## ‘numpy.random.normal’ generates different numbers on different systems

I’m comparing using `np.random.normal `

The generated numbers use the following code on two different systems (details below) (I’m using the old version `np.random.seed`

because it is used by another program , I eventually want to verify its output) ^{(1)} :

```
import numpy as np
np.random.seed(0)
x = np.random.normal(scale=1e-3, size=10**5)
np.save('test.npy', x)
```

Then I copied `test.npy`

from one system to another and compared the two versions:

>>> other = np.load('test.npy') >>> (x != other).sum(), len(x) (29, 100000) >>> mask = x != other >>> np.abs(x[mask] - other[mask]) array([5.42101086e-20, 1.35525272e-20, 2.71050543e-20, 5.42101086e-20, 1.08420217e-19, 1.08420217e-19, 2.16840434e-19, 2.16840434e-19, 1.35525272e-20, 1.08420217e-19, 1.08420217e-19, 5.42101086e-20, 2.71050543e-20, 1.08420217e-19, 2.16840434e-19, 5.42101086e-20, 2.71050543e-20, 2.16840434e-19, 2.16840434e-19, 2.71050543e-20, 2.71050543e-20, 1.08420217e-19, 1.08420217e-19, 1.08420217e-19, 5.42101086e-20, 1.08420217e-19, 1.08420217e-19, 5.42101086e-20, 2.71050543e-20]) >>> x[mask] array([ 4.52489093e-04, 9.78961454e-05, -1.47113076e-04, -3.67859222e-04, -5.33279620e-04, 8.40794952e-04, -7.75987295e-04, 1.34205479e-03, 6.34459482e-05, 5.07109360e-04, -7.68363366e-04, 3.33350262e-04, -2.19367067e-04, 6.11402140e-04, -1.30486526e-03, -4.42699624e-04, 1.45463287e-04, -1.22491651e-03, 1.05226781e-03, -2.43032730e-04, -2.40551279e-04, 4.95396595e-04, -7.25454745e-04, -8.50779215e-04, -2.66274662e-04, 7.28854386e-04, 8.38515107e-04, 3.36152654e-04, -1.26550328e-04])

So 29 out of 100,000 elements is a small difference. However, I don’t understand where this difference comes from. I confirm that I have the same version of Python and NumPy installed on both systems: `python==3.9.4`

and numpy==1.20.2 (get ` python by -m pip install numpy==1.20.2`

; ` But I also checked the latest version `

`numpy==1.23.0`

and the result is exactly the same). I verified that the RNG state (via `np.random.get_state())`

was the same on both systems before and after calling `np.random.normal.`

I saved and copied the `test.npy`

file several times, and I also verified it with an MD5 checksum, so the difference must stem from the random number generation itself ^{(1).} However, I don’t see how this is possible, as both are started in the same random state.

## System information

**System A** (the one that holds `test.npy`

):

```
$ uname -a
Linux SystemA 3.10.0-1160.31.1.el7.x86_64 #1 SMP Thu Jun 10 13:32:12 UTC 2021 x86_64 x86_64 x86_64 GNU/Linux
```

(I also tested another system, A2, which installed the same OS version as A, but

with a different CPU, but the result did not change from A to A2, i.e. I suspect the OS version).

**System B** (the system on `which test.npy`

is loaded):

```
$ uname -a
Linux SystemB 5.4.0-113-generic #127-Ubuntu SMP Wed May 18 14:30:56 UTC 2022 x86_64 x86_64 x86_64 GNU/Linux
```

**Footnote (1):** When I use ` When the recommended approach given in the documentation for np.random.seed`

, i.e. `rs = RandomState(MT19937(SeedSequence(0)),`

I found that the differences between the two systems still exist. However, when I use `np.random.default_rng (seed=0)`

instead, that is, the new one `PCG64`

, I noticed that the difference disappeared.

### Solution

Given that the difference is so small, this suggests that the underlying bit generator is doing the same thing. This is just related to the differences between the underlying math libraries.

NumPy legacy Generator uses `sqrt`

and `log`

in `libm`

, and you can see that it extracts these symbols by first finding the shared object that provides the generator:

```
import numpy as np
print(np.random.mtrand.__file__)
```

Then dump the symbol:

```
nm -C -gD mtrand.*.so | grep GLIBC
```

`The mtrand`

file name comes from the output above.

I get a lot of other symbol output, but that might explain the difference.

I’m guessing this is related to the log implementation, so you can test with `the`

following approach:

```
import numpy as np
np.random.seed(0)
x = 2 * np.random.rand(2, 10**5) - 1
r2 = np.sum(x * x, axis=0)
np.save('test-log.npy', np.log(r2))
```

And compare the two systems.