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*To*: srfi-69@xxxxxxxxxxxxxxxxx*Subject*: Re: Discussion about your comments*From*: Sebastian Egner <sebastian_egner@xxxxxxxxx>*Date*: Sat, 21 May 2005 18:20:57 +0200*Delivered-to*: srfi-69@xxxxxxxxxxxxxxxxx*Old-date*: Sat, 21 May 2005 08:01:03 -0700 (PDT)*Reply-to*: sebastian_egner@xxxxxxxxx*User-agent*: Gnus/5.110003 (No Gnus v0.3) XEmacs/21.5-b20 (berkeley-unix)

Panu wrote: > ... bounds or no bounds to hash functions? > > I don't get this argument. For the modular polynomial method to work, > it suffices for the mantissa and modulus to be relatively prime. This > can achieved easily by picking a prime modulus, but also by picking > a prime mantissa. No. The modular polynomial method works if and only if the mantissa has sufficient multiplicative order modulo m. Example: I choose modulus m = 120 and you are to combine five hash functions h_0, .., h_4 using the polynomial method into h = x -> h_0(x) + r h_1(x) + r^2 h_2(x) + .. + r^4 h_4(x) mod m. How do you choose r to get a decent hash function? The sad answer: You don't. Reason: Units(Z/120*Z) = Z2^3 x Z4. There are no elements of order 5 or more modulo 120, which means h effectively just *adds* at least two of the component functions no matter how you choose r. If you want another example: Load your own reference implementation, construct a hash table using (make-string-hash-table 37) and insert a couple of strings that end in the same character. You will find that they all end up in the same bin. Why? Because I have chosen a bad modulus m (by giving size hint 37) and string-hash uses the modular polynomial method with r = 37, which is 0 mod m. > I would have thought it to be more general if the hash > function gets to know the modulus on beforehand, not more restrictive. In the end, both approaches are equivalent. In your current setup the target range is communicated to the hash function with every call. The hash function needs to produce a value in that range, but it can call helper hash functions with other ranges (i.e. a large prime). In the other approach, there is a single large range (probably a prime close to but not exceeding the maximal immediate integer) known to every hash function beforehand---and it is the task of the hash table to reduce it to the range it needs. > That said, I don't have much reason for requiring the bound parameter. > The most important reasons for it were (1) the observation that the hash > seems to almost always be converted to some range anyway, so (hash obj > bound) seems cleaner than (modulo (hash obj) bound), and (2) the bonus > of getting arbitrarily big hash ranges on request (with a fixed range, > it is easy to reduce it but not extend it). Correct, there is also not so much reason to have no bound parameter. In the end it is about efficiency, and easily defining good hash functions is probably the key for that. (Not sure, (2) is a bonus; bignums can hurt performance quite a bit here.) > As any non-bounded hash function h1 can be made into bound-aware hash > function h2 by > > (define (h2 obj bound) (modulo (h1 obj) bound)) > > one can't say that it makes it much more difficult to define bound-aware > hash functions than boundless ones. Am I missing something? "Unbounded hash functions" sounds like a bad idea to me, I am proposing a global statically-known default range that is implementation-dependent but prime and sufficiently large. (Aside: Is it on purpose that *default-bound* in the reference implementation is not a prime? m = 2^29 - 3 would be prime and r = 256592988 is a primitive element mod m with some interesting bit-pattern; r = 2 and r = 2^16 + 1 are others. Your choice is m = 2^29 - 2 and r = 37, which only has order 1008 mod m.) (Another aside: It might be worth it using SRFI-16 [case-lambda] in the reference implementation.) --- > hash-table-get, -put!, -remove!: > These are provided as compatibility procedures to ease porting > of non-SRFI-69 code onto SRFI-69? If you think this is not a > worthwhile goal, I can purge them from the SRFI. -ref, -set!, > -delete! are IMO clearly better but less used. I added a "don't > use this" note to the compatibility versions. If you want to get rid of these procedures in legacy code you can better do it in this SRFI. It might be the only chance there is in a long time. --- > order independence of -keys and -values: > This is not because of prospective performance merits, but to > discourage bad programming style. If one wants to process the > association pairs of a hash table, one should not be using -keys > and -values. I am afraid that the pragmatics is exactly the other way around: By not specifying -keys and -values to be in sync, you do not discourage anybody from anything. It is more an invitation to the user to hurt himself with some unexpected unportable feature. It is also not obvious to me that using -keys and -values in sync, provided they are specified to be, is "bad programming style." What is the harm? "Unspecified" in a standard usually means "I would like to give choice to the implementors." If you really want to discourage people from assuming that -keys and -values are (map car (hash-table->alist h)) and (map cdr (hash-table->alist h)) then you can better *specify* -keys and -values to disagree: Then programs assuming -keys and -values being in sync fail right away, and not at the time they are ported to some other implementation of this SRFI. Sebastian. __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! 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