Very small number plus zero becomes zero

[crusaderky]

Description

Tiny numbers (float64 ~1e-313) compare as equal to zero. When added to an actual zero, they become zero.
I could reproduce this on CPU, but not on GPU.

import jax
import jax.numpy as xp
import numpy as np

jax.config.update("jax_enable_x64", True)
device = jax.devices("cpu")[0]
x = xp.asarray(2.22507386e-313, dtype=xp.float64, device=device)
y = x + 0.
print(f"{jax.__version__=} {x=} {y=}")  # jax.__version__='0.5.0' x=Array(2.22507386e-313, dtype=float64) y=Array(0., dtype=float64)
assert x == 0.  # Passes
assert x == y  # Passes
np.testing.assert_allclose(y, x)  # Fails

System info (python version, jaxlib version, accelerator, etc.)

WARNING:2025-02-21 12:19:03,076:jax._src.xla_bridge:987: An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.
jax:    0.5.0
jaxlib: 0.5.0
numpy:  2.2.3
python: 3.10.16 | packaged by conda-forge | (main, Dec  5 2024, 14:16:10) [GCC 13.3.0]
device info: cpu-1, 1 local devices"
process_count: 1
platform: uname_result(system='Linux', node='melody', release='6.8.0-53-generic', version='#55-Ubuntu SMP PREEMPT_DYNAMIC Fri Jan 17 15:37:52 UTC 2025', machine='x86_64')


$ nvidia-smi
Fri Feb 21 12:19:03 2025       
+-----------------------------------------------------------------------------------------+
| NVIDIA-SMI 550.120                Driver Version: 550.120        CUDA Version: 12.4     |
|-----------------------------------------+------------------------+----------------------+
| GPU  Name                 Persistence-M | Bus-Id          Disp.A | Volatile Uncorr. ECC |
| Fan  Temp   Perf          Pwr:Usage/Cap |           Memory-Usage | GPU-Util  Compute M. |
|                                         |                        |               MIG M. |
|=========================================+========================+======================|
|   0  NVIDIA GeForce RTX 3080        Off |   00000000:09:00.0  On |                  N/A |
| 36%   34C    P5             43W /  340W |    2139MiB /  10240MiB |      4%      Default |
|                                         |                        |                  N/A |
+-----------------------------------------+------------------------+----------------------+
                                                                                         
+-----------------------------------------------------------------------------------------+
| Processes:                                                                              |
|  GPU   GI   CI        PID   Type   Process name                              GPU Memory |
|        ID   ID                                                               Usage      |
|=========================================================================================|
|    0   N/A  N/A      3358      G   /usr/lib/xorg/Xorg                           1093MiB |
|    0   N/A  N/A      3621      G   /usr/bin/gnome-shell                          203MiB |
|    0   N/A  N/A      5267      G   ...17c7a8468c1673444724fa825054c54bf4f        135MiB |
|    0   N/A  N/A      5314      G   ...erProcess --variations-seed-version        306MiB |
|    0   N/A  N/A      5940      G   ...yOnDemand --variations-seed-version        112MiB |
|    0   N/A  N/A     82923      G   ...17c7a8468c1673444724fa825054c54bf4f        207MiB |
+-----------------------------------------------------------------------------------------+

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[jakevdp]

Thanks for the report: this is expected behavior. JAX operations will generally flush denormals to zero, although this behavior is backend-dependent. We should probably add this to the Sharp Bits doc, but it's mentioned in a few places (e.g. https://docs.jax.dev/en/latest/_autosummary/jax.lax.nextafter.html).