perf(math): accelerate FHT with SIMD

[zhangzhenghao]

Summary

• keep the FHT implementation in internal/ailego/math and add runtime-dispatched AVX2, AVX-512, and NEON kernels
• generate pure-Go assembly with GoAT from C sources under internal/ailego/math/src, following the layout used by internal/floats
• retain scalar fallbacks for noasm, unsupported CPUs, short inputs, and architecture-safe AVX-512 fallback paths
• add SIMD-vs-scalar coverage for sign flips, Kac walks, inverse walks, and in-place transforms, including tails and odd lengths

Verification

• go test ./... -count=1
• go test -tags noasm ./... -count=1
• go vet ./...
• GODEBUG=cpu.avx2=off go test ./internal/ailego/math -run '^TestFHTAVX512ScalarFallback$' -count=1
• ARM64 test binary under QEMU: TestFHTNEON
• Windows amd64 cross-compilation for internal/ailego/math and internal/core/algorithm
• make -C internal/ailego/math generate followed by a clean generated diff

Benchmark (1024 floats, amd64 AVX2 host)

• FHTInPlace: ~3.76 µs SIMD vs ~7.51 µs scalar (noasm)
• FHTKacWalk: ~72.7 ns SIMD vs ~550 ns scalar (noasm)

[cloudflare-workers-and-pages]

Deploying with    Cloudflare Workers

The latest updates on your project. Learn more about integrating Git with Workers.

Status	Name	Latest Commit	Updated (UTC)
❌ Deployment failed View logs	xvec	e41b494	Aug 31 2026, 10:28 AM

[codecov]

Codecov Report

❌ Patch coverage is 80.59701% with 13 lines in your changes missing coverage. Please review.
✅ Project coverage is 82.38%. Comparing base (69c503e) to head (e41b494).

Files with missing lines	Patch %	Lines
internal/ailego/math/fht_amd64.go	74.50%	13 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #33      +/-   ##
==========================================
- Coverage   82.39%   82.38%   -0.01%     
==========================================
  Files         121      122       +1     
  Lines       26011    26066      +55     
==========================================
+ Hits        21431    21474      +43     
- Misses       4580     4592      +12     

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.