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7.3 Defining Hash Comparisons

You can define new methods of key lookup by means of define-hash-table-test. In order to use this feature, you need to understand how hash tables work, and what a hash code means.

You can think of a hash table conceptually as a large array of many slots, each capable of holding one association. To look up a key, gethash first computes an integer, the hash code, from the key. It reduces this integer modulo the length of the array, to produce an index in the array. Then it looks in that slot, and if necessary in other nearby slots, to see if it has found the key being sought.

Thus, to define a new method of key lookup, you need to specify both a function to compute the hash code from a key, and a function to compare two keys directly.

— Function: define-hash-table-test name test-fn hash-fn

This function defines a new hash table test, named name.

After defining name in this way, you can use it as the test argument in make-hash-table. When you do that, the hash table will use test-fn to compare key values, and hash-fn to compute a “hash code” from a key value.

The function test-fn should accept two arguments, two keys, and return non-nil if they are considered “the same”.

The function hash-fn should accept one argument, a key, and return an integer that is the “hash code” of that key. For good results, the function should use the whole range of integer values for hash codes, including negative integers.

The specified functions are stored in the property list of name under the property hash-table-test; the property value's form is (test-fn hash-fn).

— Function: sxhash obj

This function returns a hash code for Lisp object obj. This is an integer which reflects the contents of obj and the other Lisp objects it points to.

If two objects obj1 and obj2 are equal, then (sxhash obj1) and (sxhash obj2) are the same integer.

If the two objects are not equal, the values returned by sxhash are usually different, but not always; once in a rare while, by luck, you will encounter two distinct-looking objects that give the same result from sxhash.

This example creates a hash table whose keys are strings that are compared case-insensitively.

     (defun case-fold-string= (a b)
       (eq t (compare-strings a nil nil b nil nil t)))
     (defun case-fold-string-hash (a)
       (sxhash (upcase a)))
     
     (define-hash-table-test 'case-fold
       'case-fold-string= 'case-fold-string-hash)
     
     (make-hash-table :test 'case-fold)

Here is how you could define a hash table test equivalent to the predefined test value equal. The keys can be any Lisp object, and equal-looking objects are considered the same key.

     (define-hash-table-test 'contents-hash 'equal 'sxhash)
     
     (make-hash-table :test 'contents-hash)