The key thing to understand about hashCodes is that they need not be unique, just as close to unique as practically possible.
HashCodes in a Nutshell
If you want to file something away for later retrieval, it can be faster if you file it numerically rather than by a long alphabetic key. A hashCode is
a way of computing a small (32-bit) digest numeric key from a long String or even an arbitrary clump of bytes. The numeric key itself is meaningless and the hashCode functions
for computing them can look a bit insane. However, when you go to look for something, you can do the same digest calculation on the long alphabetic key you are looking for,
and no matter how bizarre an algorithm you used, you will calculate the same hashCode, and will be able to look up numerically with it. Of course there is always the
possibility two different Strings will have the same digest hashCode. However, even then, all is not lost; it greatly narrows down the search, hence speeding it up. A Hashtable
goes a step further, scrunching down the hashCode even further to an even smaller number that it can use to directly index an array, usually by dividing it by some (ideally
prime) number and taking the remainder.
HashCode Misconceptions
- Uniqueness: Some people try to use HashCodes as unique identifiers. You can’t count on hashCodes to be unique. They way they are properly used, this does not cause any
serious problem.
- Denseness: Some people fret over trying to make hashCodes come out in some narrow band of numbers. The way they are used, they are trimmed down to size by taking the modulus
relative to some prime or by discarding high order bits, so there is no point.
- Negative hashcodes: You can safely treat hashcodes as unsigned or signed when computing them. You don't have to go to any special lengths to keep them positive.
String.hashCode Implementation
In JDK 1.0.x and 1.1.x the hashCode function for long Strings worked by sampling every nth character. This pretty well guaranteed you would have
many Strings hashing to the same value, thus slowing down Hashtable lookup. In JDK 1.2 the function has been improved to multiply the result so far
by 31 then add the next character in sequence. This is a little slower, but is much better at avoiding collisions.
Object.hashCode Implementation
The default hashCode() method uses the 32-bit internal JVM address of the Object as its hashCode.
However, if the Object is moved in memory during garbage collection, the hashCode stays constant. This default hashCode
is not very useful, since to look up an Object in a HashMap, you need the exact same key Object
by which the key/value pair was originally filed. Normally, when you go to look up, you don’t have the original key Object itself, just some
data for a key. So, unless your key is a String, nearly always you will need to implement a hashCode and equals method
on your key class.
The Gemini Twins: equals and hashCode
Equal hashCodes in general are not sufficient to ensure Object equality. However, if the hashCodes are not equal, you know the Objects
can’t possibly be equal. Consider how many 50-character Strings there are (65535^50) and how many possible hashCodes there are (2^32). It should be obvious there are way
more Strings than hashCodes. So the same hashCode has to be reused over and over for different Strings.
The default hashCode just uses the address of the Object and the default equals method just
compares addresses. If you override one of these two methods, you must override the other to match. The rules are:
- It is ok, unavoidable, but not desirable, if two Objects that do not compare equal have the same hashCode.
- Two Objects that compare equal must have the same hashCode.
So if you had a Fruit Object with a flavour and colour field, and you
decided that any two Objects with the same flavour were for all intents and purposes equal, you would define your equals
and hashCode methods like this:
As a rule of thumb, any time you use an Object as a key in a Map or Set (e.g. Hashtable,
HashMap, HashSet, TreeMap etc.) you must redefine both equals
and hashCode in such a way both incorporate that same and all the fields of the logical key. Fields in the key Object
irrelevant to lookup should not be included in either method.
Simple HashCodes
Let us say you hand three ints in your Object. field1 had a range 0..99, field2
had a range -10..+10 and field3 has a range 100..1000 you could pack them into a unique,
dense hashCode like this: The formula would be:
Calculating Aggregate hashCodes with XOR
The xor ^ operator is useful in computing hashing functions. To create a hashCode based on two fields, compute the hashCodes
of the two fields separately and xor them together with the ^ operator. To create an hash on all the elements of an array you could xor all the
values together. The result independent of the order. If you want the order to matter, use some digest function. xor also has the odd properly that
if you have a pair of identical hashCodes xored together, it is as if they were not there. When you are expecting duplicates, you might want to use some other combining
technique.
XOR has the following nice properties:
- It does not depend on order of computation.
- It does not “waste” bits. If you change even one bit in one of the components, the final value will change.
- It is quick, a single cycle on even the most primitive computer.
- It preserves uniform distribution. If the two pieces you combine are uniformly distributed so will the combination be. In other words, it does not tend to collapse the range
of the digest into a narrower band.
The nasty properties of XOR are:
- It treats identical pairs of components as if they were not there.
- It ignores order. A ^ B is the same a B ^ A. If order matters, you want some sort of checksum/digest such as
Adlerian. XOR would not be suitable to compute the hashCode for a List which depends on the order of the elements as part of its identity.
- If the values to be combined are only 8 bits wide, there will be effectively only 8 bits in the xored result. In contrast, multiplying by a prime and adding would scramble the
entire 32 bits of the result, giving a much broader range of possible values, hence greater chance that each hashcode will unique to a single Object.
In other words, it tends to expand the range of the digest into the widest possible band (32 bits).
- XOR is fairly easily degraded by patterns in the data. If you are not getting an even spread, it might pay to go for a higher overhead scrambling mechanism such as Aldlerian,
CRC or even MD5 or SHA1.
- If you XOR a number of small quantities the result is still a small quantity. It does not exploit the high order bits for additional variability unless you do some sort of
shifting.
Here is another approach that would work better if you had two Strings in your Object. It gives a different hash code for
your two Objects when:
o1.string1 = "apple";
o1.string2 = "orange";
o2.string1 = "orange";
o2.string2 = "apple";
It works like this to combine hash codes of the fields in your object:
Here is a faster, but not as universally applicable technique:
Here is roughly how String.hashCode works inside:
Here is a fast hash algorithm you can apply to bytes, short, chars, ints, arrays etc. I used an assembler version of it in my BBL Forth compiler hashCode where it is
essentially implemented in two instructions, ROL and XOR.
Here is a straight-forward xor hash of all the bytes. The disadvantage is the result is only 8-bits.
Consider using an CRC-32 or an Adlerian digest for your hashCode when you can reduce the key part
of your Object to a long string of bytes. This give a nice even spread over the range of possible integers.
Tips
- Don’t sweat writing a perfect hashCode. Test your code to see if look up is the bottleneck before fussing too much.
- It is easy to concoct a variety of hashCode methods and test them far more quickly than you can mathematically analyse the tradeoffs.
- If you write a Collection that uses hashCode, stress test it with a HashCode method that always returns 0.
- If you have an expensive hashCode calculation, consider caching the result.
When Do You Need A Custom equals and hashCode?
The hashCode method only gets invoked when you use the Object as the key to a Hashtable. It
is not used when the Object is merely a Hashtable value. Most of the time your Hashtable keys
are simple Strings, so you rarely need to write custom equals and hashCode methods. When you
use a HashSet to help you check for duplicate Objects, then you likely will need a custom equals
and hashCode method. There your Objects act as both key and value.
If you know the key values in advance, it is possible to construct a hashCode
function that has no collisions.
The One Key Catch
You can define only one hashCode/equals method for your HashSet Objects.
That limits you to one type of HashSet lookup for your Objects. There is no equivalent to Comparator
for HashSets. You can look up your Objects by only one key, though that key might contain several fields. You can’t
have several HashSets each accessing the same Objects by different keys. You can of course have several HashSets
each accessing a different subset of the same group of Objects using the same key.
In contrast, with HashMap you have more freedom. Your Objects don’t have to implement a useful hashCode/equals,
but any keys you use do. Since you can define different hashCode/equals for different types of key, you can have multiple HashMaps
on the same group of Objects looking up by different keys.
- Arrays are Objects and use the lame Object. hashCode. To get a proper hashCode
that is based on the values in the array, you need Arrays. hashCode.
- The packing method of creating hashCodes will not work will with HashMap, because HashMap discards the high order bits of
the hashCode.
Learning More
Sun’s Javadoc on
Object.
hashCode() : available:
Sun’s Javadoc on
Object.
equals( Object ) : available:
Sun’s Javadoc on
Arrays.
hashCode() : available:
Sun’s Javadoc on
Arrays.
deepHashCode() : available:
2009-06-10 by Roedy Green ©1996-2009 Canadian Mind Products
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