69: Basic hash tables69: Basic hash tablesby Panu Kalliokoski
This SRFI is currently in final status. Here is an explanation of each status that a SRFI can hold. To provide input on this SRFI, please send email to srfi-69 @nospamsrfi.schemers.org. To subscribe to the list, follow these instructions. You can access previous messages via the mailing list archive.
This SRFI defines basic hash tables. Hash tables are widely recognised as a fundamental data structure for a wide variety of applications. A hash table is a data structure that:
This SRFI aims to accomplish these goals:
There is no single best way to make hash tables. The tables presented in this SRFI aim at being both conceptually simple and usable for a wide variety of applications. Even though a portable implementation is provided, Scheme implementations can speed things up considerably by e.g. providing an internal hash function for symbols. Moreover, almost every Scheme implementation already has some kind of low-level hash table functionality, because that's the natural way to implement the global environment, and specifically, to provide support for string->symbol. There might be some benefit in integration between implementation-specific environment data types and the hash table API presented here; however, these issues are left open.
This SRFI does not conform to the interface of maps presented in SRFI 44. Following SRFI 44 would seriously cripple the interface of hash tables. The naming of the operations for maps in SRFI 44 goes against common use and is unnatural. However, this SRFI has been written so that it does not prevent a SRFI-44 API to hash tables. An implementation supporting both SRFI 44 and this SRFI is encouraged to provide a SRFI 44 interface to hash tables in addition to the one presented here.
Hash tables are widely recognised as a fundamental data structure for many kinds of computational tasks. Thus far, there is no existing standard for Scheme hash tables; however, almost every non-minimal Scheme implementation provides some kind of hash table functionality.
Alas, although somewhat similar, these hash table APIs have many differences: some trivial, like the naming of certain functions; some complex, like revealing different aspects of the internal implementation to the user; some coarse, like requiring keys to be of some specific type(s); some subtle, like requiring the user to guess the size of the hash table in advance to get optimal performance. As a result, the existing hash table facilities cannot be used to write portable programs.
The primary aim of this SRFI is to establish a standard API for hash tables so that portable programs can be written that make efficient use of common hash table functionality. The SRFI resolves discrepancies that exist between the various hash table API's with respect to naming and semantics of hash table operations. A lot of effort has been put into making the the API consistent, simple and generic. The SRFI also defines some of the most common utility routines that would otherwise need to be written and rewritten for various applications.
Incorporating this SRFI as a standard feature in Scheme implementations makes it possible to write efficient and portable programs that use hash tables.
Names defined in this SRFI:
An implementation that does not provide hash-table-ref, hash-table-set!, hash-table-delete!, hash-table-update!, hash-table-exists?, and hash-table-size in amortised constant time (when a good hash function is used), or fails to provide good hash function definitions for hash, string-hash, string-ci-hash, and hash-by-identity, does not conform to this SRFI.
Hash table implementations are allowed to rely on the fact that the hash value of a key in hash table does not change. In most cases, modifying a key in-place after it has been inserted into the hash table will violate this constraint and thus leads to unspecified behaviour.
Procedure: make-hash-table [ equal? [ hash [ args … ]]] → hash-table
Create a new hash table with no associations. equal? is a predicate that should accept two keys and return a boolean telling whether they denote the same key value; it defaults to equal?.
hash is a hash function, and defaults to an appropriate hash function
for the given equal? predicate (see section Hashing). However,
an acceptable default is not guaranteed to be given for any equivalence
predicate coarser than equal?, except for string-ci=?.[1] The function hash must be acceptable for equal?, so if
you use coarser equivalence than equal? other than string-ci=?,
you must always provide the function hash yourself.
[1] An
equivalence predicate c1 is coarser than a equivalence predicate c2
iff there exist values x and y such that (and (c1 x y) (not (c2 x
y))).
Implementations are allowed to use the rest args for implementation-specific extensions. Be warned, though, that using these extensions will make your program less portable.
Procedure: hash-table? obj → boolean
A predicate to test whether a given object obj is a hash table. The hash table type should be disjoint from all other types, if possible.
Procedure: alist->hash-table alist [ equal? [ hash [ args … ]]] → hash-table
Takes an association list
alist and creates a hash table
hash-table which maps the car of every element in alist to the
cdr of corresponding elements in alist. equal?, hash, and
args are interpreted as in make-hash-table. If some key occurs
multiple times in alist, the value in the first association will take
precedence over later ones. (Note: the choice of using cdr (instead
of cadr) for values tries to strike balance between the two
approaches: using cadr would render this procedure unusable for
cdr alists, but not vice versa.)
The rest args are passed to make-hash-table and can thus be used for implementation-specific extensions.
Procedure: hash-table-equivalence-function hash-table
Returns the equivalence predicate used for keys of hash-table.
Procedure: hash-table-hash-function hash-table
Returns the hash function used for keys of hash-table.
Procedure: hash-table-ref hash-table key [ thunk ] → value
This procedure returns the value associated to key in hash-table. If no value is associated to key and thunk is given, it is called with no arguments and its value is returned; if thunk is not given, an error is signalled. Given a good hash function, this operation should have an (amortised) complexity of O(1) with respect to the number of associations in hash-table. (Note: this rules out implementation by association lists or fixed-length hash tables.)
Procedure: hash-table-ref/default hash-table key default → value
Evaluates to the same value as (hash-table-ref hash-table key (lambda () default)). Given a good hash function, this operation should have an (amortised) complexity of O(1) with respect to the number of associations in hash-table. (Note: this rules out implementation by association lists or fixed-length hash tables.)
Procedure: hash-table-set! hash-table key value → undefined
This procedure sets the value associated to key in hash-table. The previous association (if any) is removed. Given a good hash function, this operation should have an (amortised) complexity of O(1) with respect to the number of associations in hash-table. (Note: this rules out implementation by association lists or fixed-length hash tables.)
Procedure: hash-table-delete! hash-table key → undefined
This procedure removes any association to key in hash-table. It is not an error if no association for that key exists; in this case, nothing is done. Given a good hash function, this operation should have an (amortised) complexity of O(1) with respect to the number of associations in hash-table. (Note: this rules out implementation by association lists or fixed-length hash tables.)
Procedure: hash-table-exists? hash-table key → boolean
This predicate tells whether there is any association to key in hash-table. Given a good hash function, this operation should have an (amortised) complexity of O(1) with respect to the number of associations in hash-table. (Note: this rules out implementation by association lists or fixed-length hash tables.)
Procedure: hash-table-update! hash-table key function [ thunk ] → undefined
Semantically equivalent to, but may be implemented more efficiently than, the following code:
(hash-table-set! hash-table key
(function (hash-table-ref hash-table key thunk)))
Procedure: hash-table-update!/default hash-table key function default → undefined
Behaves as if it evaluates to (hash-table-update! hash-table key function (lambda () default)).
Procedure: hash-table-size hash-table → integer
Returns the number of associations in hash-table. This operation must have a complexity of O(1) with respect to the number of associations in hash-table.
Procedure: hash-table-keys hash-table → list
Returns a list of keys in hash-table. The order of the keys is unspecified.
Procedure: hash-table-values hash-table → list
Returns a list of values in hash-table. The order of the values is unspecified, and is not guaranteed to match the order of keys in the result of hash-table-keys.
Procedure: hash-table-walk hash-table proc → unspecified
proc should be a function taking two arguments, a key and a value. This procedure calls proc for each association in hash-table, giving the key of the association as key and the value of the association as value. The results of proc are discarded. The order in which proc is called for the different associations is unspecified.
(Note: in some implementations, there is a procedure called hash-table-map which does the same as this procedure. However, in other implementations, hash-table-map does something else. In no implementation that I know of, hash-table-map does a real functorial map that lifts an ordinary function to the domain of hash tables. Because of these reasons, hash-table-map is left outside this SRFI.)
Procedure: hash-table-fold hash-table f init-value → final-value
This procedure calls f for every association in hash-table with
three arguments: the key of the association key, the value of the
association value, and an accumulated value
, val. val is
init-value for the first invocation of f, and for subsequent
invocations of f, the return value of the previous invocation of f.
The value final-value returned by hash-table-fold is the return
value of the last invocation of f. The order in which f is called
for different associations is unspecified.
Procedure: hash-table->alist hash-table → alist
Returns an association list such that the car of each element in alist is a key in hash-table and the corresponding cdr of each element in alist is the value associated to the key in hash-table. The order of the elements is unspecified.
The following should always produce a hash table with the same mappings as a hash table h:
(alist->hash-table (hash-table->alist h)
(hash-table-equivalence-function h)
(hash-table-hash-function h))
Procedure: hash-table-copy hash-table → hash-table
Returns a new hash table with the same equivalence predicate, hash function and mappings as in hash-table.
Procedure: hash-table-merge! hash-table1 hash-table2 → hash-table
Adds all mappings in hash-table2 into hash-table1 and returns the resulting hash table. This function may modify hash-table1 destructively.
Hashing means the act of taking some value and producing a number from the value. A hash function is a function that does this. Every equivalence predicate e has a set of acceptable hash functions for that predicate; a hash funtion hash is acceptable iff (e obj1 obj2) → (= (hash obj1) (hash obj2)).
A hash function h is good for a equivalence predicate e if it distributes the result numbers (hash values) for non-equal objects (by e) as uniformly as possible over the numeric range of hash values, especially in the case when some (non-equal) objects resemble each other by e.g. having common subsequences. This definition is vague but should be enough to assert that e.g. a constant function is not a good hash function.
When the definition of make-hash-table above talks about an
appropriate
hashing function for e, it means a hashing function that
gives decent performance (for the hashing operation) while being both
acceptable and good for e. This definition, too, is intentionally
vague.
Procedure: hash object [ bound ] → integer
Produces a hash value for object in the range ( 0, bound (. If bound is not given, the implementation is free to choose any bound, given that the default bound is greater than the size of any imaginable hash table in a normal application. (This is so that the implementation may choose some very big value in fixnum range for the default bound.) This hash function is acceptable for equal?.
Procedure: string-hash string [ bound ] → integer
The same as hash, except that the argument string must be a string.
Procedure: string-ci-hash string [ bound ] → integer
The same as string-hash, except that the case of characters in string does not affect the hash value produced.
Procedure: hash-by-identity object [ bound ] → integer
The same as hash, except that this function is only guaranteed to be acceptable for eq?. The reason for providing this function is that it might be implemented significantly more efficiently than hash. Implementations are encouraged to provide this function as a builtin.
This implementation relies on SRFI-9 for distinctness of the hash table type, and on SRFI-23 for error reporting. Otherwise, the implementation is pure R5RS.
(define *default-bound* (- (expt 2 29) 3))
(define (%string-hash s ch-conv bound)
(let ((hash 31)
(len (string-length s)))
(do ((index 0 (+ index 1)))
((>= index len) (modulo hash bound))
(set! hash (modulo (+ (* 37 hash)
(char->integer (ch-conv (string-ref s index))))
*default-bound*)))))
(define (string-hash s . maybe-bound)
(let ((bound (if (null? maybe-bound) *default-bound* (car maybe-bound))))
(%string-hash s (lambda (x) x) bound)))
(define (string-ci-hash s . maybe-bound)
(let ((bound (if (null? maybe-bound) *default-bound* (car maybe-bound))))
(%string-hash s char-downcase bound)))
(define (symbol-hash s . maybe-bound)
(let ((bound (if (null? maybe-bound) *default-bound* (car maybe-bound))))
(%string-hash (symbol->string s) (lambda (x) x) bound)))
(define (hash obj . maybe-bound)
(let ((bound (if (null? maybe-bound) *default-bound* (car maybe-bound))))
(cond ((integer? obj) (modulo obj bound))
((string? obj) (string-hash obj bound))
((symbol? obj) (symbol-hash obj bound))
((real? obj) (modulo (+ (numerator obj) (denominator obj)) bound))
((number? obj)
(modulo (+ (hash (real-part obj)) (* 3 (hash (imag-part obj))))
bound))
((char? obj) (modulo (char->integer obj) bound))
((vector? obj) (vector-hash obj bound))
((pair? obj) (modulo (+ (hash (car obj)) (* 3 (hash (cdr obj))))
bound))
((null? obj) 0)
((not obj) 0)
((procedure? obj) (error "hash: procedures cannot be hashed" obj))
(else 1))))
(define hash-by-identity hash)
(define (vector-hash v bound)
(let ((hashvalue 571)
(len (vector-length v)))
(do ((index 0 (+ index 1)))
((>= index len) (modulo hashvalue bound))
(set! hashvalue (modulo (+ (* 257 hashvalue) (hash (vector-ref v index)))
*default-bound*)))))
(define %make-hash-node cons)
(define %hash-node-set-value! set-cdr!)
(define %hash-node-key car)
(define %hash-node-value cdr)
(define-record-type <srfi-hash-table>
(%make-hash-table size hash compare associate entries)
hash-table?
(size hash-table-size hash-table-set-size!)
(hash hash-table-hash-function)
(compare hash-table-equivalence-function)
(associate hash-table-association-function)
(entries hash-table-entries hash-table-set-entries!))
(define *default-table-size* 64)
(define (appropriate-hash-function-for comparison)
(or (and (eq? comparison eq?) hash-by-identity)
(and (eq? comparison string=?) string-hash)
(and (eq? comparison string-ci=?) string-ci-hash)
hash))
(define (make-hash-table . args)
(let* ((comparison (if (null? args) equal? (car args)))
(hash
(if (or (null? args) (null? (cdr args)))
(appropriate-hash-function-for comparison) (cadr args)))
(size
(if (or (null? args) (null? (cdr args)) (null? (cddr args)))
*default-table-size* (caddr args)))
(association
(or (and (eq? comparison eq?) assq)
(and (eq? comparison eqv?) assv)
(and (eq? comparison equal?) assoc)
(letrec
((associate
(lambda (val alist)
(cond ((null? alist) #f)
((comparison val (caar alist)) (car alist))
(else (associate val (cdr alist)))))))
associate))))
(%make-hash-table 0 hash comparison association (make-vector size '()))))
(define (make-hash-table-maker comp hash)
(lambda args (apply make-hash-table (cons comp (cons hash args)))))
(define make-symbol-hash-table
(make-hash-table-maker eq? symbol-hash))
(define make-string-hash-table
(make-hash-table-maker string=? string-hash))
(define make-string-ci-hash-table
(make-hash-table-maker string-ci=? string-ci-hash))
(define make-integer-hash-table
(make-hash-table-maker = modulo))
(define (%hash-table-hash hash-table key)
((hash-table-hash-function hash-table)
key (vector-length (hash-table-entries hash-table))))
(define (%hash-table-find entries associate hash key)
(associate key (vector-ref entries hash)))
(define (%hash-table-add! entries hash key value)
(vector-set! entries hash
(cons (%make-hash-node key value)
(vector-ref entries hash))))
(define (%hash-table-delete! entries compare hash key)
(let ((entrylist (vector-ref entries hash)))
(cond ((null? entrylist) #f)
((compare key (caar entrylist))
(vector-set! entries hash (cdr entrylist)) #t)
(else
(let loop ((current (cdr entrylist)) (previous entrylist))
(cond ((null? current) #f)
((compare key (caar current))
(set-cdr! previous (cdr current)) #t)
(else (loop (cdr current) current))))))))
(define (%hash-table-walk proc entries)
(do ((index (- (vector-length entries) 1) (- index 1)))
((< index 0)) (for-each proc (vector-ref entries index))))
(define (%hash-table-maybe-resize! hash-table)
(let* ((old-entries (hash-table-entries hash-table))
(hash-length (vector-length old-entries)))
(if (> (hash-table-size hash-table) hash-length)
(let* ((new-length (* 2 hash-length))
(new-entries (make-vector new-length '()))
(hash (hash-table-hash-function hash-table)))
(%hash-table-walk
(lambda (node)
(%hash-table-add! new-entries
(hash (%hash-node-key node) new-length)
(%hash-node-key node) (%hash-node-value node)))
old-entries)
(hash-table-set-entries! hash-table new-entries)))))
(define (hash-table-ref hash-table key . maybe-default)
(cond ((%hash-table-find (hash-table-entries hash-table)
(hash-table-association-function hash-table)
(%hash-table-hash hash-table key) key)
=> %hash-node-value)
((null? maybe-default)
(error "hash-table-ref: no value associated with" key))
(else ((car maybe-default)))))
(define (hash-table-ref/default hash-table key default)
(hash-table-ref hash-table key (lambda () default)))
(define (hash-table-set! hash-table key value)
(let ((hash (%hash-table-hash hash-table key))
(entries (hash-table-entries hash-table)))
(cond ((%hash-table-find entries
(hash-table-association-function hash-table)
hash key)
=> (lambda (node) (%hash-node-set-value! node value)))
(else (%hash-table-add! entries hash key value)
(hash-table-set-size! hash-table
(+ 1 (hash-table-size hash-table)))
(%hash-table-maybe-resize! hash-table)))))
(define (hash-table-update! hash-table key function . maybe-default)
(let ((hash (%hash-table-hash hash-table key))
(entries (hash-table-entries hash-table)))
(cond ((%hash-table-find entries
(hash-table-association-function hash-table)
hash key)
=> (lambda (node)
(%hash-node-set-value!
node (function (%hash-node-value node)))))
((null? maybe-default)
(error "hash-table-update!: no value exists for key" key))
(else (%hash-table-add! entries hash key
(function ((car maybe-default))))
(hash-table-set-size! hash-table
(+ 1 (hash-table-size hash-table)))
(%hash-table-maybe-resize! hash-table)))))
(define (hash-table-update!/default hash-table key function default)
(hash-table-update! hash-table key function (lambda () default)))
(define (hash-table-delete! hash-table key)
(if (%hash-table-delete! (hash-table-entries hash-table)
(hash-table-equivalence-function hash-table)
(%hash-table-hash hash-table key) key)
(hash-table-set-size! hash-table (- (hash-table-size hash-table) 1))))
(define (hash-table-exists? hash-table key)
(and (%hash-table-find (hash-table-entries hash-table)
(hash-table-association-function hash-table)
(%hash-table-hash hash-table key) key) #t))
(define (hash-table-walk hash-table proc)
(%hash-table-walk
(lambda (node) (proc (%hash-node-key node) (%hash-node-value node)))
(hash-table-entries hash-table)))
(define (hash-table-fold hash-table f acc)
(hash-table-walk hash-table
(lambda (key value) (set! acc (f key value acc))))
acc)
(define (alist->hash-table alist . args)
(let* ((comparison (if (null? args) equal? (car args)))
(hash
(if (or (null? args) (null? (cdr args)))
(appropriate-hash-function-for comparison) (cadr args)))
(size
(if (or (null? args) (null? (cdr args)) (null? (cddr args)))
(max *default-table-size* (* 2 (length alist))) (caddr args)))
(hash-table (make-hash-table comparison hash size)))
(for-each
(lambda (elem)
(hash-table-update!/default
hash-table (car elem) (lambda (x) x) (cdr elem)))
alist)
hash-table))
(define (hash-table->alist hash-table)
(hash-table-fold hash-table
(lambda (key val acc) (cons (cons key val) acc)) '()))
(define (hash-table-copy hash-table)
(let ((new (make-hash-table (hash-table-equivalence-function hash-table)
(hash-table-hash-function hash-table)
(max *default-table-size*
(* 2 (hash-table-size hash-table))))))
(hash-table-walk hash-table
(lambda (key value) (hash-table-set! new key value)))
new))
(define (hash-table-merge! hash-table1 hash-table2)
(hash-table-walk
hash-table2
(lambda (key value) (hash-table-set! hash-table1 key value)))
hash-table1)
(define (hash-table-keys hash-table)
(hash-table-fold hash-table (lambda (key val acc) (cons key acc)) '()))
(define (hash-table-values hash-table)
(hash-table-fold hash-table (lambda (key val acc) (cons val acc)) '()))
Copyright © Panu Kalliokoski (2005). All Rights Reserved.
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