Mathematica 10 twice as slow as Mathematica 8 -Reap and Sow is all it takes

Ideas
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1

Trimmed my code to the critical section - Reap and Sow

10.0 for Microsoft Windows (64-bit) Session=1.5340877 Absolute=1.531088 Time=0.842405

8.0 for Microsoft Windows (64-bit) Session=0.7360421 Absolute=0.7340420 Time=0.359

8.0 for Microsoft Windows (64-bit) Session=0.7530431 Absolute=0.7530431 Time=0.328

10.0 for Microsoft Windows (64-bit) Session=1.5580891 Absolute=1.555089 Time=0.702005

data = Reap[Do [Sow[Range[i^2]~Partition~i,{i,1000}]];

Notebook with driver attached. I had to type the line in because Chrome locks up on every “Paste” of code.

2

I think this is just because V9 and later uses 64-bit machine integers, so there is twice as much data to handle compared to V8 which is limited to 32-bit machine integers even on 64-bit platforms.

What would be the timing if this example were run in the 32-bit Windows kernel (found under Mathematica\10.0\SystemFiles\Kernel\Binaries\Windows\MathKernel.exe)?

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3

My investigation started with an M9 program that I benchmarked and published on RosettaCode.org. After I installed M10 (and uninstalled M9 in the process) the program was much slower.
The facts are clear. M10 is slower. M10 needs a fix. If you have a 32 bit kernel go ahead and test.

4

The Mathematica installation includes both 32-bit and 64-bit kernels, so one can try both. This particular operation is as fast in the 32-bit V10 kernel as it was in V8.

Obviously there is some tradeoff, but 64-bit integers allow for computations with much larger arrays and expressions, up to any amount of installed memory that were simply inconceivable before.

The above comparison with V8 performance is as expected: 64-bits integers are twice as heavy as 32-bit integers. However, it does not explain why your program would run slower with V10 than V9.

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5

I am seeing very little diffference between versions 9 and 10 on 64 bit platforms. Likewise on the 32 bit machine I checked.

To elaborate on the point made by Ilian, enlarging the size of the integers to the 32-64 bit range shows a markedly different behavior.

Clear[data];Clear[data];
now = SessionTime[];
abs = AbsoluteTiming[
   tim = Timing[
      data = Reap[
         Do[Sow[Partition[Range[i^2]^2,i]], {i, 1000}]
         ];
      ];
   ];
ver = StringTake[$Version, StringPosition[$Version, ")"][[1, 1]]];
Print[ver, " Session=", SessionTime[] - now, " Absolute=", abs[[1]], 
  " Time=", tim[[1]]];
ByteCount[data]
Clear[data

]

In versions 9 and 10 this takes around 6 seconds. In version 8 it takes 120 seconds.

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6

You’re right that M8 is 32-bit. In fact the ByteCount[data] confirms it. I was focused on problems with the system running out of physical memory, hence the need for Clear[data]. The system can appear to freeze on successive runs when using virtual memory.

7

“In versions 9 and 10 this takes around 6 seconds. In version 8 it takes 120 seconds.”

Is that a misprint or are you referring to M8 on a very slow machine?

8

Not a misprint; I tested all three versions on the same machine. Notice that I changed the problem so as to use integers larger than 32 bit but smaller than 64. This means that version 8 cannot work with packed arrays whereas the later versions can do so.

2 Likes
9

Hello all, how can I run a notebook created in mathematica 8, in a win7 64bit pc with mathematica 10.3, in 32 bit and not 64 bit?
M10 seems indeed much slower than M8.

Thank you in advance