Repository: pytorch
Issue: inconsistency in ```torch.special.xlogy``` on CPU and GPU
Labels: module: numerical-stability,triaged,module: bfloat16

### 🐛 Describe the bug

inconsistent results of ```torch.special.xlogy``` function on CPU and GPU
```python #
import torch

self = torch.tensor([[-0.6914]], dtype=torch.bfloat16)
other = torch.tensor([[3070.0]], dtype=torch.bfloat16)

result_cpu = torch.special.xlogy(self, other)

self_cuda = self.cuda()
other_cuda = other.cuda()

result_gpu = torch.special.xlogy(self_cuda, other_cuda)

print("CPU result:\n", result_cpu)
print("GPU result:\n", result_gpu)

inconsistent = not torch.allclose(result_cpu, result_gpu.cpu(), atol=1e-02, rtol=1e-03)
print("Inconsistency with atol=1e-02 and rtol=1e-03:", inconsistent)
```
outputs:
```
CPU result:
 tensor([[-5.5312]], dtype=torch.bfloat16)

GPU result:
 tensor([[-5.5625]], device='cuda:0', dtype=torch.bfloat16)

Inconsistency with atol=1e-02 and rtol=1e-03: True
```

### Versions

(executed on google colab)
PyTorch version: 2.5.0+cu121
Is debug build: False
CUDA used to build PyTorch: 12.1
ROCM used to build PyTorch: N/A

OS: Ubuntu 22.04.3 LTS (x86_64)
GCC version: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0
Clang version: 14.0.0-1ubuntu1.1
CMake version: version 3.30.5
Libc version: glibc-2.35

Python version: 3.10.12 (main, Sep 11 2024, 15:47:36) [GCC 11.4.0] (64-bit runtime)
Python platform: Linux-6.1.85+-x86_64-with-glibc2.35
Is CUDA available: True
CUDA runtime version: 12.2.140
CUDA_MODULE_LOADING set to: LAZY
GPU models and configuration: GPU 0: Tesla T4
Nvidia driver version: 535.104.05
cuDNN version: Probably one of the following:
/usr/lib/x86_64-linux-gnu/libcudnn.so.8.9.6
/usr/lib/x86_64-linux-gnu/libcudnn_adv_infer.so.8.9.6
/usr/lib/x86_64-linux-gnu/libcudnn_adv_train.so.8.9.6
/usr/lib/x86_64-linux-gnu/libcudnn_cnn_infer.so.8.9.6
/usr/lib/x86_64-linux-gnu/libcudnn_cnn_train.so.8.9.6
/usr/lib/x86_64-linux-gnu/libcudnn_ops_infer.so.8.9.6
/usr/lib/x86_64-linux-gnu/libcudnn_ops_train.so.8.9.6
HIP runtime version: N/A
MIOpen runtime version: N/A
Is XNNPACK available: True

CPU:
Architecture: x86_64
CPU op-mode(s): 32-bit, 64-bit
Address sizes: 46 bits physical, 48 bits virtual
Byte Order: Little Endian
CPU(s): 2
On-line CPU(s) list: 0,1
Vendor ID: GenuineIntel
Model name: Intel(R) Xeon(R) CPU @ 2.00GHz
CPU family: 6
Model: 85
Thread(s) per core: 2
Core(s) per socket: 1
Socket(s): 1
Stepping: 3
BogoMIPS: 4000.31
Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ss ht syscall nx pdpe1gb rdtscp lm constant_tsc rep_good nopl xtopology nonstop_tsc cpuid tsc_known_freq pni pclmulqdq ssse3 fma cx16 pcid sse4_1 sse4_2 x2apic movbe popcnt aes xsave avx f16c rdrand hypervisor lahf_lm abm 3dnowprefetch invpcid_single ssbd ibrs ibpb stibp fsgsbase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm mpx avx512f avx512dq rdseed adx smap clflushopt clwb avx512cd avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves arat md_clear arch_capabilities
Hypervisor vendor: KVM
Virtualization type: full
L1d cache: 32 KiB (1 instance)
L1i cache: 32 KiB (1 instance)
L2 cache: 1 MiB (1 instance)
L3 cache: 38.5 MiB (1 instance)
NUMA node(s): 1
NUMA node0 CPU(s): 0,1
Vulnerability Gather data sampling: Not affected
Vulnerability Itlb multihit: Not affected
Vulnerability L1tf: Mitigation; PTE Inversion
Vulnerability Mds: Vulnerable; SMT Host state unknown
Vulnerability Meltdown: Vulnerable
Vulnerability Mmio stale data: Vulnerable
Vulnerability Reg file data sampling: Not affected
Vulnerability Retbleed: Vulnerable
Vulnerability Spec rstack overflow: Not affected
Vulnerability Spec store bypass: Vulnerable
Vulnerability Spectre v1: Vulnerable: __user pointer sanitization and usercopy barriers only; no swapgs barriers
Vulnerability Spectre v2: Vulnerable; IBPB: disabled; STIBP: disabled; PBRSB-eIBRS: Not affected; BHI: Vulnerable (Syscall hardening enabled)
Vulnerability Srbds: Not affected
Vulnerability Tsx async abort: Vulnerable

Versions of relevant libraries:
[pip3] numpy==1.26.4
[pip3] nvidia-cublas-cu12==12.6.3.3
[pip3] nvidia-cuda-cupti-cu12==12.6.80
[pip3] nvidia-cuda-runtime-cu12==12.6.77
[pip3] nvidia-cudnn-cu12==9.5.1.17
[pip3] nvidia-cufft-cu12==11.3.0.4
[pip3] nvidia-curand-cu12==10.3.7.77
[pip3] nvidia-cusolver-cu12==11.7.1.2
[pip3] nvidia-cusparse-cu12==12.5.4.2
[pip3] nvidia-nccl-cu12==2.23.4
[pip3] nvidia-nvjitlink-cu12==12.6.77
[pip3] nvtx==0.2.10
[pip3] optree==0.13.0
[pip3] pynvjitlink-cu12==0.4.0
[pip3] torch==2.5.0+cu121
[pip3] torchaudio==2.5.0+cu121
[pip3] torchsummary==1.5.1
[pip3] torchvision==0.20.0+cu121
[conda] Could not collect