Fix: Types in sparse dot-products generic macro

[real-eren]

Re: types
The dot-product intrinsics _mm256_dpbf16_ps, _mm256_dpwssd_epi32, and svbfdot_f32 each widen the values before multiplying them, so the scalar algorithm should also do that. Also, the macro currently uses the counter_type, which is an unsigned int.

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Re: saturating addition
Same links, none of them perform saturating addition other than the currently used _mm256_dpwssds_epi32, so the current spdot_counts_u16_turin kernel is the odd one out.

[ashvardanian]

Would it be hard to use saturating addition everywhere? I can imagine receiving really large inputs in those functions.

PS: Thanks for following the commit naming convention!

[real-eren]

Would it be hard to use saturating addition everywhere? I can imagine receiving really large inputs in those functions.

Good point.

bf16

Would overflowing into infinity be the desired behavior? Edit: should be signaling NaN. I think you could check for infinity at the end and replace it with NaN.

i16

Scalar

add_sat (Edit: C++26, not usable here)

AVX512

_mm256_dpwssds_epi32 for inside the loop

No intrinsic for saturating horizontal add, but can easily adapt the reduce_add_epi32 routine from the earlier PR to use saturating adds. Edit: Would need to emulate for adds_epi32.

SVE2

I don't see a dot product intrinsic with saturation built-in, but here's an idea for inside the loop:

auto tmp = svdot_s64(zero_vec, a_weights_vec, b_equal_weights_vec);
product_vec = svaddq_s64_z(svptrue_b64(), product_vec, tmp);

I'm unfamiliar with SVE, so take the above with a grain of salt.

[real-eren]

I realize now that there are some subtleties to handling overflows in each backend, both for the implementation and the API design, so I will open a separate issue for that.

[ashvardanian]

Thank you @real-eren! Sorry, I forgot to merge this sooner 🤦‍♂️