Expand description
Generic runtime-dispatch transposed matrix–vector product (y += Aᵀ · x).
Plumbs the core register-blocked transposed-GEMV micro-kernel
(hermes_simd_core::tiling::TilingStrategy::gemv_transpose) through runtime
backend selection, the complement of super::gemv(). A is row-major
nrows × ncols, x length nrows, y length ncols; the result
accumulates into y (y += Aᵀ·x), so callers wanting y = Aᵀ·x zero
y first.
§Theorem (output reuse, reduction-free)
Aᵀx = Σᵢ xᵢ·A[i,:] — a sum of the rows of A scaled by x. Each row is
contiguous, so the update vectorizes across the ncols output lanes with no
horizontal reduction (unlike A·x). Blocking TILE_N output lane-chunks of
y in registers reuses each accumulator across all nrows rows and breaks the
per-chunk FMA dependency chain; TILE_N scales with the register file. ∎