Once the code is loaded, from the Tools menu use Hash Analysis Tool.
There's a manual below, and also the Fundamentals book has a somewhat in
depth discussion on how it works.
ftp://sqrmax.us.to/pub/Smalltalk/Papers/Hash%20Analysis%20Tool.pdf
On 3/2/14 15:06 , p...@highoctane.be wrote:
I have found the tools in the Cincom public repo.
Now, I have to see how this works in VW, I am not that proficient with it.
Phil
On Wed, Feb 26, 2014 at 8:55 AM, p...@highoctane.be
<mailto:p...@highoctane.be> <p...@highoctane.be
<mailto:p...@highoctane.be>> wrote:
Andres,
Thanks for the insights.
hash quality is indeed an key factor. At least, my mind is somewhat
grasping this hashing field a bit better.
I'll have a look at the tools, I haven't used them yet.
And a shot at the ASM version with NativeBoost in Pharo.
For what occurs in modern CPUs, well, no. Surprising to see that a
mul would be faster than a shr or shl. How comes?
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.
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
