Repository: pytorch
Issue: Tensor.index_reduce produces incorrect result
Labels: high priority,triaged,module: advanced indexing

### 🐛 Describe the bug

Code to reproduce:

```python
import torch

device = torch.device('cpu')
dtype = torch.bfloat16

n = 512

x = torch.tensor([0, 1], dtype=dtype, device=device).repeat(n // 2)
y = torch.zeros(n, device=device, dtype=torch.int32)

print("x[:10] =", x[:10])
print('index_reduce mean :', torch.zeros(1, dtype=dtype, device=device).index_reduce(0, y, x, 'mean').item())
print('mean              :', x.mean().item())
```

Output: 

```
x[:10] = tensor([0., 1., 0., 1., 0., 1., 0., 1., 0., 1.], dtype=torch.bfloat16)
index_reduce mean : 1.0
mean              : 0.5
```

The correct mean of [0, 1, 0, 1, ..., 0, 1] is 0.5, so the result of `index_reduce` is wrong. 

If `n` is 256, the output will be correct. 


### Versions

```
PyTorch version: 2.5.1+cu121
Is debug build: False
CUDA used to build PyTorch: 12.1
ROCM used to build PyTorch: N/A

OS: Ubuntu 22.04.4 LTS (x86_64)
GCC version: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0
Clang version: Could not collect
CMake version: Could not collect
Libc version: glibc-2.35

Python version: 3.12.0 | packaged by Anaconda, Inc. | (main, Oct  2 2023, 17:29:18) [GCC 11.2.0] (64-bit runtime)
Python platform: Linux-5.15.0-112-generic-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: NVIDIA H100 80GB HBM3
GPU 1: NVIDIA H100 80GB HBM3
GPU 2: NVIDIA H100 80GB HBM3
GPU 3: NVIDIA H100 80GB HBM3
GPU 4: NVIDIA H100 80GB HBM3
GPU 5: NVIDIA H100 80GB HBM3
GPU 6: NVIDIA H100 80GB HBM3
GPU 7: NVIDIA H100 80GB HBM3

Nvidia driver version: 535.183.01
cuDNN version: Could not collect
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, 57 bits virtual
Byte Order:                         Little Endian
CPU(s):                             176
On-line CPU(s) list:                0-175
Vendor ID:                          GenuineIntel
Model name:                         Intel(R) Xeon(R) Platinum 8468V
CPU family:                         6
Model:                              143
Thread(s) per core:                 2
Core(s) per socket:                 44
Socket(s):                          2
Stepping:                           8
BogoMIPS:                           4800.00
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 arch_perfmon rep_good nopl xtopology nonstop_tsc cpuid tsc_known_freq pni pclmulqdq vmx ssse3 fma cx16 pdcm pcid sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand hypervisor lahf_lm abm 3dnowprefetch cpuid_fault invpcid_single ssbd ibrs ibpb stibp ibrs_enhanced tpr_shadow vnmi flexpriority ept vpid ept_ad fsgsbase tsc_adjust bmi1 avx2 smep bmi2 erms invpcid avx512f avx512dq rdseed adx smap avx512ifma clflushopt clwb avx512cd sha_ni avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves avx_vnni avx512_bf16 wbnoinvd arat avx512vbmi umip pku ospke waitpkg avx512_vbmi2 gfni vaes vpclmulqdq avx512_vnni avx512_bitalg avx512_vpopcntdq la57 rdpid bus_lock_detect cldemote movdiri movdir64b fsrm md_clear serialize tsxldtrk avx512_fp16 arch_capabilities
Virtualization:                     VT-x
Hypervisor vendor:                  KVM
Virtualization type:                full
L1d cache:                          4.1 MiB (88 instances)
L1i cache:                          2.8 MiB (88 instances)
L2 cache:                           176 MiB (88 instances)
L3 cache:                           195 MiB (2 instances)
NUMA node(s):                       2
NUMA node0 CPU(s):                  0-87
NUMA node1 CPU(s):                  88-175
Vulnerability Gather data sampling: Not affected
Vulnerability Itlb multihit:        Not affected
Vulnerability L1tf:                 Not affected
Vulnerability Mds:                  Not affected
Vulnerability Meltdown:             Not affected
Vulnerability Mmio stale data:      Not affected
Vulnerability Retbleed:             Not affected
Vulnerability Spec rstack overflow: Not affected
Vulnerability Spec store bypass:    Mitigation; Speculative Store Bypass disabled via prctl and seccomp
Vulnerability Spectre v1:           Mitigation; usercopy/swapgs barriers and __user pointer sanitization
Vulnerability Spectre v2:           Mitigation; Enhanced IBRS; IBPB conditional; RSB filling; PBRSB-eIBRS SW sequence; BHI Syscall hardening, KVM SW loop
Vulnerability Srbds:                Not affected
Vulnerability Tsx async abort:      Mitigation; TSX disabled

Versions of relevant libraries:
[pip3] nvidia-cublas-cu12==12.1.3.1
[pip3] nvidia-cuda-cupti-cu12==12.1.105
[pip3] nvidia-cuda-nvrtc-cu12==12.1.105
[pip3] nvidia-cuda-runtime-cu12==12.1.105
[pip3] nvidia-cudnn-cu12==9.1.0.70
[pip3] nvidia-cufft-cu12==11.0.2.54
[pip3] nvidia-curand-cu12==10.3.2.106
[pip3] nvidia-cusolver-cu12==11.4.5.107
[pip3] nvidia-cusparse-cu12==12.1.0.106
[pip3] nvidia-nccl-cu12==2.21.5
[pip3] nvidia-nvjitlink-cu12==12.1.105
[pip3] nvidia-nvtx-cu12==12.1.105
[pip3] torch==2.5.1+cu121
[pip3] triton==3.1.0
[conda] nvidia-cublas-cu12        12.1.3.1                 pypi_0    pypi
[conda] nvidia-cuda-cupti-cu12    12.1.105                 pypi_0    pypi
[conda] nvidia-cuda-nvrtc-cu12    12.1.105                 pypi_0    pypi
[conda] nvidia-cuda-runtime-cu12  12.1.105                 pypi_0    pypi
[conda] nvidia-cudnn-cu12         9.1.0.70                 pypi_0    pypi
[conda] nvidia-cufft-cu12         11.0.2.54                pypi_0    pypi
[conda] nvidia-curand-cu12        10.3.2.106               pypi_0    pypi
[conda] nvidia-cusolver-cu12      11.4.5.107               pypi_0    pypi
[conda] nvidia-cusparse-cu12      12.1.0.106               pypi_0    pypi
[conda] nvidia-nccl-cu12          2.21.5                   pypi_0    pypi
[conda] nvidia-nvjitlink-cu12     12.1.105                 pypi_0    pypi
[conda] nvidia-nvtx-cu12          12.1.105                 pypi_0    pypi
[conda] torch                     2.5.1+cu121              pypi_0    pypi
[conda] triton                    3.1.0                    pypi_0    pypi
```

cc @ezyang @gchanan @zou3519 @kadeng @msaroufim @frank-wei @jgong5 @mingfeima @XiaobingSuper @sanchitintel @ashokei @jingxu10