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Re: Re: Re: Re: Re: Slowdown
On Jan 5, 2005, at 1:21 AM, Andrzej Kozlowski wrote:
> OK., I should have written "dive". But I would expect that the people
> who wrote to point out this important difference should also explain
> why it is so important. As for me I only wanted to note that the
> rather dramatic change in hash values that corresponds with a
> dramatic slowdown.
I think the slowdown is
either
it goes to that portion of the memory which might be already out on
disk when it is called,
or
the Mod[FromDigits[list, k], m] structure of Hash - I am just guessing
based upon Wolfram's NKS page 1100
http://www.wolframscience.com/nksonline/page-1100d-text - where m is a
prime in the form of k^s-1 has some issue with the selected prime, and
it takes longer to compute.
János
> This suggests that indeed the problem is related to the hashing of
> names of the form name$number.
> On the other hand if you look at any sequence of hash values of names
> constructed by starting with some name and appending $number, where
> number changes through successive values, you will find that you get
> sequences of successive positive integers with periodic "dives" or
> "jumps". However, in no other case I have noticed any slowdown. If the
> slowdown is caused by a "collision" of hash values, as seems likely,
> there should be other cases too, but they would be extremely rare and
> I do not know of any way to find them except by relying on chance
> (very unlikely to produce any result).
>
> Andrzej
>
> On 5 Jan 2005, at 02:42, DrBob wrote:
>
>
>>>> You can see a big jump in the hash value at weirdness$10.
>>>>
>> Actually, the hash value gets much SMALLER at that point.
>>
>> Bobby
>>
>
>> On Tue, 4 Jan 2005 03:13:00 -0500 (EST), Andrzej Kozlowski
>> <akoz at mimuw.edu.pl> wrote:
>>
>>
>>> I just noticed another thing, which seems to throw more light at what
>>> is happenng. Look carefully at the Hash values of the different names
>>> of the form weirdness$number:
>>>
>>>
>>> MapIndexed[{First[#2], Hash[#1]} & ,
>>> ToExpression /@ (StringJoin["weirdness", "$",
>>> ToString[#1]] & ) /@ Range[20]]
>>>
>>>
>>> {{1, 1783099877}, {2, 1783099878}, {3, 1783099879},
>>> {4, 1783099880}, {5, 1783099881}, {6, 1783099882},
>>> {7, 1783099883}, {8, 1783099884}, {9, 1783099885},
>>> {10, 667842086}, {11, 667842087}, {12, 667842088},
>>> {13, 667842089}, {14, 667842090}, {15, 667842091},
>>> {16, 667842092}, {17, 667842093}, {18, 667842094},
>>> {19, 667842095}, {20, 667843323}}
>>>
>>> You can see a big jump in the hash value at weirdness$10. That is
>>> exactly the point at which the slowdown occurs.
>>>
>>> Andrzej Kozlowski
>>>
>>>
>>> On 3 Jan 2005, at 21:55, Andrzej Kozlowski wrote:
>>>
>>>
>>>> I can't see any siginificant slowdowns demonstrated by your code.
>>>> The
>>>> differences in timings between different combinations seem
>>>> insignificant. Cna you suggest any other name but "weirdness" that
>>>> shows significant slowdown?
>>>>
>>>> Besides, using Module only obsures what is really happening. Module
>>>> simply renames local variables by appending $somenumber to their
>>>> name
>>>> but the "number" that is used is different each time. You can do
>>>> that
>>>> whiteout Module and see exactly which names produce the slowdown
>>>> effect. It seems that the names weirdness$1 to weirdness$9 do not.
>>>>
>>>> In[1]:=
>>>> L=weirdness$1[];
>>>> Do[L=weirdness$1[L,i],{i,10^4}]//Timing
>>>>
>>>> Out[2]=
>>>> {0.03 Second,Null}
>>>>
>>>> In[3]:=
>>>> L=weirdness$9[];
>>>> Do[L=weirdness$9[L,i],{i,10^4}]//Timing
>>>>
>>>> Out[4]=
>>>> {0.08 Second,Null}
>>>>
>>>> The problem seems to begin with weirdness$10
>>>>
>>>> In[5]:=
>>>> L=weirdness$10[];
>>>> Do[L=weirdness$10[L,i],{i,10^4}]//Timing
>>>>
>>>> Out[6]=
>>>> {13.2 Second,Null}
>>>>
>>>> and continues for higher values, as far as I have checked.
>>>>
>>>> When you run Module with a fresh Kernel Mathematica seems to always
>>>> begin by appending $17:
>>>>
>>>> In[1]:=
>>>> Module[{weirdness, L},
>>>> L = weirdness[];
>>>> Do[L = weirdness[L, i], {i, 1}]
>>>> ] // Trace
>>>>
>>>> Out[1]=
>>>> {Module[{weirdness,L},L=weirdness[];
>>>> Do[L=weirdness[L,i],{i,1}]],{L$17=\
>>>> weirdness$17[];Do[L$17=weirdness$17[L$17,
>>>>
>>>> i],{i,1}],{L$17=weirdness$17[],weirdness$17[]},{Do[L$17=weirdness
>>>> $17[ L$
>>>> \
>>>> 17,i],{i,1}],{{{L$17,weirdness$17[]},{i,1},weirdness$17[weirdness
>>>> $17[ ],
>>>>
>>>> 1]},L$17=weirdness$17[weirdness$17[],1],weirdness$17[weirdness$17
>>>> [],1 ]\
>>>> },Null},Null},Null}
>>>>
>>>> on subsequent runs this is increased:
>>>>
>>>> In[2]:=
>>>> Module[{weirdness, L},
>>>> L = weirdness[];
>>>> Do[L = weirdness[L, i], {i, 1}]
>>>> ] // Trace
>>>>
>>>> Out[2]=
>>>> {Module[{weirdness,L},L=weirdness[];
>>>> Do[L=weirdness[L,i],{i,1}]],{L$19=\
>>>> weirdness$19[];Do[L$19=weirdness$19[L$19,
>>>>
>>>> i],{i,1}],{L$19=weirdness$19[],weirdness$19[]},{Do[L$19=weirdness
>>>> $19[ L$
>>>> \
>>>> 19,i],{i,1}],{{{L$19,weirdness$19[]},{i,1},weirdness$19[weirdness
>>>> $19[ ],
>>>>
>>>> 1]},L$19=weirdness$19[weirdness$19[],1],weirdness$19[weirdness$19
>>>> [],1 ]\
>>>> },Null},Null},Null}
>>>>
>>>> in any case all these numbers are larger than 10 and produce
>>>> slowdown,
>>>> but the numbers 10-16 which never occur inside Module also suffer
>>>> form
>>>> this problem:
>>>>
>>>> In[3]:=
>>>> L=weirdness$11[];
>>>> Do[L=weirdness$11[L,i],{i,10^4}]//Timing
>>>>
>>>> Out[4]=
>>>> {13.1 Second,Null}
>>>>
>>>> In[5]:=
>>>> L=weirdness$16[];
>>>> Do[L=weirdness$16[L,i],{i,10^4}]//Timing
>>>>
>>>> Out[6]=
>>>> {14.62 Second,Null}
>>>>
>>>> However, I have not been able to find any other name but weirdness
>>>> that produces this effect. This seems weird.
>>>>
>>>> Andrzej Kozlowski
>>>>
>>>>
>>>>
>>>> On 3 Jan 2005, at 18:29, yehuda ben-shimol wrote:
>>>>
>>>>
>>>>> Hi Roland,
>>>>> I'm afraid this is not true. Just try to run the code I sent with
>>>>> my
>>>>> post. "weirdness" was time consuming while weirdness1 was not. In
>>>>> addition it happened (not consistently) that function name of a
>>>>> SINGLE
>>>>> character suffered from this behavior as well.
>>>>> the code is given below for your convenience.
>>>>>
>>>>> t = CharacterRange["a", "z"];
>>>>> Do[fname = StringJoin[t[[Table[Random[Integer, {1,26}], {i}]]]];
>>>>> Print[i, "\t", fname, "\t",
>>>>> Timing[
>>>>> Module[{fs = ToExpression[fname], L},
>>>>> L = fs[];
>>>>> Do[L = fs[L, j], {j, 104}]]]], {i, 1, 50}, {5}]
>>>>>
>>>>>
>>>>> yehuda
>>>>>
>>>>> Roland Franzius wrote:
>>>>>
>>>>>
>>>>>> Maxim wrote:
>>>>>>
>>>>>>
>>>>>>
>>>>>>> Consider:
>>>>>>>
>>>>>>> In[1]:=
>>>>>>> Module[{f, L},
>>>>>>> L = f[];
>>>>>>> Do[L = f[L, i], {i, 10^4}]
>>>>>>> ] // Timing
>>>>>>>
>>>>>>> Module[{weirdness, L},
>>>>>>> L = weirdness[];
>>>>>>> Do[L = weirdness[L, i], {i, 10^4}]
>>>>>>> ] // Timing
>>>>>>>
>>>>>>> Out[1]=
>>>>>>> {0.015*Second, Null}
>>>>>>>
>>>>>>> Out[2]=
>>>>>>> {3.063*Second, Null}
>>>>>>>
>>>>>>> Here the timings differ by a factor of 200. Besides, the timing
>>>>>>> grows
>>>>>>> linearly in the first case and quadratically in the second
>>>>>>> (therefore, for
>>>>>>> n=10^5 there will be an approximately 2000 times slowdown). We
>>>>>>> can
>>>>>>> only
>>>>>>> guess that something goes wrong with the symbol name hashing.
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>> The timing difference occurs when the symbol "wierdness" exceeds 8
>>>>>> characters. Test it for "wierdnes". That seems to be a
>>>>>> consequence of
>>>>>> the machine routine for string comparison. Up to 8 characters can
>>>>>> be
>>>>>> used without using a memory to memory compare. Of course it
>>>>>> should be
>>>>>> possible to write a compare routine that makes not such a bit
>>>>>> step.
>>>>>>
>>>>>>
>>>>>
>>>>
>>>
>> -- DrBob at bigfoot.com
>> www.eclecticdreams.net
>>
>>
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