Hello again...
For what occurs in modern CPUs, well, no. Surprising to see that a mul would be faster than a shr or shl. How comes?
No, not faster. But definitely way faster than >30 cycles not so long ago.
I used to be ok with these things when I was writing demoscene code a loong time ago but I'd need an extremely serious refresh.
You said "demoscene"?!... do you have a handle??? Andres.
As a side note, there is a huge uptake in the BigData/mapreduce/hadoop environment where Smalltalk is sorely absent. Scala seems to fill the void on the JVM. There hashing is quite key, to remap all of the mapping phase results to the reduce nodes. I am surprised to see that Smalltalk vendors haven't jumped in that space. Phil On Wed, Feb 26, 2014 at 2:04 AM, Andres Valloud <avall...@smalltalk.comcastbiz.net <mailto:avall...@smalltalk.comcastbiz.net>> wrote: Hello... On 2/25/14 1:17 , p...@highoctane.be <mailto:p...@highoctane.be> wrote: I am currently reading through the Hashing in Smalltalk book (http://www.lulu.com/shop/__andres-valloud/hashing-in-__smalltalk-theory-and-practice/__paperback/product-3788892.html <http://www.lulu.com/shop/andres-valloud/hashing-in-smalltalk-theory-and-practice/paperback/product-3788892.html>__) and, my head hurting notwithstanding, there are indeed a ton of gems in this system. As he mentions, doing the exercises brings a lot of extra :-) :) thank you. When going to 64-bit, and with the new ObjectMemory scheme, I guess a couple of identity hashing functions will come under scrutiny. e.g. SmallInteger>>hashMultiply | low | low := self bitAnd: 16383. ^(16r260D * low + ((16r260D * (self bitShift: -14) + (16r0065 * low) bitAnd: 16383) * 16384)) bitAnd: 16r0FFFFFFF which will need some more bits. IMO it's not clear that SmallInteger>>identityHash should be implemented that way. Finding a permutation of the small integers that also behaves like a good quality hash function and evaluates quickly (in significantly less time and complexity than, say, Bob Jenkins' lookup3) would be a really interesting research project. I don't know if it's possible. If no such thing exists, then getting at least some rough idea of what's the minimum necessary complexity for such hash functions would be valuable. Looking at hashMultiply as a non-identity hash function, one would start having problems when significantly more than 2^28 objects are stored in a single hashed collection. 2^28 objects with e.g. 12 bytes per header and a minimum of one instance variable (so the hash value isn't a instance-constant) stored in a hashed collection requires more than 4gb, so that is clearly a 64 bit image problem. In 64 bits, 2^28 objects with e.g. 16 bytes per header and a minimum of one instance variable each is already 6gb, and a minimum of 8gb with the hashed collection itself. Because of these figures, I'd think improving the implementation of hashed collections takes priority over adding more non-identity hash function bits (as long as the existing hash values are of good quality). Did you look at the Hash Analysis Tool I wrote? It's in the Cincom public Store repository. It comes in two bundles: Hash Analysis Tool, and Hash Analysis Tool - Extensions. With everything loaded, the tool comes with 300+ hash functions and 100+ data sets out of the box. The code is MIT. I had a look at how it was done in VisualWorks; The implementation of hashMultiply, yes. Note however that SmallInteger>>hash is ^self. hashMultiply "Multiply the receiver by 16r0019660D mod 2^28 without using large integer arithmetic for speed. The constant is a generator of the multiplicative subgroup of Z_2^30, see Knuth's TAOCP vol 2." <primitive: 1747> | low14Bits | low14Bits := self bitAnd: 16r3FFF. ^16384 * (16r260D * (self bitShift: -14) + (16r0065 * low14Bits) bitAnd: 16r3FFF) + (16r260D * low14Bits) bitAnd: 16rFFFFFFF The hashing book version has: multiplication "Computes self times 1664525 mod 2^38 while avoiding overflow into a large integer by making the multiplication into two 14 bits chunks. Do not use any division or modulo operation." | lowBits highBits| lowBits := self bitAnd: 16r3FFF. highBits := self bitShift: -14. ^(lowBits * 16r260D) + (((lowBits * 16r0065) bitAnd: 16r3FFF) bitShift: 14) + (((highBits * 16r260D) bitAnd: 16r3FFF) bitShift: 14) bitAnd: 16rFFFFFFF So, 16384 * is the same as bitShift: 14 and it looks like done once, which may be better. It should be a primitive (or otherwise optimized somehow). At some point though that hash function was implemented for e.g. ByteArray in Squeak, I thought at that point the multiplication step was also implemented as a primitive? Also VW marks it as a primitive, which Pharo does not. In VW it is also a translated primitive, i.e. it's executed directly in the JIT without calling C. Keep in mind that the speed at which hash values are calculated is only part of the story. If the hash function quality is not great, or the hashed collection implementation is not efficient and induces collisions or other extra work, improving the efficiency of the hash functions won't do much. I think it's mentioned in the hash book (I'd have to check), but once I made a hash function 5x times slower to get better quality and the result was that a report that was taking 30 minutes took 90 seconds instead (and hashing was gone from the profiler output). Would we gain some speed doing that? hashMultiply is used a lof for identity hashes. Bytecode has quite some work to do: 37 <70> self 38 <20> pushConstant: 16383 39 <BE> send: bitAnd: 40 <68> popIntoTemp: 0 41 <21> pushConstant: 9741 42 <10> pushTemp: 0 43 <B8> send: * 44 <21> pushConstant: 9741 45 <70> self 46 <22> pushConstant: -14 47 <BC> send: bitShift: 48 <B8> send: * 49 <23> pushConstant: 101 50 <10> pushTemp: 0 51 <B8> send: * 52 <B0> send: + 53 <20> pushConstant: 16383 54 <BE> send: bitAnd: 55 <24> pushConstant: 16384 56 <B8> send: * 57 <B0> send: + 58 <25> pushConstant: 268435455 59 <BE> send: bitAnd: 60 <7C> returnTop If this is a primitive instead, then you can also avoid the overflow into large integers and do the math with (basically) mov eax, smallInteger shr eax, numberOfTagBits mul eax, 1664525 "the multiplication that throws out the high bits" shl eax, 4 "throw out bits 29-32" shr eax, 4 lea eax, [eax * 2^numberOfTagBits + smallIntegerTagBits] Please excuse trivial omissions in the above, it's written only for the sake of illustration (e.g. it looks like the 3 last instructions can be combined into two... lea followed by shr). Also, did you see the latency of integer multiplication instructions in modern x86 processors?... I ran some experiments timing things. It looks like that replacing 16384 * by bitShift:14 leads to a small gain, bitShift (primitive 17) being faster than * (primitive 9) Keep in mind those operations still have to check for overflow into large integers. In this case, large integers are not necessary. Andres. The bytecode is identical, except send: bitShift instead of send: * multiplication3 | low | low := self bitAnd: 16383. ^(16r260D * low + ((16r260D * (self bitShift: -14) + (16r0065 * low) bitAnd: 16383) bitShift: 14)) bitAnd: 16r0FFFFFFF [500000 timesRepeat: [ 15000 hashMultiply ]] timeToRun 12 [500000 timesRepeat: [ 15000 multiplication ]] timeToRun 41 (worse) [500000 timesRepeat: [ 15000 multiplication3 ]] timeToRun 10 (better) It looks like correct for SmallInteger minVal to: SmallInteger maxVal Now, VW gives: [500000 timesRepeat: [ 15000 hashMultiply ]] timeToRun 1.149 milliseconds Definitely worth investigating the primitive thing, or some NB Asm as this is used about everywhere (Collections etc). Toughts? Phil
