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End-to-end split-KV (FlashDecoding-style) for the CK unified attention
kernel. The host launches a single 3D grid with z == num_splits; each
CTA computes its KV-range slice and writes a normalized (o_acc, lse)
partial to FP32 workspaces, which the caller reduces into the final
output.
Pipeline changes:
- operator() returns ck_tile::make_tuple(o_acc, lse) instead of just
o_acc. The masked-empty early-exit returns lse = -inf so downstream
combine weighs the partial as zero.
- LSE is built in the natural-log domain from the pipeline's *unscaled*
rowmax: lse = (scale_s / log2(e)) * m + log(l). Previously we used
m / log2(e) + log(l), which dropped the per-head scale and produced
LSE values ~1/scale too large.
- Fix post-process parity: which SP register is left in the
alu0-done/alu1-pending state at loop exit depends on the parity of
the *iteration count* (= num_total_loop - num_blocks_start), not on
num_total_loop alone. For non-split (num_blocks_start == 0) the two
parities coincide; for splits starting at an odd tile they don't.
- Fix split-KV page-table offset: num_blocks_start is counted in
kPageBlockSize-sized tiles, but block_tables is indexed in
page_size-sized pages — shifting block_table_offset by num_blocks_start
reads the wrong pages whenever kPageBlockSize != page_size. Replaced
with split_token_offset = num_blocks_start * kPageBlockSize added to
logical_token before /page_size, so the page lookup uses the absolute
token position.
Kernel + dispatcher:
- Drop kargs.i_split; each CTA reads i_split = blockIdx.z.
- GridSize{2D,Decode} now take num_splits and add it as the z-dim
(defaults to 1, so non-split callers see dim3(..., 1, 1)).
- New write path: when num_splits > 1, the kernel skips the user
epilogue and instead writes the FP32 (o_acc, lse) tile pair into
workspace tensors at [head, split, batch_start_token, ...] using
Default2DEpilogue (UseRawStore=true) for o_acc and store_tile for
lse. Host strides come from kargs.
Co-authored-by: Cursor <cursoragent@cursor.com>