Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-07-18 Thread Aleksey Khudyakov

On 17.07.2013 16:11, Brian Lewis wrote:

On 2013.07.17, at 08:03, Jan-Willem Maessen wrote:

This has all the marks of a 64-bit-only code running on a 32 bit
machine.


This discussion is interesting, but I'm not sure why so much of it is
taking place here instead of on the mwc-random issue tracker:
https://github.com/bos/mwc-random/issues

It's way past time to file an issue and/or talk to the maintainer.


Issue turned out to be GHC bug. Here are relevant tickets

https://github.com/bos/mwc-random/issues/25
http://ghc.haskell.org/trac/ghc/ticket/8072

No workaround for mwc-random yet

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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-07-17 Thread Brian Lewis
On 2013.07.17, at 08:03, Jan-Willem Maessen wrote:
> This has all the marks of a 64-bit-only code running on a 32 bit
> machine.

This discussion is interesting, but I'm not sure why so much of it is
taking place here instead of on the mwc-random issue tracker:
https://github.com/bos/mwc-random/issues

It's way past time to file an issue and/or talk to the maintainer.

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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-07-17 Thread Jan-Willem Maessen
This has all the marks of a 64-bit-only code running on a 32 bit machine.
 It looks like you're getting the high bits of the rng with a signed shift
right, ultimately yielding only the sign bit.

I suspect mwc-random needs to use Int64 rather than Int internally in a few
critical places.


On Wed, Jul 17, 2013 at 7:22 AM, kudah  wrote:

> Test triggers the bug, only zeros and ones like you said, but
> only for native-sized types:
>
> -O2:
> Int
> 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0
> Int32
> 41 37 25 85 27 84 70 8 70 32 36 1 14 92 1 74 17 28 38 76
> Int64
> 37 77 57 75 17 58 28 77 23 51 1 13 50 35 21 11 70 43 6 5
> Word
> 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0
> Word32
> 52 45 86 4 85 44 71 59 91 10 65 89 41 78 84 88 3 60 71 0
> Word64
> 12 82 25 1 11 14 76 58 1 77 9 25 57 20 41 8 2 29 21 29
>
> ghci:
> Int
> 53 13 24 58 66 71 19 16 73 54 95 87 2 34 62 67 2 45 56 2
> Int32
> 41 37 25 85 27 84 70 8 70 32 36 1 14 92 1 74 17 28 38 76
> Int64
> 37 77 57 75 17 58 28 77 23 51 1 13 50 35 21 11 70 43 6 5
> Word
> 41 19 99 69 27 58 92 45 9 38 51 39 50 14 2 21 25 94 96 2
> Word32
> 52 45 86 4 85 44 71 59 91 10 65 89 41 78 84 88 3 60 71 0
> Word64
> 12 82 25 1 11 14 76 58 1 77 9 25 57 20 41 8 2 29 21 29
>
> I run a 32-bit system, as I've said before.
>
> > Gentoo Linux _i686_ 3.8.2-pf
>
> Could perhaps be something with my system, I'll test on Ubuntu later
> today, and if there are no problems with compiling mwc-random on ghc
> git — on it too.
>
> On Wed, 17 Jul 2013 12:19:29 +0400 Aleksey Khudyakov
>  wrote:
>
> > On 10 July 2013 14:10, kudah  wrote:
> > > Yes, it does. Without optimizations the result is
> > > "ndgorsfesnywaiqraloa", while with optimizations the result is
> > > always "aabb".
> > >
> > Sorry for taking so long. So problem is uniformR. You can reproduce
> > bug reliably and I cannot. Are you on 32-bit system? I only tested on
> > 64-bit ones. If this isn't the case I'm out of ideas.
> >
> > I finally wrote test case that doesn't depends on anything besides
> > mwc-random (it's
> > in attachment). Could you check whether it still triggers the bug
>
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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-07-17 Thread kudah
Test triggers the bug, only zeros and ones like you said, but
only for native-sized types:

-O2:
Int
0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 
Int32
41 37 25 85 27 84 70 8 70 32 36 1 14 92 1 74 17 28 38 76 
Int64
37 77 57 75 17 58 28 77 23 51 1 13 50 35 21 11 70 43 6 5 
Word
0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 
Word32
52 45 86 4 85 44 71 59 91 10 65 89 41 78 84 88 3 60 71 0 
Word64
12 82 25 1 11 14 76 58 1 77 9 25 57 20 41 8 2 29 21 29 

ghci:
Int
53 13 24 58 66 71 19 16 73 54 95 87 2 34 62 67 2 45 56 2 
Int32
41 37 25 85 27 84 70 8 70 32 36 1 14 92 1 74 17 28 38 76 
Int64
37 77 57 75 17 58 28 77 23 51 1 13 50 35 21 11 70 43 6 5 
Word
41 19 99 69 27 58 92 45 9 38 51 39 50 14 2 21 25 94 96 2 
Word32
52 45 86 4 85 44 71 59 91 10 65 89 41 78 84 88 3 60 71 0 
Word64
12 82 25 1 11 14 76 58 1 77 9 25 57 20 41 8 2 29 21 29 

I run a 32-bit system, as I've said before.

> Gentoo Linux _i686_ 3.8.2-pf

Could perhaps be something with my system, I'll test on Ubuntu later
today, and if there are no problems with compiling mwc-random on ghc
git — on it too.

On Wed, 17 Jul 2013 12:19:29 +0400 Aleksey Khudyakov
 wrote:

> On 10 July 2013 14:10, kudah  wrote:
> > Yes, it does. Without optimizations the result is
> > "ndgorsfesnywaiqraloa", while with optimizations the result is
> > always "aabb".
> >
> Sorry for taking so long. So problem is uniformR. You can reproduce
> bug reliably and I cannot. Are you on 32-bit system? I only tested on
> 64-bit ones. If this isn't the case I'm out of ideas.
> 
> I finally wrote test case that doesn't depends on anything besides
> mwc-random (it's
> in attachment). Could you check whether it still triggers the bug

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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-07-17 Thread Aleksey Khudyakov
On 10 July 2013 14:10, kudah  wrote:
> Yes, it does. Without optimizations the result is
> "ndgorsfesnywaiqraloa", while with optimizations the result is always
> "aabb".
>
Sorry for taking so long. So problem is uniformR. You can reproduce bug
reliably and I cannot. Are you on 32-bit system? I only tested on 64-bit ones.
If this isn't the case I'm out of ideas.

I finally wrote test case that doesn't depends on anything besides
mwc-random (it's
in attachment). Could you check whether it still triggers the bug


testcase.hs
Description: Binary data
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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-07-10 Thread kudah
Yes, it does. Without optimizations the result is
"ndgorsfesnywaiqraloa", while with optimizations the result is always
"aabb".

On Wed, 10 Jul 2013 02:21:10 +0400 Aleksey Khudyakov
 wrote:

> On 10.07.2013 01:38, kudah wrote:
> > I've attached the script that I had trouble with. It tries to
> > replicate one directory structure in another directory, while
> > replacing filenames and file contents with random data. When
> > compiled with -O1 or -O2 resulting file and directory names are
> > composed only of a's and b's, but file contents seem properly
> > randomized.
> >
> No luck. On my computer script works correctly with and without 
> optimizations. My best guess that uniformR is problematic. Does
> 
>  > (\g -> randName g 20) =<< create
> 
> show different behavior with and without optimizations?

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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-07-09 Thread Aleksey Khudyakov

On 10.07.2013 01:38, kudah wrote:

I've attached the script that I had trouble with. It tries to replicate
one directory structure in another directory, while replacing filenames
and file contents with random data. When compiled with -O1 or -O2
resulting file and directory names are composed only of a's and b's,
but file contents seem properly randomized.

No luck. On my computer script works correctly with and without 
optimizations. My best guess that uniformR is problematic. Does


> (\g -> randName g 20) =<< create

show different behavior with and without optimizations?

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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-07-09 Thread kudah
I've attached the script that I had trouble with. It tries to replicate
one directory structure in another directory, while replacing filenames
and file contents with random data. When compiled with -O1 or -O2
resulting file and directory names are composed only of a's and b's,
but file contents seem properly randomized.

ghc-7.6.2, vector-0.10.0.1, primitive-0.5.0.1, mwc-random-0.12.0.1,
Gentoo Linux i686 3.8.2-pf.

On Tue, 09 Jul 2013 22:43:36 +0400 Aleksey Khudyakov
 wrote:

> On 09.07.2013 22:10, kudah wrote:
> > Same here, I used mwc-random to generate random strings. It works in
> > ghci and when compiled with -O0, but with -O1 and -O2 I've been
> > getting exclusively a's and b's.
> >
> It looks like MWC generates only 0 and 1 for some reason. I've tried
> to write simple test but everything works fine. Could you post test
> case and compiler/libraries/OS versions you use?
> 
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{-# LANGUAGE OverloadedStrings #-}
{-# OPTIONS_GHC
-fno-warn-name-shadowing
-fno-warn-unused-imports
#-}
module Main where

import Shelly
import Filesystem.Path.CurrentOS (splitDirectories, encodeString, decodeString)
import qualified Filesystem as F

import qualified Data.Text as T
import qualified Data.ByteString as B

import Control.Monad.IO.Class
import System.Random.MWC
import Control.Monad.Primitive

import Control.Monad
import Control.Applicative
import Prelude hiding (FilePath)
import Data.String
import System.Environment

rands :: (PrimMonad m, Variate a) => Gen (PrimState m) -> Int -> m [a]
rands gen i = replicateM i (uniform gen)

randRs :: (PrimMonad m, Variate a) => Gen (PrimState m) -> Int -> (a, a) -> m [a]
randRs gen i z = replicateM i (uniformR z gen)

lastElemLength :: FilePath -> Int
lastElemLength fd = case splitDirectories fd of
[] -> error $ "Empty filepath " ++ show fd
g -> T.length $ toTextIgnore $ last g

randName :: Gen (PrimState IO) -> Int -> IO FilePath
randName gen l = decodeString . map toEnum <$> randRs gen l (fromEnum 'a', fromEnum 'z')

main :: IO ()
main = do
g <- getArgs
case g of
[inDir, outDir] ->
withSystemRandom . asGenIO $ \gen -> do
shellyNoDir $ do
escaping False $ do
-- verbosely $ do
out <- absPath (decodeString outDir)
in' <- absPath (decodeString inDir)
descent gen out in'
_ -> putStrLn "Specify input directory and output directory"

descent :: Gen (PrimState IO) -> FilePath -> FilePath -> Sh ()
descent gen outDir fd = do
isDir <- test_d fd
if isDir
  then do
n <- liftIO $ randName gen $ lastElemLength fd
let newDir = outDir  n
mkdir_p newDir
chdir fd $ do
filesOrDirs <- ls "."
mapM_ (descent gen newDir) filesOrDirs
  else do
file <- absPath fd
liftIO $ do
size <- F.getSize file
newFname <- randName gen $ lastElemLength file
bs <- B.pack <$> rands gen (fromInteger size)
B.writeFile (encodeString $ outDir  newFname) bs
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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-07-09 Thread Aleksey Khudyakov

On 09.07.2013 22:10, kudah wrote:

Same here, I used mwc-random to generate random strings. It works in
ghci and when compiled with -O0, but with -O1 and -O2 I've been getting
exclusively a's and b's.

It looks like MWC generates only 0 and 1 for some reason. I've tried to 
write simple test but everything works fine. Could you post test case 
and compiler/libraries/OS versions you use?


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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-07-09 Thread kudah
Same here, I used mwc-random to generate random strings. It works in
ghci and when compiled with -O0, but with -O1 and -O2 I've been getting
exclusively a's and b's.

On Sun, 17 Mar 2013 18:48:06 +0500 Azeem -ul-Hasan 
wrote:

> I am using
>GHC 7.6.1
>mwc-random 0.12.0.1
>vector 0.9.1
>primitive 0.4.1
> 
> Azeem
>   
> On 16.03.2013 13:31, Azeem -ul-Hasan wrote:
> > Nope that isn't the case either. Even if I make use of defaultSeed
> > through create the problem still remains. The problem seems to be
> > in the generation of a vector of (a,a) i.e in the part
> >
> > V.generateM ((round $ p*(fromIntegral $ l*z)) `div` 2) (\i->
> > R.uniformR ((0,0) , (l-1,l-1)) gen)
> >
> > in line 16. Thanks again.
> >
> I've tried to run you program and I've got approximately same results 
> regardless of optimization level. Which versions of GHC, mwc-random, 
> vector and primitive do you use?
>  
>  
> 

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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-03-18 Thread Aleksey Khudyakov
On 17 March 2013 21:49, Dominic Steinitz  wrote:
> Aleksey Khudyakov  gmail.com> writes:
>
>> I've tried to run you program and I've got approximately same results
>> regardless of optimization level. Which versions of GHC, mwc-random,
>> vector and primitive do you use?
>>
>
> By approximate do you mean you are getting Monte Carlo noise
> or Floating Point noise? If the latter then that's reasonable;
> if the former then that's worrying.
>
Difficult to say. I got values around 10 with and without optimizations. Most
likely it's MC noise

I was using GHC-7.6.2 and latest vector/primitive/mwc-random. I didn't tried
to reproduce bug with versions which Azeem Ul Hasan use.

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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-03-17 Thread Dominic Steinitz
Aleksey Khudyakov  gmail.com> writes:

> I've tried to run you program and I've got approximately same results 
> regardless of optimization level. Which versions of GHC, mwc-random, 
> vector and primitive do you use?
> 

By approximate do you mean you are getting Monte Carlo noise
or Floating Point noise? If the latter then that's reasonable;
if the former then that's worrying.

Dominic.



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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-03-17 Thread Azeem -ul-Hasan
I am using
   GHC 7.6.1
   mwc-random 0.12.0.1
   vector 0.9.1
   primitive 0.4.1

Azeem
  
On 16.03.2013 13:31, Azeem -ul-Hasan wrote:
> Nope that isn't the case either. Even if I make use of defaultSeed
> through create the problem still remains. The problem seems to be in the
> generation of a vector of (a,a) i.e in the part
>
> V.generateM ((round $ p*(fromIntegral $ l*z)) `div` 2) (\i-> R.uniformR
> ((0,0) , (l-1,l-1)) gen)
>
> in line 16. Thanks again.
>
I've tried to run you program and I've got approximately same results 
regardless of optimization level. Which versions of GHC, mwc-random, 
vector and primitive do you use?
 
 
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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-03-17 Thread Aleksey Khudyakov

On 16.03.2013 13:31, Azeem -ul-Hasan wrote:

Nope that isn't the case either. Even if I make use of defaultSeed
through create the problem still remains. The problem seems to be in the
generation of a vector of (a,a) i.e in the part

V.generateM ((round $ p*(fromIntegral $ l*z)) `div` 2) (\i-> R.uniformR
((0,0) , (l-1,l-1)) gen)

in line 16. Thanks again.

I've tried to run you program and I've got approximately same results 
regardless of optimization level. Which versions of GHC, mwc-random, 
vector and primitive do you use?


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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-03-16 Thread Azeem -ul-Hasan
Nope that isn't the case either. Even if I make use of defaultSeed through 
create the problem still remains. The problem seems to be in the generation of 
a vector of (a,a) i.e in the part 

V.generateM ((round $ p*(fromIntegral $ l*z)) `div` 2) (\i-> R.uniformR ((0,0) 
, (l-1,l-1)) gen)

in line 16. Thanks again.

Azeem

> Date: Sat, 16 Mar 2013 10:58:50 +0200
> From: r...@ro-che.info
> To: aze...@live.com
> CC: carter.schonw...@gmail.com; haskell-cafe@haskell.org
> Subject: Re: [Haskell-cafe] Optimization flag changing result of code 
> execution
> 
> Perhaps the problem is in withSystemRandom, which uses unsafePerformIO?
> 
> Does the problem persist if you seed your program with some predefined
> seed?
> 
> Roman
> 
> * Azeem -ul-Hasan  [2013-03-16 13:46:54+0500]
> > 
> > Hi Carter,
> > 
> >  Thank you for your help, but I can confirm that this is not due to 
> > floating point errors. My own hunch is that it is due to the way I am using 
> > random number generation from System.Random.MWC. To check it I wrote a 
> > version of mkNetwork function using random number generation from 
> > System.Random and it works fine with optimizations turned on. So any ideas 
> > why optimizations are messing with System.Random.MWC?
> > 
> > Azeem
> > From: carter.schonw...@gmail.com
> > Date: Fri, 15 Mar 2013 17:09:36 -0400
> > Subject: Re: [Haskell-cafe] Optimization flag changing result of code 
> > execution
> > To: aze...@live.com
> > CC: haskell-cafe@haskell.org
> > 
> > Hey Azeem,have you tried running the same calculation using rationals? 
> > Theres some subtleties to writing numerically stable code using floats and 
> > doubles, where simple optimizations change the orders of operations in ways 
> > that *significantly* change the result. In this case it looks like you're 
> > averaging the averages, which i *believe* can get pretty nasty in terms of 
> > numerical precision.  Rationals would be a bit slower, but you could then 
> > sort out which number is more correct.
> > 
> > 
> > 
> > On Fri, Mar 15, 2013 at 4:07 PM, Azeem -ul-Hasan  wrote:
> > 
> > 
> > 
> > 
> > 
> > I was trying to solve a computational problem form James P Sethna's book 
> > Statistical Mechanics: Entropy, Order Parameters, and Complexity[1]. The 
> > problem is on page 19 of the pdf linked and is titled Six degrees of 
> > separation. For it I came up with this code: http://hpaste.org/84114
> > 
> > 
> >  
> > It runs fine when compiled with -O0 and consistently yields an answer 
> > around 10, but with -O1 and -O2 it consistently gives an answer around 25. 
> > Can somebody explain what is happening here?
> > 
> > 
> > 
> > [1] 
> > http://pages.physics.cornell.edu/~sethna/StatMech/EntropyOrderParametersComplexity.pdf
> > 
> > 
> > 
> > Azeem
> > 
> >   
> > 
> > ___
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> > 
> > 
> > 
> >   
> 
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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-03-16 Thread Roman Cheplyaka
Perhaps the problem is in withSystemRandom, which uses unsafePerformIO?

Does the problem persist if you seed your program with some predefined
seed?

Roman

* Azeem -ul-Hasan  [2013-03-16 13:46:54+0500]
> 
> Hi Carter,
> 
>  Thank you for your help, but I can confirm that this is not due to 
> floating point errors. My own hunch is that it is due to the way I am using 
> random number generation from System.Random.MWC. To check it I wrote a 
> version of mkNetwork function using random number generation from 
> System.Random and it works fine with optimizations turned on. So any ideas 
> why optimizations are messing with System.Random.MWC?
> 
> Azeem
> From: carter.schonw...@gmail.com
> Date: Fri, 15 Mar 2013 17:09:36 -0400
> Subject: Re: [Haskell-cafe] Optimization flag changing result of code 
> execution
> To: aze...@live.com
> CC: haskell-cafe@haskell.org
> 
> Hey Azeem,have you tried running the same calculation using rationals? Theres 
> some subtleties to writing numerically stable code using floats and doubles, 
> where simple optimizations change the orders of operations in ways that 
> *significantly* change the result. In this case it looks like you're 
> averaging the averages, which i *believe* can get pretty nasty in terms of 
> numerical precision.  Rationals would be a bit slower, but you could then 
> sort out which number is more correct.
> 
> 
> 
> On Fri, Mar 15, 2013 at 4:07 PM, Azeem -ul-Hasan  wrote:
> 
> 
> 
> 
> 
> I was trying to solve a computational problem form James P Sethna's book 
> Statistical Mechanics: Entropy, Order Parameters, and Complexity[1]. The 
> problem is on page 19 of the pdf linked and is titled Six degrees of 
> separation. For it I came up with this code: http://hpaste.org/84114
> 
> 
>  
> It runs fine when compiled with -O0 and consistently yields an answer around 
> 10, but with -O1 and -O2 it consistently gives an answer around 25. Can 
> somebody explain what is happening here?
> 
> 
> 
> [1] 
> http://pages.physics.cornell.edu/~sethna/StatMech/EntropyOrderParametersComplexity.pdf
> 
> 
> 
> Azeem
> 
> 
> 
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> 
> 
> 

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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-03-16 Thread Azeem -ul-Hasan

Hi Carter,

 Thank you for your help, but I can confirm that this is not due to 
floating point errors. My own hunch is that it is due to the way I am using 
random number generation from System.Random.MWC. To check it I wrote a version 
of mkNetwork function using random number generation from System.Random and it 
works fine with optimizations turned on. So any ideas why optimizations are 
messing with System.Random.MWC?

Azeem
From: carter.schonw...@gmail.com
Date: Fri, 15 Mar 2013 17:09:36 -0400
Subject: Re: [Haskell-cafe] Optimization flag changing result of code execution
To: aze...@live.com
CC: haskell-cafe@haskell.org

Hey Azeem,have you tried running the same calculation using rationals? Theres 
some subtleties to writing numerically stable code using floats and doubles, 
where simple optimizations change the orders of operations in ways that 
*significantly* change the result. In this case it looks like you're averaging 
the averages, which i *believe* can get pretty nasty in terms of numerical 
precision.  Rationals would be a bit slower, but you could then sort out which 
number is more correct.



On Fri, Mar 15, 2013 at 4:07 PM, Azeem -ul-Hasan  wrote:





I was trying to solve a computational problem form James P Sethna's book 
Statistical Mechanics: Entropy, Order Parameters, and Complexity[1]. The 
problem is on page 19 of the pdf linked and is titled Six degrees of 
separation. For it I came up with this code: http://hpaste.org/84114


 
It runs fine when compiled with -O0 and consistently yields an answer around 
10, but with -O1 and -O2 it consistently gives an answer around 25. Can 
somebody explain what is happening here?



[1] 
http://pages.physics.cornell.edu/~sethna/StatMech/EntropyOrderParametersComplexity.pdf



Azeem

  

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Re: [Haskell-cafe] Optimization flag changing result of code execution

2013-03-15 Thread Carter Schonwald
Hey Azeem,
have you tried running the same calculation using rationals? Theres some
subtleties to writing numerically stable code using floats and doubles,
where simple optimizations change the orders of operations in ways that
*significantly* change the result. In this case it looks like you're
averaging the averages, which i *believe* can get pretty nasty in terms of
numerical precision.  Rationals would be a bit slower, but you could then
sort out which number is more correct.


On Fri, Mar 15, 2013 at 4:07 PM, Azeem -ul-Hasan  wrote:

> I was trying to solve a computational problem form James P Sethna's book
> Statistical Mechanics: Entropy, Order Parameters, and Complexity[1]. The
> problem is on page 19 of the pdf linked and is titled Six degrees of
> separation. For it I came up with this code: http://hpaste.org/84114
>   
> It runs fine when compiled with -O0 and consistently yields an answer
> around 10, but with -O1 and -O2 it consistently gives an answer around 25.
> Can somebody explain what is happening here?
>
> [1]
> http://pages.physics.cornell.edu/~sethna/StatMech/EntropyOrderParametersComplexity.pdf
>
> Azeem
>
>
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[Haskell-cafe] Optimization flag changing result of code execution

2013-03-15 Thread Azeem -ul-Hasan
I was trying to solve a computational problem form James P Sethna's book 
Statistical Mechanics: Entropy, Order Parameters, and Complexity[1]. The 
problem is on page 19 of the pdf linked and is titled Six degrees of 
separation. For it I came up with this code: http://hpaste.org/84114
 
It runs fine when compiled with -O0 and consistently yields an answer around 
10, but with -O1 and -O2 it consistently gives an answer around 25. Can 
somebody explain what is happening here?

[1] 
http://pages.physics.cornell.edu/~sethna/StatMech/EntropyOrderParametersComplexity.pdf

Azeem

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