Clean up alibi, implement non-causal alibi

5ab9b366 · Tri Dao · bc28eacc · 5ab9b366 · 5ab9b366 · 5ab9b366
Commit 5ab9b366 authored Dec 21, 2023 by Tri Dao
11 changed files
--- a/csrc/flash_attn/flash_api.cpp
+++ b/csrc/flash_attn/flash_api.cpp
@@ -253,12 +253,12 @@ mha_fwd(at::Tensor &q,         // batch_size x seqlen_q x num_heads x head_size
        const at::Tensor &k,         // batch_size x seqlen_k x num_heads_k x head_size
        const at::Tensor &v,         // batch_size x seqlen_k x num_heads_k x head_size
        c10::optional<at::Tensor> &out_,             // batch_size x seqlen_q x num_heads x head_size
+        c10::optional<at::Tensor> &alibi_slopes_, // num_heads or batch_size x num_heads
        const float p_dropout,
        const float softmax_scale,
        bool is_causal,
        const int window_size_left,
        int window_size_right,
-        c10::optional<at::Tensor> &alibi_slopes_, // batch_size x num_heads
        const bool return_softmax,
        c10::optional<at::Generator> gen_) {
@@ -297,13 +297,13 @@ mha_fwd(at::Tensor &q,         // batch_size x seqlen_q x num_heads x head_size
    TORCH_CHECK(head_size_og <= 256, "FlashAttention forward only supports head dimension at most 256");
    TORCH_CHECK(num_heads % num_heads_k == 0, "Number of heads in key/value must divide number of heads in query");
-    if (seqlen_q == 1) { is_causal = false; }  // causal=true is the same as causal=false in this case
+    // causal=true is the same as causal=false in this case
+    if (seqlen_q == 1 && !alibi_slopes_.has_value()) { is_causal = false; }
    if (is_causal) { window_size_right = 0; }
    // Faster to transpose q from (b, 1, (nheads_kv ngroups), d) to (b, ngroups, nheads_kv, d) in this case
    // H/t Daniel Haziza
-    // TODO: how to make "seqlenq_ngroups_swapped" and ALiBi work together?
+    const int seqlenq_ngroups_swapped = seqlen_q == 1 && num_heads > num_heads_k && window_size_left < 0 && window_size_right < 0 && p_dropout == 0.f && head_size_og % 8 == 0 && !alibi_slopes_.has_value();
-    const int seqlenq_ngroups_swapped = seqlen_q == 1 && num_heads > num_heads_k && window_size_left < 0 && window_size_right < 0 && p_dropout == 0.f && head_size_og % 8 == 0 && !(alibi_slopes_.has_value());
    if (seqlenq_ngroups_swapped) {
        const int ngroups = num_heads / num_heads_k;
        q = q.reshape({batch_size, num_heads_k, ngroups, head_size_og}).transpose(1, 2);
@@ -416,12 +416,11 @@ mha_fwd(at::Tensor &q,         // batch_size x seqlen_q x num_heads x head_size
        TORCH_CHECK(alibi_slopes.dtype() == torch::kFloat32, "ALiBi slopes must have dtype fp32");
        CHECK_DEVICE(alibi_slopes);
        TORCH_CHECK(alibi_slopes.stride(-1) == 1, "ALiBi slopes tensor must have contiguous last dimension");
-        CHECK_SHAPE(alibi_slopes, batch_size, num_heads);
+        TORCH_CHECK(alibi_slopes.sizes() == torch::IntArrayRef({num_heads}) || alibi_slopes.sizes() == torch::IntArrayRef({batch_size, num_heads}));
-        params.has_alibi = true;
        params.alibi_slopes_ptr = alibi_slopes.data_ptr();
-        params.alibi_slopes_batch_stride = alibi_slopes.stride(0);
+        params.alibi_slopes_batch_stride = alibi_slopes.dim() == 2 ? alibi_slopes.stride(0) : 0;
    } else {
-        params.has_alibi = false;
+        params.alibi_slopes_ptr = nullptr;
    }
    if (seqlen_k > 0) {
@@ -456,6 +455,7 @@ mha_varlen_fwd(const at::Tensor &q,  // total_q x num_heads x head_size, total_q
               const at::Tensor &cu_seqlens_q,  // b+1
               const at::Tensor &cu_seqlens_k,  // b+1
               c10::optional<at::Tensor> &seqused_k, // b. If given, only this many elements of each batch element's keys are used.
+               c10::optional<at::Tensor> &alibi_slopes_, // num_heads or b x num_heads
               const int max_seqlen_q,
               const int max_seqlen_k,
               const float p_dropout,
@@ -464,7 +464,6 @@ mha_varlen_fwd(const at::Tensor &q,  // total_q x num_heads x head_size, total_q
               const bool is_causal,
               const int window_size_left,
               int window_size_right,
-               c10::optional<at::Tensor> &alibi_slopes_, // b x num_heads
               const bool return_softmax,
               c10::optional<at::Generator> gen_) {
@@ -612,12 +611,11 @@ mha_varlen_fwd(const at::Tensor &q,  // total_q x num_heads x head_size, total_q
        TORCH_CHECK(alibi_slopes.dtype() == torch::kFloat32, "ALiBi slopes must have dtype fp32");
        CHECK_DEVICE(alibi_slopes);
        TORCH_CHECK(alibi_slopes.stride(-1) == 1, "ALiBi slopes tensor must have contiguous last dimension");
-        CHECK_SHAPE(alibi_slopes, batch_size, num_heads);
+        TORCH_CHECK(alibi_slopes.sizes() == torch::IntArrayRef({num_heads}) || alibi_slopes.sizes() == torch::IntArrayRef({batch_size, num_heads}));
-        params.has_alibi = true;
        params.alibi_slopes_ptr = alibi_slopes.data_ptr();
-        params.alibi_slopes_batch_stride = alibi_slopes.stride(0);
+        params.alibi_slopes_batch_stride = alibi_slopes.dim() == 2 ? alibi_slopes.stride(0) : 0;
    } else {
-        params.has_alibi = false;
+        params.alibi_slopes_ptr = nullptr;
    }
    auto stream = at::cuda::getCurrentCUDAStream().stream();
@@ -664,12 +662,12 @@ mha_bwd(const at::Tensor &dout,  // batch_size x seqlen_q x num_heads, x head_si
        c10::optional<at::Tensor> &dq_,   // batch_size x seqlen_q x num_heads x head_size
        c10::optional<at::Tensor> &dk_,   // batch_size x seqlen_k x num_heads_k x head_size
        c10::optional<at::Tensor> &dv_,   // batch_size x seqlen_k x num_heads_k x head_size
+        c10::optional<at::Tensor> &alibi_slopes_, // num_heads or batch_size x num_heads
        const float p_dropout,         // probability to drop
        const float softmax_scale,
        const bool is_causal,
        const int window_size_left,
        int window_size_right,
-        c10::optional<at::Tensor> &alibi_slopes_, // batch_size x num_heads
        c10::optional<at::Generator> gen_,
        c10::optional<at::Tensor> &rng_state) {
@@ -848,12 +846,11 @@ mha_bwd(const at::Tensor &dout,  // batch_size x seqlen_q x num_heads, x head_si
        TORCH_CHECK(alibi_slopes.dtype() == torch::kFloat32, "ALiBi slopes must have dtype fp32");
        CHECK_DEVICE(alibi_slopes);
        TORCH_CHECK(alibi_slopes.stride(-1) == 1, "ALiBi slopes tensor must have contiguous last dimension");
-        CHECK_SHAPE(alibi_slopes, batch_size, num_heads);
+        TORCH_CHECK(alibi_slopes.sizes() == torch::IntArrayRef({num_heads}) || alibi_slopes.sizes() == torch::IntArrayRef({batch_size, num_heads}));
-        params.has_alibi = true;
        params.alibi_slopes_ptr = alibi_slopes.data_ptr();
-        params.alibi_slopes_batch_stride = alibi_slopes.stride(0);
+        params.alibi_slopes_batch_stride = alibi_slopes.dim() == 2 ? alibi_slopes.stride(0) : 0;
    } else {
-        params.has_alibi = false;
+        params.alibi_slopes_ptr = nullptr;
    }
    if (seqlen_q > 0) {
@@ -891,6 +888,7 @@ mha_varlen_bwd(const at::Tensor &dout,  // total_q x num_heads, x head_size
               c10::optional<at::Tensor> &dv_,   // total_k x num_heads_k x head_size, total_k := \sum_{i=0}^{b} s_i
               const at::Tensor &cu_seqlens_q,  // b+1
               const at::Tensor &cu_seqlens_k,  // b+1
+               c10::optional<at::Tensor> &alibi_slopes_, // num_heads or b x num_heads
               const int max_seqlen_q,
               const int max_seqlen_k,          // max sequence length to choose the kernel
               const float p_dropout,         // probability to drop
@@ -899,7 +897,6 @@ mha_varlen_bwd(const at::Tensor &dout,  // total_q x num_heads, x head_size
               const bool is_causal,
               const int window_size_left,
               int window_size_right,
-               c10::optional<at::Tensor> &alibi_slopes_, // b x num_heads
               c10::optional<at::Generator> gen_,
               c10::optional<at::Tensor> &rng_state) {
@@ -1094,12 +1091,11 @@ mha_varlen_bwd(const at::Tensor &dout,  // total_q x num_heads, x head_size
        TORCH_CHECK(alibi_slopes.dtype() == torch::kFloat32, "ALiBi slopes must have dtype fp32");
        CHECK_DEVICE(alibi_slopes);
        TORCH_CHECK(alibi_slopes.stride(-1) == 1, "ALiBi slopes tensor must have contiguous last dimension");
-        CHECK_SHAPE(alibi_slopes, batch_size, num_heads);
+        TORCH_CHECK(alibi_slopes.sizes() == torch::IntArrayRef({num_heads}) || alibi_slopes.sizes() == torch::IntArrayRef({batch_size, num_heads}));
-        params.has_alibi = true;
        params.alibi_slopes_ptr = alibi_slopes.data_ptr();
-        params.alibi_slopes_batch_stride = alibi_slopes.stride(0);
+        params.alibi_slopes_batch_stride = alibi_slopes.dim() == 2 ? alibi_slopes.stride(0) : 0;
    } else {
-        params.has_alibi = false;
+        params.alibi_slopes_ptr = nullptr;
    }
    launch(params, stream, /*configure=*/false);
@@ -1128,14 +1124,14 @@ mha_fwd_kvcache(at::Tensor &q,                 // batch_size x seqlen_q x num_he
                c10::optional<const at::Tensor> &rotary_cos_, // seqlen_ro x (rotary_dim / 2)
                c10::optional<const at::Tensor> &rotary_sin_, // seqlen_ro x (rotary_dim / 2)
                c10::optional<const at::Tensor> &cache_batch_idx_, // indices to index into the KV cache
+                c10::optional<at::Tensor> &alibi_slopes_, // num_heads or batch_size x num_heads
                c10::optional<at::Tensor> &out_,             // batch_size x seqlen_q x num_heads x head_size
                const float softmax_scale,
                bool is_causal,
                const int window_size_left,
                int window_size_right,
                bool is_rotary_interleaved,   // if true, rotary combines indices 0 & 1, else indices 0 & rotary_dim / 2
-                int num_splits,
+                int num_splits
-                c10::optional<at::Tensor> &alibi_slopes_ // batch_size x num_heads
                ) {
    auto dprops = at::cuda::getCurrentDeviceProperties();
@@ -1174,13 +1170,13 @@ mha_fwd_kvcache(at::Tensor &q,                 // batch_size x seqlen_q x num_he
    TORCH_CHECK(head_size_og <= 256, "FlashAttention forward only supports head dimension at most 256");
    TORCH_CHECK(num_heads % num_heads_k == 0, "Number of heads in key/value must divide number of heads in query");
-    if (seqlen_q == 1) { is_causal = false; }  // causal=true is the same as causal=false in this case
+    // causal=true is the same as causal=false in this case
+    if (seqlen_q == 1 && !alibi_slopes_.has_value()) { is_causal = false; }
    if (is_causal) { window_size_right = 0; }
    // Faster to transpose q from (b, 1, (nheads_kv ngroups), d) to (b, ngroups, nheads_kv, d) in this case
    // H/t Daniel Haziza
-    // TODO: how to make "seqlenq_ngroups_swapped" and ALiBi work together?
+    const int seqlenq_ngroups_swapped = seqlen_q == 1 && num_heads > num_heads_k && window_size_left < 0 && window_size_right < 0 && head_size_og % 8 == 0 && !alibi_slopes_.has_value();
-    const int seqlenq_ngroups_swapped = seqlen_q == 1 && num_heads > num_heads_k && window_size_left < 0 && window_size_right < 0 && head_size_og % 8 == 0 && !(alibi_slopes_.has_value());
    if (seqlenq_ngroups_swapped) {
        const int ngroups = num_heads / num_heads_k;
        q = q.reshape({batch_size, num_heads_k, ngroups, head_size_og}).transpose(1, 2);
@@ -1347,12 +1343,11 @@ mha_fwd_kvcache(at::Tensor &q,                 // batch_size x seqlen_q x num_he
        TORCH_CHECK(alibi_slopes.dtype() == torch::kFloat32, "ALiBi slopes must have dtype fp32");
        CHECK_DEVICE(alibi_slopes);
        TORCH_CHECK(alibi_slopes.stride(-1) == 1, "ALiBi slopes tensor must have contiguous last dimension");
-        CHECK_SHAPE(alibi_slopes, batch_size, num_heads);
+        TORCH_CHECK(alibi_slopes.sizes() == torch::IntArrayRef({num_heads}) || alibi_slopes.sizes() == torch::IntArrayRef({batch_size, num_heads}));
-        params.has_alibi = true;
        params.alibi_slopes_ptr = alibi_slopes.data_ptr();
-        params.alibi_slopes_batch_stride = alibi_slopes.stride(0);
+        params.alibi_slopes_batch_stride = alibi_slopes.dim() == 2 ? alibi_slopes.stride(0) : 0;
    } else {
-        params.has_alibi = false;
+        params.alibi_slopes_ptr = nullptr;
    }
    auto stream = at::cuda::getCurrentCUDAStream().stream();

--- a/csrc/flash_attn/src/alibi.h
+++ b/csrc/flash_attn/src/alibi.h
@@ -13,22 +13,32 @@ using namespace cute;
 ////////////////////////////////////////////////////////////////////////////////////////////////////
-template <typename Engine, typename Layout>
+template <bool Is_causal, typename Engine, typename Layout>
 inline __device__ void apply_alibi(Tensor<Engine, Layout> &tensor, 
                                   const int col_idx_offset_,
                                   const int max_seqlen_k, 
-                                   const int row_idx_offset_,
+                                   const int row_idx_offset,
                                   const int max_seqlen_q, 
                                   const int warp_row_stride,
-                                   const int head_idx,
-                                   const float softmax_scale,
                                   const float alibi_slope) {
    // tensor has shape (ncol=(2, MMA_M), nrow=(2, MMA_N))
    static_assert(Layout::rank == 2, "Only support 2D Tensor");
    const int lane_id = threadIdx.x % 32;
-    const int row_idx_offset = row_idx_offset_;
    const int col_idx_offset = col_idx_offset_ + (lane_id % 4) * 2;
-    const float alibi_slope_unscaled = alibi_slope / softmax_scale;
+    if constexpr (Is_causal) {  // Simpler, we add the same bias vector to all rows
+        #pragma unroll
+        for (int nj = 0; nj < size<1, 1>(tensor); ++nj) {
+            const int col_idx_base = col_idx_offset + nj * 8;
+            #pragma unroll
+            for (int j = 0; j < size<1, 0>(tensor); ++j) {
+                const int col_idx = col_idx_base + j;
+                #pragma unroll
+                for (int mi = 0; mi < size<0>(tensor); ++mi) {
+                    tensor(mi, make_coord(j, nj)) += alibi_slope * col_idx;
+                }
+            }
+        }
+    } else {  // Bias depends on both row_idx and col_idx
        #pragma unroll
        for (int mi = 0; mi < size<0, 1>(tensor); ++mi) {
            const int row_idx_base = row_idx_offset + mi * warp_row_stride;
@@ -41,9 +51,7 @@ inline __device__ void apply_alibi(Tensor<Engine, Layout> &tensor,
                    #pragma unroll
                    for (int j = 0; j < size<1, 0>(tensor); ++j) {
                        const int col_idx = col_idx_base + j;
-                    const float alibi = alibi_slope_unscaled * col_idx;
+                        tensor(make_coord(i, mi), make_coord(j, nj)) -= alibi_slope * abs(row_idx + max_seqlen_k - max_seqlen_q - col_idx);
-                    if (col_idx < max_seqlen_k && row_idx < max_seqlen_q) {
-                        tensor(make_coord(i, mi), make_coord(j, nj)) += alibi;
                    }
                }
            }

--- a/csrc/flash_attn/src/flash.h
+++ b/csrc/flash_attn/src/flash.h
@@ -131,10 +131,6 @@ struct Flash_fwd_params : public Qkv_params {
    int num_splits;  // For split-KV version
-    // float alibi_start;
-    // float alibi_ratio;
-    bool has_alibi;
    void * __restrict__ alibi_slopes_ptr;
    index_t alibi_slopes_batch_stride;
 };

--- a/csrc/flash_attn/src/flash_bwd_kernel.h
+++ b/csrc/flash_attn/src/flash_bwd_kernel.h
@@ -753,8 +753,12 @@ inline __device__ void compute_dq_dk_dv_1colblock(const Params &params, const in
    #pragma unroll
    for (int mi = 0; mi < size(lse); ++mi) {
        const int row = get<0>(taccScS_row(mi));
-        lse(mi) = Is_even_MN || row < binfo.actual_seqlen_q - m_block * kBlockM ? gLSE(row) : 0;
+        lse(mi) = Is_even_MN || row < binfo.actual_seqlen_q - m_block * kBlockM ? gLSE(row) : INFINITY;
    }
+    // We want LSE = inf if the row is OOB. In that case Q would be zero, K would be zero,
+    // and scores would be zero. With LSE = 0, probs will be all 1's, and when we multiply
+    // with V (which would be zero), we're fine. However, with ALiBi, we might modify these
+    // scores, and probs can become NaN. Instead if we set LSE = inf for OOB rows, probs are always 0.
    // Tensor tKrK = make_fragment_like(tKsK);
    // // cute::copy(gmem_tiled_copy_QKV, tKgK(_, _, _, 0), tKrK);
@@ -792,18 +796,7 @@ inline __device__ void compute_dq_dk_dv_1colblock(const Params &params, const in
    clear(acc_dv);
    clear(acc_dk);
-    float alibi_slope = 0.0f;
+    float alibi_slope = !Has_alibi ? 0.0f : reinterpret_cast<float *>(params.alibi_slopes_ptr)[bidb * params.alibi_slopes_batch_stride + bidh] / params.scale_softmax;
-    if (Has_alibi) {
-        Tensor gAS = make_tensor(
-        make_gmem_ptr(
-            reinterpret_cast<ElementAccum *>(params.alibi_slopes_ptr) 
-            + bidb * params.alibi_slopes_batch_stride + bidh
-        ),
-        Shape<_1>{});
-        Tensor rAS = make_fragment_like(gAS);
-        cute::copy(gAS, rAS);
-        alibi_slope = rAS(0);
-    }
    for (; m_block >= m_block_min; --m_block) {
        Tensor acc_s = partition_fragment_C(tiled_mma_sdp, Shape<Int<kBlockM>, Int<kBlockN>>{});  // (MMA=4, MMA_N, MMA_N)
@@ -830,14 +823,13 @@ inline __device__ void compute_dq_dk_dv_1colblock(const Params &params, const in
        // if (cute::thread(32, 0)) { print(scores); }
        if (Has_alibi) {
-            flash::apply_alibi(
+            flash::apply_alibi<Is_causal>(
                scores, 
                n_block * kBlockN + (tidx / 32 / AtomLayoutMS) * MMA_N_SdP * 16,
                binfo.actual_seqlen_k, 
                m_block * kBlockM + get<0>(taccScS_row(0)),
                binfo.actual_seqlen_q, 
                AtomLayoutMS * 16,
-                bidh, params.scale_softmax, 
                alibi_slope
            );
        }
@@ -1403,18 +1395,7 @@ inline __device__ void compute_dq_dk_dv_1rowblock(const Params &params, const in
    clear(acc_dq);
-    float alibi_slope = 0.0f;
+    float alibi_slope = !Has_alibi ? 0.0f : reinterpret_cast<float *>(params.alibi_slopes_ptr)[bidb * params.alibi_slopes_batch_stride + bidh] / params.scale_softmax;
-    if (Has_alibi) {
-        Tensor gAS = make_tensor(
-        make_gmem_ptr(
-            reinterpret_cast<ElementAccum *>(params.alibi_slopes_ptr) 
-            + bidb * params.alibi_slopes_batch_stride + bidh
-        ),
-        Shape<_1>{});
-        Tensor rAS = make_fragment_like(gAS);
-        cute::copy(gAS, rAS);
-        alibi_slope = rAS(0);
-    }
    for (; n_block >= 0; --n_block) {
        Tensor acc_s = partition_fragment_C(tiled_mma_sdp, Shape<Int<kBlockM>, Int<kBlockN>>{});  // (MMA=4, MMA_M_SdP, MMA_N)
@@ -1429,14 +1410,13 @@ inline __device__ void compute_dq_dk_dv_1rowblock(const Params &params, const in
        Tensor scores = make_tensor(acc_s.data(), flash::convert_layout_acc_rowcol(acc_s.layout()));
        if (Has_alibi) {
-            flash::apply_alibi(
+            flash::apply_alibi<Is_causal>(
                scores, 
                n_block * kBlockN + (tidx / 32 / AtomLayoutMS) * MMA_N_SdP * 16,
                binfo.actual_seqlen_k, 
                m_block * kBlockM + get<0>(taccScS_row(0)),
                binfo.actual_seqlen_q, 
                AtomLayoutMS * 16,
-                bidh, params.scale_softmax, 
                alibi_slope
            );
        }

--- a/csrc/flash_attn/src/flash_bwd_launch_template.h
+++ b/csrc/flash_attn/src/flash_bwd_launch_template.h
@@ -64,12 +64,11 @@ void run_flash_bwd_seqk_parallel(Flash_bwd_params &params, cudaStream_t stream,
        BOOL_SWITCH(is_even_MN, IsEvenMNConst, [&] {
            BOOL_SWITCH(is_even_K, IsEvenKConst, [&] {
                BOOL_SWITCH((params.window_size_left >= 0 || params.window_size_right >= 0) && !params.is_causal, Is_local, [&] {
-                    BOOL_SWITCH(params.has_alibi, Has_alibi, [&] {
+                    BOOL_SWITCH(params.alibi_slopes_ptr != nullptr, Has_alibi, [&] {
                        // If not IsEvenKConst, we also set IsEvenMNConst to false to reduce number of templates.
                        // If head dim > 128, set IsEvenMNConst to false to reduce number of templates
                        // If Is_local, set Is_causal to false
-                        auto kernel = &flash_bwd_dq_dk_dv_loop_seqk_parallel_kernel<Kernel_traits, Is_dropout, Is_causal && !Is_local, Is_local, Has_alibi, IsEvenMNConst && IsEvenKConst && !Is_local && Kernel_traits::kHeadDim <= 128, IsEvenKConst>;
+                        auto kernel = &flash_bwd_dq_dk_dv_loop_seqk_parallel_kernel<Kernel_traits, Is_dropout, Is_causal, Is_local && !Is_causal, Has_alibi, IsEvenMNConst && IsEvenKConst && !Is_local && Kernel_traits::kHeadDim <= 128, IsEvenKConst>;
-                        // auto kernel = &flash_bwd_dq_dk_dv_loop_seqk_parallel_kernel<Kernel_traits, Is_dropout, IsCausalConst, IsEvenMNConst, true>;
                        if (smem_size_dq_dk_dv >= 48 * 1024)  {
                            C10_CUDA_CHECK(cudaFuncSetAttribute(
                                kernel, cudaFuncAttributeMaxDynamicSharedMemorySize, smem_size_dq_dk_dv));
@@ -109,7 +108,7 @@ void run_flash_bwd_seqq_parallel(Flash_bwd_params &params, cudaStream_t stream,
    BOOL_SWITCH(params.is_causal, Is_causal, [&] {
        BOOL_SWITCH(is_even_N, IsEvenNConst, [&] {
            BOOL_SWITCH(is_even_K, IsEvenKConst, [&] {
-                BOOL_SWITCH(params.has_alibi, Has_alibi, [&] {
+                BOOL_SWITCH(params.alibi_slopes_ptr != nullptr, Has_alibi, [&] {
                    // If not IsEvenKConst, we also set IsEvenMNConst to false to reduce number of templates.
                    auto kernel = &flash_bwd_dq_dk_dv_loop_seqq_parallel_kernel<Kernel_traits, Is_dropout, Is_causal, Has_alibi, IsEvenNConst && IsEvenKConst, IsEvenKConst>;
                    // auto kernel = &flash_bwd_dq_dk_dv_loop_seqq_parallel_kernel<Kernel_traits, false, false, IsEvenNConst, IsEvenKConst>;

--- a/csrc/flash_attn/src/flash_fwd_kernel.h
+++ b/csrc/flash_attn/src/flash_fwd_kernel.h
@@ -322,28 +322,14 @@ inline __device__ void compute_attn_1rowblock(const Params &params, const int bi
    clear(acc_o);
+    float alibi_slope = !Has_alibi ? 0.0f : reinterpret_cast<float *>(params.alibi_slopes_ptr)[bidb * params.alibi_slopes_batch_stride + bidh] / params.scale_softmax;
    // For performance reason, we separate out two kinds of iterations:
    // those that need masking on S, and those that don't.
    // We need masking on S for the very last block when K and V has length not multiple of kBlockN.
    // We also need masking on S if it's causal, for the last ceil_div(kBlockM, kBlockN) blocks.
    // We will have at least 1 "masking" iteration.
-    float alibi_slope = 0.0f;
-    if (Has_alibi) {
-        Tensor gAS = make_tensor(
-        make_gmem_ptr(
-            reinterpret_cast<ElementAccum *>(params.alibi_slopes_ptr) 
-            + bidb * params.alibi_slopes_batch_stride + bidh
-        ),
-        Shape<_1>{});
-        Tensor rAS = make_fragment_like(gAS);
-        cute::copy(gAS, rAS);
-        alibi_slope = rAS(0);
-        // if (m_block == 0 && tidx == 0) {
-        //     printf("%d,%d,%f\n", bidb, bidh, alibi_slope);
-        // }
-    }
    // If not even_N, then seqlen_k might end in the middle of a block. In that case we need to
    // mask 2 blocks (e.g. when kBlockM == kBlockN), not just 1.
    constexpr int n_masking_steps = (!Is_causal && !Is_local)
@@ -382,14 +368,13 @@ inline __device__ void compute_attn_1rowblock(const Params &params, const int bi
        // can produce Inf / NaN.
        if (Has_alibi) {
-            flash::apply_alibi(
+            flash::apply_alibi<Is_causal>(
                scores, 
                n_block * kBlockN, 
                binfo.actual_seqlen_k,
                m_block * kBlockM + (tidx / 32) * 16 + (tidx % 32) / 4,
                binfo.actual_seqlen_q, 
                kNWarps * 16,
-                bidh, params.scale_softmax, 
                alibi_slope
            );
        }
@@ -500,14 +485,13 @@ inline __device__ void compute_attn_1rowblock(const Params &params, const int bi
        Tensor scores = make_tensor(acc_s.data(), flash::convert_layout_acc_rowcol(acc_s.layout()));
        if (Has_alibi) {
-            flash::apply_alibi(
+            flash::apply_alibi<Is_causal>(
                scores, 
                n_block * kBlockN, 
                binfo.actual_seqlen_k,
                m_block * kBlockM + (tidx / 32) * 16 + (tidx % 32) / 4,
                binfo.actual_seqlen_q, 
                kNWarps * 16,
-                bidh, params.scale_softmax, 
                alibi_slope
            );
        }
@@ -950,28 +934,14 @@ inline __device__ void compute_attn_1rowblock_splitkv(const Params &params, cons
    clear(acc_o);
+    float alibi_slope = !Has_alibi ? 0.0f : reinterpret_cast<float *>(params.alibi_slopes_ptr)[bidb * params.alibi_slopes_batch_stride + bidh] / params.scale_softmax;
    // For performance reason, we separate out two kinds of iterations:
    // those that need masking on S, and those that don't.
    // We need masking on S for the very last block when K and V has length not multiple of kBlockN.
    // We also need masking on S if it's causal, for the last ceil_div(kBlockM, kBlockN) blocks.
    // We will have at least 1 "masking" iteration.
-    float alibi_slope = 0.0f;
-    if (Has_alibi) {
-        Tensor gAS = make_tensor(
-        make_gmem_ptr(
-            reinterpret_cast<ElementAccum *>(params.alibi_slopes_ptr) 
-            + bidb * params.alibi_slopes_batch_stride + bidh
-        ),
-        Shape<_1>{});
-        Tensor rAS = make_fragment_like(gAS);
-        cute::copy(gAS, rAS);
-        alibi_slope = rAS(0);
-        // if (m_block == 0 && tidx == 0) {
-        //     printf("%d,%d,%f\n", bidb, bidh, alibi_slope);
-        // }
-    }
    // If not even_N, then seqlen_k might end in the middle of a block. In that case we need to
    // mask 2 blocks (e.g. when kBlockM == kBlockN), not just 1.
    constexpr int n_masking_steps = (!Is_causal && !Is_local)
@@ -1006,14 +976,13 @@ inline __device__ void compute_attn_1rowblock_splitkv(const Params &params, cons
        Tensor scores = make_tensor(acc_s.data(), flash::convert_layout_acc_rowcol(acc_s.layout()));
        if (Has_alibi) {
-            flash::apply_alibi(
+            flash::apply_alibi<Is_causal>(
                scores, 
                n_block * kBlockN, 
                binfo.actual_seqlen_k,
                m_block * kBlockM + (tidx / 32) * 16 + (tidx % 32) / 4,
                binfo.actual_seqlen_q, 
                kNWarps * 16,
-                bidh, params.scale_softmax, 
                alibi_slope
            );
        }
@@ -1099,14 +1068,13 @@ inline __device__ void compute_attn_1rowblock_splitkv(const Params &params, cons
        Tensor scores = make_tensor(acc_s.data(), flash::convert_layout_acc_rowcol(acc_s.layout()));
        if (Has_alibi) {
-            flash::apply_alibi(
+            flash::apply_alibi<Is_causal>(
                scores, 
                n_block * kBlockN, 
                binfo.actual_seqlen_k,
                m_block * kBlockM + (tidx / 32) * 16 + (tidx % 32) / 4,
                binfo.actual_seqlen_q, 
                kNWarps * 16,
-                bidh, params.scale_softmax, 
                alibi_slope
            );
        }

--- a/csrc/flash_attn/src/flash_fwd_launch_template.h
+++ b/csrc/flash_attn/src/flash_fwd_launch_template.h
@@ -45,7 +45,7 @@ void run_flash_fwd(Flash_fwd_params &params, cudaStream_t stream) {
        BOOL_SWITCH(is_even_K, IsEvenKConst, [&] {
            BOOL_SWITCH((params.window_size_left >= 0 || params.window_size_right >= 0) && !Is_causal, Is_local, [&] {
                BOOL_SWITCH(return_softmax, ReturnSoftmaxConst, [&] {
-                    BOOL_SWITCH(params.has_alibi, Has_alibi, [&] {
+                    BOOL_SWITCH(params.alibi_slopes_ptr != nullptr, Has_alibi, [&] {
                        // Will only return softmax if dropout, to reduce compilation time.
                        // If not IsEvenKConst, we also set IsEvenMNConst to false to reduce number of templates.
                        // If return_softmax, set IsEvenMNConst to false to reduce number of templates
@@ -86,7 +86,7 @@ void run_flash_splitkv_fwd(Flash_fwd_params &params, cudaStream_t stream) {
                BOOL_SWITCH((params.window_size_left >= 0 || params.window_size_right >= 0) && !Is_causal, Is_local, [&] {
                    BOOL_SWITCH(params.num_splits > 1, Split, [&] {
                        BOOL_SWITCH(params.knew_ptr != nullptr, Append_KV, [&] {
-                            BOOL_SWITCH(params.has_alibi, Has_alibi, [&] {
+                            BOOL_SWITCH(params.alibi_slopes_ptr != nullptr, Has_alibi, [&] {
                                // If Append_KV, then we must have seqlen_offsets, which means cu_seqlens_k != nullptr.
                                // If not IsEvenKConst, we also set IsEvenMNConst to false to reduce number of templates.
                                // If Is_local, set Is_causal to false

--- a/csrc/flash_attn/src/softmax.h
+++ b/csrc/flash_attn/src/softmax.h
@@ -141,14 +141,12 @@ inline __device__ void apply_mask(Tensor<Engine, Layout> &tensor, const int max_
 template <bool HasWSLeft=true, typename Engine, typename Layout>
 inline __device__ void apply_mask_local(Tensor<Engine, Layout> &tensor, const int col_idx_offset_,
-                                        const int max_seqlen_k, const int row_idx_offset_,
+                                        const int max_seqlen_k, const int row_idx_offset,
                                        const int max_seqlen_q, const int warp_row_stride,
                                        const int window_size_left, const int window_size_right) {
    // tensor has shape (ncol=(2, MMA_M), nrow=(2, MMA_N))
    static_assert(Layout::rank == 2, "Only support 2D Tensor");
    const int lane_id = threadIdx.x % 32;
-    // const int row_idx_offset = row_idx_offset_ + lane_id / 4;
-    const int row_idx_offset = row_idx_offset_;
    const int col_idx_offset = col_idx_offset_ + (lane_id % 4) * 2;
    #pragma unroll
    for (int mi = 0; mi < size<0, 1>(tensor); ++mi) {
@@ -180,17 +178,17 @@ inline __device__ void apply_mask_local(Tensor<Engine, Layout> &tensor, const in
 template <typename Engine, typename Layout>
 inline __device__ void apply_mask_causal(Tensor<Engine, Layout> &tensor, const int col_idx_offset_,
-                                         const int max_seqlen_k, const int row_idx_offset_,
+                                         const int max_seqlen_k, const int row_idx_offset,
                                         const int max_seqlen_q, const int warp_row_stride) {
    // Causal masking is equivalent to local masking with window_size_left = infinity and window_size_right = 0
-    apply_mask_local</*HasWSLeft=*/false>(tensor, col_idx_offset_, max_seqlen_k, row_idx_offset_,
+    apply_mask_local</*HasWSLeft=*/false>(tensor, col_idx_offset_, max_seqlen_k, row_idx_offset,
                                          max_seqlen_q, warp_row_stride, -1, 0);
 }
 template <typename Engine0, typename Layout0, typename Engine1, typename Layout1>
 inline __device__ void apply_mask_causal_w_idx(
    Tensor<Engine0, Layout0> &tensor, Tensor<Engine1, Layout1> const &idx_rowcol,
-    const int col_idx_offset_, const int max_seqlen_k, const int row_idx_offset_)
+    const int col_idx_offset_, const int max_seqlen_k, const int row_idx_offset)
 {
    // tensor has shape (ncol=(2, MMA_M), nrow=(2, MMA_N))
    static_assert(Layout0::rank == 2, "Only support 2D Tensor");
@@ -199,7 +197,7 @@ inline __device__ void apply_mask_causal_w_idx(
    CUTE_STATIC_ASSERT_V(size<1>(tensor) == size<1>(idx_rowcol));
    #pragma unroll
    for (int mi = 0; mi < size<0>(tensor); ++mi) {
-        const int col_idx_limit = std::min(max_seqlen_k, 1 + row_idx_offset_ + get<0>(idx_rowcol(mi, 0)));
+        const int col_idx_limit = std::min(max_seqlen_k, 1 + row_idx_offset + get<0>(idx_rowcol(mi, 0)));
        #pragma unroll
        for (int ni = 0; ni < size<1, 1>(tensor); ++ni) {
            if (col_idx_offset_ + get<1>(idx_rowcol(0, ni)) >= col_idx_limit) {

--- a/flash_attn/flash_attn_interface.py
+++ b/flash_attn/flash_attn_interface.py
@@ -53,12 +53,12 @@ def _flash_attn_forward(
        k,
        v,
        None,
+        alibi_slopes,
        dropout_p,
        softmax_scale,
        causal,
        window_size[0],
        window_size[1],
-        alibi_slopes,
        return_softmax,
        None,
    )
@@ -90,6 +90,7 @@ def _flash_attn_varlen_forward(
        cu_seqlens_q,
        cu_seqlens_k,
        None,
+        alibi_slopes,
        max_seqlen_q,
        max_seqlen_k,
        dropout_p,
@@ -98,7 +99,6 @@ def _flash_attn_varlen_forward(
        causal,
        window_size[0],
        window_size[1],
-        alibi_slopes,
        return_softmax,
        None,
    )
@@ -137,12 +137,12 @@ def _flash_attn_backward(
        dq,
        dk,
        dv,
+        alibi_slopes,
        dropout_p,
        softmax_scale,
        causal,
        window_size[0],
        window_size[1],
-        alibi_slopes,
        None,
        rng_state,
    )
@@ -185,6 +185,7 @@ def _flash_attn_varlen_backward(
        dv,
        cu_seqlens_q,
        cu_seqlens_k,
+        alibi_slopes,
        max_seqlen_q,
        max_seqlen_k,
        dropout_p,
@@ -193,7 +194,6 @@ def _flash_attn_varlen_backward(
        causal,
        window_size[0],
        window_size[1],
-        alibi_slopes,
        None,
        rng_state,
    )
@@ -613,6 +613,8 @@ def flash_attn_qkvpacked_func(
            Default to 1 / sqrt(headdim).
        causal: bool. Whether to apply causal attention mask (e.g., for auto-regressive modeling).
        window_size: (left, right). If not (-1, -1), implements sliding window local attention.
+        alibi_slopes: (nheads,) or (batch_size, nheads), fp32. A bias of (-alibi_slope * |i - j|) is added to
+            the attention score of query i and key j.
        return_attn_probs: bool. Whether to return the attention probabilities. This option is for
           testing only. The returned probabilities are not guaranteed to be correct
           (they might not have the right scaling).
@@ -673,6 +675,9 @@ def flash_attn_kvpacked_func(
            Default to 1 / sqrt(headdim).
        causal: bool. Whether to apply causal attention mask (e.g., for auto-regressive modeling).
        window_size: (left, right). If not (-1, -1), implements sliding window local attention.
+        alibi_slopes: (nheads,) or (batch_size, nheads), fp32. A bias of
+            (-alibi_slope * |i + seqlen_k - seqlen_q - j|)
+            is added to the attention score of query i and key j.
        return_attn_probs: bool. Whether to return the attention probabilities. This option is for
           testing only. The returned probabilities are not guaranteed to be correct
           (they might not have the right scaling).
@@ -732,6 +737,9 @@ def flash_attn_func(
            Default to 1 / sqrt(headdim).
        causal: bool. Whether to apply causal attention mask (e.g., for auto-regressive modeling).
        window_size: (left, right). If not (-1, -1), implements sliding window local attention.
+        alibi_slopes: (nheads,) or (batch_size, nheads), fp32. A bias of
+            (-alibi_slope * |i + seqlen_k - seqlen_q - j|)
+            is added to the attention score of query i and key j.
        return_attn_probs: bool. Whether to return the attention probabilities. This option is for
           testing only. The returned probabilities are not guaranteed to be correct
           (they might not have the right scaling).
@@ -780,6 +788,8 @@ def flash_attn_varlen_qkvpacked_func(
            Default to 1 / sqrt(headdim).
        causal: bool. Whether to apply causal attention mask (e.g., for auto-regressive modeling).
        window_size: (left, right). If not (-1, -1), implements sliding window local attention.
+        alibi_slopes: (nheads,) or (batch_size, nheads), fp32. A bias of (-alibi_slope * |i - j|)
+            is added to the attention score of query i and key j.
        return_attn_probs: bool. Whether to return the attention probabilities. This option is for
           testing only. The returned probabilities are not guaranteed to be correct
           (they might not have the right scaling).
@@ -858,6 +868,9 @@ def flash_attn_varlen_kvpacked_func(
            Default to 1 / sqrt(headdim).
        causal: bool. Whether to apply causal attention mask (e.g., for auto-regressive modeling).
        window_size: (left, right). If not (-1, -1), implements sliding window local attention.
+        alibi_slopes: (nheads,) or (batch_size, nheads), fp32. A bias of
+            (-alibi_slope * |i + seqlen_k - seqlen_q - j|)
+            is added to the attention score of query i and key j.
        return_attn_probs: bool. Whether to return the attention probabilities. This option is for
           testing only. The returned probabilities are not guaranteed to be correct
           (they might not have the right scaling).
@@ -938,6 +951,9 @@ def flash_attn_varlen_func(
            Default to 1 / sqrt(headdim).
        causal: bool. Whether to apply causal attention mask (e.g., for auto-regressive modeling).
        window_size: (left, right). If not (-1, -1), implements sliding window local attention.
+        alibi_slopes: (nheads,) or (batch_size, nheads), fp32. A bias of
+            (-alibi_slope * |i + seqlen_k - seqlen_q - j|)
+            is added to the attention score of query i and key j.
        return_attn_probs: bool. Whether to return the attention probabilities. This option is for
           testing only. The returned probabilities are not guaranteed to be correct
           (they might not have the right scaling).
@@ -981,8 +997,8 @@ def flash_attn_with_kvcache(
    causal=False,
    window_size=(-1, -1),  # -1 means infinite context window
    rotary_interleaved=True,
-    num_splits=0,
    alibi_slopes=None,
+    num_splits=0,
 ):
    """
    If k and v are not None, k_cache and v_cache will be updated *inplace* with the new values from
@@ -1050,6 +1066,9 @@ def flash_attn_with_kvcache(
            If True, rotary embedding will combine dimensions 0 & 1, 2 & 3, etc. If False,
            rotary embedding will combine dimensions 0 & rotary_dim / 2, 1 & rotary_dim / 2 + 1
            (i.e. GPT-NeoX style).
+        alibi_slopes: (nheads,) or (batch_size, nheads), fp32. A bias of
+            (-alibi_slope * |i + seqlen_k - seqlen_q - j|)
+            is added to the attention score of query i and key j.
        num_splits: int. If > 1, split the key/value into this many chunks along the sequence.
           If num_splits == 1, we don't split the key/value. If num_splits == 0, we use a heuristic
           to automatically determine the number of splits.
@@ -1080,6 +1099,7 @@ def flash_attn_with_kvcache(
        rotary_cos,
        rotary_sin,
        cache_batch_idx,
+        alibi_slopes,
        None,
        softmax_scale,
        causal,
@@ -1087,6 +1107,5 @@ def flash_attn_with_kvcache(
        window_size[1],
        rotary_interleaved,
        num_splits,
-        alibi_slopes,
    )
    return out
--- a/tests/test_alibi.py
+++ b/tests/test_alibi.py
-import math
-import pytest
-import torch
-import torch.nn.functional as F
-from einops import rearrange, repeat
-from flash_attn import (flash_attn_func, flash_attn_kvpacked_func,
-                        flash_attn_qkvpacked_func, flash_attn_varlen_func,
-                        flash_attn_varlen_kvpacked_func,
-                        flash_attn_varlen_qkvpacked_func,
-                        flash_attn_with_kvcache)
-from flash_attn.bert_padding import pad_input, unpad_input
-from flash_attn.flash_attn_interface import _get_block_size
-from flash_attn.flash_attn_triton import \
-    flash_attn_func as flash_attn_func_triton
-from flash_attn.layers.rotary import apply_rotary_emb
-MAX_HEADDIM_SM8x = 192
-is_sm75 = torch.cuda.get_device_capability("cuda") == (7, 5)
-is_sm8x = torch.cuda.get_device_capability("cuda")[0] == 8
-is_sm80 = torch.cuda.get_device_capability("cuda") == (8, 0)
-is_sm90 = torch.cuda.get_device_capability("cuda") == (9, 0)
-def generate_alibi(max_seq_len, num_attention_heads, tp_world_size, tp_index, key_padding_mask=None, device="cuda"):
-    def get_slopes(n):
-        def get_slopes_power_of_2(n):
-            start = (2 ** (-2 ** -(math.log2(n) - 3)))
-            ratio = start
-            return [start * ratio ** i for i in range(n)]
-        if math.log2(n).is_integer():
-            return get_slopes_power_of_2(n)
-        else:
-            closest_power_of_2 = 2 ** math.floor(math.log2(n))
-            return get_slopes_power_of_2(closest_power_of_2) + get_slopes(2 * closest_power_of_2)[0::2][
-                                                                :n - closest_power_of_2]
-    slopes = torch.tensor(get_slopes(num_attention_heads)).to(device=device)
-    # Select the part of the tensor that corresponds to our tensor parallel index.
-    assert (num_attention_heads/tp_world_size).is_integer(
-    ), "it works only when (num_attention_heads/tp_world_size) is integer"
-    nh_tp = num_attention_heads // tp_world_size
-    slopes = slopes[nh_tp * tp_index:nh_tp * (tp_index + 1)]
-    if (key_padding_mask is None):
-        arange_tensor = rearrange(torch.arange(max_seq_len), "sqk -> 1 sqk").to(device=device)
-    else:
-        arange_tensor = (key_padding_mask.cumsum(dim=-1, dtype=slopes.dtype) - 1) \
-            .masked_fill_(~key_padding_mask, torch.finfo(torch.float).min).to(device=device)
-    arange_tensor = rearrange(arange_tensor, 'b sqk -> b 1 1 sqk')
-    # (1, nheads, 1, seqlen_k) or (batch, nheads, 1, seqlen_k)
-    alibi_tensor = rearrange(slopes, 'nh -> 1 nh 1 1') * arange_tensor
-    return alibi_tensor, slopes
-def generate_random_padding_mask(max_seqlen, batch_size, device, mode="random", right_padding=True):
-    assert mode in ["full", "random", "third"]
-    if mode == "full":
-        lengths = torch.full((batch_size, 1), max_seqlen,
-                             device=device, dtype=torch.int32)
-    elif mode == "random":
-        lengths = torch.randint(
-            max(1, max_seqlen - 20), max_seqlen + 1, (batch_size, 1), device=device
-        )
-    elif mode == "third":
-        lengths = torch.randint(
-            max_seqlen // 3, max_seqlen + 1, (batch_size, 1), device=device)
-    if right_padding:
-        padding_mask = (
-            repeat(torch.arange(max_seqlen, device=device),
-                "s -> b s", b=batch_size) < lengths
-        )
-    else:
-        padding_mask = (
-            repeat(torch.arange(start=max_seqlen-1, end=-1, step=-1, device=device),
-                "s -> b s", b=batch_size) < lengths
-        )
-    return padding_mask
-def generate_qkv(
-    q, k, v, query_padding_mask=None, key_padding_mask=None, kvpacked=False, qkvpacked=False
-):
-    """
-    Arguments:
-        q: (batch_size, seqlen_q, nheads, d)
-        k: (batch_size, seqlen_k, nheads_k, d)
-        v: (batch_size, seqlen_k, nheads_k, d)
-        query_padding_mask: (batch_size, seqlen), bool
-        key_padding_mask: (batch_size, seqlen), bool
-    """
-    assert not (kvpacked and qkvpacked)
-    batch_size, seqlen_q, nheads, d = q.shape
-    _, seqlen_k, nheads_k, _ = k.shape
-    assert k.shape == (batch_size, seqlen_k, nheads_k, d)
-    assert v.shape == (batch_size, seqlen_k, nheads_k, d)
-    if query_padding_mask is not None:
-        q_unpad, indices_q, cu_seqlens_q, max_seqlen_q = unpad_input(
-            q, query_padding_mask)
-        def output_pad_fn(output_unpad): return pad_input(
-            output_unpad, indices_q, batch_size, seqlen_q
-        )
-    else:
-        q_unpad = rearrange(q, "b s h d -> (b s) h d")
-        cu_seqlens_q = torch.arange(
-            0, (batch_size + 1) * seqlen_q, step=seqlen_q, dtype=torch.int32, device=q_unpad.device
-        )
-        max_seqlen_q = seqlen_q
-        def output_pad_fn(output_unpad): return rearrange(
-            output_unpad, "(b s) h d -> b s h d", b=batch_size
-        )
-    if key_padding_mask is not None:
-        k_unpad, indices_k, cu_seqlens_k, max_seqlen_k = unpad_input(
-            k, key_padding_mask)
-        v_unpad, _, _, _ = unpad_input(v, key_padding_mask)
-    else:
-        k_unpad = rearrange(k, "b s h d -> (b s) h d")
-        v_unpad = rearrange(v, "b s h d -> (b s) h d")
-        cu_seqlens_k = torch.arange(
-            0, (batch_size + 1) * seqlen_k, step=seqlen_k, dtype=torch.int32, device=k_unpad.device
-        )
-        max_seqlen_k = seqlen_k
-    if qkvpacked:
-        assert (query_padding_mask == key_padding_mask).all()
-        assert nheads == nheads_k
-        qkv_unpad = torch.stack([q_unpad, k_unpad, v_unpad], dim=1)
-        qkv = torch.stack([q, k, v], dim=2)
-        if query_padding_mask is not None:
-            def dqkv_pad_fn(dqkv_unpad): return pad_input(
-                dqkv_unpad, indices_q, batch_size, seqlen_q)
-        else:
-            def dqkv_pad_fn(dqkv_unpad): return rearrange(
-                dqkv_unpad, "(b s) t h d -> b s t h d", b=batch_size
-            )
-        return (
-            qkv_unpad.detach().requires_grad_(),
-            cu_seqlens_q,
-            max_seqlen_q,
-            qkv.detach().requires_grad_(),
-            output_pad_fn,
-            dqkv_pad_fn,
-        )
-    elif kvpacked:
-        kv_unpad = torch.stack([k_unpad, v_unpad], dim=1)
-        kv = torch.stack([k, v], dim=2)
-        dq_pad_fn = output_pad_fn
-        if key_padding_mask is not None:
-            def dkv_pad_fn(dkv_unpad): return pad_input(
-                dkv_unpad, indices_k, batch_size, seqlen_k)
-        else:
-            def dkv_pad_fn(dkv_unpad): return rearrange(
-                dkv_unpad, "(b s) t h d -> b s t h d", b=batch_size
-            )
-        return (
-            q_unpad.detach().requires_grad_(),
-            kv_unpad.detach().requires_grad_(),
-            cu_seqlens_q,
-            cu_seqlens_k,
-            max_seqlen_q,
-            max_seqlen_k,
-            q.detach().requires_grad_(),
-            kv.detach().requires_grad_(),
-            output_pad_fn,
-            dq_pad_fn,
-            dkv_pad_fn,
-        )
-    else:
-        dq_pad_fn = output_pad_fn
-        if key_padding_mask is not None:
-            def dk_pad_fn(dk_unpad): return pad_input(
-                dk_unpad, indices_k, batch_size, seqlen_k)
-        else:
-            def dk_pad_fn(dk_unpad): return rearrange(
-                dk_unpad, "(b s) h d -> b s h d", b=batch_size)
-        return (
-            q_unpad.detach().requires_grad_(),
-            k_unpad.detach().requires_grad_(),
-            v_unpad.detach().requires_grad_(),
-            cu_seqlens_q,
-            cu_seqlens_k,
-            max_seqlen_q,
-            max_seqlen_k,
-            q.detach().requires_grad_(),
-            k.detach().requires_grad_(),
-            v.detach().requires_grad_(),
-            output_pad_fn,
-            dq_pad_fn,
-            dk_pad_fn,
-        )
-def construct_local_mask(
-    seqlen_q,
-    seqlen_k,
-    window_size=(-1, -1),  # -1 means infinite window size
-    query_padding_mask=None,
-    key_padding_mask=None,
-    device=None,
-):
-    row_idx = rearrange(torch.arange(
-        seqlen_q, device=device, dtype=torch.long), "s -> s 1")
-    col_idx = torch.arange(seqlen_k, device=device, dtype=torch.long)
-    sk = (
-        seqlen_k
-        if key_padding_mask is None
-        else rearrange(key_padding_mask.sum(-1), "b -> b 1 1 1")
-    )
-    sq = (
-        seqlen_q
-        if query_padding_mask is None
-        else rearrange(query_padding_mask.sum(-1), "b -> b 1 1 1")
-    )
-    if window_size[0] < 0:
-        return col_idx > row_idx + sk - sq + window_size[1]
-    else:
-        sk = torch.full_like(
-            col_idx, seqlen_k) if key_padding_mask is None else sk
-        return torch.logical_or(
-            col_idx > torch.minimum(row_idx + sk - sq + window_size[1], sk),
-            col_idx < row_idx + sk - sq - window_size[0],
-        )
-def attention_ref(
-    q,
-    k,
-    v,
-    query_padding_mask=None,
-    key_padding_mask=None,
-    dropout_p=0.0,
-    dropout_mask=None,
-    causal=False,
-    window_size=(-1, -1),  # -1 means infinite window size
-    upcast=True,
-    reorder_ops=False,
-    bias=None
-):
-    """
-    Arguments:
-        q: (batch_size, seqlen_q, nheads, head_dim)
-        k: (batch_size, seqlen_k, nheads_k, head_dim)
-        v: (batch_size, seqlen_k, nheads_k, head_dim)
-        query_padding_mask: (batch_size, seqlen_q)
-        key_padding_mask: (batch_size, seqlen_k)
-        dropout_p: float
-        dropout_mask: (batch_size, nheads, seqlen_q, seqlen_k)
-        causal: whether to apply causal masking
-        window_size: (int, int), left and right window size
-        upcast: whether to cast all inputs to fp32, do all computation in fp32, then cast
-            output back to fp16/bf16.
-        reorder_ops: whether to change the order of operations (scaling k instead of scaling k, etc.)
-            without changing the math. This is to estimate the numerical error from operation
-            reordering.
-    Output:
-        output: (batch_size, seqlen_q, nheads, head_dim)
-        attention: (batch_size, nheads, seqlen_q, seqlen_k), softmax after dropout
-    """
-    if causal:
-        window_size = (window_size[0], 0)
-    dtype_og = q.dtype
-    if upcast:
-        q, k, v = q.float(), k.float(), v.float()
-    seqlen_q, seqlen_k = q.shape[1], k.shape[1]
-    k = repeat(k, "b s h d -> b s (h g) d", g=q.shape[2] // k.shape[2])
-    v = repeat(v, "b s h d -> b s (h g) d", g=q.shape[2] // v.shape[2])
-    d = q.shape[-1]
-    if not reorder_ops:
-        scores = torch.einsum("bthd,bshd->bhts", q / math.sqrt(d), k)
-    else:
-        scores = torch.einsum("bthd,bshd->bhts", q, k / math.sqrt(d))
-    if bias is not None:
-        bias = bias.to(scores.dtype)
-        scores += bias
-    if key_padding_mask is not None:
-        scores.masked_fill_(rearrange(~key_padding_mask,
-                            "b s -> b 1 1 s"), float("-inf"))
-    if window_size[0] >= 0 or window_size[1] >= 0:
-        local_mask = construct_local_mask(
-            seqlen_q,
-            seqlen_k,
-            window_size,
-            query_padding_mask,
-            key_padding_mask,
-            q.device,
-        )
-        scores.masked_fill_(local_mask, float("-inf"))
-    attention = torch.softmax(scores, dim=-1)
-    # Some rows might be completely masked out so we fill them with zero instead of NaN
-    if window_size[0] >= 0 or window_size[1] >= 0:
-        attention = attention.masked_fill(
-            torch.all(local_mask, dim=-1, keepdim=True), 0.0)
-    # We want to mask here so that the attention matrix doesn't have any NaNs
-    # Otherwise we'll get NaN in dV
-    if query_padding_mask is not None:
-        attention = attention.masked_fill(
-            rearrange(~query_padding_mask, "b s -> b 1 s 1"), 0.0)
-    dropout_scaling = 1.0 / (1 - dropout_p)
-    # attention_drop = attention.masked_fill(~dropout_mask, 0.0) * dropout_scaling
-    # output = torch.einsum('bhts,bshd->bthd', attention_drop , v)
-    if dropout_mask is not None:
-        attention_drop = attention.masked_fill(~dropout_mask, 0.0)
-    else:
-        attention_drop = attention
-    output = torch.einsum(
-        "bhts,bshd->bthd", attention_drop, v * dropout_scaling)
-    if query_padding_mask is not None:
-        output.masked_fill_(
-            rearrange(~query_padding_mask, "b s -> b s 1 1"), 0.0)
-    return output.to(dtype=dtype_og), attention.to(dtype=dtype_og)
-def attention_kvpacked_ref(
-    q,
-    kv,
-    query_padding_mask=None,
-    key_padding_mask=None,
-    dropout_p=0.0,
-    dropout_mask=None,
-    causal=False,
-    window_size=(-1, -1),  # -1 means infinite window size
-    upcast=True,
-    reorder_ops=False,
-):
-    return attention_ref(
-        q,
-        kv[:, :, 0],
-        kv[:, :, 1],
-        query_padding_mask,
-        key_padding_mask,
-        dropout_p,
-        dropout_mask,
-        upcast=upcast,
-        causal=causal,
-        window_size=window_size,
-        reorder_ops=reorder_ops,
-    )
-def attention_qkvpacked_ref(
-    qkv,
-    key_padding_mask=None,
-    dropout_p=0.0,
-    dropout_mask=None,
-    causal=False,
-    window_size=(-1, -1),  # -1 means infinite window size
-    upcast=True,
-    reorder_ops=False,
-):
-    return attention_ref(
-        qkv[:, :, 0],
-        qkv[:, :, 1],
-        qkv[:, :, 2],
-        key_padding_mask,
-        key_padding_mask,
-        dropout_p,
-        dropout_mask,
-        upcast=upcast,
-        causal=causal,
-        window_size=window_size,
-        reorder_ops=reorder_ops,
-    )
-def generate_sparsity_mask(seqlen, sparsity=0.3):
-    repeats = seqlen // 16 // 2
-    # mask = torch.stack([torch.tensor([1, 0] * repeats, dtype=torch.bool, device='cuda'),
-    #                     torch.tensor([0, 1] * repeats, dtype=torch.bool, device='cuda')], dim=-1)
-    # mask = torch.stack([torch.tensor([1, 1] * repeats, dtype=torch.bool, device='cuda'),
-    #                     torch.tensor([1, 1] * repeats, dtype=torch.bool, device='cuda')], dim=-1)
-    # mask = torch.stack([torch.tensor([1, 1] * repeats, dtype=torch.bool, device='cuda')], dim=-1)
-    # mask = torch.stack([torch.tensor([1, 0] * repeats, dtype=torch.bool, device='cuda')], dim=-1)
-    nrow, ncol = seqlen // 16, seqlen // 256
-    mask = torch.rand(nrow, ncol, device="cuda") < sparsity
-    return mask
-def attention_blocksparse_ref(qkv, blockmask, attn_mask, dropout_p, dropout_mask):
-    """
-    Arguments:
-        qkv: (batch_size, seqlen, 3, nheads, head_dim)
-        blockmask: (seqlen / 16, seqlen / 256)
-        attn_mask: (batch_size, seqlen)
-        dropout_p: float
-        dropout_mask: (batch_size, nheads, seqlen, seqlen)
-    Output:
-        output: (batch_size, seqlen, nheads, head_dim)
-        attention: softmax after dropout
-    """
-    q, k, v = qkv.float().unbind(dim=2)
-    d = qkv.shape[-1]
-    seqlen = qkv.shape[1]
-    scores = torch.einsum("bthd,bshd->bhts", q / math.sqrt(d), k)
-    scores.masked_fill_(rearrange(~attn_mask, "b s -> b 1 1 s"), float("-inf"))
-    blockmask = repeat(blockmask, "s_16 s_256 -> (s_16 16) (s_256 256)")
-    blockmask = blockmask[:seqlen, :seqlen]
-    scores.masked_fill_(rearrange(~blockmask, "t s -> 1 1 t s"), float("-inf"))
-    attention = torch.softmax(scores, dim=-1)
-    attention = attention.masked_fill(
-        rearrange(~attn_mask, "b s -> b 1 s 1"), 0.0)
-    attention = attention.masked_fill_(
-        rearrange(~blockmask, "t s -> 1 1 t s"), 0.0)
-    attention_drop = attention.masked_fill(
-        ~dropout_mask, 0.0) / (1 - dropout_p)
-    output = torch.einsum("bhts,bshd->bthd", attention_drop, v)
-    output.masked_fill_(rearrange(~attn_mask, "b s -> b s 1 1"), 0)
-    return output.to(dtype=qkv.dtype), attention.to(dtype=qkv.dtype)
-def convert_flash_attn_S_to_softmax(
-    S,
-    seqlen_q,
-    seqlen_k,
-    query_padding_mask,
-    key_padding_mask,
-    head_dim,
-    is_dropout,
-    causal=False,
-    window_size=(-1, -1),  # -1 means infinite window size
-):
-    """FlashAttention stores the S matrix in a different way.
-    Arguments:
-        S: (batch_size, nheads, seqlen_q_rounded, seqlen_k_rounded)
-        query_padding_mask: (batch_size, seqlen_q_rounded)
-        key_padding_mask: (batch_size, seqlen_k_rounded)
-    """
-    if causal:
-        window_size = (window_size[0], 0)
-    seqlen_q_rounded, seqlen_k_rounded = S.shape[-2:]
-    warps_n = 4
-    blocksize_m, blocksize_n = _get_block_size(
-        S.device, head_dim, is_dropout, causal)
-    nblocks_n = (seqlen_k_rounded + blocksize_n - 1) // blocksize_n
-    nblocks_m = (seqlen_q_rounded + blocksize_m - 1) // blocksize_m
-    mmas_n = (blocksize_n + 16 - 1) // 16
-    S_flat = rearrange(
-        S,
-        "b h (nblocks_m blocksize_m) (nblocks_n blocksize_n) -> b h nblocks_m nblocks_n (blocksize_m blocksize_n)",
-        blocksize_m=blocksize_m,
-        blocksize_n=blocksize_n,
-    )
-    S_converted = rearrange(
-        S_flat,
-        "b h nblocks_m nblocks_n (mmas_n mmas_m warps_n eight four c2 c1 c0) -> b h (nblocks_m mmas_m warps_n c1 eight) (nblocks_n mmas_n c2 four c0)",
-        mmas_n=mmas_n,
-        warps_n=warps_n,
-        eight=8,
-        c0=2,
-        c1=2,
-        c2=2,
-        four=4,
-    )
-    if window_size[0] >= 0 or window_size[1] >= 0:
-        local_mask = construct_local_mask(
-            seqlen_q,
-            seqlen_k,
-            window_size,
-            query_padding_mask,
-            key_padding_mask,
-            S.device,
-        )
-        local_mask = F.pad(
-            local_mask,
-            (0, seqlen_k_rounded - seqlen_k, 0, seqlen_q_rounded - seqlen_q),
-            value=True,
-        )
-        S_converted.masked_fill_(local_mask, 0.0)
-    # Need to zero out things not in attention_mask in case S was initialized with random values
-    # and some of those values aren't overwritten.
-    seqlen_q_og = (
-        query_padding_mask.shape[-1] if query_padding_mask is not None else seqlen_q_rounded
-    )
-    if query_padding_mask is not None:
-        query_padding_mask = F.pad(
-            query_padding_mask, (0, seqlen_q_rounded - seqlen_q_og))
-        S_converted = S_converted.masked_fill(
-            rearrange(~query_padding_mask, "b s -> b 1 s 1"), 0.0)
-    seqlen_k_og = key_padding_mask.shape[-1] if key_padding_mask is not None else seqlen_k
-    if key_padding_mask is not None:
-        key_padding_mask = F.pad(
-            key_padding_mask, (0, seqlen_k_rounded - seqlen_k_og))
-        S_converted = S_converted.masked_fill(
-            rearrange(~key_padding_mask, "b s -> b 1 1 s"), 0.0)
-    S_converted = F.pad(S_converted, (0, 0, 0, seqlen_q_og - seqlen_q_rounded))
-    S_converted = F.pad(S_converted, (0, seqlen_k_og - seqlen_k_rounded))
-    return S_converted[:, :, :seqlen_q, :seqlen_k]
-def normalize_flash_attn_S(
-    attn_unnorm,
-    q,
-    k,
-    v,
-    query_padding_mask=None,
-    key_padding_mask=None,
-    is_dropout=False,
-    causal=False,
-    window_size=(-1, -1),  # -1 means infinite window size
-):
-    """
-    Arguments:
-        q: (batch_size, seqlen_q, nheads, head_dim)
-        k, v: (batch_size, seqlen_k, nheads, head_dim)
-        key_padding_mask: (batch_size, seqlen_q)
-    Output:
-        softmax_lse: (batch_size, nheads, seqlen_q)
-        softmax_max: (batch_size, nheads, seqlen_q)
-    """
-    if causal:
-        window_size = (window_size[0], 0)
-    q, k, v = q.float(), k.float(), v.float()
-    _, seqlen_q, _, head_dim = q.shape
-    seqlen_k = k.shape[1]
-    scores = torch.einsum("bthd,bshd->bhts", q / math.sqrt(head_dim), k)
-    if key_padding_mask is not None:
-        scores.masked_fill_(rearrange(~key_padding_mask,
-                            "b s -> b 1 1 s"), float("-inf"))
-    if window_size[0] >= 0 or window_size[1] >= 0:
-        local_mask = construct_local_mask(
-            seqlen_q,
-            seqlen_k,
-            window_size,
-            query_padding_mask,
-            key_padding_mask,
-            q.device,
-        )
-        scores.masked_fill_(local_mask, float("-inf"))
-    _, block_size_n = _get_block_size(
-        scores.device, head_dim, is_dropout, causal)
-    scores_block = scores.split(block_size_n, dim=-1)
-    lse_block = torch.stack([torch.logsumexp(s, dim=-1)
-                            for s in scores_block], dim=-1)
-    lse = torch.logsumexp(lse_block, dim=-1)
-    # lse could be -inf (i.e. all values in scores are -inf), and we want to set those to inf
-    # so that when we do torch.exp(m - lse), we get 0.0 instead of NaN.
-    lse[lse == float("-inf")] = float("inf")
-    scores_max_block = torch.stack(
-        [torch.amax(s, dim=-1) for s in scores_block], dim=-1)
-    cummax_block = torch.cummax(
-        scores_max_block.flip(-1), dim=-1).values.flip(-1).unbind(dim=-1)
-    attn_unnorm_block = attn_unnorm.split(block_size_n, dim=-1)
-    attn_norm = torch.cat(
-        [
-            a * rearrange(torch.exp(m - lse), "b h s -> b h s 1")
-            for a, m in zip(attn_unnorm_block, cummax_block)
-        ],
-        dim=-1,
-    )
-    if query_padding_mask is not None:
-        attn_norm.masked_fill_(
-            rearrange(~query_padding_mask, "b s -> b 1 s 1"), 0.0)
-    return attn_norm.to(dtype=attn_unnorm.dtype)
-def get_dropout_fraction(
-    dropout_mask,
-    query_padding_mask=None,
-    key_padding_mask=None,
-    causal=False,
-    window_size=(-1, -1),  # -1 means infinite window size
-):
-    """
-    dropout_mask: (batch_size, nheads, seqlen_q, seqlen_k), bool. True means keep, False means drop.
-    query_padding_mask: (batch_size, seqlen_q)
-    key_padding_mask: (batch_size, seqlen_k)
-    """
-    if causal:
-        window_size = (window_size[0], 0)
-    batch_size, nheads, seqlen_q, seqlen_k = dropout_mask.shape
-    dropped = ~dropout_mask
-    valid = torch.ones_like(dropout_mask)
-    if query_padding_mask is not None:
-        dropped.masked_fill_(
-            rearrange(~query_padding_mask, "b s -> b 1 s 1"), False)
-        valid.masked_fill_(
-            rearrange(~query_padding_mask, "b s -> b 1 s 1"), False)
-    if key_padding_mask is not None:
-        dropped.masked_fill_(
-            rearrange(~key_padding_mask, "b s -> b 1 1 s"), False)
-        valid.masked_fill_(
-            rearrange(~key_padding_mask, "b s -> b 1 1 s"), False)
-    if window_size[0] >= 0 or window_size[1] >= 0:
-        local_mask = construct_local_mask(
-            seqlen_q,
-            seqlen_k,
-            window_size,
-            query_padding_mask,
-            key_padding_mask,
-            dropout_mask.device,
-        )
-        dropped.masked_fill_(local_mask, False)
-        valid.masked_fill_(local_mask, False)
-    dropped_total = dropped.sum()
-    return dropped.sum() / valid.sum()
-@pytest.mark.parametrize(
-    "dtype", [torch.float16]
-)
-@pytest.mark.parametrize(
-    "b_sq", 
-    [
-        (32, 512), 
-        (16, 1024), 
-        (8, 2048),
-        (4, 4096), 
-        (2, 8192), 
-        (1, 16384)
-    ]
-)
-@pytest.mark.parametrize(
-    "nh_hd", 
-    [
-        (32, 64),
-        (16, 128),
-        (40, 128) # non power of 2 nh
-    ]
-)
-@pytest.mark.parametrize(
-    "tp_world_size", [1, 2, 4]
-)
-def test_flash_attn_func(b_sq, nh_hd, tp_world_size, dtype):
-    b, sq = b_sq
-    nh, hd = nh_hd
-    nh_tp = nh // tp_world_size
-    q, k, v = [torch.randn(b, sq, nh_tp, hd, device="cuda", 
-                           dtype=dtype, requires_grad=True) for _ in range(3)]
-    dout = torch.rand_like(q)
-    for tp_index in range(tp_world_size):
-        alibi, alibi_slopes = generate_alibi(
-            max_seq_len=sq,
-            num_attention_heads=nh,
-            tp_world_size=tp_world_size,
-            tp_index=tp_index,
-            key_padding_mask=None,
-            device="cuda"
-        )
-        triton_out = flash_attn_func_triton(
-            q, k, v, alibi, True, hd**(-0.5))
-        triton_out.backward(dout)
-        triton_dq, q.grad = q.grad.clone(), None
-        triton_dk, k.grad = k.grad.clone(), None
-        triton_dv, v.grad = v.grad.clone(), None
-        flash_out = flash_attn_func(q, k, v, causal=True, alibi_slopes=repeat(alibi_slopes, "nh -> b nh", b=b))
-        flash_out.backward(dout)
-        flash_dq, q.grad = q.grad.clone(), None
-        flash_dk, k.grad = k.grad.clone(), None
-        flash_dv, v.grad = v.grad.clone(), None
-        assert torch.allclose(flash_out, triton_out, atol=1e-2, rtol=0.)
-        assert torch.allclose(flash_dq, triton_dq, atol=1e-2, rtol=0.)
-        assert torch.allclose(flash_dk, triton_dk, atol=1e-2, rtol=0.)
-        assert torch.allclose(flash_dv, triton_dv, atol=1e-2, rtol=0.)
-@pytest.mark.parametrize(
-    "dtype", [torch.float16]
-)
-@pytest.mark.parametrize(
-    "right_padding", [True, False]
-)
-@pytest.mark.parametrize(
-    "b_sq", 
-    [
-        (32, 512), 
-        (16, 1024), 
-        (8, 2048),
-        (4, 4096), 
-        (2, 8192), 
-        (1, 16384)
-    ]
-)
-@pytest.mark.parametrize(
-    "nh_hd", 
-    [
-        (32, 64),
-        (16, 128),
-        (40, 128) # non power of 2 nh
-    ]
-)
-@pytest.mark.parametrize(
-    "tp_world_size", [1, 2, 4]
-)
-def test_flash_attn_varlen_func(b_sq, nh_hd, tp_world_size, right_padding, dtype):
-    b, sqk = b_sq
-    nh, hd = nh_hd
-    nh_tp = nh // tp_world_size
-    # flash_attn_func_triton(), flash-attention v2 (above v2.1) causal logic are different
-    # so only (seqlen_q == 1, causal=False to triton ver.) shows correct results
-    # https://github.com/huggingface/text-generation-inference/blob/v1.1.1/server/text_generation_server/models/custom_modeling/mpt_modeling.py#L53-L63
-    q = torch.randn(b, 1, nh_tp, hd, device="cuda", dtype=dtype, requires_grad=True)
-    k, v = [torch.randn(b, sqk, nh_tp, hd, device="cuda",
-                        dtype=dtype, requires_grad=True) for _ in range(2)]
-    dout = torch.rand_like(q)
-    padding_mask = generate_random_padding_mask(sqk, b, "cuda", "random", right_padding)
-    (
-        q_unpad,
-        k_unpad,
-        v_unpad,
-        cu_seqlens_q,
-        cu_seqlens_k,
-        max_seqlen_q,
-        max_seqlen_k,
-        q,
-        k,
-        v,
-        output_pad_fn,
-        dq_pad_fn,
-        dk_pad_fn,
-    ) = generate_qkv(q, k, v, None, padding_mask, kvpacked=False)
-    for tp_index in range(tp_world_size):
-        alibi, alibi_slopes = generate_alibi(
-            max_seq_len=sqk,
-            num_attention_heads=nh,
-            tp_world_size=tp_world_size,
-            tp_index=tp_index,
-            key_padding_mask=padding_mask,
-            device="cuda"
-        )
-        triton_out = flash_attn_func_triton(
-            q, k, v, alibi, False, hd**(-0.5))
-        triton_out.backward(dout)
-        triton_dq, q.grad = q.grad.clone(), None
-        triton_dk, k.grad = k.grad.clone(), None
-        triton_dv, v.grad = v.grad.clone(), None
-        flash_out_unpad = flash_attn_varlen_func(
-            q_unpad,
-            k_unpad,
-            v_unpad,
-            cu_seqlens_q,
-            cu_seqlens_k,
-            max_seqlen_q,
-            max_seqlen_k,
-            causal=True,
-            alibi_slopes=repeat(alibi_slopes, "nh -> b nh", b=b)
-        )
-        flash_out = output_pad_fn(flash_out_unpad)
-        flash_out.backward(dout)
-        flash_dq_unpad, q_unpad.grad = q_unpad.grad.clone(), None
-        flash_dk_unpad, k_unpad.grad = k_unpad.grad.clone(), None
-        flash_dv_unpad, v_unpad.grad = v_unpad.grad.clone(), None
-        flash_dq = dq_pad_fn(flash_dq_unpad)
-        flash_dk = dk_pad_fn(flash_dk_unpad)
-        flash_dv = dk_pad_fn(flash_dv_unpad)
-        assert torch.allclose(flash_out, triton_out, atol=1e-2, rtol=0.)
-        assert torch.allclose(flash_dq, triton_dq, atol=1e-2, rtol=0.)
-        assert torch.allclose(flash_dk, triton_dk, atol=1e-2, rtol=0.)
-        assert torch.allclose(flash_dv, triton_dv, atol=1e-2, rtol=0.)
-@pytest.mark.parametrize("alibi", [True])
-@pytest.mark.parametrize("dtype", ([torch.float16] if is_sm75 else [torch.float16, torch.bfloat16]))
-# @pytest.mark.parametrize("dtype", [torch.float16])
-@pytest.mark.parametrize("num_splits", [1, 0])
-# @pytest.mark.parametrize("num_splits", [0])
-@pytest.mark.parametrize("mha_type", ["mha", "mqa", "gqa"])
-# @pytest.mark.parametrize("mha_type", ["mha"])
-@pytest.mark.parametrize("new_kv", [False, True])
-# @pytest.mark.parametrize("new_kv", [True])
-# @pytest.mark.parametrize("local", [False, True])
-@pytest.mark.parametrize("local", [False])
-# @pytest.mark.parametrize("causal", [False, True])
-@pytest.mark.parametrize("causal", [True])
-@pytest.mark.parametrize("seqlen_new_eq_seqlen_q", [True, False])
-# @pytest.mark.parametrize("seqlen_new_eq_seqlen_q", [True])
-@pytest.mark.parametrize("rotary_interleaved", [False, True])
-# @pytest.mark.parametrize("rotary_interleaved", [False])
-@pytest.mark.parametrize("rotary_fraction", [0.0, 0.5, 1.0])
-# @pytest.mark.parametrize("rotary_fraction", [0.0])
-@pytest.mark.parametrize("has_batch_idx", [False, True])
-# @pytest.mark.parametrize("has_batch_idx", [True])
-@pytest.mark.parametrize("d", [32, 59, 64, 80, 96, 128, 160, 192, 224, 256])
-# @pytest.mark.parametrize('d', [32, 64, 96, 128, 160, 192, 224, 256])
-# @pytest.mark.parametrize('d', [32, 40, 64, 80, 96, 128, 160, 192])
-# @pytest.mark.parametrize('d', [56, 80])
-# @pytest.mark.parametrize("d", [128])
-@pytest.mark.parametrize(
-    "seqlen_q,seqlen_k",
-    [
-        (1, 128),
-        (1, 339),
-        (3, 1024),
-        (64, 800),
-        (64, 256),
-        (3, 799),
-        (64, 2048),
-        (16, 20000),
-        (1, 128 * 1024),
-        (16, 128 * 1024),
-        (128, 128),
-    ],
-)
-# @pytest.mark.parametrize('seqlen_q,seqlen_k', [(256, 128)])
-def test_flash_attn_kvcache(
-    seqlen_q,
-    seqlen_k,
-    d,
-    has_batch_idx,
-    rotary_fraction,
-    rotary_interleaved,
-    seqlen_new_eq_seqlen_q,
-    causal,
-    local,
-    new_kv,
-    mha_type,
-    num_splits,
-    dtype,
-    alibi,
-):
-    if seqlen_q > seqlen_k and new_kv:
-        pytest.skip()
-    if not new_kv and rotary_fraction > 0.0:
-        pytest.skip()
-    device = "cuda"
-    # set seed
-    torch.random.manual_seed(0)
-    batch_size = 2
-    batch_size_cache = batch_size if not has_batch_idx else batch_size * 2
-    nheads = 8
-    # rotary_dim must be a multiple of 16, and must be <= d
-    rotary_dim = math.floor(int(rotary_fraction * d) / 16) * 16
-    nheads_k = nheads if mha_type == "mha" else (1 if mha_type == "mqa" else 4)
-    assert nheads % nheads_k == 0
-    window_size = (-1, -1) if not local else torch.randint(0, seqlen_k, (2,))
-    q = torch.randn(batch_size, seqlen_q, nheads,
-                    d, device=device, dtype=dtype)
-    seqlen_new = seqlen_q if seqlen_new_eq_seqlen_q else torch.randint(
-        1, seqlen_q + 1, (1,)).item()
-    if new_kv:
-        k = torch.randn(batch_size, seqlen_new, nheads_k,
-                        d, device=device, dtype=dtype)
-        v = torch.randn(batch_size, seqlen_new, nheads_k,
-                        d, device=device, dtype=dtype)
-    else:
-        k, v = None, None
-    k_cache = torch.randn(batch_size_cache, seqlen_k,
-                          nheads_k, d, device=device, dtype=dtype)
-    v_cache = torch.randn(batch_size_cache, seqlen_k,
-                          nheads_k, d, device=device, dtype=dtype)
-    cache_seqlens = torch.randint(
-        0,
-        # If we don't use seqlen_q in the case of causal and rotary, cos/sin won't be long enough
-        (seqlen_k - (seqlen_q if (causal or local)
-         and rotary_dim > 1 else seqlen_new) + 1)
-        if new_kv
-        else (seqlen_k + 1),
-        (batch_size,),
-        dtype=torch.int32,
-        device=device,
-    )
-    if has_batch_idx:
-        cache_batch_idx = torch.randperm(
-            batch_size_cache, dtype=torch.int32, device=device)[:batch_size]
-    else:
-        cache_batch_idx = None
-    # cache_seqlens = torch.tensor([64], dtype=torch.int32, device=device)
-    if rotary_dim > 0:
-        angle = torch.rand(seqlen_k, rotary_dim // 2,
-                           device=device) * 2 * math.pi
-        cos = torch.cos(angle).to(dtype=dtype)
-        sin = torch.sin(angle).to(dtype=dtype)
-        if causal or local:
-            q_ro = apply_rotary_emb(
-                q, cos, sin, seqlen_offsets=cache_seqlens, interleaved=rotary_interleaved
-            )
-        else:
-            q_ro = rearrange(
-                apply_rotary_emb(
-                    rearrange(q, "b s h d -> b 1 (s h) d"),
-                    cos,
-                    sin,
-                    seqlen_offsets=cache_seqlens,
-                    interleaved=rotary_interleaved,
-                ),
-                "b 1 (s h) d -> b s h d",
-                s=seqlen_q,
-            )
-        # q_ro = q
-        k_ro = apply_rotary_emb(
-            k, cos, sin, seqlen_offsets=cache_seqlens, interleaved=rotary_interleaved
-        )
-    else:
-        cos, sin = None, None
-        q_ro, k_ro = q, k
-    # k_cache[:, 64:] = -1
-    k_cache_ref = (
-        k_cache if not has_batch_idx else k_cache[cache_batch_idx]).clone()
-    v_cache_ref = (
-        v_cache if not has_batch_idx else v_cache[cache_batch_idx]).clone()
-    arange = rearrange(torch.arange(seqlen_k, device=device), "s -> 1 s")
-    cache_seqlens_expanded = rearrange(cache_seqlens, "b -> b 1")
-    if new_kv:
-        update_mask = torch.logical_and(
-            cache_seqlens_expanded <= arange, arange < cache_seqlens_expanded + seqlen_new
-        )
-        k_cache_ref[update_mask] = rearrange(k_ro, "b s ... -> (b s) ...")
-        v_cache_ref[update_mask] = rearrange(v, "b s ... -> (b s) ...")
-    k_cache_rep = repeat(
-        k_cache_ref, "b s h d -> b s (h g) d", g=nheads // nheads_k)
-    v_cache_rep = repeat(
-        v_cache_ref, "b s h d -> b s (h g) d", g=nheads // nheads_k)
-    if alibi:
-        seqlen_alibi = k_cache_rep.shape[1]
-        alibi_tensor, alibi_slopes = generate_alibi(
-            max_seq_len=seqlen_alibi,
-            num_attention_heads=nheads,
-            tp_world_size=1,
-            tp_index=0,
-            key_padding_mask=None,
-            device="cuda"
-        )
-        # alibi_tensor = alibi_tensor.expand(batch_size, -1, seqlen_q, -1)
-        alibi_slopes = repeat(alibi_slopes, "nh -> b nh", b=batch_size)
-        if alibi_tensor.abs().max().item() >= torch.finfo(dtype).max:
-            pytest.skip()
-    else:
-        alibi_tensor, alibi_slopes = None, None
-    out = flash_attn_with_kvcache(
-        q,
-        k_cache,
-        v_cache,
-        k,
-        v,
-        cos,
-        sin,
-        cache_seqlens,
-        cache_batch_idx,
-        causal=causal,
-        window_size=window_size,
-        rotary_interleaved=rotary_interleaved,
-        num_splits=num_splits,
-        alibi_slopes=alibi_slopes
-    )
-    # out = flash_attn_with_kvcache(
-    #     q, k_cache, v_cache, cache_seqlens=cache_seqlens, causal=causal, window_size=window_size
-    # )
-    # out = flash_attn_with_kvcache(q, k_cache, v_cache, causal=causal, window_size=window_size)
-    # qk = torch.einsum("bqhd,bkhd->bhqk", q, k_cache_ref)
-    # m = qk.amax(-1, keepdim=True)
-    # s_tmp = torch.exp((qk - m) / math.sqrt(d))
-    # o1 = torch.einsum('bhst,bthd->bshd', s_tmp, v_cache_ref)
-    # lse_ref = torch.logsumexp(qk / math.sqrt(d), -1)
-    # probs = torch.softmax(qk, dim=-1)
-    key_padding_mask = arange < cache_seqlens_expanded + \
-        (seqlen_new if new_kv else 0)
-    out_ref, _ = attention_ref(
-        q_ro,
-        k_cache_rep,
-        v_cache_rep,
-        None,
-        key_padding_mask,
-        0.0,
-        None,
-        causal=causal,
-        window_size=window_size,
-        bias=alibi_tensor
-    )
-    out_pt, _ = attention_ref(
-        q_ro,
-        k_cache_rep,
-        v_cache_rep,
-        None,
-        key_padding_mask,
-        0.0,
-        None,
-        causal=causal,
-        window_size=window_size,
-        upcast=False,
-        reorder_ops=True,
-        bias=alibi_tensor
-    )
-    print(f"Output max diff: {(out - out_ref).abs().max().item()}")
-    print(f"Output mean diff: {(out - out_ref).abs().mean().item()}")
-    print(f"Pytorch max diff: {(out_pt - out_ref).abs().max().item()}")
-    print(f"Pytorch mean diff: {(out_pt - out_ref).abs().mean().item()}")
-    # Check that FlashAttention's numerical error is at most twice the numerical error
-    # of a Pytorch implementation.
-    if new_kv:
-        k_cache_select = k_cache if not has_batch_idx else k_cache[cache_batch_idx]
-        v_cache_select = v_cache if not has_batch_idx else v_cache[cache_batch_idx]
-        assert torch.allclose(k_cache_select, k_cache_ref,
-                              rtol=1e-3, atol=1e-3)
-        assert torch.equal(v_cache_select, v_cache_ref)
-    assert (out - out_ref).abs().max().item() <= 3 * \
-        (out_pt - out_ref).abs().max().item() + 1e-5
--- a/tests/test_flash_attn.py
+++ b/tests/test_flash_attn.py
@@ -26,6 +26,31 @@ is_sm80 = torch.cuda.get_device_capability("cuda") == (8, 0)
 is_sm90 = torch.cuda.get_device_capability("cuda") == (9, 0)
+def attn_bias_from_alibi_slopes(
+    slopes, seqlen_q, seqlen_k, query_padding_mask=None, key_padding_mask=None, causal=False
+):
+    batch, nheads = slopes.shape
+    device = slopes.device
+    slopes = rearrange(slopes, "b h -> b h 1 1")
+    if causal:
+        return torch.arange(-seqlen_k + 1, 1, device=device, dtype=torch.float32) * slopes
+    else:
+        row_idx = rearrange(torch.arange(seqlen_q, device=device, dtype=torch.long), "s -> s 1")
+        col_idx = torch.arange(seqlen_k, device=device, dtype=torch.long)
+        sk = (
+            seqlen_k
+            if key_padding_mask is None
+            else rearrange(key_padding_mask.sum(-1), "b -> b 1 1 1")
+        )
+        sq = (
+            seqlen_q
+            if query_padding_mask is None
+            else rearrange(query_padding_mask.sum(-1), "b -> b 1 1 1")
+        )
+        relative_pos = torch.abs(row_idx + sk - sq - col_idx)
+        return -slopes * relative_pos.to(dtype=slopes.dtype)
 def generate_random_padding_mask(max_seqlen, batch_size, device, mode="random"):
    assert mode in ["full", "random", "third"]
    if mode == "full":
@@ -186,6 +211,7 @@ def attention_ref(
    v,
    query_padding_mask=None,
    key_padding_mask=None,
+    attn_bias=None,
    dropout_p=0.0,
    dropout_mask=None,
    causal=False,
@@ -200,6 +226,7 @@ def attention_ref(
        v: (batch_size, seqlen_k, nheads_k, head_dim)
        query_padding_mask: (batch_size, seqlen_q)
        key_padding_mask: (batch_size, seqlen_k)
+        attn_bias: broadcastable to (batch_size, nheads, seqlen_q, seqlen_k)
        dropout_p: float
        dropout_mask: (batch_size, nheads, seqlen_q, seqlen_k)
        causal: whether to apply causal masking
@@ -238,7 +265,9 @@ def attention_ref(
            q.device,
        )
        scores.masked_fill_(local_mask, float("-inf"))
-    attention = torch.softmax(scores, dim=-1)
+    if attn_bias is not None:
+        scores = scores + attn_bias
+    attention = torch.softmax(scores, dim=-1).to(v.dtype)
    # Some rows might be completely masked out so we fill them with zero instead of NaN
    if window_size[0] >= 0 or window_size[1] >= 0:
        attention = attention.masked_fill(torch.all(local_mask, dim=-1, keepdim=True), 0.0)
@@ -264,6 +293,7 @@ def attention_kvpacked_ref(
    kv,
    query_padding_mask=None,
    key_padding_mask=None,
+    attn_bias=None,
    dropout_p=0.0,
    dropout_mask=None,
    causal=False,
@@ -277,6 +307,7 @@ def attention_kvpacked_ref(
        kv[:, :, 1],
        query_padding_mask,
        key_padding_mask,
+        attn_bias,
        dropout_p,
        dropout_mask,
        upcast=upcast,
@@ -289,6 +320,7 @@ def attention_kvpacked_ref(
 def attention_qkvpacked_ref(
    qkv,
    key_padding_mask=None,
+    attn_bias=None,
    dropout_p=0.0,
    dropout_mask=None,
    causal=False,
@@ -302,6 +334,7 @@ def attention_qkvpacked_ref(
        qkv[:, :, 2],
        key_padding_mask,
        key_padding_mask,
+        attn_bias,
        dropout_p,
        dropout_mask,
        upcast=upcast,
@@ -436,6 +469,7 @@ def normalize_flash_attn_S(
    v,
    query_padding_mask=None,
    key_padding_mask=None,
+    attn_bias=None,
    is_dropout=False,
    causal=False,
    window_size=(-1, -1),  # -1 means infinite window size
@@ -445,6 +479,7 @@ def normalize_flash_attn_S(
        q: (batch_size, seqlen_q, nheads, head_dim)
        k, v: (batch_size, seqlen_k, nheads, head_dim)
        key_padding_mask: (batch_size, seqlen_q)
+        attn_bias: broadcastable to (batch_size, nheads, seqlen_q, seqlen_k)
    Output:
        softmax_lse: (batch_size, nheads, seqlen_q)
        softmax_max: (batch_size, nheads, seqlen_q)
@@ -467,6 +502,8 @@ def normalize_flash_attn_S(
            q.device,
        )
        scores.masked_fill_(local_mask, float("-inf"))
+    if attn_bias is not None:
+        scores = scores + attn_bias.to(dtype=scores.dtype)
    _, block_size_n = _get_block_size(scores.device, head_dim, is_dropout, causal)
    scores_block = scores.split(block_size_n, dim=-1)
    lse_block = torch.stack([torch.logsumexp(s, dim=-1) for s in scores_block], dim=-1)
@@ -529,6 +566,8 @@ def get_dropout_fraction(
 @pytest.mark.parametrize("dtype", ([torch.float16] if is_sm75 else [torch.float16, torch.bfloat16]))
 # @pytest.mark.parametrize("dtype", [torch.float16])
+@pytest.mark.parametrize("alibi", [False, True])
+# @pytest.mark.parametrize("alibi", [True])
 @pytest.mark.parametrize("local", [False, True])
 # @pytest.mark.parametrize("local", [True])
 @pytest.mark.parametrize("causal", [False, True])
@@ -538,24 +577,34 @@ def get_dropout_fraction(
 # @pytest.mark.parametrize('d', [32, 64, 96, 128])
 # @pytest.mark.parametrize("d", [64])
 # @pytest.mark.parametrize('seqlen', [128, 256, 384, 512, 768, 1024, 2048])
-@pytest.mark.parametrize("seqlen", [97, 128, 200, 256, 257, 384, 512, 768, 1024, 1025, 2048])
+@pytest.mark.parametrize("seqlen", [97, 128, 200, 384, 768, 1024, 1025, 2048])
-# @pytest.mark.parametrize("seqlen", [128])
+# @pytest.mark.parametrize("seqlen", [97])
 @pytest.mark.parametrize("dropout_p", [0.0, 0.17])
 # @pytest.mark.parametrize("dropout_p", [0.0])
-def test_flash_attn_qkvpacked(seqlen, d, dropout_p, causal, local, dtype):
+def test_flash_attn_qkvpacked(seqlen, d, dropout_p, causal, local, alibi, dtype):
    if seqlen >= 2048 and torch.cuda.get_device_properties("cuda").total_memory <= 16 * 2**30:
        pytest.skip()  # Reference implementation OOM
    device = "cuda"
    # set seed
    torch.random.manual_seed(0)
-    batch_size = 13
+    batch_size = 8
    nheads = 9
    window_size = (-1, -1) if not local else torch.randint(0, seqlen, (2,))
    qkv = torch.randn(
        batch_size, seqlen, 3, nheads, d, device=device, dtype=dtype, requires_grad=True
    )
+    if alibi:
+        alibi_slopes = torch.rand(batch_size, nheads, device=device, dtype=torch.float32) * 0.3
+        attn_bias = attn_bias_from_alibi_slopes(alibi_slopes, seqlen, seqlen, causal=causal)
+    else:
+        alibi_slopes, attn_bias = None, None
    out, lse, S_dmask = flash_attn_qkvpacked_func(
-        qkv, dropout_p, causal=causal, window_size=window_size, return_attn_probs=True
+        qkv,
+        dropout_p,
+        causal=causal,
+        window_size=window_size,
+        alibi_slopes=alibi_slopes,
+        return_attn_probs=True,
    )
    if dropout_p > 0.0:
        S_dmask_converted = convert_flash_attn_S_to_softmax(
@@ -578,6 +627,7 @@ def test_flash_attn_qkvpacked(seqlen, d, dropout_p, causal, local, dtype):
            qkv[:, :, 2],
            None,
            None,
+            attn_bias,
            dropout_p > 0.0,
            causal=causal,
            window_size=window_size,
@@ -590,11 +640,12 @@ def test_flash_attn_qkvpacked(seqlen, d, dropout_p, causal, local, dtype):
        dropout_mask = None
    out_ref, attn_ref = attention_qkvpacked_ref(
-        qkv, None, dropout_p, dropout_mask, causal=causal, window_size=window_size
+        qkv, None, attn_bias, dropout_p, dropout_mask, causal=causal, window_size=window_size
    )
    out_pt, attn_pt = attention_qkvpacked_ref(
        qkv,
        None,
+        attn_bias,
        dropout_p,
        dropout_mask,
        causal=causal,
@@ -651,6 +702,8 @@ def test_flash_attn_qkvpacked(seqlen, d, dropout_p, causal, local, dtype):
    if dropout_p > 0.0:
        assert (attn - attn_ref).abs().max().item() <= 2 * (attn_pt - attn_ref).abs().max().item()
+        # With alibi, many of the prob values are 0.0 & -0.0 so dropout_fraction isn't accurate
+        if not alibi:
            assert abs(dropout_fraction - dropout_p) <= (0.01 if not local else 0.025)
    if d <= MAX_HEADDIM_SM8x or (is_sm80 or is_sm90):
@@ -659,18 +712,20 @@ def test_flash_attn_qkvpacked(seqlen, d, dropout_p, causal, local, dtype):
 @pytest.mark.parametrize("dtype", ([torch.float16] if is_sm75 else [torch.float16, torch.bfloat16]))
 # @pytest.mark.parametrize('dtype', [torch.float16])
+@pytest.mark.parametrize("alibi", [False, True])
+# @pytest.mark.parametrize("alibi", [True])
 @pytest.mark.parametrize("local", [False, True])
 # @pytest.mark.parametrize("local", [True])
 @pytest.mark.parametrize("causal", [False, True])
 # @pytest.mark.parametrize('causal', [False])
-@pytest.mark.parametrize("d", [32, 40, 59, 64, 80, 96, 111, 128, 160, 192, 224, 256])
+@pytest.mark.parametrize("d", [32, 59, 64, 80, 96, 128, 160, 192, 224, 256])
 # @pytest.mark.parametrize("d", [32, 64, 96, 128, 160, 192, 224, 256])
 # @pytest.mark.parametrize('d', [64])
-@pytest.mark.parametrize("seqlen", [97, 128, 200, 256, 257, 384, 512, 768, 1024, 1025, 2048])
+@pytest.mark.parametrize("seqlen", [97, 128, 200, 257, 384, 512, 768, 1025, 2048])
 # @pytest.mark.parametrize('seqlen', [128])
 @pytest.mark.parametrize("dropout_p", [0.0, 0.17])
 # @pytest.mark.parametrize('dropout_p', [0.0])
-def test_flash_attn_varlen_qkvpacked(seqlen, d, dropout_p, causal, local, dtype):
+def test_flash_attn_varlen_qkvpacked(seqlen, d, dropout_p, causal, local, alibi, dtype):
    if seqlen >= 2048 and torch.cuda.get_device_properties("cuda").total_memory <= 16 * 2**30:
        pytest.skip()  # Reference implementation OOM
    device = "cuda"
@@ -685,6 +740,13 @@ def test_flash_attn_varlen_qkvpacked(seqlen, d, dropout_p, causal, local, dtype)
    key_padding_mask = generate_random_padding_mask(seqlen, batch_size, device, mode="random")
    # key_padding_mask = generate_random_padding_mask(seqlen, batch_size, device, mode='full')
+    if alibi:
+        alibi_slopes = torch.rand(batch_size, nheads, device=device, dtype=torch.float32) * 0.3
+        attn_bias = attn_bias_from_alibi_slopes(
+            alibi_slopes, seqlen, seqlen, key_padding_mask, key_padding_mask, causal=causal
+        )
+    else:
+        alibi_slopes, attn_bias = None, None
    qkv_unpad, cu_seqlens, max_seqlen, qkv, output_pad_fn, dqkv_pad_fn = generate_qkv(
        *qkv.unbind(dim=2), key_padding_mask, key_padding_mask, qkvpacked=True
@@ -697,6 +759,7 @@ def test_flash_attn_varlen_qkvpacked(seqlen, d, dropout_p, causal, local, dtype)
        dropout_p,
        causal=causal,
        window_size=window_size,
+        alibi_slopes=alibi_slopes,
        return_attn_probs=True,
    )
    out = output_pad_fn(out_unpad)
@@ -721,6 +784,7 @@ def test_flash_attn_varlen_qkvpacked(seqlen, d, dropout_p, causal, local, dtype)
            qkv[:, :, 2],
            key_padding_mask,
            key_padding_mask,
+            attn_bias,
            dropout_p > 0.0,
            causal=causal,
            window_size=window_size,
@@ -733,11 +797,18 @@ def test_flash_attn_varlen_qkvpacked(seqlen, d, dropout_p, causal, local, dtype)
        dropout_mask = None
    out_ref, attn_ref = attention_qkvpacked_ref(
-        qkv, key_padding_mask, dropout_p, dropout_mask, causal=causal, window_size=window_size
+        qkv,
+        key_padding_mask,
+        attn_bias,
+        dropout_p,
+        dropout_mask,
+        causal=causal,
+        window_size=window_size,
    )
    out_pt, attn_pt = attention_qkvpacked_ref(
        qkv,
        key_padding_mask,
+        attn_bias,
        dropout_p,
        dropout_mask,
        causal=causal,
@@ -774,6 +845,8 @@ def test_flash_attn_varlen_qkvpacked(seqlen, d, dropout_p, causal, local, dtype)
    if dropout_p > 0.0:
        assert (attn - attn_ref).abs().max().item() <= 2 * (attn_pt - attn_ref).abs().max().item()
+        # With alibi, many of the prob values are 0.0 & -0.0 so dropout_fraction isn't accurate
+        if not alibi:
            assert abs(dropout_fraction - dropout_p) <= (0.01 if not local else 0.025)
    if d <= MAX_HEADDIM_SM8x or (is_sm80 or is_sm90):
@@ -786,11 +859,13 @@ def test_flash_attn_varlen_qkvpacked(seqlen, d, dropout_p, causal, local, dtype)
 # @pytest.mark.parametrize("dtype", [torch.bfloat16])
 @pytest.mark.parametrize("mha_type", ["mha", "mqa", "gqa"])
 # @pytest.mark.parametrize("mha_type", ["mha"])
+@pytest.mark.parametrize("alibi", [False, True])
+# @pytest.mark.parametrize("alibi", [True])
 @pytest.mark.parametrize("local", [False, True])
 # @pytest.mark.parametrize("local", [True])
 @pytest.mark.parametrize("causal", [False, True])
 # @pytest.mark.parametrize("causal", [True])
-@pytest.mark.parametrize("d", [32, 40, 59, 64, 80, 96, 111, 128, 160, 192, 224, 256])
+@pytest.mark.parametrize("d", [32, 40, 59, 64, 96, 111, 128, 160, 192, 224, 256])
 # @pytest.mark.parametrize("d", [32, 64, 96, 128, 160, 192, 224, 256])
 # @pytest.mark.parametrize('d', [32, 40, 64, 80, 96, 128, 160, 192])
 # @pytest.mark.parametrize('d', [32, 64, 96, 128, 160, 192])
@@ -815,7 +890,7 @@ def test_flash_attn_varlen_qkvpacked(seqlen, d, dropout_p, causal, local, dtype)
 @pytest.mark.parametrize("dropout_p", [0.0, 0.17])
 # @pytest.mark.parametrize("dropout_p", [0.17])
 def test_flash_attn_output(
-    seqlen_q, seqlen_k, d, dropout_p, causal, local, mha_type, dtype, kvpacked
+    seqlen_q, seqlen_k, d, dropout_p, causal, local, alibi, mha_type, dtype, kvpacked
 ):
    if (
        max(seqlen_q, seqlen_k) >= 2048
@@ -825,7 +900,7 @@ def test_flash_attn_output(
    device = "cuda"
    # set seed
    torch.random.manual_seed(0)
-    batch_size = 13
+    batch_size = 8
    nheads = 9
    nheads_k = nheads if mha_type == "mha" else (1 if mha_type == "mqa" else 3)
    assert nheads % nheads_k == 0
@@ -842,14 +917,32 @@ def test_flash_attn_output(
        v = torch.randn(
            batch_size, seqlen_k, nheads_k, d, device=device, dtype=dtype, requires_grad=True
        )
+    if alibi:
+        alibi_slopes = torch.rand(batch_size, nheads, device=device, dtype=torch.float32) * 0.3
+        attn_bias = attn_bias_from_alibi_slopes(alibi_slopes, seqlen_q, seqlen_k, causal=causal)
+    else:
+        alibi_slopes, attn_bias = None, None
    if kvpacked:
        out, lse, S_dmask = flash_attn_kvpacked_func(
-            q, kv, dropout_p, causal=causal, window_size=window_size, return_attn_probs=True
+            q,
+            kv,
+            dropout_p,
+            causal=causal,
+            window_size=window_size,
+            alibi_slopes=alibi_slopes,
+            return_attn_probs=True,
        )
    else:
        out, lse, S_dmask = flash_attn_func(
-            q, k, v, dropout_p, causal=causal, window_size=window_size, return_attn_probs=True
+            q,
+            k,
+            v,
+            dropout_p,
+            causal=causal,
+            window_size=window_size,
+            alibi_slopes=alibi_slopes,
+            return_attn_probs=True,
        )
    if dropout_p > 0.0:
        S_dmask_converted = convert_flash_attn_S_to_softmax(
@@ -878,6 +971,7 @@ def test_flash_attn_output(
            v_rep,
            None,
            None,
+            attn_bias,
            dropout_p > 0.0,
            causal=causal,
            window_size=window_size,
@@ -895,6 +989,7 @@ def test_flash_attn_output(
            kv,
            None,
            None,
+            attn_bias,
            dropout_p,
            dropout_mask,
            causal=causal,
@@ -905,6 +1000,7 @@ def test_flash_attn_output(
            kv,
            None,
            None,
+            attn_bias,
            dropout_p,
            dropout_mask,
            causal=causal,
@@ -919,6 +1015,7 @@ def test_flash_attn_output(
            v,
            None,
            None,
+            attn_bias,
            dropout_p,
            dropout_mask,
            causal=causal,
@@ -930,6 +1027,7 @@ def test_flash_attn_output(
            v,
            None,
            None,
+            attn_bias,
            dropout_p,
            dropout_mask,
            causal=causal,
@@ -1000,6 +1098,8 @@ def test_flash_attn_output(
    if dropout_p > 0.0:
        assert (attn - attn_ref).abs().max().item() <= 2 * (attn_pt - attn_ref).abs().max().item()
+        # With alibi, many of the prob values are 0.0 & -0.0 so dropout_fraction isn't accurate
+        if not alibi:
            assert abs(dropout_fraction - dropout_p) <= (0.01 if not local else 0.025)
    if d <= MAX_HEADDIM_SM8x or (is_sm80 or is_sm90):
@@ -1014,11 +1114,13 @@ def test_flash_attn_output(
 # @pytest.mark.parametrize('dtype', [torch.float16])
 @pytest.mark.parametrize("mha_type", ["mha", "mqa", "gqa"])
 # @pytest.mark.parametrize('mha_type', ["mqa"])
+@pytest.mark.parametrize("alibi", [False, True])
+# @pytest.mark.parametrize("alibi", [True])
 @pytest.mark.parametrize("local", [False, True])
 # @pytest.mark.parametrize("local", [True])
 @pytest.mark.parametrize("causal", [False, True])
 # @pytest.mark.parametrize('causal', [True])
-@pytest.mark.parametrize("d", [32, 40, 59, 64, 80, 96, 111, 128, 160, 192, 224, 256])
+@pytest.mark.parametrize("d", [32, 59, 64, 80, 96, 111, 128, 160, 192, 224, 256])
 # @pytest.mark.parametrize("d", [32, 64, 96, 128, 160, 192, 224, 256])
 # @pytest.mark.parametrize('d', [64])
 @pytest.mark.parametrize(
@@ -1041,7 +1143,7 @@ def test_flash_attn_output(
 @pytest.mark.parametrize("dropout_p", [0.0, 0.17])
 # @pytest.mark.parametrize('dropout_p', [0.0])
 def test_flash_attn_varlen_output(
-    seqlen_q, seqlen_k, d, dropout_p, causal, local, mha_type, dtype, kvpacked
+    seqlen_q, seqlen_k, d, dropout_p, causal, local, alibi, mha_type, dtype, kvpacked
 ):
    if (
        max(seqlen_q, seqlen_k) >= 2048
@@ -1051,7 +1153,7 @@ def test_flash_attn_varlen_output(
    device = "cuda"
    # set seed
    torch.random.manual_seed(0)
-    batch_size = 13
+    batch_size = 8
    nheads = 9
    nheads_k = nheads if mha_type == "mha" else (1 if mha_type == "mqa" else 3)
    assert nheads % nheads_k == 0
@@ -1072,6 +1174,13 @@ def test_flash_attn_varlen_output(
    query_padding_mask = generate_random_padding_mask(seqlen_q, batch_size, device, mode="random")
    key_padding_mask = generate_random_padding_mask(seqlen_k, batch_size, device, mode="random")
    # key_padding_mask = generate_random_padding_mask(seqlen_k, batch_size, device, mode='full')
+    if alibi:
+        alibi_slopes = torch.rand(batch_size, nheads, device=device, dtype=torch.float32) * 0.3
+        attn_bias = attn_bias_from_alibi_slopes(
+            alibi_slopes, seqlen_q, seqlen_k, query_padding_mask, key_padding_mask, causal=causal
+        )
+    else:
+        alibi_slopes, attn_bias = None, None
    if kvpacked:
        (
@@ -1095,9 +1204,10 @@ def test_flash_attn_varlen_output(
            max_seqlen_q,
            max_seqlen_k,
            dropout_p,
-            return_attn_probs=True,
            causal=causal,
            window_size=window_size,
+            alibi_slopes=alibi_slopes,
+            return_attn_probs=True,
        )
    else:
        (
@@ -1124,9 +1234,10 @@ def test_flash_attn_varlen_output(
            max_seqlen_q,
            max_seqlen_k,
            dropout_p,
-            return_attn_probs=True,
            causal=causal,
            window_size=window_size,
+            alibi_slopes=alibi_slopes,
+            return_attn_probs=True,
        )
    out = output_pad_fn(out_unpad)
    if dropout_p > 0.0:
@@ -1156,6 +1267,7 @@ def test_flash_attn_varlen_output(
            v_rep,
            query_padding_mask,
            key_padding_mask,
+            attn_bias,
            dropout_p > 0.0,
            causal=causal,
            window_size=window_size,
@@ -1177,6 +1289,7 @@ def test_flash_attn_varlen_output(
            kv,
            query_padding_mask,
            key_padding_mask,
+            attn_bias,
            dropout_p,
            dropout_mask,
            causal=causal,
@@ -1187,6 +1300,7 @@ def test_flash_attn_varlen_output(
            kv,
            query_padding_mask,
            key_padding_mask,
+            attn_bias,
            dropout_p,
            dropout_mask,
            causal=causal,
@@ -1201,6 +1315,7 @@ def test_flash_attn_varlen_output(
            v,
            query_padding_mask,
            key_padding_mask,
+            attn_bias,
            dropout_p,
            dropout_mask,
            causal=causal,
@@ -1212,6 +1327,7 @@ def test_flash_attn_varlen_output(
            v,
            query_padding_mask,
            key_padding_mask,
+            attn_bias,
            dropout_p,
            dropout_mask,
            causal=causal,
@@ -1284,12 +1400,14 @@ def test_flash_attn_varlen_output(
    if dropout_p > 0.0:
        assert (attn - attn_ref).abs().max().item() <= 2 * (attn_pt - attn_ref).abs().max().item()
+        # With alibi, many of the prob values are 0.0 & -0.0 so dropout_fraction isn't accurate
+        if not alibi:
            assert abs(dropout_fraction - dropout_p) <= (0.01 if not local else 0.025)
    if d <= MAX_HEADDIM_SM8x or (is_sm80 or is_sm90):
-        assert (dq - dq_ref).abs().max().item() <= 2 * (dq_pt - dq_ref).abs().max().item()
+        assert (dq - dq_ref).abs().max().item() <= 3 * (dq_pt - dq_ref).abs().max().item()
-        assert (dk - dk_ref).abs().max().item() <= 2 * (dk_pt - dk_ref).abs().max().item()
+        assert (dk - dk_ref).abs().max().item() <= 3 * (dk_pt - dk_ref).abs().max().item()
-        assert (dv - dv_ref).abs().max().item() <= 2 * (dv_pt - dv_ref).abs().max().item()
+        assert (dv - dv_ref).abs().max().item() <= 3 * (dv_pt - dv_ref).abs().max().item()
 @pytest.mark.parametrize("dtype", ([torch.float16] if is_sm75 else [torch.float16, torch.bfloat16]))
@@ -1332,7 +1450,7 @@ def test_flash_attn_causal(seqlen_q, seqlen_k, swap_sq_sk, d, local, dtype):
    causal = True
    # set seed
    torch.random.manual_seed(0)
-    batch_size = 13
+    batch_size = 8
    nheads = 9
    window_size = (-1, -1) if not local else torch.randint(0, seqlen_k, (2,))
    q = torch.randn(batch_size, seqlen_q, nheads, d, device=device, dtype=dtype, requires_grad=True)
@@ -1340,7 +1458,7 @@ def test_flash_attn_causal(seqlen_q, seqlen_k, swap_sq_sk, d, local, dtype):
    v = torch.randn(batch_size, seqlen_k, nheads, d, device=device, dtype=dtype, requires_grad=True)
    out = flash_attn_func(q, k, v, 0.0, causal=causal, window_size=window_size)
    out_ref, attn_ref = attention_ref(
-        q, k, v, None, None, 0.0, None, causal=causal, window_size=window_size
+        q, k, v, None, None, None, 0.0, None, causal=causal, window_size=window_size
    )
    out_pt, attn_pt = attention_ref(
        q,
@@ -1348,6 +1466,7 @@ def test_flash_attn_causal(seqlen_q, seqlen_k, swap_sq_sk, d, local, dtype):
        v,
        None,
        None,
+        None,
        0.0,
        None,
        causal=causal,
@@ -1442,7 +1561,7 @@ def test_flash_attn_varlen_causal(seqlen_q, seqlen_k, swap_sq_sk, d, local, dtyp
    causal = True
    # set seed
    torch.random.manual_seed(0)
-    batch_size = 13
+    batch_size = 8
    nheads = 9
    window_size = (-1, -1) if not local else torch.randint(0, seqlen_k, (2,))
    q = torch.randn(batch_size, seqlen_q, nheads, d, device=device, dtype=dtype, requires_grad=True)
@@ -1484,6 +1603,7 @@ def test_flash_attn_varlen_causal(seqlen_q, seqlen_k, swap_sq_sk, d, local, dtyp
        v,
        query_padding_mask,
        key_padding_mask,
+        None,
        0.0,
        None,
        causal=causal,
@@ -1495,6 +1615,7 @@ def test_flash_attn_varlen_causal(seqlen_q, seqlen_k, swap_sq_sk, d, local, dtyp
        v,
        query_padding_mask,
        key_padding_mask,
+        None,
        0.0,
        None,
        causal=causal,
@@ -1554,8 +1675,10 @@ def test_flash_attn_varlen_causal(seqlen_q, seqlen_k, swap_sq_sk, d, local, dtyp
 @pytest.mark.parametrize("dtype", ([torch.float16] if is_sm75 else [torch.float16, torch.bfloat16]))
 # @pytest.mark.parametrize("dtype", [torch.float16])
+@pytest.mark.parametrize("alibi", [False, True])
+# @pytest.mark.parametrize("alibi", [True])
 @pytest.mark.parametrize("local", [False, True])
-# @pytest.mark.parametrize("local", [True])
+# @pytest.mark.parametrize("local", [False])
 @pytest.mark.parametrize("causal", [False, True])
 # @pytest.mark.parametrize("causal", [True])
 @pytest.mark.parametrize("d", [32, 40, 59, 64, 80, 96, 111, 128, 160, 192, 224, 256])
@@ -1581,7 +1704,7 @@ def test_flash_attn_varlen_causal(seqlen_q, seqlen_k, swap_sq_sk, d, local, dtyp
    ],
 )
 # @pytest.mark.parametrize('seqlen_q,seqlen_k', [(256, 128)])
-def test_flash_attn_splitkv(seqlen_q, seqlen_k, swap_sq_sk, d, causal, local, dtype):
+def test_flash_attn_splitkv(seqlen_q, seqlen_k, swap_sq_sk, d, causal, local, alibi, dtype):
    if swap_sq_sk:
        seqlen_q, seqlen_k = seqlen_k, seqlen_q
    device = "cuda"
@@ -1593,11 +1716,23 @@ def test_flash_attn_splitkv(seqlen_q, seqlen_k, swap_sq_sk, d, causal, local, dt
    q = torch.randn(batch_size, seqlen_q, nheads, d, device=device, dtype=dtype, requires_grad=True)
    k = torch.randn(batch_size, seqlen_k, nheads, d, device=device, dtype=dtype, requires_grad=True)
    v = torch.randn(batch_size, seqlen_k, nheads, d, device=device, dtype=dtype, requires_grad=True)
+    if alibi:
+        alibi_slopes = torch.rand(batch_size, nheads, device=device, dtype=torch.float32) * 0.3
+        attn_bias = attn_bias_from_alibi_slopes(alibi_slopes, seqlen_q, seqlen_k, causal=causal)
+    else:
+        alibi_slopes, attn_bias = None, None
    out, lse, _ = flash_attn_func(
-        q, k, v, 0.0, causal=causal, window_size=window_size, return_attn_probs=True
+        q,
+        k,
+        v,
+        0.0,
+        causal=causal,
+        window_size=window_size,
+        alibi_slopes=alibi_slopes,
+        return_attn_probs=True,
    )
    out_ref, attn_ref = attention_ref(
-        q, k, v, None, None, 0.0, None, causal=causal, window_size=window_size
+        q, k, v, None, None, attn_bias, 0.0, None, causal=causal, window_size=window_size
    )
    out_pt, attn_pt = attention_ref(
        q,
@@ -1605,6 +1740,7 @@ def test_flash_attn_splitkv(seqlen_q, seqlen_k, swap_sq_sk, d, causal, local, dt
        v,
        None,
        None,
+        attn_bias,
        0.0,
        None,
        causal=causal,
@@ -1653,24 +1789,27 @@ def test_flash_attn_splitkv(seqlen_q, seqlen_k, swap_sq_sk, d, causal, local, dt
    # of a Pytorch implementation.
    assert (out - out_ref).abs().max().item() <= 2 * (out_pt - out_ref).abs().max().item() + 1e-5
+    mult = 2 if not alibi else 8
    if d <= MAX_HEADDIM_SM8x or (is_sm80 or is_sm90):
-        assert (dq - dq_ref).abs().max().item() <= 2 * (dq_pt - dq_ref).abs().max().item() + 2e-4
+        assert (dq - dq_ref).abs().max().item() <= mult * (dq_pt - dq_ref).abs().max().item() + 2e-4
-        assert (dk - dk_ref).abs().max().item() <= 2 * (dk_pt - dk_ref).abs().max().item() + 2e-4
+        assert (dk - dk_ref).abs().max().item() <= mult * (dk_pt - dk_ref).abs().max().item() + 2e-4
-        assert (dv - dv_ref).abs().max().item() <= 2 * (dv_pt - dv_ref).abs().max().item() + 2e-4
+        assert (dv - dv_ref).abs().max().item() <= mult * (dv_pt - dv_ref).abs().max().item() + 2e-4
-@pytest.mark.parametrize("dtype", ([torch.float16] if is_sm75 else [torch.float16, torch.bfloat16]))
+# @pytest.mark.parametrize("dtype", ([torch.float16] if is_sm75 else [torch.float16, torch.bfloat16]))
-# @pytest.mark.parametrize("dtype", [torch.float16])
+@pytest.mark.parametrize("dtype", [torch.float16])
 @pytest.mark.parametrize("num_splits", [1, 0])
-# @pytest.mark.parametrize("num_splits", [0])
+# @pytest.mark.parametrize("num_splits", [1])
 @pytest.mark.parametrize("mha_type", ["mha", "mqa", "gqa"])
 # @pytest.mark.parametrize("mha_type", ["mha"])
 @pytest.mark.parametrize("new_kv", [False, True])
-# @pytest.mark.parametrize("new_kv", [True])
+# @pytest.mark.parametrize("new_kv", [False])
+@pytest.mark.parametrize("alibi", [False, True])
+# @pytest.mark.parametrize("alibi", [True])
 @pytest.mark.parametrize("local", [False, True])
 # @pytest.mark.parametrize("local", [False])
 @pytest.mark.parametrize("causal", [False, True])
-# @pytest.mark.parametrize("causal", [True])
+# @pytest.mark.parametrize("causal", [False])
 @pytest.mark.parametrize("seqlen_new_eq_seqlen_q", [True, False])
 # @pytest.mark.parametrize("seqlen_new_eq_seqlen_q", [True])
 @pytest.mark.parametrize("rotary_interleaved", [False, True])
@@ -1678,7 +1817,7 @@ def test_flash_attn_splitkv(seqlen_q, seqlen_k, swap_sq_sk, d, causal, local, dt
 @pytest.mark.parametrize("rotary_fraction", [0.0, 0.5, 1.0])
 # @pytest.mark.parametrize("rotary_fraction", [0.0])
 @pytest.mark.parametrize("has_batch_idx", [False, True])
-# @pytest.mark.parametrize("has_batch_idx", [True])
+# @pytest.mark.parametrize("has_batch_idx", [False])
 @pytest.mark.parametrize("d", [32, 59, 64, 80, 96, 128, 160, 192, 224, 256])
 # @pytest.mark.parametrize('d', [32, 64, 96, 128, 160, 192, 224, 256])
 # @pytest.mark.parametrize('d', [32, 40, 64, 80, 96, 128, 160, 192])
@@ -1711,6 +1850,7 @@ def test_flash_attn_kvcache(
    seqlen_new_eq_seqlen_q,
    causal,
    local,
+    alibi,
    new_kv,
    mha_type,
    num_splits,
@@ -1750,10 +1890,22 @@ def test_flash_attn_kvcache(
        dtype=torch.int32,
        device=device,
    )
+    arange = rearrange(torch.arange(seqlen_k, device=device), "s -> 1 s")
+    cache_seqlens_expanded = rearrange(cache_seqlens, "b -> b 1")
+    key_padding_mask = arange < cache_seqlens_expanded + (seqlen_new if new_kv else 0)
    if has_batch_idx:
-        cache_batch_idx = torch.randperm(batch_size_cache, dtype=torch.int32, device=device)[:batch_size]
+        cache_batch_idx = torch.randperm(batch_size_cache, dtype=torch.int32, device=device)[
+            :batch_size
+        ]
    else:
        cache_batch_idx = None
+    if alibi:
+        alibi_slopes = torch.rand(batch_size, nheads, device=device, dtype=torch.float32) * 0.3
+        attn_bias = attn_bias_from_alibi_slopes(
+            alibi_slopes, seqlen_q, seqlen_k, None, key_padding_mask, causal=causal
+        )
+    else:
+        alibi_slopes, attn_bias = None, None
    # cache_seqlens = torch.tensor([64], dtype=torch.int32, device=device)
    if rotary_dim > 0:
        angle = torch.rand(seqlen_k, rotary_dim // 2, device=device) * 2 * math.pi
@@ -1785,8 +1937,6 @@ def test_flash_attn_kvcache(
    # k_cache[:, 64:] = -1
    k_cache_ref = (k_cache if not has_batch_idx else k_cache[cache_batch_idx]).clone()
    v_cache_ref = (v_cache if not has_batch_idx else v_cache[cache_batch_idx]).clone()
-    arange = rearrange(torch.arange(seqlen_k, device=device), "s -> 1 s")
-    cache_seqlens_expanded = rearrange(cache_seqlens, "b -> b 1")
    if new_kv:
        update_mask = torch.logical_and(
            cache_seqlens_expanded <= arange, arange < cache_seqlens_expanded + seqlen_new
@@ -1808,6 +1958,7 @@ def test_flash_attn_kvcache(
        causal=causal,
        window_size=window_size,
        rotary_interleaved=rotary_interleaved,
+        alibi_slopes=alibi_slopes,
        num_splits=num_splits,
    )
    # out = flash_attn_with_kvcache(
@@ -1820,13 +1971,13 @@ def test_flash_attn_kvcache(
    # o1 = torch.einsum('bhst,bthd->bshd', s_tmp, v_cache_ref)
    # lse_ref = torch.logsumexp(qk / math.sqrt(d), -1)
    # probs = torch.softmax(qk, dim=-1)
-    key_padding_mask = arange < cache_seqlens_expanded + (seqlen_new if new_kv else 0)
    out_ref, _ = attention_ref(
        q_ro,
        k_cache_rep,
        v_cache_rep,
        None,
        key_padding_mask,
+        attn_bias,
        0.0,
        None,
        causal=causal,
@@ -1838,6 +1989,7 @@ def test_flash_attn_kvcache(
        v_cache_rep,
        None,
        key_padding_mask,
+        attn_bias,
        0.0,
        None,
        causal=causal,
@@ -1857,7 +2009,8 @@ def test_flash_attn_kvcache(
        v_cache_select = v_cache if not has_batch_idx else v_cache[cache_batch_idx]
        assert torch.allclose(k_cache_select, k_cache_ref, rtol=1e-3, atol=1e-3)
        assert torch.equal(v_cache_select, v_cache_ref)
-    assert (out - out_ref).abs().max().item() <= 3 * (out_pt - out_ref).abs().max().item() + 1e-5
+    mult = 3 if not alibi else 5
+    assert (out - out_ref).abs().max().item() <= mult * (out_pt - out_ref).abs().max().item() + 1e-5
 # @pytest.mark.parametrize("dtype", ([torch.float16] if is_sm75 else [torch.float16, torch.bfloat16]))