copy of the tree with the specified key-value pair set. */
with<V2>(key: K, value: V2, overwrite?: boolean): BTree<K, V | V2>;
with<V2>(
key: K,
value?: V2,
overwrite?: boolean,
): BTree<K, V | V2 | undefined> {
let nu = this.clone() as BTree<K, V | V2 | undefined>;
return nu.set(key, value, overwrite) || overwrite ? nu : this;
}
/** Returns a copy of the tree with the specified key-value pairs set. */
withPairs<V2>(pairs: [K, V | V2][], overwrite: boolean): BTree<K, V | V2> {
let nu = this.clone() as BTree<K, V | V2>;
return nu.setPairs(pairs, overwrite) !== 0 || overwrite ? nu : this;
}
/** Returns a copy of the tree with the specified keys present.
* @param keys The keys to add. If a key is already present in the tree,
* neither the existing key nor the existing value is modified.
* @param returnThisIfUnchanged if true, returns this if all keys already
* existed. Performance note: due to the architecture of this class, all
* node(s) leading to existing keys are cloned even if the collection is
* ultimately unchanged.
*/
withKeys(
keys: K[],
returnThisIfUnchanged?: boolean,
): BTree<K, V | undefined> {
let nu = this.clone() as BTree<K, V | undefined>,
changed = false;
for (var i = 0; i < keys.length; i++)
changed = nu.set(keys[i], undefined, false) || changed;
return returnThisIfUnchanged && !changed ? this : nu;
}
/** Returns a copy of the tree with the specified key removed.
* @param returnThisIfUnchanged if true, returns this if the key didn't exist.
* Performance note: due to the architecture of this class, node(s) leading
* to where the key would have been stored are cloned even when the key
* turns out not to exist and the collection is unchanged.
*/
without(key: K, returnThisIfUnchanged?: boolean): BTree<K, V> {
return this.withoutRange(key, key, true, returnThisIfUnchanged);
}
/** Returns a copy of the tree with the specified keys removed.
* @param returnThisIfUnchanged if true, returns this if none of the keys
* existed. Performance note: due to the architecture of this class,
* node(s) leading to where the key would have been stored are cloned
* even when the key turns out not to exist.
*/
withoutKeys(keys: K[], returnThisIfUnchanged?: boolean): BTree<K, V> {
let nu = this.clone();
return nu.deleteKeys(keys) || !returnThisIfUnchanged ? nu : this;
}
/** Returns a copy of the tree with the specified range of keys removed. */
withoutRange(
low: K,
high: K,
includeHigh: boolean,
returnThisIfUnchanged?: boolean,
): BTree<K, V> {
let nu = this.clone();
if (nu.deleteRange(low, high, includeHigh) === 0 && returnThisIfUnchanged)
return this;
return nu;
}
/** Returns a copy of the tree with pairs removed whenever the callback
* function returns false. `where()` is a synonym for this method. */
filter(
callback: (k: K, v: V, counter: number) => boolean,
returnThisIfUnchanged?: boolean,
): BTree<K, V> {
var nu = this.greedyClone();
var del: any;
nu.editAll((k, v, i) => {
if (!callback(k, v, i)) return (del = Delete);
});
if (!del && returnThisIfUnchanged) return this;
return nu;
}
/** Returns a copy of the tree with all values altered by a callback function. */
mapValues<R>(callback: (v: V, k: K, counter: number) => R): BTree<K, R> {
var tmp = {} as { value: R };
var nu = this.greedyClone();
nu.editAll((k, v, i) => {
return (tmp.value = callback(v, k, i)), tmp as any;
});
return nu as any as BTree<K, R>;
}
/** Performs a reduce operation like the `reduce` method of `Array`.
* It is used to combine all pairs into a single value, or perform
* conversions. `reduce` is best understood by example. For example,
* `tree.reduce((P, pair) => P * pair[0], 1)` multiplies all keys
* together. It means "start with P=1, and for each pair multiply
* it by the key in pair[0]". Another example would be converting
* the tree to a Map (in this example, note that M.set returns M):
*
* var M = tree.reduce((M, pair) => M.set(pair[0],pair[1]), new Map())
*
* **Note**: the same array is sent to the callback on every iteration.
*/
reduce<R>(
callback: (
previous: R,
currentPair: [K, V],
counter: number,
tree: BTree<K, V>,
) => R,
initialValue: R,
): R;
reduce<R>(
callback: (
previous: R | undefined,
currentPair: [K, V],
counter: number,
tree: BTree<K, V>,
) => R,
): R | undefined;
reduce<R>(
callback: (
previous: R | undefined,
currentPair: [K, V],
counter: number,
tree: BTree<K, V>,
) => R,
initialValue?: R,
): R | undefined {
let i = 0,
p = initialValue;
var it = this.entries(this.minKey(), ReusedArray),
next;
while (!(next = it.next()).done) p = callback(p, next.value, i++, this);
return p;
}
/////////////////////////////////////////////////////////////////////////////
// Iterator methods /////////////////////////////////////////////////////////
/** Returns an iterator that provides items in order (ascending order if
* the collection's comparator uses ascending order, as is the default.)
* @param lowestKey First key to be iterated, or undefined to start at
* minKey(). If the specified key doesn't exist then iteration
* starts at the next higher key (according to the comparator).
* @param reusedArray Optional array used repeatedly to store key-value
* pairs, to avoid creating a new array on every iteration.
*/
entries(lowestKey?: K, reusedArray?: (K | V)[]): IterableIterator<[K, V]> {
var info = this.findPath(lowestKey);
if (info === undefined) return iterator<[K, V]>();
var { nodequeue, nodeindex, leaf } = info;
var state = reusedArray !== undefined ? 1 : 0;
var i =
lowestKey === undefined
? -1
: leaf.indexOf(lowestKey, 0, this._compare) - 1;
return iterator<[K, V]>(() => {
jump: for (;;) {
switch (state) {
case 0:
if (++i < leaf.keys.length)
return { done: false, value: [leaf.keys[i], leaf.values[i]] };
state = 2;
continue;
case 1:
if (++i < leaf.keys.length) {
(reusedArray![0] = leaf.keys[i]),
(reusedArray![1] = leaf.values[i]);
return { done: false, value: reusedArray as [K, V] };
}
state = 2;
case 2:
// Advance to the next leaf node
for (var level = -1; ; ) {
if (++level >= nodequeue.length) {
state = 3;
continue jump;
}
if (++nodeindex[level] < nodequeue[level].length) break;
}
for (; level > 0; level--) {
nodequeue[level - 1] = (
nodequeue[level][nodeindex[level]] as BNodeInternal<K, V>
).children;
nodeindex[level - 1] = 0;
}
leaf = nodequeue[0][nodeindex[0]];
i = -1;
state = reusedArray !== undefined ? 1 : 0;
continue;
case 3:
return { done: true, value: undefined };
}
}
});
}
/** Returns an iterator that provides items in reversed order.
* @param highestKey Key at which to start iterating, or undefined to
* start at maxKey(). If the specified key doesn't exist then iteration
* starts at the next lower key (according to the comparator).
* @param reusedArray Optional array used repeatedly to store key-value
* pairs, to avoid creating a new array on every iteration.
* @param skipHighest Iff this flag is true and the highestKey exists in the
* collection, the pair matching highestKey is skipped, not iterated.
*/
entriesReversed(
highestKey?: K,
reusedArray?: (K | V)[],
skipHighest?: boolean,
): IterableIterator<[K, V]> {
if (highestKey === undefined) {
highestKey = this.maxKey();
skipHighest = undefined;
if (highestKey === undefined) return iterator<[K, V]>(); // collection is empty
}
var { nodequeue, nodeindex, leaf } =
this.findPath(highestKey) || this.findPath(this.maxKey())!;
check(!nodequeue[0] || leaf === nodequeue[0][nodeindex[0]], "wat!");
var i = leaf.indexOf(highestKey, 0, this._compare);
if (
!skipHighest &&
i < leaf.keys.length &&
this._compare(leaf.keys[i], highestKey) <= 0
)
i++;
var state = reusedArray !== undefined ? 1 : 0;
return iterator<[K, V]>(() => {
jump: for (;;) {
switch (state) {
case 0:
if (--i >= 0)
return { done: false, value: [leaf.keys[i], leaf.values[i]] };
state = 2;
continue;
case 1:
if (--i >= 0) {
(reusedArray![0] = leaf.keys[i]),
(reusedArray![1] = leaf.values[i]);
return { done: false, value: reusedArray as [K, V] };
}
state = 2;
case 2:
// Advance to the next leaf node
for (var level = -1; ; ) {
if (++level >= nodequeue.length) {
state = 3;
continue jump;
}
if (--nodeindex[level] >= 0) break;
}
for (; level > 0; level--) {
nodequeue[level - 1] = (
nodequeue[level][nodeindex[level]] as BNodeInternal<K, V>
).children;
nodeindex[level - 1] = nodequeue[level - 1].length - 1;
}
leaf = nodequeue[0][nodeindex[0]];
i = leaf.keys.length;
state = reusedArray !== undefined ? 1 : 0;
continue;
case 3:
return { done: true, value: undefined };
}
}
});
}
/* Used by entries() and entriesReversed() to prepare to start iterating.
* It develops a "node queue" for each non-leaf level of the tree.
* Levels are numbered "bottom-up" so that level 0 is a list of leaf
* nodes from a low-level non-leaf node. The queue at a given level L
* consists of nodequeue[L] which is the children of a BNodeInternal,
* and nodeindex[L], the current index within that child list, such
* such that nodequeue[L-1] === nodequeue[L][nodeindex[L]].children.
* (However inside this function the order is reversed.)
*/
private findPath(
key?: K,
):
| { nodequeue: BNode<K, V>[][]; nodeindex: number[]; leaf: BNode<K, V> }
| undefined {
var nextnode = this._root;
var nodequeue: BNode<K, V>[][], nodeindex: number[];
if (nextnode.isLeaf) {
(nodequeue = EmptyArray), (nodeindex = EmptyArray); // avoid allocations
} else {
(nodequeue = []), (nodeindex = []);
for (var d = 0; !nextnode.isLeaf; d++) {
nodequeue[d] = (nextnode as BNodeInternal<K, V>).children;
nodeindex[d] =
key === undefined ? 0 : nextnode.indexOf(key, 0, this._compare);
if (nodeindex[d] >= nodequeue[d].length) return; // first key > maxKey()
nextnode = nodequeue[d][nodeindex[d]];
}
nodequeue.reverse();
nodeindex.reverse();
}
return { nodequeue, nodeindex, leaf: nextnode };
}
/**
* Computes the differences between `this` and `other`.
* For efficiency, the diff is returned via invocations of supplied handlers.
* The computation is optimized for the case in which the two trees have large amounts
* of shared data (obtained by calling the `clone` or `with` APIs) and will avoid
* any iteration of shared state.
* The handlers can cause computation to early exit by returning {break: R}.
* Neither of the collections should be changed during the comparison process (in your callbacks), as this method assumes they will not be mutated.
* @param other The tree to compute a diff against.
* @param onlyThis Callback invoked for all keys only present in `this`.
* @param onlyOther Callback invoked for all keys only present in `other`.
* @param different Callback invoked for all keys with differing values.
*/
diffAgainst<R>(
other: BTree<K, V>,
onlyThis?: (k: K, v: V) => { break?: R } | void,
onlyOther?: (k: K, v: V) => { break?: R } | void,
different?: (k: K, vThis: V, vOther: V) => { break?: R } | void,
): R | undefined {
if (other._compare !== this._compare) {
throw new Error("Tree comparators are not the same.");
}
if (this.isEmpty || other.isEmpty) {
if (this.isEmpty && other.isEmpty) return undefined;
// If one tree is empty, everything will be an onlyThis/onlyOther.
if (this.isEmpty)
return onlyOther === undefined
? undefined
: BTree.stepToEnd(BTree.makeDiffCursor(other), onlyOther);
return onlyThis === undefined
? undefined
: BTree.stepToEnd(BTree.makeDiffCursor(this), onlyThis);
}
// Cursor-based diff algorithm is as follows:
// - Until neither cursor has navigated to the end of the tree, do the following:
// - If the `this` cursor is "behind" the `other` cursor (strictly <, via compare), advance it.
// - Otherwise, advance the `other` cursor.
// - Any time a cursor is stepped, perform the following:
// - If either cursor points to a key/value pair:
// - If thisCursor === otherCursor and the values differ, it is a Different.
// - If thisCursor > otherCursor and otherCursor is at a key/value pair, it is an OnlyOther.
// - If thisCursor < otherCursor and thisCursor is at a key/value pair, it is an OnlyThis as long as the most recent
// cursor step was *not* otherCursor advancing from a tie. The extra condition avoids erroneous OnlyOther calls
// that would occur due to otherCursor being the "leader".
// - Otherwise, if both cursors point to nodes, compare them. If they are equal by reference (shared), skip
// both cursors to the next node in the walk.
// - Once one cursor has finished stepping, any remaining steps (if any) are taken and key/value pairs are logged
// as OnlyOther (if otherCursor is stepping) or OnlyThis (if thisCursor is stepping).
// This algorithm gives the critical guarantee that all locations (both nodes and key/value pairs) in both trees that
// are identical by value (and possibly by reference) will be visited *at the same time* by the cursors.
// This removes the possibility of emitting incorrect diffs, as well as allowing for skipping shared nodes.
const { _compare } = this;
const thisCursor = BTree.makeDiffCursor(this);
const otherCursor = BTree.makeDiffCursor(other);
// It doesn't matter how thisSteppedLast is initialized.
// Step order is only used when either cursor is at a leaf, and cursors always start at a node.
let thisSuccess = true,
otherSuccess = true,
prevCursorOrder = BTree.compare(thisCursor, otherCursor, _compare);
while (thisSuccess && otherSuccess) {
const cursorOrder = BTree.compare(thisCursor, otherCursor, _compare);
const {
leaf: thisLeaf,
internalSpine: thisInternalSpine,
levelIndices: thisLevelIndices,
} = thisCursor;
const {
leaf: otherLeaf,
internalSpine: otherInternalSpine,
levelIndices: otherLevelIndices,
} = otherCursor;
if (thisLeaf || otherLeaf) {
// If the cursors were at the same location last step, then there is no work to be done.
if (prevCursorOrder !== 0) {
if (cursorOrder === 0) {
if (thisLeaf && otherLeaf && different) {
// Equal keys, check for modifications
const valThis =
thisLeaf.values[thisLevelIndices[thisLevelIndices.length - 1]];
const valOther =
otherLeaf.values[
otherLevelIndices[otherLevelIndices.length - 1]
];
if (!Object.is(valThis, valOther)) {
const result = different(
thisCursor.currentKey,
valThis,
valOther,
);
if (result && result.break) return result.break;
}
}
} else if (cursorOrder > 0) {
// If this is the case, we know that either:
// 1. otherCursor stepped last from a starting position that trailed thisCursor, and is still behind, or
// 2. thisCursor stepped last and leapfrogged otherCursor
// Either of these cases is an "only other"
if (otherLeaf && onlyOther) {
const otherVal =
otherLeaf.values[
otherLevelIndices[otherLevelIndices.length - 1]
];
const result = onlyOther(otherCursor.currentKey, otherVal);
if (result && result.break) return result.break;
}
} else if (onlyThis) {
if (thisLeaf && prevCursorOrder !== 0) {
const valThis =
thisLeaf.values[thisLevelIndices[thisLevelIndices.length - 1]];
const result = onlyThis(thisCursor.currentKey, valThis);
if (result && result.break) return result.break;
}
}
}
} else if (!thisLeaf && !otherLeaf && cursorOrder === 0) {
const lastThis = thisInternalSpine.length - 1;
const lastOther = otherInternalSpine.length - 1;
const nodeThis =
thisInternalSpine[lastThis][thisLevelIndices[lastThis]];
const nodeOther =
otherInternalSpine[lastOther][otherLevelIndices[lastOther]];
if (nodeOther === nodeThis) {
prevCursorOrder = 0;
thisSuccess = BTree.step(thisCursor, true);
otherSuccess = BTree.step(otherCursor, true);
continue;
}
}
prevCursorOrder = cursorOrder;
if (cursorOrder < 0) {
thisSuccess = BTree.step(thisCursor);
} else {
otherSuccess = BTree.step(otherCursor);
}
}
if (thisSuccess && onlyThis)
return BTree.finishCursorWalk(
thisCursor,
otherCursor,
_compare,
onlyThis,
);
if (otherSuccess && onlyOther)
return BTree.finishCursorWalk(
otherCursor,
thisCursor,
_compare,
onlyOther,
);
}
///////////////////////////////////////////////////////////////////////////
// Helper methods for diffAgainst /////////////////////////////////////////
private static finishCursorWalk<K, V, R>(
cursor: DiffCursor<K, V>,
cursorFinished: DiffCursor<K, V>,
compareKeys: (a: K, b: K) => number,
callback: (k: K, v: V) => { break?: R } | void,
): R | undefined {
const compared = BTree.compare(cursor, cursorFinished, compareKeys);
if (compared === 0) {
if (!BTree.step(cursor)) return undefined;
} else if (compared < 0) {
check(false, "cursor walk terminated early");
}
return BTree.stepToEnd(cursor, callback);
}
private static stepToEnd<K, V, R>(
cursor: DiffCursor<K, V>,
callback: (k: K, v: V) => { break?: R } | void,
): R | undefined {
let canStep: boolean = true;
while (canStep) {
const { leaf, levelIndices, currentKey } = cursor;
if (leaf) {
const value = leaf.values[levelIndices[levelIndices.length - 1]];
const result = callback(currentKey, value);
if (result && result.break) return result.break;
}
canStep = BTree.step(cursor);
}
return undefined;
}
private static makeDiffCursor<K, V>(tree: BTree<K, V>): DiffCursor<K, V> {
const { _root, height } = tree;
return {
height: height,
internalSpine: [[_root]],
levelIndices: [0],
leaf: undefined,
currentKey: _root.maxKey(),
};
}
/**
* Advances the cursor to the next step in the walk of its tree.
* Cursors are walked backwards in sort order, as this allows them to leverage maxKey() in order to be compared in O(1).
* @param cursor The cursor to step
* @param stepToNode If true, the cursor will be advanced to the next node (skipping values)
* @returns true if the step was completed and false if the step would have caused the cursor to move beyond the end of the tree.
*/
private static step<K, V>(
cursor: DiffCursor<K, V>,
stepToNode?: boolean,
): boolean {
const { internalSpine, levelIndices, leaf } = cursor;
if (stepToNode === true || leaf) {
const levelsLength = levelIndices.length;
// Step to the next node only if:
// - We are explicitly directed to via stepToNode, or
// - There are no key/value pairs left to step to in this leaf
if (stepToNode === true || levelIndices[levelsLength - 1] === 0) {
const spineLength = internalSpine.length;
// Root is leaf
if (spineLength === 0) return false;
// Walk back up the tree until we find a new subtree to descend into
const nodeLevelIndex = spineLength - 1;
let levelIndexWalkBack = nodeLevelIndex;
while (levelIndexWalkBack >= 0) {
if (levelIndices[levelIndexWalkBack] > 0) {
if (levelIndexWalkBack < levelsLength - 1) {
// Remove leaf state from cursor
cursor.leaf = undefined;
levelIndices.pop();
}
// If we walked upwards past any internal node, slice them out
if (levelIndexWalkBack < nodeLevelIndex)
cursor.internalSpine = internalSpine.slice(
0,
levelIndexWalkBack + 1,
);
// Move to new internal node
cursor.currentKey =
internalSpine[levelIndexWalkBack][
--levelIndices[levelIndexWalkBack]
].maxKey();
return true;
}
levelIndexWalkBack--;
}
// Cursor is in the far left leaf of the tree, no more nodes to enumerate
return false;
} else {
// Move to new leaf value
const valueIndex = --levelIndices[levelsLength - 1];
cursor.currentKey = (leaf as unknown as BNode<K, V>).keys[valueIndex];
return true;
}
} else {
// Cursor does not point to a value in a leaf, so move downwards
const nextLevel = internalSpine.length;
const currentLevel = nextLevel - 1;
const node = internalSpine[currentLevel][levelIndices[currentLevel]];
if (node.isLeaf) {
// Entering into a leaf. Set the cursor to point at the last key/value pair.
cursor.leaf = node;
const valueIndex = (levelIndices[nextLevel] = node.values.length - 1);
cursor.currentKey = node.keys[valueIndex];
} else {
const children = (node as BNodeInternal<K, V>).children;
internalSpine[nextLevel] = children;
const childIndex = children.length - 1;
levelIndices[nextLevel] = childIndex;
cursor.currentKey = children[childIndex].maxKey();
}
return true;
}
}
/**
* Compares the two cursors. Returns a value indicating which cursor is ahead in a walk.
* Note that cursors are advanced in reverse sorting order.
*/
private static compare<K, V>(
cursorA: DiffCursor<K, V>,
cursorB: DiffCursor<K, V>,
compareKeys: (a: K, b: K) => number,
): number {
const {
height: heightA,
currentKey: currentKeyA,
levelIndices: levelIndicesA,
} = cursorA;
const {
height: heightB,
currentKey: currentKeyB,
levelIndices: levelIndicesB,
} = cursorB;
// Reverse the comparison order, as cursors are advanced in reverse sorting order
const keyComparison = compareKeys(currentKeyB, currentKeyA);
if (keyComparison !== 0) {
return keyComparison;
}
// Normalize depth values relative to the shortest tree.
// This ensures that concurrent cursor walks of trees of differing heights can reliably land on shared nodes at the same time.
// To accomplish this, a cursor that is on an internal node at depth D1 with maxKey X is considered "behind" a cursor on an
// internal node at depth D2 with maxKey Y, when D1 < D2. Thus, always walking the cursor that is "behind" will allow the cursor
// at shallower depth (but equal maxKey) to "catch up" and land on shared nodes.
const heightMin = heightA < heightB ? heightA : heightB;
const depthANormalized = levelIndicesA.length - (heightA - heightMin);
const depthBNormalized = levelIndicesB.length - (heightB - heightMin);
return depthANormalized - depthBNormalized;
}
// End of helper methods for diffAgainst //////////////////////////////////
///////////////////////////////////////////////////////////////////////////
/** Returns a new iterator for iterating the keys of each pair in ascending order.
* @param firstKey: Minimum key to include in the output. */
keys(firstKey?: K): IterableIterator<K> {
var it = this.entries(firstKey, ReusedArray);
return iterator<K>(() => {
var n: IteratorResult<any> = it.next();
if (n.value) n.value = n.value[0];
return n;
});
}
/** Returns a new iterator for iterating the values of each pair in order by key.
* @param firstKey: Minimum key whose associated value is included in the output. */
values(firstKey?: K): IterableIterator<V> {
var it = this.entries(firstKey, ReusedArray);
return iterator<V>(() => {
var n: IteratorResult<any> = it.next();
if (n.value) n.value = n.value[1];
return n;
});
}
/////////////////////////////////////////////////////////////////////////////
// Additional methods ///////////////////////////////////////////////////////
/** Returns the maximum number of children/values before nodes will split. */
get maxNodeSize() {
return this._maxNodeSize;
}
/** Gets the lowest key in the tree. Complexity: O(log size) */
minKey(): K | undefined {
return this._root.minKey();
}
/** Gets the highest key in the tree. Complexity: O(1) */
maxKey(): K | undefined {
return this._root.maxKey();
}
/** Quickly clones the tree by marking the root node as shared.
* Both copies remain editable. When you modify either copy, any
* nodes that are shared (or potentially shared) between the two
* copies are cloned so that the changes do not affect other copies.
* This is known as copy-on-write behavior, or "lazy copying". */
clone(): BTree<K, V> {
this._root.isShared = true;
var result = new BTree<K, V>(undefined, this._compare, this._maxNodeSize);
result._root = this._root;
result._size = this._size;
return result;
}
/** Performs a greedy clone, immediately duplicating any nodes that are
* not currently marked as shared, in order to avoid marking any nodes
* as shared.
* @param force Clone all nodes, even shared ones.
*/
greedyClone(force?: boolean): BTree<K, V> {
var result = new BTree<K, V>(undefined, this._compare, this._maxNodeSize);
result._root = this._root.greedyClone(force);
result._size = this._size;
return result;
}
/** Gets an array filled with the contents of the tree, sorted by key */
toArray(maxLength: number = 0x7fffffff): [K, V][] {
let min = this.minKey(),
max = this.maxKey();
if (min !== undefined) return this.getRange(min, max!, true, maxLength);
return [];
}
/** Gets an array of all keys, sorted */
keysArray() {
var results: K[] = [];
this._root.forRange(
this.minKey()!,
this.maxKey()!,
true,
false,
this,
0,
(k, v) => {
results.push(k);
},
);
return results;
}
/** Gets an array of all values, sorted by key */
valuesArray() {
var results: V[] = [];
this._root.forRange(
this.minKey()!,
this.maxKey()!,
true,
false,
this,
0,
(k, v) => {
results.push(v);
},
);
return results;
}
/** Gets a string representing the tree's data based on toArray(). */
toString() {
return this.toArray().toString();
}
/** Stores a key-value pair only if the key doesn't already exist in the tree.
* @returns true if a new key was added
*/
setIfNotPresent(key: K, value: V): boolean {
return this.set(key, value, false);
}
/** Returns the next pair whose key is larger than the specified key (or undefined if there is none).
* If key === undefined, this function returns the lowest pair.
* @param key The key to search for.
* @param reusedArray Optional array used repeatedly to store key-value pairs, to
* avoid creating a new array on every iteration.
*/
nextHigherPair(key: K | undefined, reusedArray?: [K, V]): [K, V] | undefined {
reusedArray = reusedArray || ([] as unknown as [K, V]);
if (key === undefined) {
return this._root.minPair(reusedArray);
}
return this._root.getPairOrNextHigher(
key,
this._compare,
false,
reusedArray,
);
}
/** Returns the next key larger than the specified key, or undefined if there is none.
* Also, nextHigherKey(undefined) returns the lowest key.
*/
nextHigherKey(key: K | undefined): K | undefined {
var p = this.nextHigherPair(key, ReusedArray as [K, V]);
return p && p[0];
}
/** Returns the next pair whose key is smaller than the specified key (or undefined if there is none).
* If key === undefined, this function returns the highest pair.
* @param key The key to search for.
* @param reusedArray Optional array used repeatedly to store key-value pairs, to
* avoid creating a new array each time you call this method.
*/
nextLowerPair(key: K | undefined, reusedArray?: [K, V]): [K, V] | undefined {
reusedArray = reusedArray || ([] as unknown as [K, V]);
if (key === undefined) {
return this._root.maxPair(reusedArray);
}
return this._root.getPairOrNextLower(
key,
this._compare,
false,
reusedArray,
);
}
/** Returns the next key smaller than the specified key, or undefined if there is none.
* Also, nextLowerKey(undefined) returns the highest key.
*/
nextLowerKey(key: K | undefined): K | undefined {
var p = this.nextLowerPair(key, ReusedArray as [K, V]);
return p && p[0];
}
/** Returns the key-value pair associated with the supplied key if it exists
* or the pair associated with the next lower pair otherwise. If there is no
* next lower pair, undefined is returned.
* @param key The key to search for.
* @param reusedArray Optional array used repeatedly to store key-value pairs, to
* avoid creating a new array each time you call this method.
* */
getPairOrNextLower(key: K, reusedArray?: [K, V]): [K, V] | undefined {
return this._root.getPairOrNextLower(
key,
this._compare,
true,
reusedArray || ([] as unknown as [K, V]),
);
}
/** Returns the key-value pair associated with the supplied key if it exists
* or the pair associated with the next lower pair otherwise. If there is no
* next lower pair, undefined is returned.
* @param key The key to search for.
* @param reusedArray Optional array used repeatedly to store key-value pairs, to
* avoid creating a new array each time you call this method.
* */
getPairOrNextHigher(key: K, reusedArray?: [K, V]): [K, V] | undefined {
return this._root.getPairOrNextHigher(
key,
this._compare,
true,
reusedArray || ([] as unknown as [K, V]),
);
}
/** Edits the value associated with a key in the tree, if it already exists.
* @returns true if the key existed, false if not.
*/
changeIfPresent(key: K, value: V): boolean {
return this.editRange(key, key, true, (k, v) => ({ value })) !== 0;
}
/**
* Builds an array of pairs from the specified range of keys, sorted by key.
* Each returned pair is also an array: pair[0] is the key, pair[1] is the value.
* @param low The first key in the array will be greater than or equal to `low`.
* @param high This method returns when a key larger than this is reached.
* @param includeHigh If the `high` key is present, its pair will be included
* in the output if and only if this parameter is true. Note: if the
* `low` key is present, it is always included in the output.
* @param maxLength Length limit. getRange will stop scanning the tree when
* the array reaches this size.
* @description Computational complexity: O(result.length + log size)
*/
getRange(
low: K,
high: K,
includeHigh?: boolean,
maxLength: number = 0x3ffffff,
): [K, V][] {
var results: [K, V][] = [];
this._root.forRange(low, high, includeHigh, false, this, 0, (k, v) => {
results.push([k, v]);
return results.length > maxLength ? Break : undefined;
});
return results;
}
/** Adds all pairs from a list of key-value pairs.
* @param pairs Pairs to add to this tree. If there are duplicate keys,
* later pairs currently overwrite earlier ones (e.g. [[0,1],[0,7]]
* associates 0 with 7.)
* @param overwrite Whether to overwrite pairs that already exist (if false,
* pairs[i] is ignored when the key pairs[i][0] already exists.)
* @returns The number of pairs added to the collection.
* @description Computational complexity: O(pairs.length * log(size + pairs.length))
*/
setPairs(pairs: [K, V][], overwrite?: boolean): number {
var added = 0;
for (var i = 0; i < pairs.length; i++)
if (this.set(pairs[i][0], pairs[i][1], overwrite)) added++;
return added;
}
forRange(
low: K,
high: K,
includeHigh: boolean,
onFound?: (k: K, v: V, counter: number) => void,
initialCounter?: number,
): number;
/**
* Scans the specified range of keys, in ascending order by key.
* Note: the callback `onFound` must not insert or remove items in the
* collection. Doing so may cause incorrect data to be sent to the
* callback afterward.
* @param low The first key scanned will be greater than or equal to `low`.
* @param high Scanning stops when a key larger than this is reached.
* @param includeHigh If the `high` key is present, `onFound` is called for
* that final pair if and only if this parameter is true.
* @param onFound A function that is called for each key-value pair. This
* function can return {break:R} to stop early with result R.
* @param initialCounter Initial third argument of onFound. This value
* increases by one each time `onFound` is called. Default: 0
* @returns The number of values found, or R if the callback returned
* `{break:R}` to stop early.
* @description Computational complexity: O(number of items scanned + log size)
*/
forRange<R = number>(
low: K,
high: K,
includeHigh: boolean,
onFound?: (k: K, v: V, counter: number) => { break?: R } | void,
initialCounter?: number,
): R | number {
var r = this._root.forRange(
low,
high,
includeHigh,
false,
this,
initialCounter || 0,
onFound,
);
return typeof r === "number" ? r : r.break!;
}
/**
* Scans and potentially modifies values for a subsequence of keys.
* Note: the callback `onFound` should ideally be a pure function.
* Specifically, it must not insert items, call clone(), or change
* the collection except via return value; out-of-band editing may
* cause an exception or may cause incorrect data to be sent to
* the callback (duplicate or missed items). It must not cause a
* clone() of the collection, otherwise the clone could be modified
* by changes requested by the callback.
* @param low The first key scanned will be greater than or equal to `low`.
* @param high Scanning stops when a key larger than this is reached.
* @param includeHigh If the `high` key is present, `onFound` is called for
* that final pair if and only if this parameter is true.
* @param onFound A function that is called for each key-value pair. This
* function can return `{value:v}` to change the value associated
* with the current key, `{delete:true}` to delete the current pair,
* `{break:R}` to stop early with result R, or it can return nothing
* (undefined or {}) to cause no effect and continue iterating.
* `{break:R}` can be combined with one of the other two commands.
* The third argument `counter` is the number of items iterated
* previously; it equals 0 when `onFound` is called the first time.
* @returns The number of values scanned, or R if the callback returned
* `{break:R}` to stop early.
* @description
* Computational complexity: O(number of items scanned + log size)
* Note: if the tree has been cloned with clone(), any shared
* nodes are copied before `onFound` is called. This takes O(n) time
* where n is proportional to the amount of shared data scanned.
*/
editRange<R = V>(
low: K,
high: K,
includeHigh: boolean,
onFound: (k: K, v: V, counter: number) => EditRangeResult<V, R> | void,
initialCounter?: number,
): R | number {
var root = this._root;
if (root.isShared) this._root = root = root.clone();
try {
var r = root.forRange(
low,
high,
includeHigh,
true,
this,
initialCounter || 0,
onFound,
);
return typeof r === "number" ? r : r.break!;
} finally {
while (root.keys.length <= 1 && !root.isLeaf)
this._root = root =
root.keys.length === 0
? EmptyLeaf
: (root as any as BNodeInternal<K, V>).children[0];
}
}
/** Same as `editRange` except that the callback is called for all pairs. */
editAll<R = V>(
onFound: (k: K, v: V, counter: number) => EditRangeResult<V, R> | void,
initialCounter?: number,
): R | number {
return this.editRange(
this.minKey()!,
this.maxKey()!,
true,
onFound,
initialCounter,
);
}
/**
* Removes a range of key-value pairs from the B+ tree.
* @param low The first key scanned will be greater than or equal to `low`.
* @param high Scanning stops when a key larger than this is reached.
* @param includeHigh Specifies whether the `high` key, if present, is deleted.
* @returns The number of key-value pairs that were deleted.
* @description Computational complexity: O(log size + number of items deleted)
*/
deleteRange(low: K, high: K, includeHigh: boolean): number {
return this.editRange(low, high, includeHigh, DeleteRange);
}
/** Deletes a series of keys from the collection. */
deleteKeys(keys: K[]): number {
for (var i = 0, r = 0; i < keys.length; i++) if (this.delete(keys[i])) r++;
return r;
}
/** Gets the height of the tree: the number of internal nodes between the
* BTree object and its leaf nodes (zero if there are no internal nodes). */
get height(): number {
let node: BNode<K, V> | undefined = this._root;
let height = -1;
while (node) {
height++;
node = node.isLeaf
? undefined
: (node as unknown as BNodeInternal<K, V>).children[0];
}
return height;
}
/** Makes the object read-only to ensure it is not accidentally modified.
* Freezing does not have to be permanent; unfreeze() reverses the effect.
* This is accomplished by replacing mutator functions with a function
* that throws an Error. Compared to using a property (e.g. this.isFrozen)
* this implementation gives better performance in non-frozen BTrees.
*/
freeze() {
var t = this as any;
// Note: all other mutators ultimately call set() or editRange()
// so we don't need to override those others.
t.clear =
t.set =
t.editRange =
function () {
throw new Error("Attempted to modify a frozen BTree");
};
}
/** Ensures mutations are allowed, reversing the effect of freeze(). */
unfreeze() {
// @ts-ignore "The operand of a 'delete' operator must be optional."
// (wrong: delete does not affect the prototype.)
delete this.clear;
// @ts-ignore
delete this.set;
// @ts-ignore
delete this.editRange;
}
/** Returns true if the tree appears to be frozen. */
get isFrozen() {
return this.hasOwnProperty("editRange");
}
/** Scans the tree for signs of serious bugs (e.g. this.size doesn't match
* number of elements, internal nodes not caching max element properly...)
* Computational complexity: O(number of nodes), i.e. O(size). This method
* skips the most expensive test - whether all keys are sorted - but it
* does check that maxKey() of the children of internal nodes are sorted. */
checkValid() {
var size = this._root.checkValid(0, this, 0);
check(
size === this.size,
"size mismatch: counted ",
size,
"but stored",
this.size,
);
}
}
declare const Symbol: any;
if (Symbol && Symbol.iterator)
// iterator is equivalent to entries()
(BTree as any).prototype[Symbol.iterator] = BTree.prototype.entries;
(BTree as any).prototype.where = BTree.prototype.filter;
(BTree as any).prototype.setRange = BTree.prototype.setPairs;
(BTree as any).prototype.add = BTree.prototype.set;
function iterator<T>(
next: () => IteratorResult<T> = () => ({ done: true, value: undefined }),
): IterableIterator<T> {
var result: any = { next };
if (Symbol && Symbol.iterator)
result[Symbol.iterator] = function () {
return this;
};
return result;
}
/** Leaf node / base class. **************************************************/
class BNode<K, V> {
// If this is an internal node, _keys[i] is the highest key in children[i].
keys: K[];
values: V[];
isShared: true | undefined;
get isLeaf() {
return (this as any).children === undefined;
}
constructor(keys: K[] = [], values?: V[]) {
this.keys = keys;
this.values = values || (undefVals as any[]);
this.isShared = undefined;
}
///////////////////////////////////////////////////////////////////////////
// Shared methods /////////////////////////////////////////////////////////
maxKey() {
return this.keys[this.keys.length - 1];
}
// If key not found, returns i^failXor where i is the insertion index.
// Callers that don't care whether there was a match will set failXor=0.
indexOf(key: K, failXor: number, cmp: (a: K, b: K) => number): index {
const keys = this.keys;
var lo = 0,
hi = keys.length,
mid = hi >> 1;
while (lo < hi) {
var c = cmp(keys[mid], key);
if (c < 0) lo = mid + 1;
else if (c > 0)
// key < keys[mid]
hi = mid;
else if (c === 0) return mid;
else {
// c is NaN or otherwise invalid
if (key === key)
// at least the search key is not NaN
return keys.length;
else throw new Error("BTree: NaN was used as a key");
}
mid = (lo + hi) >> 1;
}
return mid ^ failXor;
// Unrolled version: benchmarks show same speed, not worth using
/*var i = 1, c: number = 0, sum = 0;
if (keys.length >= 4) {
i = 3;
if (keys.length >= 8) {
i = 7;
if (keys.length >= 16) {
i = 15;
if (keys.length >= 32) {
i = 31;
if (keys.length >= 64) {
i = 127;
i += (c = i < keys.length ? cmp(keys[i], key) : 1) < 0 ? 64 : -64;
sum += c;
i += (c = i < keys.length ? cmp(keys[i], key) : 1) < 0 ? 32 : -32;
sum += c;
}
i += (c = i < keys.length ? cmp(keys[i], key) : 1) < 0 ? 16 : -16;
sum += c;
}
i += (c = i < keys.length ? cmp(keys[i], key) : 1) < 0 ? 8 : -8;
sum += c;
}
i += (c = i < keys.length ? cmp(keys[i], key) : 1) < 0 ? 4 : -4;
sum += c;
}
i += (c = i < keys.length ? cmp(keys[i], key) : 1) < 0 ? 2 : -2;
sum += c;
}
i += (c = i < keys.length ? cmp(keys[i], key) : 1) < 0 ? 1 : -1;
c = i < keys.length ? cmp(keys[i], key) : 1;
sum += c;
if (c < 0) {
++i;
c = i < keys.length ? cmp(keys[i], key) : 1;
sum += c;
}
if (sum !== sum) {
if (key === key) // at least the search key is not NaN
return keys.length ^ failXor;
else
throw new Error("BTree: NaN was used as a key");
}
return c === 0 ? i : i ^ failXor;*/
}
/////////////////////////////////////////////////////////////////////////////
// Leaf Node: misc //////////////////////////////////////////////////////////
minKey(): K | undefined {
return this.keys[0];
}
minPair(reusedArray: [K, V]): [K, V] | undefined {
if (this.keys.length === 0) return undefined;
reusedArray[0] = this.keys[0];
reusedArray[1] = this.values[0];
return reusedArray;
}
maxPair(reusedArray: [K, V]): [K, V] | undefined {
if (this.keys.length === 0) return undefined;
const lastIndex = this.keys.length - 1;
reusedArray[0] = this.keys[lastIndex];
reusedArray[1] = this.values[lastIndex];
return reusedArray;
}
clone(): BNode<K, V> {
var v = this.values;
return new BNode<K, V>(
this.keys.slice(0),
v === undefVals ? v : v.slice(0),
);
}
greedyClone(force?: boolean): BNode<K, V> {
return this.isShared && !force ? this : this.clone();
}
get(key: K, defaultValue: V | undefined, tree: BTree<K, V>): V | undefined {
var i = this.indexOf(key, -1, tree._compare);
return i < 0 ? defaultValue : this.values[i];
}
getPairOrNextLower(
key: K,
compare: (a: K, b: K) => number,
inclusive: boolean,
reusedArray: [K, V],
): [K, V] | undefined {
var i = this.indexOf(key, -1, compare);
const indexOrLower = i < 0 ? ~i - 1 : inclusive ? i : i - 1;
if (indexOrLower >= 0) {
reusedArray[0] = this.keys[indexOrLower];
reusedArray[1] = this.values[indexOrLower];
return reusedArray;
}
return undefined;
}
getPairOrNextHigher(
key: K,
compare: (a: K, b: K) => number,
inclusive: boolean,
reusedArray: [K, V],
): [K, V] | undefined {
var i = this.indexOf(key, -1, compare);
const indexOrLower = i < 0 ? ~i : inclusive ? i : i + 1;
const keys = this.keys;
if (indexOrLower < keys.length) {
reusedArray[0] = keys[indexOrLower];
reusedArray[1] = this.values[indexOrLower];
return reusedArray;
}
return undefined;
}
checkValid(depth: number, tree: BTree<K, V>, baseIndex: number): number {
var kL = this.keys.length,
vL = this.values.length;
check(
this.values === undefVals ? kL <= vL : kL === vL,
"keys/values length mismatch: depth",
depth,
"with lengths",
kL,
vL,
"and baseIndex",
baseIndex,
);
// Note: we don't check for "node too small" because sometimes a node
// can legitimately have size 1. This occurs if there is a batch
// deletion, leaving a node of size 1, and the siblings are full so
// it can't be merged with adjacent nodes. However, the parent will
// verify that the average node size is at least half of the maximum.
check(
depth == 0 || kL > 0,
"empty leaf at depth",
depth,
"and baseIndex",
baseIndex,
);
return kL;
}
/////////////////////////////////////////////////////////////////////////////
// Leaf Node: set & node splitting //////////////////////////////////////////
set(
key: K,
value: V,
overwrite: boolean | undefined,
tree: BTree<K, V>,
): boolean | BNode<K, V> {
var i = this.indexOf(key, -1, tree._compare);
if (i < 0) {
// key does not exist yet
i = ~i;
tree._size++;
if (this.keys.length < tree._maxNodeSize) {
return this.insertInLeaf(i, key, value, tree);
} else {
// This leaf node is full and must split
var newRightSibling = this.splitOffRightSide(),
target: BNode<K, V> = this;
if (i > this.keys.length) {
i -= this.keys.length;
target = newRightSibling;
}
target.insertInLeaf(i, key, value, tree);
return newRightSibling;
}
} else {
// Key already exists
if (overwrite !== false) {
if (value !== undefined) this.reifyValues();
// usually this is a no-op, but some users may wish to edit the key
this.keys[i] = key;
this.values[i] = value;
}
return false;
}
}
reifyValues() {
if (this.values === undefVals)
return (this.values = this.values.slice(0, this.keys.length));
return this.values;
}
insertInLeaf(i: index, key: K, value: V, tree: BTree<K, V>) {
this.keys.splice(i, 0, key);
if (this.values === undefVals) {
while (undefVals.length < tree._maxNodeSize) undefVals.push(undefined);
if (value === undefined) {
return true;
} else {
this.values = undefVals.slice(0, this.keys.length - 1);
}
}
this.values.splice(i, 0, value);
return true;
}
takeFromRight(rhs: BNode<K, V>) {
// Reminder: parent node must update its copy of key for this node
// assert: neither node is shared
// assert rhs.keys.length > (maxNodeSize/2 && this.keys.length<maxNodeSize)
var v = this.values;
if (rhs.values === undefVals) {
if (v !== undefVals) v.push(undefined as any);
} else {
v = this.reifyValues();
v.push(rhs.values.shift()!);
}
this.keys.push(rhs.keys.shift()!);
}
takeFromLeft(lhs: BNode<K, V>) {
// Reminder: parent node must update its copy of key for this node
// assert: neither node is shared
// assert rhs.keys.length > (maxNodeSize/2 && this.keys.length<maxNodeSize)
var v = this.values;
if (lhs.values === undefVals) {
if (v !== undefVals) v.unshift(undefined as any);
} else {
v = this.reifyValues();
v.unshift(lhs.values.pop()!);
}
this.keys.unshift(lhs.keys.pop()!);
}
splitOffRightSide(): BNode<K, V> {
// Reminder: parent node must update its copy of key for this node
var half = this.keys.length >> 1,
keys = this.keys.splice(half);
var values =
this.values === undefVals ? undefVals : this.values.splice(half);
return new BNode<K, V>(keys, values);
}
/////////////////////////////////////////////////////////////////////////////
// Leaf Node: scanning & deletions //////////////////////////////////////////
forRange<R>(
low: K,
high: K,
includeHigh: boolean | undefined,
editMode: boolean,
tree: BTree<K, V>,
count: number,
onFound?: (k: K, v: V, counter: number) => EditRangeResult<V, R> | void,
): EditRangeResult<V, R> | number {
var cmp = tree._compare;
var iLow, iHigh;
if (high === low) {
if (!includeHigh) return count;
iHigh = (iLow = this.indexOf(low, -1, cmp)) + 1;
if (iLow < 0) return count;
} else {
iLow = this.indexOf(low, 0, cmp);
iHigh = this.indexOf(high, -1, cmp);
if (iHigh < 0) iHigh = ~iHigh;
else if (includeHigh === true) iHigh++;
}
var keys = this.keys,
values = this.values;
if (onFound !== undefined) {
for (var i = iLow; i < iHigh; i++) {
var key = keys[i];
var result = onFound(key, values[i], count++);
if (result !== undefined) {
if (editMode === true) {
if (key !== keys[i] || this.isShared === true)
throw new Error("BTree illegally changed or cloned in editRange");
if (result.delete) {
this.keys.splice(i, 1);
if (this.values !== undefVals) this.values.splice(i, 1);
tree._size--;
i--;
iHigh--;
} else if (result.hasOwnProperty("value")) {
values![i] = result.value!;
}
}
if (result.break !== undefined) return result;
}
}
} else count += iHigh - iLow;
return count;
}
/** Adds entire contents of right-hand sibling (rhs is left unchanged) */
mergeSibling(rhs: BNode<K, V>, _: number) {
this.keys.push.apply(this.keys, rhs.keys);
if (this.values === undefVals) {
if (rhs.values === undefVals) return;
this.values = this.values.slice(0, this.keys.length);
}
this.values.push.apply(this.values, rhs.reifyValues());
}
}
/** Internal node (non-leaf node) ********************************************/
class BNodeInternal<K, V> extends BNode<K, V> {
// Note: conventionally B+ trees have one fewer key than the number of
// children, but I find it easier to keep the array lengths equal: each
// keys[i] caches the value of children[i].maxKey().
children: BNode<K, V>[];
constructor(children: BNode<K, V>[], keys?: K[]) {
if (!keys) {
keys = [];
for (var i = 0; i < children.length; i++) keys[i] = children[i].maxKey();
}
super(keys);
this.children = children;
}
clone(): BNode<K, V> {
var children = this.children.slice(0);
for (var i = 0; i < children.length; i++) children[i].isShared = true;
return new BNodeInternal<K, V>(children, this.keys.slice(0));
}
greedyClone(force?: boolean): BNode<K, V> {
if (this.isShared && !force) return this;
var nu = new BNodeInternal<K, V>(
this.children.slice(0),
this.keys.slice(0),
);
for (var i = 0; i < nu.children.length; i++)
nu.children[i] = nu.children[i].greedyClone();
return nu;
}
minKey() {
return this.children[0].minKey();
}
minPair(reusedArray: [K, V]): [K, V] | undefined {
return this.children[0].minPair(reusedArray);
}
maxPair(reusedArray: [K, V]): [K, V] | undefined {
return this.children[this.children.length - 1].maxPair(reusedArray);
}
get(key: K, defaultValue: V | undefined, tree: BTree<K, V>): V | undefined {
var i = this.indexOf(key, 0, tree._compare),
children = this.children;
return i < children.length
? children[i].get(key, defaultValue, tree)
: undefined;
}
getPairOrNextLower(
key: K,
compare: (a: K, b: K) => number,
inclusive: boolean,
reusedArray: [K, V],
): [K, V] | undefined {
var i = this.indexOf(key, 0, compare),
children = this.children;
if (i >= children.length) return this.maxPair(reusedArray);
const result = children[i].getPairOrNextLower(
key,
compare,
inclusive,
reusedArray,
);
if (result === undefined && i > 0) {
return children[i - 1].maxPair(reusedArray);
}
return result;
}
getPairOrNextHigher(
key: K,
compare: (a: K, b: K) => number,
inclusive: boolean,
reusedArray: [K, V],
): [K, V] | undefined {
var i = this.indexOf(key, 0, compare),
children = this.children,
length = children.length;
if (i >= length) return undefined;
const result = children[i].getPairOrNextHigher(
key,
compare,
inclusive,
reusedArray,
);
if (result === undefined && i < length - 1) {
return children[i + 1].minPair(reusedArray);
}
return result;
}
checkValid(depth: number, tree: BTree<K, V>, baseIndex: number): number {
let kL = this.keys.length,
cL = this.children.length;
check(
kL === cL,
"keys/children length mismatch: depth",
depth,
"lengths",
kL,
cL,
"baseIndex",
baseIndex,
);
check(
kL > 1 || depth > 0,
"internal node has length",
kL,
"at depth",
depth,
"baseIndex",
baseIndex,
);
let size = 0,
c = this.children,
k = this.keys,
childSize = 0;
for (var i = 0; i < cL; i++) {
size += c[i].checkValid(depth + 1, tree, baseIndex + size);
childSize += c[i].keys.length;
check(size >= childSize, "wtf", baseIndex); // no way this will ever fail
check(
i === 0 || c[i - 1].constructor === c[i].constructor,
"type mismatch, baseIndex:",
baseIndex,
);
if (c[i].maxKey() != k[i])
check(
false,
"keys[",
i,
"] =",
k[i],
"is wrong, should be ",
c[i].maxKey(),
"at depth",
depth,
"baseIndex",
baseIndex,
);
if (!(i === 0 || tree._compare(k[i - 1], k[i]) < 0))
check(
false,
"sort violation at depth",
depth,
"index",
i,
"keys",
k[i - 1],
k[i],
);
}
// 2020/08: BTree doesn't always avoid grossly undersized nodes,
// but AFAIK such nodes are pretty harmless, so accept them.
let toofew = childSize === 0; // childSize < (tree.maxNodeSize >> 1)*cL;
if (toofew || childSize > tree.maxNodeSize * cL)
check(
false,
toofew ? "too few" : "too many",
"children (",
childSize,
size,
") at depth",
depth,
"maxNodeSize:",
tree.maxNodeSize,
"children.length:",
cL,
"baseIndex:",
baseIndex,
);
return size;
}
/////////////////////////////////////////////////////////////////////////////
// Internal Node: set & node splitting //////////////////////////////////////
set(
key: K,
value: V,
overwrite: boolean | undefined,
tree: BTree<K, V>,
): boolean | BNodeInternal<K, V> {
var c = this.children,
max = tree._maxNodeSize,
cmp = tree._compare;
var i = Math.min(this.indexOf(key, 0, cmp), c.length - 1),
child = c[i];
if (child.isShared) c[i] = child = child.clone();
if (child.keys.length >= max) {
// child is full; inserting anything else will cause a split.
// Shifting an item to the left or right sibling may avoid a split.
// We can do a shift if the adjacent node is not full and if the
// current key can still be placed in the same node after the shift.
var other: BNode<K, V>;
if (
i > 0 &&
(other = c[i - 1]).keys.length < max &&
cmp(child.keys[0], key) < 0
) {
if (other.isShared) c[i - 1] = other = other.clone();
other.takeFromRight(child);
this.keys[i - 1] = other.maxKey();
} else if (
(other = c[i + 1]) !== undefined &&
other.keys.length < max &&
cmp(child.maxKey(), key) < 0
) {
if (other.isShared) c[i + 1] = other = other.clone();
other.takeFromLeft(child);
this.keys[i] = c[i].maxKey();
}
}
var result = child.set(key, value, overwrite, tree);
if (result === false) return false;
this.keys[i] = child.maxKey();
if (result === true) return true;
// The child has split and `result` is a new right child... does it fit?
if (this.keys.length < max) {
// yes
this.insert(i + 1, result);
return true;
} else {
// no, we must split also
var newRightSibling = this.splitOffRightSide(),
target: BNodeInternal<K, V> = this;
if (cmp(result.maxKey(), this.maxKey()) > 0) {
target = newRightSibling;
i -= this.keys.length;
}
target.insert(i + 1, result);
return newRightSibling;
}
}
insert(i: index, child: BNode<K, V>) {
this.children.splice(i, 0, child);
this.keys.splice(i, 0, child.maxKey());
}
splitOffRightSide() {
var half = this.children.length >> 1;
return new BNodeInternal<K, V>(
this.children.splice(half),
this.keys.splice(half),
);
}
takeFromRight(rhs: BNode<K, V>) {
// Reminder: parent node must update its copy of key for this node
// assert: neither node is shared
// assert rhs.keys.length > (maxNodeSize/2 && this.keys.length<maxNodeSize)
this.keys.push(rhs.keys.shift()!);
this.children.push((rhs as BNodeInternal<K, V>).children.shift()!);
}
takeFromLeft(lhs: BNode<K, V>) {
// Reminder: parent node must update its copy of key for this node
// assert: neither node is shared
// assert rhs.keys.length > (maxNodeSize/2 && this.keys.length<maxNodeSize)
this.keys.unshift(lhs.keys.pop()!);
this.children.unshift((lhs as BNodeInternal<K, V>).children.pop()!);
}
/////////////////////////////////////////////////////////////////////////////
// Internal Node: scanning & deletions //////////////////////////////////////
// Note: `count` is the next value of the third argument to `onFound`.
// A leaf node's `forRange` function returns a new value for this counter,
// unless the operation is to stop early.
forRange<R>(
low: K,
high: K,
includeHigh: boolean | undefined,
editMode: boolean,
tree: BTree<K, V>,
count: number,
onFound?: (k: K, v: V, counter: number) => EditRangeResult<V, R> | void,
): EditRangeResult<V, R> | number {
var cmp = tree._compare;
var keys = this.keys,
children = this.children;
var iLow = this.indexOf(low, 0, cmp),
i = iLow;
var iHigh = Math.min(
high === low ? iLow : this.indexOf(high, 0, cmp),
keys.length - 1,
);
if (!editMode) {
// Simple case
for (; i <= iHigh; i++) {
var result = children[i].forRange(
low,
high,
includeHigh,
editMode,
tree,
count,
onFound,
);
if (typeof result !== "number") return result;
count = result;
}
} else if (i <= iHigh) {
try {
for (; i <= iHigh; i++) {
if (children[i].isShared) children[i] = children[i].clone();
var result = children[i].forRange(
low,
high,
includeHigh,
editMode,
tree,
count,
onFound,
);
// Note: if children[i] is empty then keys[i]=undefined.
// This is an invalid state, but it is fixed below.
keys[i] = children[i].maxKey();
if (typeof result !== "number") return result;
count = result;
}
} finally {
// Deletions may have occurred, so look for opportunities to merge nodes.
var half = tree._maxNodeSize >> 1;
if (iLow > 0) iLow--;
for (i = iHigh; i >= iLow; i--) {
if (children[i].keys.length <= half) {
if (children[i].keys.length !== 0) {
this.tryMerge(i, tree._maxNodeSize);
} else {
// child is empty! delete it!
keys.splice(i, 1);
children.splice(i, 1);
}
}
}
if (children.length !== 0 && children[0].keys.length === 0)
check(false, "emptiness bug");
}
}
return count;
}
/** Merges child i with child i+1 if their combined size is not too large */
tryMerge(i: index, maxSize: number): boolean {
var children = this.children;
if (i >= 0 && i + 1 < children.length) {
if (children[i].keys.length + children[i + 1].keys.length <= maxSize) {
if (children[i].isShared)
// cloned already UNLESS i is outside scan range
children[i] = children[i].clone();
children[i].mergeSibling(children[i + 1], maxSize);
children.splice(i + 1, 1);
this.keys.splice(i + 1, 1);
this.keys[i] = children[i].maxKey();
return true;
}
}
return false;
}
mergeSibling(rhs: BNode<K, V>, maxNodeSize: number) {
// assert !this.isShared;
var oldLength = this.keys.length;
this.keys.push.apply(this.keys, rhs.keys);
this.children.push.apply(
this.children,
(rhs as any as BNodeInternal<K, V>).children,
);
// If our children are themselves almost empty due to a mass-delete,
// they may need to be merged too (but only the oldLength-1 and its
// right sibling should need this).
this.tryMerge(oldLength - 1, maxNodeSize);
}
}
/**
* A walkable pointer into a BTree for computing efficient diffs between trees with shared data.
* - A cursor points to either a key/value pair (KVP) or a node (which can be either a leaf or an internal node).
* As a consequence, a cursor cannot be created for an empty tree.
* - A cursor can be walked forwards using `step`. A cursor can be compared to another cursor to
* determine which is ahead in advancement.
* - A cursor is valid only for the tree it was created from, and only until the first edit made to
* that tree since the cursor's creation.
* - A cursor contains a key for the current location, which is the maxKey when the cursor points to a node
* and a key corresponding to a value when pointing to a leaf.
* - Leaf is only populated if the cursor points to a KVP. If this is the case, levelIndices.length === internalSpine.length + 1
* and levelIndices[levelIndices.length - 1] is the index of the value.
*/
type DiffCursor<K, V> = {
height: number;
internalSpine: BNode<K, V>[][];
levelIndices: number[];
leaf: BNode<K, V> | undefined;
currentKey: K;
};
// Optimization: this array of `undefined`s is used instead of a normal
// array of values in nodes where `undefined` is the only value.
// Its length is extended to max node size on first use; since it can
// be shared between trees with different maximums, its length can only
// increase, never decrease. Its type should be undefined[] but strangely
// TypeScript won't allow the comparison V[] === undefined[]. To prevent
// users from making this array too large, BTree has a maximum node size.
//
// FAQ: undefVals[i] is already undefined, so why increase the array size?
// Reading outside the bounds of an array is relatively slow because it
// has the side effect of scanning the prototype chain.
var undefVals: any[] = [];
const Delete = { delete: true },
DeleteRange = () => Delete;
const Break = { break: true };
const EmptyLeaf = (function () {
var n = new BNode<any, any>();
n.isShared = true;
return n;
})();
const EmptyArray: any[] = [];
const ReusedArray: any[] = []; // assumed thread-local
function check(fact: boolean, ...args: any[]) {
if (!fact) {
args.unshift("B+ tree"); // at beginning of message
throw new Error(args.join(" "));
}
}
/** A BTree frozen in the empty state. */
export const EmptyBTree = (() => {
let t = new BTree();
t.freeze();
return t;
})();