Function step_tile_ref 

pub fn step_tile_ref(
    state: &mut AttnState,
    q: &[bf16],
    k_pool: &[bf16],
    v_pool: &[bf16],
    tile_blocks: &[i32],
    tile_block_counts: &[i32],
    num_seqs: usize,
    num_q_heads: usize,
    num_kv_heads: usize,
    head_dim: usize,
    block_size: usize,
    tile_capacity: usize,
    gqa_ratio: usize,
)

2026-09-25: One tile update over the paged layout [num_blocks, block_size, num_kv_heads, head_dim], with no causal mask. tile_blocks is [num_seqs, tile_capacity], tile_block_counts is [num_seqs]. It runs the kernel’s per-token recurrence in fp32, but sums each dot product sequentially and uses exp where the kernel uses a warp-tree sum and __expf.