[Example] Implement TileLang Native Sparse Attention Kernel (#121)

* Add DeepSeek MLA decode example with Flash Attention implementation

* Add GEMM SplitK and StreamK example implementations

This commit introduces two new example scripts demonstrating advanced GEMM (matrix multiplication) techniques:
- `example_tilelang_gemm_splitk.py`: Implements a Split-K GEMM kernel using TileLang
- `example_tilelang_gemm_streamk.py`: Implements a Stream-K GEMM kernel using TileLang

Both examples showcase different parallel computation strategies for matrix multiplication, with comprehensive testing using PyTorch reference implementations.

* Refactor GEMM SplitK and StreamK example implementations

Clean up and improve code formatting for the SplitK and StreamK GEMM example scripts:
- Remove unused import (Profiler) in splitk example
- Simplify line breaks and improve code readability
- Standardize indentation and remove unnecessary whitespace
- Optimize atomic add and copy operations for better clarity

* Add block sparse attention benchmarks for multiple libraries

This commit introduces comprehensive block sparse attention benchmarks for different libraries:
- TileLang block sparse FMHA implementation
- Triton block sparse FMHA implementation
- PyTorch reference block sparse FMHA implementation
- FlashAttention dense FMHA reference implementation

The benchmarks include:
- Configurable benchmark parameters (batch size, heads, sequence length, etc.)
- Sparse mask generation using top-k and threshold methods
- Performance measurement for different sparse attention configurations
- Utility functions for mask generation and benchmarking

* Refactor block sparse attention benchmarks with code style improvements

- Add Ruff linter ignore comments to benchmark files
- Improve code formatting and line breaks
- Remove unused imports
- Standardize print statement formatting
- Enhance code readability across multiple library benchmarks

* lint fix

* Add CUDA atomic operations for BFLOAT16 and update function naming

- Implement AtomicAdd functions for BFLOAT16 and BFLOAT16x2 in CUDA common header
- Rename existing atomic add functions to use PascalCase (atomicAdd -> AtomicAdd)
- Add a new __pack_nv_bfloat162 function for packing BFLOAT16 values
- Update kernel and language customization to use new function names
- Add return type annotations in profiler module

* lint fix

* Add example for Group Query Attention (GQA) forward pass using Flash Attention in TileLang

This commit introduces a new example script `example_gqa_fwd_bshd.py` that demonstrates:
- Group Query Attention (GQA) implementation
- Flash Attention forward pass
- Performance benchmarking
- Configurable parameters for batch, heads, sequence length, and dimension
- Autotuning support
- Reference implementation comparison

* Refactor IR lowering pipeline into modular phases

This commit introduces a new module `phase.py` to modularize the IR lowering process by splitting the complex lowering pipeline into two distinct phases:
- `LowerAndLegalize`: Handles initial IR legalization and transformation
- `OptimizeForTarget`: Applies target-specific optimizations

The changes simplify the lowering logic in multiple files by extracting the transformation steps into reusable functions, improving code readability and maintainability.

* lintfix

* nas kernel

* Enhance Native Sparse Attention Examples with Code Improvements and Parameter Updates

- Updated example_tilelang_nsa.py and example_triton_nsa.py with code formatting and style improvements
- Increased default number of heads and selected blocks in TileLang NSA example
- Added Ruff linter ignore comments to reference.py
- Standardized function signatures and improved code readability across NSA implementations

* Add utility math functions for integer operations

- Implement `next_power_of_2()` to calculate the next power of 2 for an integer
- Add `cdiv()` function for ceiling division of integers

examples/native_sparse_attention/example_tilelang_nsa.py

+# Copyright (c) Microsoft Corporation.
+# Licensed under the MIT License.
+
+import torch
+from reference import naive_nsa
+import tilelang
+from tilelang import language as T
+import tilelang.testing
+
+tilelang.testing.set_random_seed(0)
+
+
+def native_sparse_attention(batch,
+                            heads,
+                            seq_len,
+                            dim,
+                            is_causal,
+                            scale=None,
+                            groups=1,
+                            selected_blocks=16):
+    if scale is None:
+        scale = (1.0 / dim)**0.5 * 1.44269504  # log2(e)
+    head_kv = heads // groups
+    q_shape = [batch, seq_len, heads, dim]
+    kv_shape = [batch, seq_len, head_kv, dim]
+    block_indices_shape = [batch, seq_len, head_kv, selected_blocks]
+    block_indices_dtype = "int32"
+    dtype = "float16"
+    accum_dtype = "float"
+    block_S = 64
+    block_T = min(128, tilelang.math.next_power_of_2(dim))
+
+    S = selected_blocks
+    NS = S
+    G = groups
+    BS = block_S
+    BK = BV = block_T
+    num_stages = 0
+    threads = 32
+
+    def kernel_func(block_S, block_T, num_stages, threads):
+
+        @T.macro
+        def MMA0(
+            K: T.Buffer(kv_shape, dtype),
+            Q_shared: T.Buffer([G, BK], dtype),
+            K_shared: T.Buffer([BS, BK], dtype),
+            acc_s: T.Buffer([G, BS], accum_dtype),
+            i_s: T.int32,
+            i_b: T.int32,
+            i_h: T.int32,
+            i_t: T.int32,
+        ):
+            T.copy(K[i_b, i_s * BS:(i_s + 1) * BS, i_h, :], K_shared)
+
+            if is_causal:
+                for i, j in T.Parallel(G, BS):
+                    acc_s[i, j] = T.if_then_else(i_t >= (i_s * BS + j), 0, -T.infinity(acc_s.dtype))
+            else:
+                T.clear(acc_s)
+            T.gemm(Q_shared, K_shared, acc_s, transpose_B=True, policy=T.GemmWarpPolicy.FullRow)
+
+        @T.macro
+        def MMA1(
+                V: T.Buffer(kv_shape, dtype),
+                V_shared: T.Buffer([G, BV], dtype),
+                acc_s_cast: T.Buffer([G, BS], dtype),
+                acc_o: T.Buffer([G, BV], accum_dtype),
+                i_s: T.int32,
+                i_b: T.int32,
+                i_h: T.int32,
+        ):
+            T.copy(V[i_b, i_s * BS:(i_s + 1) * BS, i_h, :], V_shared)
+            T.gemm(acc_s_cast, V_shared, acc_o, policy=T.GemmWarpPolicy.FullRow)
+
+        @T.macro
+        def Softmax(
+                acc_s: T.Buffer([G, BS], accum_dtype),
+                acc_s_cast: T.Buffer([G, BS], dtype),
+                scores_max: T.Buffer([G], accum_dtype),
+                scores_max_prev: T.Buffer([G], accum_dtype),
+                scores_scale: T.Buffer([G], accum_dtype),
+                scores_sum: T.Buffer([G], accum_dtype),
+                logsum: T.Buffer([G], accum_dtype),
+        ):
+            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=True)
+            # To do causal softmax, we need to set the scores_max to 0 if it is -inf
+            # This process is called Check_inf in FlashAttention3 code, and it only need to be done
+            # in the first ceil_div(kBlockM, kBlockN) steps.
+            # for i in T.Parallel(block_M):
+            #     scores_max[i] = T.if_then_else(scores_max[i] == -T.infinity(accum_dtype), 0, scores_max[i])
+            for i in T.Parallel(G):
+                scores_scale[i] = T.exp2(scores_max_prev[i] * scale - scores_max[i] * scale)
+            for i, j in T.Parallel(G, BS):
+                # Instead of computing exp(x - max), we compute exp2(x * log_2(e) -
+                # max * log_2(e)) This allows the compiler to use the ffma
+                # instruction instead of fadd and fmul separately.
+                acc_s[i, j] = T.exp2(acc_s[i, j] * scale - scores_max[i] * scale)
+            T.reduce_sum(acc_s, scores_sum, dim=1)
+            for i in T.Parallel(G):
+                logsum[i] = logsum[i] * scores_scale[i] + scores_sum[i]
+            T.copy(acc_s, acc_s_cast)
+
+        @T.macro
+        def Rescale(
+                acc_o: T.Buffer([G, BV], accum_dtype),
+                scores_scale: T.Buffer([G], accum_dtype),
+        ):
+            for i, j in T.Parallel(G, BV):
+                acc_o[i, j] *= scores_scale[i]
+
+        @T.prim_func
+        def main(
+                Q: T.Buffer(q_shape, dtype),
+                K: T.Buffer(kv_shape, dtype),
+                V: T.Buffer(kv_shape, dtype),
+                BlockIndices: T.Buffer(block_indices_shape, block_indices_dtype),
+                Output: T.Buffer(q_shape, dtype),
+        ):
+            with T.Kernel(
+                    dim // block_T, seq_len, batch * head_kv, threads=threads) as (bx, by, bz):
+                Q_shared = T.alloc_shared([G, BK], dtype)
+                K_shared = T.alloc_shared([BS, BK], dtype)
+                V_shared = T.alloc_shared([BS, BV], dtype)
+                O_shared = T.alloc_shared([G, BV], dtype)
+
+                acc_s = T.alloc_fragment([G, BS], accum_dtype)
+                acc_s_cast = T.alloc_fragment([G, BS], dtype)
+                acc_o = T.alloc_fragment([G, BV], accum_dtype)
+                scores_max = T.alloc_fragment([G], accum_dtype)
+                scores_max_prev = T.alloc_fragment([G], accum_dtype)
+                scores_scale = T.alloc_fragment([G], accum_dtype)
+                scores_sum = T.alloc_fragment([G], accum_dtype)
+                logsum = T.alloc_fragment([G], accum_dtype)
+
+                i_v, i_t, i_bh = bx, by, bz
+                i_b, i_h = i_bh // heads, i_bh % heads
+
+                T.copy(Q[i_b, i_t, i_h * G:(i_h + 1) * G, :], Q_shared)
+
+                T.fill(acc_o, 0)
+                T.fill(logsum, 0)
+                T.fill(scores_max, -T.infinity(accum_dtype))
+
+                for i in T.Pipelined(NS, num_stages=num_stages):
+                    i_s = BlockIndices[i_b, i_t, i_h, i]
+                    if i_s <= i_t:
+                        MMA0(K, Q_shared, K_shared, acc_s, i_s, i_b, i_h, i_t)
+                        Softmax(acc_s, acc_s_cast, scores_max, scores_max_prev, scores_scale,
+                                scores_sum, logsum)
+                        Rescale(acc_o, scores_scale)
+                        MMA1(V, V_shared, acc_s_cast, acc_o, i_s, i_b, i_h)
+
+                for i, j in T.Parallel(G, BV):
+                    acc_o[i, j] /= logsum[i]
+                T.copy(acc_o, O_shared)
+                T.copy(O_shared, Output[i_b, i_t, i_h * G:(i_h + 1) * G, :])
+
+        return main
+
+    def kernel(block_S, block_T, num_stages, threads):
+        return kernel_func(block_S, block_T, num_stages, threads)
+
+    return kernel(block_S, block_T, num_stages, threads)
+
+
+if __name__ == "__main__":
+    B, SEQ_LEN, H, HQ, D, S, block_size, dtype, scale = 1, 64, 4, 64, 32, 16, 64, torch.float16, None
+
+    program = native_sparse_attention(
+        batch=B,
+        heads=HQ,
+        seq_len=SEQ_LEN,
+        dim=D,
+        is_causal=True,
+        scale=scale,
+        groups=HQ // H,
+        selected_blocks=S,
+    )
+    kernel = tilelang.compile(program, out_idx=[4])
+
+    Q = torch.randn((B, SEQ_LEN, HQ, D), dtype=dtype, device='cuda').requires_grad_(True)
+    K = torch.randn((B, SEQ_LEN, H, D), dtype=dtype, device='cuda').requires_grad_(True)
+    V = torch.randn((B, SEQ_LEN, H, D), dtype=dtype, device='cuda').requires_grad_(True)
+    DO = torch.randn((B, SEQ_LEN, HQ, D), dtype=dtype, device='cuda')
+
+    block_indices = torch.full((B, SEQ_LEN, H, S), SEQ_LEN, dtype=torch.long, device='cuda')
+    for b in range(B):
+        for t in range(SEQ_LEN):
+            for h in range(H):
+                i_i = torch.randperm(max(1, (t // block_size)))[:S]
+                block_indices[b, t, h, :len(i_i)] = i_i
+    block_indices = block_indices.sort(-1)[0]
+    block_counts = torch.randint(1, S + 1, (B, SEQ_LEN, H), device='cuda')
+
+    out = kernel(Q, K, V, block_indices.to(torch.int32))
+
+    print(out)
+
+    ref = naive_nsa(
+        q=Q,
+        k=K,
+        v=V,
+        block_indices=block_indices,
+        block_counts=block_counts,
+        block_size=block_size,
+        scale=scale)
+
+    print(ref)
+    torch.testing.assert_close(ref, out, atol=1e-2, rtol=1e-2)

examples/native_sparse_attention/example_triton_nsa.py

+# Copyright (c) Microsoft Corporation.
+# Licensed under the MIT License.
+# ruff: noqa
+import torch
+from typing import Optional
+
+import torch
+import triton
+import triton.language as tl
+from einops import rearrange
+
+from fla.ops.common.utils import (prepare_chunk_indices, prepare_lens, prepare_token_indices)
+from fla.utils import autocast_custom_bwd, autocast_custom_fwd, contiguous
+
+from reference import naive_nsa
+
+
+@triton.autotune(
+    configs=[triton.Config({}, num_warps=num_warps) for num_warps in [1, 2, 4, 8, 16]],
+    key=['BS', 'BK', 'BV'],
+)
+@triton.jit
+def parallel_nsa_fwd_kernel(
+    q,
+    k,
+    v,
+    o,
+    lse,
+    scale,
+    block_indices,
+    T,
+    H: tl.constexpr,
+    HQ: tl.constexpr,
+    G: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    S: tl.constexpr,
+    BS: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+):
+    i_v, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_b, i_h = i_bh // H, i_bh % H
+
+    bos, eos = i_b * T, i_b * T + T
+
+    k += (bos * H + i_h) * K
+    v += (bos * H + i_h) * V
+    block_indices += (bos + i_t) * H * S + i_h * S
+
+    NS = S
+
+    p_q = tl.make_block_ptr(q + (bos + i_t) * HQ * K, (HQ, K), (K, 1), (i_h * G, 0), (G, BK),
+                            (1, 0))
+    p_o = tl.make_block_ptr(o + (bos + i_t) * HQ * V, (HQ, V), (V, 1), (i_h * G, i_v * BV), (G, BV),
+                            (1, 0))
+    p_lse = lse + (bos + i_t) * HQ + i_h * G + tl.arange(0, G)
+
+    # the Q block is kept in the shared memory throughout the whole kernel
+    # [G, BK]
+    b_q = tl.load(p_q, boundary_check=(0, 1))
+    b_q = (b_q * scale).to(b_q.dtype)
+    # [G, BV]
+    b_o = tl.zeros([G, BV], dtype=tl.float32)
+
+    b_m = tl.full([G], float('-inf'), dtype=tl.float32)
+    b_acc = tl.zeros([G], dtype=tl.float32)
+    for i in range(NS):
+        i_s = tl.load(block_indices + i).to(tl.int32) * BS
+        if i_s <= i_t:
+            p_k = tl.make_block_ptr(k, (K, T), (1, H * K), (0, i_s), (BK, BS), (0, 1))
+            p_v = tl.make_block_ptr(v, (T, V), (H * V, 1), (i_s, i_v * BV), (BS, BV), (1, 0))
+            # [BK, BS]
+            b_k = tl.load(p_k, boundary_check=(0, 1))
+            # [BS, BV]
+            b_v = tl.load(p_v, boundary_check=(0, 1))
+            # [G, BS]
+            b_s = tl.dot(b_q, b_k)
+            b_s = tl.where((i_t >= (i_s + tl.arange(0, BS)))[None, :], b_s, float('-inf'))
+
+            # [G]
+            b_m, b_mp = tl.maximum(b_m, tl.max(b_s, 1)), b_m
+            b_r = tl.exp(b_mp - b_m)
+            # [G, BS]
+            b_p = tl.exp(b_s - b_m[:, None])
+            # [G]
+            b_acc = b_acc * b_r + tl.sum(b_p, 1)
+            # [G, BV]
+            b_o = b_o * b_r[:, None] + tl.dot(b_p.to(b_q.dtype), b_v)
+
+            b_mp = b_m
+    b_o = b_o / b_acc[:, None]
+    b_m += tl.log(b_acc)
+    tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))
+    tl.store(p_lse, b_m.to(p_lse.dtype.element_ty))
+
+
+def parallel_nsa_fwd(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    block_indices: torch.Tensor,
+    block_size: int,
+    scale: float,
+):
+    B, T, H, K, V, S = *k.shape, v.shape[-1], block_indices.shape[-1]
+    HQ = q.shape[2]
+    G = HQ // H
+    BS = block_size
+    if torch.cuda.get_device_capability()[0] >= 9:
+        BK = min(256, triton.next_power_of_2(K))
+        BV = min(256, triton.next_power_of_2(V))
+    else:
+        BK = min(128, triton.next_power_of_2(K))
+        BV = min(128, triton.next_power_of_2(V))
+    NK = triton.cdiv(K, BK)
+    NV = triton.cdiv(V, BV)
+    assert NK == 1, "The key dimension can not be larger than 256"
+
+    grid = (NV, T, B * H)
+    o = torch.empty(B, T, HQ, V, dtype=v.dtype, device=q.device)
+    lse = torch.empty(B, T, HQ, dtype=torch.float32, device=q.device)
+    print("grid", grid)
+    parallel_nsa_fwd_kernel[grid](
+        q=q,
+        k=k,
+        v=v,
+        o=o,
+        lse=lse,
+        scale=scale,
+        block_indices=block_indices,
+        H=H,
+        HQ=HQ,
+        G=G,
+        T=T,
+        K=K,
+        V=V,
+        S=S,
+        BS=BS,
+        BK=BK,
+        BV=BV,
+    )
+    return o, lse
+
+
+class ParallelNSAFunction(torch.autograd.Function):
+
+    @staticmethod
+    @contiguous
+    @autocast_custom_fwd
+    def forward(ctx, q, k, v, block_indices, block_size, scale, offsets):
+        ctx.dtype = q.dtype
+
+        # 2-d sequence indices denoting the offsets of tokens in each sequence
+        # for example, if the passed `offsets` is [0, 2, 6],
+        # then there are 2 and 4 tokens in the 1st and 2nd sequences respectively, and `token_indices` will be
+        # [[0, 0], [0, 1], [1, 0], [1, 1], [1, 2], [1, 3]]
+        token_indices = prepare_token_indices(offsets) if offsets is not None else None
+
+        o, lse = parallel_nsa_fwd(
+            q=q, k=k, v=v, block_indices=block_indices, block_size=block_size, scale=scale)
+        ctx.save_for_backward(q, k, v, o, lse)
+        ctx.block_indices = block_indices
+        ctx.block_size = block_size
+        ctx.scale = scale
+        return o.to(q.dtype)
+
+
+def parallel_nsa(q: torch.Tensor,
+                 k: torch.Tensor,
+                 v: torch.Tensor,
+                 block_indices: torch.LongTensor,
+                 block_size: int = 64,
+                 scale: Optional[float] = None,
+                 cu_seqlens: Optional[torch.LongTensor] = None,
+                 head_first: bool = False) -> torch.Tensor:
+    r"""
+    Args:
+        q (torch.Tensor):
+            queries of shape `[B, T, HQ, K]` if `head_first=False` else `[B, HQ, T, K]`.
+        k (torch.Tensor):
+            keys of shape `[B, T, H, K]` if `head_first=False` else `[B, H, T, K]`.
+            GQA is enforced here. The ratio of query heads (HQ) to key/value heads (H) must be a power of 2 and >=16.
+        v (torch.Tensor):
+            values of shape `[B, T, H, V]` if `head_first=False` else `[B, H, T, V]`.
+        block_indices (torch.LongTensor):
+            Block indices of shape `[B, T, H, S]` if `head_first=False` else `[B, H, T, S]`.
+            `S` is the number of selected blocks for each query token, which is set to 16 in the paper.
+        block_size (int):
+            Selected block size. Default: 64.
+        scale (Optional[int]):
+            Scale factor for attention scores.
+            If not provided, it will default to `1 / sqrt(K)`. Default: `None`.
+        head_first (Optional[bool]):
+            Whether the inputs are in the head-first format. Default: `False`.
+        cu_seqlens (torch.LongTensor):
+            Cumulative sequence lengths of shape `[N+1]` used for variable-length training,
+            consistent with the FlashAttention API.
+
+    Returns:
+        o (torch.Tensor):
+            Outputs of shape `[B, T, HQ, V]` if `head_first=False` else `[B, HQ, T, V]`.
+    """
+    if scale is None:
+        scale = k.shape[-1]**-0.5
+    if cu_seqlens is not None:
+        assert q.shape[0] == 1, "batch size must be 1 when cu_seqlens are provided"
+    if head_first:
+        q, k, v, block_indices = map(lambda x: rearrange(x, 'b h t d -> b t h d'),
+                                     (q, k, v, block_indices))
+    o = ParallelNSAFunction.apply(q, k, v, block_indices, block_size, scale, cu_seqlens)
+    if head_first:
+        o = rearrange(o, 'b t h d -> b h t d')
+    return o
+
+
+if __name__ == "__main__":
+    B, T, H, HQ, D, S, block_size, dtype, scale = 1, 64, 1, 16, 32, 1, 64, torch.float16, 0.1
+
+    q = torch.randn((B, T, HQ, D), dtype=dtype, device='cuda').requires_grad_(True)
+    k = torch.randn((B, T, H, D), dtype=dtype, device='cuda').requires_grad_(True)
+    v = torch.randn((B, T, H, D), dtype=dtype, device='cuda').requires_grad_(True)
+    do = torch.randn((B, T, HQ, D), dtype=dtype, device='cuda')
+
+    block_indices = torch.full((B, T, H, S), T, dtype=torch.long, device='cuda')
+    for b in range(B):
+        for t in range(T):
+            for h in range(H):
+                i_i = torch.randperm(max(1, (t // block_size)))[:S]
+                block_indices[b, t, h, :len(i_i)] = i_i
+    block_indices = block_indices.sort(-1)[0]
+
+    block_counts = torch.randint(1, S + 1, (B, T, H), device='cuda')
+
+    ref = naive_nsa(
+        q=q,
+        k=k,
+        v=v,
+        block_indices=block_indices,
+        block_counts=block_counts,
+        block_size=block_size,
+        scale=scale)
+
+    # print(ref)
+
+    tri = parallel_nsa(
+        q=q, k=k, v=v, block_indices=block_indices, block_size=block_size, scale=scale)
+
+    # print(tri)
+
+    torch.testing.assert_close(ref, tri, atol=1e-2, rtol=1e-2)
+
+    # import flash_attn
+    # # gqa
+    # o_gqa = flash_attn.flash_attn_func(
+    #     q,
+    #     k,
+    #     v,
+    #     softmax_scale=scale,
+    # )
+    # print(o_gqa)
+
+    # torch.testing.assert_close(o_gqa, tri, atol=1e-2, rtol=1e-2)

examples/native_sparse_attention/reference.py

+# Copyright (c) Microsoft Corporation.
+# Licensed under the MIT License.
+# ruff: noqa
+from typing import Optional
+
+import torch
+import torch.nn.functional as F
+from einops import rearrange, repeat
+
+
+def naive_nsa(q: torch.Tensor,
+              k: torch.Tensor,
+              v: torch.Tensor,
+              block_indices: torch.LongTensor,
+              block_counts: torch.LongTensor,
+              block_size: int = 64,
+              scale: Optional[float] = None,
+              head_first: bool = False,
+              cu_seqlens: Optional[torch.LongTensor] = None) -> torch.Tensor:
+    r"""
+    Args:
+        q (torch.Tensor):
+            queries of shape `[B, T, HQ, K]` if `head_first=False` else `[B, HQ, T, K]`.
+        k (torch.Tensor):
+            keys of shape `[B, T, H, K]` if `head_first=False` else `[B, H, T, K]`.
+            GQA is enforced here. The ratio of query heads (HQ) to key/value heads (H) must be a power of 2 and >=16.
+        v (torch.Tensor):
+            values of shape `[B, T, H, V]` if `head_first=False` else `[B, H, T, V]`.
+        block_indices (torch.LongTensor):
+            Block indices of shape `[B, T, H, S]` if `head_first=False` else `[B, H, T, S]`.
+            `S` is the maximum number of selected blocks for each query token, which is set to 16 in the paper.
+        block_counts (torch.LongTensor):
+            Block counts of shape `[B, T, H]` if `head_first=False` else `[B, H, T]`.
+        block_size (int):
+            Selected block size. Default: 64.
+        scale (Optional[int]):
+            Scale factor for attention scores.
+            If not provided, it will default to `1 / sqrt(K)`. Default: `None`.
+        head_first (Optional[bool]):
+            Whether the inputs are in the head-first format. Default: `False`.
+        cu_seqlens (torch.LongTensor):
+            Cumulative sequence lengths of shape `[N+1]` used for variable-length training,
+            consistent with the FlashAttention API.
+
+    Returns:
+        o (torch.Tensor):
+            Outputs of shape `[B, T, HQ, V]` if `head_first=False` else `[B, HQ, T, V]`.
+    """
+    if scale is None:
+        scale = k.shape[-1]**-0.5
+    if cu_seqlens is not None:
+        if head_first:
+            raise RuntimeError(
+                "Sequences with variable lengths are not supported for head-first mode")
+    if head_first:
+        q, k, v, block_indices = map(lambda x: rearrange(x, 'b h t d -> b t h d'),
+                                     (q, k, v, block_indices))
+        block_counts = rearrange(block_counts, 'b h t -> b t h')
+
+    dtype = q.dtype
+    G = q.shape[2] // k.shape[2]
+    BS = block_size
+    S = block_indices.shape[-1]
+    k, v, block_indices = (repeat(x, 'b t h d -> b t (h g) d', g=G) for x in (k, v, block_indices))
+    block_counts = repeat(block_counts, 'b t h -> b t (h g)', g=G)
+    c = torch.arange(S).repeat_interleave(BS).unsqueeze(1).expand(-1, q.shape[2]).to(q.device)
+    q, k, v = map(lambda x: x.float(), (q, k, v))
+
+    o = torch.zeros_like(v)
+    varlen = True
+    if cu_seqlens is None:
+        varlen = False
+        B, T = q.shape[:2]
+        cu_seqlens = torch.cat(
+            [block_indices.new_tensor(range(0, B * T, T)),
+             block_indices.new_tensor([B * T])])
+
+    for i in range(len(cu_seqlens) - 1):
+        if not varlen:
+            q_b, k_b, v_b, i_b, s_b = q[i], k[i], v[i], block_indices[i], block_counts[i]
+        else:
+            T = cu_seqlens[i + 1] - cu_seqlens[i]
+            q_b, k_b, v_b, i_b, s_b = map(lambda x: x[0][cu_seqlens[i]:cu_seqlens[i + 1]],
+                                          (q, k, v, block_indices, block_counts))
+
+        i_b = i_b.unsqueeze(-1) * BS + i_b.new_tensor(range(BS))
+        # [T, S*BS, HQ]
+        i_b = i_b.view(T, block_indices.shape[2], -1).transpose(1, 2)
+        for i_q in range(T):
+            # [HQ, D]
+            q_i = q_b[i_q] * scale
+            # [S*BS, HQ]
+            i_i = i_b[i_q]
+            # [1, HQ]
+            s_i = s_b[i_q]
+            # [S*BS, HQ, -1]
+            k_i, v_i = map(
+                lambda x: x.gather(
+                    0,
+                    i_i.clamp(0, T - 1).unsqueeze(-1).expand(*i_i.shape, x.shape[-1])), (k_b, v_b))
+            # [S*BS, HQ]
+            attn = torch.einsum('h d, n h d -> n h', q_i, k_i).masked_fill((i_i > i_q) | (c >= s_i),
+                                                                           float('-inf')).softmax(0)
+            if not varlen:
+                o[i, i_q] = torch.einsum('n h, n h v -> h v', attn, v_i)
+            else:
+                o[0][cu_seqlens[i] + i_q] = torch.einsum('n h, n h v -> h v', attn, v_i)
+
+    if head_first:
+        o = rearrange(o, 'b t h d -> b h t d')
+    return o.to(dtype)

examples/native_sparse_attention/requirements.txt

+git+https://github.com/fla-org/flash-linear-attention
\ No newline at end of file

tilelang/__init__.py

@@ -125,3 +125,5 @@ from . import (
 from .engine import lower  # noqa: F401
 
 from .version import __version__  # noqa: F401
+
+from .math import *  # noqa: F403

tilelang/math/__init__.py

+# Copyright (c) Microsoft Corporation.
+# Licensed under the MIT License.
+
+
+def next_power_of_2(x: int) -> int:
+    return 1 << (x - 1).bit_length()
+
+
+def cdiv(a: int, b: int) -> int:
+    return (a + b - 1) // b

tilelang/testing/__init__.py

@@ -80,7 +80,7 @@ def torch_assert_close(tensor_a,
         return True
 
 
-def set_random_seed(seed: int) -> None:
+def set_random_seed(seed: int = 42) -> None:
     random.seed(seed)
     np.random.seed(seed)
     torch.manual_seed(seed)