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- Subject: LuaJIT BitOp Bug with large numbers
- From: Eliot Eikenberry <eliot.darkwolf@...>
- Date: Sun, 01 Jan 2012 16:25:24 -0500
I've been spending the weekend trying to gain a deeper understanding of
noise functions and trying to see what interesting things I can get out
of them. After getting through Perlin/Simplex noise and diving into
Worley(Cell) Noise, I discovered what appears to be a bug with the
LuaJIT BitOp library when dealing with exceedingly large numbers.
Namely, i'm experiencing this bug with the BitOp.band function.
Here is the function that I am using to generate sudo random values
(copied from the perlin noise site:
http://freespace.virgin.net/hugo.elias/models/m_perlin.htm)
noise1d = function(x, r)
local n = x * r
n = bit.bxor(bit.lshift(n, 13), n)
n = n * (n * n * 15731 + 789221) + 1376312589
n = (1.0 - bit.band(n, 2147483647) / 1073741824.0)
return n
end
More often than not, this function works as expected and returns the
same output given the same input. But, randomly it fails to do so and
so far i've seen 3 or 4 variations with the same input. I've narrowed
it down to the following 2 lines:
n = n * (n * n * 15731 + 789221) + 1376312589
n = (1.0 - bit.band(n, 2147483647) / 1073741824.0)
If I take away the "+ 1376312589" in the first line above, the problem
vanishes and the function works as expected (the problem seems to also
vanish if I use print(n) in the function call, i had to make a global
table and add things to it instead to see track variables then print it
after everything was done).
I don't suspect this is a value overflow b/c then I would still be
getting the same output given same input every time. I've taken the "+
1376312589" out completely for now since I still get sudo random values,
but the bug is there non the less.
If the entire code is necessary for anyone, i'll happily post I just
thought this post was long enough already...
Here are a few input/output tables that I got (sorry if this comes
through poorly formated):
Columns are: x, r, value of n before the bit.band call, value returned
by function
No addition (without the "+ 1376312589"), always returns the same output
1024 57 1.7203215615285e+30 0.42778676841408
1 57 1.6021743062178e+21 0.42647737916559
2048 57 1.3762572492228e+31 0.4277867898345
2 57 1.2817394447531e+22 -0.57254056073725
3072 57 4.6448682161269e+31 -0.17030489537865
3 57 4.3258706259035e+22 -0.92042765114456
4096 57 1.1010057993782e+32 0.42778679262847
4 57 1.0253915557582e+23 0.052704953588545
2048 57 1.3762572492228e+31 0.4277867898345
0.5 57 1.8991500972246e+20 -0.22280406951904
4096 57 1.1010057993782e+32 0.42778679262847
1 57 1.6021743062178e+21 0.42647737916559
6144 57 -4.5588237152993e+31 -0.24167815316468
1.5 57 5.5027597176147e+21 0.57001950312406
8192 57 -1.6259021345399e+30 0.10560003388673
2 57 1.2817394447531e+22 -0.57254056073725
3072 57 4.6448682161269e+31 -0.17030489537865
0.33333333333333 57 5.9339789228382e+19 0.011558014899492
6144 57 -4.5588237152993e+31 -0.24167815316468
0.66666666666667 57 4.7471831308992e+20 0.02203331887722
9216 57 1.1141983919572e+25 -0.27148926816881
1 57 1.6021743062178e+21 0.42647737916559
12288 57 4.7319886470795e+31 -0.58460648916662
1.3333333333333 57 3.7977465032451e+21 0.024652144871652
4096 57 1.1010057993782e+32 0.42778679262847
0.25 57 2.3739376283201e+19 -0.23824135959148
8192 57 -1.6259021345399e+30 0.10560003388673
0.5 57 1.8991500972246e+20 -0.22280406951904
12288 57 4.7319886470795e+31 -0.58460648916662
0.75 57 6.8784496491036e+20 0.56853779964149
16384 57 -1.3007217076319e+31 0.1056000161916
1 57 1.6021743062178e+21 0.42647737916559
With addition and the most common output
1024 57 1.7203215615285e+30 0.42778676841408
1 57 1.6021743062192e+21 0.42647248972207
2048 57 1.3762572492228e+31 0.4277867898345
2 57 1.2817394447532e+22 -0.57254117168486
3072 57 4.6448682161269e+31 -0.17030489537865
3 57 4.3258706259036e+22 -0.92042780388147
4096 57 1.1010057993782e+32 0.42778679262847
4 57 1.0253915557583e+23 0.052704877220094
2048 57 1.3762572492228e+31 0.4277867898345
0.5 57 1.8991500972383e+20 -0.22284318692982
4096 57 1.1010057993782e+32 0.42778679262847
1 57 1.6021743062192e+21 0.42647248972207
6144 57 -4.5588237152993e+31 -0.24167815316468
1.5 57 5.502759717616e+21 0.57001828029752
8192 57 -1.6259021345399e+30 0.10560003388673
2 57 1.2817394447532e+22 -0.57254117168486
3072 57 4.6448682161269e+31 -0.17030489537865
0.33333333333333 57 5.9339789229759e+19 0.011401546187699
6144 57 -4.5588237152993e+31 -0.24167815316468
0.66666666666667 57 4.747183130913e+20 0.022013760171831
9216 57 1.1141983919572e+25 -0.27148926910013
1 57 1.6021743062192e+21 0.42647248972207
12288 57 4.7319886470795e+31 -0.58460648916662
1.3333333333333 57 3.7977465032465e+21 0.024649700149894
4096 57 1.1010057993782e+32 0.42778679262847
0.25 57 2.3739376284578e+19 -0.23855429701507
8192 57 -1.6259021345399e+30 0.10560003388673
0.5 57 1.8991500972383e+20 -0.22284318692982
12288 57 4.7319886470795e+31 -0.58460648916662
0.75 57 6.8784496491174e+20 0.56852802075446
16384 57 -1.3007217076319e+31 0.1056000161916
1 57 1.6021743062192e+21 0.42647248972207
With addition and an unexpected output, maybe 1 in 10 times of
generating the noise
1024 57 1.7203215615285e+30 0.42778676841408
1 57 1.6021743062192e+21 0.42647248972207
2048 57 1.3762572492228e+31 0.4277867898345
2 57 1.2817394447532e+22 -0.57254117168486
3072 57 4.6448682161269e+31 -0.17030489537865
3 57 4.3258706259036e+22 -0.92042780388147
4096 57 1.1010057993782e+32 0.42778679262847
4 57 1.0253915557583e+23 0.052704877220094
2048 57 1.3762572492228e+31 0.4277867898345
0.5 57 1.8991500972383e+20 -0.22284318692982
4096 57 1.1010057993782e+32 0.42778679262847
1 57 1.6021743062192e+21 0.42647248972207
6144 57 -4.5588237152993e+31 -0.24167815316468
1.5 57 5.502759717616e+21 0.57001828029752
8192 57 -1.6259021345399e+30 0.10560003388673
2 57 1.2817394447532e+22 -0.57254117168486
3072 57 4.6448682161269e+31 -0.17030489537865
0.33333333333333 57 5.9339789229759e+19 0.011401546187699
6144 57 -4.5588237152993e+31 -0.24167815316468
0.66666666666667 57 4.747183130913e+20 0.022013760171831
9216 57 1.1141983919572e+25 -0.27148926910013
1 57 1.6021743062192e+21 -0.85531360469759
12288 57 4.7319886470795e+31 0.13360252697021
1.3333333333333 57 3.7977465032465e+21 0.74286116100848
4096 57 1.1010057993782e+32 -0.85400419123471
0.25 57 2.3739376284578e+19 0.47996765654534
8192 57 -1.6259021345399e+30 0.82380905002356
0.5 57 1.8991500972383e+20 0.49540494661778
12288 57 4.7319886470795e+31 0.13360252697021
0.75 57 6.8784496491174e+20 -0.71325318422168
16384 57 -1.3007217076319e+31 0.82380903232843
1 57 1.6021743062192e+21 -0.85531360469759
With addition, another unexpected output, probably 1 in 25 or so times
of generating the noise
1024 57 1.7203215615285e+30 0.42778676841408
1 57 1.6021743062192e+21 0.42647248972207
2048 57 1.3762572492228e+31 0.4277867898345
2 57 1.2817394447532e+22 -0.57254117168486
3072 57 4.6448682161269e+31 -0.17030489537865
3 57 4.3258706259036e+22 -0.92042780388147
4096 57 1.1010057993782e+32 0.42778679262847
4 57 1.0253915557583e+23 0.052704877220094
2048 57 1.3762572492228e+31 0.4277867898345
0.5 57 1.8991500972383e+20 -0.22284318692982
4096 57 1.1010057993782e+32 0.42778679262847
1 57 1.6021743062192e+21 0.42647248972207
6144 57 -4.5588237152993e+31 -0.24167815316468
1.5 57 5.502759717616e+21 0.57001828029752
8192 57 -1.6259021345399e+30 0.10560003388673
2 57 1.2817394447532e+22 -0.57254117168486
3072 57 4.6448682161269e+31 -0.17030489537865
0.33333333333333 57 5.9339789229759e+19 0.011401546187699
6144 57 -4.5588237152993e+31 -0.24167815316468
0.66666666666667 57 4.747183130913e+20 0.022013760171831
9216 57 1.1141983919572e+25 -0.27148926910013
1 57 1.6021743062192e+21 0.42647248972207
12288 57 4.7319886470795e+31 -0.58460648916662
1.3333333333333 57 3.7977465032465e+21 0.024649700149894
4096 57 1.1010057993782e+32 0.42778679262847
0.25 57 2.3739376284578e+19 -0.23855429701507
8192 57 -1.6259021345399e+30 0.10560003388673
0.5 57 1.8991500972383e+20 -0.22284318692982
12288 57 4.7319886470795e+31 0.13360252697021
0.75 57 6.8784496491174e+20 -0.71325318422168
16384 57 -1.3007217076319e+31 0.82380903232843
1 57 1.6021743062192e+21 -0.85531360469759
