[Example] Handle Scenarios in Which a Threadblock is Assigned Only Invalid...

[Example] Handle Scenarios in Which a Threadblock is Assigned Only Invalid Block Indices for Sparse Attention  (#361)

* Fix issue where threadblock with only invalid blocks produces incorrect output.

* fix score scale

* format

examples/blocksparse_attention/example_tilelang_sparse_gqa_decode_varlen_indice.py

@@ -16,8 +16,8 @@ def flashattn(batch, heads, heads_kv, dim, dim_v):
     accum_dtype = "float"
     kv_group_num = heads // heads_kv
 
-
-    def kernel_func(block_N, block_H, num_split, num_stages, threads, max_cache_seqlen, max_selected_blocks):
+    def kernel_func(block_N, block_H, num_split, num_stages, threads, max_cache_seqlen,
+                    max_selected_blocks):
         shape_q = [batch, heads, dim]
         shape_k = [batch, max_cache_seqlen, heads_kv, dim]
         shape_v = [batch, max_cache_seqlen, heads_kv, dim_v]
@@ -52,8 +52,7 @@ def flashattn(batch, heads, heads_kv, dim, dim_v):
                 scores_scale = T.alloc_fragment([block_H], accum_dtype)
                 scores_sum = T.alloc_fragment([block_H], accum_dtype)
                 logsum = T.alloc_fragment([block_H], accum_dtype)
-                has_valid_block=T.alloc_var("bool")
-                # num_blocks = T.alloc_local([1], "int32")
+                has_valid_block = T.alloc_var("bool")
 
                 bid = bx
                 hid = by
@@ -64,21 +63,19 @@ def flashattn(batch, heads, heads_kv, dim, dim_v):
                 T.fill(acc_o, 0)
                 T.fill(logsum, 0)
                 T.fill(scores_max, -T.infinity(accum_dtype))
-                # num_blocks = actual_num_blocks[bid]
+
                 num_blocks = max_selected_blocks
                 blocks_per_split = T.floordiv(num_blocks, num_split)
                 remaining_blocks = T.floormod(num_blocks, num_split)
                 loop_range = (blocks_per_split + T.if_then_else(sid < remaining_blocks, 1, 0))
                 start = blocks_per_split * sid + T.min(sid, remaining_blocks)
-                has_valid_block=False
+                has_valid_block = False
                 # if (start < num_blocks):
                 for k in T.Pipelined(loop_range, num_stages=num_stages):
-                    i_s = block_indices[bid, cur_kv_head, start + k] 
+                    i_s = block_indices[bid, cur_kv_head, start + k]
                     if i_s >= 0:
                         has_valid_block = True
-                        T.copy(
-                            K[bid, i_s * block_N: (i_s + 1) * block_N,
-                            cur_kv_head, :], K_shared)
+                        T.copy(K[bid, i_s * block_N:(i_s + 1) * block_N, cur_kv_head, :], K_shared)
                         T.clear(acc_s)
                         T.gemm(
                             Q_shared,
@@ -86,14 +83,19 @@ def flashattn(batch, heads, heads_kv, dim, dim_v):
                             acc_s,
                             transpose_B=True,
                             policy=T.GemmWarpPolicy.FullRow)
-                        if k == 0: # assume block_indices is sorted in reverse order, otherwise, remove this if condition
+                        if k == 0:  # assume block_indices is sorted in reverse order, otherwise, remove this if condition
                             for i, j in T.Parallel(block_H, block_N):
-                                acc_s[i, j] = T.if_then_else(i_s * block_N + j >= cache_seqlens[bid], -T.infinity(accum_dtype), acc_s[i, j])
+                                acc_s[i,
+                                      j] = T.if_then_else(i_s * block_N + j >= cache_seqlens[bid],
+                                                          -T.infinity(accum_dtype), acc_s[i, j])
                         T.copy(scores_max, scores_max_prev)
                         T.fill(scores_max, -T.infinity(accum_dtype))
                         T.reduce_max(acc_s, scores_max, dim=1, clear=False)
                         for i in T.Parallel(block_H):
-                            scores_scale[i] = T.exp2(scores_max_prev[i] * scale - scores_max[i] * scale)
+                            scores_max[i] = T.if_then_else(scores_max[i] > scores_max_prev[i],
+                                                           scores_max[i], scores_max_prev[i])
+                            scores_scale[i] = T.exp2(scores_max_prev[i] * scale -
+                                                     scores_max[i] * scale)
                         for i, j in T.Parallel(block_H, block_N):
                             acc_s[i, j] = T.exp2(acc_s[i, j] * scale - scores_max[i] * scale)
                         T.reduce_sum(acc_s, scores_sum, dim=1)
@@ -102,17 +104,15 @@ def flashattn(batch, heads, heads_kv, dim, dim_v):
                         T.copy(acc_s, acc_s_cast)
                         for i, j in T.Parallel(block_H, dim_v):
                             acc_o[i, j] *= scores_scale[i]
-                        T.copy(
-                            V[bid, i_s * block_N: (i_s + 1) * block_N,
-                            cur_kv_head, :], V_shared)
+                        T.copy(V[bid, i_s * block_N:(i_s + 1) * block_N, cur_kv_head, :], V_shared)
                         T.gemm(acc_s_cast, V_shared, acc_o, policy=T.GemmWarpPolicy.FullRow)
                 if has_valid_block:
                     for i, j in T.Parallel(block_H, dim_v):
                         acc_o[i, j] /= logsum[i]
-                    
+
                     for i in T.Parallel(block_H):
                         logsum[i] = T.log2(logsum[i]) + scores_max[i] * scale
-                
+
                 for i in T.Parallel(block_H):
                     if i < valid_block_H:
                         glse[bid, hid * valid_block_H + i, sid] = logsum[i]
@@ -120,7 +120,7 @@ def flashattn(batch, heads, heads_kv, dim, dim_v):
                 for i, j in T.Parallel(block_H, dim_v):
                     if i < valid_block_H:
                         Output_partial[bid, hid * valid_block_H + i, sid, j] = acc_o[i, j]
-                              
+
         @T.macro
         def combine(
                 glse: T.Tensor([batch, heads, num_split], accum_dtype),
@@ -134,31 +134,38 @@ def flashattn(batch, heads, heads_kv, dim, dim_v):
                 lse_logsum_local = T.alloc_local([1], accum_dtype)
                 lse_max_local = T.alloc_local([1], accum_dtype)
                 scale_local = T.alloc_local([1], accum_dtype)
+                max_split = T.alloc_local([1], "int32")
 
                 T.annotate_layout({
-                    lse_logsum_local: T.Fragment(lse_logsum_local.shape, forward_thread_fn=lambda i: i),
+                    lse_logsum_local:
+                        T.Fragment(lse_logsum_local.shape, forward_thread_fn=lambda i: i),
                 })
 
                 T.clear(lse_logsum_local)
                 T.clear(o_accum_local)
                 lse_max_local[0] = -T.infinity(accum_dtype)
                 for k in T.serial(num_split):
-                    lse_max_local[0] = T.max(lse_max_local[0], glse[bz, by, k])
-                for k in T.Pipelined(num_split, num_stages=1):
                     lse_local_split[0] = glse[bz, by, k]
-                    lse_logsum_local[0] += T.exp2(lse_local_split[0] - lse_max_local[0])
+                    if (lse_local_split[0] != 0):
+                        max_split[0] = k
+                        lse_max_local[0] = T.max(lse_max_local[0], glse[bz, by, k])
+
+                for k in T.Pipelined(num_split, num_stages=1):
+                    if k <= max_split[0]:
+                        lse_local_split[0] = glse[bz, by, k]
+                        lse_logsum_local[0] += T.exp2(lse_local_split[0] - lse_max_local[0])
                 lse_logsum_local[0] = T.log2(lse_logsum_local[0]) + lse_max_local[0]
                 for k in T.serial(num_split):
-                    for i in T.Parallel(dim_v):
-                        po_local[i] = Output_partial[bz, by, k, i]
-                    lse_local_split[0] = glse[bz, by, k]
-                    scale_local[0] = T.exp2(lse_local_split[0] - lse_logsum_local[0])
-                    for i in T.Parallel(dim_v):
-                        o_accum_local[i] += po_local[i] * scale_local[0]
+                    if k <= max_split[0]:
+                        for i in T.Parallel(dim_v):
+                            po_local[i] = Output_partial[bz, by, k, i]
+                        lse_local_split[0] = glse[bz, by, k]
+                        scale_local[0] = T.exp2(lse_local_split[0] - lse_logsum_local[0])
+                        for i in T.Parallel(dim_v):
+                            o_accum_local[i] += po_local[i] * scale_local[0]
                 for i in T.Parallel(dim_v):
                     Output[bz, by, i] = o_accum_local[i]
 
-        
         @T.prim_func
         def main(
                 Q: T.Tensor(shape_q, dtype),
@@ -181,6 +188,7 @@ def flashattn(batch, heads, heads_kv, dim, dim_v):
 
 
 class SparseFlashAttn(torch.nn.Module):
+
     def __init__(self, batch, heads, heads_kv, dim, dim_v, block_size):
         super(SparseFlashAttn, self).__init__()
         self.batch = batch
@@ -199,15 +207,10 @@ class SparseFlashAttn(torch.nn.Module):
             num_stages=2,
             threads=128,
             max_cache_seqlen=T.symbolic("max_cache_seqlen"),
-            max_selected_blocks=T.symbolic("max_selected_blocks")
-        )
+            max_selected_blocks=T.symbolic("max_selected_blocks"))
 
         self.kernel = tilelang.compile(
-            program,
-            out_idx=-1,
-            target='cuda',
-            execution_backend="cython"
-        )
+            program, out_idx=-1, target='cuda', execution_backend="cython")
 
         props = torch.cuda.get_device_properties(torch.device("cuda:0"))
         self.num_sm = props.multi_processor_count
@@ -218,7 +221,6 @@ class SparseFlashAttn(torch.nn.Module):
         heads_kv = self.heads_kv
         dim_v = self.dim_v
         block_size = self.block_size
-        block_H = self.block_H
         max_selected_blocks = block_indices.shape[-1]
 
         # Compute static scheduling parameters
@@ -226,14 +228,18 @@ class SparseFlashAttn(torch.nn.Module):
         num_n_blocks = max_selected_blocks
         size_one_kv_head = max_selected_blocks * block_size * (dim + dim_v) * 2
         total_mblocks = batch * heads_kv * num_m_blocks
-        # num_sm = 132
+
         num_sm = self.num_sm
 
         num_split = num_splits_heuristic(
-            total_mblocks, num_sm, num_n_blocks, num_m_blocks,
-            size_one_kv_head, is_causal_or_local=True, max_splits=128
-        )
-
+            total_mblocks,
+            num_sm,
+            num_n_blocks,
+            num_m_blocks,
+            size_one_kv_head,
+            is_causal_or_local=True,
+            max_splits=128)
+        # print("num_split: ", num_split)
         # Function to compile
         # def compute_actual_num_blocks(block_indices):
         #     actual_num_blocks = torch.sum(block_indices != -1, dim=-1).to(torch.int32)
@@ -242,20 +248,20 @@ class SparseFlashAttn(torch.nn.Module):
         # compiled_fn = torch.compile(compute_actual_num_blocks)
         # actual_num_blocks = compiled_fn(block_indices)
         glse = torch.empty((batch, heads, num_split), dtype=torch.float32, device='cuda')
-        output_partial = torch.empty((batch, heads, num_split, dim_v), dtype=torch.float32, device='cuda')
+        output_partial = torch.empty((batch, heads, num_split, dim_v),
+                                     dtype=torch.float32,
+                                     device='cuda')
 
-        
         # output = self.kernel(
         #     query, key, value, block_indices, cache_seqlens,
         #     actual_num_blocks, glse, output_partial
         # )
-        output = self.kernel(
-            query, key, value, block_indices, cache_seqlens,
-            glse, output_partial
-        )
+        output = self.kernel(query, key, value, block_indices, cache_seqlens, glse, output_partial)
         return output
 
-def sparse_gqa_decode_varlen_indice(query, key, value, block_indices, cache_seqlens, max_cache_seqlen, block_size):
+
+def sparse_gqa_decode_varlen_indice(query, key, value, block_indices, cache_seqlens,
+                                    max_cache_seqlen, block_size):
     """
     Args:
         query: [batch, heads, dim]
@@ -269,34 +275,48 @@ def sparse_gqa_decode_varlen_indice(query, key, value, block_indices, cache_seql
         output: [batch, heads, dim_v]
 
     """
-    
+
     batch, heads, dim = query.shape
     heads_kv = key.shape[2]
     dim_v = value.shape[-1]
     max_selected_blocks = block_indices.shape[-1]
     block_H = 64
 
-
     actual_num_blocks = torch.sum(block_indices != -1, dim=-1).to(torch.int32)
-    actual_num_blocks = actual_num_blocks[:,0] #[batch],  number of valid blocks, assum all groups in the same batch have the same number of blocks
-   
+    actual_num_blocks = actual_num_blocks[:,
+                                          0]  #[batch],  number of valid blocks, assume all groups in the same batch have the same number of blocks
+
     # get num_split
     num_m_blocks = 1 * (heads // heads_kv + block_H - 1) // block_H
-    num_n_blocks = max_selected_blocks#(kv_seqlen  + block_size - 1 ) // block_size
+    num_n_blocks = max_selected_blocks  #(kv_seqlen  + block_size - 1 ) // block_size
     # num_n_blocks = torch.sum(actual_num_blocks, dim=-1).item() * heads_kv # total number of blocks
 
-    size_one_kv_head = max_selected_blocks * block_size * (dim + dim_v) * 2 #kv_seqlen * (dim + dim_v) * 2
+    size_one_kv_head = max_selected_blocks * block_size * (
+        dim + dim_v) * 2  #kv_seqlen * (dim + dim_v) * 2
     total_mblocks = batch * heads_kv * num_m_blocks
     num_sm = 132
-    num_split = num_splits_heuristic(total_mblocks, num_sm, num_n_blocks, num_m_blocks, size_one_kv_head, is_causal_or_local=True, max_splits=128)
-   
-    program = flashattn(
-        batch, heads, heads_kv, dim, dim_v)(
-                block_N=block_size, block_H=block_H, num_split=T.symbolic("num_split"), num_stages=2, threads=128, 
-                max_cache_seqlen=T.symbolic("max_cache_seqlen"), max_selected_blocks=T.symbolic("max_selected_blocks"))
+    num_split = num_splits_heuristic(
+        total_mblocks,
+        num_sm,
+        num_n_blocks,
+        num_m_blocks,
+        size_one_kv_head,
+        is_causal_or_local=True,
+        max_splits=128)
+
+    program = flashattn(batch, heads, heads_kv, dim, dim_v)(
+        block_N=block_size,
+        block_H=block_H,
+        num_split=T.symbolic("num_split"),
+        num_stages=2,
+        threads=128,
+        max_cache_seqlen=T.symbolic("max_cache_seqlen"),
+        max_selected_blocks=T.symbolic("max_selected_blocks"))
 
     glse = torch.empty((batch, heads, num_split), dtype=torch.float32, device='cuda')
-    Output_partial = torch.empty((batch, heads, num_split, dim_v), dtype=torch.float32, device='cuda')
+    Output_partial = torch.empty((batch, heads, num_split, dim_v),
+                                 dtype=torch.float32,
+                                 device='cuda')
     kernel = tilelang.compile(program, out_idx=-1, target='cuda', execution_backend="cython")
     # print(kernel.get_kernel_source())
 
@@ -304,11 +324,12 @@ def sparse_gqa_decode_varlen_indice(query, key, value, block_indices, cache_seql
     output = kernel(query, key, value, block_indices, cache_seqlens, glse, Output_partial)
     return output
 
-def ref_program_torch(query, key, value,  block_indices, cache_seqlens, max_cache_seqlen, num_blocks, block_size):
+
+def ref_program_torch(query, key, value, block_indices, cache_seqlens, max_cache_seqlen, num_blocks,
+                      block_size):
 
     batch, heads, dim = query.shape
     heads_kv = key.shape[2]
-    dim_v = value.shape[-1]
     num_head_groups = query.shape[1] // key.shape[2]
     scale = dim**0.5
     key = rearrange(key, 'b n h d -> b h n d')  # [batch_size, heads_kv, seqlen_kv, dim]
@@ -329,13 +350,12 @@ def ref_program_torch(query, key, value,  block_indices, cache_seqlens, max_cach
             valid_indices = block_indices[b, h]  # Extract indices for this batch and head
             for idx in valid_indices:
                 if idx >= 0:
-                    sparse_mask[b, :, h, idx * block_size: (idx + 1) * block_size] = 1
+                    sparse_mask[b, :, h, idx * block_size:(idx + 1) * block_size] = 1
     scores = scores.masked_fill(sparse_mask == 0, float('-inf'))
-    
 
     range_len = torch.arange(scores.shape[-1], device='cuda').unsqueeze(0)
     cache_seqlens_expanded = cache_seqlens.unsqueeze(1)
-    pad_mask = range_len >= cache_seqlens_expanded     
+    pad_mask = range_len >= cache_seqlens_expanded
     pad_mask = pad_mask[:, None, None, :]
     scores = scores.masked_fill(pad_mask, float('-inf'))
     attention = F.softmax(
@@ -347,35 +367,40 @@ def ref_program_torch(query, key, value,  block_indices, cache_seqlens, max_cach
     return out
 
 
-def ref_program_fa(query, key, value,  block_indices, cache_seqlens, max_cache_seqlen, num_blocks, block_size):
+def ref_program_fa(query, key, value, block_indices, cache_seqlens, max_cache_seqlen, num_blocks,
+                   block_size):
     # latency reference
-    # from flash_attn_interface import flash_attn_with_kvcache, flash_attn_func # fa3
-    from flash_attn import flash_attn_with_kvcache, flash_attn_func #fa2
+    # from flash_attn_interface import flash_attn_with_kvcache # fa3
+    from flash_attn import flash_attn_with_kvcache  #fa2
     query = query.unsqueeze(1)
     output = flash_attn_with_kvcache(query, key, value, cache_seqlens=cache_seqlens)
     output = output.squeeze(1)
     return output
 
 
-
-def debug(name,expect, actual, atol=1e-3, rtol=1e-3):
+def debug(name, expect, actual, atol=1e-3, rtol=1e-3):
     all_close = torch.allclose(expect, actual, atol=atol, rtol=rtol)
     print(name + "  all_close={}".format(all_close))
     if not all_close:
         # print(expect[3, 28])
         # print(actual[3, 28])
         diff = (expect - actual).abs()
-        print("all_close={}, max={}, min={}, mean={}".format(all_close, diff.max().item(), diff.min().item(), diff.mean().item()))
-        max_indices  = torch.nonzero(diff == diff.max().item())
+        print("all_close={}, max={}, min={}, mean={}".format(all_close,
+                                                             diff.max().item(),
+                                                             diff.min().item(),
+                                                             diff.mean().item()))
+        max_indices = torch.nonzero(diff == diff.max().item())
         first_index = tuple(max_indices[0].tolist())
-        print(f"Index: {first_index}, expect: {expect[first_index]}, actual: {actual[first_index]}") 
+        print(f"Index: {first_index}, expect: {expect[first_index]}, actual: {actual[first_index]}")
+
 
 if __name__ == "__main__":
     parser = argparse.ArgumentParser()
     parser.add_argument('--batch', type=int, default=8, help='batch size')
     parser.add_argument('--heads', type=int, default=32, help='heads')
     parser.add_argument('--heads_kv', type=int, default=8, help='heads_kv')
-    parser.add_argument('--max_cache_seqlen', type=int, default=8192, help='kvcache sequence length')
+    parser.add_argument(
+        '--max_cache_seqlen', type=int, default=8192, help='kvcache sequence length')
     parser.add_argument('--dim', type=int, default=128, help='dim')
     parser.add_argument('--dim_v', type=int, default=128, help='dim_v')
     parser.add_argument('--sparse_ratio', type=float, default=0.8, help='sparse ratio')
@@ -389,77 +414,80 @@ if __name__ == "__main__":
     pv_flops = 2 * batch * heads * max_cache_seqlen * dim_v
     total_flops = qk_flops + pv_flops
 
-    max_selected_blocks = int(math.ceil(max_cache_seqlen * (1-sparse_ratio)/ block_size))
+    max_selected_blocks = int(math.ceil(max_cache_seqlen * (1 - sparse_ratio) / block_size))
     print("max_selected_blocks: ", max_selected_blocks)
     dtype = torch.float16
     block_H = 64
 
-
-    
     Q = torch.randn((batch, heads, dim), dtype=dtype, device='cuda')
     K = torch.randn((batch, max_cache_seqlen, heads_kv, dim), dtype=dtype, device='cuda')
     V = torch.randn((batch, max_cache_seqlen, heads_kv, dim_v), dtype=dtype, device='cuda')
     cache_seqlens = torch.randint(1, max_cache_seqlen, (batch,), dtype=torch.int32, device='cuda')
     # cache_seqlens = torch.full((batch,), max_cache_seqlen, dtype=torch.int32, device='cuda')
-    # Ensure at least one element equals cache_seqlen
-    random_index = torch.randint(0, batch, (1,), device='cuda').item()  # Select a random index
-    cache_seqlens[random_index] = max_cache_seqlen  # Assign cache_seqlen to ensure at least one occurrence
+    # # Ensure at least one element equals cache_seqlen
+    # random_index = torch.randint(0, batch, (1,), device='cuda').item()  # Select a random index
+    # # cache_seqlens[random_index] = max_cache_seqlen  # Assign cache_seqlen to ensure at least one occurrence
 
     print("cache_seqlens: ", cache_seqlens)
 
     max_valid_num_blocks = torch.ceil(cache_seqlens / block_size).int()
     print("max_valid_num_blocks: ", max_valid_num_blocks)
     # Initialize block_indices with -1 (for padding blocks)
-    block_indices = torch.full((batch, heads_kv, max_selected_blocks), -1, dtype=torch.int32, device='cuda')
+    block_indices = torch.full((batch, heads_kv, max_selected_blocks),
+                               -1,
+                               dtype=torch.int32,
+                               device='cuda')
+    # max_num_blocks = int((max_cache_seqlen + block_size - 1)/ block_size)
+    # block_indices = torch.full((batch, heads_kv, max_num_blocks), -1, dtype=torch.int32, device='cuda')
 
     # Assign valid indices while ensuring no duplicates within each batch-group
     for b in range(batch):
         max_valid_block = max_valid_num_blocks[b].item()  # Max valid blocks for this batch
         if max_valid_block > 0:  # Ensure there's at least one valid block
             for h in range(heads_kv):
-                valid_indices = torch.randperm(max_valid_block, device='cuda', dtype=torch.int32)[:max_selected_blocks]
-                block_indices[b, h, :len(valid_indices)] = valid_indices 
+                valid_indices = torch.randperm(
+                    max_valid_block, device='cuda', dtype=torch.int32)[:max_selected_blocks]
+                # valid_indices = torch.randperm(max_valid_block, device='cuda', dtype=torch.int32)[:max_num_blocks]
+                block_indices[b, h, :len(valid_indices)] = valid_indices
 
     # Sort indices within each batch-group for consistency
     block_indices, _ = block_indices.sort(dim=-1, descending=True)
     # print("block_indices: ", block_indices)
-    actual_num_blocks = torch.sum(block_indices != -1, dim=-1).to(torch.int32)[:,0]
+    actual_num_blocks = torch.sum(block_indices != -1, dim=-1).to(torch.int32)[:, 0]
     print("actual_num_blocks: ", actual_num_blocks)
     # print(block_indices.shape, actual_num_blocks.shape)
-   
+
     max_num_blocks = torch.max(max_valid_num_blocks).item()
     print("max_num_blocks: ", max_num_blocks)
 
     # parity reference
-    ref = ref_program_torch(Q, K, V, block_indices, cache_seqlens, max_cache_seqlen, max_num_blocks, block_size)
-    # ref = ref_program_triton(Q, K, V, block_indices, cache_seqlens, max_cache_seqlen, max_num_blocks, block_size)
-    # out = kernel(Q, K, V, block_indices, cache_seqlens, actual_num_blocks, glse, Output_partial)
+    ref = ref_program_torch(Q, K, V, block_indices, cache_seqlens, max_cache_seqlen, max_num_blocks,
+                            block_size)
+
     # out = sparse_gqa_decode_varlen_indice(Q, K, V, block_indices, cache_seqlens, max_cache_seqlen, block_size)
     sparse_kernel = SparseFlashAttn(batch, heads, heads_kv, dim, dim_v, block_size)
     out = sparse_kernel(Q, K, V, block_indices, cache_seqlens)
     debug("output", ref, out, atol=1e-3, rtol=1e-3)
 
     ## latency reference
-    for i in range(10):
-        ref = ref_program_fa(Q, K, V, block_indices, cache_seqlens, max_cache_seqlen, max_num_blocks, block_size)
+    for _ in range(10):
+        ref = ref_program_fa(Q, K, V, block_indices, cache_seqlens, max_cache_seqlen,
+                             max_num_blocks, block_size)
     torch.cuda.synchronize()
     start = time.time()
-    for i in range(100):
-        ref = ref_program_fa(Q, K, V, block_indices, cache_seqlens, max_cache_seqlen, max_num_blocks, block_size)
+    for _ in range(100):
+        ref = ref_program_fa(Q, K, V, block_indices, cache_seqlens, max_cache_seqlen,
+                             max_num_blocks, block_size)
     torch.cuda.synchronize()
-    print("dense time: ", (time.time() - start) / 100*1000)
+    print("dense time: ", (time.time() - start) / 100 * 1000)
 
-    for i in range(10):
+    for _ in range(10):
         # out = sparse_gqa_decode_varlen_indice(Q, K, V, block_indices, cache_seqlens, max_cache_seqlen, block_size)
         out = sparse_kernel(Q, K, V, block_indices, cache_seqlens)
     torch.cuda.synchronize()
     start = time.time()
-    for i in range(100):
+    for _ in range(100):
         # out = sparse_gqa_decode_varlen_indice(Q, K, V, block_indices, cache_seqlens, max_cache_seqlen, block_size)
         out = sparse_kernel(Q, K, V, block_indices, cache_seqlens)
     torch.cuda.synchronize()
-    print("sparse time: ", (time.time() - start) / 100*1000)
-
-
-
-
+    print("sparse time: ", (time.time() - start) / 100 * 1000)