[CUDA] Use accumulate type to improve accuracy of grid_sample on half precision inputs [v2] (#96586)
Fixes #96429
This PR is also a follow up for #90427. In that PR, we also discussed whether calculations of grid indices `grid_sampler_compute_source_index` should also be upcasted to `opmath_t` https://github.com/pytorch/pytorch/pull/90427/files#r1048876708. Due to another unit test failure, we didn't upcast those calculations in that PR.
After some investigations, I found that the inaccurate results have nothing to do with the internals of `affine_grid`, even if it's calculated using `double` internally. As long as input `grid` is passed to `grid_sample` in **half** precision, the results will be less inaccurate than a **float** `grid`. This can be verified with a short C++ program like this (by setting `TYPE_T` to `__half` and `float` in compilations)
```cpp
#include <cuda.h>
#include <cuda_runtime.h>
#include <cuda_fp16.h>
#include <iostream>
#ifndef TYPE_T
#define TYPE_T float
#endif
int main() {
using type_t = TYPE_T;
type_t d = static_cast<__half>((double)2.0 / 3.0);
type_t s = (((float)d + 1.f) * 3 - 1) / 2;
printf("%.15f %.15f\n", (double)d, (double)s);
}
```
Outputs are
```
./float.out
0.666503906250000 1.999755859375000
./half.out
0.666503906250000 2.000000000000000
```
To resolve the discussion back in https://github.com/pytorch/pytorch/pull/90427/files#r1048876708, I've also increased the test tolerance in the failed unit test `issue_24823_1(torch.half)`.
For the original script in #96429, I got more accurate results with `align_corners = True`
```
align_corners = True
Expected result has mean absolute value of 0.5285 and maximum absolute value of 3.2067.
Half precision result is off by 0.0001 (0.02%) on average and 0.0010 (0.03%) at maximum.
align_corners = False
Expected result has mean absolute value of 0.5189 and maximum absolute value of 3.0101.
Half precision result is off by 0.0001 (0.02%) on average and 0.0010 (0.03%) at maximum.
```
Pull Request resolved: https://github.com/pytorch/pytorch/pull/96586
Approved by: https://github.com/ngimel
pytorch
1716709d - [CUDA] Use accumulate type to improve accuracy of grid_sample on half precision inputs [v2] (#96586)
