The following is the accepted proposal for the new string hash function,
followed by a report justifying its selection:
New String Hash Function (Bugs 4045622, 1258091)
The Problem: The currently specified String hash function does not match
the currently implemented function. The specified function
is not implementable. (It addresses characters outside of
the input string.) The implemented function performs very
poorly on certain classes of strings, including URLs. (The
poor performance is due to the "sampling" nature of the
function for strings over 15 characters.) I view the
specification problem as the perfect opportunity to replace
the unfortunate implementation.
Requesters: The problems with the implementation have been mentioned
on comp.sys.java.lang.programmer, though the extent of the
problem may not be known outside of JavaSoft. The problems
with the spec were discovered by Peter Kessler and myself.
Proposed API change: No API would change, per se. The function computed
by String.hashCode() would change to:
s * 31^(n-1) + s * 31^(n-2) + ... + s[n-1]
where s[i] is the ith character of string s.
The Java Language Specification (which specifies the
value to be returned by String.hashCode()) would be
modified to reflect this.
The new hash function was selected after a fair amount
of study, as described in Exhibit A. In the unlikely
event that you want even more detail, see me.
Implementation: Trivial. (4 lines of code, which have already been
Performance impact: Hashing large strings will be somewhat more expensive,
as the new hash function examines every character,
but Hashtables performance will, on balance, improve,
as hash collisions will be vastly reduced. While one
could construct a program to demonstrate the reduced
speed of the new hash function, I would be very
surprised if any real applications were adversely
affected in any measurable way.
Risk Assessment: Surprisingly small. Serialization of Hashtables does
not depend on consistent hash values. It is possible
that some customer has implemented some persistent data
structure that relies on the String hash function not
changing, but it is highly unlikely that more than a
handful of customers have done so.
Testing Impact: None, really. I've performed a fair number of tests
on the proposed hash function already. (See below.)
Doc Impact: The release notes would have to mention the change, so
that any "researchy" customers who do rely on the precise
behavior of the hash function would be alerted.
The JLS would have to be modified in its next edition.
The actual text would be very short (1-2 paragraphs).
As per Guy's request, here's a note describing the "Pedigree" of my
proposed String hash function. Surprisingly, I could find very little in the
way of published literature on practical, general-purpose string hash
functions; much of what is published is either outdated (e.g., Knuth V. 3,
Pp. 508-513) or arcane (lots of journal articles on 'perfect hashing').
Most of the standard algorithms and data structures textbooks barely
mention the subject. The best treatment I was able to find was in Aho,
Sethi and Ullman's "Compilers: Principles, Techniques and Tools" AKA "The
Dragon Book" (Pp. 433-438).
The class of hash function that I recommend using is polynomials whose
coefficients are the characters in the string:
P(x) = s * x^(n-1) + s * x^(n-2) + ... + s[n-1]
This polynomial is calculated by the following code fragment:
int hashVal = 0;
for (int i=0; i<string.length; i++)
hashVal = x*hashVal + s.charAt(i);
The value of x is part of the definition of the hash function; choosing
this value is somewhat of a black art. Clearly 1 or any multiple of 2 is
bad. Primes seem safer than composite numbers, though some composite
numbers yield excellent performance (as shown below).
While this class of hash function is recommended in The Dragon Book
(P(65599)) and Kernighan and Ritchie's "The C Programming Language, 2 Ed."
(P(31)), it is not attributed in either of these books. I went so far as
to call up Dennis Ritchie, who said that he did not know where the hash
function came from. He walked across the hall and asked Brian Kernighan,
who also had no recollection. A shareware library from Germany called
"Matpack" contains ten string hash functions, including P(33), which it
attributes to noted Unix hacker Chris Torek. I sincerely doubt that it's
original with him. P(37) is used in the definition of the current Java
String hash function for short (< 16 characters) strings. I'm afraid that
the origins of this little function are lost to history.
So why do I think we should use this function? Simply put, it's the
best general purpose string hash function that I was able to find, and
it's cheap to calculate. By 'general purpose', I mean that it's not
optimized for any specific type of strings (e.g., compiler symbols), but
seems to resist collisions across every collection of strings that I was
able to throw at it. This is critical given that we have no idea what
sort of strings people will store in Java hash tables. Also, the
performance of this class of hash functions seems largely unaffected by
whether the size of the hash table is prime or not. This is important
because Java's auto-growing hash table is typically does not contain a
prime number of buckets.
In addition to the class of hash functions described above, The Dragon
Book highly recommends a slightly more complex hash function due to P. J.
Weinberger, originally used internally in his C compiler. Matpak's author,
Dr. Berndt M. Gammel (of Technische Universit??t M??nchen), however, claims that
Weinberger's function does not work well for large collections of arbitrary
strings. It turns out that Matpak's implementation of Weinberger's function
contains a typo, and the resulting function is far, far worse even than the
currently implemented Java string hash function (see table below). I notified
Dr. Gammel, and he promised to fix the typo. The published version of
Weinberger's function (in the Dragon book) differs slightly from the version
that he (Peter Weinberger) personally recommends. (They differ in the number
of bits to which the hash value is shifted: the published value is 24, the
recommended value is 28.) The recommended version is significantly better
Gammel recommends only three of the ten hash functions in Matpak for
"general use." One is P(33), one is a minor variant on P(129), ascribed
to Phong Vo, and the third is a table lookup based, S-box like algorithm,
relying on a table of 256 "random" 32-bit numbers, from the WAIS project.
(The Vo variant merely adds the constant 987654321 to each character to
form the polynomial coefficients.)
The table below summarizes the performance of the various hash functions
described above, for three data sets:
1) All of the words and phrases with entries in Merriam-Webster's
2nd Int'l Unabridged Dictionary (311,141 strings, avg length 10 chars).
2) All of the strings in /bin/*, /usr/bin/*, /usr/lib/*, /usr/ucb/*
and /usr/openwin/bin/* (66,304 strings, avg length 21 characters).
3) A list of URLs gathered by a web-crawler that ran for several
hours last night (28,372 strings, avg length 49 characters).
The performance metric shown in the table is the "average chain size"
over all elements in the hash table (i.e., the expected value of the
number of key compares to look up an element).
Webster's Code Strings URLs
--------- ------------ ----
Current Java Fn. 1.2509 1.2738 13.2560
P(37) [Java] 1.2508 1.2481 1.2454
P(65599) [Aho et al] 1.2490 1.2510 1.2450
P(31) [K+R] 1.2500 1.2488 1.2425
P(33) [Torek] 1.2500 1.2500 1.2453
Vo's Fn 1.2487 1.2471 1.2462
WAIS Fn 1.2497 1.2519 1.2452
Weinberger's Fn(MatPak) 6.5169 7.2142 30.6864
Weinberger's Fn(24) 1.3222 1.2791 1.9732
Weinberger's Fn(28) 1.2530 1.2506 1.2439
Looking at this table, it's clear that all of the functions except for the
current Java function and the two broken versions of Weinberger's function
offer excellent, nearly indistinguishable performance. I strongly conjecture
that this performance is essentially the "theoretical ideal", which is what
you'd get if you used a true random number generator in place of a hash
I'd rule out the WAIS function as its specification contains pages of
random numbers, and its performance is no better than any of the far simpler
functions. Any of the remaining six functions seem like excellent choices,
but we have to pick one. I suppose I'd rule out Vo's variant and Weinberger's
function because of their added complexity, albeit minor. Of the remaining
four, I'd probably select P(31), as it's the cheapest to calculate on a RISC
machine (because 31 is the difference of two powers of two). P(33) is
similarly cheap to calculate, but it's performance is marginally worse, and
33 is composite, which makes me a bit nervous.
From: Guy Steele - Sun Microsystems Labs <###@###.###>
Cc: gls@East, James.Gosling@Eng, wnj@central, ###@###.###,
Subject: Re: String Hash Function Redux (long)
Date: Mon, 28 Apr 1997 09:47:22 -0400 (EDT)
Good work! Besides the fact that you have clearly established that
we ought to revamp Java's hash function and have found a good solution,
I think you have an MPU here (Minimum Publishable Unit)---that is, I would
encourage you to write this up even more carefully and send it to an
ACM conference (PLDI?) or journal.