aloha1357 opened a new pull request, #1390:
URL: https://github.com/apache/mahout/pull/1390
### Related Issues
<!-- Closes #123 -->
related #1385
### Changes
- [ ] Bug fix
- [x] New feature
- [ ] Refactoring
- [ ] Documentation
- [ ] Test
- [ ] CI/CD pipeline
- [ ] Other
### Why
As established in the previous Kronecker Decomposition PR, a significant
bottleneck in processing high-qubit circuits ($N \ge 14$) is memory. A
traditional $O(4^N)$ matrix representation for the full Dense Hadamard
transform completely exhausts modern GPU VRAM limits (causing Out-Of-Memory
errors).
Even with the Kronecker Decomposition splitting the matrix into smaller
blocks, generating and storing the explicit dense $H$ matrices in memory before
applying Tensor Core operations is highly inefficient.
We need a way to perform Dense Matrix Multiplications (GEMM) on the Tensor
Cores *without ever storing the Hadamard Matrix in Global Memory*.
### How
This PR introduces the **Matrix-Free Implicit Hadamard Ozaki Engine**.
- **Implicit Matrix Generation:** The `ImplicitHadamardOzakiEngine`
leverages the structural properties of the Hadamard matrix ($h_{i,j} =
(-1)^{\text{popc}(i \& j)}$) to calculate the matrix elements *on-the-fly*
directly inside Shared Memory.
- **Ozaki Multi-pass Tensor Core Execution:** Using the Ozaki INT8 scheme,
we utilize the `.m16n8k32.s8` Tensor Core instructions to perform the GEMM
natively in hardware. Because the Hadamard values are always $\pm 1$, we
experience absolutely zero quantization error despite using the INT8 pipeline.
- **Removed Fallback:** Replaced the `naive_implicit_hadamard_gemm_kernel`
placeholder from PR 4 with the actual calls to
`engine.execute_implicit_hadamard`.
- **Build System Fix:** Updated `build.rs` to drop the unsupported `sm_75`
(Turing) target fallback, as this specific Tensor Core instruction explicitly
requires `sm_80` (Ampere) or higher.
## Checklist
- [x] Added or updated unit tests for all changes (Verified passing against
existing CI test suite)
- [x] Added or updated documentation for all changes (Added explanatory
inline comments for PR)
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