Repository: pytorch
Issue: The unexpected behavior of `can_cast()`
Labels: triaged,topic: docs,module: python frontend

### 🐛 Describe the bug

[can_cast()](https://pytorch.org/docs/stable/generated/torch.can_cast.html) returns `True` even for the dtypes which are not promotable about type conversion according to [the doc](https://pytorch.org/docs/stable/tensor_attributes.html#type-promotion-doc) as shown below:

```python
import torch

""" From `int64` to `int32` """

torch.can_cast(torch.int64, to=torch.int32) # True

tensor1 = torch.tensor([0, 1, 2], dtype=torch.int32)
tensor2 = torch.tensor([3, 4, 5], dtype=torch.int64)
torch.add(input=tensor1, other=tensor2).dtype # torch.int64

""" From `float64` to `float32` """

torch.can_cast(torch.float64, to=torch.float32) # True

tensor1 = torch.tensor([0., 1., 2.], dtype=torch.float32)
tensor2 = torch.tensor([3., 4., 5.], dtype=torch.float64)
torch.add(input=tensor1, other=tensor2).dtype # torch.float64

""" From `complex64` to `complex32` """

torch.can_cast(torch.complex64, to=torch.complex32) # True

tensor1 = torch.tensor([0.+0.j, 1.+0.j, 2.+0.j], dtype=torch.complex32)
tensor2 = torch.tensor([3.+0.j, 4.+0.j, 5.+0.j], dtype=torch.complex64)
torch.add(input=tensor1, other=tensor2).dtype # torch.complex64
```

And, `can_cast()` returns `False` even for the dtypes which are convertible as shown below:

```python
import torch

""" From `int64` to `bool` """

torch.can_cast(torch.int64, to=torch.bool) # False

my_tensor = torch.tensor([0, 1, 2], dtype=torch.int64)

my_tensor.type(torch.bool) # tensor([False,  True,  True])

""" From `float32` to `int64` """

torch.can_cast(torch.float32, to=torch.int64) # False

my_tensor = torch.tensor([0., 1., 2.], dtype=torch.float32)

my_tensor.type(torch.int64) # tensor([0, 1, 2])
```

### Versions

PyTorch version: N/A
Is debug build: N/A
CUDA used to build PyTorch: N/A
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: version 3.22.1
Libc version: glibc-2.35

Python version: 3.10.12 (main, Nov 20 2023, 15:14:05) [GCC 11.4.0] (64-bit runtime)
Python platform: Linux-6.1.75+-x86_64-with-glibc2.35
Is CUDA available: N/A
CUDA runtime version: Could not collect
CUDA_MODULE_LOADING set to: N/A
GPU models and configuration: Could not collect
Nvidia driver version: Could not collect
cuDNN version: Could not collect
HIP runtime version: N/A
MIOpen runtime version: N/A
Is XNNPACK available: N/A

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): 4
On-line CPU(s) list: 0-3
Vendor ID: GenuineIntel
Model name: Intel(R) Xeon(R) CPU @ 2.20GHz
CPU family: 6
Model: 79
Thread(s) per core: 2
Core(s) per socket: 2
Socket(s): 1
Stepping: 0
BogoMIPS: 4399.99
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 pti ssbd ibrs ibpb stibp fsgsbase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm rdseed adx smap xsaveopt arat md_clear arch_capabilities
Hypervisor vendor: KVM
Virtualization type: full
L1d cache: 64 KiB (2 instances)
L1i cache: 64 KiB (2 instances)
L2 cache: 512 KiB (2 instances)
L3 cache: 55 MiB (1 instance)
NUMA node(s): 1
NUMA node0 CPU(s): 0-3
Vulnerability Gather data sampling: Not affected
Vulnerability Itlb multihit: Not affected
Vulnerability L1tf: Mitigation; PTE Inversion
Vulnerability Mds: Mitigation; Clear CPU buffers; SMT Host state unknown
Vulnerability Meltdown: Mitigation; PTI
Vulnerability Mmio stale data: Vulnerable: Clear CPU buffers attempted, no microcode; SMT Host state unknown
Vulnerability Retbleed: Mitigation; IBRS
Vulnerability Spec rstack overflow: Not affected
Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl
Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization
Vulnerability Spectre v2: Mitigation; IBRS, IBPB conditional, STIBP conditional, RSB filling, PBRSB-eIBRS Not affected
Vulnerability Srbds: Not affected
Vulnerability Tsx async abort: Mitigation; Clear CPU buffers; SMT Host state unknown

Versions of relevant libraries:
[pip3] flake8==3.8.4
[pip3] mypy==1.10.0
[pip3] mypy-extensions==1.0.0
[pip3] numpy==1.26.4
[pip3] optree==0.11.0
[pip3] pyls-mypy==0.1.8
[conda] Could not collect


cc @albanD