Implement product

[oleksandr-pavlyk]

This is PR builds on top of work of #1399 and implements _prod_over_axis and the satellite associated type query function.

In [1]: import dpctl.tensor as dpt
In [2]: import dpctl.tensor._tensor_impl as ti
In [4]: x = dpt.linspace(1, 2, num=32, dtype="f4")
In [5]: x
Out[5]:
usm_ndarray([1. , 1.032258 , 1.0645161, 1.0967741, 1.1290323,
1.1612903, 1.1935483, 1.2258065, 1.2580645, 1.2903225,
1.3225806, 1.3548386, 1.3870968, 1.4193548, 1.4516128,
1.483871 , 1.516129 , 1.548387 , 1.5806451, 1.6129032,
1.6451613, 1.6774192, 1.7096773, 1.7419355, 1.7741935,
1.8064516, 1.8387096, 1.8709677, 1.9032258, 1.9354837,
1.9677418, 2. ], dtype=float32)
In [6]: z = dpt.empty(tuple(), dtype="f4")
In [7]: ti._prod_over_axis(src=x, trailing_dims_to_reduce=1, dst=z, sycl_queue=x.sycl_queue)[0].wait()
In [8]: z
Out[8]: usm_ndarray(224213.45, dtype=float32)
In [9]: dpt.asnumpy(x).prod()
Out[9]: 224213.47

The product runs into problems for complex types, and does not give the expected output for integral types, so this is a work-in-progress.

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• Have you added a test, reproducer or referred to an issue with a reproducer?
• Have you tested your changes locally for CPU and GPU devices?
• Have you made sure that new changes do not introduce compiler warnings?
• Have you checked performance impact of proposed changes?
• If this PR is a work in progress, are you opening the PR as a draft?

[github-actions]

Array API standard conformance tests for dpctl=0.15.1dev0=py310ha25a700_23 ran successfully.
Passed: 930
Failed: 70
Skipped: 119

[github-actions]

Array API standard conformance tests for dpctl=0.15.1dev0=py310ha25a700_23 ran successfully.
Passed: 930
Failed: 70
Skipped: 119

[ndgrigorian]

@oleksandr-pavlyk In testing out a prod implementation, I ran into the same issue with integers. It seems to only happen for 64-bit integers on GPU, CPU worked fine. I believe it's a bug. I didn't test it for 64-bit floats, but I suspect it may have the same problem.

The workaround that I used was a Multiplies struct that returns x * y.

[github-actions]

View rendered docs @ https://intelpython.github.io/dpctl/pulls/1426/index.html

[github-actions]

Array API standard conformance tests for dpctl=0.15.1dev0=py310ha25a700_24 ran successfully.
Passed: 930
Failed: 70
Skipped: 119

[github-actions]

Array API standard conformance tests for dpctl=0.15.1dev0=py310ha25a700_25 ran successfully.
Passed: 934
Failed: 66
Skipped: 119

[github-actions]

Array API standard conformance tests for dpctl=0.15.1dev0=py310ha25a700_26 ran successfully.
Passed: 935
Failed: 65
Skipped: 119

[ndgrigorian]

@oleksandr-pavlyk
I pushed a small change with a tweak to some docstrings.

I think this is good to go in.

[github-actions]

Array API standard conformance tests for dpctl=0.15.1dev0=py310ha25a700_27 ran successfully.
Passed: 935
Failed: 65
Skipped: 119

[github-actions]

Deleted rendered PR docs from intelpython.github.com/dpctl, latest should be updated shortly. 🤞