Author: Frank Phillips
Date: 11:09:18 09/03/03
Go up one level in this thread
On September 03, 2003 at 13:43:13, Tom Likens wrote: >On September 03, 2003 at 13:28:20, Frank Phillips wrote: > >>On September 03, 2003 at 10:52:35, Tom Likens wrote: >> >>>On September 03, 2003 at 02:36:33, Tony Werten wrote: >>> >>>>On September 02, 2003 at 13:00:05, Tom Likens wrote: >>>> >>>>> >>>>>This is a general query about an issue I've run into and >>>>>I'm wondering if anyone else has dealt with it or if I'm >>>>>just off base. Essentially, the issue is this- recently >>>>>I started playing around with my hash table's random >>>>>numbers to see if I could improve them. Currently, for >>>>>the main table I have a Hamming distance of 24 for >>>>>roughly 800 random 64-bit values. >>>>> >>>>>This is where my inquiry comes in, I use the lower N >>>>>bits of my hash key as an index into the table. I'm >>>>>wondering, even though the overall Hamming distance is >>>>>24 shouldn't I be concerned about the Hamming distance >>>>>of the lower N bits? >>>> >>>>It could be, but it's unlikely it would give problems. >>>> >>>>To make your keys better, you should not strive for the biggest average hamming >>>>distance, but for the biggest minimum hamming distance. >>>> >>>>22 is doable, wich should give you a collision every never. >>> >>>Tony, >>> >>>I was a little imprecise, my *minimum* Hamming distance is 24, >>>the average is closer to 32. I don't generate my random numbers >>>on the fly, but instead have a separate program that creates >>>the numbers and saves them to a static array that becomes part of >>>the program proper. >>> >>>Last night I changed this program slightly to give me a minimum >>>Hamming distance of 10 on the lower 32-bits (I tried 12 initially >>>but killed it after four hours of run time, without any results). >>>It also verified that the overall minimum distance for the 64-bit >>>values was still 24. >>> >>>Anyway, long story short, my collision rate in the repetition >>>hash table went down significantly. I intend to run a final >>>experiment tonight to actually measure the collisions for >>>different 32-bit distances (there has to be a graph in here >>>somewhere ;) >>> >>>regards, >>>--tom >>> >>>> >>>>Of coarse you still have the risk of the lower part being worse than the upper >>>>part, but you can just let your computer search a bit longer for a minimum >>>>hamming distance of 11 in the lower part. >>>> >>>>Tony >>>> >>>>>If these bits are alike, even >>>>>though the overal value is reasonable don't it increase >>>>>the probablity of hash collisions considerably? >>>>>Of course, I won't get a false match since I still use >>>>>all 64-bits of the key to indicate if the hash entry >>>>>is valid, but it's time wasted performing multiple >>>>>probes into the table. >>>>> >>>>>I'm also guessing that this could be more of an issue >>>>>for the repetition hash table, since it is quite a bit >>>>>smaller than the main table. Currently, I don't do >>>>>multiple probes into this table and I've never seen >>>>>an issue. Still, I'm starting to wonder if there is >>>>>a problem lurking below the surface that I may >>>>>have missed. >>>>> >>>>>Anyway, I'm probably missing something obvious here. >>>>>I intend to run a number of experiments this evening, >>>>>but I was curious if anyone else has given this much >>>>>thought. >>>>> >>>>>regards, >>>>>--tom >> >> >>Do you have a link to the code (in C) to calculate the hamming distance? >> >>I searched a bit, but found nothing. >> >>(I used the mersene twister to calcuate 32 bit random numbers that I concatonate >>to 64 bit. It would be nice to know how 'good' they are.). >> >>Frank > >If you're interested I'd be happy to send you the program I use >to calculate my random numbers. It uses the Mersenne Twister or >another algorithm I ripped out of Booth's __Inner Loops__ book >that seemed to produce decent random numbers (the default is the >MT PRNG). > >Getting the hamming distance in pseudo-code for N random numbers: > >1. Generate a random number (index=M) > >2. Compare it to the 0 ... M-1 valid random numbers alread saved > > if (popcnt64(new_rand64 ^ array[0..M-1]) >= MIN_HAM) then OK > >3. If valid, save it into slot M > If not valid (hamming distance is too small) goto 1 > >4. Repeat until you have N random numbers > >This was off-the-cuff, so I may have left something out but it >should give you the basic idea. > >Of course, this will run forever if you pick a Hamming distance >that is too large, so beware! > >regards, >--tom Thanks. I will give your pseudo code above a try, which unless I misunderstand counts the number of different bits - irrespective of their position. Frank
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