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,
)

One tile update. Mirrors the CUDA kernel’s per-token online-softmax recurrence exactly (same accumulation order, fp32 throughout).