Import mamba-ssm kernels

README.md

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+---
+license: apache-2.0
+---
+
+## Mamba
+
+Mamba state space kernels + models from [state-spaces/mamba](https://github.com/state-spaces/mamba).
+
+## Warning
+
+Some functionality is dependent on `einops` and `transformers`, however we
+currently don't have any way of defining these dependencies yet. The scope
+of the Hub kernel is probably too large (should maybe only contain the
+selective-scan and Triton kernels).

build.toml

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+[general]
+version = "0.0.1"
+
+[torch]
+name = "mamba_ssm"
+src = [
+  "torch-ext/registration.h",
+  "torch-ext/torch_binding.cpp",
+  "torch-ext/torch_binding.h"
+]
+pyroot = "torch-ext"
+
+[kernel.selective_scan]
+capabilities = [ "7.0", "7.2", "7.5", "8.0", "8.6", "8.7", "8.9", "9.0" ]
+src = [
+  "selective-scan/reverse_scan.cuh",
+  "selective-scan/selective_scan.cpp",
+  "selective-scan/selective_scan.h",
+  "selective-scan/selective_scan_bwd_bf16_complex.cu",
+  "selective-scan/selective_scan_bwd_bf16_real.cu",
+  "selective-scan/selective_scan_bwd_fp16_complex.cu",
+  "selective-scan/selective_scan_bwd_fp16_real.cu",
+  "selective-scan/selective_scan_bwd_fp32_complex.cu",
+  "selective-scan/selective_scan_bwd_fp32_real.cu",
+  "selective-scan/selective_scan_bwd_kernel.cuh",
+  "selective-scan/selective_scan_common.h",
+  "selective-scan/selective_scan_fwd_bf16.cu",
+  "selective-scan/selective_scan_fwd_fp16.cu",
+  "selective-scan/selective_scan_fwd_fp32.cu",
+  "selective-scan/selective_scan_fwd_kernel.cuh",
+  "selective-scan/static_switch.h",
+  "selective-scan/uninitialized_copy.cuh",
+]
+depends = [ "torch" ]

selective-scan/reverse_scan.cuh

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+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+#pragma once
+
+#ifndef USE_ROCM
+    #include <cub/config.cuh>
+    
+    #include <cub/util_ptx.cuh>
+    #include <cub/util_type.cuh>
+    #include <cub/block/block_raking_layout.cuh>
+    // #include <cub/detail/uninitialized_copy.cuh>
+#else
+    #include <hipcub/hipcub.hpp>
+    namespace cub = hipcub;
+#endif
+#include "uninitialized_copy.cuh"
+
+/**
+ * Perform a reverse sequential reduction over \p LENGTH elements of the \p input array.  The aggregate is returned.
+ */
+template <
+    int         LENGTH,
+    typename    T,
+    typename    ReductionOp>
+__device__ __forceinline__ T ThreadReverseReduce(const T (&input)[LENGTH], ReductionOp reduction_op) {
+    static_assert(LENGTH > 0);
+    T retval = input[LENGTH - 1];
+    #pragma unroll
+    for (int i = LENGTH - 2; i >= 0; --i) { retval = reduction_op(retval, input[i]); }
+    return retval;
+}
+
+/**
+ * Perform a sequential inclusive postfix reverse scan over the statically-sized \p input array, seeded with the specified \p postfix.  The aggregate is returned.
+ */
+template <
+    int         LENGTH,
+    typename    T,
+    typename    ScanOp>
+__device__ __forceinline__ T ThreadReverseScanInclusive(
+    const T (&input)[LENGTH],
+    T (&output)[LENGTH],
+    ScanOp scan_op,
+    const T postfix)
+{
+    T inclusive = postfix;
+    #pragma unroll
+    for (int i = LENGTH - 1; i >= 0; --i) {
+        inclusive = scan_op(inclusive, input[i]);
+        output[i] = inclusive;
+    }
+    return inclusive; 
+}
+
+/**
+ * Perform a sequential exclusive postfix reverse scan over the statically-sized \p input array, seeded with the specified \p postfix.  The aggregate is returned.
+ */
+template <
+    int         LENGTH,
+    typename    T,
+    typename    ScanOp>
+__device__ __forceinline__ T ThreadReverseScanExclusive(
+    const T (&input)[LENGTH],
+    T (&output)[LENGTH],
+    ScanOp scan_op,
+    const T postfix)
+{
+    // Careful, output maybe be aliased to input
+    T exclusive = postfix;
+    T inclusive;
+    #pragma unroll
+    for (int i = LENGTH - 1; i >= 0; --i) {
+        inclusive = scan_op(exclusive, input[i]);
+        output[i] = exclusive;
+        exclusive = inclusive;
+    }
+    return inclusive;
+}
+
+
+/**
+ * \brief WarpReverseScan provides SHFL-based variants of parallel postfix scan of items partitioned across a CUDA thread warp.
+ *
+ * LOGICAL_WARP_THREADS must be a power-of-two
+ */
+template <
+    typename    T,                      ///< Data type being scanned
+    int         LOGICAL_WARP_THREADS    ///< Number of threads per logical warp
+    >
+struct WarpReverseScan {
+    //---------------------------------------------------------------------
+    // Constants and type definitions
+    //---------------------------------------------------------------------
+
+    /// Whether the logical warp size and the PTX warp size coincide
+
+    // In hipcub, warp_threads is defined as HIPCUB_WARP_THREADS ::rocprim::warp_size()
+    // While in cub, it's defined as a macro that takes a redundant unused argument.
+    #ifndef USE_ROCM
+        #define WARP_THREADS CUB_WARP_THREADS(0)
+    #else
+        #define WARP_THREADS HIPCUB_WARP_THREADS
+    #endif
+    static constexpr bool IS_ARCH_WARP = (LOGICAL_WARP_THREADS == WARP_THREADS);
+    /// The number of warp scan steps
+    static constexpr int STEPS = cub::Log2<LOGICAL_WARP_THREADS>::VALUE;
+    static_assert(LOGICAL_WARP_THREADS == 1 << STEPS);
+
+
+    //---------------------------------------------------------------------
+    // Thread fields
+    //---------------------------------------------------------------------
+
+    /// Lane index in logical warp
+    unsigned int lane_id;
+
+    /// Logical warp index in 32-thread physical warp
+    unsigned int warp_id;
+
+    /// 32-thread physical warp member mask of logical warp
+    unsigned int member_mask;
+
+    //---------------------------------------------------------------------
+    // Construction
+    //---------------------------------------------------------------------
+
+    /// Constructor
+    explicit __device__ __forceinline__
+    WarpReverseScan()
+        : lane_id(cub::LaneId())
+        , warp_id(IS_ARCH_WARP ? 0 : (lane_id / LOGICAL_WARP_THREADS))
+        , member_mask(cub::WarpMask<LOGICAL_WARP_THREADS>(warp_id))
+    {
+        if (!IS_ARCH_WARP) {
+            lane_id = lane_id % LOGICAL_WARP_THREADS;
+        }
+    }
+
+
+    /// Broadcast
+    __device__ __forceinline__ T Broadcast(
+        T               input,              ///< [in] The value to broadcast
+        int             src_lane)           ///< [in] Which warp lane is to do the broadcasting
+    {
+        return cub::ShuffleIndex<LOGICAL_WARP_THREADS>(input, src_lane, member_mask);
+    }
+
+
+    /// Inclusive scan
+    template <typename ScanOpT>
+    __device__ __forceinline__ void InclusiveReverseScan(
+        T               input,              ///< [in] Calling thread's input item.
+        T               &inclusive_output,  ///< [out] Calling thread's output item.  May be aliased with \p input.
+        ScanOpT         scan_op)            ///< [in] Binary scan operator
+    {
+        inclusive_output = input;
+        #pragma unroll
+        for (int STEP = 0; STEP < STEPS; STEP++) {
+            int offset = 1 << STEP;
+            T temp = cub::ShuffleDown<LOGICAL_WARP_THREADS>(
+                inclusive_output, offset, LOGICAL_WARP_THREADS - 1, member_mask
+            );
+            // Perform scan op if from a valid peer
+            inclusive_output = static_cast<int>(lane_id) >= LOGICAL_WARP_THREADS - offset
+                ? inclusive_output : scan_op(temp, inclusive_output);
+        }
+    }
+
+    /// Exclusive scan
+    // Get exclusive from inclusive
+    template <typename ScanOpT>
+    __device__ __forceinline__ void ExclusiveReverseScan(
+        T              input,              ///< [in] Calling thread's input item.
+        T              &exclusive_output,  ///< [out] Calling thread's output item.  May be aliased with \p input.
+        ScanOpT        scan_op,            ///< [in] Binary scan operator
+        T              &warp_aggregate)    ///< [out] Warp-wide aggregate reduction of input items.
+    {
+        T inclusive_output;
+        InclusiveReverseScan(input, inclusive_output, scan_op);
+        warp_aggregate = cub::ShuffleIndex<LOGICAL_WARP_THREADS>(inclusive_output, 0, member_mask);
+        // initial value unknown
+        exclusive_output = cub::ShuffleDown<LOGICAL_WARP_THREADS>(
+            inclusive_output, 1, LOGICAL_WARP_THREADS - 1, member_mask
+        );
+    }
+
+    /**
+     * \brief Computes both inclusive and exclusive reverse scans using the specified binary scan functor across the calling warp.  Because no initial value is supplied, the \p exclusive_output computed for the last <em>warp-lane</em> is undefined.
+     */
+    template <typename ScanOpT>
+    __device__ __forceinline__ void ReverseScan(
+        T               input,              ///< [in] Calling thread's input item.
+        T               &inclusive_output,  ///< [out] Calling thread's inclusive-scan output item.
+        T               &exclusive_output,  ///< [out] Calling thread's exclusive-scan output item.
+        ScanOpT         scan_op)            ///< [in] Binary scan operator
+    {
+        InclusiveReverseScan(input, inclusive_output, scan_op);
+        // initial value unknown
+        exclusive_output = cub::ShuffleDown<LOGICAL_WARP_THREADS>(
+            inclusive_output, 1, LOGICAL_WARP_THREADS - 1, member_mask
+        );
+    }
+
+};
+
+/**
+ * \brief BlockReverseScan provides variants of raking-based parallel postfix scan across a CUDA thread block.
+ */
+template <
+    typename    T,              ///< Data type being scanned
+    int         BLOCK_DIM_X,    ///< The thread block length in threads along the X dimension
+    bool        MEMOIZE=false   ///< Whether or not to buffer outer raking scan partials to incur fewer shared memory reads at the expense of higher register pressure
+    >
+struct BlockReverseScan {
+    //---------------------------------------------------------------------
+    // Types and constants
+    //---------------------------------------------------------------------
+
+    /// Constants
+    /// The thread block size in threads
+    static constexpr int BLOCK_THREADS = BLOCK_DIM_X;
+
+    /// Layout type for padded thread block raking grid
+    using BlockRakingLayout = cub::BlockRakingLayout<T, BLOCK_THREADS>;
+    // The number of reduction elements is not a multiple of the number of raking threads for now
+    static_assert(BlockRakingLayout::UNGUARDED);
+
+    /// Number of raking threads
+    static constexpr int RAKING_THREADS = BlockRakingLayout::RAKING_THREADS;
+    /// Number of raking elements per warp synchronous raking thread
+    static constexpr int SEGMENT_LENGTH = BlockRakingLayout::SEGMENT_LENGTH;
+    /// Cooperative work can be entirely warp synchronous
+    static constexpr bool WARP_SYNCHRONOUS = (int(BLOCK_THREADS) == int(RAKING_THREADS));
+
+    ///  WarpReverseScan utility type
+    using WarpReverseScan = WarpReverseScan<T, RAKING_THREADS>;
+
+    /// Shared memory storage layout type
+    struct _TempStorage {
+        typename BlockRakingLayout::TempStorage raking_grid;     ///< Padded thread block raking grid
+    };
+
+
+    /// Alias wrapper allowing storage to be unioned
+    struct TempStorage : cub::Uninitialized<_TempStorage> {};
+
+
+    //---------------------------------------------------------------------
+    // Per-thread fields
+    //---------------------------------------------------------------------
+
+    // Thread fields
+    _TempStorage    &temp_storage;
+    unsigned int    linear_tid;
+    T               cached_segment[SEGMENT_LENGTH];
+
+
+    //---------------------------------------------------------------------
+    // Utility methods
+    //---------------------------------------------------------------------
+
+    /// Performs upsweep raking reduction, returning the aggregate
+    template <typename ScanOp>
+    __device__ __forceinline__ T Upsweep(ScanOp scan_op) {
+        T *smem_raking_ptr = BlockRakingLayout::RakingPtr(temp_storage.raking_grid, linear_tid);
+        // Read data into registers
+        #pragma unroll
+        for (int i = 0; i < SEGMENT_LENGTH; ++i) { cached_segment[i] = smem_raking_ptr[i]; }
+        T raking_partial = cached_segment[SEGMENT_LENGTH - 1];
+        #pragma unroll
+        for (int i = SEGMENT_LENGTH - 2; i >= 0; --i) {
+            raking_partial = scan_op(raking_partial, cached_segment[i]);
+        }
+        return raking_partial;
+    }
+
+
+    /// Performs exclusive downsweep raking scan
+    template <typename ScanOp>
+    __device__ __forceinline__ void ExclusiveDownsweep(
+        ScanOp          scan_op,
+        T               raking_partial)
+    {
+        T *smem_raking_ptr = BlockRakingLayout::RakingPtr(temp_storage.raking_grid, linear_tid);
+        // Read data back into registers
+        if (!MEMOIZE) {
+            #pragma unroll
+            for (int i = 0; i < SEGMENT_LENGTH; ++i) { cached_segment[i] = smem_raking_ptr[i]; }
+        }
+        ThreadReverseScanExclusive(cached_segment, cached_segment, scan_op, raking_partial);
+        // Write data back to smem
+        #pragma unroll
+        for (int i = 0; i < SEGMENT_LENGTH; ++i) { smem_raking_ptr[i] = cached_segment[i]; }
+    }
+
+
+    //---------------------------------------------------------------------
+    // Constructors
+    //---------------------------------------------------------------------
+
+    /// Constructor
+    __device__ __forceinline__ BlockReverseScan(
+        TempStorage &temp_storage)
+    :
+        temp_storage(temp_storage.Alias()),
+        linear_tid(cub::RowMajorTid(BLOCK_DIM_X, 1, 1))
+    {}
+
+
+    /// Computes an exclusive thread block-wide postfix scan using the specified binary \p scan_op functor.  Each thread contributes one input element.  the call-back functor \p block_postfix_callback_op is invoked by the first warp in the block, and the value returned by <em>lane</em><sub>0</sub> in that warp is used as the "seed" value that logically postfixes the thread block's scan inputs.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
+    template <
+        typename ScanOp,
+        typename BlockPostfixCallbackOp>
+    __device__ __forceinline__ void ExclusiveReverseScan(
+        T                       input,                          ///< [in] Calling thread's input item
+        T                       &exclusive_output,              ///< [out] Calling thread's output item (may be aliased to \p input)
+        ScanOp                  scan_op,                        ///< [in] Binary scan operator
+        BlockPostfixCallbackOp  &block_postfix_callback_op)     ///< [in-out] <b>[<em>warp</em><sub>0</sub> only]</b> Call-back functor for specifying a thread block-wide postfix to be applied to all inputs.
+    {
+        if (WARP_SYNCHRONOUS) {
+            // Short-circuit directly to warp-synchronous scan
+            T block_aggregate;
+            WarpReverseScan warp_scan;
+            warp_scan.ExclusiveReverseScan(input, exclusive_output, scan_op, block_aggregate);
+            // Obtain warp-wide postfix in lane0, then broadcast to other lanes
+            T block_postfix = block_postfix_callback_op(block_aggregate);
+            block_postfix = warp_scan.Broadcast(block_postfix, 0);
+            exclusive_output = linear_tid == BLOCK_THREADS - 1 ? block_postfix : scan_op(block_postfix, exclusive_output);
+        } else {
+            // Place thread partial into shared memory raking grid
+            T *placement_ptr = BlockRakingLayout::PlacementPtr(temp_storage.raking_grid, linear_tid);
+            detail::uninitialized_copy(placement_ptr, input);
+            cub::CTA_SYNC();
+            // Reduce parallelism down to just raking threads
+            if (linear_tid < RAKING_THREADS) {
+                WarpReverseScan warp_scan;
+                // Raking upsweep reduction across shared partials
+                T upsweep_partial = Upsweep(scan_op);
+                // Warp-synchronous scan
+                T exclusive_partial, block_aggregate;
+                warp_scan.ExclusiveReverseScan(upsweep_partial, exclusive_partial, scan_op, block_aggregate);
+                // Obtain block-wide postfix in lane0, then broadcast to other lanes
+                T block_postfix = block_postfix_callback_op(block_aggregate);
+                block_postfix = warp_scan.Broadcast(block_postfix, 0);
+                // Update postfix with warpscan exclusive partial
+                T downsweep_postfix = linear_tid == RAKING_THREADS - 1
+                    ? block_postfix : scan_op(block_postfix, exclusive_partial);
+                // Exclusive raking downsweep scan
+                ExclusiveDownsweep(scan_op, downsweep_postfix);
+            }
+            cub::CTA_SYNC();
+            // Grab thread postfix from shared memory
+            exclusive_output = *placement_ptr;
+
+            // // Compute warp scan in each warp.
+            // // The exclusive output from the last lane in each warp is invalid.
+            // T inclusive_output;
+            // WarpReverseScan warp_scan;
+            // warp_scan.ReverseScan(input, inclusive_output, exclusive_output, scan_op);
+
+            // // Compute the warp-wide postfix and block-wide aggregate for each warp.  Warp postfix for the last warp is invalid.
+            // T block_aggregate;
+            // T warp_postfix = ComputeWarpPostfix(scan_op, inclusive_output, block_aggregate);
+
+            // // Apply warp postfix to our lane's partial
+            // if (warp_id != 0) {
+            //     exclusive_output = scan_op(warp_postfix, exclusive_output);
+            //     if (lane_id == 0) { exclusive_output = warp_postfix; }
+            // }
+
+            // // Use the first warp to determine the thread block postfix, returning the result in lane0
+            // if (warp_id == 0) {
+            //     T block_postfix = block_postfix_callback_op(block_aggregate);
+            //     if (lane_id == 0) {
+            //         // Share the postfix with all threads
+            //         detail::uninitialized_copy(&temp_storage.block_postfix,
+            //                                   block_postfix);
+
+            //         exclusive_output = block_postfix; // The block postfix is the exclusive output for tid0
+            //     }
+            // }
+
+            // cub::CTA_SYNC();
+
+            // // Incorporate thread block postfix into outputs
+            // T block_postfix = temp_storage.block_postfix;
+            // if (linear_tid > 0) { exclusive_output = scan_op(block_postfix, exclusive_output); }
+        }
+    }
+
+
+    /**
+     * \brief Computes an inclusive block-wide postfix scan using the specified binary \p scan_op functor.  Each thread contributes an array of consecutive input elements.  the call-back functor \p block_postfix_callback_op is invoked by the first warp in the block, and the value returned by <em>lane</em><sub>0</sub> in that warp is used as the "seed" value that logically postfixes the thread block's scan inputs.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
+     */
+    template <
+        int             ITEMS_PER_THREAD,
+        typename        ScanOp,
+        typename        BlockPostfixCallbackOp>
+    __device__ __forceinline__ void InclusiveReverseScan(
+        T                       (&input)[ITEMS_PER_THREAD],     ///< [in] Calling thread's input items
+        T                       (&output)[ITEMS_PER_THREAD],    ///< [out] Calling thread's output items (may be aliased to \p input)
+        ScanOp                  scan_op,                        ///< [in] Binary scan functor
+        BlockPostfixCallbackOp   &block_postfix_callback_op)    ///< [in-out] <b>[<em>warp</em><sub>0</sub> only]</b> Call-back functor for specifying a block-wide postfix to be applied to the logical input sequence.
+    {
+        // Reduce consecutive thread items in registers
+        T thread_postfix = ThreadReverseReduce(input, scan_op);
+        // Exclusive thread block-scan
+        ExclusiveReverseScan(thread_postfix, thread_postfix, scan_op, block_postfix_callback_op);
+        // Inclusive scan in registers with postfix as seed
+        ThreadReverseScanInclusive(input, output, scan_op, thread_postfix);
+    }
+
+};

selective-scan/selective_scan.cpp

@@ -0,0 +1,497 @@
+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+#include <c10/cuda/CUDAGuard.h>
+#include <c10/cuda/CUDAStream.h>
+#include <torch/all.h>
+#include <vector>
+
+#include "selective_scan.h"
+
+#define CHECK_SHAPE(x, ...) TORCH_CHECK(x.sizes() == torch::IntArrayRef({__VA_ARGS__}), #x " must have shape (" #__VA_ARGS__ ")")
+
+#define DISPATCH_ITYPE_FLOAT_AND_HALF_AND_BF16(ITYPE, NAME, ...)                    \
+    if (ITYPE == at::ScalarType::Half) {                                            \
+        using input_t = at::Half;                                                   \
+        __VA_ARGS__();                                                              \
+    } else if (ITYPE == at::ScalarType::BFloat16) {                                 \
+        using input_t = at::BFloat16;                                               \
+        __VA_ARGS__();                                                              \
+    } else if (ITYPE == at::ScalarType::Float)  {                                   \
+        using input_t = float;                                                      \
+        __VA_ARGS__();                                                              \
+    } else {                                                                        \
+        AT_ERROR(#NAME, " not implemented for input type '", toString(ITYPE), "'"); \
+    }
+
+#define DISPATCH_WTYPE_FLOAT_AND_HALF_AND_BF16(WTYPE, NAME, ...)                     \
+    if (WTYPE == at::ScalarType::Half) {                                             \
+        using weight_t = at::Half;                                                   \
+        __VA_ARGS__();                                                               \
+    } else if (WTYPE == at::ScalarType::BFloat16) {                                  \
+        using weight_t = at::BFloat16;                                               \
+        __VA_ARGS__();                                                               \
+    } else if (WTYPE == at::ScalarType::Float)  {                                    \
+        using weight_t = float;                                                      \
+        __VA_ARGS__();                                                               \
+    } else {                                                                         \
+        AT_ERROR(#NAME, " not implemented for weight type '", toString(WTYPE), "'"); \
+    }
+
+#define DISPATCH_WTYPE_FLOAT_AND_COMPLEX(WTYPE, NAME, ...)                           \
+    if (WTYPE == at::ScalarType::Float) {                                            \
+       using weight_t = float;                                                       \
+        __VA_ARGS__();                                                               \
+    } else if (WTYPE == at::ScalarType::ComplexFloat) {                              \
+        using weight_t = c10::complex<float>;                                        \
+        __VA_ARGS__();                                                               \
+    } else {                                                                         \
+        AT_ERROR(#NAME, " not implemented for weight type '", toString(WTYPE), "'"); \
+    }
+
+template<typename input_t, typename weight_t>
+void selective_scan_fwd_cuda(SSMParamsBase &params, cudaStream_t stream);
+
+template <typename input_t, typename weight_t>
+void selective_scan_bwd_cuda(SSMParamsBwd &params, cudaStream_t stream);
+
+void set_ssm_params_fwd(SSMParamsBase &params,
+                        // sizes
+                        const size_t batch,
+                        const size_t dim,
+                        const size_t seqlen,
+                        const size_t dstate,
+                        const size_t n_groups,
+                        const size_t n_chunks,
+                        const bool is_variable_B,
+                        const bool is_variable_C,
+                        // device pointers
+                        const at::Tensor u,
+                        const at::Tensor delta,
+                        const at::Tensor A,
+                        const at::Tensor B,
+                        const at::Tensor C,
+                        const at::Tensor out,
+                        const at::Tensor z,
+                        const at::Tensor out_z,
+                        void* D_ptr,
+                        void* delta_bias_ptr,
+                        void* x_ptr,
+                        bool has_z,
+                        bool delta_softplus) {
+
+    // Reset the parameters
+    memset(&params, 0, sizeof(params));
+
+    params.batch = batch;
+    params.dim = dim;
+    params.seqlen = seqlen;
+    params.dstate = dstate;
+    params.n_groups = n_groups;
+    params.n_chunks = n_chunks;
+    params.dim_ngroups_ratio = dim / n_groups;
+
+    params.delta_softplus = delta_softplus;
+
+    params.is_variable_B = is_variable_B;
+    params.is_variable_C = is_variable_C;
+
+    // Set the pointers and strides.
+    params.u_ptr = u.data_ptr();
+    params.delta_ptr = delta.data_ptr();
+    params.A_ptr = A.data_ptr();
+    params.B_ptr = B.data_ptr();
+    params.C_ptr = C.data_ptr();
+    params.D_ptr = D_ptr;
+    params.delta_bias_ptr = delta_bias_ptr;
+    params.out_ptr = out.data_ptr();
+    params.x_ptr = x_ptr;
+    params.z_ptr = has_z ? z.data_ptr() : nullptr;
+    params.out_z_ptr = has_z ? out_z.data_ptr() : nullptr;
+    // All stride are in elements, not bytes.
+    params.A_d_stride = A.stride(0);
+    params.A_dstate_stride = A.stride(1);
+    if (!is_variable_B) {
+        params.B_d_stride = B.stride(0);
+    } else {
+        params.B_batch_stride = B.stride(0);
+        params.B_group_stride = B.stride(1);
+    }
+    params.B_dstate_stride = !is_variable_B ? B.stride(1) : B.stride(2);
+    if (!is_variable_C) {
+        params.C_d_stride = C.stride(0);
+    } else {
+        params.C_batch_stride = C.stride(0);
+        params.C_group_stride = C.stride(1);
+    }
+    params.C_dstate_stride = !is_variable_C ? C.stride(1) : C.stride(2);
+    params.u_batch_stride = u.stride(0);
+    params.u_d_stride = u.stride(1);
+    params.delta_batch_stride = delta.stride(0);
+    params.delta_d_stride = delta.stride(1);
+    if (has_z) {
+        params.z_batch_stride = z.stride(0);
+        params.z_d_stride = z.stride(1);
+        params.out_z_batch_stride = out_z.stride(0);
+        params.out_z_d_stride = out_z.stride(1);
+    }
+    params.out_batch_stride = out.stride(0);
+    params.out_d_stride = out.stride(1);
+}
+
+void set_ssm_params_bwd(SSMParamsBwd &params,
+                        // sizes
+                        const size_t batch,
+                        const size_t dim,
+                        const size_t seqlen,
+                        const size_t dstate,
+                        const size_t n_groups,
+                        const size_t n_chunks,
+                        const bool is_variable_B,
+                        const bool is_variable_C,
+                        // device pointers
+                        const at::Tensor u,
+                        const at::Tensor delta,
+                        const at::Tensor A,
+                        const at::Tensor B,
+                        const at::Tensor C,
+                        const at::Tensor z,
+                        const at::Tensor out,
+                        const at::Tensor out_z,
+                        void* D_ptr,
+                        void* delta_bias_ptr,
+                        void* x_ptr,
+                        const at::Tensor dout,
+                        const at::Tensor du,
+                        const at::Tensor ddelta,
+                        const at::Tensor dA,
+                        const at::Tensor dB,
+                        const at::Tensor dC,
+                        const at::Tensor dz,
+                        void* dD_ptr,
+                        void* ddelta_bias_ptr,
+                        bool has_z,
+                        bool delta_softplus,
+                        bool recompute_out_z) {
+    // Pass in "dout" instead of "out", we're not gonna use "out" unless we have z
+    set_ssm_params_fwd(params, batch, dim, seqlen, dstate, n_groups, n_chunks, is_variable_B, is_variable_C,
+                       u, delta, A, B, C, has_z ? out : dout,
+                       has_z ? z : dout,
+                       // If not recompute_out_z, pass dout instead of out_z.
+                       // This won't be used by the bwd kernel
+                       recompute_out_z ? out_z : dout,
+                       D_ptr, delta_bias_ptr, x_ptr, has_z, delta_softplus);
+    if (!recompute_out_z) { params.out_z_ptr = nullptr; }
+
+    // Set the pointers and strides.
+    params.dout_ptr = dout.data_ptr();
+    params.du_ptr = du.data_ptr();
+    params.dA_ptr = dA.data_ptr();
+    params.dB_ptr = dB.data_ptr();
+    params.dC_ptr = dC.data_ptr();
+    params.dD_ptr = dD_ptr;
+    params.ddelta_ptr = ddelta.data_ptr();
+    params.ddelta_bias_ptr = ddelta_bias_ptr;
+    params.dz_ptr = has_z ? dz.data_ptr() : nullptr;
+    // All stride are in elements, not bytes.
+    params.dout_batch_stride = dout.stride(0);
+    params.dout_d_stride = dout.stride(1);
+    params.dA_d_stride = dA.stride(0);
+    params.dA_dstate_stride = dA.stride(1);
+    if (!is_variable_B) {
+        params.dB_d_stride = dB.stride(0);
+    } else {
+        params.dB_batch_stride = dB.stride(0);
+        params.dB_group_stride = dB.stride(1);
+    }
+    params.dB_dstate_stride = !is_variable_B ? dB.stride(1) : dB.stride(2);
+    if (!is_variable_C) {
+        params.dC_d_stride = dC.stride(0);
+    } else {
+        params.dC_batch_stride = dC.stride(0);
+        params.dC_group_stride = dC.stride(1);
+    }
+    params.dC_dstate_stride = !is_variable_C ? dC.stride(1) : dC.stride(2);
+    params.du_batch_stride = du.stride(0);
+    params.du_d_stride = du.stride(1);
+    params.ddelta_batch_stride = ddelta.stride(0);
+    params.ddelta_d_stride = ddelta.stride(1);
+    if (has_z) {
+        params.dz_batch_stride = dz.stride(0);
+        params.dz_d_stride = dz.stride(1);
+    }
+}
+
+std::vector<at::Tensor>
+selective_scan_fwd(const at::Tensor &u, const at::Tensor &delta,
+                  const at::Tensor &A, const at::Tensor &B, const at::Tensor &C,
+                  const c10::optional<at::Tensor> &D_,
+                  const c10::optional<at::Tensor> &z_,
+                  const c10::optional<at::Tensor> &delta_bias_,
+                  bool delta_softplus) {
+    auto input_type = u.scalar_type();
+    auto weight_type = A.scalar_type();
+    TORCH_CHECK(input_type == at::ScalarType::Float || input_type == at::ScalarType::Half || input_type == at::ScalarType::BFloat16);
+    TORCH_CHECK(weight_type == at::ScalarType::Float || weight_type == at::ScalarType::ComplexFloat);
+
+    const bool is_variable_B = B.dim() >= 3;
+    const bool is_variable_C = C.dim() >= 3;
+    const bool is_complex = weight_type == at::ScalarType::ComplexFloat;
+
+    TORCH_CHECK(delta.scalar_type() == input_type);
+    TORCH_CHECK(B.scalar_type() == (!is_variable_B ? weight_type : input_type));
+    TORCH_CHECK(C.scalar_type() == (!is_variable_C ? weight_type : input_type));
+
+    TORCH_CHECK(u.is_cuda());
+    TORCH_CHECK(delta.is_cuda());
+    TORCH_CHECK(A.is_cuda());
+    TORCH_CHECK(B.is_cuda());
+    TORCH_CHECK(C.is_cuda());
+
+    TORCH_CHECK(u.stride(-1) == 1 || u.size(-1) == 1);
+    TORCH_CHECK(delta.stride(-1) == 1 || delta.size(-1) == 1);
+
+    const auto sizes = u.sizes();
+    const int batch_size = sizes[0];
+    const int dim = sizes[1];
+    const int seqlen = sizes[2];
+    const int dstate = A.size(1);
+    const int n_groups = is_variable_B ? B.size(1) : 1;
+
+    TORCH_CHECK(dstate <= 256, "selective_scan only supports state dimension <= 256");
+
+    CHECK_SHAPE(u, batch_size, dim, seqlen);
+    CHECK_SHAPE(delta, batch_size, dim, seqlen);
+    CHECK_SHAPE(A, dim, dstate);
+    if (!is_variable_B) {
+        CHECK_SHAPE(B, dim, dstate);
+    } else {
+        CHECK_SHAPE(B, batch_size, n_groups, dstate, !is_complex ? seqlen : seqlen * 2);
+        TORCH_CHECK(B.stride(-1) == 1 || B.size(-1) == 1);
+    }
+    if (!is_variable_C) {
+        CHECK_SHAPE(C, dim, dstate);
+    } else {
+        CHECK_SHAPE(C, batch_size, n_groups, dstate, !is_complex ? seqlen: seqlen * 2);
+        TORCH_CHECK(C.stride(-1) == 1 || C.size(-1) == 1);
+    }
+
+    if (D_.has_value()) {
+        auto D = D_.value();
+        TORCH_CHECK(D.scalar_type() == at::ScalarType::Float);
+        TORCH_CHECK(D.is_cuda());
+        TORCH_CHECK(D.stride(-1) == 1 || D.size(-1) == 1);
+        CHECK_SHAPE(D, dim);
+    }
+
+    if (delta_bias_.has_value()) {
+        auto delta_bias = delta_bias_.value();
+        TORCH_CHECK(delta_bias.scalar_type() == at::ScalarType::Float);
+        TORCH_CHECK(delta_bias.is_cuda());
+        TORCH_CHECK(delta_bias.stride(-1) == 1 || delta_bias.size(-1) == 1);
+        CHECK_SHAPE(delta_bias, dim);
+    }
+
+    at::Tensor z, out_z;
+    const bool has_z = z_.has_value();
+    if (has_z) {
+        z = z_.value();
+        TORCH_CHECK(z.scalar_type() == input_type);
+        TORCH_CHECK(z.is_cuda());
+        TORCH_CHECK(z.stride(-1) == 1 || z.size(-1) == 1);
+        CHECK_SHAPE(z, batch_size, dim, seqlen);
+        out_z = torch::empty_like(z);
+    }
+
+    const int n_chunks = (seqlen + 2048 - 1) / 2048;
+    // const int n_chunks = (seqlen + 1024 - 1) / 1024;
+    // at::Tensor out = torch::empty_like(u);
+    // Right now u has BHL layout and delta has HBL layout, and we want out to have HBL layout
+    at::Tensor out = torch::empty_like(delta);
+    at::Tensor x;
+    x = torch::empty({batch_size, dim, n_chunks, dstate * 2}, u.options().dtype(weight_type));
+
+    SSMParamsBase params;
+    set_ssm_params_fwd(params, batch_size, dim, seqlen, dstate, n_groups, n_chunks, is_variable_B, is_variable_C,
+                       u, delta, A, B, C, out, z, out_z,
+                       D_.has_value() ? D_.value().data_ptr() : nullptr,
+                       delta_bias_.has_value() ? delta_bias_.value().data_ptr() : nullptr,
+                       x.data_ptr(),
+                       has_z,
+                       delta_softplus);
+
+    // Otherwise the kernel will be launched from cuda:0 device
+    // Cast to char to avoid compiler warning about narrowing
+    at::cuda::CUDAGuard device_guard{u.device()};
+    auto stream = at::cuda::getCurrentCUDAStream().stream();
+    DISPATCH_ITYPE_FLOAT_AND_HALF_AND_BF16(u.scalar_type(), "selective_scan_fwd", [&] {
+        DISPATCH_WTYPE_FLOAT_AND_COMPLEX(A.scalar_type(), "selective_scan_fwd", [&] {
+            selective_scan_fwd_cuda<input_t, weight_t>(params, stream);
+        });
+    });
+    std::vector<at::Tensor> result = {out, x};
+    if (has_z) { result.push_back(out_z); }
+    return result;
+}
+
+std::vector<at::Tensor>
+selective_scan_bwd(const at::Tensor &u, const at::Tensor &delta,
+                  const at::Tensor &A, const at::Tensor &B, const at::Tensor &C,
+                  const c10::optional<at::Tensor> &D_,
+                  const c10::optional<at::Tensor> &z_,
+                  const c10::optional<at::Tensor> &delta_bias_,
+                  const at::Tensor &dout,
+                  const c10::optional<at::Tensor> &x_,
+                  const c10::optional<at::Tensor> &out_,
+                  c10::optional<at::Tensor> dz_,
+                  bool delta_softplus,
+                  bool recompute_out_z) {
+    auto input_type = u.scalar_type();
+    auto weight_type = A.scalar_type();
+    TORCH_CHECK(input_type == at::ScalarType::Float || input_type == at::ScalarType::Half || input_type == at::ScalarType::BFloat16);
+    TORCH_CHECK(weight_type == at::ScalarType::Float || weight_type == at::ScalarType::ComplexFloat);
+
+    const bool is_variable_B = B.dim() >= 3;
+    const bool is_variable_C = C.dim() >= 3;
+    const bool is_complex = weight_type == at::ScalarType::ComplexFloat;
+
+    TORCH_CHECK(delta.scalar_type() == input_type);
+    TORCH_CHECK(B.scalar_type() == (!is_variable_B ? weight_type : input_type));
+    TORCH_CHECK(C.scalar_type() == (!is_variable_C ? weight_type : input_type));
+    TORCH_CHECK(dout.scalar_type() == input_type);
+
+    TORCH_CHECK(u.is_cuda());
+    TORCH_CHECK(delta.is_cuda());
+    TORCH_CHECK(A.is_cuda());
+    TORCH_CHECK(B.is_cuda());
+    TORCH_CHECK(C.is_cuda());
+    TORCH_CHECK(dout.is_cuda());
+
+    TORCH_CHECK(u.stride(-1) == 1 || u.size(-1) == 1);
+    TORCH_CHECK(delta.stride(-1) == 1 || delta.size(-1) == 1);
+    TORCH_CHECK(dout.stride(-1) == 1 || dout.size(-1) == 1);
+
+    const auto sizes = u.sizes();
+    const int batch_size = sizes[0];
+    const int dim = sizes[1];
+    const int seqlen = sizes[2];
+    const int dstate = A.size(1);
+    const int n_groups = is_variable_B ? B.size(1) : 1;
+
+    TORCH_CHECK(dstate <= 256, "selective_scan only supports state dimension <= 256");
+
+    CHECK_SHAPE(u, batch_size, dim, seqlen);
+    CHECK_SHAPE(delta, batch_size, dim, seqlen);
+    CHECK_SHAPE(A, dim, dstate);
+    if (!is_variable_B) {
+        CHECK_SHAPE(B, dim, dstate);
+    } else {
+        CHECK_SHAPE(B, batch_size, n_groups, dstate, !is_complex ? seqlen : seqlen * 2);
+        TORCH_CHECK(B.stride(-1) == 1 || B.size(-1) == 1);
+    }
+    if (!is_variable_C) {
+        CHECK_SHAPE(C, dim, dstate);
+    } else {
+        CHECK_SHAPE(C, batch_size, n_groups, dstate, !is_complex ? seqlen: seqlen * 2);
+        TORCH_CHECK(C.stride(-1) == 1 || C.size(-1) == 1);
+    }
+    CHECK_SHAPE(dout, batch_size, dim, seqlen);
+
+    if (D_.has_value()) {
+        auto D = D_.value();
+        TORCH_CHECK(D.scalar_type() == at::ScalarType::Float);
+        TORCH_CHECK(D.is_cuda());
+        TORCH_CHECK(D.stride(-1) == 1 || D.size(-1) == 1);
+        CHECK_SHAPE(D, dim);
+    }
+
+    if (delta_bias_.has_value()) {
+        auto delta_bias = delta_bias_.value();
+        TORCH_CHECK(delta_bias.scalar_type() == at::ScalarType::Float);
+        TORCH_CHECK(delta_bias.is_cuda());
+        TORCH_CHECK(delta_bias.stride(-1) == 1 || delta_bias.size(-1) == 1);
+        CHECK_SHAPE(delta_bias, dim);
+    }
+
+    at::Tensor z, out, dz, out_z;
+    const bool has_z = z_.has_value();
+    if (has_z) {
+        z = z_.value();
+        TORCH_CHECK(z.scalar_type() == input_type);
+        TORCH_CHECK(z.is_cuda());
+        TORCH_CHECK(z.stride(-1) == 1 || z.size(-1) == 1);
+        CHECK_SHAPE(z, batch_size, dim, seqlen);
+
+        TORCH_CHECK(out_.has_value());
+        out = out_.value();
+        TORCH_CHECK(out.scalar_type() == input_type);
+        TORCH_CHECK(out.is_cuda());
+        TORCH_CHECK(out.stride(-1) == 1 || out.size(-1) == 1);
+        CHECK_SHAPE(out, batch_size, dim, seqlen);
+
+        if (dz_.has_value()) {
+            dz = dz_.value();
+            TORCH_CHECK(dz.scalar_type() == input_type);
+            TORCH_CHECK(dz.is_cuda());
+            TORCH_CHECK(dz.stride(-1) == 1 || dz.size(-1) == 1);
+            CHECK_SHAPE(dz, batch_size, dim, seqlen);
+        } else {
+            dz = torch::empty_like(z);
+        }
+        if (recompute_out_z) {
+            out_z = torch::empty_like(out);
+        }
+    }
+
+    const int n_chunks = (seqlen + 2048 - 1) / 2048;
+    // const int n_chunks = (seqlen + 1024 - 1) / 1024;
+    if (n_chunks > 1) { TORCH_CHECK(x_.has_value()); }
+    if (x_.has_value()) {
+        auto x = x_.value();
+        TORCH_CHECK(x.scalar_type() == weight_type);
+        TORCH_CHECK(x.is_cuda());
+        TORCH_CHECK(x.is_contiguous());
+        CHECK_SHAPE(x, batch_size, dim, n_chunks, 2 * dstate);
+    }
+
+    at::Tensor du = torch::empty_like(u);
+    at::Tensor ddelta = torch::empty_like(delta);
+    at::Tensor dA = torch::zeros_like(A);
+    at::Tensor dB = !is_variable_B ? torch::zeros_like(B) : torch::zeros_like(B, B.options().dtype(torch::kFloat32));
+    at::Tensor dC = !is_variable_C ? torch::zeros_like(C) : torch::zeros_like(C, C.options().dtype(torch::kFloat32));
+    at::Tensor dD;
+    if (D_.has_value()) { dD = torch::zeros_like(D_.value()); }
+    at::Tensor ddelta_bias;
+    if (delta_bias_.has_value()) { ddelta_bias = torch::zeros_like(delta_bias_.value()); }
+
+    SSMParamsBwd params;
+    set_ssm_params_bwd(params, batch_size, dim, seqlen, dstate, n_groups, n_chunks, is_variable_B, is_variable_C,
+                       u, delta, A, B, C, z, out, out_z,
+                       D_.has_value() ? D_.value().data_ptr() : nullptr,
+                       delta_bias_.has_value() ? delta_bias_.value().data_ptr() : nullptr,
+                       x_.has_value() ? x_.value().data_ptr() : nullptr,
+                       dout, du, ddelta, dA, dB, dC, dz,
+                       D_.has_value() ? dD.data_ptr() : nullptr,
+                       delta_bias_.has_value() ? ddelta_bias.data_ptr() : nullptr,
+                       has_z, delta_softplus, recompute_out_z);
+
+    // Otherwise the kernel will be launched from cuda:0 device
+    // Cast to char to avoid compiler warning about narrowing
+    at::cuda::CUDAGuard device_guard{u.device()};
+    auto stream = at::cuda::getCurrentCUDAStream().stream();
+    DISPATCH_ITYPE_FLOAT_AND_HALF_AND_BF16(u.scalar_type(), "selective_scan_bwd", [&] {
+        DISPATCH_WTYPE_FLOAT_AND_COMPLEX(A.scalar_type(), "selective_scan_bwd", [&] {
+            selective_scan_bwd_cuda<input_t, weight_t>(params, stream);
+        });
+    });
+    std::vector<at::Tensor> result = {du, ddelta, dA, dB.to(B.dtype()), dC.to(C.dtype()), dD, ddelta_bias};
+    if (has_z) { result.push_back(dz); }
+    if (recompute_out_z) { result.push_back(out_z); }
+    return result;
+}
+
+//PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
+//    m.def("fwd", &selective_scan_fwd, "Selective scan forward");
+//    m.def("bwd", &selective_scan_bwd, "Selective scan backward");
+//}

selective-scan/selective_scan.h

@@ -0,0 +1,101 @@
+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+#pragma once
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+struct SSMScanParamsBase {
+    using index_t = uint32_t;
+
+    int batch, seqlen, n_chunks;
+    index_t a_batch_stride;
+    index_t b_batch_stride;
+    index_t out_batch_stride;
+
+    // Common data pointers.
+    void *__restrict__ a_ptr;
+    void *__restrict__ b_ptr;
+    void *__restrict__ out_ptr;
+    void *__restrict__ x_ptr;
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+struct SSMParamsBase {
+    using index_t = uint32_t;
+
+    int batch, dim, seqlen, dstate, n_groups, n_chunks;
+    int dim_ngroups_ratio;
+    bool is_variable_B;
+    bool is_variable_C;
+
+    bool delta_softplus;
+
+    index_t A_d_stride;
+    index_t A_dstate_stride;
+    index_t B_batch_stride;
+    index_t B_d_stride;
+    index_t B_dstate_stride;
+    index_t B_group_stride;
+    index_t C_batch_stride;
+    index_t C_d_stride;
+    index_t C_dstate_stride;
+    index_t C_group_stride;
+    index_t u_batch_stride;
+    index_t u_d_stride;
+    index_t delta_batch_stride;
+    index_t delta_d_stride;
+    index_t z_batch_stride;
+    index_t z_d_stride;
+    index_t out_batch_stride;
+    index_t out_d_stride;
+    index_t out_z_batch_stride;
+    index_t out_z_d_stride;
+
+    // Common data pointers.
+    void *__restrict__ A_ptr;
+    void *__restrict__ B_ptr;
+    void *__restrict__ C_ptr;
+    void *__restrict__ D_ptr;
+    void *__restrict__ u_ptr;
+    void *__restrict__ delta_ptr;
+    void *__restrict__ delta_bias_ptr;
+    void *__restrict__ out_ptr;
+    void *__restrict__ x_ptr;
+    void *__restrict__ z_ptr;
+    void *__restrict__ out_z_ptr;
+};
+
+struct SSMParamsBwd: public SSMParamsBase {
+    index_t dout_batch_stride;
+    index_t dout_d_stride;
+    index_t dA_d_stride;
+    index_t dA_dstate_stride;
+    index_t dB_batch_stride;
+    index_t dB_group_stride;
+    index_t dB_d_stride;
+    index_t dB_dstate_stride;
+    index_t dC_batch_stride;
+    index_t dC_group_stride;
+    index_t dC_d_stride;
+    index_t dC_dstate_stride;
+    index_t du_batch_stride;
+    index_t du_d_stride;
+    index_t dz_batch_stride;
+    index_t dz_d_stride;
+    index_t ddelta_batch_stride;
+    index_t ddelta_d_stride;
+
+    // Common data pointers.
+    void *__restrict__ dout_ptr;
+    void *__restrict__ dA_ptr;
+    void *__restrict__ dB_ptr;
+    void *__restrict__ dC_ptr;
+    void *__restrict__ dD_ptr;
+    void *__restrict__ du_ptr;
+    void *__restrict__ dz_ptr;
+    void *__restrict__ ddelta_ptr;
+    void *__restrict__ ddelta_bias_ptr;
+};

selective-scan/selective_scan_bwd_bf16_complex.cu

@@ -0,0 +1,9 @@
+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+// Split into multiple files to compile in paralell
+
+#include "selective_scan_bwd_kernel.cuh"
+
+template void selective_scan_bwd_cuda<at::BFloat16, complex_t>(SSMParamsBwd &params, cudaStream_t stream);

selective-scan/selective_scan_bwd_bf16_real.cu

@@ -0,0 +1,9 @@
+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+// Split into multiple files to compile in paralell
+
+#include "selective_scan_bwd_kernel.cuh"
+
+template void selective_scan_bwd_cuda<at::BFloat16, float>(SSMParamsBwd &params, cudaStream_t stream);

selective-scan/selective_scan_bwd_fp16_complex.cu

@@ -0,0 +1,9 @@
+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+// Split into multiple files to compile in paralell
+
+#include "selective_scan_bwd_kernel.cuh"
+
+template void selective_scan_bwd_cuda<at::Half, complex_t>(SSMParamsBwd &params, cudaStream_t stream);

selective-scan/selective_scan_bwd_fp16_real.cu

@@ -0,0 +1,9 @@
+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+// Split into multiple files to compile in paralell
+
+#include "selective_scan_bwd_kernel.cuh"
+
+template void selective_scan_bwd_cuda<at::Half, float>(SSMParamsBwd &params, cudaStream_t stream);

selective-scan/selective_scan_bwd_fp32_complex.cu

@@ -0,0 +1,9 @@
+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+// Split into multiple files to compile in paralell
+
+#include "selective_scan_bwd_kernel.cuh"
+
+template void selective_scan_bwd_cuda<float, complex_t>(SSMParamsBwd &params, cudaStream_t stream);

selective-scan/selective_scan_bwd_fp32_real.cu

@@ -0,0 +1,9 @@
+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+// Split into multiple files to compile in paralell
+
+#include "selective_scan_bwd_kernel.cuh"
+
+template void selective_scan_bwd_cuda<float, float>(SSMParamsBwd &params, cudaStream_t stream);

selective-scan/selective_scan_bwd_kernel.cuh

@@ -0,0 +1,561 @@
+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+#pragma once
+
+#include <c10/util/BFloat16.h>
+#include <c10/util/Half.h>
+#include <c10/cuda/CUDAException.h>  // For C10_CUDA_CHECK and C10_CUDA_KERNEL_LAUNCH_CHECK
+#include <ATen/cuda/Atomic.cuh>  // For atomicAdd on complex
+
+#ifndef USE_ROCM
+    #include <cub/block/block_load.cuh>
+    #include <cub/block/block_store.cuh>
+    #include <cub/block/block_scan.cuh>
+    #include <cub/block/block_reduce.cuh>
+#else
+    #include <hipcub/hipcub.hpp>
+    namespace cub = hipcub;
+#endif
+
+#include "selective_scan.h"
+#include "selective_scan_common.h"
+#include "reverse_scan.cuh"
+#include "static_switch.h"
+
+template<typename scalar_t> __device__ __forceinline__ scalar_t conj(scalar_t x);
+template<> __device__ __forceinline__ float conj<float>(float x) { return x; }
+template<> __device__ __forceinline__ complex_t conj<complex_t>(complex_t x) { return std::conj(x); }
+
+template<int kNThreads_, int kNItems_, bool kIsEvenLen_, bool kIsVariableB_, bool kIsVariableC_,
+         bool kDeltaSoftplus_, bool kHasZ_, typename input_t_, typename weight_t_>
+struct Selective_Scan_bwd_kernel_traits {
+    static_assert(kNItems_ % 4 == 0);
+    using input_t = input_t_;
+    using weight_t = weight_t_;
+    static constexpr int kNThreads = kNThreads_;
+    static constexpr int kNItems = kNItems_;
+    static constexpr int kNBytes = sizeof(input_t);
+    static_assert(kNBytes == 2 || kNBytes == 4);
+    static constexpr int kNElts = kNBytes == 4 ? 4 : constexpr_min(8, kNItems);
+    static_assert(kNItems % kNElts == 0);
+    static constexpr int kNLoads = kNItems / kNElts;
+    static constexpr bool kIsComplex = std::is_same_v<weight_t, complex_t>;
+    static constexpr bool kIsEvenLen = kIsEvenLen_;
+    static constexpr bool kIsVariableB = kIsVariableB_;
+    static constexpr bool kIsVariableC = kIsVariableC_;
+    static constexpr bool kDeltaSoftplus = kDeltaSoftplus_;
+    static constexpr bool kHasZ = kHasZ_;
+    // Setting MinBlocksPerMP to be 3 (instead of 2) for 128 threads with float improves occupancy.
+    // For complex this would lead to massive register spilling, so we keep it at 2.
+    static constexpr int kMinBlocks = kNThreads == 128 && !kIsComplex ? 3 : 2;
+    using vec_t = typename BytesToType<kNBytes * kNElts>::Type;
+    using scan_t = std::conditional_t<!kIsComplex, float2, float4>;
+    using BlockLoadT = cub::BlockLoad<input_t, kNThreads, kNItems, cub::BLOCK_LOAD_WARP_TRANSPOSE>;
+    using BlockLoadVecT = cub::BlockLoad<vec_t, kNThreads, kNLoads, cub::BLOCK_LOAD_WARP_TRANSPOSE>;
+    using BlockLoadWeightT = cub::BlockLoad<input_t, kNThreads, !kIsComplex ? kNItems : kNItems * 2, cub::BLOCK_LOAD_WARP_TRANSPOSE>;
+    using BlockLoadWeightVecT = cub::BlockLoad<vec_t, kNThreads, !kIsComplex ? kNLoads : kNLoads * 2, cub::BLOCK_LOAD_WARP_TRANSPOSE>;
+    using BlockStoreT = cub::BlockStore<input_t, kNThreads, kNItems, cub::BLOCK_STORE_WARP_TRANSPOSE>;
+    using BlockStoreVecT = cub::BlockStore<vec_t, kNThreads, kNLoads, cub::BLOCK_STORE_WARP_TRANSPOSE>;
+    // using BlockScanT = cub::BlockScan<scan_t, kNThreads, cub::BLOCK_SCAN_RAKING_MEMOIZE>;
+    using BlockScanT = cub::BlockScan<scan_t, kNThreads, cub::BLOCK_SCAN_RAKING>;
+    // using BlockScanT = cub::BlockScan<scan_t, kNThreads, cub::BLOCK_SCAN_WARP_SCANS>;
+    using BlockReverseScanT = BlockReverseScan<scan_t, kNThreads>;
+    using BlockReduceT = cub::BlockReduce<scan_t, kNThreads>;
+    using BlockReduceFloatT = cub::BlockReduce<float, kNThreads>;
+    using BlockReduceComplexT = cub::BlockReduce<complex_t, kNThreads>;
+    using BlockExchangeT = cub::BlockExchange<float, kNThreads, !kIsComplex ? kNItems : kNItems * 2>;
+
+    static constexpr int kSmemIOSize = custom_max({sizeof(typename BlockLoadT::TempStorage),
+                                                    sizeof(typename BlockLoadVecT::TempStorage),
+                                                    (int(kIsVariableB) + int(kIsVariableC)) * sizeof(typename BlockLoadWeightT::TempStorage),
+                                                    (int(kIsVariableB) + int(kIsVariableC)) * sizeof(typename BlockLoadWeightVecT::TempStorage),
+                                                    sizeof(typename BlockStoreT::TempStorage),
+                                                    sizeof(typename BlockStoreVecT::TempStorage)});
+    static constexpr int kSmemExchangeSize = (int(kIsVariableB) + int(kIsVariableC)) * sizeof(typename BlockExchangeT::TempStorage);
+    static constexpr int kSmemReduceSize = sizeof(typename BlockReduceT::TempStorage);
+    static constexpr int kSmemSize = kSmemIOSize + kSmemExchangeSize + kSmemReduceSize + sizeof(typename BlockScanT::TempStorage) + sizeof(typename BlockReverseScanT::TempStorage);
+};
+
+template<typename Ktraits>
+__global__ __launch_bounds__(Ktraits::kNThreads, Ktraits::kMinBlocks)
+void selective_scan_bwd_kernel(SSMParamsBwd params) {
+    constexpr bool kIsComplex = Ktraits::kIsComplex;
+    constexpr bool kIsVariableB = Ktraits::kIsVariableB;
+    constexpr bool kIsVariableC = Ktraits::kIsVariableC;
+    constexpr bool kDeltaSoftplus = Ktraits::kDeltaSoftplus;
+    constexpr bool kHasZ = Ktraits::kHasZ;
+    constexpr int kNThreads = Ktraits::kNThreads;
+    constexpr int kNItems = Ktraits::kNItems;
+    using input_t = typename Ktraits::input_t;
+    using weight_t = typename Ktraits::weight_t;
+    using scan_t = typename Ktraits::scan_t;
+
+    // Shared memory.
+    extern __shared__ char smem_[];
+    // cast to lvalue reference of expected type
+    // char *smem_loadstorescan = smem_ + 2 * MAX_DSTATE * sizeof(weight_t);
+    // auto& smem_load = reinterpret_cast<typename BlockLoadT::TempStorage&>(smem_ + 2 * MAX_DSTATE * sizeof(weight_t));
+    // auto& smem_load = reinterpret_cast<typename BlockLoadT::TempStorage&>(smem_loadstorescan);
+    auto& smem_load = reinterpret_cast<typename Ktraits::BlockLoadT::TempStorage&>(smem_);
+    auto& smem_load_weight = reinterpret_cast<typename Ktraits::BlockLoadWeightT::TempStorage&>(smem_);
+    auto& smem_load_weight1 = *reinterpret_cast<typename Ktraits::BlockLoadWeightT::TempStorage*>(smem_ + sizeof(typename Ktraits::BlockLoadWeightT::TempStorage));
+    auto& smem_store = reinterpret_cast<typename Ktraits::BlockStoreT::TempStorage&>(smem_);
+    auto& smem_exchange = *reinterpret_cast<typename Ktraits::BlockExchangeT::TempStorage*>(smem_ + Ktraits::kSmemIOSize);
+    auto& smem_exchange1 = *reinterpret_cast<typename Ktraits::BlockExchangeT::TempStorage*>(smem_ + Ktraits::kSmemIOSize + sizeof(typename Ktraits::BlockExchangeT::TempStorage));
+    auto& smem_reduce = *reinterpret_cast<typename Ktraits::BlockReduceT::TempStorage*>(reinterpret_cast<char *>(&smem_exchange) + Ktraits::kSmemExchangeSize);
+    auto& smem_reduce_float = *reinterpret_cast<typename Ktraits::BlockReduceFloatT::TempStorage*>(&smem_reduce);
+    auto& smem_reduce_complex = *reinterpret_cast<typename Ktraits::BlockReduceComplexT::TempStorage*>(&smem_reduce);
+    auto& smem_scan = *reinterpret_cast<typename Ktraits::BlockScanT::TempStorage*>(reinterpret_cast<char *>(&smem_reduce) + Ktraits::kSmemReduceSize);
+    auto& smem_reverse_scan = *reinterpret_cast<typename Ktraits::BlockReverseScanT::TempStorage*>(reinterpret_cast<char *>(&smem_scan) + sizeof(typename Ktraits::BlockScanT::TempStorage));
+    weight_t *smem_delta_a = reinterpret_cast<weight_t *>(smem_ + Ktraits::kSmemSize);
+    scan_t *smem_running_postfix = reinterpret_cast<scan_t *>(smem_delta_a + 2 * MAX_DSTATE + kNThreads);
+    weight_t *smem_da = reinterpret_cast<weight_t *>(smem_running_postfix + MAX_DSTATE);
+    weight_t *smem_dbc = reinterpret_cast<weight_t *>(smem_da + MAX_DSTATE);
+
+    const int batch_id = blockIdx.x;
+    const int dim_id = blockIdx.y;
+    const int group_id = dim_id / (params.dim_ngroups_ratio);
+    input_t *u = reinterpret_cast<input_t *>(params.u_ptr) + batch_id * params.u_batch_stride
+        + dim_id * params.u_d_stride;
+    input_t *delta = reinterpret_cast<input_t *>(params.delta_ptr) + batch_id * params.delta_batch_stride
+        + dim_id * params.delta_d_stride;
+    input_t *dout = reinterpret_cast<input_t *>(params.dout_ptr) + batch_id * params.dout_batch_stride
+        + dim_id * params.dout_d_stride;
+    weight_t *A = reinterpret_cast<weight_t *>(params.A_ptr) + dim_id * params.A_d_stride;
+    weight_t *B = reinterpret_cast<weight_t *>(params.B_ptr) + dim_id * params.B_d_stride;
+    input_t *Bvar = reinterpret_cast<input_t *>(params.B_ptr) + batch_id * params.B_batch_stride + group_id * params.B_group_stride;
+    weight_t *C = reinterpret_cast<weight_t *>(params.C_ptr) + dim_id * params.C_d_stride;
+    input_t *Cvar = reinterpret_cast<input_t *>(params.C_ptr) + batch_id * params.C_batch_stride + group_id * params.C_group_stride;
+    weight_t *dA = reinterpret_cast<weight_t *>(params.dA_ptr) + dim_id * params.dA_d_stride;
+    weight_t *dB = reinterpret_cast<weight_t *>(params.dB_ptr)
+        + (!kIsVariableB ? dim_id * params.dB_d_stride : batch_id * (!kIsComplex ? params.dB_batch_stride : params.dB_batch_stride / 2) + group_id * params.dB_group_stride);
+    weight_t *dC = reinterpret_cast<weight_t *>(params.dC_ptr)
+        + (!kIsVariableC ? dim_id * params.dC_d_stride : batch_id * (!kIsComplex ? params.dC_batch_stride : params.dC_batch_stride / 2) + group_id * params.dC_group_stride);
+    float *dD = params.dD_ptr == nullptr ? nullptr : reinterpret_cast<float *>(params.dD_ptr) + dim_id;
+    float D_val = params.D_ptr == nullptr ? 0 : reinterpret_cast<float *>(params.D_ptr)[dim_id];
+    float *ddelta_bias = params.ddelta_bias_ptr == nullptr ? nullptr : reinterpret_cast<float *>(params.ddelta_bias_ptr) + dim_id;
+    float delta_bias = params.delta_bias_ptr == nullptr ? 0 : reinterpret_cast<float *>(params.delta_bias_ptr)[dim_id];
+    scan_t *x = params.x_ptr == nullptr
+        ? nullptr
+        : reinterpret_cast<scan_t *>(params.x_ptr) + (batch_id * params.dim + dim_id) * (params.n_chunks) * params.dstate;
+    float dD_val = 0;
+    float ddelta_bias_val = 0;
+
+    constexpr int kChunkSize = kNThreads * kNItems;
+    u += (params.n_chunks - 1) * kChunkSize;
+    delta += (params.n_chunks - 1) * kChunkSize;
+    dout += (params.n_chunks - 1) * kChunkSize;
+    Bvar += (params.n_chunks - 1) * kChunkSize * (!kIsComplex ? 1 : 2);
+    Cvar += (params.n_chunks - 1) * kChunkSize * (!kIsComplex ? 1 : 2);
+    for (int chunk = params.n_chunks - 1; chunk >= 0; --chunk) {
+        input_t u_vals[kNItems];
+        input_t delta_vals_load[kNItems];
+        input_t dout_vals_load[kNItems];
+        __syncthreads();
+        load_input<Ktraits>(u, u_vals, smem_load, params.seqlen - chunk * kChunkSize);
+        u -= kChunkSize;
+        __syncthreads();
+        load_input<Ktraits>(delta, delta_vals_load, smem_load, params.seqlen - chunk * kChunkSize);
+        // Will reload delta at the same location if kDeltaSoftplus
+        if constexpr (!kDeltaSoftplus) { delta -= kChunkSize; }
+        __syncthreads();
+        load_input<Ktraits>(dout, dout_vals_load, smem_load, params.seqlen - chunk * kChunkSize);
+        dout -= kChunkSize;
+
+        float dout_vals[kNItems], delta_vals[kNItems];
+        #pragma unroll
+        for (int i = 0; i < kNItems; ++i) {
+            dout_vals[i] = float(dout_vals_load[i]);
+            delta_vals[i] = float(delta_vals_load[i]) + delta_bias;
+            if constexpr (kDeltaSoftplus) {
+                delta_vals[i] = delta_vals[i] <= 20.f ? log1pf(expf(delta_vals[i])) : delta_vals[i];
+            }
+        }
+
+        if constexpr (kHasZ) {
+            input_t *z = reinterpret_cast<input_t *>(params.z_ptr) + batch_id * params.z_batch_stride
+                + dim_id * params.z_d_stride + chunk * kChunkSize;
+            input_t *out = reinterpret_cast<input_t *>(params.out_ptr) + batch_id * params.out_batch_stride
+                + dim_id * params.out_d_stride + chunk * kChunkSize;
+            input_t *dz = reinterpret_cast<input_t *>(params.dz_ptr) + batch_id * params.dz_batch_stride
+                + dim_id * params.dz_d_stride + chunk * kChunkSize;
+            input_t z_vals[kNItems], out_vals[kNItems];
+            __syncthreads();
+            load_input<Ktraits>(z, z_vals, smem_load, params.seqlen - chunk * kChunkSize);
+            __syncthreads();
+            load_input<Ktraits>(out, out_vals, smem_load, params.seqlen - chunk * kChunkSize);
+            float dz_vals[kNItems], z_silu_vals[kNItems];
+            #pragma unroll
+            for (int i = 0; i < kNItems; ++i) {
+                float z_val = z_vals[i];
+                float z_sigmoid_val = 1.0f / (1.0f + expf(-z_val));
+                z_silu_vals[i] = z_val * z_sigmoid_val;
+                dz_vals[i] = dout_vals[i] * float(out_vals[i]) * z_sigmoid_val
+                             * (1.0f + z_val * (1.0f - z_sigmoid_val));
+                dout_vals[i] *= z_silu_vals[i];
+            }
+            __syncthreads();
+            store_output<Ktraits>(dz, dz_vals, smem_store, params.seqlen - chunk * kChunkSize);
+            if (params.out_z_ptr != nullptr) {  // Recompute and store out_z
+                float out_z_vals[kNItems];
+                #pragma unroll
+                for (int i = 0; i < kNItems; ++i) { out_z_vals[i] = float(out_vals[i]) * z_silu_vals[i]; }
+                // if (blockIdx.x == 0 && blockIdx.y == 0 && threadIdx.x == 0) {
+                    // printf("out_val=%f, z_silu_val = %f, out_z_val = %f\n", float(out_vals[0]), z_silu_vals[0], out_z_vals[0]);
+                // }
+                input_t *out_z = reinterpret_cast<input_t *>(params.out_z_ptr) + batch_id * params.out_z_batch_stride
+                    + dim_id * params.out_z_d_stride + chunk * kChunkSize;
+                __syncthreads();
+                store_output<Ktraits>(out_z, out_z_vals, smem_store, params.seqlen - chunk * kChunkSize);
+            }
+        }
+
+        float du_vals[kNItems];
+        #pragma unroll
+        for (int i = 0; i < kNItems; ++i) { du_vals[i] = D_val * dout_vals[i]; }
+        #pragma unroll
+        for (int i = 0; i < kNItems; ++i) { dD_val += dout_vals[i] * float(u_vals[i]); }
+
+        float ddelta_vals[kNItems] = {0};
+        __syncthreads();
+        for (int state_idx = 0; state_idx < params.dstate; ++state_idx) {
+            const weight_t A_val = A[state_idx * params.A_dstate_stride];
+            // Multiply the real part of A with LOG2E so we can use exp2f instead of expf.
+            weight_t A_scaled;
+            constexpr float kLog2e = M_LOG2E;
+            if constexpr (!kIsComplex) {
+                A_scaled = A_val * kLog2e;
+            } else {
+                A_scaled = complex_t(A_val.real_ * kLog2e, A_val.imag_);
+            }
+            weight_t B_val, C_val;
+            weight_t B_vals[kNItems], C_vals[kNItems];
+            if constexpr (!kIsVariableB) {
+                B_val = B[state_idx * params.B_dstate_stride];
+            } else {
+                load_weight<Ktraits>(Bvar + state_idx * params.B_dstate_stride, B_vals,
+                    smem_load_weight, (params.seqlen - chunk * kChunkSize) * (!kIsComplex ? 1 : 2));
+            }
+            if constexpr (!kIsVariableC) {
+                C_val = C[state_idx * params.C_dstate_stride];
+            } else {
+                auto &smem_load_weight_C = !kIsVariableB ? smem_load_weight : smem_load_weight1;
+                load_weight<Ktraits>(Cvar + state_idx * params.C_dstate_stride, C_vals,
+                    smem_load_weight_C, (params.seqlen - chunk * kChunkSize) * (!kIsComplex ? 1 : 2));
+            }
+            // const weight_t A_val = smem_a[state_idx];
+            scan_t thread_data[kNItems], thread_reverse_data[kNItems];
+            if constexpr (!kIsComplex) {
+                #pragma unroll
+                for (int i = 0; i < kNItems; ++i) {
+                    const float delta_a_exp = exp2f(delta_vals[i] * A_scaled);
+                    thread_data[i] = make_float2(delta_a_exp, !kIsVariableB ? delta_vals[i] * float(u_vals[i]) : delta_vals[i] * float(u_vals[i]) * B_vals[i]);
+                    if (i == 0) {
+                        smem_delta_a[threadIdx.x == 0 ? state_idx + (chunk % 2) * MAX_DSTATE : threadIdx.x + 2 * MAX_DSTATE] = delta_a_exp;
+                    } else {
+                        thread_reverse_data[i - 1].x = delta_a_exp;
+                    }
+                    thread_reverse_data[i].y = dout_vals[i] *
+                        (!kIsVariableC
+                         ? (!kIsVariableB ? B_val * C_val : C_val)
+                         : (!kIsVariableB ? B_val * C_vals[i] : C_vals[i]));
+                }
+                __syncthreads();
+                thread_reverse_data[kNItems - 1].x = threadIdx.x == kNThreads - 1
+                    ? (chunk == params.n_chunks - 1 ? 1.f : smem_delta_a[state_idx + ((chunk + 1) % 2) * MAX_DSTATE])
+                    : smem_delta_a[threadIdx.x + 1 + 2 * MAX_DSTATE];
+                // Initialize running total
+                scan_t running_prefix = chunk > 0 && threadIdx.x % 32 == 0 ? x[(chunk - 1) * params.dstate + state_idx] : make_float2(1.f, 0.f);
+                SSMScanPrefixCallbackOp<weight_t> prefix_op(running_prefix);
+                typename Ktraits::BlockScanT(smem_scan).InclusiveScan(
+                    thread_data, thread_data, SSMScanOp<weight_t>(), prefix_op
+                );
+                scan_t running_postfix = chunk < params.n_chunks - 1 && threadIdx.x % 32 == 0 ? smem_running_postfix[state_idx] : make_float2(1.f, 0.f);
+                SSMScanPrefixCallbackOp<weight_t> postfix_op(running_postfix);
+                typename Ktraits::BlockReverseScanT(smem_reverse_scan).InclusiveReverseScan(
+                    thread_reverse_data, thread_reverse_data, SSMScanOp<weight_t>(), postfix_op
+                );
+                if (threadIdx.x == 0) { smem_running_postfix[state_idx] = postfix_op.running_prefix; }
+                weight_t dA_val = 0, dBC_val = 0;
+                weight_t dB_vals[kNItems], dC_vals[kNItems];
+                #pragma unroll
+                for (int i = 0; i < kNItems; ++i) {
+                    const float dx = thread_reverse_data[i].y;
+                    const float ddelta_u = !kIsVariableB ? dx : dx * B_vals[i];
+                    du_vals[i] += ddelta_u * delta_vals[i];
+                    const float a = thread_data[i].y - (!kIsVariableB ? delta_vals[i] * float(u_vals[i]) : delta_vals[i] * float(u_vals[i]) * B_vals[i]);
+                    ddelta_vals[i] += ddelta_u * float(u_vals[i]) + dx * A_val * a;
+                    dA_val += dx * delta_vals[i] * a;
+                    if constexpr (!kIsVariableB || !kIsVariableC) {
+                        if constexpr (!kIsVariableB) {  // dBC_val is dB_val
+                            dBC_val += dout_vals[i] * (!kIsVariableC ? thread_data[i].y : thread_data[i].y * C_vals[i]);
+                        } else {  // dBC_val is dC_val
+                            dBC_val += dout_vals[i] * thread_data[i].y;
+                        }
+                    }
+                    if constexpr (kIsVariableB) { dB_vals[i] = dx * delta_vals[i] * float(u_vals[i]); }
+                    if constexpr (kIsVariableC) {
+                        dC_vals[i] = dout_vals[i] * (!kIsVariableB ? thread_data[i].y * B_val : thread_data[i].y);
+                    }
+                }
+                // Block-exchange to make the atomicAdd's coalesced, otherwise they're much slower
+                if constexpr (kIsVariableB || kIsVariableC) {
+                    if constexpr (kIsVariableB) {
+                        typename Ktraits::BlockExchangeT(smem_exchange).BlockedToStriped(dB_vals, dB_vals);
+                    }
+                    if constexpr (kIsVariableC) {
+                        auto &smem_exchange_C = !kIsVariableB ? smem_exchange : smem_exchange1;
+                        typename Ktraits::BlockExchangeT(smem_exchange_C).BlockedToStriped(dC_vals, dC_vals);
+                    }
+                    const int seqlen_remaining = params.seqlen - chunk * kChunkSize - threadIdx.x;
+                    weight_t *dB_cur = dB + state_idx * params.dB_dstate_stride + chunk * kChunkSize + threadIdx.x;
+                    weight_t *dC_cur = dC + state_idx * params.dC_dstate_stride + chunk * kChunkSize + threadIdx.x;
+                    #pragma unroll
+                    for (int i = 0; i < kNItems; ++i) {
+                        if (i * kNThreads < seqlen_remaining) {
+                            if constexpr (kIsVariableB) { gpuAtomicAdd(dB_cur + i * kNThreads, dB_vals[i]); }
+                            if constexpr (kIsVariableC) { gpuAtomicAdd(dC_cur + i * kNThreads, dC_vals[i]); }
+                        }
+                    }
+                }
+                if constexpr (!kIsVariableB || !kIsVariableC) {
+                    float2 dA_dBC_val = make_float2(dA_val, dBC_val);
+                    dA_dBC_val = typename Ktraits::BlockReduceT(smem_reduce).Sum(dA_dBC_val);
+                    dA_val = dA_dBC_val.x;
+                    if (threadIdx.x == 0) {
+                        smem_dbc[state_idx] = chunk == params.n_chunks - 1 ? dA_dBC_val.y : dA_dBC_val.y + smem_dbc[state_idx];
+                    }
+                } else {
+                    dA_val = typename Ktraits::BlockReduceFloatT(smem_reduce_float).Sum(dA_val);
+                }
+                if (threadIdx.x == 0) {
+                    smem_da[state_idx] = chunk == params.n_chunks - 1 ? dA_val : dA_val + smem_da[state_idx];
+                }
+            } else {
+                #pragma unroll
+                for (int i = 0; i < kNItems; ++i) {
+                    // Pytorch's implementation of complex exp (which calls thrust) is very slow
+                    complex_t delta_a_exp = cexp2f(delta_vals[i] * A_scaled);
+                    weight_t B_delta_u_val = !kIsVariableB ? delta_vals[i] * float(u_vals[i]) : B_vals[i] * delta_vals[i] * float(u_vals[i]);
+                    thread_data[i] = make_float4(delta_a_exp.real_, delta_a_exp.imag_, B_delta_u_val.real_, B_delta_u_val.imag_);
+                    if (i == 0) {
+                        smem_delta_a[threadIdx.x == 0 ? state_idx + (chunk % 2) * MAX_DSTATE : threadIdx.x + 2 * MAX_DSTATE] = delta_a_exp;
+                    } else {
+                        thread_reverse_data[i - 1].x = delta_a_exp.real_;
+                        thread_reverse_data[i - 1].y = -delta_a_exp.imag_;
+                    }
+                    complex_t dout_BC = 2 * dout_vals[i]
+                        * conj(!kIsVariableC
+                                ? (!kIsVariableB ? B_val * C_val : C_val)
+                                : (!kIsVariableB ? B_val * C_vals[i] : C_vals[i]));
+                    thread_reverse_data[i].z = dout_BC.real_;
+                    thread_reverse_data[i].w = dout_BC.imag_;
+                }
+                __syncthreads();
+                complex_t delta_a_exp = threadIdx.x == kNThreads - 1
+                    ? (chunk == params.n_chunks - 1 ? 1.f : smem_delta_a[state_idx + ((chunk + 1) % 2) * MAX_DSTATE])
+                    : smem_delta_a[threadIdx.x + 1 + 2 * MAX_DSTATE];
+                thread_reverse_data[kNItems - 1].x = delta_a_exp.real_;
+                thread_reverse_data[kNItems - 1].y = -delta_a_exp.imag_;
+                // Initialize running total
+                scan_t running_prefix = chunk > 0 && threadIdx.x % 32 == 0 ? x[(chunk - 1) * params.dstate + state_idx] : make_float4(1.f, 0.f, 0.f, 0.f);
+                SSMScanPrefixCallbackOp<weight_t> prefix_op(running_prefix);
+                typename Ktraits::BlockScanT(smem_scan).InclusiveScan(
+                    thread_data, thread_data, SSMScanOp<weight_t>(), prefix_op
+                );
+                scan_t running_postfix = chunk < params.n_chunks - 1 && threadIdx.x % 32 == 0 ? smem_running_postfix[state_idx] : make_float4(1.f, 0.f, 0.f, 0.f);
+                SSMScanPrefixCallbackOp<weight_t> postfix_op(running_postfix);
+                typename Ktraits::BlockReverseScanT(smem_reverse_scan).InclusiveReverseScan(
+                    thread_reverse_data, thread_reverse_data, SSMScanOp<weight_t>(), postfix_op
+                );
+                if (threadIdx.x == 0) { smem_running_postfix[state_idx] = postfix_op.running_prefix; }
+                weight_t dA_val = 0, dBC_val = 0;
+                weight_t dB_vals[kNItems], dC_vals[kNItems];
+                #pragma unroll
+                for (int i = 0; i < kNItems; ++i) {
+                    complex_t x = complex_t(thread_data[i].z, thread_data[i].w);
+                    complex_t dx = complex_t(thread_reverse_data[i].z, thread_reverse_data[i].w);
+                    float ddelta_u = !kIsVariableB ? dx.real_ : (dx * conj(B_vals[i])).real_;
+                    if constexpr (!kIsVariableB || !kIsVariableC) {
+                        if constexpr (!kIsVariableB) {  // dBC_val is dB_val
+                            dBC_val += (2 * dout_vals[i]) * conj(!kIsVariableC ? x : x * C_vals[i]);
+                        } else {  // dBC_val is dC_val
+                            dBC_val += (2 * dout_vals[i]) * conj(x);
+                        }
+                    }
+                    const complex_t a_conj = conj(x - (!kIsVariableB ? delta_vals[i] * float(u_vals[i]) : delta_vals[i] * float(u_vals[i]) * B_vals[i]));
+                    du_vals[i] += ddelta_u * delta_vals[i];
+                    ddelta_vals[i] += ddelta_u * float(u_vals[i]) + (dx * conj(A_val) * a_conj).real_;
+                    dA_val += delta_vals[i] * dx * a_conj;
+                    if constexpr (kIsVariableB) { dB_vals[i] = dx * delta_vals[i] * float(u_vals[i]); }
+                    if constexpr (kIsVariableC) {
+                        dC_vals[i] = (2 * dout_vals[i]) * conj(!kIsVariableB ? x * B_val : x);
+                    }
+                }
+                // Block-exchange to make the atomicAdd's coalesced, otherwise they're much slower
+                if constexpr (kIsVariableB || kIsVariableC) {
+                    float dB_vals_f[kNItems * 2], dC_vals_f[kNItems * 2];
+                    if constexpr (kIsVariableB) {
+                        #pragma unroll
+                        for (int i = 0; i < kNItems; ++i) {
+                            dB_vals_f[i * 2] = dB_vals[i].real_;
+                            dB_vals_f[i * 2 + 1] = dB_vals[i].imag_;
+                        }
+                        typename Ktraits::BlockExchangeT(smem_exchange).BlockedToStriped(dB_vals_f, dB_vals_f);
+                    }
+                    if constexpr (kIsVariableC) {
+                        #pragma unroll
+                        for (int i = 0; i < kNItems; ++i) {
+                            dC_vals_f[i * 2] = dC_vals[i].real_;
+                            dC_vals_f[i * 2 + 1] = dC_vals[i].imag_;
+                        }
+                        auto &smem_exchange_C = !kIsVariableB ? smem_exchange : smem_exchange1;
+                        typename Ktraits::BlockExchangeT(smem_exchange_C).BlockedToStriped(dC_vals_f, dC_vals_f);
+                    }
+                    const int seqlen_remaining = (params.seqlen - chunk * kChunkSize) * 2 - threadIdx.x;
+                    float *dB_cur = reinterpret_cast<float *>(dB) + state_idx * params.dB_dstate_stride + chunk * kChunkSize * 2 + threadIdx.x;
+                    float *dC_cur = reinterpret_cast<float *>(dC) + state_idx * params.dC_dstate_stride + chunk * kChunkSize * 2 + threadIdx.x;
+                    #pragma unroll
+                    for (int i = 0; i < kNItems * 2; ++i) {
+                        if (i * kNThreads < seqlen_remaining) {
+                            if constexpr (kIsVariableB) { gpuAtomicAdd(dB_cur + i * kNThreads, dB_vals_f[i]); }
+                            if constexpr (kIsVariableC) { gpuAtomicAdd(dC_cur + i * kNThreads, dC_vals_f[i]); }
+                        }
+                    }
+                }
+                if constexpr (!kIsVariableB || !kIsVariableC) {
+                    float4 dA_dBC_val = make_float4(dA_val.real_, dA_val.imag_, dBC_val.real_, dBC_val.imag_);
+                    dA_dBC_val = typename Ktraits::BlockReduceT(smem_reduce).Sum(dA_dBC_val);
+                    dA_val = complex_t(dA_dBC_val.x, dA_dBC_val.y);
+                    dBC_val = complex_t(dA_dBC_val.z, dA_dBC_val.w);
+                    if (threadIdx.x == 0) {
+                        smem_dbc[state_idx] = chunk == params.n_chunks - 1 ? dBC_val : dBC_val + smem_dbc[state_idx];
+                    }
+                } else {
+                    dA_val = typename Ktraits::BlockReduceComplexT(smem_reduce_complex).Sum(dA_val);
+                }
+                if (threadIdx.x == 0) {
+                    smem_da[state_idx] = chunk == params.n_chunks - 1 ? dA_val : dA_val + smem_da[state_idx];
+                }
+            }
+        }
+
+        if constexpr (kDeltaSoftplus) {
+            __syncthreads();
+            input_t delta_vals_load[kNItems];
+            load_input<Ktraits>(delta, delta_vals_load, smem_load, params.seqlen - chunk * kChunkSize);
+            delta -= kChunkSize;
+            #pragma unroll
+            for (int i = 0; i < kNItems; ++i) {
+                float delta_val = float(delta_vals_load[i]) + delta_bias;
+                float delta_val_neg_exp = expf(-delta_val);
+                ddelta_vals[i] = delta_val <= 20.f
+                    ? ddelta_vals[i] / (1.f + delta_val_neg_exp)
+                    : ddelta_vals[i];
+            }
+        }
+        for (int i = 0; i < kNItems; ++i) { ddelta_bias_val += ddelta_vals[i]; }
+
+        input_t *du = reinterpret_cast<input_t *>(params.du_ptr) + batch_id * params.du_batch_stride
+            + dim_id * params.du_d_stride + chunk * kChunkSize;
+        input_t *ddelta = reinterpret_cast<input_t *>(params.ddelta_ptr) + batch_id * params.ddelta_batch_stride
+            + dim_id * params.ddelta_d_stride + chunk * kChunkSize;
+        __syncthreads();
+        store_output<Ktraits>(du, du_vals, smem_store, params.seqlen - chunk * kChunkSize);
+        __syncthreads();
+        store_output<Ktraits>(ddelta, ddelta_vals, smem_store, params.seqlen - chunk * kChunkSize);
+
+        Bvar -= kChunkSize * (!kIsComplex ? 1 : 2);
+        Cvar -= kChunkSize * (!kIsComplex ? 1 : 2);
+    }
+    if (params.dD_ptr != nullptr) {
+        dD_val = typename Ktraits::BlockReduceFloatT(smem_reduce_float).Sum(dD_val);
+        if (threadIdx.x == 0) { gpuAtomicAdd(dD, dD_val); }
+    }
+    if (params.ddelta_bias_ptr != nullptr) {
+        __syncthreads();
+        ddelta_bias_val = typename Ktraits::BlockReduceFloatT(smem_reduce_float).Sum(ddelta_bias_val);
+        if (threadIdx.x == 0) { gpuAtomicAdd(ddelta_bias, ddelta_bias_val); }
+    }
+    for (int state_idx = threadIdx.x; state_idx < params.dstate; state_idx += blockDim.x) {
+        gpuAtomicAdd(&(dA[state_idx * params.dA_dstate_stride]), smem_da[state_idx]);
+        weight_t dBC_val;
+        if (!kIsVariableB || !kIsVariableC) { dBC_val = smem_dbc[state_idx]; }
+        if constexpr (!kIsVariableB) {
+            gpuAtomicAdd(&(dB[state_idx * params.dB_dstate_stride]),
+                         !kIsVariableC ? dBC_val * conj(C[state_idx * params.C_dstate_stride]) : dBC_val);
+        }
+        if constexpr (!kIsVariableC) {
+            gpuAtomicAdd(&(dC[state_idx * params.dC_dstate_stride]),
+                        !kIsVariableB ? dBC_val * conj(B[state_idx * params.B_dstate_stride]) : dBC_val);
+        }
+    }
+}
+
+template<int kNThreads, int kNItems, typename input_t, typename weight_t>
+void selective_scan_bwd_launch(SSMParamsBwd &params, cudaStream_t stream) {
+    BOOL_SWITCH(params.seqlen % (kNThreads * kNItems) == 0, kIsEvenLen, [&] {
+        BOOL_SWITCH(params.is_variable_B, kIsVariableB, [&] {
+            BOOL_SWITCH(params.is_variable_C, kIsVariableC, [&] {
+                BOOL_SWITCH(params.delta_softplus, kDeltaSoftplus, [&] {
+                    BOOL_SWITCH(params.z_ptr != nullptr , kHasZ, [&] {
+                        using Ktraits = Selective_Scan_bwd_kernel_traits<kNThreads, kNItems, kIsEvenLen, kIsVariableB, kIsVariableC, kDeltaSoftplus, kHasZ, input_t, weight_t>;
+                        // using Ktraits = Selective_Scan_bwd_kernel_traits<kNThreads, kNItems, true, kIsVariableB, kIsVariableC, kDeltaSoftplus, kHasZ, input_t, weight_t>;
+                        // TODO: check this
+                        constexpr int kSmemSize = Ktraits::kSmemSize + MAX_DSTATE * sizeof(typename Ktraits::scan_t) + (kNThreads + 4 * MAX_DSTATE) * sizeof(typename Ktraits::weight_t);
+
+                        dim3 grid(params.batch, params.dim);
+                        
+                        auto kernel = &selective_scan_bwd_kernel<Ktraits>;
+
+                        if (kSmemSize >= 48 * 1024) {
+
+                            #ifndef USE_ROCM
+                            C10_CUDA_CHECK(cudaFuncSetAttribute(
+                                kernel, cudaFuncAttributeMaxDynamicSharedMemorySize, kSmemSize));
+                            #else
+                            C10_CUDA_CHECK(cudaFuncSetAttribute(
+                                (void *) kernel, cudaFuncAttributeMaxDynamicSharedMemorySize, kSmemSize));
+                            std::cerr << "Warning (selective_scan_bwd_kernel): attempting to set maxDynamicSharedMemorySize on an AMD GPU which is currently a non-op (in ROCm versions <= 6.1). This might lead to undefined behavior. \n" << std::endl;
+                            #endif
+
+                        }
+
+                        kernel<<<grid, Ktraits::kNThreads, kSmemSize, stream>>>(params);
+                        C10_CUDA_KERNEL_LAUNCH_CHECK();
+                    });
+                });
+            });
+        });
+    });
+}
+
+template<typename input_t, typename weight_t>
+void selective_scan_bwd_cuda(SSMParamsBwd &params, cudaStream_t stream) {
+
+    #ifndef USE_ROCM
+        if (params.seqlen <= 128) {
+            selective_scan_bwd_launch<32, 4, input_t, weight_t>(params, stream);
+        } else if (params.seqlen <= 256) {
+            selective_scan_bwd_launch<32, 8, input_t, weight_t>(params, stream);
+        } else if (params.seqlen <= 512) {
+            selective_scan_bwd_launch<32, 16, input_t, weight_t>(params, stream);
+        } else if (params.seqlen <= 1024) {
+            selective_scan_bwd_launch<64, 16, input_t, weight_t>(params, stream);
+        } else {
+            selective_scan_bwd_launch<128, 16, input_t, weight_t>(params, stream);
+        }
+    #else 
+        if (params.seqlen <= 256) {
+            selective_scan_bwd_launch<64, 4, input_t, weight_t>(params, stream);
+        } else if (params.seqlen <= 512) {
+            selective_scan_bwd_launch<64, 8, input_t, weight_t>(params, stream);
+        } else if (params.seqlen <= 1024) {
+            selective_scan_bwd_launch<64, 16, input_t, weight_t>(params, stream);
+        } else {
+            selective_scan_bwd_launch<128, 16, input_t, weight_t>(params, stream);
+        }
+    #endif
+}

selective-scan/selective_scan_common.h

@@ -0,0 +1,255 @@
+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+#pragma once
+
+#ifndef USE_ROCM
+    #include <cuda_bf16.h>
+#else
+    #include <hip/hip_bf16.h>
+#endif
+#include <cuda_fp16.h>
+#include <c10/util/complex.h>  // For scalar_value_type
+
+
+#ifndef USE_ROCM
+
+    constexpr size_t custom_max(std::initializer_list<size_t> ilist) 
+    {
+        return std::max(ilist);
+    }
+
+    template<typename T>
+    constexpr T constexpr_min(T a, T b) {
+        return std::min(a, b);
+    }
+
+#else
+    constexpr size_t custom_max(std::initializer_list<size_t> ilist) 
+    {
+        return *std::max_element(ilist.begin(), ilist.end());
+    }
+
+    template<typename T>
+    constexpr T constexpr_min(T a, T b) {
+        return a < b ? a : b;
+    }
+#endif
+
+
+#define MAX_DSTATE 256
+
+using complex_t = c10::complex<float>;
+
+inline __device__ float2 operator+(const float2 & a, const float2 & b){
+    return {a.x + b.x, a.y + b.y};
+}
+
+inline __device__ float3 operator+(const float3 &a, const float3 &b) {
+  return {a.x + b.x, a.y + b.y, a.z + b.z};
+}
+
+inline __device__ float4 operator+(const float4 & a, const float4 & b){
+    return {a.x + b.x, a.y + b.y, a.z + b.z, a.w + b.w};
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+template<int BYTES> struct BytesToType {};
+
+template<> struct BytesToType<16> {
+    using Type = uint4;
+    static_assert(sizeof(Type) == 16);
+};
+
+template<> struct BytesToType<8> {
+    using Type = uint64_t;
+    static_assert(sizeof(Type) == 8);
+};
+
+template<> struct BytesToType<4> {
+    using Type = uint32_t;
+    static_assert(sizeof(Type) == 4);
+};
+
+template<> struct BytesToType<2> {
+    using Type = uint16_t;
+    static_assert(sizeof(Type) == 2);
+};
+
+template<> struct BytesToType<1> {
+    using Type = uint8_t;
+    static_assert(sizeof(Type) == 1);
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+template<typename scalar_t, int N>
+struct Converter{
+    static inline __device__ void to_float(const scalar_t (&src)[N], float (&dst)[N]) {
+        #pragma unroll
+        for (int i = 0; i < N; ++i) { dst[i] = src[i]; }
+    }
+};
+
+template<int N>
+struct Converter<at::Half, N>{
+    static inline __device__ void to_float(const at::Half (&src)[N], float (&dst)[N]) {
+        static_assert(N % 2 == 0);
+        auto &src2 = reinterpret_cast<const half2 (&)[N / 2]>(src);
+        auto &dst2 = reinterpret_cast<float2 (&)[N / 2]>(dst);
+        #pragma unroll
+        for (int i = 0; i < N / 2; ++i) { dst2[i] = __half22float2(src2[i]); }
+    }
+};
+
+#if __CUDA_ARCH__ >= 800
+template<int N>
+struct Converter<at::BFloat16, N>{
+    static inline __device__ void to_float(const at::BFloat16 (&src)[N], float (&dst)[N]) {
+        static_assert(N % 2 == 0);
+        auto &src2 = reinterpret_cast<const nv_bfloat162 (&)[N / 2]>(src);
+        auto &dst2 = reinterpret_cast<float2 (&)[N / 2]>(dst);
+        #pragma unroll
+        for (int i = 0; i < N / 2; ++i) { dst2[i] = __bfloat1622float2(src2[i]); }
+    }
+};
+#endif
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+// From https://stackoverflow.com/questions/9860711/cucomplex-h-and-exp
+// and https://forums.developer.nvidia.com/t/complex-number-exponential-function/24696
+__device__ __forceinline__ complex_t cexp2f(complex_t z) {
+    float t = exp2f(z.real_);
+    float c, s;
+    sincosf(z.imag_, &s, &c);
+    return complex_t(c * t, s * t);
+}
+
+__device__ __forceinline__ complex_t cexpf(complex_t z) {
+    float t = expf(z.real_);
+    float c, s;
+    sincosf(z.imag_, &s, &c);
+    return complex_t(c * t, s * t);
+}
+
+template<typename scalar_t> struct SSMScanOp;
+
+template<>
+struct SSMScanOp<float> {
+    __device__ __forceinline__ float2 operator()(const float2 &ab0, const float2 &ab1) const {
+        return make_float2(ab1.x * ab0.x, ab1.x * ab0.y + ab1.y);
+    }
+};
+
+template<>
+struct SSMScanOp<complex_t> {
+    __device__ __forceinline__ float4 operator()(const float4 &ab0, const float4 &ab1) const {
+        complex_t a0 = complex_t(ab0.x, ab0.y);
+        complex_t b0 = complex_t(ab0.z, ab0.w);
+        complex_t a1 = complex_t(ab1.x, ab1.y);
+        complex_t b1 = complex_t(ab1.z, ab1.w);
+        complex_t out_a = a1 * a0;
+        complex_t out_b = a1 * b0 + b1;
+        return make_float4(out_a.real_, out_a.imag_, out_b.real_, out_b.imag_);
+    }
+};
+
+// A stateful callback functor that maintains a running prefix to be applied
+// during consecutive scan operations.
+template <typename scalar_t> struct SSMScanPrefixCallbackOp {
+    using scan_t = std::conditional_t<std::is_same_v<scalar_t, float>, float2, float4>;
+    scan_t running_prefix;
+    // Constructor
+    __device__ SSMScanPrefixCallbackOp(scan_t running_prefix_) : running_prefix(running_prefix_) {}
+    // Callback operator to be entered by the first warp of threads in the block.
+    // Thread-0 is responsible for returning a value for seeding the block-wide scan.
+    __device__ scan_t operator()(scan_t block_aggregate) {
+        scan_t old_prefix = running_prefix;
+        running_prefix = SSMScanOp<scalar_t>()(running_prefix, block_aggregate);
+        return old_prefix;
+    }
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+template<typename Ktraits>
+inline __device__ void load_input(typename Ktraits::input_t *u,
+                                  typename Ktraits::input_t (&u_vals)[Ktraits::kNItems],
+                                  typename Ktraits::BlockLoadT::TempStorage &smem_load,
+                                  int seqlen) {
+    if constexpr (Ktraits::kIsEvenLen) {
+        auto& smem_load_vec = reinterpret_cast<typename Ktraits::BlockLoadVecT::TempStorage&>(smem_load);
+        using vec_t = typename Ktraits::vec_t;
+        typename Ktraits::BlockLoadVecT(smem_load_vec).Load(
+            reinterpret_cast<vec_t*>(u),
+            reinterpret_cast<vec_t(&)[Ktraits::kNLoads]>(u_vals)
+            #ifdef USE_ROCM
+                , Ktraits::kNThreads * Ktraits::kNLoads
+            #endif
+            
+       );
+    } else {
+        typename Ktraits::BlockLoadT(smem_load).Load(u, u_vals, seqlen, 0.f);
+    }
+}
+
+template<typename Ktraits>
+inline __device__ void load_weight(typename Ktraits::input_t *Bvar,
+                                   typename Ktraits::weight_t (&B_vals)[Ktraits::kNItems],
+                                   typename Ktraits::BlockLoadWeightT::TempStorage &smem_load_weight,
+                                   int seqlen) {
+    constexpr int kNItems = Ktraits::kNItems;
+    if constexpr (!Ktraits::kIsComplex) {
+        typename Ktraits::input_t B_vals_load[kNItems];
+        if constexpr (Ktraits::kIsEvenLen) {
+            auto& smem_load_weight_vec = reinterpret_cast<typename Ktraits::BlockLoadWeightVecT::TempStorage&>(smem_load_weight);
+            using vec_t = typename Ktraits::vec_t;
+            typename Ktraits::BlockLoadWeightVecT(smem_load_weight_vec).Load(
+                reinterpret_cast<vec_t*>(Bvar),
+                reinterpret_cast<vec_t(&)[Ktraits::kNLoads]>(B_vals_load)
+          );
+        } else {
+            typename Ktraits::BlockLoadWeightT(smem_load_weight).Load(Bvar, B_vals_load, seqlen, 0.f);
+        }
+        // #pragma unroll
+        // for (int i = 0; i < kNItems; ++i) { B_vals[i] = B_vals_load[i]; }
+        Converter<typename Ktraits::input_t, kNItems>::to_float(B_vals_load, B_vals);
+    } else {
+        typename Ktraits::input_t B_vals_load[kNItems * 2];
+        if constexpr (Ktraits::kIsEvenLen) {
+            auto& smem_load_weight_vec = reinterpret_cast<typename Ktraits::BlockLoadWeightVecT::TempStorage&>(smem_load_weight);
+            using vec_t = typename Ktraits::vec_t;
+            typename Ktraits::BlockLoadWeightVecT(smem_load_weight_vec).Load(
+                reinterpret_cast<vec_t*>(Bvar),
+                reinterpret_cast<vec_t(&)[Ktraits::kNLoads * 2]>(B_vals_load)
+          );
+        } else {
+            typename Ktraits::BlockLoadWeightT(smem_load_weight).Load(Bvar, B_vals_load, seqlen, 0.f);
+        }
+        #pragma unroll
+        for (int i = 0; i < kNItems; ++i) { B_vals[i] = complex_t(B_vals_load[i * 2], B_vals_load[i * 2 + 1]); }
+    }
+}
+
+template<typename Ktraits>
+inline __device__ void store_output(typename Ktraits::input_t *out,
+                                    const float (&out_vals)[Ktraits::kNItems],
+                                    typename Ktraits::BlockStoreT::TempStorage &smem_store,
+                                    int seqlen) {
+    typename Ktraits::input_t write_vals[Ktraits::kNItems];
+    #pragma unroll
+    for (int i = 0; i < Ktraits::kNItems; ++i) { write_vals[i] = out_vals[i]; }
+    if constexpr (Ktraits::kIsEvenLen) {
+        auto& smem_store_vec = reinterpret_cast<typename Ktraits::BlockStoreVecT::TempStorage&>(smem_store);
+        using vec_t = typename Ktraits::vec_t;
+        typename Ktraits::BlockStoreVecT(smem_store_vec).Store(
+            reinterpret_cast<vec_t*>(out),
+            reinterpret_cast<vec_t(&)[Ktraits::kNLoads]>(write_vals)
+       );
+    } else {
+        typename Ktraits::BlockStoreT(smem_store).Store(out, write_vals, seqlen);
+    }
+}

selective-scan/selective_scan_fwd_bf16.cu

@@ -0,0 +1,10 @@
+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+// Split into multiple files to compile in paralell
+
+#include "selective_scan_fwd_kernel.cuh"
+
+template void selective_scan_fwd_cuda<at::BFloat16, float>(SSMParamsBase &params, cudaStream_t stream);
+template void selective_scan_fwd_cuda<at::BFloat16, complex_t>(SSMParamsBase &params, cudaStream_t stream);

selective-scan/selective_scan_fwd_fp16.cu

@@ -0,0 +1,10 @@
+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+// Split into multiple files to compile in paralell
+
+#include "selective_scan_fwd_kernel.cuh"
+
+template void selective_scan_fwd_cuda<at::Half, float>(SSMParamsBase &params, cudaStream_t stream);
+template void selective_scan_fwd_cuda<at::Half, complex_t>(SSMParamsBase &params, cudaStream_t stream);

selective-scan/selective_scan_fwd_fp32.cu

@@ -0,0 +1,10 @@
+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+// Split into multiple files to compile in paralell
+
+#include "selective_scan_fwd_kernel.cuh"
+
+template void selective_scan_fwd_cuda<float, float>(SSMParamsBase &params, cudaStream_t stream);
+template void selective_scan_fwd_cuda<float, complex_t>(SSMParamsBase &params, cudaStream_t stream);

selective-scan/selective_scan_fwd_kernel.cuh

@@ -0,0 +1,376 @@
+/******************************************************************************
+ * Copyright (c) 2023, Tri Dao.
+ ******************************************************************************/
+
+#pragma once
+
+#include <c10/util/BFloat16.h>
+#include <c10/util/Half.h>
+#include <c10/cuda/CUDAException.h>  // For C10_CUDA_CHECK and C10_CUDA_KERNEL_LAUNCH_CHECK
+
+#ifndef USE_ROCM
+    #include <cub/block/block_load.cuh>
+    #include <cub/block/block_store.cuh>
+    #include <cub/block/block_scan.cuh>
+#else
+    #include <hipcub/hipcub.hpp>
+    namespace cub = hipcub;
+#endif
+
+#include "selective_scan.h"
+#include "selective_scan_common.h"
+#include "static_switch.h"
+
+template<int kNThreads_, int kNItems_, int kNRows_, bool kIsEvenLen_,
+         bool kIsVariableB_, bool kIsVariableC_,
+         bool kHasZ_, typename input_t_, typename weight_t_>
+struct Selective_Scan_fwd_kernel_traits {
+    static_assert(kNItems_ % 4 == 0);
+    using input_t = input_t_;
+    using weight_t = weight_t_;
+    static constexpr int kNThreads = kNThreads_;
+    // Setting MinBlocksPerMP to be 3 (instead of 2) for 128 threads improves occupancy.
+    static constexpr int kMinBlocks = kNThreads < 128 ? 5 : 3;
+    static constexpr int kNItems = kNItems_;
+    static constexpr int kNRows = kNRows_;
+    static constexpr int kNBytes = sizeof(input_t);
+    static_assert(kNBytes == 2 || kNBytes == 4);
+    static constexpr int kNElts = kNBytes == 4 ? 4 : constexpr_min(8, kNItems);
+    static_assert(kNItems % kNElts == 0);
+    static constexpr int kNLoads = kNItems / kNElts;
+    static constexpr bool kIsComplex = std::is_same_v<weight_t, complex_t>;
+    static constexpr bool kIsEvenLen = kIsEvenLen_;
+    static constexpr bool kIsVariableB = kIsVariableB_;
+    static constexpr bool kIsVariableC = kIsVariableC_;
+    static constexpr bool kHasZ = kHasZ_;
+
+    static constexpr bool kDirectIO = kIsEvenLen && kNLoads == 1;
+
+    using vec_t = typename BytesToType<kNBytes * kNElts>::Type;
+    using scan_t = std::conditional_t<!kIsComplex, float2, float4>;
+    using BlockLoadT = cub::BlockLoad<input_t, kNThreads, kNItems, cub::BLOCK_LOAD_WARP_TRANSPOSE>;
+    using BlockLoadVecT = cub::BlockLoad<vec_t, kNThreads, kNLoads,
+        !kDirectIO ? cub::BLOCK_LOAD_WARP_TRANSPOSE : cub::BLOCK_LOAD_DIRECT>;
+    using BlockLoadWeightT = cub::BlockLoad<input_t, kNThreads, !kIsComplex ? kNItems : kNItems * 2, cub::BLOCK_LOAD_WARP_TRANSPOSE>;
+    using BlockLoadWeightVecT = cub::BlockLoad<vec_t, kNThreads, !kIsComplex ? kNLoads : kNLoads * 2,
+        !kDirectIO ? cub::BLOCK_LOAD_WARP_TRANSPOSE  : cub::BLOCK_LOAD_DIRECT>;
+    using BlockStoreT = cub::BlockStore<input_t, kNThreads, kNItems, cub::BLOCK_STORE_WARP_TRANSPOSE>;
+    using BlockStoreVecT = cub::BlockStore<vec_t, kNThreads, kNLoads,
+        !kDirectIO ? cub::BLOCK_STORE_WARP_TRANSPOSE : cub::BLOCK_STORE_DIRECT>;
+    // using BlockScanT = cub::BlockScan<scan_t, kNThreads, cub::BLOCK_SCAN_RAKING_MEMOIZE>;
+    // using BlockScanT = cub::BlockScan<scan_t, kNThreads, cub::BLOCK_SCAN_RAKING>;
+    using BlockScanT = cub::BlockScan<scan_t, kNThreads, cub::BLOCK_SCAN_WARP_SCANS>;
+    static constexpr int kSmemIOSize = custom_max({sizeof(typename BlockLoadT::TempStorage),
+                                                 sizeof(typename BlockLoadVecT::TempStorage),
+                                                 (int(kIsVariableB) + int(kIsVariableC)) * sizeof(typename BlockLoadWeightT::TempStorage),
+                                                 (int(kIsVariableB) + int(kIsVariableC)) * sizeof(typename BlockLoadWeightVecT::TempStorage),
+                                                 sizeof(typename BlockStoreT::TempStorage),
+                                                 sizeof(typename BlockStoreVecT::TempStorage)});
+    static constexpr int kSmemSize = kSmemIOSize + sizeof(typename BlockScanT::TempStorage);
+};
+
+template<typename Ktraits>
+__global__ __launch_bounds__(Ktraits::kNThreads, Ktraits::kMinBlocks)
+void selective_scan_fwd_kernel(SSMParamsBase params) {
+    constexpr bool kIsComplex = Ktraits::kIsComplex;
+    constexpr bool kIsVariableB = Ktraits::kIsVariableB;
+    constexpr bool kIsVariableC = Ktraits::kIsVariableC;
+    constexpr bool kHasZ = Ktraits::kHasZ;
+    constexpr int kNThreads = Ktraits::kNThreads;
+    constexpr int kNItems = Ktraits::kNItems;
+    constexpr int kNRows = Ktraits::kNRows;
+    constexpr bool kDirectIO = Ktraits::kDirectIO;
+    using input_t = typename Ktraits::input_t;
+    using weight_t = typename Ktraits::weight_t;
+    using scan_t = typename Ktraits::scan_t;
+
+    // Shared memory.
+    extern __shared__ char smem_[];
+    // cast to lvalue reference of expected type
+    // char *smem_loadstorescan = smem_ + 2 * MAX_DSTATE * sizeof(weight_t);
+    // auto& smem_load = reinterpret_cast<typename BlockLoadT::TempStorage&>(smem_ + 2 * MAX_DSTATE * sizeof(weight_t));
+    // auto& smem_load = reinterpret_cast<typename BlockLoadT::TempStorage&>(smem_loadstorescan);
+    auto& smem_load = reinterpret_cast<typename Ktraits::BlockLoadT::TempStorage&>(smem_);
+    auto& smem_load_weight = reinterpret_cast<typename Ktraits::BlockLoadWeightT::TempStorage&>(smem_);
+    auto& smem_load_weight1 = *reinterpret_cast<typename Ktraits::BlockLoadWeightT::TempStorage*>(smem_ + sizeof(typename Ktraits::BlockLoadWeightT::TempStorage));
+    auto& smem_store = reinterpret_cast<typename Ktraits::BlockStoreT::TempStorage&>(smem_);
+    auto& smem_scan = *reinterpret_cast<typename Ktraits::BlockScanT::TempStorage*>(smem_ + Ktraits::kSmemIOSize);
+    // weight_t *smem_a = reinterpret_cast<weight_t *>(smem_ + smem_loadstorescan_size);
+    // weight_t *smem_bc = reinterpret_cast<weight_t *>(smem_a + MAX_DSTATE);
+    scan_t *smem_running_prefix = reinterpret_cast<scan_t *>(smem_ + Ktraits::kSmemSize);
+
+    const int batch_id = blockIdx.x;
+    const int dim_id = blockIdx.y;
+    const int group_id = dim_id / (params.dim_ngroups_ratio);
+    input_t *u = reinterpret_cast<input_t *>(params.u_ptr) + batch_id * params.u_batch_stride
+        + dim_id * kNRows * params.u_d_stride;
+    input_t *delta = reinterpret_cast<input_t *>(params.delta_ptr) + batch_id * params.delta_batch_stride
+        + dim_id * kNRows * params.delta_d_stride;
+    weight_t *A = reinterpret_cast<weight_t *>(params.A_ptr) + dim_id * kNRows * params.A_d_stride;
+    weight_t *B = reinterpret_cast<weight_t *>(params.B_ptr) + dim_id * kNRows * params.B_d_stride;
+    input_t *Bvar = reinterpret_cast<input_t *>(params.B_ptr) + batch_id * params.B_batch_stride + group_id * params.B_group_stride;
+    weight_t *C = reinterpret_cast<weight_t *>(params.C_ptr) + dim_id * kNRows * params.C_d_stride;
+    input_t *Cvar = reinterpret_cast<input_t *>(params.C_ptr) + batch_id * params.C_batch_stride + group_id * params.C_group_stride;
+    scan_t *x = reinterpret_cast<scan_t *>(params.x_ptr) + (batch_id * params.dim + dim_id * kNRows) * params.n_chunks * params.dstate;
+
+    float D_val[kNRows] = {0};
+    if (params.D_ptr != nullptr) {
+        #pragma unroll
+        for (int r = 0; r < kNRows; ++r) {
+            D_val[r] = reinterpret_cast<float *>(params.D_ptr)[dim_id * kNRows + r];
+        }
+    }
+    float delta_bias[kNRows] = {0};
+    if (params.delta_bias_ptr != nullptr) {
+        #pragma unroll
+        for (int r = 0; r < kNRows; ++r) {
+            delta_bias[r] = reinterpret_cast<float *>(params.delta_bias_ptr)[dim_id * kNRows + r];
+        }
+    }
+
+    // for (int state_idx = threadIdx.x; state_idx < params.dstate; state_idx += blockDim.x) {
+    //     smem_a[state_idx] = A[state_idx * params.A_dstate_stride];
+    //     smem_bc[state_idx] = B[state_idx * params.B_dstate_stride] * C[state_idx * params.C_dstate_stride];
+    // }
+
+    constexpr int kChunkSize = kNThreads * kNItems;
+    for (int chunk = 0; chunk < params.n_chunks; ++chunk) {
+        input_t u_vals[kNRows][kNItems], delta_vals_load[kNRows][kNItems];
+        __syncthreads();
+        #pragma unroll
+        for (int r = 0; r < kNRows; ++r) {
+            if constexpr (!kDirectIO) {
+                if (r > 0) { __syncthreads(); }
+            }
+            load_input<Ktraits>(u + r * params.u_d_stride, u_vals[r], smem_load, params.seqlen - chunk * kChunkSize);
+            if constexpr (!kDirectIO) { __syncthreads(); }
+            load_input<Ktraits>(delta + r * params.delta_d_stride, delta_vals_load[r], smem_load, params.seqlen - chunk * kChunkSize);
+        }
+        u += kChunkSize;
+        delta += kChunkSize;
+    
+        float delta_vals[kNRows][kNItems], delta_u_vals[kNRows][kNItems], out_vals[kNRows][kNItems];
+        #pragma unroll
+        for (int r = 0; r < kNRows; ++r) {
+            #pragma unroll
+            for (int i = 0; i < kNItems; ++i) {
+                float u_val = float(u_vals[r][i]);
+                delta_vals[r][i] = float(delta_vals_load[r][i]) + delta_bias[r];
+                if (params.delta_softplus) {
+                    delta_vals[r][i] = delta_vals[r][i] <= 20.f ? log1pf(expf(delta_vals[r][i])) : delta_vals[r][i];
+                }
+                delta_u_vals[r][i] = delta_vals[r][i] * u_val;
+                out_vals[r][i] = D_val[r] * u_val;
+            }
+        }
+
+        __syncthreads();
+        for (int state_idx = 0; state_idx < params.dstate; ++state_idx) {
+            weight_t A_val[kNRows];
+            #pragma unroll
+            for (int r = 0; r < kNRows; ++r) {
+                A_val[r] = A[state_idx * params.A_dstate_stride + r * params.A_d_stride];
+                // Multiply the real part of A with LOG2E so we can use exp2f instead of expf.
+                constexpr float kLog2e = M_LOG2E;
+                if constexpr (!kIsComplex) {
+                    A_val[r] *= kLog2e;
+                } else {
+                    A_val[r].real_ *= kLog2e;
+                }
+            }
+            // This variable holds B * C if both B and C are constant across seqlen. If only B varies
+            // across seqlen, this holds C. If only C varies across seqlen, this holds B.
+            // If both B and C vary, this is unused.
+            weight_t BC_val[kNRows];
+            weight_t B_vals[kNItems], C_vals[kNItems];
+            if constexpr (kIsVariableB) {
+                load_weight<Ktraits>(Bvar + state_idx * params.B_dstate_stride, B_vals,
+                    smem_load_weight, (params.seqlen - chunk * kChunkSize) * (!kIsComplex ? 1 : 2));
+                if constexpr (!kIsVariableC) {
+                    #pragma unroll
+                    for (int r = 0; r < kNRows; ++r) {
+                        BC_val[r] = C[state_idx * params.C_dstate_stride + r * params.C_d_stride];
+                    }
+                }
+            }
+            if constexpr (kIsVariableC) {
+                auto &smem_load_weight_C = !kIsVariableB ? smem_load_weight : smem_load_weight1;
+                load_weight<Ktraits>(Cvar + state_idx * params.C_dstate_stride, C_vals,
+                    smem_load_weight_C, (params.seqlen - chunk * kChunkSize) * (!kIsComplex ? 1 : 2));
+                if constexpr (!kIsVariableB) {
+                    #pragma unroll
+                    for (int r = 0; r < kNRows; ++r) {
+                        BC_val[r] = B[state_idx * params.B_dstate_stride + r * params.B_d_stride];
+                    }
+                }
+            }
+            if constexpr (!kIsVariableB && !kIsVariableC) {
+                #pragma unroll
+                for (int r = 0; r < kNRows; ++r) {
+                    BC_val[r] = B[state_idx * params.B_dstate_stride + r * params.B_d_stride] * C[state_idx * params.C_dstate_stride + r * params.C_d_stride];
+                }
+            }
+
+            #pragma unroll
+            for (int r = 0; r < kNRows; ++r) {
+                if (r > 0) { __syncthreads(); }  // Scan could be using the same smem
+                scan_t thread_data[kNItems];
+                #pragma unroll
+                for (int i = 0; i < kNItems; ++i) {
+                    if constexpr (!kIsComplex) {
+                        thread_data[i] = make_float2(exp2f(delta_vals[r][i] * A_val[r]),
+                                                     !kIsVariableB ? delta_u_vals[r][i] : B_vals[i] * delta_u_vals[r][i]);
+                        if constexpr (!Ktraits::kIsEvenLen) {  // So that the last state is correct
+                            if (threadIdx.x * kNItems + i >= params.seqlen - chunk * kChunkSize) {
+                                thread_data[i] = make_float2(1.f, 0.f);
+                            }
+                        }
+                    } else {
+                        // Pytorch's implementation of complex exp (which calls thrust) is very slow
+                        complex_t delta_a_exp = cexp2f(delta_vals[r][i] * A_val[r]);
+                        weight_t B_delta_u_val = !kIsVariableB ? delta_u_vals[r][i] : B_vals[i] * delta_u_vals[r][i];
+                        thread_data[i] = make_float4(delta_a_exp.real_, delta_a_exp.imag_, B_delta_u_val.real_, B_delta_u_val.imag_);
+                        if constexpr (!Ktraits::kIsEvenLen) {  // So that the last state is correct
+                            if (threadIdx.x * kNItems + i >= params.seqlen - chunk * kChunkSize) {
+                                thread_data[i] = make_float4(1.f, 0.f, 0.f, 0.f);
+                            }
+                        }
+                    }
+                }
+                // Initialize running total
+                scan_t running_prefix;
+                if constexpr (!kIsComplex) {
+                    // If we use WARP_SCAN then all lane 0 of all warps (not just thread 0) needs to read
+                    running_prefix = chunk > 0 && threadIdx.x % 32 == 0 ? smem_running_prefix[state_idx + r * MAX_DSTATE] : make_float2(1.f, 0.f);
+                    // running_prefix = chunk > 0 && threadIdx.x == 0 ? smem_running_prefix[state_idx] : make_float2(1.f, 0.f);
+                } else {
+                    running_prefix = chunk > 0 && threadIdx.x % 32 == 0 ? smem_running_prefix[state_idx + r * MAX_DSTATE] : make_float4(1.f, 0.f, 0.f, 0.f);
+                    // running_prefix = chunk > 0 && threadIdx.x == 0 ? smem_running_prefix[state_idx] : make_float4(1.f, 0.f, 0.f, 0.f);
+                }
+                SSMScanPrefixCallbackOp<weight_t> prefix_op(running_prefix);
+                typename Ktraits::BlockScanT(smem_scan).InclusiveScan(
+                    thread_data, thread_data, SSMScanOp<weight_t>(), prefix_op
+                );
+                // There's a syncthreads in the scan op, so we don't need to sync here.
+                // Unless there's only 1 warp, but then it's the same thread (0) reading and writing.
+                if (threadIdx.x == 0) {
+                    smem_running_prefix[state_idx] = prefix_op.running_prefix;
+                    x[(r * params.n_chunks + chunk) * params.dstate + state_idx] = prefix_op.running_prefix;
+                }
+                #pragma unroll
+                for (int i = 0; i < kNItems; ++i) {
+                    const weight_t C_val = !kIsVariableC
+                        ? BC_val[r]
+                        : (!kIsVariableB ? BC_val[r] * C_vals[i] : C_vals[i]);
+                    if constexpr (!kIsComplex) {
+                        out_vals[r][i] += thread_data[i].y * C_val;
+                    } else {
+                        out_vals[r][i] += (complex_t(thread_data[i].z, thread_data[i].w) * C_val).real_ * 2;
+                    }
+                }
+            }
+        }
+        
+        input_t *out = reinterpret_cast<input_t *>(params.out_ptr) + batch_id * params.out_batch_stride
+            + dim_id * kNRows * params.out_d_stride + chunk * kChunkSize;
+        __syncthreads();
+        #pragma unroll
+        for (int r = 0; r < kNRows; ++r) {
+            if constexpr (!kDirectIO) {
+                if (r > 0) { __syncthreads(); }
+            }
+            store_output<Ktraits>(out + r * params.out_d_stride, out_vals[r], smem_store, params.seqlen - chunk * kChunkSize);
+        }
+
+        if constexpr (kHasZ) {
+            input_t *z = reinterpret_cast<input_t *>(params.z_ptr) + batch_id * params.z_batch_stride
+                + dim_id * kNRows * params.z_d_stride + chunk * kChunkSize;
+            input_t *out_z = reinterpret_cast<input_t *>(params.out_z_ptr) + batch_id * params.out_z_batch_stride
+                + dim_id * kNRows * params.out_z_d_stride + chunk * kChunkSize;
+            #pragma unroll
+            for (int r = 0; r < kNRows; ++r) {
+                input_t z_vals[kNItems];
+                __syncthreads();
+                load_input<Ktraits>(z + r * params.z_d_stride, z_vals, smem_load, params.seqlen - chunk * kChunkSize);
+                #pragma unroll
+                for (int i = 0; i < kNItems; ++i) {
+                    float z_val = z_vals[i];
+                    out_vals[r][i] *= z_val / (1 + expf(-z_val));
+                }
+                __syncthreads();
+                store_output<Ktraits>(out_z + r * params.out_z_d_stride, out_vals[r], smem_store, params.seqlen - chunk * kChunkSize);
+            }
+        }
+
+        Bvar += kChunkSize * (!kIsComplex ? 1 : 2);
+        Cvar += kChunkSize * (!kIsComplex ? 1 : 2);
+    }
+}
+
+template<int kNThreads, int kNItems, typename input_t, typename weight_t>
+void selective_scan_fwd_launch(SSMParamsBase &params, cudaStream_t stream) {
+    // Only kNRows == 1 is tested for now, which ofc doesn't differ from previously when we had each block
+    // processing 1 row.
+    constexpr int kNRows = 1;
+    BOOL_SWITCH(params.seqlen % (kNThreads * kNItems) == 0, kIsEvenLen, [&] {
+        BOOL_SWITCH(params.is_variable_B, kIsVariableB, [&] {
+            BOOL_SWITCH(params.is_variable_C, kIsVariableC, [&] {
+                BOOL_SWITCH(params.z_ptr != nullptr , kHasZ, [&] {
+                    using Ktraits = Selective_Scan_fwd_kernel_traits<kNThreads, kNItems, kNRows, kIsEvenLen, kIsVariableB, kIsVariableC, kHasZ, input_t, weight_t>;
+                    
+                    constexpr int kSmemSize = Ktraits::kSmemSize + kNRows * MAX_DSTATE * sizeof(typename Ktraits::scan_t);
+                    dim3 grid(params.batch, params.dim / kNRows);
+
+                    // Had to change this substantially since potentially the hip 
+                    // interface for setting kernel launch attributes is slightly different from 
+                    // cuda's. In particualar, it seems to expect a plain const void * pointer.
+
+                    auto kernel = &selective_scan_fwd_kernel<Ktraits>;
+
+                    
+                    if (kSmemSize >= 48 * 1024) {
+                        #ifndef USE_ROCM
+                        C10_CUDA_CHECK(cudaFuncSetAttribute(
+                            kernel, cudaFuncAttributeMaxDynamicSharedMemorySize, kSmemSize));
+                        #else
+                        C10_CUDA_CHECK(cudaFuncSetAttribute(
+                            (void *) kernel, cudaFuncAttributeMaxDynamicSharedMemorySize, kSmemSize));
+                            std::cerr << "Warning (selective_scan_fwd_kernel): attempting to set maxDynamicSharedMemorySize on an AMD GPU which is currently a non-op (in ROCm versions <= 6.1). This might lead to undefined behavior. \n" << std::endl;
+                        #endif
+                    }
+
+                    kernel<<<grid, Ktraits::kNThreads, kSmemSize, stream>>>(params);
+                    C10_CUDA_KERNEL_LAUNCH_CHECK();
+                });
+            });
+        });
+    });
+}
+
+template<typename input_t, typename weight_t>
+void selective_scan_fwd_cuda(SSMParamsBase &params, cudaStream_t stream) {
+
+    #ifndef USE_ROCM
+        if (params.seqlen <= 128) {           
+            selective_scan_fwd_launch<32, 4, input_t, weight_t>(params, stream);
+        } else if (params.seqlen <= 256) {
+            selective_scan_fwd_launch<32, 8, input_t, weight_t>(params, stream);
+        } else if (params.seqlen <= 512) {
+            selective_scan_fwd_launch<32, 16, input_t, weight_t>(params, stream);
+        } else if (params.seqlen <= 1024) {
+            selective_scan_fwd_launch<64, 16, input_t, weight_t>(params, stream);
+        } else {
+            selective_scan_fwd_launch<128, 16, input_t, weight_t>(params, stream);
+        }
+    #else
+        if (params.seqlen <= 256) {
+            selective_scan_fwd_launch<64, 4, input_t, weight_t>(params, stream);
+        } else if (params.seqlen <= 512) {
+            selective_scan_fwd_launch<64, 8, input_t, weight_t>(params, stream);
+        } else if (params.seqlen <= 1024) {
+            selective_scan_fwd_launch<64, 16, input_t, weight_t>(params, stream);
+        } else {
+            selective_scan_fwd_launch<128, 16, input_t, weight_t>(params, stream);
+        }
+    #endif
+}

selective-scan/static_switch.h

@@ -0,0 +1,25 @@
+// Inspired by https://github.com/NVIDIA/DALI/blob/main/include/dali/core/static_switch.h
+// and https://github.com/pytorch/pytorch/blob/master/aten/src/ATen/Dispatch.h
+
+#pragma once
+
+/// @param COND       - a boolean expression to switch by
+/// @param CONST_NAME - a name given for the constexpr bool variable.
+/// @param ...       - code to execute for true and false
+///
+/// Usage:
+/// ```
+/// BOOL_SWITCH(flag, BoolConst, [&] {
+///     some_function<BoolConst>(...);
+/// });
+/// ```
+#define BOOL_SWITCH(COND, CONST_NAME, ...)                                           \
+    [&] {                                                                            \
+        if (COND) {                                                                  \
+            constexpr bool CONST_NAME = true;                                        \
+            return __VA_ARGS__();                                                    \
+        } else {                                                                     \
+            constexpr bool CONST_NAME = false;                                       \
+            return __VA_ARGS__();                                                    \
+        }                                                                            \
+    }()

selective-scan/uninitialized_copy.cuh

@@ -0,0 +1,77 @@
+/******************************************************************************
+ * Copyright (c) 2011-2022, NVIDIA CORPORATION.  All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the NVIDIA CORPORATION nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL NVIDIA CORPORATION BE LIABLE FOR ANY
+ * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+ * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ ******************************************************************************/
+
+#pragma once
+
+#ifndef USE_ROCM
+    #include <cub/config.cuh>
+
+    #include <cuda/std/type_traits>
+#else
+    #include <hipcub/hipcub.hpp>
+    // Map ::cuda::std to the standard std namespace
+    namespace cuda {
+        namespace std = ::std;
+    }
+#endif
+
+
+namespace detail
+{
+
+#if defined(_NVHPC_CUDA)
+template <typename T, typename U>
+__host__ __device__ void uninitialized_copy(T *ptr, U &&val)
+{
+  // NVBug 3384810
+  new (ptr) T(::cuda::std::forward<U>(val));
+}
+#else
+template <typename T,
+          typename U,
+          typename ::cuda::std::enable_if<
+            ::cuda::std::is_trivially_copyable<T>::value,
+            int
+          >::type = 0>
+__host__ __device__ void uninitialized_copy(T *ptr, U &&val)
+{
+  *ptr = ::cuda::std::forward<U>(val);
+}
+
+template <typename T,
+         typename U,
+         typename ::cuda::std::enable_if<
+           !::cuda::std::is_trivially_copyable<T>::value,
+           int
+         >::type = 0>
+__host__ __device__ void uninitialized_copy(T *ptr, U &&val)
+{
+  new (ptr) T(::cuda::std::forward<U>(val));
+}
+#endif
+
+} // namespace detail

tests/ops/test_selective_scan.py

@@ -0,0 +1,247 @@
+# Copyright (C) 2023, Tri Dao.
+
+import math
+
+import torch
+import torch.nn.functional as F
+import pytest
+
+from einops import rearrange
+
+from mamba_ssm.ops.selective_scan_interface import selective_scan_fn, selective_scan_ref
+from mamba_ssm.ops.selective_scan_interface import mamba_inner_fn, mamba_inner_ref
+
+
+# @pytest.mark.parametrize('wtype', [torch.float32, torch.complex64])
+@pytest.mark.parametrize('wtype', [torch.float32])
+# @pytest.mark.parametrize('itype', [torch.float32, torch.float16, torch.bfloat16])
+@pytest.mark.parametrize('itype', [torch.float32])
+# @pytest.mark.parametrize('seqlen', [8, 16, 32, 64, 128, 256, 372, 512, 784, 1024, 1134, 2048, 4096])
+@pytest.mark.parametrize('seqlen', [128, 256, 512, 1024, 2048, 4096])
+# @pytest.mark.parametrize('seqlen', [128])
+# @pytest.mark.parametrize("return_last_state", [False, True])
+@pytest.mark.parametrize("return_last_state", [True])
+# @pytest.mark.parametrize('has_delta_bias', [False, True])
+@pytest.mark.parametrize('has_delta_bias', [True])
+# @pytest.mark.parametrize('delta_softplus', [False, True])
+@pytest.mark.parametrize('delta_softplus', [True])
+# @pytest.mark.parametrize('has_z', [False, True])
+@pytest.mark.parametrize('has_z', [True])
+# @pytest.mark.parametrize('has_D', [False, True])
+@pytest.mark.parametrize('has_D', [True])
+@pytest.mark.parametrize("varBC_groups", [1, 2])
+# @pytest.mark.parametrize("varBC_groups", [1])
+# @pytest.mark.parametrize("is_variable_C", [False, True])
+@pytest.mark.parametrize("is_variable_C", [True])
+# @pytest.mark.parametrize("is_variable_B", [False, True])
+@pytest.mark.parametrize("is_variable_B", [True])
+def test_selective_scan(is_variable_B, is_variable_C, varBC_groups, has_D, has_z, has_delta_bias,
+                        delta_softplus, return_last_state, seqlen, itype, wtype):
+    if varBC_groups > 1 and (not is_variable_B or not is_variable_C):
+        pytest.skip()  # This config is not applicable
+    device = 'cuda'
+    rtol, atol = (6e-4, 2e-3) if itype == torch.float32 else (3e-3, 5e-3)
+    if itype == torch.bfloat16:
+        rtol, atol = 3e-2, 5e-2
+    rtolw, atolw = (1e-3, 1e-3)
+    if has_z:  # If we have z, the errors on the weights seem higher
+        rtolw = max(rtolw, rtol)
+        atolw = max(atolw, atol)
+    # set seed
+    torch.random.manual_seed(0)
+    batch_size = 2
+    dim = 4
+    dstate = 8
+    is_complex = wtype == torch.complex64
+    A = (-0.5 * torch.rand(dim, dstate, device=device, dtype=wtype)).requires_grad_()
+    if not is_variable_B:
+        B_shape = (dim, dstate)
+    elif varBC_groups == 1:
+        B_shape = (batch_size, dstate, seqlen if not is_complex else seqlen * 2)
+    else:
+        B_shape = (batch_size, varBC_groups, dstate, seqlen if not is_complex else seqlen * 2)
+    B = torch.randn(*B_shape, device=device, dtype=wtype if not is_variable_B else itype,
+                    requires_grad=True)
+    if not is_variable_C:
+        C_shape = (dim, dstate)
+    elif varBC_groups == 1:
+        C_shape = (batch_size, dstate, seqlen if not is_complex else seqlen * 2)
+    else:
+        C_shape = (batch_size, varBC_groups, dstate, seqlen if not is_complex else seqlen * 2)
+    C = torch.randn(*C_shape, device=device, dtype=wtype if not is_variable_C else itype,
+                    requires_grad=True)
+    if has_D:
+        D = torch.randn(dim, device=device, dtype=torch.float32, requires_grad=True)
+    else:
+        D = None
+    if has_z:
+        z = torch.randn(batch_size, dim, seqlen, device=device, dtype=itype, requires_grad=True)
+    else:
+        z = None
+    if has_delta_bias:
+        delta_bias = (0.5 * torch.rand(dim, device=device, dtype=torch.float32)).requires_grad_()
+    else:
+        delta_bias = None
+    u = torch.randn(batch_size, dim, seqlen, device=device, dtype=itype, requires_grad=True)
+    delta = (0.5 * torch.rand(batch_size, dim, seqlen, device=device, dtype=itype)).requires_grad_()
+    A_ref = A.detach().clone().requires_grad_()
+    B_ref = B.detach().clone().requires_grad_()
+    C_ref = C.detach().clone().requires_grad_()
+    D_ref = D.detach().clone().requires_grad_() if D is not None else None
+    z_ref = z.detach().clone().requires_grad_() if z is not None else None
+    u_ref = u.detach().clone().requires_grad_()
+    delta_ref = delta.detach().clone().requires_grad_()
+    delta_bias_ref = delta_bias.detach().clone().requires_grad_() if delta_bias is not None else None
+    out, *rest = selective_scan_fn(
+        u, delta, A, B, C, D, z=z,
+        delta_bias=delta_bias, delta_softplus=delta_softplus,
+        return_last_state=return_last_state
+    )
+    if return_last_state:
+        state = rest[0]
+    out_ref, *rest = selective_scan_ref(
+        u_ref, delta_ref, A_ref, B_ref, C_ref, D_ref, z=z_ref,
+        delta_bias=delta_bias_ref, delta_softplus=delta_softplus,
+        return_last_state=return_last_state
+    )
+    if return_last_state:
+        state_ref = rest[0]
+    # dA = torch.exp(torch.einsum('bdl,dn->bdln', delta, A))
+    # dt_u = delta * u
+
+    print(f'Output max diff: {(out - out_ref).abs().max().item()}')
+    print(f'Output mean diff: {(out - out_ref).abs().mean().item()}')
+    assert torch.allclose(out, out_ref, rtol=rtol, atol=atol)
+    if return_last_state:
+        print(f'State max diff: {(state - state_ref).abs().max().item()}')
+        assert torch.allclose(state, state_ref, rtol=rtol, atol=atol)
+
+    g = torch.randn_like(out)
+    out_ref.backward(g)
+    out.backward(g)
+
+    print(f'du max diff: {(u.grad - u_ref.grad).abs().max().item()}')
+    print(f'ddelta max diff: {(delta.grad - delta_ref.grad).abs().max().item()}')
+    print(f'dA max diff: {(A.grad - A_ref.grad).abs().max().item()}')
+    print(f'dB max diff: {(B.grad - B_ref.grad).abs().max().item()}')
+    print(f'dC max diff: {(C.grad - C_ref.grad).abs().max().item()}')
+    if has_D:
+        print(f'dD max diff: {(D.grad - D_ref.grad).abs().max().item()}')
+    if has_z:
+        print(f'dz max diff: {(z.grad - z_ref.grad).abs().max().item()}')
+    if has_delta_bias:
+        print(f'ddelta_bias max diff: {(delta_bias.grad - delta_bias_ref.grad).abs().max().item()}')
+
+    assert torch.allclose(u.grad, u_ref.grad.to(dtype=itype), rtol=rtol * 2, atol=atol * 2)
+    assert torch.allclose(delta.grad, delta_ref.grad.to(dtype=itype), rtol=rtol * 5, atol=atol * 10)
+    assert torch.allclose(A.grad, A_ref.grad, rtol=rtolw, atol=atolw * 5)
+    assert torch.allclose(B.grad, B_ref.grad, rtol=rtolw if not is_variable_B else rtol,
+                          atol=atolw if not is_variable_B else atol)
+    assert torch.allclose(C.grad, C_ref.grad, rtol=rtolw if not is_variable_C else rtol,
+                          atol=atolw if not is_variable_C else atol)
+    if has_D:
+        assert torch.allclose(D.grad, D_ref.grad, rtol=rtolw, atol=atolw)
+    if has_z:
+        assert torch.allclose(z.grad, z_ref.grad, rtol=rtolw, atol=atolw)
+    if has_delta_bias:
+        assert torch.allclose(delta_bias.grad, delta_bias_ref.grad, rtol=rtolw, atol=atolw)
+
+
+@pytest.mark.parametrize('wtype', [torch.float32, torch.complex64])
+# @pytest.mark.parametrize('wtype', [torch.complex64])
+# @pytest.mark.parametrize('itype', [torch.float32, torch.float16, torch.bfloat16])
+@pytest.mark.parametrize('itype', [torch.float32])
+# @pytest.mark.parametrize('seqlen', [8, 16, 32, 64, 128, 256, 372, 512, 784, 1024, 1134, 2048, 4096])
+@pytest.mark.parametrize('seqlen', [128])
+@pytest.mark.parametrize("is_variable_C", [False, True])
+# @pytest.mark.parametrize("is_variable_C", [False])
+@pytest.mark.parametrize("is_variable_B", [False, True])
+# @pytest.mark.parametrize("is_variable_B", [True])
+def test_mamba_inner_fn(is_variable_B, is_variable_C, seqlen, itype, wtype):
+    device = 'cuda'
+    rtol, atol = (6e-4, 2e-3) if itype == torch.float32 else (3e-3, 5e-3)
+    if itype == torch.bfloat16:
+        rtol, atol = 3e-2, 5e-2
+    rtolw, atolw = (1e-3, 1e-3)
+    # If we have z, the errors on the weights seem higher
+    rtolw = max(rtolw, rtol)
+    atolw = max(atolw, atol)
+    # set seed
+    torch.random.manual_seed(0)
+    batch_size = 2
+    dim = 768
+    dstate = 8
+    dt_rank = 48
+    is_complex = wtype == torch.complex64
+    xz = torch.randn(batch_size, 2 * dim, seqlen, device=device, dtype=itype, requires_grad=True)
+    conv1d_weight = torch.randn(dim, 1, 3, device=device, dtype=torch.float32, requires_grad=True)
+    conv1d_bias = torch.randn(dim, device=device, dtype=torch.float32, requires_grad=True)
+    x_proj_weight = torch.randn(dt_rank + (bool(is_variable_B) + bool(is_variable_C)) * dstate
+                                * (1 if not is_complex else 2),
+                                dim, device=device, dtype=itype, requires_grad=True)
+    delta_proj_weight = torch.randn(dim, dt_rank, device=device, dtype=itype, requires_grad=True)
+    out_proj_weight = torch.randn(dim // 2, dim, device=device, dtype=itype, requires_grad=True)
+    out_proj_bias = None
+    A = (-0.5 * torch.rand(dim, dstate, device=device, dtype=wtype)).requires_grad_()
+    B = (torch.randn(dim, dstate, device=device, dtype=wtype, requires_grad=True)
+         if not is_variable_B else None)
+    C = (torch.randn(dim, dstate, device=device, dtype=wtype, requires_grad=True)
+         if not is_variable_C else None)
+    D = torch.randn(dim, device=device, dtype=torch.float32, requires_grad=True)
+    delta_bias = (0.5 * torch.rand(dim, device=device, dtype=torch.float32)).requires_grad_()
+    B_proj_bias = None
+    C_proj_bias = None
+    xz_ref = xz.detach().clone().requires_grad_()
+    conv1d_weight_ref = conv1d_weight.detach().clone().requires_grad_()
+    conv1d_bias_ref = conv1d_bias.detach().clone().requires_grad_()
+    x_proj_weight_ref = x_proj_weight.detach().clone().requires_grad_()
+    delta_proj_weight_ref = delta_proj_weight.detach().clone().requires_grad_()
+    out_proj_weight_ref = out_proj_weight.detach().clone().requires_grad_()
+    out_proj_bias_ref = (out_proj_bias.detach().clone().requires_grad_()
+                         if out_proj_bias is not None else None)
+    A_ref = A.detach().clone().requires_grad_()
+    B_ref = B.detach().clone().requires_grad_() if B is not None else None
+    C_ref = C.detach().clone().requires_grad_() if C is not None else None
+    D_ref = D.detach().clone().requires_grad_()
+    delta_bias_ref = delta_bias.detach().clone().requires_grad_() if delta_bias is not None else None
+    out = mamba_inner_fn(xz, conv1d_weight, conv1d_bias, x_proj_weight, delta_proj_weight,
+                         out_proj_weight, out_proj_bias,
+                         A, B, C, D, delta_bias=delta_bias, delta_softplus=True)
+    out_ref = mamba_inner_ref(xz_ref, conv1d_weight_ref, conv1d_bias_ref, x_proj_weight_ref,
+                              delta_proj_weight_ref, out_proj_weight_ref, out_proj_bias_ref,
+                              A_ref, B_ref, C_ref, D_ref,
+                              delta_bias=delta_bias_ref, delta_softplus=True)
+    # dA = torch.exp(torch.einsum('bdl,dn->bdln', delta, A))
+    # dt_u = delta * u
+
+    print(f'Output max diff: {(out - out_ref).abs().max().item()}')
+    print(f'Output mean diff: {(out - out_ref).abs().mean().item()}')
+    assert torch.allclose(out, out_ref, rtol=rtol, atol=atol)
+
+    g = torch.randn_like(out)
+    out_ref.backward(g)
+    out.backward(g)
+
+    print(f'dxz max diff: {(xz.grad - xz_ref.grad).abs().max().item()}')
+    print(f'dA max diff: {(A.grad - A_ref.grad).abs().max().item()}')
+    if not is_variable_B:
+        print(f'dB max diff: {(B.grad - B_ref.grad).abs().max().item()}')
+    if not is_variable_C:
+        print(f'dC max diff: {(C.grad - C_ref.grad).abs().max().item()}')
+    print(f'dD max diff: {(D.grad - D_ref.grad).abs().max().item()}')
+    print(f'ddelta_bias max diff: {(delta_bias.grad - delta_bias_ref.grad).abs().max().item()}')
+    print(f'dout_proj_weight max diff: {(out_proj_weight.grad - out_proj_weight_ref.grad).abs().max().item()}')
+    print(f'ddelta_proj_weight max diff: {(delta_proj_weight.grad - delta_proj_weight_ref.grad).abs().max().item()}')
+    print(f'dx_proj_weight max diff: {(x_proj_weight.grad - x_proj_weight_ref.grad).abs().max().item()}')
+    print(f'dconv1d_weight max diff: {(conv1d_weight.grad - conv1d_weight_ref.grad).abs().max().item()}')
+    print(f'dconv1d_bias max diff: {(conv1d_bias.grad - conv1d_bias_ref.grad).abs().max().item()}')
+
+    # assert torch.allclose(xz.grad, xz_ref.grad.to(dtype=itype), rtol=rtol * 2, atol=atol * 2)
+    # assert torch.allclose(delta.grad, delta_ref.grad.to(dtype=itype), rtol=rtol * 5, atol=atol * 10)
+    # assert torch.allclose(A.grad, A_ref.grad, rtol=rtolw, atol=atolw * 5)
+    # assert torch.allclose(B.grad, B_ref.grad, rtol=rtolw if not is_variable_B else rtol,
+    #                       atol=atolw if not is_variable_B else atol)
+    # assert torch.allclose(C.grad, C_ref.grad, rtol=rtolw if not is_variable_C else rtol,
+    #                       atol=atolw if not is_variable_C else atol)
+    # assert torch.allclose(D.grad, D_ref.grad, rtol=rtolw, atol=atolw)
+    # assert torch.allclose(delta_bias.grad, delta_bias_ref.grad, rtol=rtolw, atol=atolw)

tests/ops/triton/test_layernorm_gated.py

@@ -0,0 +1,103 @@
+import math
+
+import torch
+import torch.nn.functional as F
+
+import pytest
+
+from einops import rearrange, repeat
+
+from mamba_ssm.ops.triton.layernorm_gated import layernorm_fn, rms_norm_ref
+
+
+@pytest.mark.parametrize("norm_before_gate", [True, False])
+# @pytest.mark.parametrize("norm_before_gate", [False])
+@pytest.mark.parametrize("has_group", [False, True])
+# @pytest.mark.parametrize("has_group", [False])
+@pytest.mark.parametrize("is_rms_norm", [False, True])
+# @pytest.mark.parametrize("is_rms_norm", [True])
+@pytest.mark.parametrize("has_z", [False, True])
+# @pytest.mark.parametrize("has_z", [True])
+@pytest.mark.parametrize("has_bias", [False, True])
+# @pytest.mark.parametrize("has_bias", [False])
+# @pytest.mark.parametrize('dtype', [torch.float32, torch.float16, torch.bfloat16])
+@pytest.mark.parametrize('dtype', [torch.float16])
+# @pytest.mark.parametrize("wtype", [torch.float32, torch.float16, torch.bfloat16])
+@pytest.mark.parametrize("wtype", [torch.float32])
+@pytest.mark.parametrize('d', [2048, 4096])
+# @pytest.mark.parametrize('d', [4096])
+def test_layer_norm_gated(d, dtype, wtype, has_bias, has_z, is_rms_norm, has_group, norm_before_gate):
+    if not has_z and not norm_before_gate:
+        pytest.skip()
+    if not norm_before_gate and not is_rms_norm:  # Reference LN isn't implemented for this case yet
+        pytest.skip()
+    device = 'cuda'
+    rtol, atol = (1e-5, 1e-5) if dtype == torch.float32 else (1e-2, 8e-3)
+    group_size = None if not has_group else 64
+    # set seed
+    torch.random.manual_seed(0)
+    batch = 16
+    seqlen = 1024
+    x = torch.randn(batch, seqlen, d, dtype=dtype, device=device, requires_grad=True)
+    if has_z:
+        z = torch.randn(batch, seqlen, d, dtype=dtype, device=device, requires_grad=True)
+    else:
+        z = None
+    weight = torch.randn(d, dtype=wtype, device=device, requires_grad=True)
+    if has_bias:
+        bias = torch.randn(d, dtype=wtype, device=device, requires_grad=True)
+    else:
+        bias = None
+    x_ref = x.detach().clone().requires_grad_()
+    x_pt = x.detach().clone().requires_grad_()
+    z_ref = z.detach().clone().requires_grad_() if z is not None else None
+    z_pt = z.detach().clone().requires_grad_() if z is not None else None
+    weight_ref = weight.detach().clone().requires_grad_()
+    weight_pt = weight.detach().clone().requires_grad_()
+    bias_ref = bias.detach().clone().requires_grad_() if bias is not None else None
+    bias_pt = bias.detach().clone().requires_grad_() if bias is not None else None
+    out = layernorm_fn(x, weight, bias, z=z, eps=1e-5, group_size=group_size, norm_before_gate=norm_before_gate,
+                       is_rms_norm=is_rms_norm)
+    if not is_rms_norm:
+        if not has_group:
+            out_ref = F.layer_norm(x_ref.float(), (d,), weight=weight_ref.float(), bias=bias_ref.float() if bias_ref is not None else None, eps=1e-5)
+            out_pt = F.layer_norm(x_pt.to(wtype), (d,), weight=weight_pt, bias=bias_pt, eps=1e-5)
+        else:
+            out_ref = rearrange(F.layer_norm(rearrange(x_ref, "... (g d) -> ... g d", d=group_size).float(), (group_size,), eps=1e-5), "... g d -> ... (g d)") * weight_ref.float()
+            if has_bias:
+                out_ref = out_ref + bias_ref.float()
+            out_pt = rearrange(F.layer_norm(rearrange(x_pt, "... (g d) -> ... g d", d=group_size), (group_size,), eps=1e-5), "... g d -> ... (g d)") * weight_pt
+            if has_bias:
+                out_pt = out_pt + bias_pt
+        if has_z and norm_before_gate:
+            out_ref = out_ref * F.silu(z_ref.float())
+            out_pt = out_pt * F.silu(z_pt)
+    else:
+        out_ref = rms_norm_ref(x_ref, weight_ref, bias_ref, z=z_ref, eps=1e-5, group_size=group_size,
+                               norm_before_gate=norm_before_gate)
+        out_pt = rms_norm_ref(x_pt, weight_pt, bias_pt, z=z_pt, eps=1e-5, group_size=group_size,
+                              norm_before_gate=norm_before_gate, upcast=False)
+    print(f"Max diff = {(out - out_ref).abs().max().item()}")
+    print(f"Max diff Pytorch = {(out_pt - out_ref).abs().max().item()}")
+    assert (out - out_ref).abs().max().item() <= 2 * (out_pt - out_ref).abs().max().item() + atol
+
+    g = torch.randn_like(out)
+    out.backward(g)
+    out_ref.backward(g)
+    out_pt.backward(g)
+    print(f"Max dx diff = {(x.grad - x_ref.grad).abs().max().item()}")
+    print(f"Max dx diff Pytorch = {(x_pt.grad - x_ref.grad).abs().max().item()}")
+    if has_z:
+        print(f"Max dz diff = {(z.grad - z_ref.grad).abs().max().item()}")
+        print(f"Max dz diff Pytorch = {(z_pt.grad - z_ref.grad).abs().max().item()}")
+    print(f"Max dw diff = {(weight.grad - weight_ref.grad).abs().max().item()}")
+    print(f"Max dw diff Pytorch = {(weight_pt.grad - weight_ref.grad).abs().max().item()}")
+    if has_bias:
+        print(f"Max db diff = {(bias.grad - bias_ref.grad).abs().max().item()}")
+        print(f"Max db diff Pytorch = {(bias_pt.grad - bias_ref.grad).abs().max().item()}")
+    assert (x.grad - x_ref.grad).abs().max().item() <= 2 * (x_pt.grad - x_ref.grad).abs().max().item() + atol
+    if has_z:
+        assert (z.grad - z_ref.grad).abs().max().item() <= 2 * (z_pt.grad - z_ref.grad).abs().max().item() + atol
+    assert (weight.grad - weight_ref.grad).abs().max().item() <= 2 * (weight_pt.grad - weight_ref.grad).abs().max().item() + atol
+    if has_bias:
+        assert (bias.grad - bias_ref.grad).abs().max().item() <= 2 * (bias_pt.grad - bias_ref.grad).abs().max().item() + atol

tests/ops/triton/test_selective_state_update.py

@@ -0,0 +1,201 @@
+# Copyright (C) 2023, Tri Dao.
+
+import math
+
+import torch
+import torch.nn.functional as F
+import pytest
+
+from einops import rearrange, repeat
+
+from mamba_ssm.ops.triton.selective_state_update import selective_state_update, selective_state_update_ref
+
+
+@pytest.mark.parametrize("itype", [torch.float32, torch.float16, torch.bfloat16])
+# @pytest.mark.parametrize('itype', [torch.float16])
+@pytest.mark.parametrize("has_z", [False, True])
+# @pytest.mark.parametrize('has_z', [True])
+@pytest.mark.parametrize("dstate", [16, 32, 64])
+# @pytest.mark.parametrize("dstate", [16])
+@pytest.mark.parametrize("dim", [2048, 2048 + 16, 4096])
+# @pytest.mark.parametrize("dim", [2048])
+def test_selective_state_update(dim, dstate, has_z, itype):
+    device = "cuda"
+    rtol, atol = (3e-4, 1e-3) if itype == torch.float32 else (5e-3, 1e-2)
+    if itype == torch.bfloat16:
+        rtol, atol = 1e-2, 5e-2
+        if torch.version.hip:
+            atol *= 2
+    # set seed
+    torch.random.manual_seed(0)
+    batch_size = 2
+    state = torch.randn(batch_size, dim, dstate, dtype=itype, device=device)
+    x = torch.randn(batch_size, dim, device=device, dtype=itype)
+    dt = torch.randn(batch_size, dim, device=device, dtype=itype)
+    dt_bias = torch.rand(dim, device=device) - 4.0
+    A = -torch.rand(dim, dstate, device=device) - 1.0
+    B = torch.randn(batch_size, dstate, device=device)
+    C = torch.randn(batch_size, dstate, device=device)
+    D = torch.randn(dim, device=device)
+    if has_z:
+        z = torch.randn_like(x)
+    else:
+        z = None
+    state_ref = state.detach().clone()
+    out = selective_state_update(state, x, dt, A, B, C, D=D, z=z, dt_bias=dt_bias, dt_softplus=True)
+    out_ref = selective_state_update_ref(state_ref, x, dt, A, B, C, D=D, z=z, dt_bias=dt_bias, dt_softplus=True)
+
+    print(f"Output max diff: {(out - out_ref).abs().max().item()}")
+    print(f"Output mean diff: {(out - out_ref).abs().mean().item()}")
+    assert torch.allclose(state, state_ref, rtol=rtol, atol=atol)
+    assert torch.allclose(out, out_ref, rtol=rtol, atol=atol)
+
+
+@pytest.mark.parametrize("itype", [torch.float32, torch.float16, torch.bfloat16])
+# @pytest.mark.parametrize('itype', [torch.float16])
+@pytest.mark.parametrize("has_z", [False, True])
+# @pytest.mark.parametrize('has_z', [True])
+@pytest.mark.parametrize("tie_hdim", [False, True])
+# @pytest.mark.parametrize('tie_hdim', [True])
+@pytest.mark.parametrize("ngroups", [1, 2, 4])
+# @pytest.mark.parametrize("ngroups", [2])
+@pytest.mark.parametrize("dstate", [16, 32, 64])
+# @pytest.mark.parametrize("dstate", [16])
+@pytest.mark.parametrize("dim", [2048, 4096])
+# @pytest.mark.parametrize("dim", [2048])
+def test_selective_state_update_with_heads(dim, dstate, ngroups, has_z, tie_hdim, itype):
+    device = "cuda"
+    rtol, atol = (3e-4, 1e-3) if itype == torch.float32 else (5e-3, 3e-2)
+    if itype == torch.bfloat16:
+        rtol, atol = 1e-2, 1e-1
+    # set seed
+    torch.random.manual_seed(0)
+    batch_size = 2
+    headdim = 64
+    nheads = dim // headdim
+    state = torch.randn(batch_size, nheads, headdim, dstate, dtype=itype, device=device)
+    x = torch.randn(batch_size, nheads, headdim, device=device, dtype=itype)
+    if not tie_hdim:
+        dt = torch.randn(batch_size, nheads, headdim, device=device, dtype=itype)
+        dt_bias = torch.rand(nheads, headdim, device=device) - 4.0
+        A = -torch.rand(nheads, headdim, dstate, device=device) - 1.0
+        D = torch.randn(nheads, headdim, device=device)
+    else:
+        dt = repeat(torch.randn(batch_size, nheads, device=device, dtype=itype), "b h -> b h p", p=headdim)
+        dt_bias = repeat(torch.rand(nheads, device=device) - 4.0, "h -> h p", p=headdim)
+        A = repeat(-torch.rand(nheads, device=device) - 1.0, "h -> h p n", p=headdim, n=dstate)
+        D = repeat(torch.randn(nheads, device=device), "h -> h p", p=headdim)
+    B = torch.randn(batch_size, ngroups, dstate, device=device)
+    C = torch.randn(batch_size, ngroups, dstate, device=device)
+    if has_z:
+        z = torch.randn_like(x)
+    else:
+        z = None
+    state_ref = state.detach().clone()
+    state_og = state.detach().clone()
+    out = selective_state_update(state, x, dt, A, B, C, D=D, z=z, dt_bias=dt_bias, dt_softplus=True)
+    out_ref = selective_state_update_ref(state_ref, x, dt, A, B, C, D=D, z=z, dt_bias=dt_bias, dt_softplus=True)
+
+    print(f"Output max diff: {(out - out_ref).abs().max().item()}")
+    print(f"Output mean diff: {(out - out_ref).abs().mean().item()}")
+    assert torch.allclose(state, state_ref, rtol=rtol, atol=atol)
+    assert torch.allclose(out, out_ref, rtol=rtol, atol=atol)
+
+@pytest.mark.parametrize("itype", [torch.float32, torch.float16, torch.bfloat16])
+# @pytest.mark.parametrize('itype', [torch.float16])
+@pytest.mark.parametrize("has_z", [False, True])
+# @pytest.mark.parametrize('has_z', [True])
+@pytest.mark.parametrize("dstate", [16, 32, 64])
+# @pytest.mark.parametrize("dstate", [16])
+@pytest.mark.parametrize("dim", [2048, 2048 + 16, 4096])
+# @pytest.mark.parametrize("dim", [2048])
+def test_selective_state_update_with_batch_indices(dim, dstate, has_z, itype):
+    device = "cuda"
+    rtol, atol = (3e-4, 1e-3) if itype == torch.float32 else (5e-3, 1e-2)
+    if itype == torch.bfloat16:
+        rtol, atol = 6e-2, 6e-2
+        if torch.version.hip:
+            atol *= 2
+    # set seed
+    torch.random.manual_seed(0)
+    batch_size = 16
+
+    total_entries = 10 * batch_size
+    state = torch.randn(total_entries, dim, dstate, dtype=itype, device=device)
+    state_indices = torch.randperm(total_entries)[:batch_size].to(dtype=torch.int32, device=device)
+
+    x = torch.randn(batch_size, dim, device=device, dtype=itype)
+    dt = torch.randn(batch_size, dim, device=device, dtype=itype)
+    dt_bias = torch.rand(dim, device=device) - 4.0
+    A = -torch.rand(dim, dstate, device=device) - 1.0
+    B = torch.randn(batch_size, dstate, device=device)
+    C = torch.randn(batch_size, dstate, device=device)
+    D = torch.randn(dim, device=device)
+    if has_z:
+        z = torch.randn_like(x)
+    else:
+        z = None
+    state_ref = state[state_indices,:].detach().clone()
+    out = selective_state_update(state, x, dt, A, B, C, D=D, z=z,
+                                 dt_bias=dt_bias, dt_softplus=True, state_batch_indices=state_indices)
+    out_ref = selective_state_update_ref(state_ref, x, dt, A, B, C, D=D, z=z, dt_bias=dt_bias, dt_softplus=True)
+
+    print(f"Output max diff: {(out - out_ref).abs().max().item()}")
+    print(f"Output mean diff: {(out - out_ref).abs().mean().item()}")
+    assert torch.allclose(state[state_indices,:], state_ref, rtol=rtol, atol=atol)
+    assert torch.allclose(out, out_ref, rtol=rtol, atol=atol)
+
+
+@pytest.mark.parametrize("itype", [torch.float32, torch.float16, torch.bfloat16])
+#@pytest.mark.parametrize('itype', [torch.float32])
+@pytest.mark.parametrize("has_z", [False, True])
+# @pytest.mark.parametrize('has_z', [True])
+@pytest.mark.parametrize("tie_hdim", [False, True])
+# @pytest.mark.parametrize('tie_hdim', [True])
+@pytest.mark.parametrize("ngroups", [1, 2, 4])
+# @pytest.mark.parametrize("ngroups", [2])
+@pytest.mark.parametrize("dstate", [16, 32, 64])
+# @pytest.mark.parametrize("dstate", [16])
+@pytest.mark.parametrize("dim", [2048, 4096])
+# @pytest.mark.parametrize("dim", [2048])
+def test_selective_state_update_with_heads_with_batch_indices(dim, dstate, ngroups, has_z, tie_hdim, itype):
+    device = "cuda"
+    rtol, atol = (3e-4, 1e-3) if itype == torch.float32 else (5e-3, 3e-2)
+    if itype == torch.bfloat16:
+        rtol, atol = 1e-1, 1e-1
+    # set seed
+    torch.random.manual_seed(0)
+    batch_size = 16
+    headdim = 64
+    nheads = dim // headdim
+
+    total_entries = 10 * batch_size
+    state = torch.randn(total_entries, nheads, headdim, dstate, dtype=itype, device=device)
+    state_indices = torch.randperm(total_entries)[:batch_size].to(dtype=torch.int32, device=device)
+
+    x = torch.randn(batch_size, nheads, headdim, device=device, dtype=itype)
+    if not tie_hdim:
+        dt = torch.randn(batch_size, nheads, headdim, device=device, dtype=itype)
+        dt_bias = torch.rand(nheads, headdim, device=device) - 4.0
+        A = -torch.rand(nheads, headdim, dstate, device=device) - 1.0
+        D = torch.randn(nheads, headdim, device=device)
+    else:
+        dt = repeat(torch.randn(batch_size, nheads, device=device, dtype=itype), "b h -> b h p", p=headdim)
+        dt_bias = repeat(torch.rand(nheads, device=device) - 4.0, "h -> h p", p=headdim)
+        A = repeat(-torch.rand(nheads, device=device) - 1.0, "h -> h p n", p=headdim, n=dstate)
+        D = repeat(torch.randn(nheads, device=device), "h -> h p", p=headdim)
+    B = torch.randn(batch_size, ngroups, dstate, device=device)
+    C = torch.randn(batch_size, ngroups, dstate, device=device)
+    if has_z:
+        z = torch.randn_like(x)
+    else:
+        z = None
+    state_ref = state[state_indices,:].detach().clone()
+    state_og = state[state_indices,:].detach().clone()
+    out = selective_state_update(state, x, dt, A, B, C, D=D, z=z, dt_bias=dt_bias, dt_softplus=True, state_batch_indices=state_indices)
+    out_ref = selective_state_update_ref(state_ref, x, dt, A, B, C, D=D, z=z, dt_bias=dt_bias, dt_softplus=True)
+
+    print(f"Output max diff: {(out - out_ref).abs().max().item()}")
+    print(f"Output mean diff: {(out - out_ref).abs().mean().item()}")
+    assert torch.allclose(state[state_indices,:], state_ref, rtol=rtol, atol=atol)
+    assert torch.allclose(out, out_ref, rtol=rtol, atol=atol)

tests/ops/triton/test_ssd.py

@@ -0,0 +1,78 @@
+import math
+
+import torch
+import torch.nn.functional as F
+
+import pytest
+
+from einops import rearrange, repeat
+
+from mamba_ssm.ops.triton.ssd_chunk_state import chunk_state, chunk_state_ref
+from mamba_ssm.ops.triton.ssd_chunk_state import _chunk_cumsum_fwd, _chunk_state_fwd
+from mamba_ssm.ops.triton.ssd_chunk_state import chunk_state_varlen
+from mamba_ssm.ops.triton.ssd_state_passing import state_passing, state_passing_ref
+from mamba_ssm.ops.triton.ssd_state_passing import _state_passing_fwd
+from mamba_ssm.ops.triton.ssd_chunk_scan import chunk_scan, chunk_scan_ref
+from mamba_ssm.ops.triton.ssd_combined import mamba_chunk_scan_combined, mamba_chunk_scan, ssd_chunk_scan_combined_ref, ssd_selective_scan
+from mamba_ssm.ops.triton.ssd_combined import mamba_split_conv1d_scan_combined, mamba_split_conv1d_scan_ref
+
+
+def detach_clone(*args):
+    return tuple([arg.detach().clone().requires_grad_() if arg is not None else None for arg in args])
+
+
+@pytest.mark.parametrize('dtype', [torch.float32, torch.float16, torch.bfloat16])
+# @pytest.mark.parametrize('dtype', [torch.bfloat16])
+@pytest.mark.parametrize('ngroups', [1, 2, 8, "max"])
+# @pytest.mark.parametrize('ngroups', [1])
+@pytest.mark.parametrize('chunk_size', [64, 128])
+# @pytest.mark.parametrize('chunk_size', [128])
+def test_chunk_state_varlen(chunk_size, ngroups, dtype):
+    device = 'cuda'
+    rtol, atol = (1e-2, 3e-3)
+    # set seed
+    torch.random.manual_seed(chunk_size + (ngroups if ngroups != "max" else 64))
+    batch = 300
+    seqlens = torch.randint(1, 200, (batch,), device=device)
+    # batch = 3
+    # seqlens = torch.tensor([201, 56, 5], device=device)
+    cu_seqlens = F.pad(seqlens.cumsum(0), (1, 0))
+    total_seqlen = seqlens.sum().item()
+    seq_idx = torch.cat([torch.full((s,), i, dtype=torch.int32, device=device) for i, s in enumerate(seqlens)], dim=0).unsqueeze(0)
+    dim = 4096
+    # dim = 64
+    headdim = 64
+    # dim = 32
+    dstate = 32
+    assert dim % headdim == 0
+    nheads = dim // headdim
+    if ngroups == "max":
+        ngroups = nheads
+    assert nheads % ngroups == 0
+    B = torch.randn(total_seqlen, ngroups, dstate, dtype=dtype, device=device) / 5
+    x = torch.randn(total_seqlen, nheads, headdim, dtype=dtype, device=device)
+    A = -0.1 * (torch.rand(nheads, device=device))
+    dt = F.softplus(torch.randn(total_seqlen, nheads, device=device, dtype=torch.float32) - 4)
+    dA_cumsum, dt_rounded = _chunk_cumsum_fwd(dt.unsqueeze(0), A, chunk_size)
+    chunk_states = _chunk_state_fwd(B.unsqueeze(0), x.unsqueeze(0), dt_rounded, dA_cumsum, seq_idx=seq_idx)
+    chunk_states, _ = _state_passing_fwd(rearrange(chunk_states, "... p n -> ... (p n)"), dA_cumsum[:, :, :, -1],
+                                         seq_idx=seq_idx, chunk_size=chunk_size)
+    chunk_states = rearrange(chunk_states, "... (p n) -> ... p n", n=dstate)
+    chunk_states = chunk_states.squeeze(0)
+    dA_cumsum = dA_cumsum.squeeze(0)
+    dt_rounded = dt_rounded.squeeze(0)
+    out = chunk_state_varlen(B, x, dt_rounded, dA_cumsum, cu_seqlens, chunk_states)
+    out_ref = []
+    for b in range(batch):
+        x_s = x[cu_seqlens[b]:cu_seqlens[b + 1]].unsqueeze(0)
+        B_s = B[cu_seqlens[b]:cu_seqlens[b + 1]].unsqueeze(0)
+        dt_s = dt[cu_seqlens[b]:cu_seqlens[b + 1]].unsqueeze(0)
+        dA_cumsum_s, dt_rounded_s = _chunk_cumsum_fwd(dt_s, A, chunk_size)
+        states = chunk_state(B_s, x_s, dt_rounded_s, dA_cumsum_s)
+        _, final_states = _state_passing_fwd(rearrange(states, "... p n -> ... (p n)"), dA_cumsum_s[:, :, :, -1],
+                                             chunk_size=chunk_size)
+        final_states = rearrange(final_states, "... (p n) -> ... p n", n=dstate)
+        out_ref.append(final_states)
+    out_ref = torch.cat(out_ref, dim=0)
+    print(f"Max diff = {(out - out_ref).abs().max().item()}")
+    assert torch.allclose(out, out_ref, rtol=rtol, atol=atol)

tests/test_generation.py

@@ -0,0 +1,113 @@
+import torch
+import torch.nn.functional as F
+
+from mamba_ssm.models.mixer_seq_simple import MambaLMHeadModel
+from mamba_ssm.models.config_mamba import MambaConfig
+from mamba_ssm.utils.generation import InferenceParams
+
+import pytest
+
+from einops import rearrange, repeat
+
+
+def test_generation():
+    batch = 3
+    seqlen = 20
+    device = "cuda"
+    dtype = torch.float16
+
+    config = MambaConfig(
+        d_model=1024,
+        n_layer=4,
+        vocab_size=50277,
+        ssm_cfg=dict(layer="Mamba2"),
+        rms_norm=True,
+        residual_in_fp32=True,
+        fused_add_norm=True,
+        pad_vocab_size_multiple=16,
+    )
+    torch.manual_seed(2357)
+    model = MambaLMHeadModel(config, device=device, dtype=dtype)
+    x = torch.randint(0, 1000, (batch, seqlen), device=device, dtype=torch.long)
+    out_ref = model(x).logits
+    prompt_len = seqlen // 2
+    out = model.generate(
+        input_ids = x[:, :prompt_len], max_length=seqlen, output_scores=True, return_dict_in_generate=True,
+        cg=True,  # Can turn off CUDA graph for easier debugging
+        # instead of sampling, we take output tokens from x, to get logits for testing
+        # For actual generation, don't pass in teacher_outputs
+        teacher_outputs=x,
+    )
+    out_scores = torch.stack(out.scores, dim=1)
+    print(f"Max diff: {(out_scores - out_ref[:, prompt_len - 1: -1]).abs().max()}")
+    assert torch.allclose(out_scores, out_ref[:, prompt_len - 1: -1], rtol=1e-3, atol=1e-2)
+
+
+def test_generation_varlen():
+    seqlens = [170, 65, 100]
+    genlen = 20
+    total_seqlen = sum(seqlens)
+    device = "cuda"
+    dtype = torch.float16
+
+    config = MambaConfig(
+        d_model=1024,
+        n_layer=4,
+        vocab_size=50277,
+        ssm_cfg=dict(layer="Mamba2"),
+        rms_norm=True,
+        residual_in_fp32=True,
+        fused_add_norm=True,
+        pad_vocab_size_multiple=16,
+    )
+    torch.manual_seed(2357)
+    model = MambaLMHeadModel(config, device=device, dtype=dtype)
+    xs = [torch.randint(0, 1000, (1, seqlen), device=device, dtype=torch.long) for seqlen in seqlens]
+
+    # Reference 1: Forward pass with seq_idx
+    x = torch.cat(xs, dim=1)
+    seq_idx = torch.cat([torch.full((ids.shape[1],), i, dtype=torch.int32, device=device)
+                         for i, ids in enumerate(xs)], dim=0).unsqueeze(0)
+    cu_seqlens = F.pad(torch.tensor(seqlens, device=device, dtype=torch.int32).cumsum(dim=0), (1, 0))
+    out_ref = model(x, seq_idx=seq_idx).logits
+    # Only take the last @genlen logits of each sequence
+    out_ref = torch.cat([out_ref[:, cu_seqlens[i + 1] - genlen - 1:cu_seqlens[i + 1] - 1]
+                         for i in range(len(seqlens))], dim=0)
+
+    # Reference 2: Generate the last @genlen tokens of each sequence in a for loop
+    out_loop = []
+    for input_ids in xs:
+        out = model.generate(
+            input_ids=input_ids[:, :-genlen], max_length=input_ids.shape[1], output_scores=True,
+            return_dict_in_generate=True, cg=True, teacher_outputs=input_ids,
+        ).scores
+        out_loop.append(torch.stack(out, dim=1))
+    out_loop = torch.cat(out_loop, dim=0)
+    print(f"Max diff between ref1 and ref2: {(out_loop - out_ref).abs().max()}")
+
+    # Varlen generation
+    input_ids = torch.cat([ids[:, :-genlen] for ids in xs], dim=1)
+    prompt_seqlens = [seqlen - genlen for seqlen in seqlens]
+    cu_seqlens = F.pad(torch.tensor(prompt_seqlens, device=device, dtype=torch.int32).cumsum(dim=0), (1, 0))
+    seq_idx = torch.cat([torch.full((seqlen,), i, dtype=torch.int32, device=device)
+                         for i, seqlen in enumerate(prompt_seqlens)], dim=0).unsqueeze(0)
+    inference_params = InferenceParams(max_seqlen=2048, max_batch_size=len(seqlens))
+
+    scores, sequences = [], []
+    # Both seq_idx and cu_seqlens must be passed in for varlen generation
+    logits = model(input_ids, inference_params=inference_params, seq_idx=seq_idx, cu_seqlens=cu_seqlens).logits
+    logits = rearrange(logits[0, cu_seqlens[1:] - 1], "b d -> b 1 d")
+    scores.append(logits)
+    # In practice we should sample. In this case we take from the teacher_output for testing
+    sampled_tokens = rearrange(torch.stack([ids[0, -genlen] for ids in xs], dim=0), "b -> b 1")
+    sequences.append(sampled_tokens)
+    for i in range(1, genlen):
+        inference_params.seqlen_offset += 1
+        logits = model(sampled_tokens, inference_params=inference_params, num_last_tokens=1).logits
+        scores.append(logits)
+        # In practice we should sample. In this case we take from the teacher_output for testing
+        sampled_tokens = rearrange(torch.stack([ids[0, -genlen + i] for ids in xs], dim=0), "b -> b 1")
+        sequences.append(sampled_tokens)
+    out_varlen = torch.cat(scores, dim=1)
+    print(f"Max diff: {(out_varlen - out_ref).abs().max()}")
+    assert (out_varlen - out_ref).abs().max() < 2 * (out_loop - out_ref).abs().max()

torch-ext/mamba_ssm/__init__.py

@@ -0,0 +1,14 @@
+__version__ = "2.2.4"
+
+from .ops.selective_scan_interface import selective_scan_fn, mamba_inner_fn
+from .modules.mamba_simple import Mamba
+from .modules.mamba2 import Mamba2
+from .models.mixer_seq_simple import MambaLMHeadModel
+
+__all__ = [
+    "selective_scan_fn",
+    "mamba_inner_fn",
+    "Mamba",
+    "Mamba2",
+    "MambaLMHeadModel",
+]

torch-ext/mamba_ssm/distributed/distributed_utils.py

@@ -0,0 +1,144 @@
+from typing import Optional
+
+import torch
+from torch import Tensor
+from torch.distributed import ProcessGroup
+
+# `all_gather_into_tensor` and `reduce_scatter_tensor` are new placeholders for
+# `_all_gather_base` and `_reduce_scatter_base`. They require the most recent
+# version of PyTorch. The following 4 lines are for backward compatibility with
+# older PyTorch.
+if "all_gather_into_tensor" not in dir(torch.distributed):
+    torch.distributed.all_gather_into_tensor = torch.distributed._all_gather_base
+if "reduce_scatter_tensor" not in dir(torch.distributed):
+    torch.distributed.reduce_scatter_tensor = torch.distributed._reduce_scatter_base
+
+
+# Raw operation, does not support autograd, but does support async
+def all_gather_raw(input_: Tensor, process_group: ProcessGroup, async_op: bool = False):
+    world_size = torch.distributed.get_world_size(process_group)
+    output = torch.empty(
+        world_size * input_.shape[0], *input_.shape[1:], dtype=input_.dtype, device=input_.device
+    )
+    handle = torch.distributed.all_gather_into_tensor(
+        output, input_.contiguous(), group=process_group, async_op=async_op
+    )
+    return output, handle
+
+
+# Raw operation, does not support autograd, but does support async
+def reduce_scatter_raw(input_: Tensor, process_group: ProcessGroup, async_op: bool = False):
+    world_size = torch.distributed.get_world_size(process_group)
+    assert input_.shape[0] % world_size == 0
+    output = torch.empty(
+        input_.shape[0] // world_size, *input_.shape[1:], dtype=input_.dtype, device=input_.device
+    )
+    handle = torch.distributed.reduce_scatter_tensor(
+        output, input_.contiguous(), group=process_group, async_op=async_op
+    )
+    return output, handle
+
+
+# Raw operation, does not support autograd, but does support async
+def all_reduce_raw(input_: Tensor, process_group: ProcessGroup, async_op: bool = False):
+    input_ = input_.contiguous()
+    handle = torch.distributed.all_reduce(input_, group=process_group, async_op=async_op)
+    return input_, handle
+
+
+class AllGatherFunc(torch.autograd.Function):
+    """Gather the input from sequence parallel region and concatenate."""
+
+    @staticmethod
+    def forward(ctx, input_: Tensor, process_group: ProcessGroup) -> Tensor:
+        ctx.process_group = process_group
+        output, _ = all_gather_raw(input_, process_group)
+        return output
+
+    @staticmethod
+    def backward(ctx, grad_output: Tensor):
+        grad_input, _ = reduce_scatter_raw(grad_output, ctx.process_group)
+        return grad_input, None
+
+
+# Supports autograd, but does not support async
+all_gather = AllGatherFunc.apply
+
+
+class ReduceScatterFunc(torch.autograd.Function):
+    """Reduce scatter the input from the sequence parallel region and concatenate."""
+
+    @staticmethod
+    def forward(ctx, input_: Tensor, process_group: ProcessGroup) -> Tensor:
+        ctx.process_group = process_group
+        output, _ = reduce_scatter_raw(input_, process_group)
+        return output
+
+    @staticmethod
+    def backward(ctx, grad_output: Tensor):
+        grad_input, _ = all_gather_raw(grad_output, ctx.process_group)
+        return grad_input, None
+
+
+# Supports autograd, but does not support async
+reduce_scatter = ReduceScatterFunc.apply
+
+
+class AllReduceFunc(torch.autograd.Function):
+    """Gather the input from sequence parallel region and concatenate."""
+
+    @staticmethod
+    def forward(ctx, input_: Tensor, process_group: ProcessGroup) -> Tensor:
+        ctx.process_group = process_group
+        output, _ = all_reduce_raw(input_, process_group)
+        return output
+
+    @staticmethod
+    def backward(ctx, grad_output: Tensor):
+        return grad_output, None
+
+
+# Supports autograd, but does not support async
+all_reduce = AllReduceFunc.apply
+
+
+def sync_shared_params(model: torch.nn.Module, process_group: ProcessGroup):
+    # We want to iterate over parameters with _shared_params=True in the same order,
+    # as different ranks might have different number of parameters (e.g., only rank 0 has bias).
+    pamams_shared = {
+        name: p for name, p in model.named_parameters() if getattr(p, "_shared_params", False)
+    }
+    for _, p in sorted(pamams_shared.items()):
+        with torch.no_grad():
+            # Broadcast needs src to be global rank, not group rank
+            torch.distributed.broadcast(
+                p, src=torch.distributed.get_global_rank(process_group, 0), group=process_group
+            )
+
+
+# Ref: https://github.com/NVIDIA/Megatron-LM/blob/52e636888cccc41e931251c417a7181fc36de926/megatron/optimizer/optimizer.py#L256
+def allreduce_sequence_parallel_grad(model: torch.nn.Module, process_group: ProcessGroup):
+    # We want to iterate over parameters with _sequence_parallel=True in the same order,
+    # as different ranks might have different number of parameters (e.g., only rank 0 has bias).
+    params_seqparallel = {
+        name: p for name, p in model.named_parameters() if getattr(p, "_sequence_parallel", False)
+    }
+    grads = [p.grad for _, p in sorted(params_seqparallel.items())]
+    if grads:
+        with torch.no_grad():
+            coalesced = torch._utils._flatten_dense_tensors(grads)
+            torch.distributed.all_reduce(coalesced, group=process_group)
+            for buf, synced in zip(grads, torch._utils._unflatten_dense_tensors(coalesced, grads)):
+                buf.copy_(synced)
+
+
+def get_dim_for_local_rank(dim: int, world_size: int, local_rank: int, multiple_of: int = 1) -> int:
+    """Get the dim for the local rank derived from splitting dim on world_size processes.
+
+    The split may not be even across the world_size processes.
+    """
+    multiple = dim // multiple_of
+    div = multiple // world_size
+    mod = multiple % world_size
+    local_multiple = div + int(local_rank < mod)
+    return local_multiple * multiple_of

torch-ext/mamba_ssm/distributed/tensor_parallel.py

@@ -0,0 +1,326 @@
+# Copyright (c) 2024, Tri Dao.
+# The TensorParallel linear modules are inspired by https://github.com/NVIDIA/apex/blob/master/apex/transformer/tensor_parallel/layers.py
+from typing import Optional
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+from torch import Tensor
+from torch.distributed import ProcessGroup
+from ..utils.torch import custom_bwd, custom_fwd
+
+from einops import rearrange
+
+from ..distributed.distributed_utils import (
+    all_gather_raw,
+    all_reduce,
+    all_reduce_raw,
+    reduce_scatter,
+    reduce_scatter_raw,
+)
+
+
+class ParallelLinearFunc(torch.autograd.Function):
+    @staticmethod
+    @custom_fwd
+    def forward(ctx, x, weight, bias, process_group=None, sequence_parallel=True):
+        """
+        If process_group is not None and sequence_parallel=True, we're doing Tensor Parallel
+        with sequence parallelism: we do an all_gather_raw of x before doing the matmul.
+        """
+        ctx.compute_weight_gradient = weight.requires_grad
+        ctx.process_group = process_group
+        ctx.sequence_parallel = sequence_parallel
+
+        if torch.is_autocast_enabled():
+            x = x.to(dtype=torch.get_autocast_gpu_dtype())
+        x = x.contiguous()
+        if process_group is not None and sequence_parallel:
+            # We want to kick off the all_gather early, before weight dtype conversion
+            total_x, handle_x = all_gather_raw(x, process_group, async_op=True)
+        else:
+            total_x = x
+
+        if torch.is_autocast_enabled():
+            weight = weight.to(dtype=torch.get_autocast_gpu_dtype())
+            bias = (
+                bias.to(dtype=torch.get_autocast_gpu_dtype())
+                if bias is not None
+                else None
+            )
+        weight = weight.contiguous()
+        if process_group is not None and sequence_parallel:
+            handle_x.wait()
+        batch_shape, n = total_x.shape[:-1], total_x.shape[-1]
+        batch_dim = batch_shape.numel()
+        # https://github.com/pytorch/pytorch/blob/5b51849b48a7dbccd297286cc0110def4706f9e7/aten/src/ATen/native/cuda/Blas.cpp#L174
+        output = F.linear(total_x, weight, bias)
+        if ctx.compute_weight_gradient:
+            ctx.save_for_backward(x, weight)
+        else:
+            ctx.save_for_backward(weight)
+        return output
+
+    @staticmethod
+    @custom_bwd
+    def backward(ctx, grad_output):
+        grad_output = grad_output.contiguous()
+        process_group = ctx.process_group
+        sequence_parallel = ctx.sequence_parallel
+        if ctx.compute_weight_gradient:
+            x, weight = ctx.saved_tensors
+            if process_group is not None and sequence_parallel:
+                total_x, handle_x = all_gather_raw(x, process_group, async_op=True)
+            else:
+                total_x = x
+        else:
+            (weight,) = ctx.saved_tensors
+            total_x = None
+        batch_shape = grad_output.shape[:-1]
+        batch_dim = batch_shape.numel()
+        grad_output = grad_output.reshape(batch_dim, grad_output.shape[-1])
+        if ctx.needs_input_grad[0]:
+            grad_input = F.linear(grad_output, weight.t())
+            grad_input = grad_input.reshape(*batch_shape, grad_input.shape[-1])
+            if process_group is not None:
+                reduce_fn = reduce_scatter_raw if sequence_parallel else all_reduce_raw
+                grad_input, handle_grad_input = reduce_fn(
+                    grad_input, process_group, async_op=True
+                )
+        else:
+            grad_input = None
+        if ctx.needs_input_grad[1]:
+            assert ctx.compute_weight_gradient
+            if process_group is not None and sequence_parallel:
+                handle_x.wait()
+            grad_weight = torch.einsum(
+                "bo,bi->oi", grad_output, total_x.reshape(batch_dim, total_x.shape[-1])
+            )
+        else:
+            grad_weight = None
+        grad_bias = grad_output.sum(dim=0) if ctx.needs_input_grad[2] else None
+        if process_group is not None and ctx.needs_input_grad[0]:
+            handle_grad_input.wait()
+        return grad_input, grad_weight, grad_bias, None, None
+
+
+def parallel_linear_func(
+    x: Tensor,
+    weight: Tensor,
+    bias: Optional[Tensor] = None,
+    process_group: Optional[ProcessGroup] = None,
+    sequence_parallel: bool = True,
+):
+    return ParallelLinearFunc.apply(x, weight, bias, process_group, sequence_parallel)
+
+
+class ColumnParallelLinear(nn.Linear):
+    def __init__(
+        self,
+        in_features: int,
+        out_features: int,
+        process_group: ProcessGroup,
+        bias: bool = True,
+        sequence_parallel=True,
+        multiple_of=1,
+        device=None,
+        dtype=None,
+    ) -> None:
+        world_size = torch.distributed.get_world_size(process_group)
+        if out_features % multiple_of:
+            raise ValueError(
+                f"out_features ({out_features}) must be a multiple of {multiple_of}"
+            )
+        multiple = out_features // multiple_of
+        # We want to split @multiple across world_size, but it could be an uneven split
+        div = multiple // world_size
+        mod = multiple % world_size
+        # The first @mod ranks get @div + 1 copies, the rest get @div copies
+        local_multiple = div + int(torch.distributed.get_rank(process_group) < mod)
+        super().__init__(
+            in_features,
+            local_multiple * multiple_of,
+            bias=bias,
+            device=device,
+            dtype=dtype,
+        )
+        self.process_group = process_group
+        self.sequence_parallel = sequence_parallel
+
+    def forward(self, x):
+        # If self.sequence_parallel is True, we're doing Tensor Parallel with sequence parallelism:
+        # we do an all_gather of x before doing the matmul.
+        # If not, then the input is already gathered.
+        return parallel_linear_func(
+            x,
+            self.weight,
+            self.bias,
+            process_group=self.process_group,
+            sequence_parallel=self.sequence_parallel,
+        )
+
+
+class RowParallelLinear(nn.Linear):
+    def __init__(
+        self,
+        in_features: int,
+        out_features: int,
+        process_group: ProcessGroup,
+        bias: bool = True,
+        sequence_parallel=True,
+        multiple_of=1,
+        device=None,
+        dtype=None,
+    ) -> None:
+        world_size = torch.distributed.get_world_size(process_group)
+        rank = torch.distributed.get_rank(process_group)
+        if in_features % multiple_of:
+            raise ValueError(
+                f"in_features ({in_features}) must be a multiple of {multiple_of}"
+            )
+        multiple = in_features // multiple_of
+        # We want to split @multiple across world_size, but it could be an uneven split
+        div = multiple // world_size
+        mod = multiple % world_size
+        # The first @mod ranks get @div + 1 copies, the rest get @div copies
+        local_multiple = div + int(torch.distributed.get_rank(process_group) < mod)
+        # Only rank 0 will have bias
+        super().__init__(
+            local_multiple * multiple_of,
+            out_features,
+            bias=bias and rank == 0,
+            device=device,
+            dtype=dtype,
+        )
+        self.process_group = process_group
+        self.sequence_parallel = sequence_parallel
+
+    def forward(self, x):
+        """
+        We're doing Tensor Parallel with sequence parallelism: we do the matmul and then
+        a reduce_scatter of the result.
+        """
+        out = parallel_linear_func(x, self.weight, self.bias)
+        reduce_fn = reduce_scatter if self.sequence_parallel else all_reduce
+        return reduce_fn(out, self.process_group)
+
+
+class VocabParallelEmbedding(nn.Embedding):
+    def __init__(
+        self, num_embeddings, *args, process_group=None, padding_idx=None, **kwargs
+    ):
+        self.process_group = process_group
+        if process_group is not None:
+            world_size = torch.distributed.get_world_size(process_group)
+            if num_embeddings % world_size != 0:
+                raise ValueError(
+                    f"num_embeddings ({num_embeddings}) must be divisible by "
+                    f"world_size ({world_size})"
+                )
+            if world_size > 1 and padding_idx is not None:
+                raise RuntimeError("ParallelEmbedding does not support padding_idx")
+        else:
+            world_size = 1
+        super().__init__(
+            num_embeddings // world_size, *args, padding_idx=padding_idx, **kwargs
+        )
+
+    def forward(self, input: Tensor) -> Tensor:
+        if self.process_group is None:
+            return super().forward(input)
+        else:
+            rank = torch.distributed.get_rank(self.process_group)
+            vocab_size = self.num_embeddings
+            vocab_start_index, vocab_end_index = (
+                rank * vocab_size,
+                (rank + 1) * vocab_size,
+            )
+            # Create a mask of valid vocab ids (1 means it needs to be masked).
+            input_ids_mask = (input < vocab_start_index) | (input >= vocab_end_index)
+            input = input - vocab_start_index
+            input[input_ids_mask] = 0
+            embeddings = super().forward(input)
+            embeddings[input_ids_mask] = 0.0
+            return embeddings
+
+
+class ColumnParallelEmbedding(nn.Embedding):
+    def __init__(
+        self, num_embeddings, embedding_dim, *args, process_group=None, **kwargs
+    ):
+        self.process_group = process_group
+        if process_group is not None:
+            world_size = torch.distributed.get_world_size(process_group)
+            if embedding_dim % world_size != 0:
+                raise ValueError(
+                    f"embedding_dim ({embedding_dim}) must be divisible by "
+                    f"world_size ({world_size})"
+                )
+        else:
+            world_size = 1
+        super().__init__(num_embeddings, embedding_dim // world_size, *args, **kwargs)
+
+
+class ParallelEmbeddings(nn.Module):
+    def __init__(
+        self,
+        embed_dim,
+        vocab_size,
+        max_position_embeddings,
+        process_group,
+        padding_idx=None,
+        sequence_parallel=True,
+        device=None,
+        dtype=None,
+    ):
+        """
+        If max_position_embeddings <= 0, there's no position embeddings
+        """
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+        self.process_group = process_group
+        self.sequence_parallel = sequence_parallel
+        self.word_embeddings = VocabParallelEmbedding(
+            vocab_size,
+            embed_dim,
+            padding_idx=padding_idx,
+            process_group=process_group,
+            **factory_kwargs,
+        )
+        self.max_position_embeddings = max_position_embeddings
+        if self.max_position_embeddings > 0:
+            self.position_embeddings = ColumnParallelEmbedding(
+                max_position_embeddings,
+                embed_dim,
+                process_group=process_group,
+                **factory_kwargs,
+            )
+
+    def forward(self, input_ids, position_ids=None, combine_batch_seqlen_dim=False):
+        """
+        input_ids: (batch, seqlen)
+        position_ids: (batch, seqlen)
+        """
+        batch_size, seqlen = input_ids.shape
+        world_size = torch.distributed.get_world_size(self.process_group)
+        embeddings = self.word_embeddings(input_ids)
+        if self.max_position_embeddings > 0:
+            if position_ids is None:
+                position_ids = torch.arange(
+                    seqlen, dtype=torch.long, device=input_ids.device
+                )
+            position_embeddings = self.position_embeddings(position_ids)
+            if world_size <= 1:
+                embeddings = embeddings + position_embeddings
+            else:
+                partition_dim = self.position_embeddings.embedding_dim
+                rank = torch.distributed.get_rank(self.process_group)
+                embeddings[
+                    ..., rank * partition_dim : (rank + 1) * partition_dim
+                ] += position_embeddings
+        if combine_batch_seqlen_dim:
+            embeddings = rearrange(embeddings, "b s d -> (b s) d")
+        reduce_fn = reduce_scatter if self.sequence_parallel else all_reduce
+        return (
+            embeddings if world_size <= 1 else reduce_fn(embeddings, self.process_group)
+        )

torch-ext/mamba_ssm/models/config_mamba.py

@@ -0,0 +1,18 @@
+from dataclasses import dataclass, field
+
+
+@dataclass
+class MambaConfig:
+
+    d_model: int = 2560
+    d_intermediate: int = 0
+    n_layer: int = 64
+    vocab_size: int = 50277
+    ssm_cfg: dict = field(default_factory=dict)
+    attn_layer_idx: list = field(default_factory=list)
+    attn_cfg: dict = field(default_factory=dict)
+    rms_norm: bool = True
+    residual_in_fp32: bool = True
+    fused_add_norm: bool = True
+    pad_vocab_size_multiple: int = 8
+    tie_embeddings: bool = True

torch-ext/mamba_ssm/models/mixer_seq_simple.py

@@ -0,0 +1,338 @@
+# Copyright (c) 2023, Albert Gu, Tri Dao.
+
+import math
+from functools import partial
+import json
+import os
+import copy
+
+from collections import namedtuple
+
+import torch
+import torch.nn as nn
+
+from .config_mamba import MambaConfig
+from ..modules.mamba_simple import Mamba
+from ..modules.mamba2 import Mamba2
+from ..modules.mha import MHA
+from ..modules.mlp import GatedMLP
+from ..modules.block import Block
+from ..utils.generation import GenerationMixin
+from ..utils.hf import load_config_hf, load_state_dict_hf
+
+try:
+    from ..ops.triton.layer_norm import RMSNorm, layer_norm_fn, rms_norm_fn
+except ImportError:
+    RMSNorm, layer_norm_fn, rms_norm_fn = None, None, None
+
+
+def create_block(
+    d_model,
+    d_intermediate,
+    ssm_cfg=None,
+    attn_layer_idx=None,
+    attn_cfg=None,
+    norm_epsilon=1e-5,
+    rms_norm=False,
+    residual_in_fp32=False,
+    fused_add_norm=False,
+    layer_idx=None,
+    device=None,
+    dtype=None,
+):
+    if ssm_cfg is None:
+        ssm_cfg = {}
+    if attn_layer_idx is None:
+        attn_layer_idx = []
+    if attn_cfg is None:
+        attn_cfg = {}
+    factory_kwargs = {"device": device, "dtype": dtype}
+    if layer_idx not in attn_layer_idx:
+        # Create a copy of the config to modify
+        ssm_cfg = copy.deepcopy(ssm_cfg) if ssm_cfg is not None else {}
+        ssm_layer = ssm_cfg.pop("layer", "Mamba1")
+        if ssm_layer not in ["Mamba1", "Mamba2"]:
+            raise ValueError(
+                f"Invalid ssm_layer: {ssm_layer}, only support Mamba1 and Mamba2"
+            )
+        mixer_cls = partial(
+            Mamba2 if ssm_layer == "Mamba2" else Mamba,
+            layer_idx=layer_idx,
+            **ssm_cfg,
+            **factory_kwargs,
+        )
+    else:
+        mixer_cls = partial(MHA, layer_idx=layer_idx, **attn_cfg, **factory_kwargs)
+    norm_cls = partial(
+        nn.LayerNorm if not rms_norm else RMSNorm, eps=norm_epsilon, **factory_kwargs
+    )
+    if d_intermediate == 0:
+        mlp_cls = nn.Identity
+    else:
+        mlp_cls = partial(
+            GatedMLP,
+            hidden_features=d_intermediate,
+            out_features=d_model,
+            **factory_kwargs,
+        )
+    block = Block(
+        d_model,
+        mixer_cls,
+        mlp_cls,
+        norm_cls=norm_cls,
+        fused_add_norm=fused_add_norm,
+        residual_in_fp32=residual_in_fp32,
+    )
+    block.layer_idx = layer_idx
+    return block
+
+
+# https://github.com/huggingface/transformers/blob/c28d04e9e252a1a099944e325685f14d242ecdcd/src/transformers/models/gpt2/modeling_gpt2.py#L454
+def _init_weights(
+    module,
+    n_layer,
+    initializer_range=0.02,  # Now only used for embedding layer.
+    rescale_prenorm_residual=True,
+    n_residuals_per_layer=1,  # Change to 2 if we have MLP
+):
+    if isinstance(module, nn.Linear):
+        if module.bias is not None:
+            if not getattr(module.bias, "_no_reinit", False):
+                nn.init.zeros_(module.bias)
+    elif isinstance(module, nn.Embedding):
+        nn.init.normal_(module.weight, std=initializer_range)
+
+    if rescale_prenorm_residual:
+        # Reinitialize selected weights subject to the OpenAI GPT-2 Paper Scheme:
+        #   > A modified initialization which accounts for the accumulation on the residual path with model depth. Scale
+        #   > the weights of residual layers at initialization by a factor of 1/√N where N is the # of residual layers.
+        #   >   -- GPT-2 :: https://openai.com/blog/better-language-models/
+        #
+        # Reference (Megatron-LM): https://github.com/NVIDIA/Megatron-LM/blob/main/megatron/model/gpt_model.py
+        for name, p in module.named_parameters():
+            if name in ["out_proj.weight", "fc2.weight"]:
+                # Special Scaled Initialization --> There are 2 Layer Norms per Transformer Block
+                # Following Pytorch init, except scale by 1/sqrt(2 * n_layer)
+                # We need to reinit p since this code could be called multiple times
+                # Having just p *= scale would repeatedly scale it down
+                nn.init.kaiming_uniform_(p, a=math.sqrt(5))
+                with torch.no_grad():
+                    p /= math.sqrt(n_residuals_per_layer * n_layer)
+
+
+class MixerModel(nn.Module):
+    def __init__(
+        self,
+        d_model: int,
+        n_layer: int,
+        d_intermediate: int,
+        vocab_size: int,
+        ssm_cfg=None,
+        attn_layer_idx=None,
+        attn_cfg=None,
+        norm_epsilon: float = 1e-5,
+        rms_norm: bool = False,
+        initializer_cfg=None,
+        fused_add_norm=False,
+        residual_in_fp32=False,
+        device=None,
+        dtype=None,
+    ) -> None:
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+        self.residual_in_fp32 = residual_in_fp32
+
+        self.embedding = nn.Embedding(vocab_size, d_model, **factory_kwargs)
+
+        # We change the order of residual and layer norm:
+        # Instead of LN -> Attn / MLP -> Add, we do:
+        # Add -> LN -> Attn / MLP / Mixer, returning both the residual branch (output of Add) and
+        # the main branch (output of MLP / Mixer). The model definition is unchanged.
+        # This is for performance reason: we can fuse add + layer_norm.
+        self.fused_add_norm = fused_add_norm
+        if self.fused_add_norm:
+            if layer_norm_fn is None or rms_norm_fn is None:
+                raise ImportError("Failed to import Triton LayerNorm / RMSNorm kernels")
+
+        self.layers = nn.ModuleList(
+            [
+                create_block(
+                    d_model,
+                    d_intermediate=d_intermediate,
+                    ssm_cfg=ssm_cfg,
+                    attn_layer_idx=attn_layer_idx,
+                    attn_cfg=attn_cfg,
+                    norm_epsilon=norm_epsilon,
+                    rms_norm=rms_norm,
+                    residual_in_fp32=residual_in_fp32,
+                    fused_add_norm=fused_add_norm,
+                    layer_idx=i,
+                    **factory_kwargs,
+                )
+                for i in range(n_layer)
+            ]
+        )
+
+        self.norm_f = (nn.LayerNorm if not rms_norm else RMSNorm)(
+            d_model, eps=norm_epsilon, **factory_kwargs
+        )
+
+        self.apply(
+            partial(
+                _init_weights,
+                n_layer=n_layer,
+                **(initializer_cfg if initializer_cfg is not None else {}),
+                n_residuals_per_layer=(
+                    1 if d_intermediate == 0 else 2
+                ),  # 2 if we have MLP
+            )
+        )
+
+    def allocate_inference_cache(self, batch_size, max_seqlen, dtype=None, **kwargs):
+        return {
+            i: layer.allocate_inference_cache(
+                batch_size, max_seqlen, dtype=dtype, **kwargs
+            )
+            for i, layer in enumerate(self.layers)
+        }
+
+    def forward(self, input_ids, inference_params=None, **mixer_kwargs):
+        hidden_states = self.embedding(input_ids)
+        residual = None
+        for layer in self.layers:
+            hidden_states, residual = layer(
+                hidden_states,
+                residual,
+                inference_params=inference_params,
+                **mixer_kwargs,
+            )
+        if not self.fused_add_norm:
+            residual = (
+                (hidden_states + residual) if residual is not None else hidden_states
+            )
+            hidden_states = self.norm_f(residual.to(dtype=self.norm_f.weight.dtype))
+        else:
+            # Set prenorm=False here since we don't need the residual
+            hidden_states = layer_norm_fn(
+                hidden_states,
+                self.norm_f.weight,
+                self.norm_f.bias,
+                eps=self.norm_f.eps,
+                residual=residual,
+                prenorm=False,
+                residual_in_fp32=self.residual_in_fp32,
+                is_rms_norm=isinstance(self.norm_f, RMSNorm),
+            )
+        return hidden_states
+
+
+class MambaLMHeadModel(nn.Module, GenerationMixin):
+
+    def __init__(
+        self,
+        config: MambaConfig,
+        initializer_cfg=None,
+        device=None,
+        dtype=None,
+    ) -> None:
+        self.config = config
+        d_model = config.d_model
+        n_layer = config.n_layer
+        d_intermediate = config.d_intermediate
+        vocab_size = config.vocab_size
+        ssm_cfg = config.ssm_cfg
+        attn_layer_idx = config.attn_layer_idx
+        attn_cfg = config.attn_cfg
+        rms_norm = config.rms_norm
+        residual_in_fp32 = config.residual_in_fp32
+        fused_add_norm = config.fused_add_norm
+        pad_vocab_size_multiple = config.pad_vocab_size_multiple
+        factory_kwargs = {"device": device, "dtype": dtype}
+
+        super().__init__()
+        if vocab_size % pad_vocab_size_multiple != 0:
+            vocab_size += pad_vocab_size_multiple - (
+                vocab_size % pad_vocab_size_multiple
+            )
+        self.backbone = MixerModel(
+            d_model=d_model,
+            n_layer=n_layer,
+            d_intermediate=d_intermediate,
+            vocab_size=vocab_size,
+            ssm_cfg=ssm_cfg,
+            attn_layer_idx=attn_layer_idx,
+            attn_cfg=attn_cfg,
+            rms_norm=rms_norm,
+            initializer_cfg=initializer_cfg,
+            fused_add_norm=fused_add_norm,
+            residual_in_fp32=residual_in_fp32,
+            **factory_kwargs,
+        )
+        self.lm_head = nn.Linear(d_model, vocab_size, bias=False, **factory_kwargs)
+
+        # Initialize weights and apply final processing
+        self.apply(
+            partial(
+                _init_weights,
+                n_layer=n_layer,
+                **(initializer_cfg if initializer_cfg is not None else {}),
+            )
+        )
+        self.tie_weights()
+
+    def tie_weights(self):
+        if self.config.tie_embeddings:
+            self.lm_head.weight = self.backbone.embedding.weight
+
+    def allocate_inference_cache(self, batch_size, max_seqlen, dtype=None, **kwargs):
+        return self.backbone.allocate_inference_cache(
+            batch_size, max_seqlen, dtype=dtype, **kwargs
+        )
+
+    def forward(
+        self,
+        input_ids,
+        position_ids=None,
+        inference_params=None,
+        num_last_tokens=0,
+        **mixer_kwargs,
+    ):
+        """
+        "position_ids" is just to be compatible with Transformer generation. We don't use it.
+        num_last_tokens: if > 0, only return the logits for the last n tokens
+        """
+        hidden_states = self.backbone(
+            input_ids, inference_params=inference_params, **mixer_kwargs
+        )
+        if num_last_tokens > 0:
+            hidden_states = hidden_states[:, -num_last_tokens:]
+        lm_logits = self.lm_head(hidden_states)
+        CausalLMOutput = namedtuple("CausalLMOutput", ["logits"])
+        return CausalLMOutput(logits=lm_logits)
+
+    @classmethod
+    def from_pretrained(cls, pretrained_model_name, device=None, dtype=None, **kwargs):
+        config_data = load_config_hf(pretrained_model_name)
+        config = MambaConfig(**config_data)
+        model = cls(config, device=device, dtype=dtype, **kwargs)
+        model.load_state_dict(
+            load_state_dict_hf(pretrained_model_name, device=device, dtype=dtype)
+        )
+        return model
+
+    def save_pretrained(self, save_directory):
+        """
+        Minimal implementation of save_pretrained for MambaLMHeadModel.
+        Save the model and its configuration file to a directory.
+        """
+        # Ensure save_directory exists
+        os.makedirs(save_directory, exist_ok=True)
+
+        # Save the model's state_dict
+        model_path = os.path.join(save_directory, "pytorch_model.bin")
+        torch.save(self.state_dict(), model_path)
+
+        # Save the configuration of the model
+        config_path = os.path.join(save_directory, "config.json")
+        with open(config_path, "w") as f:
+            json.dump(self.config.__dict__, f, indent=4)

torch-ext/mamba_ssm/modules/block.py

@@ -0,0 +1,107 @@
+# Copyright (c) 2024, Tri Dao, Albert Gu.
+from typing import Optional
+
+import torch
+from torch import nn, Tensor
+
+from ..ops.triton.layer_norm import RMSNorm, layer_norm_fn
+
+
+class Block(nn.Module):
+    def __init__(
+        self,
+        dim,
+        mixer_cls,
+        mlp_cls,
+        norm_cls=nn.LayerNorm,
+        fused_add_norm=False,
+        residual_in_fp32=False,
+    ):
+        """
+        Simple block wrapping a mixer class with LayerNorm/RMSNorm and residual connection"
+
+        This Block has a slightly different structure compared to a regular
+        prenorm Transformer block.
+        The standard block is: LN -> MHA/MLP -> Add.
+        [Ref: https://arxiv.org/abs/2002.04745]
+        Here we have: Add -> LN -> Mixer, returning both
+        the hidden_states (output of the mixer) and the residual.
+        This is purely for performance reasons, as we can fuse add and LayerNorm.
+        The residual needs to be provided (except for the very first block).
+        """
+        super().__init__()
+        self.residual_in_fp32 = residual_in_fp32
+        self.fused_add_norm = fused_add_norm
+        self.norm = norm_cls(dim)
+        self.mixer = mixer_cls(dim)
+        if mlp_cls is not nn.Identity:
+            self.norm2 = norm_cls(dim)
+            self.mlp = mlp_cls(dim)
+        else:
+            self.mlp = None
+        if self.fused_add_norm:
+            assert RMSNorm is not None, "RMSNorm import fails"
+            assert isinstance(
+                self.norm, (nn.LayerNorm, RMSNorm)
+            ), "Only LayerNorm and RMSNorm are supported for fused_add_norm"
+
+    def forward(
+        self,
+        hidden_states: Tensor,
+        residual: Optional[Tensor] = None,
+        inference_params=None,
+        **mixer_kwargs
+    ):
+        r"""Pass the input through the encoder layer.
+
+        Args:
+            hidden_states: the sequence to the encoder layer (required).
+            residual: hidden_states = Mixer(LN(residual))
+        """
+        if not self.fused_add_norm:
+            residual = (
+                (hidden_states + residual) if residual is not None else hidden_states
+            )
+            hidden_states = self.norm(residual.to(dtype=self.norm.weight.dtype))
+            if self.residual_in_fp32:
+                residual = residual.to(torch.float32)
+        else:
+            hidden_states, residual = layer_norm_fn(
+                hidden_states,
+                self.norm.weight,
+                self.norm.bias,
+                residual=residual,
+                prenorm=True,
+                residual_in_fp32=self.residual_in_fp32,
+                eps=self.norm.eps,
+                is_rms_norm=isinstance(self.norm, RMSNorm),
+            )
+        hidden_states = self.mixer(
+            hidden_states, inference_params=inference_params, **mixer_kwargs
+        )
+
+        if self.mlp is not None:
+            if not self.fused_add_norm:
+                residual = hidden_states + residual
+                hidden_states = self.norm2(residual.to(dtype=self.norm2.weight.dtype))
+                if self.residual_in_fp32:
+                    residual = residual.to(torch.float32)
+            else:
+                hidden_states, residual = layer_norm_fn(
+                    hidden_states,
+                    self.norm2.weight,
+                    self.norm2.bias,
+                    residual=residual,
+                    prenorm=True,
+                    residual_in_fp32=self.residual_in_fp32,
+                    eps=self.norm2.eps,
+                    is_rms_norm=isinstance(self.norm2, RMSNorm),
+                )
+            hidden_states = self.mlp(hidden_states)
+
+        return hidden_states, residual
+
+    def allocate_inference_cache(self, batch_size, max_seqlen, dtype=None, **kwargs):
+        return self.mixer.allocate_inference_cache(
+            batch_size, max_seqlen, dtype=dtype, **kwargs
+        )

torch-ext/mamba_ssm/modules/mamba2.py

@@ -0,0 +1,502 @@
+# Copyright (c) 2024, Tri Dao, Albert Gu.
+
+import math
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+
+from einops import rearrange, repeat
+
+try:
+    from causal_conv1d import causal_conv1d_fn, causal_conv1d_update
+except ImportError:
+    causal_conv1d_fn, causal_conv1d_update = None, None
+
+try:
+    from causal_conv1d.causal_conv1d_varlen import causal_conv1d_varlen_states
+except ImportError:
+    causal_conv1d_varlen_states = None
+
+try:
+    from ..ops.triton.selective_state_update import selective_state_update
+except ImportError:
+    selective_state_update = None
+
+from ..ops.triton.layernorm_gated import RMSNorm as RMSNormGated
+
+from ..distributed.tensor_parallel import ColumnParallelLinear, RowParallelLinear
+from ..distributed.distributed_utils import all_reduce, reduce_scatter
+
+from ..ops.triton.ssd_combined import mamba_chunk_scan_combined
+from ..ops.triton.ssd_combined import mamba_split_conv1d_scan_combined
+
+from huggingface_hub import PyTorchModelHubMixin
+
+
+class Mamba2(nn.Module, PyTorchModelHubMixin):
+    def __init__(
+        self,
+        d_model,
+        d_state=128,
+        d_conv=4,
+        conv_init=None,
+        expand=2,
+        headdim=64,
+        d_ssm=None,  # If not None, we only apply SSM on this many dimensions, the rest uses gated MLP
+        ngroups=1,
+        A_init_range=(1, 16),
+        D_has_hdim=False,
+        rmsnorm=True,
+        norm_before_gate=False,
+        dt_min=0.001,
+        dt_max=0.1,
+        dt_init_floor=1e-4,
+        dt_limit=(0.0, float("inf")),
+        bias=False,
+        conv_bias=True,
+        # Fused kernel and sharding options
+        chunk_size=256,
+        use_mem_eff_path=True,
+        layer_idx=None,  # Absorb kwarg for general module
+        process_group=None,
+        sequence_parallel=True,
+        device=None,
+        dtype=None,
+    ):
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+        self.d_model = d_model
+        self.d_state = d_state
+        self.d_conv = d_conv
+        self.conv_init = conv_init
+        self.expand = expand
+        self.process_group = process_group
+        self.sequence_parallel = sequence_parallel
+        self.world_size = 1 if process_group is None else process_group.size()
+        self.local_rank = 0 if process_group is None else process_group.rank()
+        self.d_inner = (self.expand * self.d_model) // self.world_size
+        assert self.d_inner * self.world_size == self.expand * self.d_model
+        self.headdim = headdim
+        self.d_ssm = self.d_inner if d_ssm is None else d_ssm // self.world_size
+        assert ngroups % self.world_size == 0
+        self.ngroups = ngroups // self.world_size
+        assert self.d_ssm % self.headdim == 0
+        self.nheads = self.d_ssm // self.headdim
+        self.D_has_hdim = D_has_hdim
+        self.rmsnorm = rmsnorm
+        self.norm_before_gate = norm_before_gate
+        self.dt_limit = dt_limit
+        self.activation = "silu"
+        self.chunk_size = chunk_size
+        self.use_mem_eff_path = use_mem_eff_path
+        self.layer_idx = layer_idx
+
+        # Order: [z, x, B, C, dt]
+        d_in_proj = 2 * self.d_inner + 2 * self.ngroups * self.d_state + self.nheads
+        if self.process_group is None:
+            self.in_proj = nn.Linear(
+                self.d_model, d_in_proj, bias=bias, **factory_kwargs
+            )
+        else:
+            self.in_proj = ColumnParallelLinear(
+                self.d_model,
+                d_in_proj * self.world_size,
+                bias=bias,
+                process_group=self.process_group,
+                sequence_parallel=self.sequence_parallel,
+                **factory_kwargs,
+            )
+
+        conv_dim = self.d_ssm + 2 * self.ngroups * self.d_state
+        self.conv1d = nn.Conv1d(
+            in_channels=conv_dim,
+            out_channels=conv_dim,
+            bias=conv_bias,
+            kernel_size=d_conv,
+            groups=conv_dim,
+            padding=d_conv - 1,
+            **factory_kwargs,
+        )
+        if self.conv_init is not None:
+            nn.init.uniform_(self.conv1d.weight, -self.conv_init, self.conv_init)
+
+        self.act = nn.SiLU()
+
+        # Initialize log dt bias
+        dt = torch.exp(
+            torch.rand(self.nheads, **factory_kwargs)
+            * (math.log(dt_max) - math.log(dt_min))
+            + math.log(dt_min)
+        )
+        dt = torch.clamp(dt, min=dt_init_floor)
+        # Inverse of softplus: https://github.com/pytorch/pytorch/issues/72759
+        inv_dt = dt + torch.log(-torch.expm1(-dt))
+        self.dt_bias = nn.Parameter(inv_dt)
+        # Just to be explicit. Without this we already don't put wd on dt_bias because of the check
+        # name.endswith("bias") in param_grouping.py
+        self.dt_bias._no_weight_decay = True
+
+        assert A_init_range[0] > 0 and A_init_range[1] >= A_init_range[0]
+        A = torch.empty(self.nheads, dtype=torch.float32, device=device).uniform_(
+            *A_init_range
+        )
+        A_log = torch.log(A).to(dtype=dtype)
+        self.A_log = nn.Parameter(A_log)
+        self.A_log._no_weight_decay = True
+
+        # D "skip" parameter
+        self.D = nn.Parameter(
+            torch.ones(self.d_ssm if self.D_has_hdim else self.nheads, device=device)
+        )
+        self.D._no_weight_decay = True
+
+        if self.rmsnorm:
+            assert RMSNormGated is not None
+            self.norm = RMSNormGated(
+                self.d_ssm,
+                eps=1e-5,
+                norm_before_gate=self.norm_before_gate,
+                group_size=self.d_ssm // ngroups,
+                **factory_kwargs,
+            )
+
+        if self.process_group is None:
+            self.out_proj = nn.Linear(
+                self.d_inner, self.d_model, bias=bias, **factory_kwargs
+            )
+        else:
+            self.out_proj = RowParallelLinear(
+                self.d_inner * self.world_size,
+                self.d_model,
+                bias=bias,
+                process_group=self.process_group,
+                sequence_parallel=self.sequence_parallel,
+                **factory_kwargs,
+            )
+
+    def forward(
+        self, u, seqlen=None, seq_idx=None, cu_seqlens=None, inference_params=None
+    ):
+        """
+        u: (batch, seqlen, hidden_dim) if seqlen=None.
+            If seqlen is not None, u is (batch * seqlen, hidden_dim). This is so that when we
+            split u during sequence parallel, we split the batch * seqlen dimension
+            (in case batch is small).
+        Returns: same shape as u
+        """
+        seqlen_og = seqlen
+        if seqlen is None:
+            batch, seqlen, dim = u.shape
+        else:
+            batch_seqlen, dim = u.shape
+            batch = batch_seqlen // seqlen
+
+        conv_state, ssm_state = None, None
+        if inference_params is not None:
+            inference_batch = (
+                cu_seqlens.shape[0] - 1 if cu_seqlens is not None else batch
+            )
+            conv_state, ssm_state = self._get_states_from_cache(
+                inference_params, inference_batch
+            )
+            if inference_params.seqlen_offset > 0:
+                # The states are updated inplace
+                out, _, _ = self.step(u, conv_state, ssm_state)
+                return out
+
+        zxbcdt = self.in_proj(u)  # (B, L, d_in_proj) or (B * L, d_in_proj)
+        if seqlen_og is not None:
+            zxbcdt = rearrange(zxbcdt, "(b l) d -> b l d", l=seqlen)
+        # If the model is loaded in fp16, without the .float() here, A might be -inf
+        A = -torch.exp(self.A_log.float())  # (nheads) or (d_inner, d_state)
+        dt_limit_kwargs = (
+            {} if self.dt_limit == (0.0, float("inf")) else dict(dt_limit=self.dt_limit)
+        )
+        if self.use_mem_eff_path and inference_params is None:
+            out = mamba_split_conv1d_scan_combined(
+                zxbcdt,
+                rearrange(self.conv1d.weight, "d 1 w -> d w"),
+                self.conv1d.bias,
+                self.dt_bias,
+                A,
+                D=(
+                    rearrange(self.D, "(h p) -> h p", p=self.headdim)
+                    if self.D_has_hdim
+                    else self.D
+                ),
+                chunk_size=self.chunk_size,
+                seq_idx=seq_idx,
+                activation=self.activation,
+                rmsnorm_weight=self.norm.weight if self.rmsnorm else None,
+                rmsnorm_eps=self.norm.eps if self.rmsnorm else 1e-6,
+                outproj_weight=self.out_proj.weight,
+                outproj_bias=self.out_proj.bias,
+                headdim=None if self.D_has_hdim else self.headdim,
+                ngroups=self.ngroups,
+                norm_before_gate=self.norm_before_gate,
+                **dt_limit_kwargs,
+            )
+            if seqlen_og is not None:
+                out = rearrange(out, "b l d -> (b l) d")
+            if self.process_group is not None:
+                reduce_fn = reduce_scatter if self.sequence_parallel else all_reduce
+                out = reduce_fn(out, self.process_group)
+        else:
+            d_mlp = (
+                zxbcdt.shape[-1]
+                - 2 * self.d_ssm
+                - 2 * self.ngroups * self.d_state
+                - self.nheads
+            ) // 2
+            z0, x0, z, xBC, dt = torch.split(
+                zxbcdt,
+                [
+                    d_mlp,
+                    d_mlp,
+                    self.d_ssm,
+                    self.d_ssm + 2 * self.ngroups * self.d_state,
+                    self.nheads,
+                ],
+                dim=-1,
+            )
+            if conv_state is not None:
+                if cu_seqlens is None:
+                    # If we just take xBC[:, :, -self.d_conv :], it will error if seqlen < self.d_conv
+                    # Instead F.pad will pad with zeros if seqlen < self.d_conv, and truncate otherwise.
+                    xBC_t = rearrange(xBC, "b l d -> b d l")
+                    conv_state.copy_(
+                        F.pad(xBC_t, (self.d_conv - xBC_t.shape[-1], 0))
+                    )  # Update state (B D W)
+                else:
+                    assert (
+                        causal_conv1d_varlen_states is not None
+                    ), "varlen inference requires causal_conv1d package"
+                    assert (
+                        batch == 1
+                    ), "varlen inference only supports batch dimension 1"
+                    conv_varlen_states = causal_conv1d_varlen_states(
+                        xBC.squeeze(0), cu_seqlens, state_len=conv_state.shape[-1]
+                    )
+                    conv_state.copy_(conv_varlen_states)
+            assert self.activation in ["silu", "swish"]
+            if causal_conv1d_fn is None or self.activation not in ["silu", "swish"]:
+                assert (
+                    seq_idx is None
+                ), "varlen conv1d requires the causal_conv1d package"
+                xBC = self.act(
+                    self.conv1d(xBC.transpose(1, 2)).transpose(1, 2)[
+                        :, : -(self.d_conv - 1)
+                    ]
+                )  # (B, L, self.d_ssm + 2 * ngroups * d_state)
+            else:
+                xBC = causal_conv1d_fn(
+                    xBC.transpose(1, 2),
+                    rearrange(self.conv1d.weight, "d 1 w -> d w"),
+                    bias=self.conv1d.bias,
+                    activation=self.activation,
+                    seq_idx=seq_idx,
+                ).transpose(1, 2)
+            x, B, C = torch.split(
+                xBC,
+                [self.d_ssm, self.ngroups * self.d_state, self.ngroups * self.d_state],
+                dim=-1,
+            )
+            y = mamba_chunk_scan_combined(
+                rearrange(x, "b l (h p) -> b l h p", p=self.headdim),
+                dt,
+                A,
+                rearrange(B, "b l (g n) -> b l g n", g=self.ngroups),
+                rearrange(C, "b l (g n) -> b l g n", g=self.ngroups),
+                chunk_size=self.chunk_size,
+                D=(
+                    rearrange(self.D, "(h p) -> h p", p=self.headdim)
+                    if self.D_has_hdim
+                    else self.D
+                ),
+                z=(
+                    rearrange(z, "b l (h p) -> b l h p", p=self.headdim)
+                    if not self.rmsnorm
+                    else None
+                ),
+                dt_bias=self.dt_bias,
+                dt_softplus=True,
+                seq_idx=seq_idx,
+                cu_seqlens=cu_seqlens,
+                **dt_limit_kwargs,
+                return_final_states=ssm_state is not None,
+                return_varlen_states=cu_seqlens is not None
+                and inference_params is not None,
+            )
+            if ssm_state is not None:
+                y, last_state, *rest = y
+                if cu_seqlens is None:
+                    ssm_state.copy_(last_state)
+                else:
+                    varlen_states = rest[0]
+                    ssm_state.copy_(varlen_states)
+            y = rearrange(y, "b l h p -> b l (h p)")
+            if self.rmsnorm:
+                y = self.norm(y, z)
+            if d_mlp > 0:
+                y = torch.cat([F.silu(z0) * x0, y], dim=-1)
+            if seqlen_og is not None:
+                y = rearrange(y, "b l d -> (b l) d")
+            out = self.out_proj(y)
+        return out
+
+    def step(self, hidden_states, conv_state, ssm_state):
+        dtype = hidden_states.dtype
+        assert (
+            hidden_states.shape[1] == 1
+        ), "Only support decoding with 1 token at a time for now"
+        zxbcdt = self.in_proj(hidden_states.squeeze(1))  # (B 2D)
+        d_mlp = (
+            zxbcdt.shape[-1]
+            - 2 * self.d_ssm
+            - 2 * self.ngroups * self.d_state
+            - self.nheads
+        ) // 2
+        z0, x0, z, xBC, dt = torch.split(
+            zxbcdt,
+            [
+                d_mlp,
+                d_mlp,
+                self.d_ssm,
+                self.d_ssm + 2 * self.ngroups * self.d_state,
+                self.nheads,
+            ],
+            dim=-1,
+        )
+
+        # Conv step
+        if causal_conv1d_update is None:
+            conv_state.copy_(
+                torch.roll(conv_state, shifts=-1, dims=-1)
+            )  # Update state (B D W)
+            conv_state[:, :, -1] = xBC
+            xBC = torch.sum(
+                conv_state * rearrange(self.conv1d.weight, "d 1 w -> d w"), dim=-1
+            )  # (B D)
+            if self.conv1d.bias is not None:
+                xBC = xBC + self.conv1d.bias
+            xBC = self.act(xBC).to(dtype=dtype)
+        else:
+            xBC = causal_conv1d_update(
+                xBC,
+                conv_state,
+                rearrange(self.conv1d.weight, "d 1 w -> d w"),
+                self.conv1d.bias,
+                self.activation,
+            )
+
+        x, B, C = torch.split(
+            xBC,
+            [self.d_ssm, self.ngroups * self.d_state, self.ngroups * self.d_state],
+            dim=-1,
+        )
+        A = -torch.exp(self.A_log.float())  # (nheads,)
+
+        # SSM step
+        if selective_state_update is None:
+            assert (
+                self.ngroups == 1
+            ), "Only support ngroups=1 for this inference code path"
+            # Discretize A and B
+            dt = F.softplus(dt + self.dt_bias.to(dtype=dt.dtype))  # (batch, nheads)
+            dA = torch.exp(dt * A)  # (batch, nheads)
+            x = rearrange(x, "b (h p) -> b h p", p=self.headdim)
+            dBx = torch.einsum("bh,bn,bhp->bhpn", dt, B, x)
+            ssm_state.copy_(ssm_state * rearrange(dA, "b h -> b h 1 1") + dBx)
+            y = torch.einsum("bhpn,bn->bhp", ssm_state.to(dtype), C)
+            y = y + rearrange(self.D.to(dtype), "h -> h 1") * x
+            y = rearrange(y, "b h p -> b (h p)")
+            if not self.rmsnorm:
+                y = y * self.act(z)  # (B D)
+        else:
+            A = repeat(A, "h -> h p n", p=self.headdim, n=self.d_state).to(
+                dtype=torch.float32
+            )
+            dt = repeat(dt, "b h -> b h p", p=self.headdim)
+            dt_bias = repeat(self.dt_bias, "h -> h p", p=self.headdim)
+            D = repeat(self.D, "h -> h p", p=self.headdim)
+            B = rearrange(B, "b (g n) -> b g n", g=self.ngroups)
+            C = rearrange(C, "b (g n) -> b g n", g=self.ngroups)
+            x_reshaped = rearrange(x, "b (h p) -> b h p", p=self.headdim)
+            if not self.rmsnorm:
+                z = rearrange(z, "b (h p) -> b h p", p=self.headdim)
+            y = selective_state_update(
+                ssm_state,
+                x_reshaped,
+                dt,
+                A,
+                B,
+                C,
+                D,
+                z=z if not self.rmsnorm else None,
+                dt_bias=dt_bias,
+                dt_softplus=True,
+            )
+            y = rearrange(y, "b h p -> b (h p)")
+        if self.rmsnorm:
+            y = self.norm(y, z)
+        if d_mlp > 0:
+            y = torch.cat([F.silu(z0) * x0, y], dim=-1)
+        out = self.out_proj(y)
+        return out.unsqueeze(1), conv_state, ssm_state
+
+    def allocate_inference_cache(self, batch_size, max_seqlen, dtype=None, **kwargs):
+        device = self.out_proj.weight.device
+        conv_dtype = self.conv1d.weight.dtype if dtype is None else dtype
+        conv_state = torch.zeros(
+            batch_size,
+            self.d_conv,
+            self.conv1d.weight.shape[0],
+            device=device,
+            dtype=conv_dtype,
+        ).transpose(1, 2)
+        ssm_dtype = self.in_proj.weight.dtype if dtype is None else dtype
+        ssm_state = torch.zeros(
+            batch_size,
+            self.nheads,
+            self.headdim,
+            self.d_state,
+            device=device,
+            dtype=ssm_dtype,
+        )
+        return conv_state, ssm_state
+
+    def _get_states_from_cache(
+        self, inference_params, batch_size, initialize_states=False
+    ):
+        assert self.layer_idx is not None
+        if self.layer_idx not in inference_params.key_value_memory_dict:
+            batch_shape = (batch_size,)
+            conv_state = torch.zeros(
+                batch_size,
+                self.d_conv,
+                self.conv1d.weight.shape[0],
+                device=self.conv1d.weight.device,
+                dtype=self.conv1d.weight.dtype,
+            ).transpose(1, 2)
+            ssm_state = torch.zeros(
+                batch_size,
+                self.nheads,
+                self.headdim,
+                self.d_state,
+                device=self.in_proj.weight.device,
+                dtype=self.in_proj.weight.dtype,
+            )
+            inference_params.key_value_memory_dict[self.layer_idx] = (
+                conv_state,
+                ssm_state,
+            )
+        else:
+            conv_state, ssm_state = inference_params.key_value_memory_dict[
+                self.layer_idx
+            ]
+            # TODO: What if batch size changes between generation, and we reuse the same states?
+            if initialize_states:
+                conv_state.zero_()
+                ssm_state.zero_()
+        return conv_state, ssm_state

torch-ext/mamba_ssm/modules/mamba2_simple.py

@@ -0,0 +1,229 @@
+# Copyright (c) 2024, Tri Dao, Albert Gu.
+
+import math
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+
+from einops import rearrange, repeat
+
+try:
+    from causal_conv1d import causal_conv1d_fn
+except ImportError:
+    causal_conv1d_fn = None
+
+try:
+    from ..ops.triton.layernorm_gated import RMSNorm as RMSNormGated, LayerNorm
+except ImportError:
+    RMSNormGated, LayerNorm = None, None
+
+from ..ops.triton.ssd_combined import mamba_chunk_scan_combined
+from ..ops.triton.ssd_combined import mamba_split_conv1d_scan_combined
+
+
+class Mamba2Simple(nn.Module):
+    def __init__(
+        self,
+        d_model,
+        d_state=64,
+        d_conv=4,
+        conv_init=None,
+        expand=2,
+        headdim=128,
+        ngroups=1,
+        A_init_range=(1, 16),
+        dt_min=0.001,
+        dt_max=0.1,
+        dt_init_floor=1e-4,
+        dt_limit=(0.0, float("inf")),
+        learnable_init_states=False,
+        activation="swish",
+        bias=False,
+        conv_bias=True,
+        # Fused kernel and sharding options
+        chunk_size=256,
+        use_mem_eff_path=True,
+        layer_idx=None,  # Absorb kwarg for general module
+        device=None,
+        dtype=None,
+    ):
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+        self.d_model = d_model
+        self.d_state = d_state
+        self.d_conv = d_conv
+        self.conv_init = conv_init
+        self.expand = expand
+        self.d_inner = self.expand * self.d_model
+        self.headdim = headdim
+        self.ngroups = ngroups
+        assert self.d_inner % self.headdim == 0
+        self.nheads = self.d_inner // self.headdim
+        self.dt_limit = dt_limit
+        self.learnable_init_states = learnable_init_states
+        self.activation = activation
+        self.chunk_size = chunk_size
+        self.use_mem_eff_path = use_mem_eff_path
+        self.layer_idx = layer_idx
+
+        # Order: [z, x, B, C, dt]
+        d_in_proj = 2 * self.d_inner + 2 * self.ngroups * self.d_state + self.nheads
+        self.in_proj = nn.Linear(self.d_model, d_in_proj, bias=bias, **factory_kwargs)
+
+        conv_dim = self.d_inner + 2 * self.ngroups * self.d_state
+        self.conv1d = nn.Conv1d(
+            in_channels=conv_dim,
+            out_channels=conv_dim,
+            bias=conv_bias,
+            kernel_size=d_conv,
+            groups=conv_dim,
+            padding=d_conv - 1,
+            **factory_kwargs,
+        )
+        if self.conv_init is not None:
+            nn.init.uniform_(self.conv1d.weight, -self.conv_init, self.conv_init)
+        # self.conv1d.weight._no_weight_decay = True
+
+        if self.learnable_init_states:
+            self.init_states = nn.Parameter(
+                torch.zeros(self.nheads, self.headdim, self.d_state, **factory_kwargs)
+            )
+            self.init_states._no_weight_decay = True
+
+        self.act = nn.SiLU()
+
+        # Initialize log dt bias
+        dt = torch.exp(
+            torch.rand(self.nheads, **factory_kwargs)
+            * (math.log(dt_max) - math.log(dt_min))
+            + math.log(dt_min)
+        )
+        dt = torch.clamp(dt, min=dt_init_floor)
+        # Inverse of softplus: https://github.com/pytorch/pytorch/issues/72759
+        inv_dt = dt + torch.log(-torch.expm1(-dt))
+        self.dt_bias = nn.Parameter(inv_dt)
+        # Just to be explicit. Without this we already don't put wd on dt_bias because of the check
+        # name.endswith("bias") in param_grouping.py
+        self.dt_bias._no_weight_decay = True
+
+        # A parameter
+        assert A_init_range[0] > 0 and A_init_range[1] >= A_init_range[0]
+        A = torch.empty(self.nheads, dtype=torch.float32, device=device).uniform_(
+            *A_init_range
+        )
+        A_log = torch.log(A).to(dtype=dtype)
+        self.A_log = nn.Parameter(A_log)
+        # self.register_buffer("A_log", torch.zeros(self.nheads, dtype=torch.float32, device=device), persistent=True)
+        self.A_log._no_weight_decay = True
+
+        # D "skip" parameter
+        self.D = nn.Parameter(torch.ones(self.nheads, device=device))
+        self.D._no_weight_decay = True
+
+        # Extra normalization layer right before output projection
+        assert RMSNormGated is not None
+        self.norm = RMSNormGated(
+            self.d_inner, eps=1e-5, norm_before_gate=False, **factory_kwargs
+        )
+
+        self.out_proj = nn.Linear(
+            self.d_inner, self.d_model, bias=bias, **factory_kwargs
+        )
+
+    def forward(self, u, seq_idx=None):
+        """
+        u: (B, L, D)
+        Returns: same shape as u
+        """
+        batch, seqlen, dim = u.shape
+
+        zxbcdt = self.in_proj(u)  # (B, L, d_in_proj)
+        A = -torch.exp(self.A_log)  # (nheads) or (d_inner, d_state)
+        initial_states = (
+            repeat(self.init_states, "... -> b ...", b=batch)
+            if self.learnable_init_states
+            else None
+        )
+        dt_limit_kwargs = (
+            {} if self.dt_limit == (0.0, float("inf")) else dict(dt_limit=self.dt_limit)
+        )
+
+        if self.use_mem_eff_path:
+            # Fully fused path
+            out = mamba_split_conv1d_scan_combined(
+                zxbcdt,
+                rearrange(self.conv1d.weight, "d 1 w -> d w"),
+                self.conv1d.bias,
+                self.dt_bias,
+                A,
+                D=self.D,
+                chunk_size=self.chunk_size,
+                seq_idx=seq_idx,
+                activation=self.activation,
+                rmsnorm_weight=self.norm.weight,
+                rmsnorm_eps=self.norm.eps,
+                outproj_weight=self.out_proj.weight,
+                outproj_bias=self.out_proj.bias,
+                headdim=self.headdim,
+                ngroups=self.ngroups,
+                norm_before_gate=False,
+                initial_states=initial_states,
+                **dt_limit_kwargs,
+            )
+        else:
+            z, xBC, dt = torch.split(
+                zxbcdt,
+                [
+                    self.d_inner,
+                    self.d_inner + 2 * self.ngroups * self.d_state,
+                    self.nheads,
+                ],
+                dim=-1,
+            )
+            dt = F.softplus(dt + self.dt_bias)  # (B, L, nheads)
+            assert self.activation in ["silu", "swish"]
+
+            # 1D Convolution
+            if causal_conv1d_fn is None or self.activation not in ["silu", "swish"]:
+                xBC = self.act(
+                    self.conv1d(xBC.transpose(1, 2)).transpose(1, 2)
+                )  # (B, L, self.d_inner + 2 * ngroups * d_state)
+                xBC = xBC[:, :seqlen, :]
+            else:
+                xBC = causal_conv1d_fn(
+                    x=xBC.transpose(1, 2),
+                    weight=rearrange(self.conv1d.weight, "d 1 w -> d w"),
+                    bias=self.conv1d.bias,
+                    activation=self.activation,
+                ).transpose(1, 2)
+
+            # Split into 3 main branches: X, B, C
+            # These correspond to V, K, Q respectively in the SSM/attention duality
+            x, B, C = torch.split(
+                xBC,
+                [
+                    self.d_inner,
+                    self.ngroups * self.d_state,
+                    self.ngroups * self.d_state,
+                ],
+                dim=-1,
+            )
+            y = mamba_chunk_scan_combined(
+                rearrange(x, "b l (h p) -> b l h p", p=self.headdim),
+                dt,
+                A,
+                rearrange(B, "b l (g n) -> b l g n", g=self.ngroups),
+                rearrange(C, "b l (g n) -> b l g n", g=self.ngroups),
+                chunk_size=self.chunk_size,
+                D=self.D,
+                z=None,
+                seq_idx=seq_idx,
+                initial_states=initial_states,
+                **dt_limit_kwargs,
+            )
+            y = rearrange(y, "b l h p -> b l (h p)")
+
+            # Multiply "gate" branch and apply extra normalization layer
+            y = self.norm(y, z)
+            out = self.out_proj(y)
+        return out

torch-ext/mamba_ssm/modules/mamba_simple.py

@@ -0,0 +1,339 @@
+# Copyright (c) 2023, Tri Dao, Albert Gu.
+
+import math
+from typing import Optional
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+from torch import Tensor
+
+from einops import rearrange, repeat
+
+from ..ops.selective_scan_interface import selective_scan_fn, mamba_inner_fn
+
+try:
+    from causal_conv1d import causal_conv1d_fn, causal_conv1d_update
+except ImportError:
+    causal_conv1d_fn, causal_conv1d_update = None, None
+
+try:
+    from ..ops.triton.selective_state_update import selective_state_update
+except ImportError:
+    selective_state_update = None
+
+try:
+    from ..ops.triton.layer_norm import RMSNorm, layer_norm_fn, rms_norm_fn
+except ImportError:
+    RMSNorm, layer_norm_fn, rms_norm_fn = None, None, None
+
+
+class Mamba(nn.Module):
+    def __init__(
+        self,
+        d_model,
+        d_state=16,
+        d_conv=4,
+        expand=2,
+        dt_rank="auto",
+        dt_min=0.001,
+        dt_max=0.1,
+        dt_init="random",
+        dt_scale=1.0,
+        dt_init_floor=1e-4,
+        conv_bias=True,
+        bias=False,
+        use_fast_path=True,  # Fused kernel options
+        layer_idx=None,
+        device=None,
+        dtype=None,
+    ):
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+        self.d_model = d_model
+        self.d_state = d_state
+        self.d_conv = d_conv
+        self.expand = expand
+        self.d_inner = int(self.expand * self.d_model)
+        self.dt_rank = math.ceil(self.d_model / 16) if dt_rank == "auto" else dt_rank
+        self.use_fast_path = use_fast_path
+        self.layer_idx = layer_idx
+
+        self.in_proj = nn.Linear(
+            self.d_model, self.d_inner * 2, bias=bias, **factory_kwargs
+        )
+
+        self.conv1d = nn.Conv1d(
+            in_channels=self.d_inner,
+            out_channels=self.d_inner,
+            bias=conv_bias,
+            kernel_size=d_conv,
+            groups=self.d_inner,
+            padding=d_conv - 1,
+            **factory_kwargs,
+        )
+
+        self.activation = "silu"
+        self.act = nn.SiLU()
+
+        self.x_proj = nn.Linear(
+            self.d_inner, self.dt_rank + self.d_state * 2, bias=False, **factory_kwargs
+        )
+        self.dt_proj = nn.Linear(
+            self.dt_rank, self.d_inner, bias=True, **factory_kwargs
+        )
+
+        # Initialize special dt projection to preserve variance at initialization
+        dt_init_std = self.dt_rank**-0.5 * dt_scale
+        if dt_init == "constant":
+            nn.init.constant_(self.dt_proj.weight, dt_init_std)
+        elif dt_init == "random":
+            nn.init.uniform_(self.dt_proj.weight, -dt_init_std, dt_init_std)
+        else:
+            raise NotImplementedError
+
+        # Initialize dt bias so that F.softplus(dt_bias) is between dt_min and dt_max
+        dt = torch.exp(
+            torch.rand(self.d_inner, **factory_kwargs)
+            * (math.log(dt_max) - math.log(dt_min))
+            + math.log(dt_min)
+        ).clamp(min=dt_init_floor)
+        # Inverse of softplus: https://github.com/pytorch/pytorch/issues/72759
+        inv_dt = dt + torch.log(-torch.expm1(-dt))
+        with torch.no_grad():
+            self.dt_proj.bias.copy_(inv_dt)
+        # Our initialization would set all Linear.bias to zero, need to mark this one as _no_reinit
+        self.dt_proj.bias._no_reinit = True
+
+        # S4D real initialization
+        A = repeat(
+            torch.arange(1, self.d_state + 1, dtype=torch.float32, device=device),
+            "n -> d n",
+            d=self.d_inner,
+        ).contiguous()
+        A_log = torch.log(A)  # Keep A_log in fp32
+        self.A_log = nn.Parameter(A_log)
+        self.A_log._no_weight_decay = True
+
+        # D "skip" parameter
+        self.D = nn.Parameter(torch.ones(self.d_inner, device=device))  # Keep in fp32
+        self.D._no_weight_decay = True
+
+        self.out_proj = nn.Linear(
+            self.d_inner, self.d_model, bias=bias, **factory_kwargs
+        )
+
+    def forward(self, hidden_states, inference_params=None):
+        """
+        hidden_states: (B, L, D)
+        Returns: same shape as hidden_states
+        """
+        batch, seqlen, dim = hidden_states.shape
+
+        conv_state, ssm_state = None, None
+        if inference_params is not None:
+            conv_state, ssm_state = self._get_states_from_cache(inference_params, batch)
+            if inference_params.seqlen_offset > 0:
+                # The states are updated inplace
+                out, _, _ = self.step(hidden_states, conv_state, ssm_state)
+                return out
+
+        # We do matmul and transpose BLH -> HBL at the same time
+        xz = rearrange(
+            self.in_proj.weight @ rearrange(hidden_states, "b l d -> d (b l)"),
+            "d (b l) -> b d l",
+            l=seqlen,
+        )
+        if self.in_proj.bias is not None:
+            xz = xz + rearrange(self.in_proj.bias.to(dtype=xz.dtype), "d -> d 1")
+
+        A = -torch.exp(self.A_log.float())  # (d_inner, d_state)
+        # In the backward pass we write dx and dz next to each other to avoid torch.cat
+        if (
+            self.use_fast_path
+            and causal_conv1d_fn is not None
+            and inference_params is None
+        ):  # Doesn't support outputting the states
+            out = mamba_inner_fn(
+                xz,
+                self.conv1d.weight,
+                self.conv1d.bias,
+                self.x_proj.weight,
+                self.dt_proj.weight,
+                self.out_proj.weight,
+                self.out_proj.bias,
+                A,
+                None,  # input-dependent B
+                None,  # input-dependent C
+                self.D.float(),
+                delta_bias=self.dt_proj.bias.float(),
+                delta_softplus=True,
+            )
+        else:
+            x, z = xz.chunk(2, dim=1)
+            # Compute short convolution
+            if conv_state is not None:
+                # If we just take x[:, :, -self.d_conv :], it will error if seqlen < self.d_conv
+                # Instead F.pad will pad with zeros if seqlen < self.d_conv, and truncate otherwise.
+                conv_state.copy_(
+                    F.pad(x, (self.d_conv - x.shape[-1], 0))
+                )  # Update state (B D W)
+            if causal_conv1d_fn is None:
+                x = self.act(self.conv1d(x)[..., :seqlen])
+            else:
+                assert self.activation in ["silu", "swish"]
+                x = causal_conv1d_fn(
+                    x=x,
+                    weight=rearrange(self.conv1d.weight, "d 1 w -> d w"),
+                    bias=self.conv1d.bias,
+                    activation=self.activation,
+                )
+
+            # We're careful here about the layout, to avoid extra transposes.
+            # We want dt to have d as the slowest moving dimension
+            # and L as the fastest moving dimension, since those are what the ssm_scan kernel expects.
+            x_dbl = self.x_proj(rearrange(x, "b d l -> (b l) d"))  # (bl d)
+            dt, B, C = torch.split(
+                x_dbl, [self.dt_rank, self.d_state, self.d_state], dim=-1
+            )
+            dt = self.dt_proj.weight @ dt.t()
+            dt = rearrange(dt, "d (b l) -> b d l", l=seqlen)
+            B = rearrange(B, "(b l) dstate -> b dstate l", l=seqlen).contiguous()
+            C = rearrange(C, "(b l) dstate -> b dstate l", l=seqlen).contiguous()
+            assert self.activation in ["silu", "swish"]
+            y = selective_scan_fn(
+                x,
+                dt,
+                A,
+                B,
+                C,
+                self.D.float(),
+                z=z,
+                delta_bias=self.dt_proj.bias.float(),
+                delta_softplus=True,
+                return_last_state=ssm_state is not None,
+            )
+            if ssm_state is not None:
+                y, last_state = y
+                ssm_state.copy_(last_state)
+            y = rearrange(y, "b d l -> b l d")
+            out = self.out_proj(y)
+        return out
+
+    def step(self, hidden_states, conv_state, ssm_state):
+        dtype = hidden_states.dtype
+        assert (
+            hidden_states.shape[1] == 1
+        ), "Only support decoding with 1 token at a time for now"
+        xz = self.in_proj(hidden_states.squeeze(1))  # (B 2D)
+        x, z = xz.chunk(2, dim=-1)  # (B D)
+
+        # Conv step
+        if causal_conv1d_update is None:
+            conv_state.copy_(
+                torch.roll(conv_state, shifts=-1, dims=-1)
+            )  # Update state (B D W)
+            conv_state[:, :, -1] = x
+            x = torch.sum(
+                conv_state * rearrange(self.conv1d.weight, "d 1 w -> d w"), dim=-1
+            )  # (B D)
+            if self.conv1d.bias is not None:
+                x = x + self.conv1d.bias
+            x = self.act(x).to(dtype=dtype)
+        else:
+            x = causal_conv1d_update(
+                x,
+                conv_state,
+                rearrange(self.conv1d.weight, "d 1 w -> d w"),
+                self.conv1d.bias,
+                self.activation,
+            )
+
+        x_db = self.x_proj(x)  # (B dt_rank+2*d_state)
+        dt, B, C = torch.split(x_db, [self.dt_rank, self.d_state, self.d_state], dim=-1)
+        # Don't add dt_bias here
+        dt = F.linear(dt, self.dt_proj.weight)  # (B d_inner)
+        A = -torch.exp(self.A_log.float())  # (d_inner, d_state)
+
+        # SSM step
+        if selective_state_update is None:
+            # Discretize A and B
+            dt = F.softplus(dt + self.dt_proj.bias.to(dtype=dt.dtype))
+            dA = torch.exp(torch.einsum("bd,dn->bdn", dt, A))
+            dB = torch.einsum("bd,bn->bdn", dt, B)
+            ssm_state.copy_(ssm_state * dA + rearrange(x, "b d -> b d 1") * dB)
+            y = torch.einsum("bdn,bn->bd", ssm_state.to(dtype), C)
+            y = y + self.D.to(dtype) * x
+            y = y * self.act(z)  # (B D)
+        else:
+            y = selective_state_update(
+                ssm_state,
+                x,
+                dt,
+                A,
+                B,
+                C,
+                self.D,
+                z=z,
+                dt_bias=self.dt_proj.bias,
+                dt_softplus=True,
+            )
+
+        out = self.out_proj(y)
+        return out.unsqueeze(1), conv_state, ssm_state
+
+    def allocate_inference_cache(self, batch_size, max_seqlen, dtype=None, **kwargs):
+        device = self.out_proj.weight.device
+        conv_dtype = self.conv1d.weight.dtype if dtype is None else dtype
+        conv_state = torch.zeros(
+            batch_size,
+            self.d_model * self.expand,
+            self.d_conv,
+            device=device,
+            dtype=conv_dtype,
+        )
+        ssm_dtype = self.dt_proj.weight.dtype if dtype is None else dtype
+        # ssm_dtype = torch.float32
+        ssm_state = torch.zeros(
+            batch_size,
+            self.d_model * self.expand,
+            self.d_state,
+            device=device,
+            dtype=ssm_dtype,
+        )
+        return conv_state, ssm_state
+
+    def _get_states_from_cache(
+        self, inference_params, batch_size, initialize_states=False
+    ):
+        assert self.layer_idx is not None
+        if self.layer_idx not in inference_params.key_value_memory_dict:
+            batch_shape = (batch_size,)
+            conv_state = torch.zeros(
+                batch_size,
+                self.d_model * self.expand,
+                self.d_conv,
+                device=self.conv1d.weight.device,
+                dtype=self.conv1d.weight.dtype,
+            )
+            ssm_state = torch.zeros(
+                batch_size,
+                self.d_model * self.expand,
+                self.d_state,
+                device=self.dt_proj.weight.device,
+                dtype=self.dt_proj.weight.dtype,
+                # dtype=torch.float32,
+            )
+            inference_params.key_value_memory_dict[self.layer_idx] = (
+                conv_state,
+                ssm_state,
+            )
+        else:
+            conv_state, ssm_state = inference_params.key_value_memory_dict[
+                self.layer_idx
+            ]
+            # TODO: What if batch size changes between generation, and we reuse the same states?
+            if initialize_states:
+                conv_state.zero_()
+                ssm_state.zero_()
+        return conv_state, ssm_state

torch-ext/mamba_ssm/modules/mha.py

@@ -0,0 +1,294 @@
+# Copyright (c) 2024, Tri Dao, Albert Gu.
+
+import math
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+from einops import rearrange
+
+try:
+    from flash_attn import flash_attn_with_kvcache
+except ImportError:
+    flash_attn_with_kvcache = None
+
+try:
+    from flash_attn.layers.rotary import RotaryEmbedding
+except ImportError:
+    RotaryEmbedding = None
+
+try:
+    from causal_conv1d import causal_conv1d_fn, causal_conv1d_update
+except ImportError:
+    causal_conv1d_fn, causal_conv1d_update = None, None
+
+
+def _update_kv_cache(kv, inference_params, layer_idx):
+    """kv: (batch_size, seqlen, 2, nheads, head_dim) or (batch_size, 1, 2, nheads, head_dim)"""
+    # Pre-allocate memory for key-values for inference.
+    num_heads, head_dim = kv.shape[-2:]
+    assert layer_idx in inference_params.key_value_memory_dict
+    kv_cache, _ = inference_params.key_value_memory_dict[layer_idx]
+    # Adjust key and value for inference
+    batch_start = inference_params.batch_size_offset
+    batch_end = batch_start + kv.shape[0]
+    sequence_start = inference_params.seqlen_offset
+    sequence_end = sequence_start + kv.shape[1]
+    assert batch_end <= kv_cache.shape[0]
+    assert sequence_end <= kv_cache.shape[1]
+    assert kv_cache is not None
+    kv_cache[batch_start:batch_end, sequence_start:sequence_end, ...] = kv
+    return kv_cache[batch_start:batch_end, :sequence_end, ...]
+
+
+class MHA(nn.Module):
+    """Multi-head self-attention and cross-attention"""
+
+    def __init__(
+        self,
+        embed_dim,
+        num_heads,
+        num_heads_kv=None,
+        head_dim=None,  # If None, use embed_dim // num_heads
+        mlp_dim=0,
+        qkv_proj_bias=True,
+        out_proj_bias=True,
+        softmax_scale=None,
+        causal=False,
+        layer_idx=None,
+        d_conv=0,
+        rotary_emb_dim=0,
+        rotary_emb_base=10000.0,
+        rotary_emb_interleaved=False,
+        device=None,
+        dtype=None,
+    ) -> None:
+        """
+        num_heads_kv: can be used to toggle MQA / GQA. If None, use num_heads.
+        return_residual: whether to return the input x along with the output. This is for
+            performance reason: for post-norm architecture, returning the input allows us
+            to fuse the backward of nn.Linear with the residual connection.
+        """
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+        self.embed_dim = embed_dim
+        self.layer_idx = layer_idx
+        self.d_conv = d_conv
+        self.rotary_emb_dim = rotary_emb_dim
+        self.softmax_scale = softmax_scale
+        self.causal = causal
+
+        self.num_heads = num_heads
+        self.num_heads_kv = num_heads_kv if num_heads_kv is not None else num_heads
+        assert (
+            self.num_heads % self.num_heads_kv == 0
+        ), "num_heads must be divisible by num_heads_kv"
+        if head_dim is None:
+            assert self.embed_dim % num_heads == 0, "embed_dim must be divisible by num_heads"
+        self.head_dim = head_dim if head_dim is not None else self.embed_dim // num_heads
+        self.mlp_dim = math.ceil(mlp_dim / 256) * 256
+        qkv_dim = self.head_dim * (self.num_heads + 2 * self.num_heads_kv)
+        out_dim = self.head_dim * self.num_heads
+
+        if self.rotary_emb_dim > 0:
+            assert RotaryEmbedding is not None, "rotary requires flash_attn to be installed"
+            self.rotary_emb = RotaryEmbedding(
+                self.rotary_emb_dim,
+                base=rotary_emb_base,
+                interleaved=rotary_emb_interleaved,
+                device=device,
+            )
+
+        self.in_proj = nn.Linear(embed_dim, qkv_dim + self.mlp_dim, bias=qkv_proj_bias, **factory_kwargs)
+        if self.d_conv > 0:
+            self.conv1d = nn.Conv1d(
+                qkv_dim, qkv_dim, kernel_size=self.d_conv, padding=self.d_conv - 1, groups=qkv_dim,
+                **factory_kwargs
+            )
+        self.out_proj = nn.Linear(out_dim + self.mlp_dim // 2, embed_dim, bias=out_proj_bias, **factory_kwargs)
+
+    def allocate_inference_cache(self, batch_size, max_seqlen, dtype=None):
+        dtype = self.out_proj.weight.dtype if dtype is None else dtype
+        device = self.out_proj.weight.device
+        if self.d_conv > 0:
+            conv_state = torch.zeros(
+                batch_size, self.conv1d.weight.shape[0], self.d_conv, device=device, dtype=dtype
+            )
+        else:
+            conv_state = None
+        kv_cache = torch.empty(
+            batch_size, max_seqlen, 2, self.num_heads_kv, self.head_dim, dtype=dtype, device=device,
+        )
+        return kv_cache, conv_state
+
+    def _update_kv_cache(self, kv, inference_params):
+        """kv: (batch_size, seqlen, 2, nheads, head_dim) or (batch_size, 1, 2, nheads, head_dim)"""
+        assert self.layer_idx is not None, "Generation requires layer_idx in the constructor"
+        return _update_kv_cache(kv, inference_params, self.layer_idx)
+
+    def _apply_rotary_update_kvcache_attention(self, q, kv, inference_params):
+        """
+        Fast path that combine 3 steps: apply rotary to Q and K, update kv cache, and apply attention.
+        q: (batch_size, seqlen_q, nheads, head_dim)
+        kv: (batch_size, seqlen_k, 2, nheads_kv, head_dim)
+        """
+        assert inference_params is not None and inference_params.seqlen_offset > 0
+        if self.rotary_emb_dim > 0:
+            self.rotary_emb._update_cos_sin_cache(
+                inference_params.max_seqlen, device=q.device, dtype=q.dtype
+            )
+            rotary_cos, rotary_sin = self.rotary_emb._cos_cached, self.rotary_emb._sin_cached
+        else:
+            rotary_cos, rotary_sin = None, None
+        batch = q.shape[0]
+        kv_cache, _ = inference_params.key_value_memory_dict[self.layer_idx]
+        kv_cache = kv_cache[:batch]
+        cache_seqlens = (
+            inference_params.lengths_per_sample[:batch]
+            if inference_params.lengths_per_sample is not None
+            else inference_params.seqlen_offset
+        )
+        assert flash_attn_with_kvcache is not None, "flash_attn must be installed"
+        context = flash_attn_with_kvcache(
+            q,
+            kv_cache[:, :, 0],
+            kv_cache[:, :, 1],
+            kv[:, :, 0],
+            kv[:, :, 1],
+            rotary_cos=rotary_cos,
+            rotary_sin=rotary_sin,
+            cache_seqlens=cache_seqlens,
+            softmax_scale=self.softmax_scale,
+            causal=self.causal,
+            rotary_interleaved=self.rotary_emb.interleaved if self.rotary_emb_dim > 0 else False,
+        )
+        return context
+
+    def _update_kvcache_attention(self, q, kv, inference_params):
+        """Write kv to inference_params, then do attention"""
+        if (
+            inference_params.seqlen_offset == 0
+            or flash_attn_with_kvcache is None
+        ):
+            # TODO: this only uses seqlen_offset and not lengths_per_sample.
+            kv = self._update_kv_cache(kv, inference_params)
+            k, v = kv.unbind(dim=-3)
+            k = torch.repeat_interleave(k, dim=2, repeats=self.num_heads // self.num_heads_kv)
+            v = torch.repeat_interleave(v, dim=2, repeats=self.num_heads // self.num_heads_kv)
+            return F.scaled_dot_product_attention(
+                q.transpose(1, 2), k.transpose(1, 2), v.transpose(1, 2), is_causal=self.causal, scale=self.softmax_scale
+            ).transpose(1, 2)
+        else:
+            batch = q.shape[0]
+            kv_cache, _ = inference_params.key_value_memory_dict[self.layer_idx]
+            kv_cache = kv_cache[:batch]
+            cache_seqlens = (
+                inference_params.lengths_per_sample[:batch]
+                if inference_params.lengths_per_sample is not None
+                else inference_params.seqlen_offset
+            )
+            return flash_attn_with_kvcache(
+                q,
+                kv_cache[:, :, 0],
+                kv_cache[:, :, 1],
+                kv[:, :, 0],
+                kv[:, :, 1],
+                cache_seqlens=cache_seqlens,
+                softmax_scale=self.softmax_scale,
+                causal=self.causal,
+            )
+
+    def forward(self, x, inference_params=None):
+        """
+        Arguments:
+            x: (batch, seqlen, hidden_dim) (where hidden_dim = num heads * head dim) if
+                cu_seqlens is None and max_seqlen is None, else (total, hidden_dim) where total
+                is the is the sum of the sequence lengths in the batch.
+            inference_params: for generation. Adapted from Megatron-LM (and Apex)
+            https://github.com/NVIDIA/apex/blob/3ff1a10f72ec07067c4e44759442329804ac5162/apex/transformer/testing/standalone_transformer_lm.py#L470
+        """
+        if inference_params is not None and self.layer_idx not in inference_params.key_value_memory_dict:
+            inference_params.key_value_memory_dict[self.layer_idx] = self.allocate_inference_cache(
+                x.shape[0], inference_params.max_seqlen, dtype=x.dtype
+            )
+        seqlen_offset = (
+            0
+            if inference_params is None
+            else (
+                inference_params.lengths_per_sample
+                if inference_params.lengths_per_sample is not None
+                else inference_params.seqlen_offset
+            )
+        )
+        rotary_max_seqlen = inference_params.max_seqlen if inference_params is not None else None
+        qkv = self.in_proj(x)
+        if self.mlp_dim > 0:
+            qkv, x_mlp = qkv.split([qkv.shape[-1] - self.mlp_dim, self.mlp_dim], dim=-1)
+            x_mlp_up, x_mlp_gate = x_mlp.chunk(2, dim=-1)
+            x_mlp = x_mlp_up * F.silu(x_mlp_gate)
+        if self.d_conv > 0:
+            # The inference code for conv1d is pretty messy, should clean it up
+            if (inference_params is None or inference_params.seqlen_offset == 0):
+                if causal_conv1d_fn is None:
+                    qkv = rearrange(
+                        self.conv1d(rearrange(qkv, "b s d -> b d s"))[..., :-(self.d_conv - 1)], "b d s -> b s d"
+                    ).contiguous()
+                else:
+                    qkv = causal_conv1d_fn(
+                        qkv.transpose(1, 2),
+                        rearrange(self.conv1d.weight, "d 1 w -> d w"),
+                        self.conv1d.bias
+                    ).transpose(1, 2)
+                if inference_params is not None:
+                    _, conv_state = inference_params.key_value_memory_dict[self.layer_idx]
+                    # If we just take qkv[:, :, -self.d_conv :], it will error if seqlen < self.d_conv
+                    # Instead F.pad will pad with zeros if seqlen < self.d_conv, and truncate otherwise.
+                    qkv_t = rearrange(qkv, "b l d -> b d l")
+                    conv_state.copy_(F.pad(qkv_t, (self.d_conv - qkv_t.shape[-1], 0)))  # Update state (B D W)
+            else:
+                _, conv_state = inference_params.key_value_memory_dict[self.layer_idx]
+                assert qkv.shape[1] == 1, "Only support decoding with 1 token at a time for now"
+                qkv = qkv.squeeze(1)
+                # Conv step
+                if causal_conv1d_update is None:
+                    conv_state.copy_(torch.roll(conv_state, shifts=-1, dims=-1))  # Update state (B D W)
+                    conv_state[:, :, -1] = qkv
+                    qkv = torch.sum(conv_state * rearrange(self.conv1d.weight, "d 1 w -> d w"), dim=-1)  # (B D)
+                    if self.conv1d.bias is not None:
+                        qkv = qkv + self.conv1d.bias
+                else:
+                    qkv = causal_conv1d_update(
+                        qkv,
+                        conv_state,
+                        rearrange(self.conv1d.weight, "d 1 w -> d w"),
+                        self.conv1d.bias
+                    )
+                qkv = qkv.unsqueeze(1)
+        q, kv = qkv.split([self.num_heads * self.head_dim, self.num_heads_kv * 2 * self.head_dim], dim=-1)
+        q = rearrange(q, "... (h d) -> ... h d", d=self.head_dim)
+        kv = rearrange(kv, "... (two hkv d) -> ... two hkv d", two=2, d=self.head_dim)
+        if (
+            inference_params is None
+            or inference_params.seqlen_offset == 0
+            or (self.rotary_emb_dim == 0 or self.rotary_emb_dim % 16 != 0)
+        ):
+            if self.rotary_emb_dim > 0:
+                q, kv = self.rotary_emb(
+                    q, kv, seqlen_offset=seqlen_offset, max_seqlen=rotary_max_seqlen
+                )
+            if inference_params is None:
+                k, v = kv.unbind(dim=-3)
+                k = torch.repeat_interleave(k, dim=2, repeats=self.num_heads // self.num_heads_kv)
+                v = torch.repeat_interleave(v, dim=2, repeats=self.num_heads // self.num_heads_kv)
+                context = F.scaled_dot_product_attention(
+                    q.transpose(1, 2), k.transpose(1, 2), v.transpose(1, 2), is_causal=self.causal, scale=self.softmax_scale
+                ).transpose(1, 2)
+            else:
+                context = self._update_kvcache_attention(q, kv, inference_params)
+        else:
+            context = self._apply_rotary_update_kvcache_attention(q, kv, inference_params)
+        context = rearrange(context, "... h d -> ... (h d)")
+        if self.mlp_dim > 0:
+            context = torch.cat([context, x_mlp], dim=-1)
+        out = self.out_proj(context)
+        return out

torch-ext/mamba_ssm/modules/mlp.py

@@ -0,0 +1,34 @@
+# Copyright (c) 2024, Tri Dao, Albert Gu.
+from torch import nn
+from torch.nn import functional as F
+
+
+class GatedMLP(nn.Module):
+    def __init__(
+        self,
+        in_features,
+        hidden_features=None,
+        out_features=None,
+        activation=F.silu,
+        bias=False,
+        multiple_of=128,
+        device=None,
+        dtype=None,
+    ):
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+        out_features = out_features if out_features is not None else in_features
+        hidden_features = (
+            hidden_features if hidden_features is not None else int(8 * in_features / 3)
+        )
+        hidden_features = (hidden_features + multiple_of - 1) // multiple_of * multiple_of
+        self.fc1 = nn.Linear(in_features, 2 * hidden_features, bias=bias, **factory_kwargs)
+        self.activation = activation
+        self.fc2 = nn.Linear(hidden_features, out_features, bias=bias, **factory_kwargs)
+
+    def forward(self, x):
+        y = self.fc1(x)
+        y, gate = y.chunk(2, dim=-1)
+        y = y * self.activation(gate)
+        y = self.fc2(y)
+        return y

torch-ext/mamba_ssm/modules/ssd_minimal.py

@@ -0,0 +1,111 @@
+# Copyright (c) 2024, Albert Gu and Tri Dao.
+"""Minimal implementation of SSD.
+
+This is the same as Listing 1 from the paper.
+"""
+
+import torch
+import torch.nn.functional as F
+from einops import rearrange, repeat
+
+from ..ops.triton.ssd_combined import mamba_chunk_scan_combined
+
+
+def segsum_unstable(x):
+    """Naive segment sum calculation."""
+    T = x.size(-1)
+    x_cumsum = torch.cumsum(x, dim=-1)
+    x_segsum = x_cumsum[..., :, None] - x_cumsum[..., None, :]
+    mask = torch.tril(torch.ones(T, T, device=x.device, dtype=bool), diagonal=0)
+    x_segsum = x_segsum.masked_fill(~mask, -torch.inf)
+    return x_segsum
+
+
+def segsum(x):
+    """More stable segment sum calculation."""
+    T = x.size(-1)
+    x = repeat(x, "... d -> ... d e", e=T)
+    mask = torch.tril(torch.ones(T, T, device=x.device, dtype=bool), diagonal=-1)
+    x = x.masked_fill(~mask, 0)
+    x_segsum = torch.cumsum(x, dim=-2)
+    mask = torch.tril(torch.ones(T, T, device=x.device, dtype=bool), diagonal=0)
+    x_segsum = x_segsum.masked_fill(~mask, -torch.inf)
+    return x_segsum
+
+
+def ssd_minimal_discrete(X, A, B, C, block_len, initial_states=None):
+    """
+    Arguments:
+        X: (batch, length, n_heads, d_head)
+        A: (batch, length, n_heads)
+        B: (batch, length, n_heads, d_state)
+        C: (batch, length, n_heads, d_state)
+    Return:
+        Y: (batch, length, n_heads, d_head)
+    """
+    assert X.dtype == A.dtype == B.dtype == C.dtype
+    assert X.shape[1] % block_len == 0
+
+    # Rearrange into blocks/chunks
+    X, A, B, C = [
+        rearrange(x, "b (c l) ... -> b c l ...", l=block_len) for x in (X, A, B, C)
+    ]
+
+    A = rearrange(A, "b c l h -> b h c l")
+    A_cumsum = torch.cumsum(A, dim=-1)
+
+    # 1. Compute the output for each intra-chunk (diagonal blocks)
+    L = torch.exp(segsum(A))
+    Y_diag = torch.einsum("bclhn,bcshn,bhcls,bcshp->bclhp", C, B, L, X)
+
+    # 2. Compute the state for each intra-chunk
+    # (right term of low-rank factorization of off-diagonal blocks; B terms)
+    decay_states = torch.exp((A_cumsum[:, :, :, -1:] - A_cumsum))
+    states = torch.einsum("bclhn,bhcl,bclhp->bchpn", B, decay_states, X)
+
+    # 3. Compute the inter-chunk SSM recurrence; produces correct SSM states at chunk boundaries
+    # (middle term of factorization of off-diag blocks; A terms)
+    if initial_states is None:
+        initial_states = torch.zeros_like(states[:, :1])
+    states = torch.cat([initial_states, states], dim=1)
+    decay_chunk = torch.exp(segsum(F.pad(A_cumsum[:, :, :, -1], (1, 0))))
+    new_states = torch.einsum("bhzc,bchpn->bzhpn", decay_chunk, states)
+    states, final_state = new_states[:, :-1], new_states[:, -1]
+
+    # 4. Compute state -> output conversion per chunk
+    # (left term of low-rank factorization of off-diagonal blocks; C terms)
+    state_decay_out = torch.exp(A_cumsum)
+    Y_off = torch.einsum("bclhn,bchpn,bhcl->bclhp", C, states, state_decay_out)
+
+    # Add output of intra-chunk and inter-chunk terms (diagonal and off-diagonal blocks)
+    Y = rearrange(Y_diag + Y_off, "b c l h p -> b (c l) h p")
+    return Y, final_state
+
+
+# Simple test
+def test_correctness():
+    torch.manual_seed(42)
+
+    ## Dimensions
+    # Denoted (B, T, Q, D, P) in the paper
+    batch, seqlen, chunk_size, dim, headdim = 1, 2048, 64, 2048, 64
+    nheads = dim // headdim  # (H) in the paper
+    ngroups = 1  # (G) in the paper
+    dstate = 64  # (N) in the paper
+    dtype = torch.float32
+    device = "cuda"
+
+    x = torch.randn(batch, seqlen, nheads, headdim, dtype=dtype, device=device)
+    dt = F.softplus(
+        torch.randn(batch, seqlen, nheads, dtype=torch.float32, device=device) - 4
+    ).requires_grad_()
+    A = (
+        -torch.exp(torch.rand(nheads, dtype=torch.float32, device=device))
+    ).requires_grad_()
+    B = torch.randn(batch, seqlen, ngroups, dstate, dtype=dtype, device=device)
+    C = torch.randn(batch, seqlen, ngroups, dstate, dtype=dtype, device=device)
+    D = torch.randn(nheads, dtype=dtype, device=device)
+
+    # Comparing fused version and minimal version
+    y = mamba_chunk_scan_combined(x, dt, A, B, C, chunk_size, D=None)
+    y_min, _ = ssd_minimal_discrete(x * dt.unsqueeze(-1), A * dt, B, C, chunk_size)

torch-ext/mamba_ssm/ops/selective_scan_interface.py

@@ -0,0 +1,659 @@
+# Copyright (c) 2023, Tri Dao, Albert Gu.
+
+import torch
+import torch.nn.functional as F
+from ..utils.torch import custom_fwd, custom_bwd
+
+from einops import rearrange, repeat
+
+try:
+    from causal_conv1d import causal_conv1d_fn
+    import causal_conv1d_cuda
+except ImportError:
+    causal_conv1d_fn = None
+    causal_conv1d_cuda = None
+
+from .triton.layer_norm import _layer_norm_fwd
+
+from .._ops import ops
+
+
+class SelectiveScanFn(torch.autograd.Function):
+
+    @staticmethod
+    def forward(
+        ctx,
+        u,
+        delta,
+        A,
+        B,
+        C,
+        D=None,
+        z=None,
+        delta_bias=None,
+        delta_softplus=False,
+        return_last_state=False,
+    ):
+        if u.stride(-1) != 1:
+            u = u.contiguous()
+        if delta.stride(-1) != 1:
+            delta = delta.contiguous()
+        if D is not None:
+            D = D.contiguous()
+        if B.stride(-1) != 1:
+            B = B.contiguous()
+        if C.stride(-1) != 1:
+            C = C.contiguous()
+        if z is not None and z.stride(-1) != 1:
+            z = z.contiguous()
+        if B.dim() == 3:
+            B = rearrange(B, "b dstate l -> b 1 dstate l")
+            ctx.squeeze_B = True
+        if C.dim() == 3:
+            C = rearrange(C, "b dstate l -> b 1 dstate l")
+            ctx.squeeze_C = True
+        out, x, *rest = ops.selective_scan_fwd(
+            u, delta, A, B, C, D, z, delta_bias, delta_softplus
+        )
+        ctx.delta_softplus = delta_softplus
+        ctx.has_z = z is not None
+        last_state = x[:, :, -1, 1::2]  # (batch, dim, dstate)
+        if not ctx.has_z:
+            ctx.save_for_backward(u, delta, A, B, C, D, delta_bias, x)
+            return out if not return_last_state else (out, last_state)
+        else:
+            ctx.save_for_backward(u, delta, A, B, C, D, z, delta_bias, x, out)
+            out_z = rest[0]
+            return out_z if not return_last_state else (out_z, last_state)
+
+    @staticmethod
+    def backward(ctx, dout, *args):
+        if not ctx.has_z:
+            u, delta, A, B, C, D, delta_bias, x = ctx.saved_tensors
+            z = None
+            out = None
+        else:
+            u, delta, A, B, C, D, z, delta_bias, x, out = ctx.saved_tensors
+        if dout.stride(-1) != 1:
+            dout = dout.contiguous()
+        # The kernel supports passing in a pre-allocated dz (e.g., in case we want to fuse the
+        # backward of selective_scan_cuda with the backward of chunk).
+        # Here we just pass in None and dz will be allocated in the C++ code.
+        du, ddelta, dA, dB, dC, dD, ddelta_bias, *rest = ops.selective_scan_bwd(
+            u,
+            delta,
+            A,
+            B,
+            C,
+            D,
+            z,
+            delta_bias,
+            dout,
+            x,
+            out,
+            None,
+            ctx.delta_softplus,
+            False,  # option to recompute out_z, not used here
+        )
+        dz = rest[0] if ctx.has_z else None
+        dB = dB.squeeze(1) if getattr(ctx, "squeeze_B", False) else dB
+        dC = dC.squeeze(1) if getattr(ctx, "squeeze_C", False) else dC
+        return (
+            du,
+            ddelta,
+            dA,
+            dB,
+            dC,
+            dD if D is not None else None,
+            dz,
+            ddelta_bias if delta_bias is not None else None,
+            None,
+            None,
+        )
+
+
+def rms_norm_forward(
+    x,
+    weight,
+    bias,
+    eps=1e-6,
+    is_rms_norm=True,
+):
+    # x (b l) d
+    if x.stride(-1) != 1:
+        x = x.contiguous()
+    weight = weight.contiguous()
+    if bias is not None:
+        bias = bias.contiguous()
+    y = _layer_norm_fwd(
+        x, weight, bias, eps, None, residual_dtype=None, is_rms_norm=is_rms_norm
+    )[0]
+    # y (b l) d
+    return y
+
+
+def selective_scan_fn(
+    u,
+    delta,
+    A,
+    B,
+    C,
+    D=None,
+    z=None,
+    delta_bias=None,
+    delta_softplus=False,
+    return_last_state=False,
+):
+    """if return_last_state is True, returns (out, last_state)
+    last_state has shape (batch, dim, dstate). Note that the gradient of the last state is
+    not considered in the backward pass.
+    """
+    return SelectiveScanFn.apply(
+        u, delta, A, B, C, D, z, delta_bias, delta_softplus, return_last_state
+    )
+
+
+def selective_scan_ref(
+    u,
+    delta,
+    A,
+    B,
+    C,
+    D=None,
+    z=None,
+    delta_bias=None,
+    delta_softplus=False,
+    return_last_state=False,
+):
+    """
+    u: r(B D L)
+    delta: r(B D L)
+    A: c(D N) or r(D N)
+    B: c(D N) or r(B N L) or r(B N 2L) or r(B G N L) or (B G N L)
+    C: c(D N) or r(B N L) or r(B N 2L) or r(B G N L) or (B G N L)
+    D: r(D)
+    z: r(B D L)
+    delta_bias: r(D), fp32
+
+    out: r(B D L)
+    last_state (optional): r(B D dstate) or c(B D dstate)
+    """
+    dtype_in = u.dtype
+    u = u.float()
+    delta = delta.float()
+    if delta_bias is not None:
+        delta = delta + delta_bias[..., None].float()
+    if delta_softplus:
+        delta = F.softplus(delta)
+    batch, dim, dstate = u.shape[0], A.shape[0], A.shape[1]
+    is_variable_B = B.dim() >= 3
+    is_variable_C = C.dim() >= 3
+    if A.is_complex():
+        if is_variable_B:
+            B = torch.view_as_complex(
+                rearrange(B.float(), "... (L two) -> ... L two", two=2)
+            )
+        if is_variable_C:
+            C = torch.view_as_complex(
+                rearrange(C.float(), "... (L two) -> ... L two", two=2)
+            )
+    else:
+        B = B.float()
+        C = C.float()
+    x = A.new_zeros((batch, dim, dstate))
+    ys = []
+    deltaA = torch.exp(torch.einsum("bdl,dn->bdln", delta, A))
+    if not is_variable_B:
+        deltaB_u = torch.einsum("bdl,dn,bdl->bdln", delta, B, u)
+    else:
+        if B.dim() == 3:
+            deltaB_u = torch.einsum("bdl,bnl,bdl->bdln", delta, B, u)
+        else:
+            B = repeat(B, "B G N L -> B (G H) N L", H=dim // B.shape[1])
+            deltaB_u = torch.einsum("bdl,bdnl,bdl->bdln", delta, B, u)
+    if is_variable_C and C.dim() == 4:
+        C = repeat(C, "B G N L -> B (G H) N L", H=dim // C.shape[1])
+    last_state = None
+    for i in range(u.shape[2]):
+        x = deltaA[:, :, i] * x + deltaB_u[:, :, i]
+        if not is_variable_C:
+            y = torch.einsum("bdn,dn->bd", x, C)
+        else:
+            if C.dim() == 3:
+                y = torch.einsum("bdn,bn->bd", x, C[:, :, i])
+            else:
+                y = torch.einsum("bdn,bdn->bd", x, C[:, :, :, i])
+        if i == u.shape[2] - 1:
+            last_state = x
+        if y.is_complex():
+            y = y.real * 2
+        ys.append(y)
+    y = torch.stack(ys, dim=2)  # (batch dim L)
+    out = y if D is None else y + u * rearrange(D, "d -> d 1")
+    if z is not None:
+        out = out * F.silu(z)
+    out = out.to(dtype=dtype_in)
+    return out if not return_last_state else (out, last_state)
+
+
+class MambaInnerFn(torch.autograd.Function):
+
+    @staticmethod
+    @custom_fwd
+    def forward(
+        ctx,
+        xz,
+        conv1d_weight,
+        conv1d_bias,
+        x_proj_weight,
+        delta_proj_weight,
+        out_proj_weight,
+        out_proj_bias,
+        A,
+        B=None,
+        C=None,
+        D=None,
+        delta_bias=None,
+        B_proj_bias=None,
+        C_proj_bias=None,
+        delta_softplus=True,
+        checkpoint_lvl=1,
+        b_rms_weight=None,
+        c_rms_weight=None,
+        dt_rms_weight=None,
+        b_c_dt_rms_eps=1e-6,
+    ):
+        """
+        xz: (batch, dim, seqlen)
+        """
+        assert (
+            causal_conv1d_cuda is not None
+        ), "causal_conv1d_cuda is not available. Please install causal-conv1d."
+        assert checkpoint_lvl in [0, 1]
+        L = xz.shape[-1]
+        delta_rank = delta_proj_weight.shape[1]
+        d_state = A.shape[-1] * (1 if not A.is_complex() else 2)
+        if torch.is_autocast_enabled():
+            x_proj_weight = x_proj_weight.to(dtype=torch.get_autocast_gpu_dtype())
+            delta_proj_weight = delta_proj_weight.to(
+                dtype=torch.get_autocast_gpu_dtype()
+            )
+            out_proj_weight = out_proj_weight.to(dtype=torch.get_autocast_gpu_dtype())
+            out_proj_bias = (
+                out_proj_bias.to(dtype=torch.get_autocast_gpu_dtype())
+                if out_proj_bias is not None
+                else None
+            )
+        if xz.stride(-1) != 1:
+            xz = xz.contiguous()
+        conv1d_weight = rearrange(conv1d_weight, "d 1 w -> d w")
+        x, z = xz.chunk(2, dim=1)
+        conv1d_bias = conv1d_bias.contiguous() if conv1d_bias is not None else None
+        conv1d_out = causal_conv1d_cuda.causal_conv1d_fwd(
+            x, conv1d_weight, conv1d_bias, None, None, None, True
+        )
+        # We're being very careful here about the layout, to avoid extra transposes.
+        # We want delta to have d as the slowest moving dimension
+        # and L as the fastest moving dimension, since those are what the ssm_scan kernel expects.
+        x_dbl = F.linear(
+            rearrange(conv1d_out, "b d l -> (b l) d"), x_proj_weight
+        )  # (bl d)
+        delta = rearrange(
+            delta_proj_weight @ x_dbl[:, :delta_rank].t(), "d (b l) -> b d l", l=L
+        )
+        ctx.is_variable_B = B is None
+        ctx.is_variable_C = C is None
+        ctx.B_proj_bias_is_None = B_proj_bias is None
+        ctx.C_proj_bias_is_None = C_proj_bias is None
+        if B is None:  # variable B
+            B = x_dbl[:, delta_rank : delta_rank + d_state]  # (bl dstate)
+            if B_proj_bias is not None:
+                B = B + B_proj_bias.to(dtype=B.dtype)
+            if not A.is_complex():
+                # B = rearrange(B, "(b l) dstate -> b dstate l", l=L).contiguous()
+                B = rearrange(B, "(b l) dstate -> b 1 dstate l", l=L).contiguous()
+            else:
+                B = rearrange(
+                    B, "(b l) (dstate two) -> b 1 dstate (l two)", l=L, two=2
+                ).contiguous()
+        else:
+            if B.stride(-1) != 1:
+                B = B.contiguous()
+        if C is None:  # variable C
+            C = x_dbl[:, -d_state:]  # (bl dstate)
+            if C_proj_bias is not None:
+                C = C + C_proj_bias.to(dtype=C.dtype)
+            if not A.is_complex():
+                # C = rearrange(C, "(b l) dstate -> b dstate l", l=L).contiguous()
+                C = rearrange(C, "(b l) dstate -> b 1 dstate l", l=L).contiguous()
+            else:
+                C = rearrange(
+                    C, "(b l) (dstate two) -> b 1 dstate (l two)", l=L, two=2
+                ).contiguous()
+        else:
+            if C.stride(-1) != 1:
+                C = C.contiguous()
+        if D is not None:
+            D = D.contiguous()
+
+        if b_rms_weight is not None:
+            B = rearrange(B, "b 1 dstate l -> (b l) dstate", l=L).contiguous()
+            B = rms_norm_forward(B, b_rms_weight, bias=None, eps=b_c_dt_rms_eps)
+            B = rearrange(B, "(b l) dstate -> b 1 dstate l", l=L).contiguous()
+        if c_rms_weight is not None:
+            C = rearrange(C, "b 1 dstate l -> (b l) dstate", l=L).contiguous()
+            C = rms_norm_forward(C, c_rms_weight, bias=None, eps=b_c_dt_rms_eps)
+            C = rearrange(C, "(b l) dstate -> b 1 dstate l", l=L).contiguous()
+        if dt_rms_weight is not None:
+            delta = rearrange(delta, "b d l -> (b l) d", l=L).contiguous()
+            delta = rms_norm_forward(
+                delta, dt_rms_weight, bias=None, eps=b_c_dt_rms_eps
+            )
+            delta = rearrange(delta, "(b l) d -> b d l", l=L).contiguous()
+
+        out, scan_intermediates, out_z = ops.selective_scan_fwd(
+            conv1d_out, delta, A, B, C, D, z, delta_bias, delta_softplus
+        )
+        ctx.delta_softplus = delta_softplus
+        ctx.out_proj_bias_is_None = out_proj_bias is None
+        ctx.checkpoint_lvl = checkpoint_lvl
+        ctx.b_rms_weight = b_rms_weight
+        ctx.c_rms_weight = c_rms_weight
+        ctx.dt_rms_weight = dt_rms_weight
+        ctx.b_c_dt_rms_eps = b_c_dt_rms_eps
+        if (
+            checkpoint_lvl >= 1
+        ):  # Will recompute conv1d_out and delta in the backward pass
+            conv1d_out, delta = None, None
+        ctx.save_for_backward(
+            xz,
+            conv1d_weight,
+            conv1d_bias,
+            x_dbl,
+            x_proj_weight,
+            delta_proj_weight,
+            out_proj_weight,
+            conv1d_out,
+            delta,
+            A,
+            B,
+            C,
+            D,
+            delta_bias,
+            scan_intermediates,
+            b_rms_weight,
+            c_rms_weight,
+            dt_rms_weight,
+            out,
+        )
+        return F.linear(
+            rearrange(out_z, "b d l -> b l d"), out_proj_weight, out_proj_bias
+        )
+
+    @staticmethod
+    @custom_bwd
+    def backward(ctx, dout):
+        # dout: (batch, seqlen, dim)
+        assert (
+            causal_conv1d_cuda is not None
+        ), "causal_conv1d_cuda is not available. Please install causal-conv1d."
+        (
+            xz,
+            conv1d_weight,
+            conv1d_bias,
+            x_dbl,
+            x_proj_weight,
+            delta_proj_weight,
+            out_proj_weight,
+            conv1d_out,
+            delta,
+            A,
+            B,
+            C,
+            D,
+            delta_bias,
+            scan_intermediates,
+            b_rms_weight,
+            c_rms_weight,
+            dt_rms_weight,
+            out,
+        ) = ctx.saved_tensors
+        L = xz.shape[-1]
+        delta_rank = delta_proj_weight.shape[1]
+        d_state = A.shape[-1] * (1 if not A.is_complex() else 2)
+        x, z = xz.chunk(2, dim=1)
+        if dout.stride(-1) != 1:
+            dout = dout.contiguous()
+        if ctx.checkpoint_lvl == 1:
+            conv1d_out = causal_conv1d_cuda.causal_conv1d_fwd(
+                x, conv1d_weight, conv1d_bias, None, None, None, True
+            )
+            delta = rearrange(
+                delta_proj_weight @ x_dbl[:, :delta_rank].t(), "d (b l) -> b d l", l=L
+            )
+            if dt_rms_weight is not None:
+                delta = rearrange(delta, "b d l -> (b l) d", l=L).contiguous()
+                delta = rms_norm_forward(
+                    delta, ctx.dt_rms_weight, None, ctx.b_c_dt_rms_eps
+                )
+                delta = rearrange(delta, "(b l) d -> b d l", l=L).contiguous()
+            if b_rms_weight is not None:
+                # Recompute & RMSNorm B
+                B = rearrange(B, "b 1 dstate l -> (b l) dstate", l=L).contiguous()
+                B = rms_norm_forward(B, ctx.b_rms_weight, None, ctx.b_c_dt_rms_eps)
+                B = rearrange(B, "(b l) dstate -> b 1 dstate l", l=L).contiguous()
+            if c_rms_weight is not None:
+                # Recompute & RMSNorm C
+                C = rearrange(C, "b 1 dstate l -> (b l) dstate", l=L).contiguous()
+                C = rms_norm_forward(C, ctx.c_rms_weight, None, ctx.b_c_dt_rms_eps)
+                C = rearrange(C, "(b l) dstate -> b 1 dstate l", l=L).contiguous()
+
+        # The kernel supports passing in a pre-allocated dz (e.g., in case we want to fuse the
+        # backward of selective_scan_cuda with the backward of chunk).
+        dxz = torch.empty_like(xz)  # (batch, dim, seqlen)
+        dx, dz = dxz.chunk(2, dim=1)
+        dout = rearrange(dout, "b l e -> e (b l)")
+        dout_y = rearrange(out_proj_weight.t() @ dout, "d (b l) -> b d l", l=L)
+        dconv1d_out, ddelta, dA, dB, dC, dD, ddelta_bias, dz, out_z = (
+            ops.selective_scan_bwd(
+                conv1d_out,
+                delta,
+                A,
+                B,
+                C,
+                D,
+                z,
+                delta_bias,
+                dout_y,
+                scan_intermediates,
+                out,
+                dz,
+                ctx.delta_softplus,
+                True,  # option to recompute out_z
+            )
+        )
+        dout_proj_weight = torch.einsum(
+            "eB,dB->ed", dout, rearrange(out_z, "b d l -> d (b l)")
+        )
+        dout_proj_bias = dout.sum(dim=(0, 1)) if not ctx.out_proj_bias_is_None else None
+        dD = dD if D is not None else None
+        dx_dbl = torch.empty_like(x_dbl)
+        dB_proj_bias = None
+        if ctx.is_variable_B:
+            if not A.is_complex():
+                dB = rearrange(dB, "b 1 dstate l -> (b l) dstate").contiguous()
+            else:
+                dB = rearrange(
+                    dB, "b 1 dstate (l two) -> (b l) (dstate two)", two=2
+                ).contiguous()
+            dB_proj_bias = dB.sum(0) if not ctx.B_proj_bias_is_None else None
+            dx_dbl[:, delta_rank : delta_rank + d_state] = dB  # (bl d)
+            dB = None
+        dC_proj_bias = None
+        if ctx.is_variable_C:
+            if not A.is_complex():
+                dC = rearrange(dC, "b 1 dstate l -> (b l) dstate").contiguous()
+            else:
+                dC = rearrange(
+                    dC, "b 1 dstate (l two) -> (b l) (dstate two)", two=2
+                ).contiguous()
+            dC_proj_bias = dC.sum(0) if not ctx.C_proj_bias_is_None else None
+            dx_dbl[:, -d_state:] = dC  # (bl d)
+            dC = None
+        ddelta = rearrange(ddelta, "b d l -> d (b l)")
+        ddelta_proj_weight = torch.einsum("dB,Br->dr", ddelta, x_dbl[:, :delta_rank])
+        dx_dbl[:, :delta_rank] = torch.einsum("dB,dr->Br", ddelta, delta_proj_weight)
+        dconv1d_out = rearrange(dconv1d_out, "b d l -> d (b l)")
+        dx_proj_weight = torch.einsum(
+            "Br,Bd->rd", dx_dbl, rearrange(conv1d_out, "b d l -> (b l) d")
+        )
+        dconv1d_out = torch.addmm(
+            dconv1d_out, x_proj_weight.t(), dx_dbl.t(), out=dconv1d_out
+        )
+        dconv1d_out = rearrange(
+            dconv1d_out, "d (b l) -> b d l", b=x.shape[0], l=x.shape[-1]
+        )
+        # The kernel supports passing in a pre-allocated dx (e.g., in case we want to fuse the
+        # backward of conv1d with the backward of chunk).
+        dx, dconv1d_weight, dconv1d_bias, *_ = causal_conv1d_cuda.causal_conv1d_bwd(
+            x,
+            conv1d_weight,
+            conv1d_bias,
+            dconv1d_out,
+            None,
+            None,
+            None,
+            dx,
+            False,
+            True,
+        )
+        dconv1d_bias = dconv1d_bias if conv1d_bias is not None else None
+        dconv1d_weight = rearrange(dconv1d_weight, "d w -> d 1 w")
+        return (
+            dxz,
+            dconv1d_weight,
+            dconv1d_bias,
+            dx_proj_weight,
+            ddelta_proj_weight,
+            dout_proj_weight,
+            dout_proj_bias,
+            dA,
+            dB,
+            dC,
+            dD,
+            ddelta_bias if delta_bias is not None else None,
+            # 6-None are delta_softplus, checkpoint_lvl, b_rms_weight, c_rms_weight, dt_rms_weight, b_c_dt_rms_eps
+            dB_proj_bias,
+            dC_proj_bias,
+            None,
+            None,
+            None,
+            None,
+            None,
+            None,
+        )
+
+
+def mamba_inner_fn(
+    xz,
+    conv1d_weight,
+    conv1d_bias,
+    x_proj_weight,
+    delta_proj_weight,
+    out_proj_weight,
+    out_proj_bias,
+    A,
+    B=None,
+    C=None,
+    D=None,
+    delta_bias=None,
+    B_proj_bias=None,
+    C_proj_bias=None,
+    delta_softplus=True,
+    checkpoint_lvl=1,
+    b_rms_weight=None,
+    c_rms_weight=None,
+    dt_rms_weight=None,
+    b_c_dt_rms_eps=1e-6,
+):
+    return MambaInnerFn.apply(
+        xz,
+        conv1d_weight,
+        conv1d_bias,
+        x_proj_weight,
+        delta_proj_weight,
+        out_proj_weight,
+        out_proj_bias,
+        A,
+        B,
+        C,
+        D,
+        delta_bias,
+        B_proj_bias,
+        C_proj_bias,
+        delta_softplus,
+        checkpoint_lvl,
+        b_rms_weight,
+        c_rms_weight,
+        dt_rms_weight,
+        b_c_dt_rms_eps,
+    )
+
+
+def mamba_inner_ref(
+    xz,
+    conv1d_weight,
+    conv1d_bias,
+    x_proj_weight,
+    delta_proj_weight,
+    out_proj_weight,
+    out_proj_bias,
+    A,
+    B=None,
+    C=None,
+    D=None,
+    delta_bias=None,
+    B_proj_bias=None,
+    C_proj_bias=None,
+    delta_softplus=True,
+):
+    assert (
+        causal_conv1d_fn is not None
+    ), "causal_conv1d_fn is not available. Please install causal-conv1d."
+    L = xz.shape[-1]
+    delta_rank = delta_proj_weight.shape[1]
+    d_state = A.shape[-1] * (1 if not A.is_complex() else 2)
+    x, z = xz.chunk(2, dim=1)
+    x = causal_conv1d_fn(
+        x, rearrange(conv1d_weight, "d 1 w -> d w"), conv1d_bias, activation="silu"
+    )
+    # We're being very careful here about the layout, to avoid extra transposes.
+    # We want delta to have d as the slowest moving dimension
+    # and L as the fastest moving dimension, since those are what the ssm_scan kernel expects.
+    x_dbl = F.linear(rearrange(x, "b d l -> (b l) d"), x_proj_weight)  # (bl d)
+    delta = delta_proj_weight @ x_dbl[:, :delta_rank].t()
+    delta = rearrange(delta, "d (b l) -> b d l", l=L)
+    if B is None:  # variable B
+        B = x_dbl[:, delta_rank : delta_rank + d_state]  # (bl d)
+        if B_proj_bias is not None:
+            B = B + B_proj_bias.to(dtype=B.dtype)
+        if not A.is_complex():
+            B = rearrange(B, "(b l) dstate -> b dstate l", l=L).contiguous()
+        else:
+            B = rearrange(
+                B, "(b l) (dstate two) -> b dstate (l two)", l=L, two=2
+            ).contiguous()
+    if C is None:  # variable B
+        C = x_dbl[:, -d_state:]  # (bl d)
+        if C_proj_bias is not None:
+            C = C + C_proj_bias.to(dtype=C.dtype)
+        if not A.is_complex():
+            C = rearrange(C, "(b l) dstate -> b dstate l", l=L).contiguous()
+        else:
+            C = rearrange(
+                C, "(b l) (dstate two) -> b dstate (l two)", l=L, two=2
+            ).contiguous()
+    y = selective_scan_fn(
+        x, delta, A, B, C, D, z=z, delta_bias=delta_bias, delta_softplus=True
+    )
+    return F.linear(rearrange(y, "b d l -> b l d"), out_proj_weight, out_proj_bias)

torch-ext/mamba_ssm/ops/triton/k_activations.py

@@ -0,0 +1,169 @@
+# Copyright (c) 2024, Tri Dao, Albert Gu.
+
+import torch
+
+import triton
+import triton.language as tl
+
+
+@triton.autotune(
+    configs=[
+        triton.Config({'BLOCK_N': 32}),
+        triton.Config({'BLOCK_N': 64}),
+        triton.Config({'BLOCK_N': 128}),
+        triton.Config({'BLOCK_N': 256}),
+        triton.Config({'BLOCK_N': 512}),
+        triton.Config({'BLOCK_N': 1024}),
+    ],
+    key=['ncols'],
+)
+@triton.jit
+def _swiglu_fwd_kernel(
+    X,
+    Y,
+    OUT,
+    stride_x_row,  # how much to increase the pointer when moving by 1 row
+    stride_y_row,
+    stride_out_row,
+    ncols,
+    BLOCK_N: tl.constexpr,
+):
+    # Map the program id to the row of X and Y it should compute.
+    row = tl.program_id(0)
+    start_col = tl.program_id(1) * BLOCK_N
+    X += row * stride_x_row
+    Y += row * stride_y_row
+    OUT += row * stride_out_row
+    cols = start_col + tl.arange(0, BLOCK_N)
+    x = tl.load(X + cols, mask=cols < ncols, other=0.).to(tl.float32)
+    y = tl.load(Y + cols, mask=cols < ncols, other=0.).to(tl.float32)
+    out = x * tl.sigmoid(x) * y
+    tl.store(OUT + cols, out, mask=cols < ncols)
+
+
+def _swiglu_fwd(xy, out=None):
+    if xy.stride(-1) != 1:
+        xy = xy.contiguous()
+    batch_shape = xy.shape[:-1]
+    xy = xy.reshape(-1, xy.shape[-1])
+    x, y = xy.chunk(2, dim=-1)
+    if out is None:
+        out = torch.empty_like(x)
+    else:
+        out = out.reshape(-1, out.shape[-1])
+        assert out.shape == x.shape
+    assert out.stride(-1) == 1
+    M, N = x.shape
+    grid = lambda META: (M, triton.cdiv(N, META['BLOCK_N']))
+    with torch.cuda.device(x.device.index):
+        _swiglu_fwd_kernel[grid](x, y, out, x.stride(0), y.stride(0), out.stride(0), N)
+    return out.reshape(*batch_shape, out.shape[-1])
+
+
+@triton.autotune(
+    configs=[
+        triton.Config({'BLOCK_N': 32}),
+        triton.Config({'BLOCK_N': 64}),
+        triton.Config({'BLOCK_N': 128}),
+        triton.Config({'BLOCK_N': 256}),
+        triton.Config({'BLOCK_N': 512}),
+        triton.Config({'BLOCK_N': 1024}),
+    ],
+    key=['ncols'],
+)
+@triton.heuristics({"RECOMPUTE_OUTPUT": lambda args: args["OUT"] is not None})
+@triton.jit
+def _swiglu_bwd_kernel(
+    X,
+    Y,
+    DOUT,
+    OUT,
+    DX,
+    DY,
+    stride_x_row,  # how much to increase the pointer when moving by 1 row
+    stride_y_row,
+    stride_dout_row,
+    stride_out_row,
+    stride_dx_row,
+    stride_dy_row,
+    ncols,
+    BLOCK_N: tl.constexpr,
+    RECOMPUTE_OUTPUT: tl.constexpr,
+):
+    # Map the program id to the row of X and Y it should compute.
+    row = tl.program_id(0)
+    start_col = tl.program_id(1) * BLOCK_N
+    X += row * stride_x_row
+    Y += row * stride_y_row
+    DOUT += row * stride_dout_row
+    if RECOMPUTE_OUTPUT:
+        OUT += row * stride_out_row
+    DX += row * stride_dx_row
+    DY += row * stride_dy_row
+    cols = start_col + tl.arange(0, BLOCK_N)
+    x = tl.load(X + cols, mask=cols < ncols, other=0.).to(tl.float32)
+    y = tl.load(Y + cols, mask=cols < ncols, other=0.).to(tl.float32)
+    dout = tl.load(DOUT + cols, mask=cols < ncols, other=0.).to(tl.float32)
+    x_sigmoid = tl.sigmoid(x)
+    dx = x_sigmoid * (1 + x * (1 - x_sigmoid)) * y * dout
+    dy = x * x_sigmoid * dout
+    tl.store(DX + cols, dx, mask=cols < ncols)
+    tl.store(DY + cols, dy, mask=cols < ncols)
+    if RECOMPUTE_OUTPUT:
+        out = x * x_sigmoid * y
+        tl.store(OUT + cols, out, mask=cols < ncols)
+
+
+def _swiglu_bwd(xy, dout, dxy=None, recompute_output=False, out=None):
+    if xy.stride(-1) != 1:
+        xy = xy.contiguous()
+    if dout.stride(-1) != 1:
+        dout = dout.contiguous()
+    batch_shape = xy.shape[:-1]
+    xy = xy.reshape(-1, xy.shape[-1])
+    x, y = xy.chunk(2, dim=-1)
+    dout = dout.reshape(-1, dout.shape[-1])
+    assert dout.shape == x.shape
+    if dxy is None:
+        dxy = torch.empty_like(xy)
+    else:
+        dxy = dxy.reshape(-1, dxy.shape[-1])
+        assert dxy.shape == xy.shape
+    dx, dy = dxy.chunk(2, dim=-1)
+    assert dx.stride(-1) == 1
+    assert dy.stride(-1) == 1
+    if recompute_output:
+        if out is None:
+            out = torch.empty_like(x)
+        else:
+            out = out.reshape(-1, out.shape[-1])
+            assert out.shape == x.shape
+        assert out.stride(-1) == 1
+    M, N = x.shape
+    grid = lambda META: (M, triton.cdiv(N, META['BLOCK_N']))
+    with torch.cuda.device(x.device.index):
+        _swiglu_bwd_kernel[grid](x, y, dout, out if recompute_output else None, dx, dy,
+                                 x.stride(0), y.stride(0), dout.stride(0),
+                                 out.stride(0) if recompute_output else 0,
+                                 dx.stride(0), dy.stride(0),
+                                 N)
+    if not recompute_output:
+        return dxy.reshape(*batch_shape, dxy.shape[-1])
+    else:
+        return dxy.reshape(*batch_shape, dxy.shape[-1]), out.reshape(*batch_shape, out.shape[-1])
+
+
+class SwiGLU(torch.autograd.Function):
+
+    @staticmethod
+    def forward(ctx, xy):
+        ctx.save_for_backward(xy)
+        return _swiglu_fwd(xy)
+
+    @staticmethod
+    def backward(ctx, dout):
+        xy, = ctx.saved_tensors
+        return _swiglu_bwd(xy, dout)
+
+
+swiglu = SwiGLU.apply

torch-ext/mamba_ssm/ops/triton/layer_norm.py

@@ -0,0 +1,1166 @@
+# Copyright (c) 2024, Tri Dao.
+# Implement dropout + residual + layer_norm / rms_norm.
+
+# Based on the Triton LayerNorm tutorial: https://triton-lang.org/main/getting-started/tutorials/05-layer-norm.html
+# For the backward pass, we keep weight_grad and bias_grad in registers and accumulate.
+# This is faster for dimensions up to 8k, but after that it's much slower due to register spilling.
+# The models we train have hidden dim up to 8k anyway (e.g. Llama 70B), so this is fine.
+
+import math
+import warnings
+
+import torch
+import torch.nn.functional as F
+from ...utils.torch import custom_bwd, custom_fwd
+
+import triton
+import triton.language as tl
+
+
+def layer_norm_ref(
+    x,
+    weight,
+    bias,
+    residual=None,
+    x1=None,
+    weight1=None,
+    bias1=None,
+    eps=1e-6,
+    dropout_p=0.0,
+    rowscale=None,
+    prenorm=False,
+    dropout_mask=None,
+    dropout_mask1=None,
+    upcast=False,
+):
+    dtype = x.dtype
+    if upcast:
+        x = x.float()
+        weight = weight.float()
+        bias = bias.float() if bias is not None else None
+        residual = residual.float() if residual is not None else residual
+        x1 = x1.float() if x1 is not None else None
+        weight1 = weight1.float() if weight1 is not None else None
+        bias1 = bias1.float() if bias1 is not None else None
+    if x1 is not None:
+        assert rowscale is None, "rowscale is not supported with parallel LayerNorm"
+    if rowscale is not None:
+        x = x * rowscale[..., None]
+    if dropout_p > 0.0:
+        if dropout_mask is not None:
+            x = x.masked_fill(~dropout_mask, 0.0) / (1.0 - dropout_p)
+        else:
+            x = F.dropout(x, p=dropout_p)
+        if x1 is not None:
+            if dropout_mask1 is not None:
+                x1 = x1.masked_fill(~dropout_mask1, 0.0) / (1.0 - dropout_p)
+            else:
+                x1 = F.dropout(x1, p=dropout_p)
+    if x1 is not None:
+        x = x + x1
+    if residual is not None:
+        x = (x + residual).to(x.dtype)
+    out = F.layer_norm(
+        x.to(weight.dtype), x.shape[-1:], weight=weight, bias=bias, eps=eps
+    ).to(dtype)
+    if weight1 is None:
+        return out if not prenorm else (out, x)
+    else:
+        out1 = F.layer_norm(
+            x.to(weight1.dtype), x.shape[-1:], weight=weight1, bias=bias1, eps=eps
+        ).to(dtype)
+        return (out, out1) if not prenorm else (out, out1, x)
+
+
+def rms_norm_ref(
+    x,
+    weight,
+    bias,
+    residual=None,
+    x1=None,
+    weight1=None,
+    bias1=None,
+    eps=1e-6,
+    dropout_p=0.0,
+    rowscale=None,
+    prenorm=False,
+    dropout_mask=None,
+    dropout_mask1=None,
+    upcast=False,
+):
+    dtype = x.dtype
+    if upcast:
+        x = x.float()
+        weight = weight.float()
+        bias = bias.float() if bias is not None else None
+        residual = residual.float() if residual is not None else residual
+        x1 = x1.float() if x1 is not None else None
+        weight1 = weight1.float() if weight1 is not None else None
+        bias1 = bias1.float() if bias1 is not None else None
+    if x1 is not None:
+        assert rowscale is None, "rowscale is not supported with parallel LayerNorm"
+    if rowscale is not None:
+        x = x * rowscale[..., None]
+    if dropout_p > 0.0:
+        if dropout_mask is not None:
+            x = x.masked_fill(~dropout_mask, 0.0) / (1.0 - dropout_p)
+        else:
+            x = F.dropout(x, p=dropout_p)
+        if x1 is not None:
+            if dropout_mask1 is not None:
+                x1 = x1.masked_fill(~dropout_mask1, 0.0) / (1.0 - dropout_p)
+            else:
+                x1 = F.dropout(x1, p=dropout_p)
+    if x1 is not None:
+        x = x + x1
+    if residual is not None:
+        x = (x + residual).to(x.dtype)
+    rstd = 1 / torch.sqrt((x.square()).mean(dim=-1, keepdim=True) + eps)
+    out = ((x * rstd * weight) + bias if bias is not None else (x * rstd * weight)).to(
+        dtype
+    )
+    if weight1 is None:
+        return out if not prenorm else (out, x)
+    else:
+        out1 = (
+            (x * rstd * weight1) + bias1 if bias1 is not None else (x * rstd * weight1)
+        ).to(dtype)
+        return (out, out1) if not prenorm else (out, out1, x)
+
+
+def config_prune(configs):
+
+    if torch.version.hip:
+        try:
+            # set warp size based on gcn architecure
+            gcn_arch_name = torch.cuda.get_device_properties(0).gcnArchName
+            if "gfx10" in gcn_arch_name or "gfx11" in gcn_arch_name:
+                # radeon
+                warp_size = 32
+            else:
+                # instinct
+                warp_size = 64
+        except AttributeError as e:
+            # fall back to crude method to set warp size
+            device_name = torch.cuda.get_device_properties(0).name
+            if "instinct" in device_name.lower():
+                warp_size = 64
+            else:
+                warp_size = 32
+            warnings.warn(
+                f"{e}, warp size set to {warp_size} based on device name: {device_name}",
+                UserWarning,
+            )
+
+    else:
+        # cuda
+        warp_size = 32
+
+    max_block_sz = 1024
+    max_num_warps = max_block_sz // warp_size
+    pruned_configs = [config for config in configs if config.num_warps <= max_num_warps]
+    return pruned_configs
+
+
+configs_autotune = [
+    triton.Config({}, num_warps=1),
+    triton.Config({}, num_warps=2),
+    triton.Config({}, num_warps=4),
+    triton.Config({}, num_warps=8),
+    triton.Config({}, num_warps=16),
+    triton.Config({}, num_warps=32),
+]
+
+pruned_configs_autotune = config_prune(configs_autotune)
+
+
+@triton.autotune(
+    configs=pruned_configs_autotune,
+    key=["N", "HAS_RESIDUAL", "STORE_RESIDUAL_OUT", "IS_RMS_NORM", "HAS_BIAS"],
+)
+# @triton.heuristics({"HAS_BIAS": lambda args: args["B"] is not None})
+# @triton.heuristics({"HAS_RESIDUAL": lambda args: args["RESIDUAL"] is not None})
+@triton.heuristics({"HAS_X1": lambda args: args["X1"] is not None})
+@triton.heuristics({"HAS_W1": lambda args: args["W1"] is not None})
+@triton.heuristics({"HAS_B1": lambda args: args["B1"] is not None})
+@triton.jit
+def _layer_norm_fwd_1pass_kernel(
+    X,  # pointer to the input
+    Y,  # pointer to the output
+    W,  # pointer to the weights
+    B,  # pointer to the biases
+    RESIDUAL,  # pointer to the residual
+    X1,
+    W1,
+    B1,
+    Y1,
+    RESIDUAL_OUT,  # pointer to the residual
+    ROWSCALE,
+    SEEDS,  # Dropout seeds for each row
+    DROPOUT_MASK,
+    Mean,  # pointer to the mean
+    Rstd,  # pointer to the 1/std
+    stride_x_row,  # how much to increase the pointer when moving by 1 row
+    stride_y_row,
+    stride_res_row,
+    stride_res_out_row,
+    stride_x1_row,
+    stride_y1_row,
+    M,  # number of rows in X
+    N,  # number of columns in X
+    eps,  # epsilon to avoid division by zero
+    dropout_p,  # Dropout probability
+    IS_RMS_NORM: tl.constexpr,
+    BLOCK_N: tl.constexpr,
+    HAS_RESIDUAL: tl.constexpr,
+    STORE_RESIDUAL_OUT: tl.constexpr,
+    HAS_BIAS: tl.constexpr,
+    HAS_DROPOUT: tl.constexpr,
+    STORE_DROPOUT_MASK: tl.constexpr,
+    HAS_ROWSCALE: tl.constexpr,
+    HAS_X1: tl.constexpr,
+    HAS_W1: tl.constexpr,
+    HAS_B1: tl.constexpr,
+):
+    # Map the program id to the row of X and Y it should compute.
+    row = tl.program_id(0)
+    X += row * stride_x_row
+    Y += row * stride_y_row
+    if HAS_RESIDUAL:
+        RESIDUAL += row * stride_res_row
+    if STORE_RESIDUAL_OUT:
+        RESIDUAL_OUT += row * stride_res_out_row
+    if HAS_X1:
+        X1 += row * stride_x1_row
+    if HAS_W1:
+        Y1 += row * stride_y1_row
+    # Compute mean and variance
+    cols = tl.arange(0, BLOCK_N)
+    x = tl.load(X + cols, mask=cols < N, other=0.0).to(tl.float32)
+    if HAS_ROWSCALE:
+        rowscale = tl.load(ROWSCALE + row).to(tl.float32)
+        x *= rowscale
+    if HAS_DROPOUT:
+        # Compute dropout mask
+        # 7 rounds is good enough, and reduces register pressure
+        keep_mask = (
+            tl.rand(tl.load(SEEDS + row).to(tl.uint32), cols, n_rounds=7) > dropout_p
+        )
+        x = tl.where(keep_mask, x / (1.0 - dropout_p), 0.0)
+        if STORE_DROPOUT_MASK:
+            tl.store(DROPOUT_MASK + row * N + cols, keep_mask, mask=cols < N)
+    if HAS_X1:
+        x1 = tl.load(X1 + cols, mask=cols < N, other=0.0).to(tl.float32)
+        if HAS_ROWSCALE:
+            rowscale = tl.load(ROWSCALE + M + row).to(tl.float32)
+            x1 *= rowscale
+        if HAS_DROPOUT:
+            # Compute dropout mask
+            # 7 rounds is good enough, and reduces register pressure
+            keep_mask = (
+                tl.rand(tl.load(SEEDS + M + row).to(tl.uint32), cols, n_rounds=7)
+                > dropout_p
+            )
+            x1 = tl.where(keep_mask, x1 / (1.0 - dropout_p), 0.0)
+            if STORE_DROPOUT_MASK:
+                tl.store(DROPOUT_MASK + (M + row) * N + cols, keep_mask, mask=cols < N)
+        x += x1
+    if HAS_RESIDUAL:
+        residual = tl.load(RESIDUAL + cols, mask=cols < N, other=0.0).to(tl.float32)
+        x += residual
+    if STORE_RESIDUAL_OUT:
+        tl.store(RESIDUAL_OUT + cols, x, mask=cols < N)
+    if not IS_RMS_NORM:
+        mean = tl.sum(x, axis=0) / N
+        tl.store(Mean + row, mean)
+        xbar = tl.where(cols < N, x - mean, 0.0)
+        var = tl.sum(xbar * xbar, axis=0) / N
+    else:
+        xbar = tl.where(cols < N, x, 0.0)
+        var = tl.sum(xbar * xbar, axis=0) / N
+    rstd = 1 / tl.sqrt(var + eps)
+    tl.store(Rstd + row, rstd)
+    # Normalize and apply linear transformation
+    mask = cols < N
+    w = tl.load(W + cols, mask=mask).to(tl.float32)
+    if HAS_BIAS:
+        b = tl.load(B + cols, mask=mask).to(tl.float32)
+    x_hat = (x - mean) * rstd if not IS_RMS_NORM else x * rstd
+    y = x_hat * w + b if HAS_BIAS else x_hat * w
+    # Write output
+    tl.store(Y + cols, y, mask=mask)
+    if HAS_W1:
+        w1 = tl.load(W1 + cols, mask=mask).to(tl.float32)
+        if HAS_B1:
+            b1 = tl.load(B1 + cols, mask=mask).to(tl.float32)
+        y1 = x_hat * w1 + b1 if HAS_B1 else x_hat * w1
+        tl.store(Y1 + cols, y1, mask=mask)
+
+
+def _layer_norm_fwd(
+    x,
+    weight,
+    bias,
+    eps,
+    residual=None,
+    x1=None,
+    weight1=None,
+    bias1=None,
+    dropout_p=0.0,
+    rowscale=None,
+    out_dtype=None,
+    residual_dtype=None,
+    is_rms_norm=False,
+    return_dropout_mask=False,
+):
+    if residual is not None:
+        residual_dtype = residual.dtype
+    M, N = x.shape
+    assert x.stride(-1) == 1
+    if residual is not None:
+        assert residual.stride(-1) == 1
+        assert residual.shape == (M, N)
+    assert weight.shape == (N,)
+    assert weight.stride(-1) == 1
+    if bias is not None:
+        assert bias.stride(-1) == 1
+        assert bias.shape == (N,)
+    if x1 is not None:
+        assert x1.shape == x.shape
+        assert rowscale is None
+        assert x1.stride(-1) == 1
+    if weight1 is not None:
+        assert weight1.shape == (N,)
+        assert weight1.stride(-1) == 1
+    if bias1 is not None:
+        assert bias1.shape == (N,)
+        assert bias1.stride(-1) == 1
+    if rowscale is not None:
+        assert rowscale.is_contiguous()
+        assert rowscale.shape == (M,)
+    # allocate output
+    y = torch.empty_like(x, dtype=x.dtype if out_dtype is None else out_dtype)
+    assert y.stride(-1) == 1
+    if weight1 is not None:
+        y1 = torch.empty_like(y)
+        assert y1.stride(-1) == 1
+    else:
+        y1 = None
+    if (
+        residual is not None
+        or (residual_dtype is not None and residual_dtype != x.dtype)
+        or dropout_p > 0.0
+        or rowscale is not None
+        or x1 is not None
+    ):
+        residual_out = torch.empty(
+            M,
+            N,
+            device=x.device,
+            dtype=residual_dtype if residual_dtype is not None else x.dtype,
+        )
+        assert residual_out.stride(-1) == 1
+    else:
+        residual_out = None
+    mean = (
+        torch.empty((M,), dtype=torch.float32, device=x.device)
+        if not is_rms_norm
+        else None
+    )
+    rstd = torch.empty((M,), dtype=torch.float32, device=x.device)
+    if dropout_p > 0.0:
+        seeds = torch.randint(
+            2**32, (M if x1 is None else 2 * M,), device=x.device, dtype=torch.int64
+        )
+    else:
+        seeds = None
+    if return_dropout_mask and dropout_p > 0.0:
+        dropout_mask = torch.empty(
+            M if x1 is None else 2 * M, N, device=x.device, dtype=torch.bool
+        )
+    else:
+        dropout_mask = None
+    # Less than 64KB per feature: enqueue fused kernel
+    MAX_FUSED_SIZE = 65536 // x.element_size()
+    BLOCK_N = min(MAX_FUSED_SIZE, triton.next_power_of_2(N))
+    if N > BLOCK_N:
+        raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
+    with torch.cuda.device(x.device.index):
+        _layer_norm_fwd_1pass_kernel[(M,)](
+            x,
+            y,
+            weight,
+            bias,
+            residual,
+            x1,
+            weight1,
+            bias1,
+            y1,
+            residual_out,
+            rowscale,
+            seeds,
+            dropout_mask,
+            mean,
+            rstd,
+            x.stride(0),
+            y.stride(0),
+            residual.stride(0) if residual is not None else 0,
+            residual_out.stride(0) if residual_out is not None else 0,
+            x1.stride(0) if x1 is not None else 0,
+            y1.stride(0) if y1 is not None else 0,
+            M,
+            N,
+            eps,
+            dropout_p,
+            is_rms_norm,
+            BLOCK_N,
+            residual is not None,
+            residual_out is not None,
+            bias is not None,
+            dropout_p > 0.0,
+            dropout_mask is not None,
+            rowscale is not None,
+        )
+    # residual_out is None if residual is None and residual_dtype == input_dtype and dropout_p == 0.0
+    if dropout_mask is not None and x1 is not None:
+        dropout_mask, dropout_mask1 = dropout_mask.tensor_split(2, dim=0)
+    else:
+        dropout_mask1 = None
+    return (
+        y,
+        y1,
+        mean,
+        rstd,
+        residual_out if residual_out is not None else x,
+        seeds,
+        dropout_mask,
+        dropout_mask1,
+    )
+
+
+@triton.autotune(
+    configs=pruned_configs_autotune,
+    key=[
+        "N",
+        "HAS_DRESIDUAL",
+        "STORE_DRESIDUAL",
+        "IS_RMS_NORM",
+        "HAS_BIAS",
+        "HAS_DROPOUT",
+    ],
+)
+# @triton.heuristics({"HAS_BIAS": lambda args: args["B"] is not None})
+# @triton.heuristics({"HAS_DRESIDUAL": lambda args: args["DRESIDUAL"] is not None})
+# @triton.heuristics({"STORE_DRESIDUAL": lambda args: args["DRESIDUAL_IN"] is not None})
+@triton.heuristics({"HAS_ROWSCALE": lambda args: args["ROWSCALE"] is not None})
+@triton.heuristics({"HAS_DY1": lambda args: args["DY1"] is not None})
+@triton.heuristics({"HAS_DX1": lambda args: args["DX1"] is not None})
+@triton.heuristics({"HAS_B1": lambda args: args["DB1"] is not None})
+@triton.heuristics({"RECOMPUTE_OUTPUT": lambda args: args["Y"] is not None})
+@triton.jit
+def _layer_norm_bwd_kernel(
+    X,  # pointer to the input
+    W,  # pointer to the weights
+    B,  # pointer to the biases
+    Y,  # pointer to the output to be recomputed
+    DY,  # pointer to the output gradient
+    DX,  # pointer to the input gradient
+    DW,  # pointer to the partial sum of weights gradient
+    DB,  # pointer to the partial sum of biases gradient
+    DRESIDUAL,
+    W1,
+    DY1,
+    DX1,
+    DW1,
+    DB1,
+    DRESIDUAL_IN,
+    ROWSCALE,
+    SEEDS,
+    Mean,  # pointer to the mean
+    Rstd,  # pointer to the 1/std
+    stride_x_row,  # how much to increase the pointer when moving by 1 row
+    stride_y_row,
+    stride_dy_row,
+    stride_dx_row,
+    stride_dres_row,
+    stride_dy1_row,
+    stride_dx1_row,
+    stride_dres_in_row,
+    M,  # number of rows in X
+    N,  # number of columns in X
+    eps,  # epsilon to avoid division by zero
+    dropout_p,
+    rows_per_program,
+    IS_RMS_NORM: tl.constexpr,
+    BLOCK_N: tl.constexpr,
+    HAS_DRESIDUAL: tl.constexpr,
+    STORE_DRESIDUAL: tl.constexpr,
+    HAS_BIAS: tl.constexpr,
+    HAS_DROPOUT: tl.constexpr,
+    HAS_ROWSCALE: tl.constexpr,
+    HAS_DY1: tl.constexpr,
+    HAS_DX1: tl.constexpr,
+    HAS_B1: tl.constexpr,
+    RECOMPUTE_OUTPUT: tl.constexpr,
+):
+    # Map the program id to the elements of X, DX, and DY it should compute.
+    row_block_id = tl.program_id(0)
+    row_start = row_block_id * rows_per_program
+    # Do not early exit if row_start >= M, because we need to write DW and DB
+    cols = tl.arange(0, BLOCK_N)
+    mask = cols < N
+    X += row_start * stride_x_row
+    if HAS_DRESIDUAL:
+        DRESIDUAL += row_start * stride_dres_row
+    if STORE_DRESIDUAL:
+        DRESIDUAL_IN += row_start * stride_dres_in_row
+    DY += row_start * stride_dy_row
+    DX += row_start * stride_dx_row
+    if HAS_DY1:
+        DY1 += row_start * stride_dy1_row
+    if HAS_DX1:
+        DX1 += row_start * stride_dx1_row
+    if RECOMPUTE_OUTPUT:
+        Y += row_start * stride_y_row
+    w = tl.load(W + cols, mask=mask).to(tl.float32)
+    if RECOMPUTE_OUTPUT and HAS_BIAS:
+        b = tl.load(B + cols, mask=mask, other=0.0).to(tl.float32)
+    if HAS_DY1:
+        w1 = tl.load(W1 + cols, mask=mask).to(tl.float32)
+    dw = tl.zeros((BLOCK_N,), dtype=tl.float32)
+    if HAS_BIAS:
+        db = tl.zeros((BLOCK_N,), dtype=tl.float32)
+    if HAS_DY1:
+        dw1 = tl.zeros((BLOCK_N,), dtype=tl.float32)
+        if HAS_B1:
+            db1 = tl.zeros((BLOCK_N,), dtype=tl.float32)
+    row_end = min((row_block_id + 1) * rows_per_program, M)
+    for row in range(row_start, row_end):
+        # Load data to SRAM
+        x = tl.load(X + cols, mask=mask, other=0).to(tl.float32)
+        dy = tl.load(DY + cols, mask=mask, other=0).to(tl.float32)
+        if HAS_DY1:
+            dy1 = tl.load(DY1 + cols, mask=mask, other=0).to(tl.float32)
+        if not IS_RMS_NORM:
+            mean = tl.load(Mean + row)
+        rstd = tl.load(Rstd + row)
+        # Compute dx
+        xhat = (x - mean) * rstd if not IS_RMS_NORM else x * rstd
+        xhat = tl.where(mask, xhat, 0.0)
+        if RECOMPUTE_OUTPUT:
+            y = xhat * w + b if HAS_BIAS else xhat * w
+            tl.store(Y + cols, y, mask=mask)
+        wdy = w * dy
+        dw += dy * xhat
+        if HAS_BIAS:
+            db += dy
+        if HAS_DY1:
+            wdy += w1 * dy1
+            dw1 += dy1 * xhat
+            if HAS_B1:
+                db1 += dy1
+        if not IS_RMS_NORM:
+            c1 = tl.sum(xhat * wdy, axis=0) / N
+            c2 = tl.sum(wdy, axis=0) / N
+            dx = (wdy - (xhat * c1 + c2)) * rstd
+        else:
+            c1 = tl.sum(xhat * wdy, axis=0) / N
+            dx = (wdy - xhat * c1) * rstd
+        if HAS_DRESIDUAL:
+            dres = tl.load(DRESIDUAL + cols, mask=mask, other=0).to(tl.float32)
+            dx += dres
+        # Write dx
+        if STORE_DRESIDUAL:
+            tl.store(DRESIDUAL_IN + cols, dx, mask=mask)
+        if HAS_DX1:
+            if HAS_DROPOUT:
+                keep_mask = (
+                    tl.rand(tl.load(SEEDS + M + row).to(tl.uint32), cols, n_rounds=7)
+                    > dropout_p
+                )
+                dx1 = tl.where(keep_mask, dx / (1.0 - dropout_p), 0.0)
+            else:
+                dx1 = dx
+            tl.store(DX1 + cols, dx1, mask=mask)
+        if HAS_DROPOUT:
+            keep_mask = (
+                tl.rand(tl.load(SEEDS + row).to(tl.uint32), cols, n_rounds=7)
+                > dropout_p
+            )
+            dx = tl.where(keep_mask, dx / (1.0 - dropout_p), 0.0)
+        if HAS_ROWSCALE:
+            rowscale = tl.load(ROWSCALE + row).to(tl.float32)
+            dx *= rowscale
+        tl.store(DX + cols, dx, mask=mask)
+
+        X += stride_x_row
+        if HAS_DRESIDUAL:
+            DRESIDUAL += stride_dres_row
+        if STORE_DRESIDUAL:
+            DRESIDUAL_IN += stride_dres_in_row
+        if RECOMPUTE_OUTPUT:
+            Y += stride_y_row
+        DY += stride_dy_row
+        DX += stride_dx_row
+        if HAS_DY1:
+            DY1 += stride_dy1_row
+        if HAS_DX1:
+            DX1 += stride_dx1_row
+    tl.store(DW + row_block_id * N + cols, dw, mask=mask)
+    if HAS_BIAS:
+        tl.store(DB + row_block_id * N + cols, db, mask=mask)
+    if HAS_DY1:
+        tl.store(DW1 + row_block_id * N + cols, dw1, mask=mask)
+        if HAS_B1:
+            tl.store(DB1 + row_block_id * N + cols, db1, mask=mask)
+
+
+def _layer_norm_bwd(
+    dy,
+    x,
+    weight,
+    bias,
+    eps,
+    mean,
+    rstd,
+    dresidual=None,
+    dy1=None,
+    weight1=None,
+    bias1=None,
+    seeds=None,
+    dropout_p=0.0,
+    rowscale=None,
+    has_residual=False,
+    has_x1=False,
+    is_rms_norm=False,
+    x_dtype=None,
+    recompute_output=False,
+):
+    M, N = x.shape
+    assert x.stride(-1) == 1
+    assert dy.stride(-1) == 1
+    assert dy.shape == (M, N)
+    if dresidual is not None:
+        assert dresidual.stride(-1) == 1
+        assert dresidual.shape == (M, N)
+    assert weight.shape == (N,)
+    assert weight.stride(-1) == 1
+    if bias is not None:
+        assert bias.stride(-1) == 1
+        assert bias.shape == (N,)
+    if dy1 is not None:
+        assert weight1 is not None
+        assert dy1.shape == dy.shape
+        assert dy1.stride(-1) == 1
+    if weight1 is not None:
+        assert weight1.shape == (N,)
+        assert weight1.stride(-1) == 1
+    if bias1 is not None:
+        assert bias1.shape == (N,)
+        assert bias1.stride(-1) == 1
+    if seeds is not None:
+        assert seeds.is_contiguous()
+        assert seeds.shape == (M if not has_x1 else M * 2,)
+    if rowscale is not None:
+        assert rowscale.is_contiguous()
+        assert rowscale.shape == (M,)
+    # allocate output
+    dx = (
+        torch.empty_like(x)
+        if x_dtype is None
+        else torch.empty(M, N, dtype=x_dtype, device=x.device)
+    )
+    dresidual_in = (
+        torch.empty_like(x)
+        if has_residual
+        and (dx.dtype != x.dtype or dropout_p > 0.0 or rowscale is not None or has_x1)
+        else None
+    )
+    dx1 = torch.empty_like(dx) if (has_x1 and dropout_p > 0.0) else None
+    y = (
+        torch.empty(M, N, dtype=dy.dtype, device=dy.device)
+        if recompute_output
+        else None
+    )
+    if recompute_output:
+        assert (
+            weight1 is None
+        ), "recompute_output is not supported with parallel LayerNorm"
+
+    # Less than 64KB per feature: enqueue fused kernel
+    MAX_FUSED_SIZE = 65536 // x.element_size()
+    BLOCK_N = min(MAX_FUSED_SIZE, triton.next_power_of_2(N))
+    if N > BLOCK_N:
+        raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
+    sm_count = torch.cuda.get_device_properties(x.device).multi_processor_count
+    _dw = torch.empty((sm_count, N), dtype=torch.float32, device=weight.device)
+    _db = (
+        torch.empty((sm_count, N), dtype=torch.float32, device=bias.device)
+        if bias is not None
+        else None
+    )
+    _dw1 = torch.empty_like(_dw) if weight1 is not None else None
+    _db1 = torch.empty_like(_db) if bias1 is not None else None
+    rows_per_program = math.ceil(M / sm_count)
+    grid = (sm_count,)
+    with torch.cuda.device(x.device.index):
+        _layer_norm_bwd_kernel[grid](
+            x,
+            weight,
+            bias,
+            y,
+            dy,
+            dx,
+            _dw,
+            _db,
+            dresidual,
+            weight1,
+            dy1,
+            dx1,
+            _dw1,
+            _db1,
+            dresidual_in,
+            rowscale,
+            seeds,
+            mean,
+            rstd,
+            x.stride(0),
+            0 if not recompute_output else y.stride(0),
+            dy.stride(0),
+            dx.stride(0),
+            dresidual.stride(0) if dresidual is not None else 0,
+            dy1.stride(0) if dy1 is not None else 0,
+            dx1.stride(0) if dx1 is not None else 0,
+            dresidual_in.stride(0) if dresidual_in is not None else 0,
+            M,
+            N,
+            eps,
+            dropout_p,
+            rows_per_program,
+            is_rms_norm,
+            BLOCK_N,
+            dresidual is not None,
+            dresidual_in is not None,
+            bias is not None,
+            dropout_p > 0.0,
+        )
+    dw = _dw.sum(0).to(weight.dtype)
+    db = _db.sum(0).to(bias.dtype) if bias is not None else None
+    dw1 = _dw1.sum(0).to(weight1.dtype) if weight1 is not None else None
+    db1 = _db1.sum(0).to(bias1.dtype) if bias1 is not None else None
+    # Don't need to compute dresidual_in separately in this case
+    if has_residual and dx.dtype == x.dtype and dropout_p == 0.0 and rowscale is None:
+        dresidual_in = dx
+    if has_x1 and dropout_p == 0.0:
+        dx1 = dx
+    return (
+        (dx, dw, db, dresidual_in, dx1, dw1, db1)
+        if not recompute_output
+        else (dx, dw, db, dresidual_in, dx1, dw1, db1, y)
+    )
+
+
+class LayerNormFn(torch.autograd.Function):
+    @staticmethod
+    def forward(
+        ctx,
+        x,
+        weight,
+        bias,
+        residual=None,
+        x1=None,
+        weight1=None,
+        bias1=None,
+        eps=1e-6,
+        dropout_p=0.0,
+        rowscale=None,
+        prenorm=False,
+        residual_in_fp32=False,
+        is_rms_norm=False,
+        return_dropout_mask=False,
+    ):
+        x_shape_og = x.shape
+        # reshape input data into 2D tensor
+        x = x.reshape(-1, x.shape[-1])
+        if x.stride(-1) != 1:
+            x = x.contiguous()
+        if residual is not None:
+            assert residual.shape == x_shape_og
+            residual = residual.reshape(-1, residual.shape[-1])
+            if residual.stride(-1) != 1:
+                residual = residual.contiguous()
+        if x1 is not None:
+            assert x1.shape == x_shape_og
+            assert rowscale is None, "rowscale is not supported with parallel LayerNorm"
+            x1 = x1.reshape(-1, x1.shape[-1])
+            if x1.stride(-1) != 1:
+                x1 = x1.contiguous()
+        weight = weight.contiguous()
+        if bias is not None:
+            bias = bias.contiguous()
+        if weight1 is not None:
+            weight1 = weight1.contiguous()
+        if bias1 is not None:
+            bias1 = bias1.contiguous()
+        if rowscale is not None:
+            rowscale = rowscale.reshape(-1).contiguous()
+        residual_dtype = (
+            residual.dtype
+            if residual is not None
+            else (torch.float32 if residual_in_fp32 else None)
+        )
+        y, y1, mean, rstd, residual_out, seeds, dropout_mask, dropout_mask1 = (
+            _layer_norm_fwd(
+                x,
+                weight,
+                bias,
+                eps,
+                residual,
+                x1,
+                weight1,
+                bias1,
+                dropout_p=dropout_p,
+                rowscale=rowscale,
+                residual_dtype=residual_dtype,
+                is_rms_norm=is_rms_norm,
+                return_dropout_mask=return_dropout_mask,
+            )
+        )
+        ctx.save_for_backward(
+            residual_out, weight, bias, weight1, bias1, rowscale, seeds, mean, rstd
+        )
+        ctx.x_shape_og = x_shape_og
+        ctx.eps = eps
+        ctx.dropout_p = dropout_p
+        ctx.is_rms_norm = is_rms_norm
+        ctx.has_residual = residual is not None
+        ctx.has_x1 = x1 is not None
+        ctx.prenorm = prenorm
+        ctx.x_dtype = x.dtype
+        y = y.reshape(x_shape_og)
+        y1 = y1.reshape(x_shape_og) if y1 is not None else None
+        residual_out = (
+            residual_out.reshape(x_shape_og) if residual_out is not None else None
+        )
+        dropout_mask = (
+            dropout_mask.reshape(x_shape_og) if dropout_mask is not None else None
+        )
+        dropout_mask1 = (
+            dropout_mask1.reshape(x_shape_og) if dropout_mask1 is not None else None
+        )
+        if not return_dropout_mask:
+            if weight1 is None:
+                return y if not prenorm else (y, residual_out)
+            else:
+                return (y, y1) if not prenorm else (y, y1, residual_out)
+        else:
+            if weight1 is None:
+                return (
+                    (y, dropout_mask, dropout_mask1)
+                    if not prenorm
+                    else (y, residual_out, dropout_mask, dropout_mask1)
+                )
+            else:
+                return (
+                    (y, y1, dropout_mask, dropout_mask1)
+                    if not prenorm
+                    else (y, y1, residual_out, dropout_mask, dropout_mask1)
+                )
+
+    @staticmethod
+    def backward(ctx, dy, *args):
+        x, weight, bias, weight1, bias1, rowscale, seeds, mean, rstd = ctx.saved_tensors
+        dy = dy.reshape(-1, dy.shape[-1])
+        if dy.stride(-1) != 1:
+            dy = dy.contiguous()
+        assert dy.shape == x.shape
+        if weight1 is not None:
+            dy1, args = args[0], args[1:]
+            dy1 = dy1.reshape(-1, dy1.shape[-1])
+            if dy1.stride(-1) != 1:
+                dy1 = dy1.contiguous()
+            assert dy1.shape == x.shape
+        else:
+            dy1 = None
+        if ctx.prenorm:
+            dresidual = args[0]
+            dresidual = dresidual.reshape(-1, dresidual.shape[-1])
+            if dresidual.stride(-1) != 1:
+                dresidual = dresidual.contiguous()
+            assert dresidual.shape == x.shape
+        else:
+            dresidual = None
+        dx, dw, db, dresidual_in, dx1, dw1, db1 = _layer_norm_bwd(
+            dy,
+            x,
+            weight,
+            bias,
+            ctx.eps,
+            mean,
+            rstd,
+            dresidual,
+            dy1,
+            weight1,
+            bias1,
+            seeds,
+            ctx.dropout_p,
+            rowscale,
+            ctx.has_residual,
+            ctx.has_x1,
+            ctx.is_rms_norm,
+            x_dtype=ctx.x_dtype,
+        )
+        return (
+            dx.reshape(ctx.x_shape_og),
+            dw,
+            db,
+            dresidual_in.reshape(ctx.x_shape_og) if ctx.has_residual else None,
+            dx1.reshape(ctx.x_shape_og) if dx1 is not None else None,
+            dw1,
+            db1,
+            None,
+            None,
+            None,
+            None,
+            None,
+            None,
+            None,
+        )
+
+
+def layer_norm_fn(
+    x,
+    weight,
+    bias,
+    residual=None,
+    x1=None,
+    weight1=None,
+    bias1=None,
+    eps=1e-6,
+    dropout_p=0.0,
+    rowscale=None,
+    prenorm=False,
+    residual_in_fp32=False,
+    is_rms_norm=False,
+    return_dropout_mask=False,
+):
+    return LayerNormFn.apply(
+        x,
+        weight,
+        bias,
+        residual,
+        x1,
+        weight1,
+        bias1,
+        eps,
+        dropout_p,
+        rowscale,
+        prenorm,
+        residual_in_fp32,
+        is_rms_norm,
+        return_dropout_mask,
+    )
+
+
+def rms_norm_fn(
+    x,
+    weight,
+    bias,
+    residual=None,
+    x1=None,
+    weight1=None,
+    bias1=None,
+    eps=1e-6,
+    dropout_p=0.0,
+    rowscale=None,
+    prenorm=False,
+    residual_in_fp32=False,
+    return_dropout_mask=False,
+):
+    return LayerNormFn.apply(
+        x,
+        weight,
+        bias,
+        residual,
+        x1,
+        weight1,
+        bias1,
+        eps,
+        dropout_p,
+        rowscale,
+        prenorm,
+        residual_in_fp32,
+        True,
+        return_dropout_mask,
+    )
+
+
+class RMSNorm(torch.nn.Module):
+
+    def __init__(self, hidden_size, eps=1e-5, dropout_p=0.0, device=None, dtype=None):
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+        self.eps = eps
+        if dropout_p > 0.0:
+            self.drop = torch.nn.Dropout(dropout_p)
+        else:
+            self.drop = None
+        self.weight = torch.nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
+        self.register_parameter("bias", None)
+        self.reset_parameters()
+
+    def reset_parameters(self):
+        torch.nn.init.ones_(self.weight)
+
+    def forward(self, x, residual=None, prenorm=False, residual_in_fp32=False):
+        return rms_norm_fn(
+            x,
+            self.weight,
+            self.bias,
+            residual=residual,
+            eps=self.eps,
+            dropout_p=self.drop.p if self.drop is not None and self.training else 0.0,
+            prenorm=prenorm,
+            residual_in_fp32=residual_in_fp32,
+        )
+
+
+class LayerNormLinearFn(torch.autograd.Function):
+    @staticmethod
+    @custom_fwd
+    def forward(
+        ctx,
+        x,
+        norm_weight,
+        norm_bias,
+        linear_weight,
+        linear_bias,
+        residual=None,
+        eps=1e-6,
+        prenorm=False,
+        residual_in_fp32=False,
+        is_rms_norm=False,
+    ):
+        x_shape_og = x.shape
+        # reshape input data into 2D tensor
+        x = x.reshape(-1, x.shape[-1])
+        if x.stride(-1) != 1:
+            x = x.contiguous()
+        if residual is not None:
+            assert residual.shape == x_shape_og
+            residual = residual.reshape(-1, residual.shape[-1])
+            if residual.stride(-1) != 1:
+                residual = residual.contiguous()
+        norm_weight = norm_weight.contiguous()
+        if norm_bias is not None:
+            norm_bias = norm_bias.contiguous()
+        residual_dtype = (
+            residual.dtype
+            if residual is not None
+            else (torch.float32 if residual_in_fp32 else None)
+        )
+        y, _, mean, rstd, residual_out, *rest = _layer_norm_fwd(
+            x,
+            norm_weight,
+            norm_bias,
+            eps,
+            residual,
+            out_dtype=(
+                None
+                if not torch.is_autocast_enabled()
+                else torch.get_autocast_gpu_dtype()
+            ),
+            residual_dtype=residual_dtype,
+            is_rms_norm=is_rms_norm,
+        )
+        y = y.reshape(x_shape_og)
+        dtype = (
+            torch.get_autocast_gpu_dtype() if torch.is_autocast_enabled() else y.dtype
+        )
+        linear_weight = linear_weight.to(dtype)
+        linear_bias = linear_bias.to(dtype) if linear_bias is not None else None
+        out = F.linear(y.to(linear_weight.dtype), linear_weight, linear_bias)
+        # We don't store y, will be recomputed in the backward pass to save memory
+        ctx.save_for_backward(
+            residual_out, norm_weight, norm_bias, linear_weight, mean, rstd
+        )
+        ctx.x_shape_og = x_shape_og
+        ctx.eps = eps
+        ctx.is_rms_norm = is_rms_norm
+        ctx.has_residual = residual is not None
+        ctx.prenorm = prenorm
+        ctx.x_dtype = x.dtype
+        ctx.linear_bias_is_none = linear_bias is None
+        return out if not prenorm else (out, residual_out.reshape(x_shape_og))
+
+    @staticmethod
+    @custom_bwd
+    def backward(ctx, dout, *args):
+        x, norm_weight, norm_bias, linear_weight, mean, rstd = ctx.saved_tensors
+        dout = dout.reshape(-1, dout.shape[-1])
+        dy = F.linear(dout, linear_weight.t())
+        dlinear_bias = None if ctx.linear_bias_is_none else dout.sum(0)
+        if dy.stride(-1) != 1:
+            dy = dy.contiguous()
+        assert dy.shape == x.shape
+        if ctx.prenorm:
+            dresidual = args[0]
+            dresidual = dresidual.reshape(-1, dresidual.shape[-1])
+            if dresidual.stride(-1) != 1:
+                dresidual = dresidual.contiguous()
+            assert dresidual.shape == x.shape
+        else:
+            dresidual = None
+        dx, dnorm_weight, dnorm_bias, dresidual_in, _, _, _, y = _layer_norm_bwd(
+            dy,
+            x,
+            norm_weight,
+            norm_bias,
+            ctx.eps,
+            mean,
+            rstd,
+            dresidual=dresidual,
+            has_residual=ctx.has_residual,
+            is_rms_norm=ctx.is_rms_norm,
+            x_dtype=ctx.x_dtype,
+            recompute_output=True,
+        )
+        dlinear_weight = torch.einsum("bo,bi->oi", dout, y)
+        return (
+            dx.reshape(ctx.x_shape_og),
+            dnorm_weight,
+            dnorm_bias,
+            dlinear_weight,
+            dlinear_bias,
+            dresidual_in.reshape(ctx.x_shape_og) if ctx.has_residual else None,
+            None,
+            None,
+            None,
+            None,
+        )
+
+
+def layer_norm_linear_fn(
+    x,
+    norm_weight,
+    norm_bias,
+    linear_weight,
+    linear_bias,
+    residual=None,
+    eps=1e-6,
+    prenorm=False,
+    residual_in_fp32=False,
+    is_rms_norm=False,
+):
+    return LayerNormLinearFn.apply(
+        x,
+        norm_weight,
+        norm_bias,
+        linear_weight,
+        linear_bias,
+        residual,
+        eps,
+        prenorm,
+        residual_in_fp32,
+        is_rms_norm,
+    )

torch-ext/mamba_ssm/ops/triton/layernorm_gated.py

@@ -0,0 +1,437 @@
+# Copyright (c) 2024, Tri Dao.
+# Based on the Triton LayerNorm tutorial: https://triton-lang.org/main/getting-started/tutorials/05-layer-norm.html
+# For the backward pass, we keep weight_grad and bias_grad in registers and accumulate.
+# This backward pass is faster for dimensions up to 8k, but after that it's much slower due to register spilling.
+# The models we train have hidden dim up to 8k anyway (e.g. Llama 70B), so this is fine.
+
+import math
+
+import torch
+import torch.nn.functional as F
+
+import triton
+import triton.language as tl
+
+from einops import rearrange
+
+
+def rms_norm_ref(x, weight, bias, z=None, eps=1e-6, group_size=None, norm_before_gate=True, upcast=True):
+    dtype = x.dtype
+    N = x.shape[-1]
+    weight = weight.float()
+    bias = bias.float() if bias is not None else None
+    if upcast:
+        x = x.float()
+        z = z.float() if z is not None else z
+    if z is not None and not norm_before_gate:
+        x = x * F.silu(z)
+    if group_size is None:
+        rstd = 1 / torch.sqrt((x.square()).mean(dim=-1, keepdim=True) + eps)
+        out = (x * rstd * weight) + bias if bias is not None else (x * rstd * weight)
+    else:
+        x_group = rearrange(x, "... (g d) -> ... g d", d=group_size)
+        rstd = 1 / torch.sqrt((x_group.square()).mean(dim=-1, keepdim=True) + eps)
+        out = rearrange(x_group * rstd, "... g d -> ... (g d)") * weight
+        if bias is not None:
+            out = out + bias
+    if z is not None and norm_before_gate:
+        out *= F.silu(z)
+    return out.to(dtype)
+
+
+@triton.heuristics({"HAS_BIAS": lambda args: args["B"] is not None})
+@triton.heuristics({"HAS_Z": lambda args: args["Z"] is not None})
+@triton.jit
+def _layer_norm_fwd_1pass_kernel(
+    X,  # pointer to the input
+    Y,  # pointer to the output
+    W,  # pointer to the weights
+    B,  # pointer to the biases
+    Z,  # pointer to the other branch
+    Mean,  # pointer to the mean
+    Rstd,  # pointer to the 1/std
+    stride_x_row,  # how much to increase the pointer when moving by 1 row
+    stride_y_row,
+    stride_z_row,
+    M,  # number of rows in X
+    N,  # number of columns in X
+    eps,  # epsilon to avoid division by zero
+    BLOCK_N: tl.constexpr,
+    HAS_BIAS: tl.constexpr,
+    HAS_Z: tl.constexpr,
+    NORM_BEFORE_GATE: tl.constexpr,
+    IS_RMS_NORM: tl.constexpr,
+):
+    # Map the program id to the row of X and Y it should compute.
+    row = tl.program_id(0)
+    group = tl.program_id(1)
+    X += row * stride_x_row + group * N
+    Y += row * stride_y_row + group * N
+    if HAS_Z:
+        Z += row * stride_z_row + group * N
+    if not IS_RMS_NORM:
+        Mean += group * M
+    Rstd += group * M
+    W += group * N
+    if HAS_BIAS:
+        B += group * N
+    # Compute mean and variance
+    cols = tl.arange(0, BLOCK_N)
+    x = tl.load(X + cols, mask=cols < N, other=0.).to(tl.float32)
+    if HAS_Z and not NORM_BEFORE_GATE:
+        z = tl.load(Z + cols, mask=cols < N).to(tl.float32)
+        x *= z * tl.sigmoid(z)
+    if not IS_RMS_NORM:
+        mean = tl.sum(x, axis=0) / N
+        tl.store(Mean + row, mean)
+        xbar = tl.where(cols < N, x - mean, 0.)
+        var = tl.sum(xbar * xbar, axis=0) / N
+    else:
+        xbar = tl.where(cols < N, x, 0.)
+        var = tl.sum(xbar * xbar, axis=0) / N
+    rstd = 1 / tl.sqrt(var + eps)
+    tl.store(Rstd + row, rstd)
+    # Normalize and apply linear transformation
+    mask = cols < N
+    w = tl.load(W + cols, mask=mask).to(tl.float32)
+    if HAS_BIAS:
+        b = tl.load(B + cols, mask=mask).to(tl.float32)
+    x_hat = (x - mean) * rstd if not IS_RMS_NORM else x * rstd
+    y = x_hat * w + b if HAS_BIAS else x_hat * w
+    if HAS_Z and NORM_BEFORE_GATE:
+        z = tl.load(Z + cols, mask=mask).to(tl.float32)
+        y *= z * tl.sigmoid(z)
+    # Write output
+    tl.store(Y + cols, y, mask=mask)
+
+
+def _layer_norm_fwd(x, weight, bias, eps, z=None, out=None, group_size=None, norm_before_gate=True, is_rms_norm=False):
+    M, N = x.shape
+    if group_size is None:
+        group_size = N
+    assert N % group_size == 0
+    ngroups = N // group_size
+    assert x.stride(-1) == 1
+    if z is not None:
+        assert z.stride(-1) == 1
+        assert z.shape == (M, N)
+    assert weight.shape == (N,)
+    assert weight.stride(-1) == 1
+    if bias is not None:
+        assert bias.stride(-1) == 1
+        assert bias.shape == (N,)
+    # allocate output
+    if out is not None:
+        assert out.shape == x.shape
+    else:
+        out = torch.empty_like(x)
+    assert out.stride(-1) == 1
+    mean = torch.empty((ngroups * M, ), dtype=torch.float32, device=x.device) if not is_rms_norm else None
+    rstd = torch.empty((ngroups * M, ), dtype=torch.float32, device=x.device)
+    # Less than 64KB per feature: enqueue fused kernel
+    MAX_FUSED_SIZE = 65536 // x.element_size()
+    BLOCK_N = min(MAX_FUSED_SIZE, triton.next_power_of_2(group_size))
+    if group_size > BLOCK_N:
+        raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
+    # heuristics for number of warps
+    num_warps = min(max(BLOCK_N // 256, 1), 8)
+    grid = (M, ngroups)
+    with torch.cuda.device(x.device.index):
+        _layer_norm_fwd_1pass_kernel[grid](x, out, weight, bias, z, mean, rstd,
+                                           x.stride(0), out.stride(0), z.stride(0) if z is not None else 0,
+                                           M, group_size, eps,
+                                           BLOCK_N=BLOCK_N,
+                                           NORM_BEFORE_GATE=norm_before_gate,
+                                           IS_RMS_NORM=is_rms_norm,
+                                           num_warps=num_warps)
+    return out, mean, rstd
+
+
+
+@triton.heuristics({"HAS_BIAS": lambda args: args["B"] is not None})
+@triton.heuristics({"HAS_Z": lambda args: args["Z"] is not None})
+@triton.heuristics({"RECOMPUTE_OUTPUT": lambda args: args["Y"] is not None})
+@triton.jit
+def _layer_norm_bwd_kernel(
+    X,   # pointer to the input
+    W,   # pointer to the weights
+    B,   # pointer to the biases
+    Z,   # pointer to the other branch
+    Y,   # pointer to the output to be recomputed
+    DY,  # pointer to the output gradient
+    DX,  # pointer to the input gradient
+    DW,  # pointer to the partial sum of weights gradient
+    DB,  # pointer to the partial sum of biases gradient
+    DZ,  # pointer to the other branch
+    Mean,   # pointer to the mean
+    Rstd,   # pointer to the 1/std
+    stride_x_row,  # how much to increase the pointer when moving by 1 row
+    stride_z_row,
+    stride_y_row,
+    stride_dy_row,
+    stride_dx_row,
+    stride_dz_row,
+    stride_dw_row,
+    stride_db_row,
+    M,  # number of rows in X
+    N,  # number of columns in X
+    eps,  # epsilon to avoid division by zero
+    rows_per_program,
+    NORM_BEFORE_GATE: tl.constexpr,
+    IS_RMS_NORM: tl.constexpr,
+    HAS_BIAS: tl.constexpr,
+    HAS_Z: tl.constexpr,
+    RECOMPUTE_OUTPUT: tl.constexpr,
+    BLOCK_N: tl.constexpr,
+):
+    # Map the program id to the elements of X, DX, and DY it should compute.
+    row_block_id = tl.program_id(0)
+    group = tl.program_id(1)
+    row_start = row_block_id * rows_per_program
+    cols = tl.arange(0, BLOCK_N)
+    mask = cols < N
+    X += row_start * stride_x_row + group * N
+    if HAS_Z:
+        Z += row_start * stride_z_row + group * N
+        DZ += row_start * stride_dz_row + group * N
+    DY += row_start * stride_dy_row + group * N
+    DX += row_start * stride_dx_row + group * N
+    if RECOMPUTE_OUTPUT:
+        Y += row_start * stride_y_row + group * N
+    if not IS_RMS_NORM:
+        Mean += group * M
+    Rstd += group * M
+    W += group * N
+    w = tl.load(W + cols, mask=mask).to(tl.float32)
+    if (RECOMPUTE_OUTPUT or HAS_Z) and HAS_BIAS:
+        B += group * N
+        b = tl.load(B + cols, mask=mask, other=0.).to(tl.float32)
+    dw = tl.zeros((BLOCK_N,), dtype=tl.float32)
+    if HAS_BIAS:
+        db = tl.zeros((BLOCK_N,), dtype=tl.float32)
+    row_end = min((row_block_id + 1) * rows_per_program, M)
+    for row in range(row_start, row_end):
+        # Load data to SRAM
+        x = tl.load(X + cols, mask=mask, other=0).to(tl.float32)
+        dy = tl.load(DY + cols, mask=mask, other=0).to(tl.float32)
+        if not IS_RMS_NORM:
+            mean = tl.load(Mean + row)
+        if HAS_Z and not NORM_BEFORE_GATE:
+            z = tl.load(Z + cols, mask=mask, other=0.).to(tl.float32)
+            x_og = x
+            x = x_og * z * tl.sigmoid(z)
+        rstd = tl.load(Rstd + row)
+        # Compute dx
+        xhat = (x - mean) * rstd if not IS_RMS_NORM else x * rstd
+        xhat = tl.where(mask, xhat, 0.)
+        if HAS_Z and NORM_BEFORE_GATE:
+            z = tl.load(Z + cols, mask=mask, other=0.).to(tl.float32)
+            z_sigmoid = tl.sigmoid(z)
+            y = xhat * w + b if HAS_BIAS else xhat * w
+            if RECOMPUTE_OUTPUT:
+                tl.store(Y + cols, y * z * z_sigmoid, mask=mask)
+            dz = dy * y * z_sigmoid * (1 + z * (1 - z_sigmoid))
+            tl.store(DZ + cols, dz, mask=mask)
+            dy *= z * z_sigmoid
+        else:
+            if RECOMPUTE_OUTPUT:
+                y = xhat * w + b if HAS_BIAS else xhat * w
+                tl.store(Y + cols, y, mask=mask)
+        wdy = w * dy
+        c1 = tl.sum(xhat * wdy, axis=0) / N
+        if not IS_RMS_NORM:
+            c2 = tl.sum(wdy, axis=0) / N
+            dx = (wdy - (xhat * c1 + c2)) * rstd
+        else:
+            dx = (wdy - xhat * c1) * rstd
+        dw += dy * xhat
+        if HAS_BIAS:
+            db += dy
+        if HAS_Z and not NORM_BEFORE_GATE:
+            z_sigmoid = tl.sigmoid(z)
+            dz = dx * x_og * z_sigmoid * (1 + z * (1 - z_sigmoid))
+            tl.store(DZ + cols, dz, mask=mask)
+            dx *= z * z_sigmoid
+        # Write dx
+        tl.store(DX + cols, dx, mask=mask)
+
+        X += stride_x_row
+        if HAS_Z:
+            Z += stride_z_row
+            DZ += stride_dz_row
+        if RECOMPUTE_OUTPUT:
+            Y += stride_y_row
+        DY += stride_dy_row
+        DX += stride_dx_row
+    tl.store(DW + row_block_id * stride_dw_row + group * N + cols, dw, mask=mask)
+    if HAS_BIAS:
+        tl.store(DB + row_block_id * stride_db_row + group * N + cols, db, mask=mask)
+
+
+def _layer_norm_bwd(dy, x, weight, bias, eps, mean, rstd, z=None, group_size=None,
+                    norm_before_gate=True, is_rms_norm=False, recompute_output=False, dz=None, out=None):
+    M, N = x.shape
+    if group_size is None:
+        group_size = N
+    assert N % group_size == 0
+    ngroups = N // group_size
+    assert x.stride(-1) == 1
+    assert dy.stride(-1) == 1
+    assert dy.shape == (M, N)
+    if z is not None:
+        assert z.stride(-1) == 1
+        assert z.shape == (M, N)
+    assert weight.shape == (N,)
+    assert weight.stride(-1) == 1
+    if bias is not None:
+        assert bias.stride(-1) == 1
+        assert bias.shape == (N,)
+    # allocate output
+    dx = torch.empty_like(x)
+    if dz is not None:
+        assert z is not None
+        assert dz.shape == z.shape
+        assert dz.stride(-1) == 1
+    else:
+        dz = torch.empty_like(z) if z is not None else None
+    if recompute_output:
+        if out is None:
+            out = torch.empty_like(x)
+        assert out.shape == x.shape
+
+    # Less than 64KB per feature: enqueue fused kernel
+    MAX_FUSED_SIZE = 65536 // x.element_size()
+    BLOCK_N = min(MAX_FUSED_SIZE, triton.next_power_of_2(group_size))
+    if group_size > BLOCK_N:
+        raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
+    # heuristics for number of warps
+    num_warps = min(max(BLOCK_N // 256, 1), 8)
+    sm_count = torch.cuda.get_device_properties(x.device).multi_processor_count
+    # If group size is small (e.g., 64), we're only using 1 warp. So having just 108 programs
+    # would limit the occupancy.
+    nrow_groups = math.ceil(sm_count * math.ceil(4 / num_warps) / ngroups)
+    _dw = torch.empty((nrow_groups, N), dtype=torch.float32, device=weight.device)
+    _db = torch.empty((nrow_groups, N), dtype=torch.float32, device=bias.device) if bias is not None else None
+    rows_per_program = math.ceil(M / nrow_groups)
+    grid = (nrow_groups, ngroups)
+    with torch.cuda.device(x.device.index):
+        _layer_norm_bwd_kernel[grid](x, weight, bias, z, out if recompute_output else None,
+                                     dy, dx, _dw, _db, dz, mean, rstd,
+                                     x.stride(0),
+                                     z.stride(0) if z is not None else 0,
+                                     0 if not recompute_output else out.stride(0),
+                                     dy.stride(0), dx.stride(0),
+                                     dz.stride(0) if dz is not None else 0,
+                                     _dw.stride(0),
+                                     _db.stride(0) if _db is not None else 0,
+                                     M, group_size, eps,
+                                     rows_per_program,
+                                     BLOCK_N=BLOCK_N,
+                                     NORM_BEFORE_GATE=norm_before_gate,
+                                     IS_RMS_NORM=is_rms_norm,
+                                     num_warps=num_warps)
+    dw = _dw.sum(0).to(weight.dtype)
+    db = _db.sum(0).to(bias.dtype) if bias is not None else None
+    return (dx, dw, db, dz) if not recompute_output else (dx, dw, db, dz, out)
+
+
+class LayerNormFn(torch.autograd.Function):
+
+    @staticmethod
+    def forward(ctx, x, weight, bias, z=None, eps=1e-6, group_size=None, norm_before_gate=True,
+                is_rms_norm=False):
+        """If z is not None, we do norm(x) * silu(z) if norm_before_gate, else norm(x * silu(z))
+        """
+
+        x_shape_og = x.shape
+        # reshape input data into 2D tensor
+        x = x.reshape(-1, x.shape[-1])
+        if x.stride(-1) != 1:
+            x = x.contiguous()
+        if z is not None:
+            assert z.shape == x_shape_og
+            z = z.reshape(-1, z.shape[-1])
+            if z.stride(-1) != 1:
+                z = z.contiguous()
+        weight = weight.contiguous()
+        if bias is not None:
+            bias = bias.contiguous()
+        y, mean, rstd = _layer_norm_fwd(x, weight, bias, eps, z=z, group_size=group_size, norm_before_gate=norm_before_gate, is_rms_norm=is_rms_norm)
+        ctx.save_for_backward(x, weight, bias, mean, rstd, z)
+        ctx.x_shape_og = x_shape_og
+        ctx.eps = eps
+        ctx.group_size = group_size
+        ctx.norm_before_gate = norm_before_gate
+        ctx.is_rms_norm = is_rms_norm
+        return y.reshape(x_shape_og)
+
+    @staticmethod
+    def backward(ctx, dy):
+        x, weight, bias, mean, rstd, z = ctx.saved_tensors
+        dy = dy.reshape(-1, dy.shape[-1])
+        if dy.stride(-1) != 1:
+            dy = dy.contiguous()
+        assert dy.shape == x.shape
+        dx, dw, db, dz = _layer_norm_bwd(dy, x, weight, bias, ctx.eps, mean, rstd, z, ctx.group_size,
+                                         ctx.norm_before_gate, ctx.is_rms_norm)
+        return dx.reshape(ctx.x_shape_og), dw, db, dz.reshape(ctx.x_shape_og) if dz is not None else None, None, None, None, None
+
+
+def layernorm_fn(x, weight, bias, z=None, eps=1e-6, group_size=None, norm_before_gate=True, is_rms_norm=False):
+    return LayerNormFn.apply(x, weight, bias, z, eps, group_size, norm_before_gate, is_rms_norm)
+
+
+def rmsnorm_fn(x, weight, bias, z=None, eps=1e-6, group_size=None, norm_before_gate=True):
+    return LayerNormFn.apply(x, weight, bias, z, eps, group_size, norm_before_gate, True)
+
+
+class LayerNorm(torch.nn.Module):
+
+    def __init__(self, hidden_size, eps=1e-5, group_size=None, norm_before_gate=True, device=None, dtype=None):
+        """If group_size is not None, we do GroupNorm with each group having group_size elements.
+        group_size=None is equivalent to group_size=hidden_size (i.e. there's only 1 group).
+        """
+
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+        self.eps = eps
+        self.weight = torch.nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
+        self.bias = torch.nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
+        self.group_size = group_size
+        self.norm_before_gate = norm_before_gate
+        self.reset_parameters()
+
+    def reset_parameters(self):
+        torch.nn.init.ones_(self.weight)
+        torch.nn.init.zeros_(self.bias)
+
+    def forward(self, x, z=None):
+        """If z is not None, we do norm(x) * silu(z) if norm_before_gate, else norm(x * silu(z))
+        """
+        return layernorm_fn(x, self.weight, self.bias, z=z, group_size=self.group_size, eps=self.eps,
+                            norm_before_gate=self.norm_before_gate)
+
+
+class RMSNorm(torch.nn.Module):
+
+    def __init__(self, hidden_size, eps=1e-5, group_size=None, norm_before_gate=True, device=None, dtype=None):
+        """If group_size is not None, we do GroupNorm with each group having group_size elements.
+        group_size=None is equivalent to group_size=hidden_size (i.e. there's only 1 group).
+        """
+        factory_kwargs = {"device": device, "dtype": dtype}
+        super().__init__()
+        self.eps = eps
+        self.weight = torch.nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
+        self.register_parameter("bias", None)
+        self.group_size = group_size
+        self.norm_before_gate = norm_before_gate
+        self.reset_parameters()
+
+    def reset_parameters(self):
+        torch.nn.init.ones_(self.weight)
+
+    def forward(self, x, z=None):
+        """If z is not None, we do norm(x) * silu(z) if norm_before_gate, else norm(x * silu(z))
+        """
+        return rmsnorm_fn(x, self.weight, self.bias, z=z, eps=self.eps, group_size=self.group_size,
+                          norm_before_gate=self.norm_before_gate)

torch-ext/mamba_ssm/ops/triton/selective_state_update.py

@@ -0,0 +1,389 @@
+# Copyright (c) 2024, Tri Dao, Albert Gu.
+
+"""We want triton==2.1.0 or triton==2.2.0 or triton==2.3.0 for this
+"""
+
+import math
+import torch
+import torch.nn.functional as F
+
+import triton
+import triton.language as tl
+
+from einops import rearrange, repeat
+
+from .softplus import softplus
+
+
+@triton.heuristics({"HAS_DT_BIAS": lambda args: args["dt_bias_ptr"] is not None})
+@triton.heuristics({"HAS_D": lambda args: args["D_ptr"] is not None})
+@triton.heuristics({"HAS_Z": lambda args: args["z_ptr"] is not None})
+@triton.heuristics(
+    {
+        "HAS_STATE_BATCH_INDICES": lambda args: args["state_batch_indices_ptr"]
+        is not None
+    }
+)
+@triton.heuristics(
+    {"BLOCK_SIZE_DSTATE": lambda args: triton.next_power_of_2(args["dstate"])}
+)
+@triton.jit
+def _selective_scan_update_kernel(
+    # Pointers to matrices
+    state_ptr,
+    x_ptr,
+    dt_ptr,
+    dt_bias_ptr,
+    A_ptr,
+    B_ptr,
+    C_ptr,
+    D_ptr,
+    z_ptr,
+    out_ptr,
+    state_batch_indices_ptr,
+    # Matrix dimensions
+    batch,
+    nheads,
+    dim,
+    dstate,
+    nheads_ngroups_ratio,
+    # Strides
+    stride_state_batch,
+    stride_state_head,
+    stride_state_dim,
+    stride_state_dstate,
+    stride_x_batch,
+    stride_x_head,
+    stride_x_dim,
+    stride_dt_batch,
+    stride_dt_head,
+    stride_dt_dim,
+    stride_dt_bias_head,
+    stride_dt_bias_dim,
+    stride_A_head,
+    stride_A_dim,
+    stride_A_dstate,
+    stride_B_batch,
+    stride_B_group,
+    stride_B_dstate,
+    stride_C_batch,
+    stride_C_group,
+    stride_C_dstate,
+    stride_D_head,
+    stride_D_dim,
+    stride_z_batch,
+    stride_z_head,
+    stride_z_dim,
+    stride_out_batch,
+    stride_out_head,
+    stride_out_dim,
+    # Meta-parameters
+    DT_SOFTPLUS: tl.constexpr,
+    TIE_HDIM: tl.constexpr,
+    BLOCK_SIZE_M: tl.constexpr,
+    HAS_DT_BIAS: tl.constexpr,
+    HAS_D: tl.constexpr,
+    HAS_Z: tl.constexpr,
+    HAS_STATE_BATCH_INDICES: tl.constexpr,
+    BLOCK_SIZE_DSTATE: tl.constexpr,
+):
+    pid_m = tl.program_id(axis=0)
+    pid_b = tl.program_id(axis=1)
+    pid_h = tl.program_id(axis=2)
+
+    if HAS_STATE_BATCH_INDICES:
+        state_batch_indices_ptr += pid_b
+        state_batch_idx = tl.load(state_batch_indices_ptr)
+        state_ptr += state_batch_idx * stride_state_batch + pid_h * stride_state_head
+    else:
+        state_ptr += pid_b * stride_state_batch + pid_h * stride_state_head
+
+    x_ptr += pid_b * stride_x_batch + pid_h * stride_x_head
+    dt_ptr += pid_b * stride_dt_batch + pid_h * stride_dt_head
+    if HAS_DT_BIAS:
+        dt_bias_ptr += pid_h * stride_dt_bias_head
+    A_ptr += pid_h * stride_A_head
+    B_ptr += pid_b * stride_B_batch + (pid_h // nheads_ngroups_ratio) * stride_B_group
+    C_ptr += pid_b * stride_C_batch + (pid_h // nheads_ngroups_ratio) * stride_C_group
+    if HAS_Z:
+        z_ptr += pid_b * stride_z_batch + pid_h * stride_z_head
+    out_ptr += pid_b * stride_out_batch + pid_h * stride_out_head
+
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = tl.arange(0, BLOCK_SIZE_DSTATE)
+    state_ptrs = state_ptr + (
+        offs_m[:, None] * stride_state_dim + offs_n[None, :] * stride_state_dstate
+    )
+    x_ptrs = x_ptr + offs_m * stride_x_dim
+    dt_ptrs = dt_ptr + offs_m * stride_dt_dim
+    if HAS_DT_BIAS:
+        dt_bias_ptrs = dt_bias_ptr + offs_m * stride_dt_bias_dim
+    if HAS_D:
+        D_ptr += pid_h * stride_D_head
+    A_ptrs = A_ptr + (
+        offs_m[:, None] * stride_A_dim + offs_n[None, :] * stride_A_dstate
+    )
+    B_ptrs = B_ptr + offs_n * stride_B_dstate
+    C_ptrs = C_ptr + offs_n * stride_C_dstate
+    if HAS_D:
+        D_ptrs = D_ptr + offs_m * stride_D_dim
+    if HAS_Z:
+        z_ptrs = z_ptr + offs_m * stride_z_dim
+    out_ptrs = out_ptr + offs_m * stride_out_dim
+
+    state = tl.load(
+        state_ptrs, mask=(offs_m[:, None] < dim) & (offs_n[None, :] < dstate), other=0.0
+    )
+    x = tl.load(x_ptrs, mask=offs_m < dim, other=0.0).to(tl.float32)
+    if not TIE_HDIM:
+        dt = tl.load(dt_ptrs, mask=offs_m < dim, other=0.0).to(tl.float32)
+        if HAS_DT_BIAS:
+            dt += tl.load(dt_bias_ptrs, mask=offs_m < dim, other=0.0).to(tl.float32)
+        if DT_SOFTPLUS:
+            dt = tl.where(dt <= 20.0, softplus(dt), dt)
+        A = tl.load(
+            A_ptrs, mask=(offs_m[:, None] < dim) & (offs_n[None, :] < dstate), other=0.0
+        ).to(tl.float32)
+        dA = tl.exp(A * dt[:, None])
+    else:
+        dt = tl.load(dt_ptr).to(tl.float32)
+        if HAS_DT_BIAS:
+            dt += tl.load(dt_bias_ptr).to(tl.float32)
+        if DT_SOFTPLUS:
+            dt = tl.where(dt <= 20.0, softplus(dt), dt)
+        A = tl.load(A_ptr).to(tl.float32)
+        dA = tl.exp(A * dt)  # scalar, not a matrix
+
+    B = tl.load(B_ptrs, mask=offs_n < dstate, other=0.0).to(tl.float32)
+    C = tl.load(C_ptrs, mask=offs_n < dstate, other=0.0).to(tl.float32)
+    if HAS_D:
+        D = tl.load(D_ptrs, mask=offs_m < dim, other=0.0).to(tl.float32)
+    if HAS_Z:
+        z = tl.load(z_ptrs, mask=offs_m < dim, other=0.0).to(tl.float32)
+
+    if not TIE_HDIM:
+        dB = B[None, :] * dt[:, None]
+    else:
+        dB = B * dt  # vector of size (dstate,)
+    state = state * dA + dB * x[:, None]
+    tl.store(
+        state_ptrs, state, mask=(offs_m[:, None] < dim) & (offs_n[None, :] < dstate)
+    )
+    out = tl.sum(state * C[None, :], axis=1)
+    if HAS_D:
+        out += x * D
+    if HAS_Z:
+        out *= z * tl.sigmoid(z)
+    tl.store(out_ptrs, out, mask=offs_m < dim)
+
+
+def selective_state_update(
+    state,
+    x,
+    dt,
+    A,
+    B,
+    C,
+    D=None,
+    z=None,
+    dt_bias=None,
+    dt_softplus=False,
+    state_batch_indices=None,
+):
+    """
+    Argument:
+        state: (batch, dim, dstate) or (batch, nheads, dim, dstate)
+        x: (batch, dim) or (batch, nheads, dim)
+        dt: (batch, dim) or (batch, nheads, dim)
+        A: (dim, dstate) or (nheads, dim, dstate)
+        B: (batch, dstate) or (batch, ngroups, dstate)
+        C: (batch, dstate) or (batch, ngroups, dstate)
+        D: (dim,) or (nheads, dim)
+        z: (batch, dim) or (batch, nheads, dim)
+        dt_bias: (dim,) or (nheads, dim)
+    Return:
+        out: (batch, dim) or (batch, nheads, dim)
+    """
+    has_heads = state.dim() > 3
+    if state.dim() == 3:
+        state = state.unsqueeze(1)
+    if x.dim() == 2:
+        x = x.unsqueeze(1)
+    if dt.dim() == 2:
+        dt = dt.unsqueeze(1)
+    if A.dim() == 2:
+        A = A.unsqueeze(0)
+    if B.dim() == 2:
+        B = B.unsqueeze(1)
+    if C.dim() == 2:
+        C = C.unsqueeze(1)
+    if D is not None and D.dim() == 1:
+        D = D.unsqueeze(0)
+    if z is not None and z.dim() == 2:
+        z = z.unsqueeze(1)
+    if dt_bias is not None and dt_bias.dim() == 1:
+        dt_bias = dt_bias.unsqueeze(0)
+    _, nheads, dim, dstate = state.shape
+    batch = x.shape[0]
+    if x.shape != (batch, nheads, dim):
+        print(f"{state.shape} {x.shape} {batch} {nheads} {dim}")
+    assert x.shape == (batch, nheads, dim)
+    assert dt.shape == x.shape
+    assert A.shape == (nheads, dim, dstate)
+    ngroups = B.shape[1]
+    assert nheads % ngroups == 0, "nheads must be divisible by ngroups"
+    assert B.shape == (batch, ngroups, dstate)
+    assert C.shape == B.shape
+    if D is not None:
+        assert D.shape == (nheads, dim)
+    if z is not None:
+        assert z.shape == x.shape
+    if dt_bias is not None:
+        assert dt_bias.shape == (nheads, dim)
+    if state_batch_indices is not None:
+        assert state_batch_indices.shape == (batch,)
+    out = torch.empty_like(x)
+    grid = lambda META: (triton.cdiv(dim, META["BLOCK_SIZE_M"]), batch, nheads)
+    z_strides = (z.stride(0), z.stride(1), z.stride(2)) if z is not None else (0, 0, 0)
+    # We don't want autotune since it will overwrite the state
+    # We instead tune by hand.
+    BLOCK_SIZE_M, num_warps = (
+        (32, 4)
+        if dstate <= 16
+        else (
+            (16, 4)
+            if dstate <= 32
+            else ((8, 4) if dstate <= 64 else ((4, 4) if dstate <= 128 else ((4, 8))))
+        )
+    )
+    tie_hdim = (
+        A.stride(-1) == 0
+        and A.stride(-2) == 0
+        and dt.stride(-1) == 0
+        and dt_bias.stride(-1) == 0
+    )
+    with torch.cuda.device(x.device.index):
+        _selective_scan_update_kernel[grid](
+            state,
+            x,
+            dt,
+            dt_bias,
+            A,
+            B,
+            C,
+            D,
+            z,
+            out,
+            state_batch_indices,
+            batch,
+            nheads,
+            dim,
+            dstate,
+            nheads // ngroups,
+            state.stride(0),
+            state.stride(1),
+            state.stride(2),
+            state.stride(3),
+            x.stride(0),
+            x.stride(1),
+            x.stride(2),
+            dt.stride(0),
+            dt.stride(1),
+            dt.stride(2),
+            *(dt_bias.stride(0), dt_bias.stride(1)) if dt_bias is not None else 0,
+            A.stride(0),
+            A.stride(1),
+            A.stride(2),
+            B.stride(0),
+            B.stride(1),
+            B.stride(2),
+            C.stride(0),
+            C.stride(1),
+            C.stride(2),
+            *(D.stride(0), D.stride(1)) if D is not None else 0,
+            z_strides[0],
+            z_strides[1],
+            z_strides[2],
+            out.stride(0),
+            out.stride(1),
+            out.stride(2),
+            dt_softplus,
+            tie_hdim,
+            BLOCK_SIZE_M,
+            num_warps=num_warps,
+        )
+    if not has_heads:
+        out = out.squeeze(1)
+    return out
+
+
+def selective_state_update_ref(
+    state, x, dt, A, B, C, D=None, z=None, dt_bias=None, dt_softplus=False
+):
+    """
+    Argument:
+        state: (batch, dim, dstate) or (batch, nheads, dim, dstate)
+        x: (batch, dim) or (batch, nheads, dim)
+        dt: (batch, dim) or (batch, nheads, dim)
+        A: (dim, dstate) or (nheads, dim, dstate)
+        B: (batch, dstate) or (batch, ngroups, dstate)
+        C: (batch, dstate) or (batch, ngroups, dstate)
+        D: (dim,) or (nheads, dim)
+        z: (batch, dim) or (batch, nheads, dim)
+        dt_bias: (dim,) or (nheads, dim)
+    Return:
+        out: (batch, dim) or (batch, nheads, dim)
+    """
+    has_heads = state.dim() > 3
+    if state.dim() == 3:
+        state = state.unsqueeze(1)
+    if x.dim() == 2:
+        x = x.unsqueeze(1)
+    if dt.dim() == 2:
+        dt = dt.unsqueeze(1)
+    if A.dim() == 2:
+        A = A.unsqueeze(0)
+    if B.dim() == 2:
+        B = B.unsqueeze(1)
+    if C.dim() == 2:
+        C = C.unsqueeze(1)
+    if D is not None and D.dim() == 1:
+        D = D.unsqueeze(0)
+    if z is not None and z.dim() == 2:
+        z = z.unsqueeze(1)
+    if dt_bias is not None and dt_bias.dim() == 1:
+        dt_bias = dt_bias.unsqueeze(0)
+    batch, nheads, dim, dstate = state.shape
+    assert x.shape == (batch, nheads, dim)
+    assert dt.shape == x.shape
+    assert A.shape == (nheads, dim, dstate)
+    ngroups = B.shape[1]
+    assert nheads % ngroups == 0, "nheads must be divisible by ngroups"
+    assert B.shape == (batch, ngroups, dstate)
+    assert C.shape == B.shape
+    if D is not None:
+        assert D.shape == (nheads, dim)
+    if z is not None:
+        assert z.shape == x.shape
+    if dt_bias is not None:
+        assert dt_bias.shape == (nheads, dim)
+        dt = dt + dt_bias
+    dt = F.softplus(dt) if dt_softplus else dt
+    dA = torch.exp(
+        rearrange(dt, "b h d -> b h d 1") * A
+    )  # (batch, nheads, dim, dstate)
+    B = repeat(B, "b g n -> b (g h) n", h=nheads // ngroups)  # (batch, nheads, dstate)
+    C = repeat(C, "b g n -> b (g h) n", h=nheads // ngroups)  # (batch, nheads, dstate)
+    dB = rearrange(dt, "b h d -> b h d 1") * rearrange(
+        B, "b h n -> b h 1 n"
+    )  # (batch, nheads, dim, dstate)
+    state.copy_(
+        state * dA + dB * rearrange(x, "b h d -> b h d 1")
+    )  # (batch, dim, dstate
+    out = torch.einsum("bhdn,bhn->bhd", state.to(C.dtype), C)
+    if D is not None:
+        out += (x * D).to(out.dtype)
+    out = (out if z is None else out * F.silu(z)).to(x.dtype)
+    if not has_heads:
+        out = out.squeeze(1)
+    return out

torch-ext/mamba_ssm/ops/triton/softplus.py

@@ -0,0 +1,15 @@
+import triton
+import triton.language as tl
+from packaging import version
+
+TRITON3 = version.parse(triton.__version__) >= version.parse("3.0.0")
+
+
+if TRITON3:
+    @triton.jit
+    def softplus(dt):
+        return tl.math.log(tl.math.exp(dt) + 1)
+else:
+    @triton.jit
+    def softplus(dt):
+        return tl.math.log1p(tl.exp(dt))

torch-ext/mamba_ssm/ops/triton/ssd_bmm.py

@@ -0,0 +1,262 @@
+# Copyright (c) 2024, Tri Dao, Albert Gu.
+
+"""We want triton==2.1.0 or 2.2.0 for this
+"""
+
+import math
+import torch
+import torch.nn.functional as F
+
+import triton
+import triton.language as tl
+
+from einops import rearrange, repeat
+
+
+def init_to_zero(names):
+    return lambda nargs: [nargs[name].zero_() for name in names if nargs[name] is not None]
+
+
+@triton.autotune(
+    configs=[
+        triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 64}, num_stages=3, num_warps=8),
+        triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 32}, num_stages=4, num_warps=4),
+        triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32}, num_stages=4, num_warps=4),
+        triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32}, num_stages=4, num_warps=4),
+        triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32}, num_stages=4, num_warps=4),
+        triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32}, num_stages=4, num_warps=4),
+        triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32}, num_stages=5, num_warps=2),
+        triton.Config({'BLOCK_SIZE_M': 32, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32}, num_stages=5, num_warps=2),
+        triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32}, num_stages=4, num_warps=2),
+    ],
+    key=['chunk_size', 'K', 'IS_CAUSAL'],
+)
+@triton.jit
+def _bmm_chunk_fwd_kernel(
+    # Pointers to matrices
+    a_ptr, b_ptr, out_ptr, seq_idx_ptr,
+    # Matrix dimensions
+    seqlen, chunk_size, K, ngroups,
+    stride_a_batch, stride_a_seqlen, stride_a_head, stride_ak,
+    stride_b_batch, stride_b_seqlen, stride_b_head, stride_bk,
+    stride_out_batch, stride_out_chunk, stride_out_head, stride_outm, stride_outn,
+    stride_seq_idx_batch, stride_seq_idx_seqlen,
+    # Meta-parameters
+    IS_CAUSAL: tl.constexpr,
+    dot_dtype: tl.constexpr,
+    HAS_SEQ_IDX: tl.constexpr,
+    BLOCK_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr, BLOCK_SIZE_K: tl.constexpr,
+):
+    pid_b = tl.program_id(axis=1)
+    pid_ch = tl.program_id(axis=2)
+    pid_c = pid_ch // ngroups
+    pid_h = pid_ch - pid_c * ngroups
+    num_pid_n = tl.cdiv(chunk_size, BLOCK_SIZE_N)
+    pid_m = tl.program_id(axis=0) // num_pid_n
+    pid_n = tl.program_id(axis=0) % num_pid_n
+    if IS_CAUSAL:
+        if pid_n * BLOCK_SIZE_N >= (pid_m + 1) * BLOCK_SIZE_M:
+            return
+    a_ptr += pid_b * stride_a_batch + pid_c * chunk_size * stride_a_seqlen + pid_h * stride_a_head
+    b_ptr += pid_b * stride_b_batch + pid_c * chunk_size * stride_b_seqlen + pid_h * stride_b_head
+    if HAS_SEQ_IDX:
+        seq_idx_ptr += pid_b * stride_seq_idx_batch + pid_c * chunk_size * stride_seq_idx_seqlen
+
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+    offs_k = tl.arange(0, BLOCK_SIZE_K)
+    a_ptrs = a_ptr + (offs_m[:, None] * stride_a_seqlen + offs_k[None, :] * stride_ak)
+    b_ptrs = b_ptr + (offs_k[:, None] * stride_bk + offs_n[None, :] * stride_b_seqlen)
+    chunk_size_limit = min(chunk_size, seqlen - pid_c * chunk_size)
+
+    acc = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
+    for k in range(0, tl.cdiv(K, BLOCK_SIZE_K)):
+        a = tl.load(a_ptrs, mask=(offs_m[:, None] < chunk_size_limit) & (offs_k[None, :] < K - k * BLOCK_SIZE_K), other=0.0).to(dot_dtype)
+        b = tl.load(b_ptrs, mask=(offs_k[:, None] < K - k * BLOCK_SIZE_K) & (offs_n[None, :] < chunk_size_limit), other=0.0).to(dot_dtype)
+        acc += tl.dot(a, b)
+        a_ptrs += BLOCK_SIZE_K * stride_ak
+        b_ptrs += BLOCK_SIZE_K * stride_bk
+
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+    if HAS_SEQ_IDX:
+        chunk_size_limit = min(chunk_size, seqlen - pid_c * chunk_size)
+        seq_idx_m = tl.load(seq_idx_ptr + offs_m * stride_seq_idx_seqlen, mask=offs_m < chunk_size_limit, other=-1)
+        seq_idx_n = tl.load(seq_idx_ptr + offs_n * stride_seq_idx_seqlen, mask=offs_n < chunk_size_limit, other=-2)
+        acc = tl.where(seq_idx_m[:, None] == seq_idx_n[None, :], acc, 0.0)
+    out = acc.to(out_ptr.dtype.element_ty)
+
+    out_ptr += pid_b * stride_out_batch + pid_c * stride_out_chunk + pid_h * stride_out_head
+    out_ptrs = out_ptr + (stride_outm * offs_m[:, None] + offs_n[None, :] * stride_outn)
+    tl.store(out_ptrs, out, mask=(offs_m[:, None] < chunk_size) & (offs_n[None, :] < chunk_size))
+
+
+@triton.autotune(
+    configs=[
+        triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_CS': 64}, num_stages=3, num_warps=8),
+        triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_CS': 32}, num_stages=4, num_warps=4),
+        triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_CS': 32}, num_stages=4, num_warps=4),
+        triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_CS': 32}, num_stages=4, num_warps=4),
+        triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_CS': 32}, num_stages=4, num_warps=4),
+        triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_CS': 32}, num_stages=4, num_warps=4),
+        triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_CS': 32}, num_stages=5, num_warps=2),
+        triton.Config({'BLOCK_SIZE_M': 32, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_CS': 32}, num_stages=5, num_warps=2),
+        triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_CS': 32}, num_stages=4, num_warps=2),
+    ],
+    key=['chunk_size', 'K'],
+)
+@triton.jit
+def _bmm_chunk_bwd_kernel(
+    # Pointers to matrices
+    a_ptr, dout_ptr, db_ptr, res_ptr,
+    # Matrix dimensions
+    seqlen, chunk_size, K, ngroups,
+    stride_a_batch, stride_a_seqlen, stride_a_head, stride_ak,
+    stride_dout_batch, stride_dout_chunk, stride_dout_head, stride_dout_csize_m, stride_dout_csize_n,
+    stride_db_batch, stride_db_seqlen, stride_db_head, stride_db_k,
+    stride_res_batch, stride_res_seqlen, stride_res_head, stride_res_k,
+    # Meta-parameters
+    dot_dtype: tl.constexpr,
+    HAS_RESIDUAL: tl.constexpr,
+    BLOCK_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr, BLOCK_SIZE_CS: tl.constexpr,
+):
+    pid_b = tl.program_id(axis=1)
+    pid_ch = tl.program_id(axis=2)
+    pid_c = pid_ch // ngroups
+    pid_h = pid_ch - pid_c * ngroups
+    num_pid_n = tl.cdiv(K, BLOCK_SIZE_N)
+    pid_m = tl.program_id(axis=0) // num_pid_n
+    pid_n = tl.program_id(axis=0) % num_pid_n
+
+    a_ptr += pid_b * stride_a_batch + pid_c * chunk_size * stride_a_seqlen + pid_h * stride_a_head
+    dout_ptr += pid_b * stride_dout_batch + pid_c * stride_dout_chunk + pid_h * stride_dout_head
+
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+    offs_cs = tl.arange(0, BLOCK_SIZE_CS)
+    dout_ptrs = dout_ptr + (offs_m[:, None] * stride_dout_csize_n + offs_cs[None, :] * stride_dout_csize_m)
+    a_ptrs = a_ptr + (offs_cs[:, None] * stride_a_seqlen + offs_n[None, :] * stride_ak)
+    chunk_size_limit = min(chunk_size, seqlen - pid_c * chunk_size)
+
+    acc = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
+    for cs in range(0, tl.cdiv(chunk_size_limit, BLOCK_SIZE_CS)):
+        dout = tl.load(dout_ptrs, mask=(offs_m[:, None] < chunk_size) & (offs_cs[None, :] < chunk_size_limit - cs * BLOCK_SIZE_CS), other=0.0).to(dot_dtype)
+        a = tl.load(a_ptrs, mask=(offs_cs[:, None] < chunk_size_limit - cs * BLOCK_SIZE_CS) & (offs_n[None, :] < K), other=0.0).to(dot_dtype)
+        acc += tl.dot(dout, a)
+        dout_ptrs += BLOCK_SIZE_CS * stride_dout_csize_m
+        a_ptrs += BLOCK_SIZE_CS * stride_a_seqlen
+
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+    if HAS_RESIDUAL:
+        res_ptr += pid_b * stride_res_batch + pid_c * chunk_size * stride_res_seqlen + pid_h * stride_res_head
+        res_ptrs = res_ptr + (offs_m[:, None] * stride_res_seqlen + offs_n[None, :] * stride_res_k)
+        res = tl.load(res_ptrs, mask=(offs_m[:, None] < chunk_size_limit) & (offs_n[None, :] < K)).to(tl.float32)
+        acc += res
+    db = acc.to(db_ptr.dtype.element_ty)
+
+    db_ptr += pid_b * stride_db_batch + pid_c * chunk_size * stride_db_seqlen + pid_h * stride_db_head
+    db_ptrs = db_ptr + (offs_m[:, None] * stride_db_seqlen + offs_n[None, :] * stride_db_k)
+    tl.store(db_ptrs, db, mask=(offs_m[:, None] < chunk_size_limit) & (offs_n[None, :] < K))
+
+
+def _bmm_chunk_fwd(a, b, chunk_size, seq_idx=None, causal=False, output_dtype=None):
+    """
+    Argument:
+        a: (batch, seqlen, k) or (batch, seqlen, ngroups, k)
+        b: (batch, seqlen, k) or (batch, seqlen, ngroups, k)
+        seq_idx: (batch, seqlen) or None. out[i, j] for seq_idx[i] != seq_idx[j] will be zeroed out.
+        causal: if True, then out[i, j] for i > j will be arbitrary, only out[i, j] for i <= j are
+            guaranteed to be correct.
+    Return:
+        out: (batch, nchunks, chunk_size, chunk_size) or (batch, nchunks, ngroups, chunk_size, chunk_size)
+    """
+    # Check constraints.
+    has_groups = a.dim() == 4
+    if not has_groups:
+        batch, seqlen, k = a.shape
+    else:
+        batch, seqlen, ngroups, k = a.shape
+    assert b.shape == a.shape
+    if seq_idx is not None:
+        assert seq_idx.shape == (batch, seqlen)
+    if a.stride(-1) != 1 and a.stride(1) != 1:
+        a = a.contiguous()
+    if b.stride(-1) != 1 and b.stride(1) != 1:
+        b = b.contiguous()
+    nchunks = math.ceil(seqlen / chunk_size)
+    # Allocates output.
+    out_dtype = a.dtype if output_dtype is None else output_dtype
+    out = torch.empty((batch, nchunks, chunk_size, chunk_size) if not has_groups else (batch, nchunks, ngroups, chunk_size, chunk_size),
+                      device=a.device, dtype=out_dtype)
+    dot_dtype = (tl.bfloat16 if a.dtype == torch.bfloat16 or b.dtype == torch.bfloat16 else
+                 (tl.float16 if a.dtype == torch.float16 or b.dtype == torch.float16 else tl.float32))
+    grid = lambda META: (triton.cdiv(chunk_size, META['BLOCK_SIZE_M']) * triton.cdiv(chunk_size, META['BLOCK_SIZE_N']),
+                    batch, nchunks if not has_groups else nchunks * ngroups)
+    with torch.cuda.device(a.device.index):
+        _bmm_chunk_fwd_kernel[grid](
+            a, b, out, seq_idx,
+            seqlen, chunk_size, k, ngroups if has_groups else 1,
+            a.stride(0), a.stride(1), 0 if not has_groups else a.stride(2), a.stride(-1),
+            b.stride(0), b.stride(1), 0 if not has_groups else b.stride(2), b.stride(-1),
+            out.stride(0), out.stride(1), 0 if not has_groups else out.stride(2), out.stride(-2), out.stride(-1),
+            *((seq_idx.stride(0), seq_idx.stride(1)) if seq_idx is not None else (0, 0)),
+            causal,
+            dot_dtype,
+            HAS_SEQ_IDX=seq_idx is not None,
+        )
+    return out
+
+
+def _bmm_chunk_bwd(a, dout, residual=None, out=None):
+    """
+    Argument:
+        a: (batch, seqlen, k) or (batch, seqlen, ngroups, k)
+        dout: (batch, nchunks, chunk_size, chunk_size) or (batch, nchunks, ngroups, chunk_size, chunk_size)
+        residual: (batch, seqlen, k) or (batch, seqlen, ngroups, k)
+    Return:
+        out: (batch, seqlen, k) or (batch, seqlen, ngroups, k)
+
+    If there was seq_idx in the fwd pass, then dout[i, j] for seq_idx[i] != seq_idx[j] should already be
+    zeroed out before calling this function.
+    """
+    # Check constraints.
+    has_groups = a.dim() == 4
+    if not has_groups:
+        batch, seqlen, k = a.shape
+    else:
+        batch, seqlen, ngroups, k = a.shape
+    nchunks, chunk_size = dout.shape[1], dout.shape[-1]
+    if a.stride(-1) != 1 and a.stride(-2) != 1:
+        a = a.contiguous()
+    if dout.stride(-1) != 1 and dout.stride(-2) != 1:
+        dout = dout.contiguous()
+    if residual is not None:
+        assert residual.shape == (batch, seqlen, k) if not has_groups else (batch, seqlen, ngroups, k)
+        if residual.stride(-1) != 1 and residual.stride(1) != 1:
+            residual = residual.contiguous()
+    # Allocates output.
+    if out is not None:
+        assert out.shape == a.shape
+        assert out.stride(-1) == 1 or out.stride(1) == 1
+    else:
+        out = torch.empty_like(a)
+    dot_dtype = (tl.bfloat16 if a.dtype == torch.bfloat16 or dout.dtype == torch.bfloat16 else
+                 (tl.float16 if a.dtype == torch.float16 or dout.dtype == torch.float16 else tl.float32))
+    grid = lambda META: (triton.cdiv(chunk_size, META['BLOCK_SIZE_M']) * triton.cdiv(k, META['BLOCK_SIZE_N']), batch,
+                    nchunks if not has_groups else nchunks * ngroups)
+    residual_strides = ((residual.stride(0), residual.stride(1), 0 if not has_groups else residual.stride(2),
+                         residual.stride(-1))
+                        if residual is not None else (0, 0, 0, 0))
+    with torch.cuda.device(a.device.index):
+        _bmm_chunk_bwd_kernel[grid](
+            a, dout, out, residual,
+            seqlen, chunk_size, k, ngroups if has_groups else 1,
+            a.stride(0), a.stride(1), 0 if not has_groups else a.stride(2), a.stride(-1),
+            dout.stride(0), dout.stride(1), 0 if not has_groups else dout.stride(2), dout.stride(-2), dout.stride(-1),
+            out.stride(0), out.stride(1), 0 if not has_groups else out.stride(2), out.stride(-1),
+            residual_strides[0], residual_strides[1], residual_strides[2], residual_strides[3],
+            dot_dtype,
+            HAS_RESIDUAL=residual is not None,
+        )
+    return out

torch-ext/mamba_ssm/ops/triton/ssd_chunk_state.py

@@ -0,0 +1,2012 @@
+# Copyright (c) 2024, Tri Dao, Albert Gu.
+
+"""We want triton==2.1.0 or 2.2.0 for this
+"""
+
+import math
+import torch
+import torch.nn.functional as F
+
+import triton
+import triton.language as tl
+
+from einops import rearrange, repeat
+
+from .softplus import softplus
+
+
+def init_to_zero(names):
+    return lambda nargs: [
+        nargs[name].zero_() for name in names if nargs[name] is not None
+    ]
+
+
+@triton.autotune(
+    configs=[
+        triton.Config({"BLOCK_SIZE_H": 1}),
+        triton.Config({"BLOCK_SIZE_H": 2}),
+        triton.Config({"BLOCK_SIZE_H": 4}),
+        triton.Config({"BLOCK_SIZE_H": 8}),
+        triton.Config({"BLOCK_SIZE_H": 16}),
+        triton.Config({"BLOCK_SIZE_H": 32}),
+        triton.Config({"BLOCK_SIZE_H": 64}),
+    ],
+    key=["chunk_size", "nheads"],
+)
+@triton.jit
+def _chunk_cumsum_fwd_kernel(
+    # Pointers to matrices
+    dt_ptr,
+    A_ptr,
+    dt_bias_ptr,
+    dt_out_ptr,
+    dA_cumsum_ptr,
+    # Matrix dimension
+    batch,
+    seqlen,
+    nheads,
+    chunk_size,
+    dt_min,
+    dt_max,
+    # Strides
+    stride_dt_batch,
+    stride_dt_seqlen,
+    stride_dt_head,
+    stride_A_head,
+    stride_dt_bias_head,
+    stride_dt_out_batch,
+    stride_dt_out_chunk,
+    stride_dt_out_head,
+    stride_dt_out_csize,
+    stride_dA_cs_batch,
+    stride_dA_cs_chunk,
+    stride_dA_cs_head,
+    stride_dA_cs_csize,
+    # Meta-parameters
+    DT_SOFTPLUS: tl.constexpr,
+    HAS_DT_BIAS: tl.constexpr,
+    BLOCK_SIZE_H: tl.constexpr,
+    BLOCK_SIZE_CHUNK: tl.constexpr,
+):
+    pid_b = tl.program_id(axis=0)
+    pid_c = tl.program_id(axis=1)
+    pid_h = tl.program_id(axis=2)
+    dt_ptr += pid_b * stride_dt_batch + pid_c * chunk_size * stride_dt_seqlen
+    dt_out_ptr += pid_b * stride_dt_out_batch + pid_c * stride_dt_out_chunk
+    dA_cumsum_ptr += pid_b * stride_dA_cs_batch + pid_c * stride_dA_cs_chunk
+
+    offs_h = pid_h * BLOCK_SIZE_H + tl.arange(0, BLOCK_SIZE_H)
+    offs_c = tl.arange(0, BLOCK_SIZE_CHUNK)
+    dt_ptrs = dt_ptr + (
+        offs_h[:, None] * stride_dt_head + offs_c[None, :] * stride_dt_seqlen
+    )
+    A_ptrs = A_ptr + offs_h * stride_A_head
+    dt_out_ptrs = dt_out_ptr + (
+        offs_h[:, None] * stride_dt_out_head + offs_c[None, :] * stride_dt_out_csize
+    )
+    dA_cs_ptrs = dA_cumsum_ptr + (
+        offs_h[:, None] * stride_dA_cs_head + offs_c[None, :] * stride_dA_cs_csize
+    )
+    chunk_size_limit = min(chunk_size, seqlen - pid_c * chunk_size)
+
+    dt = tl.load(
+        dt_ptrs,
+        mask=(offs_h[:, None] < nheads) & (offs_c[None, :] < chunk_size_limit),
+        other=0.0,
+    ).to(tl.float32)
+    if HAS_DT_BIAS:
+        dt_bias = tl.load(
+            dt_bias_ptr + offs_h * stride_dt_bias_head, mask=offs_h < nheads, other=0.0
+        ).to(tl.float32)
+        dt += dt_bias[:, None]
+    if DT_SOFTPLUS:
+        dt = tl.where(dt <= 20.0, softplus(dt), dt)
+    # As of Triton 2.2.0, tl.clamp is not available yet
+    # dt = tl.clamp(dt, dt_min, dt_max)
+    dt = tl.minimum(tl.maximum(dt, dt_min), dt_max)
+    dt = tl.where(
+        (offs_h[:, None] < nheads) & (offs_c[None, :] < chunk_size_limit), dt, 0.0
+    )
+    tl.store(
+        dt_out_ptrs,
+        dt,
+        mask=(offs_h[:, None] < nheads) & (offs_c[None, :] < chunk_size),
+    )
+    A = tl.load(A_ptrs, mask=offs_h < nheads, other=0.0).to(tl.float32)
+    dA = dt * A[:, None]
+    dA_cs = tl.cumsum(dA, axis=1)
+    tl.store(
+        dA_cs_ptrs,
+        dA_cs,
+        mask=(offs_h[:, None] < nheads) & (offs_c[None, :] < chunk_size),
+    )
+
+
+@triton.autotune(
+    configs=[
+        triton.Config(
+            {"BLOCK_SIZE_H": 1}, pre_hook=init_to_zero(["dA_ptr", "ddt_bias_ptr"])
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_H": 2}, pre_hook=init_to_zero(["dA_ptr", "ddt_bias_ptr"])
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_H": 4}, pre_hook=init_to_zero(["dA_ptr", "ddt_bias_ptr"])
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_H": 8}, pre_hook=init_to_zero(["dA_ptr", "ddt_bias_ptr"])
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_H": 16}, pre_hook=init_to_zero(["dA_ptr", "ddt_bias_ptr"])
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_H": 32}, pre_hook=init_to_zero(["dA_ptr", "ddt_bias_ptr"])
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_H": 64}, pre_hook=init_to_zero(["dA_ptr", "ddt_bias_ptr"])
+        ),
+    ],
+    key=["chunk_size", "nheads"],
+)
+@triton.jit
+def _chunk_cumsum_bwd_kernel(
+    # Pointers to matrices
+    ddA_ptr,
+    ddt_out_ptr,
+    dt_ptr,
+    A_ptr,
+    dt_bias_ptr,
+    ddt_ptr,
+    dA_ptr,
+    ddt_bias_ptr,
+    # Matrix dimensions
+    batch,
+    seqlen,
+    nheads,
+    chunk_size,
+    dt_min,
+    dt_max,
+    # Strides
+    stride_ddA_batch,
+    stride_ddA_chunk,
+    stride_ddA_head,
+    stride_ddA_csize,
+    stride_ddt_out_batch,
+    stride_ddt_out_chunk,
+    stride_ddt_out_head,
+    stride_ddt_out_csize,
+    stride_dt_batch,
+    stride_dt_seqlen,
+    stride_dt_head,
+    stride_A_head,
+    stride_dt_bias_head,
+    stride_ddt_batch,
+    stride_ddt_seqlen,
+    stride_ddt_head,
+    stride_dA_head,
+    stride_ddt_bias_head,
+    # Meta-parameters
+    DT_SOFTPLUS: tl.constexpr,
+    HAS_DT_BIAS: tl.constexpr,
+    BLOCK_SIZE_H: tl.constexpr,
+    BLOCK_SIZE_CHUNK: tl.constexpr,
+):
+    pid_b = tl.program_id(axis=0)
+    pid_c = tl.program_id(axis=1)
+    pid_h = tl.program_id(axis=2)
+    ddt_out_ptr += pid_b * stride_ddt_out_batch + pid_c * stride_ddt_out_chunk
+    ddA_ptr += pid_b * stride_ddA_batch + pid_c * stride_ddA_chunk
+    dt_ptr += pid_b * stride_dt_batch + pid_c * chunk_size * stride_dt_seqlen
+    ddt_ptr += pid_b * stride_ddt_batch + pid_c * chunk_size * stride_ddt_seqlen
+
+    offs_h = pid_h * BLOCK_SIZE_H + tl.arange(0, BLOCK_SIZE_H)
+    offs_c = tl.arange(0, BLOCK_SIZE_CHUNK)
+    ddt_out_ptrs = ddt_out_ptr + (
+        offs_h[:, None] * stride_ddt_out_head + offs_c[None, :] * stride_ddt_out_csize
+    )
+    ddA_ptrs = ddA_ptr + (
+        offs_h[:, None] * stride_ddA_head + offs_c[None, :] * stride_ddA_csize
+    )
+    dt_ptrs = dt_ptr + (
+        offs_h[:, None] * stride_dt_head + offs_c[None, :] * stride_dt_seqlen
+    )
+    ddt_ptrs = ddt_ptr + (
+        offs_h[:, None] * stride_ddt_head + offs_c[None, :] * stride_ddt_seqlen
+    )
+    A_ptrs = A_ptr + offs_h * stride_A_head
+    chunk_size_limit = min(chunk_size, seqlen - pid_c * chunk_size)
+
+    ddA = tl.load(
+        ddA_ptrs,
+        mask=(offs_h[:, None] < nheads) & (offs_c[None, :] < chunk_size_limit),
+        other=0.0,
+    ).to(tl.float32)
+    ddt_out = tl.load(
+        ddt_out_ptrs,
+        mask=(offs_h[:, None] < nheads) & (offs_c[None, :] < chunk_size_limit),
+        other=0.0,
+    ).to(tl.float32)
+    A = tl.load(A_ptrs, mask=offs_h < nheads, other=0.0).to(tl.float32)
+    ddt = ddA * A[:, None] + ddt_out
+    dt = tl.load(
+        dt_ptrs,
+        mask=(offs_h[:, None] < nheads) & (offs_c[None, :] < chunk_size_limit),
+        other=0.0,
+    ).to(tl.float32)
+    if HAS_DT_BIAS:
+        dt_bias = tl.load(
+            dt_bias_ptr + offs_h * stride_dt_bias_head, mask=offs_h < nheads, other=0.0
+        ).to(tl.float32)
+        dt += dt_bias[:, None]
+    if DT_SOFTPLUS:
+        dt_presoftplus = dt
+        dt = tl.where(dt <= 20.0, softplus(dt), ddt)
+    clamp_mask = (dt < dt_min) | (dt > dt_max)
+    # As of Triton 2.2.0, tl.clamp is not available yet
+    # dt = tl.clamp(dt, dt_min, dt_max)
+    dt = tl.minimum(tl.maximum(dt, dt_min), dt_max)
+    dt = tl.where(
+        (offs_h[:, None] < nheads) & (offs_c[None, :] < chunk_size_limit), dt, 0.0
+    )
+    ddt = tl.where(
+        (offs_h[:, None] < nheads) & (offs_c[None, :] < chunk_size_limit), ddt, 0.0
+    )
+    ddt = tl.where(clamp_mask, 0.0, ddt)
+    if DT_SOFTPLUS:
+        ddt = tl.where(dt_presoftplus <= 20.0, ddt * tl.sigmoid(dt_presoftplus), ddt)
+    tl.store(
+        ddt_ptrs,
+        ddt,
+        mask=(offs_h[:, None] < nheads) & (offs_c[None, :] < chunk_size_limit),
+    )
+    dA = tl.sum(ddA * dt, axis=1)
+    tl.atomic_add(dA_ptr + offs_h * stride_dA_head, dA, mask=offs_h < nheads)
+    if HAS_DT_BIAS:
+        ddt_bias = tl.sum(ddt, axis=1)
+        tl.atomic_add(
+            ddt_bias_ptr + offs_h * stride_ddt_bias_head, ddt_bias, mask=offs_h < nheads
+        )
+
+
+@triton.autotune(
+    configs=[
+        triton.Config(
+            {"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 64},
+            num_stages=3,
+            num_warps=8,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 128, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 64, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 128, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 32, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 32, "BLOCK_SIZE_K": 32},
+            num_stages=5,
+            num_warps=2,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 32, "BLOCK_SIZE_N": 64, "BLOCK_SIZE_K": 32},
+            num_stages=5,
+            num_warps=2,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 64, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=2,
+        ),
+    ],
+    key=["hdim", "dstate", "chunk_size"],
+)
+@triton.jit
+def _chunk_state_fwd_kernel(
+    # Pointers to matrices
+    x_ptr,
+    b_ptr,
+    states_ptr,
+    dt_ptr,
+    dA_cumsum_ptr,
+    seq_idx_ptr,
+    # Matrix dimensions
+    hdim,
+    dstate,
+    chunk_size,
+    batch,
+    seqlen,
+    nheads_ngroups_ratio,
+    # Strides
+    stride_x_batch,
+    stride_x_seqlen,
+    stride_x_head,
+    stride_x_hdim,
+    stride_b_batch,
+    stride_b_seqlen,
+    stride_b_head,
+    stride_b_dstate,
+    stride_states_batch,
+    stride_states_chunk,
+    stride_states_head,
+    stride_states_hdim,
+    stride_states_dstate,
+    stride_dt_batch,
+    stride_dt_chunk,
+    stride_dt_head,
+    stride_dt_csize,
+    stride_dA_cs_batch,
+    stride_dA_cs_chunk,
+    stride_dA_cs_head,
+    stride_dA_cs_csize,
+    stride_seq_idx_batch,
+    stride_seq_idx_seqlen,
+    # Meta-parameters
+    HAS_SEQ_IDX: tl.constexpr,
+    BLOCK_SIZE_M: tl.constexpr,
+    BLOCK_SIZE_N: tl.constexpr,
+    BLOCK_SIZE_K: tl.constexpr,
+):
+    pid_bc = tl.program_id(axis=1)
+    pid_c = pid_bc // batch
+    pid_b = pid_bc - pid_c * batch
+    pid_h = tl.program_id(axis=2)
+    num_pid_n = tl.cdiv(dstate, BLOCK_SIZE_N)
+    pid_m = tl.program_id(axis=0) // num_pid_n
+    pid_n = tl.program_id(axis=0) % num_pid_n
+    b_ptr += (
+        pid_b * stride_b_batch
+        + pid_c * chunk_size * stride_b_seqlen
+        + (pid_h // nheads_ngroups_ratio) * stride_b_head
+    )
+    x_ptr += (
+        pid_b * stride_x_batch
+        + pid_c * chunk_size * stride_x_seqlen
+        + pid_h * stride_x_head
+    )
+    dt_ptr += pid_b * stride_dt_batch + pid_c * stride_dt_chunk + pid_h * stride_dt_head
+    dA_cumsum_ptr += (
+        pid_b * stride_dA_cs_batch
+        + pid_c * stride_dA_cs_chunk
+        + pid_h * stride_dA_cs_head
+    )
+    if HAS_SEQ_IDX:
+        seq_idx_ptr += (
+            pid_b * stride_seq_idx_batch + pid_c * chunk_size * stride_seq_idx_seqlen
+        )
+
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+    offs_k = tl.arange(0, BLOCK_SIZE_K)
+    x_ptrs = x_ptr + (
+        offs_m[:, None] * stride_x_hdim + offs_k[None, :] * stride_x_seqlen
+    )
+    b_ptrs = b_ptr + (
+        offs_n[None, :] * stride_b_dstate + offs_k[:, None] * stride_b_seqlen
+    )
+    dt_ptrs = dt_ptr + offs_k * stride_dt_csize
+    dA_cs_last = tl.load(dA_cumsum_ptr + (chunk_size - 1) * stride_dA_cs_csize).to(
+        tl.float32
+    )
+    dA_cumsum_ptrs = dA_cumsum_ptr + offs_k * stride_dA_cs_csize
+    if HAS_SEQ_IDX:
+        seq_idx_ptrs = seq_idx_ptr + offs_k * stride_seq_idx_seqlen
+
+    chunk_size_limit = min(chunk_size, seqlen - pid_c * chunk_size)
+    if HAS_SEQ_IDX:
+        seq_idx_last = tl.load(
+            seq_idx_ptr + (chunk_size_limit - 1) * stride_seq_idx_seqlen
+        )
+
+    acc = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
+    for k in range(0, chunk_size_limit, BLOCK_SIZE_K):
+        x = tl.load(
+            x_ptrs,
+            mask=(offs_m[:, None] < hdim) & (offs_k[None, :] < chunk_size_limit - k),
+            other=0.0,
+        )
+        b = tl.load(
+            b_ptrs,
+            mask=(offs_k[:, None] < chunk_size_limit - k) & (offs_n[None, :] < dstate),
+            other=0.0,
+        ).to(tl.float32)
+        dA_cs_k = tl.load(
+            dA_cumsum_ptrs, mask=offs_k < chunk_size_limit - k, other=0.0
+        ).to(tl.float32)
+        if HAS_SEQ_IDX:
+            seq_idx_k = tl.load(
+                seq_idx_ptrs, mask=offs_k < chunk_size_limit - k, other=-1
+            )
+        dt_k = tl.load(dt_ptrs, mask=offs_k < chunk_size_limit - k, other=0.0).to(
+            tl.float32
+        )
+        if not HAS_SEQ_IDX:
+            scale = tl.exp((dA_cs_last - dA_cs_k)) * dt_k
+        else:
+            scale = tl.where(
+                seq_idx_k == seq_idx_last, tl.exp((dA_cs_last - dA_cs_k)) * dt_k, 0.0
+            )
+        b *= scale[:, None]
+        b = b.to(x_ptr.dtype.element_ty)
+        acc += tl.dot(x, b)
+        x_ptrs += BLOCK_SIZE_K * stride_x_seqlen
+        b_ptrs += BLOCK_SIZE_K * stride_b_seqlen
+        dt_ptrs += BLOCK_SIZE_K * stride_dt_csize
+        dA_cumsum_ptrs += BLOCK_SIZE_K * stride_dA_cs_csize
+        if HAS_SEQ_IDX:
+            seq_idx_ptrs += BLOCK_SIZE_K * stride_seq_idx_seqlen
+    states = acc.to(states_ptr.dtype.element_ty)
+
+    states_ptr += (
+        pid_b * stride_states_batch
+        + pid_c * stride_states_chunk
+        + pid_h * stride_states_head
+    )
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+    states_ptrs = states_ptr + (
+        offs_m[:, None] * stride_states_hdim + offs_n[None, :] * stride_states_dstate
+    )
+    c_mask = (offs_m[:, None] < hdim) & (offs_n[None, :] < dstate)
+    tl.store(states_ptrs, states, mask=c_mask)
+
+
+@triton.autotune(
+    configs=[
+        triton.Config(
+            {"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 64},
+            num_stages=3,
+            num_warps=8,
+            pre_hook=init_to_zero(["ddt_ptr", "ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddt_ptr", "ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 128, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddt_ptr", "ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 64, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddt_ptr", "ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 128, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddt_ptr", "ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 32, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddt_ptr", "ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 32, "BLOCK_SIZE_K": 32},
+            num_stages=5,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddt_ptr", "ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 32, "BLOCK_SIZE_N": 64, "BLOCK_SIZE_K": 32},
+            num_stages=5,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddt_ptr", "ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 64, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddt_ptr", "ddA_cumsum_ptr"]),
+        ),
+    ],
+    key=["chunk_size", "hdim", "dstate"],
+)
+@triton.jit
+def _chunk_state_bwd_dx_kernel(
+    # Pointers to matrices
+    x_ptr,
+    b_ptr,
+    dstates_ptr,
+    dt_ptr,
+    dA_cumsum_ptr,
+    dx_ptr,
+    ddt_ptr,
+    ddA_cumsum_ptr,
+    # Matrix dimensions
+    chunk_size,
+    hdim,
+    dstate,
+    batch,
+    seqlen,
+    nheads_ngroups_ratio,
+    # Strides
+    stride_x_batch,
+    stride_x_seqlen,
+    stride_x_head,
+    stride_x_hdim,
+    stride_b_batch,
+    stride_b_seqlen,
+    stride_b_head,
+    stride_b_dstate,
+    stride_dstates_batch,
+    stride_dstates_chunk,
+    stride_states_head,
+    stride_states_hdim,
+    stride_states_dstate,
+    stride_dt_batch,
+    stride_dt_chunk,
+    stride_dt_head,
+    stride_dt_csize,
+    stride_dA_cs_batch,
+    stride_dA_cs_chunk,
+    stride_dA_cs_head,
+    stride_dA_cs_csize,
+    stride_dx_batch,
+    stride_dx_seqlen,
+    stride_dx_head,
+    stride_dx_hdim,
+    stride_ddt_batch,
+    stride_ddt_chunk,
+    stride_ddt_head,
+    stride_ddt_csize,
+    stride_ddA_cs_batch,
+    stride_ddA_cs_chunk,
+    stride_ddA_cs_head,
+    stride_ddA_cs_csize,
+    # Meta-parameters
+    BLOCK_SIZE_M: tl.constexpr,
+    BLOCK_SIZE_N: tl.constexpr,
+    BLOCK_SIZE_K: tl.constexpr,
+    BLOCK_SIZE_DSTATE: tl.constexpr,
+):
+    pid_bc = tl.program_id(axis=1)
+    pid_c = pid_bc // batch
+    pid_b = pid_bc - pid_c * batch
+    pid_h = tl.program_id(axis=2)
+    num_pid_n = tl.cdiv(hdim, BLOCK_SIZE_N)
+    pid_m = tl.program_id(axis=0) // num_pid_n
+    pid_n = tl.program_id(axis=0) % num_pid_n
+    x_ptr += (
+        pid_b * stride_x_batch
+        + pid_c * chunk_size * stride_x_seqlen
+        + pid_h * stride_x_head
+    )
+    b_ptr += (
+        pid_b * stride_b_batch
+        + pid_c * chunk_size * stride_b_seqlen
+        + (pid_h // nheads_ngroups_ratio) * stride_b_head
+    )
+    dstates_ptr += (
+        pid_b * stride_dstates_batch
+        + pid_c * stride_dstates_chunk
+        + pid_h * stride_states_head
+    )
+    dt_ptr += pid_b * stride_dt_batch + pid_c * stride_dt_chunk + pid_h * stride_dt_head
+    ddt_ptr += (
+        pid_b * stride_ddt_batch + pid_c * stride_ddt_chunk + pid_h * stride_ddt_head
+    )
+    ddA_cumsum_ptr += (
+        pid_b * stride_ddA_cs_batch
+        + pid_c * stride_ddA_cs_chunk
+        + pid_h * stride_ddA_cs_head
+    )
+    dA_cumsum_ptr += (
+        pid_b * stride_dA_cs_batch
+        + pid_c * stride_dA_cs_chunk
+        + pid_h * stride_dA_cs_head
+    )
+
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+
+    chunk_size_limit = min(chunk_size, seqlen - pid_c * chunk_size)
+    # Faster to just do 1 iteration with larger BLOCK_SIZE_K, up to block size 128
+    offs_k = tl.arange(
+        0, BLOCK_SIZE_DSTATE if BLOCK_SIZE_DSTATE <= 128 else BLOCK_SIZE_K
+    )
+    b_ptrs = b_ptr + (
+        offs_m[:, None] * stride_b_seqlen + offs_k[None, :] * stride_b_dstate
+    )
+    dstates_ptrs = dstates_ptr + (
+        offs_n[None, :] * stride_states_hdim + offs_k[:, None] * stride_states_dstate
+    )
+    if BLOCK_SIZE_DSTATE <= 128:
+        b = tl.load(
+            b_ptrs,
+            mask=(offs_m[:, None] < chunk_size_limit) & (offs_k[None, :] < dstate),
+            other=0.0,
+        )
+        dstates = tl.load(
+            dstates_ptrs,
+            mask=(offs_k[:, None] < dstate) & (offs_n[None, :] < hdim),
+            other=0.0,
+        )
+        dstates = dstates.to(b_ptr.dtype.element_ty)
+        acc = tl.dot(b, dstates)
+    else:
+        acc = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
+        for k in range(0, dstate, BLOCK_SIZE_K):
+            b = tl.load(
+                b_ptrs,
+                mask=(offs_m[:, None] < chunk_size_limit)
+                & (offs_k[None, :] < dstate - k),
+                other=0.0,
+            )
+            dstates = tl.load(
+                dstates_ptrs,
+                mask=(offs_k[:, None] < dstate - k) & (offs_n[None, :] < hdim),
+                other=0.0,
+            )
+            dstates = dstates.to(b_ptr.dtype.element_ty)
+            acc += tl.dot(b, dstates)
+            b_ptrs += BLOCK_SIZE_K * stride_b_dstate
+            dstates_ptrs += BLOCK_SIZE_K * stride_states_dstate
+
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+
+    dA_cs_last = tl.load(dA_cumsum_ptr + (chunk_size - 1) * stride_dA_cs_csize).to(
+        tl.float32
+    )
+    dt_ptrs = dt_ptr + offs_m * stride_dt_csize
+    dA_cumsum_ptrs = dA_cumsum_ptr + offs_m * stride_dA_cs_csize
+    dA_cs_m = tl.load(dA_cumsum_ptrs, mask=offs_m < chunk_size, other=0.0).to(
+        tl.float32
+    )
+    dt_m = tl.load(dt_ptrs, mask=offs_m < chunk_size, other=0.0).to(tl.float32)
+    acc *= tl.exp(dA_cs_last - dA_cs_m)[:, None]
+
+    x_ptrs = x_ptr + (
+        offs_m[:, None] * stride_x_seqlen + offs_n[None, :] * stride_x_hdim
+    )
+    x = tl.load(
+        x_ptrs,
+        mask=(offs_m[:, None] < chunk_size_limit) & (offs_n[None, :] < hdim),
+        other=0.0,
+    ).to(tl.float32)
+    ddt = tl.sum(acc * x, axis=1)
+    ddt_ptrs = ddt_ptr + offs_m * stride_ddt_csize
+    tl.atomic_add(ddt_ptrs, ddt, mask=offs_m < chunk_size)
+    ddA_cs = -(ddt * dt_m)
+    ddA_cs_last = -tl.sum(ddA_cs)
+    ddA_cumsum_ptrs = ddA_cumsum_ptr + offs_m * stride_ddA_cs_csize
+    tl.atomic_add(ddA_cumsum_ptrs, ddA_cs, mask=offs_m < chunk_size)
+    tl.atomic_add(ddA_cumsum_ptr + (chunk_size - 1) * stride_ddA_cs_csize, ddA_cs_last)
+
+    dx = (acc * dt_m[:, None]).to(dx_ptr.dtype.element_ty)
+    dx_ptr += (
+        pid_b * stride_dx_batch
+        + pid_c * chunk_size * stride_dx_seqlen
+        + pid_h * stride_dx_head
+    )
+    dx_ptrs = dx_ptr + (
+        offs_m[:, None] * stride_dx_seqlen + offs_n[None, :] * stride_dx_hdim
+    )
+    tl.store(
+        dx_ptrs,
+        dx,
+        mask=(offs_m[:, None] < chunk_size_limit) & (offs_n[None, :] < hdim),
+    )
+
+
+@triton.autotune(
+    configs=[
+        triton.Config(
+            {"BLOCK_SIZE_M": 32, "BLOCK_SIZE_N": 128},
+            num_stages=3,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 32},
+            num_stages=3,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 128},
+            num_stages=3,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 64},
+            num_stages=3,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 64},
+            num_stages=3,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 32},
+            num_stages=3,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 32, "BLOCK_SIZE_N": 64},
+            num_stages=3,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 32, "BLOCK_SIZE_N": 32},
+            num_stages=3,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+    ],
+    key=["chunk_size", "dstate", "hdim"],
+)
+@triton.jit
+def _chunk_state_bwd_db_kernel(
+    # Pointers to matrices
+    x_ptr,
+    dstates_ptr,
+    b_ptr,
+    dt_ptr,
+    dA_cumsum_ptr,
+    seq_idx_ptr,
+    db_ptr,
+    ddA_cumsum_ptr,
+    # Matrix dimensions
+    chunk_size,
+    dstate,
+    hdim,
+    batch,
+    seqlen,
+    nheads,
+    nheads_per_program,
+    ngroups,
+    # Strides
+    stride_x_batch,
+    stride_x_seqlen,
+    stride_x_head,
+    stride_x_hdim,
+    stride_dstates_batch,
+    stride_dstates_chunk,
+    stride_states_head,
+    stride_states_hdim,
+    stride_states_dstate,
+    stride_b_batch,
+    stride_b_seqlen,
+    stride_b_head,
+    stride_b_dstate,
+    stride_dt_batch,
+    stride_dt_chunk,
+    stride_dt_head,
+    stride_dt_csize,
+    stride_dA_cs_batch,
+    stride_dA_cs_chunk,
+    stride_dA_cs_head,
+    stride_dA_cs_csize,
+    stride_seq_idx_batch,
+    stride_seq_idx_seqlen,
+    stride_db_batch,
+    stride_db_seqlen,
+    stride_db_split,
+    stride_db_group,
+    stride_db_dstate,
+    stride_ddA_cs_batch,
+    stride_ddA_cs_chunk,
+    stride_ddA_cs_head,
+    stride_ddA_cs_csize,
+    # Meta-parameters
+    HAS_DDA_CS: tl.constexpr,
+    HAS_SEQ_IDX: tl.constexpr,
+    BLOCK_SIZE_M: tl.constexpr,
+    BLOCK_SIZE_N: tl.constexpr,
+    BLOCK_SIZE_K: tl.constexpr,
+):
+    pid_bc = tl.program_id(axis=1)
+    pid_c = pid_bc // batch
+    pid_b = pid_bc - pid_c * batch
+    pid_sg = tl.program_id(axis=2)
+    pid_s = pid_sg // ngroups
+    pid_g = pid_sg - pid_s * ngroups
+    num_pid_n = tl.cdiv(dstate, BLOCK_SIZE_N)
+    pid_m = tl.program_id(axis=0) // num_pid_n
+    pid_n = tl.program_id(axis=0) % num_pid_n
+    x_ptr += (
+        pid_b * stride_x_batch
+        + pid_c * chunk_size * stride_x_seqlen
+        + (pid_g * (nheads // ngroups) + pid_s * nheads_per_program) * stride_x_head
+    )
+    db_ptr += (
+        pid_b * stride_db_batch
+        + pid_c * chunk_size * stride_db_seqlen
+        + pid_g * stride_db_group
+        + pid_s * stride_db_split
+    )
+    dstates_ptr += (
+        pid_b * stride_dstates_batch
+        + pid_c * stride_dstates_chunk
+        + (pid_g * (nheads // ngroups) + pid_s * nheads_per_program)
+        * stride_states_head
+    )
+    dt_ptr += (
+        pid_b * stride_dt_batch
+        + pid_c * stride_dt_chunk
+        + (pid_g * (nheads // ngroups) + pid_s * nheads_per_program) * stride_dt_head
+    )
+    dA_cumsum_ptr += (
+        pid_b * stride_dA_cs_batch
+        + pid_c * stride_dA_cs_chunk
+        + (pid_g * (nheads // ngroups) + pid_s * nheads_per_program) * stride_dA_cs_head
+    )
+    if HAS_DDA_CS:
+        b_ptr += (
+            pid_b * stride_b_batch
+            + pid_c * chunk_size * stride_b_seqlen
+            + pid_g * stride_b_head
+        )
+        ddA_cumsum_ptr += (
+            pid_b * stride_ddA_cs_batch
+            + pid_c * stride_ddA_cs_chunk
+            + (pid_g * (nheads // ngroups) + pid_s * nheads_per_program)
+            * stride_ddA_cs_head
+        )
+    if HAS_SEQ_IDX:
+        seq_idx_ptr += (
+            pid_b * stride_seq_idx_batch + pid_c * chunk_size * stride_seq_idx_seqlen
+        )
+
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+    offs_k = tl.arange(0, BLOCK_SIZE_K)
+    x_ptrs = x_ptr + (
+        offs_m[:, None] * stride_x_seqlen + offs_k[None, :] * stride_x_hdim
+    )
+    dstates_ptrs = dstates_ptr + (
+        offs_n[None, :] * stride_states_dstate + offs_k[:, None] * stride_states_hdim
+    )
+    dt_ptrs = dt_ptr + offs_m * stride_dt_csize
+    dA_cumsum_ptrs = dA_cumsum_ptr + offs_m * stride_dA_cs_csize
+    if HAS_DDA_CS:
+        b_ptrs = b_ptr + (
+            offs_m[:, None] * stride_b_seqlen + offs_n[None, :] * stride_b_dstate
+        )
+        ddA_cumsum_ptrs = ddA_cumsum_ptr + offs_m * stride_ddA_cs_csize
+
+    chunk_size_limit = min(chunk_size, seqlen - pid_c * chunk_size)
+    acc = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
+    if HAS_DDA_CS:
+        b = tl.load(
+            b_ptrs,
+            mask=(offs_m[:, None] < chunk_size_limit) & (offs_n[None, :] < dstate),
+            other=0.0,
+        ).to(tl.float32)
+    if HAS_SEQ_IDX:
+        seq_idx_m = tl.load(
+            seq_idx_ptr + offs_m * stride_seq_idx_seqlen,
+            mask=offs_m < chunk_size_limit,
+            other=-1,
+        )
+        seq_idx_last = tl.load(
+            seq_idx_ptr + (chunk_size_limit - 1) * stride_seq_idx_seqlen
+        )
+    nheads_iter = min(
+        nheads_per_program, nheads // ngroups - pid_s * nheads_per_program
+    )
+    for h in range(nheads_iter):
+        x = tl.load(
+            x_ptrs,
+            mask=(offs_m[:, None] < chunk_size_limit) & (offs_k[None, :] < hdim),
+            other=0.0,
+        )
+        dstates = tl.load(
+            dstates_ptrs,
+            mask=(offs_k[:, None] < hdim) & (offs_n[None, :] < dstate),
+            other=0.0,
+        )
+        dstates = dstates.to(x_ptrs.dtype.element_ty)
+        db = tl.dot(x, dstates)
+        dA_cs_last = tl.load(dA_cumsum_ptr + (chunk_size - 1) * stride_dA_cs_csize).to(
+            tl.float32
+        )
+        dA_cs_m = tl.load(dA_cumsum_ptrs, mask=offs_m < chunk_size, other=0.0).to(
+            tl.float32
+        )
+        dt_m = tl.load(dt_ptrs, mask=offs_m < chunk_size, other=0.0).to(tl.float32)
+        if not HAS_SEQ_IDX:
+            scale = tl.exp(dA_cs_last - dA_cs_m)
+        else:
+            scale = tl.where(
+                seq_idx_m == seq_idx_last, tl.exp(dA_cs_last - dA_cs_m), 0.0
+            )
+        db *= (scale * dt_m)[:, None]
+        if HAS_DDA_CS:
+            # This is the gradient wrt (dA_cs_last - dA_cs_m), i.e. the exclusive reverse cumsum
+            ddA_cs = tl.sum(db * b, axis=1)
+            tl.atomic_add(
+                ddA_cumsum_ptrs + stride_ddA_cs_csize,
+                ddA_cs,
+                mask=offs_m < chunk_size - 1,
+            )
+        acc += db
+        x_ptrs += stride_x_head
+        dstates_ptrs += stride_states_head
+        dt_ptrs += stride_dt_head
+        dA_cumsum_ptr += stride_dA_cs_head
+        dA_cumsum_ptrs += stride_dA_cs_head
+        if HAS_DDA_CS:
+            ddA_cumsum_ptrs += stride_ddA_cs_head
+
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+    # if HAS_SEQ_IDX:
+    #     seq_idx_last = tl.load(seq_idx_ptr + (chunk_size_limit - 1) * stride_seq_idx_seqlen)
+    #     seq_idx_m = tl.load(seq_idx_ptr + offs_m * stride_seq_idx_seqlen, mask=offs_m < chunk_size_limit, other=-1)
+    #     acc = tl.where(seq_idx_m[:, None] == seq_idx_last, acc, 0.0)
+    db_ptrs = db_ptr + (
+        offs_m[:, None] * stride_db_seqlen + offs_n[None, :] * stride_db_dstate
+    )
+    tl.store(
+        db_ptrs,
+        acc,
+        mask=(offs_m[:, None] < chunk_size_limit) & (offs_n[None, :] < dstate),
+    )
+
+
+@triton.autotune(
+    configs=[
+        # triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 64}, num_stages=3, num_warps=8, pre_hook=init_to_zero(["ddA_cumsum_ptr"])),
+        # triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 32}, num_stages=4, num_warps=4, pre_hook=init_to_zero(["ddA_cumsum_ptr"])),
+        # triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32}, num_stages=4, num_warps=4, pre_hook=init_to_zero(["ddA_cumsum_ptr"])),
+        # triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32}, num_stages=4, num_warps=4, pre_hook=init_to_zero(["ddA_cumsum_ptr"])),
+        # triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32}, num_stages=4, num_warps=4, pre_hook=init_to_zero(["ddA_cumsum_ptr"])),
+        # triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32}, num_stages=4, num_warps=4, pre_hook=init_to_zero(["ddA_cumsum_ptr"])),
+        # triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32}, num_stages=5, num_warps=4, pre_hook=init_to_zero(["ddA_cumsum_ptr"])),
+        # triton.Config({'BLOCK_SIZE_M': 32, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32}, num_stages=5, num_warps=4, pre_hook=init_to_zero(["ddA_cumsum_ptr"])),
+        # triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32}, num_stages=4, num_warps=4, pre_hook=init_to_zero(["ddA_cumsum_ptr"])),
+        triton.Config(
+            {"BLOCK_SIZE_N": 16, "BLOCK_SIZE_K": 32},
+            num_stages=3,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_N": 32, "BLOCK_SIZE_K": 32},
+            num_stages=3,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_N": 64, "BLOCK_SIZE_K": 32},
+            num_stages=3,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_N": 128, "BLOCK_SIZE_K": 32},
+            num_stages=3,
+            num_warps=4,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_N": 16, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=8,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_N": 32, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=8,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_N": 64, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=8,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_N": 128, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=8,
+            pre_hook=init_to_zero(["ddA_cumsum_ptr"]),
+        ),
+    ],
+    key=["chunk_size", "hdim", "dstate"],
+)
+@triton.jit
+def _chunk_state_bwd_ddAcs_stable_kernel(
+    # Pointers to matrices
+    x_ptr,
+    b_ptr,
+    dstates_ptr,
+    dt_ptr,
+    dA_cumsum_ptr,
+    seq_idx_ptr,
+    ddA_cumsum_ptr,
+    # Matrix dimensions
+    chunk_size,
+    hdim,
+    dstate,
+    batch,
+    seqlen,
+    nheads_ngroups_ratio,
+    # Strides
+    stride_x_batch,
+    stride_x_seqlen,
+    stride_x_head,
+    stride_x_hdim,
+    stride_b_batch,
+    stride_b_seqlen,
+    stride_b_head,
+    stride_b_dstate,
+    stride_dstates_batch,
+    stride_dstates_chunk,
+    stride_states_head,
+    stride_states_hdim,
+    stride_states_dstate,
+    stride_dt_batch,
+    stride_dt_chunk,
+    stride_dt_head,
+    stride_dt_csize,
+    stride_dA_cs_batch,
+    stride_dA_cs_chunk,
+    stride_dA_cs_head,
+    stride_dA_cs_csize,
+    stride_seq_idx_batch,
+    stride_seq_idx_seqlen,
+    stride_ddA_cs_batch,
+    stride_ddA_cs_chunk,
+    stride_ddA_cs_head,
+    stride_ddA_cs_csize,
+    # Meta-parameters
+    HAS_SEQ_IDX: tl.constexpr,
+    BLOCK_SIZE_M: tl.constexpr,
+    BLOCK_SIZE_N: tl.constexpr,
+    BLOCK_SIZE_K: tl.constexpr,
+    BLOCK_SIZE_DSTATE: tl.constexpr,
+):
+    pid_bc = tl.program_id(axis=1)
+    pid_c = pid_bc // batch
+    pid_b = pid_bc - pid_c * batch
+    pid_h = tl.program_id(axis=2)
+    num_pid_n = tl.cdiv(hdim, BLOCK_SIZE_N)
+    pid_m = tl.program_id(axis=0) // num_pid_n
+    pid_n = tl.program_id(axis=0) % num_pid_n
+    x_ptr += (
+        pid_b * stride_x_batch
+        + pid_c * chunk_size * stride_x_seqlen
+        + pid_h * stride_x_head
+    )
+    b_ptr += (
+        pid_b * stride_b_batch
+        + pid_c * chunk_size * stride_b_seqlen
+        + (pid_h // nheads_ngroups_ratio) * stride_b_head
+    )
+    dstates_ptr += (
+        pid_b * stride_dstates_batch
+        + pid_c * stride_dstates_chunk
+        + pid_h * stride_states_head
+    )
+    dt_ptr += pid_b * stride_dt_batch + pid_c * stride_dt_chunk + pid_h * stride_dt_head
+    ddA_cumsum_ptr += (
+        pid_b * stride_ddA_cs_batch
+        + pid_c * stride_ddA_cs_chunk
+        + pid_h * stride_ddA_cs_head
+    )
+    dA_cumsum_ptr += (
+        pid_b * stride_dA_cs_batch
+        + pid_c * stride_dA_cs_chunk
+        + pid_h * stride_dA_cs_head
+    )
+    if HAS_SEQ_IDX:
+        seq_idx_ptr += (
+            pid_b * stride_seq_idx_batch + pid_c * chunk_size * stride_seq_idx_seqlen
+        )
+
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+
+    chunk_size_limit = min(chunk_size, seqlen - pid_c * chunk_size)
+    # Faster to just do 1 iteration with larger BLOCK_SIZE_K, up to block size 128
+    offs_k = tl.arange(
+        0, BLOCK_SIZE_DSTATE if BLOCK_SIZE_DSTATE <= 128 else BLOCK_SIZE_K
+    )
+    b_ptrs = b_ptr + (
+        offs_m[:, None] * stride_b_seqlen + offs_k[None, :] * stride_b_dstate
+    )
+    dstates_ptrs = dstates_ptr + (
+        offs_n[None, :] * stride_states_hdim + offs_k[:, None] * stride_states_dstate
+    )
+    if BLOCK_SIZE_DSTATE <= 128:
+        b = tl.load(
+            b_ptrs,
+            mask=(offs_m[:, None] < chunk_size_limit) & (offs_k[None, :] < dstate),
+            other=0.0,
+        )
+        dstates = tl.load(
+            dstates_ptrs,
+            mask=(offs_k[:, None] < dstate) & (offs_n[None, :] < hdim),
+            other=0.0,
+        )
+        dstates = dstates.to(b_ptr.dtype.element_ty)
+        acc = tl.dot(b, dstates)
+    else:
+        acc = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
+        for k in range(0, dstate, BLOCK_SIZE_K):
+            b = tl.load(
+                b_ptrs,
+                mask=(offs_m[:, None] < chunk_size_limit)
+                & (offs_k[None, :] < dstate - k),
+                other=0.0,
+            )
+            dstates = tl.load(
+                dstates_ptrs,
+                mask=(offs_k[:, None] < dstate - k) & (offs_n[None, :] < hdim),
+                other=0.0,
+            )
+            dstates = dstates.to(b_ptr.dtype.element_ty)
+            acc += tl.dot(b, dstates)
+            b_ptrs += BLOCK_SIZE_K * stride_b_dstate
+            dstates_ptrs += BLOCK_SIZE_K * stride_states_dstate
+
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+
+    dA_cs_m = tl.load(
+        dA_cumsum_ptr + offs_m * stride_dA_cs_csize, mask=offs_m < chunk_size, other=0.0
+    ).to(tl.float32)
+    dA_cs_last = tl.load(dA_cumsum_ptr + (chunk_size - 1) * stride_dA_cs_csize).to(
+        tl.float32
+    )
+    if not HAS_SEQ_IDX:
+        scale = tl.exp(dA_cs_last - dA_cs_m)
+    else:
+        seq_idx_m = tl.load(
+            seq_idx_ptr + offs_m * stride_seq_idx_seqlen,
+            mask=offs_m < chunk_size_limit,
+            other=-1,
+        )
+        seq_idx_last = tl.load(
+            seq_idx_ptr + (chunk_size_limit - 1) * stride_seq_idx_seqlen
+        )
+        scale = tl.where(seq_idx_m == seq_idx_last, tl.exp(dA_cs_last - dA_cs_m), 0.0)
+    acc *= scale[:, None]
+
+    x_ptrs = x_ptr + (
+        offs_m[:, None] * stride_x_seqlen + offs_n[None, :] * stride_x_hdim
+    )
+    x = tl.load(
+        x_ptrs,
+        mask=(offs_m[:, None] < chunk_size_limit) & (offs_n[None, :] < hdim),
+        other=0.0,
+    ).to(tl.float32)
+    dt_ptrs = dt_ptr + offs_m * stride_dt_csize
+    dt_m = tl.load(dt_ptrs, mask=offs_m < chunk_size, other=0.0).to(tl.float32)
+    ddt = tl.sum(acc * x, axis=1)
+    # ddA_cs = -(ddt * dt_m)
+    # Triton 2.2.0 errors if we have the cumsum here, so we just write it out
+    # then call torch.cumsum outside this kernel.
+    # ddA_cs = tl.cumsum(ddt * dt_m)
+    ddA_cs = ddt * dt_m
+    ddA_cumsum_ptrs = ddA_cumsum_ptr + offs_m * stride_ddA_cs_csize
+    # tl.atomic_add(ddA_cumsum_ptrs, ddA_cs, mask=offs_m < chunk_size)
+    tl.atomic_add(
+        ddA_cumsum_ptrs + stride_ddA_cs_csize, ddA_cs, mask=offs_m < chunk_size - 1
+    )
+
+
+@triton.autotune(
+    configs=[
+        triton.Config(
+            {"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 64},
+            num_stages=3,
+            num_warps=8,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 128, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 64, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 128, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 32, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=4,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 32, "BLOCK_SIZE_K": 32},
+            num_stages=5,
+            num_warps=2,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 32, "BLOCK_SIZE_N": 64, "BLOCK_SIZE_K": 32},
+            num_stages=5,
+            num_warps=2,
+        ),
+        triton.Config(
+            {"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 64, "BLOCK_SIZE_K": 32},
+            num_stages=4,
+            num_warps=2,
+        ),
+    ],
+    key=["hdim", "dstate", "chunk_size"],
+)
+@triton.jit
+def _chunk_state_varlen_kernel(
+    # Pointers to matrices
+    x_ptr,
+    b_ptr,
+    dt_ptr,
+    dA_cumsum_ptr,
+    chunk_states_ptr,
+    cu_seqlens_ptr,
+    states_ptr,
+    # Matrix dimensions
+    hdim,
+    dstate,
+    chunk_size,
+    seqlen,
+    nheads_ngroups_ratio,
+    # Strides
+    stride_x_seqlen,
+    stride_x_head,
+    stride_x_hdim,
+    stride_b_seqlen,
+    stride_b_head,
+    stride_b_dstate,
+    stride_dt_chunk,
+    stride_dt_head,
+    stride_dt_csize,
+    stride_dA_cs_chunk,
+    stride_dA_cs_head,
+    stride_dA_cs_csize,
+    stride_chunk_states_chunk,
+    stride_chunk_states_head,
+    stride_chunk_states_hdim,
+    stride_chunk_states_dstate,
+    stride_states_batch,
+    stride_states_head,
+    stride_states_hdim,
+    stride_states_dstate,
+    # Meta-parameters
+    BLOCK_SIZE_M: tl.constexpr,
+    BLOCK_SIZE_N: tl.constexpr,
+    BLOCK_SIZE_K: tl.constexpr,
+):
+    pid_b = tl.program_id(axis=1)
+    pid_h = tl.program_id(axis=2)
+    num_pid_n = tl.cdiv(dstate, BLOCK_SIZE_N)
+    pid_m = tl.program_id(axis=0) // num_pid_n
+    pid_n = tl.program_id(axis=0) % num_pid_n
+    end_idx = tl.load(cu_seqlens_ptr + pid_b + 1)
+    pid_c = (end_idx - 1) // chunk_size
+    b_ptr += (
+        pid_c * chunk_size * stride_b_seqlen
+        + (pid_h // nheads_ngroups_ratio) * stride_b_head
+    )
+    x_ptr += pid_c * chunk_size * stride_x_seqlen + pid_h * stride_x_head
+    dt_ptr += pid_c * stride_dt_chunk + pid_h * stride_dt_head
+    dA_cumsum_ptr += pid_c * stride_dA_cs_chunk + pid_h * stride_dA_cs_head
+    chunk_states_ptr += (
+        pid_c * stride_chunk_states_chunk + pid_h * stride_chunk_states_head
+    )
+
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+    offs_k = tl.arange(0, BLOCK_SIZE_K)
+    x_ptrs = x_ptr + (
+        offs_m[:, None] * stride_x_hdim + offs_k[None, :] * stride_x_seqlen
+    )
+    b_ptrs = b_ptr + (
+        offs_n[None, :] * stride_b_dstate + offs_k[:, None] * stride_b_seqlen
+    )
+    dt_ptrs = dt_ptr + offs_k * stride_dt_csize
+    dA_cs_last = tl.load(
+        dA_cumsum_ptr + (end_idx - pid_c * chunk_size - 1) * stride_dA_cs_csize
+    ).to(tl.float32)
+    dA_cumsum_ptrs = dA_cumsum_ptr + offs_k * stride_dA_cs_csize
+
+    chunk_size_limit = end_idx - pid_c * chunk_size
+    start_idx = tl.load(cu_seqlens_ptr + pid_b)
+    start_idx_cur = tl.maximum(start_idx - pid_c * chunk_size, 0)
+
+    acc = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
+    for k in range(0, chunk_size_limit, BLOCK_SIZE_K):
+        x = tl.load(
+            x_ptrs,
+            mask=(offs_m[:, None] < hdim)
+            & (offs_k[None, :] < chunk_size_limit - k)
+            & (offs_k[None, :] >= start_idx_cur - k),
+            other=0.0,
+        )
+        b = tl.load(
+            b_ptrs,
+            mask=(offs_k[:, None] < chunk_size_limit - k)
+            & (offs_n[None, :] < dstate)
+            & (offs_k[:, None] >= start_idx_cur - k),
+            other=0.0,
+        ).to(tl.float32)
+        dA_cs_k = tl.load(
+            dA_cumsum_ptrs, mask=offs_k < chunk_size_limit - k, other=0.0
+        ).to(tl.float32)
+        dt_k = tl.load(dt_ptrs, mask=offs_k < chunk_size_limit - k, other=0.0).to(
+            tl.float32
+        )
+        scale = tl.where(
+            (offs_k >= start_idx_cur - k) & (offs_k < chunk_size_limit - k),
+            tl.exp((dA_cs_last - dA_cs_k)) * dt_k,
+            0.0,
+        )
+        b *= scale[:, None]
+        b = b.to(x_ptr.dtype.element_ty)
+        acc += tl.dot(x, b)
+        x_ptrs += BLOCK_SIZE_K * stride_x_seqlen
+        b_ptrs += BLOCK_SIZE_K * stride_b_seqlen
+        dt_ptrs += BLOCK_SIZE_K * stride_dt_csize
+        dA_cumsum_ptrs += BLOCK_SIZE_K * stride_dA_cs_csize
+
+    # If the sequence starts after the last chunk idx, we don't need to add the contribution from the last chunk
+    if start_idx < pid_c * chunk_size:
+        chunk_states_ptrs = chunk_states_ptr + (
+            offs_m[:, None] * stride_chunk_states_hdim
+            + offs_n[None, :] * stride_chunk_states_dstate
+        )
+        chunk_states = tl.load(
+            chunk_states_ptrs,
+            mask=(offs_m[:, None] < hdim) & (offs_n[None, :] < dstate),
+            other=0.0,
+        ).to(tl.float32)
+        # scale = tl.where(start_idx < pid_c * chunk_size, tl.exp(dA_cs_last), 0.0)
+        scale = tl.exp(dA_cs_last)
+        acc += chunk_states * scale
+
+    states = acc.to(states_ptr.dtype.element_ty)
+
+    states_ptr += pid_b * stride_states_batch + pid_h * stride_states_head
+    offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+    states_ptrs = states_ptr + (
+        offs_m[:, None] * stride_states_hdim + offs_n[None, :] * stride_states_dstate
+    )
+    c_mask = (offs_m[:, None] < hdim) & (offs_n[None, :] < dstate)
+    tl.store(states_ptrs, states, mask=c_mask)
+
+
+def _chunk_cumsum_fwd(
+    dt, A, chunk_size, dt_bias=None, dt_softplus=False, dt_limit=(0.0, float("inf"))
+):
+    batch, seqlen, nheads = dt.shape
+    assert A.shape == (nheads,)
+    if dt_bias is not None:
+        assert dt_bias.shape == (nheads,)
+    nchunks = math.ceil(seqlen / chunk_size)
+    dt_out = torch.empty(
+        batch, nheads, nchunks, chunk_size, device=dt.device, dtype=torch.float32
+    )
+    dA_cumsum = torch.empty(
+        batch, nheads, nchunks, chunk_size, device=dt.device, dtype=torch.float32
+    )
+    grid_chunk_cs = lambda META: (
+        batch,
+        nchunks,
+        triton.cdiv(nheads, META["BLOCK_SIZE_H"]),
+    )
+    with torch.cuda.device(dt.device.index):
+        _chunk_cumsum_fwd_kernel[grid_chunk_cs](
+            dt,
+            A,
+            dt_bias,
+            dt_out,
+            dA_cumsum,
+            batch,
+            seqlen,
+            nheads,
+            chunk_size,
+            dt_limit[0],
+            dt_limit[1],
+            dt.stride(0),
+            dt.stride(1),
+            dt.stride(2),
+            A.stride(0),
+            dt_bias.stride(0) if dt_bias is not None else 0,
+            dt_out.stride(0),
+            dt_out.stride(2),
+            dt_out.stride(1),
+            dt_out.stride(3),
+            dA_cumsum.stride(0),
+            dA_cumsum.stride(2),
+            dA_cumsum.stride(1),
+            dA_cumsum.stride(3),
+            dt_softplus,
+            HAS_DT_BIAS=dt_bias is not None,
+            BLOCK_SIZE_CHUNK=triton.next_power_of_2(chunk_size),
+        )
+    return dA_cumsum, dt_out
+
+
+def _chunk_cumsum_bwd(
+    ddA,
+    ddt_out,
+    dt,
+    A,
+    dt_bias=None,
+    dt_softplus=False,
+    dt_limit=(0.0, float("inf")),
+    ddt=None,
+):
+    batch, seqlen, nheads = dt.shape
+    _, _, nchunks, chunk_size = ddA.shape
+    assert ddA.shape == (batch, nheads, nchunks, chunk_size)
+    assert ddt_out.shape == (batch, nheads, nchunks, chunk_size)
+    assert A.shape == (nheads,)
+    if dt_bias is not None:
+        assert dt_bias.shape == (nheads,)
+        ddt_bias = torch.empty_like(dt_bias, dtype=torch.float32)
+    else:
+        ddt_bias = None
+    if ddt is not None:
+        assert ddt.shape == dt.shape
+    else:
+        ddt = torch.empty_like(dt)
+    dA = torch.empty_like(A, dtype=torch.float32)
+    grid_chunk_cs = lambda META: (
+        batch,
+        nchunks,
+        triton.cdiv(nheads, META["BLOCK_SIZE_H"]),
+    )
+    with torch.cuda.device(dt.device.index):
+        _chunk_cumsum_bwd_kernel[grid_chunk_cs](
+            ddA,
+            ddt_out,
+            dt,
+            A,
+            dt_bias,
+            ddt,
+            dA,
+            ddt_bias,
+            batch,
+            seqlen,
+            nheads,
+            chunk_size,
+            dt_limit[0],
+            dt_limit[1],
+            ddA.stride(0),
+            ddA.stride(2),
+            ddA.stride(1),
+            ddA.stride(3),
+            ddt_out.stride(0),
+            ddt_out.stride(2),
+            ddt_out.stride(1),
+            ddt_out.stride(3),
+            dt.stride(0),
+            dt.stride(1),
+            dt.stride(2),
+            A.stride(0),
+            dt_bias.stride(0) if dt_bias is not None else 0,
+            ddt.stride(0),
+            ddt.stride(1),
+            ddt.stride(2),
+            dA.stride(0),
+            ddt_bias.stride(0) if ddt_bias is not None else 0,
+            dt_softplus,
+            HAS_DT_BIAS=dt_bias is not None,
+            BLOCK_SIZE_CHUNK=triton.next_power_of_2(chunk_size),
+        )
+    return ddt, dA, ddt_bias
+
+
+def _chunk_state_fwd(
+    B, x, dt, dA_cumsum, seq_idx=None, states=None, states_in_fp32=True
+):
+    batch, seqlen, nheads, headdim = x.shape
+    _, _, nchunks, chunk_size = dt.shape
+    _, _, ngroups, dstate = B.shape
+    assert nheads % ngroups == 0
+    assert B.shape == (batch, seqlen, ngroups, dstate)
+    assert dt.shape == (batch, nheads, nchunks, chunk_size)
+    assert dA_cumsum.shape == dt.shape
+    if seq_idx is not None:
+        assert seq_idx.shape == (batch, seqlen)
+    if states is not None:
+        assert states.shape == (batch, nchunks, nheads, headdim, dstate)
+    else:
+        states_dtype = torch.float32 if states_in_fp32 else B.dtype
+        states = torch.empty(
+            (batch, nchunks, nheads, headdim, dstate),
+            device=x.device,
+            dtype=states_dtype,
+        )
+    grid = lambda META: (
+        triton.cdiv(headdim, META["BLOCK_SIZE_M"])
+        * triton.cdiv(dstate, META["BLOCK_SIZE_N"]),
+        batch * nchunks,
+        nheads,
+    )
+    with torch.cuda.device(x.device.index):
+        _chunk_state_fwd_kernel[grid](
+            x,
+            B,
+            states,
+            dt,
+            dA_cumsum,
+            seq_idx,
+            headdim,
+            dstate,
+            chunk_size,
+            batch,
+            seqlen,
+            nheads // ngroups,
+            x.stride(0),
+            x.stride(1),
+            x.stride(2),
+            x.stride(3),
+            B.stride(0),
+            B.stride(1),
+            B.stride(2),
+            B.stride(-1),
+            states.stride(0),
+            states.stride(1),
+            states.stride(2),
+            states.stride(3),
+            states.stride(4),
+            dt.stride(0),
+            dt.stride(2),
+            dt.stride(1),
+            dt.stride(3),
+            dA_cumsum.stride(0),
+            dA_cumsum.stride(2),
+            dA_cumsum.stride(1),
+            dA_cumsum.stride(3),
+            *(
+                (seq_idx.stride(0), seq_idx.stride(1))
+                if seq_idx is not None
+                else (0, 0)
+            ),
+            HAS_SEQ_IDX=seq_idx is not None,
+        )
+    return states
+
+
+def _chunk_state_bwd_dx(B, x, dt, dA_cumsum, dstates, dx=None):
+    batch, seqlen, nheads, headdim = x.shape
+    _, _, nchunks, chunk_size = dt.shape
+    _, _, ngroups, dstate = B.shape
+    assert nheads % ngroups == 0
+    assert B.shape == (batch, seqlen, ngroups, dstate)
+    assert dt.shape == (batch, nheads, nchunks, chunk_size)
+    assert dA_cumsum.shape == dt.shape
+    assert dstates.shape == (batch, nchunks, nheads, headdim, dstate)
+    if dx is not None:
+        assert dx.shape == x.shape
+    else:
+        dx = torch.empty_like(x)
+    ddt = torch.empty(
+        batch, nheads, nchunks, chunk_size, device=dt.device, dtype=torch.float32
+    )
+    ddA_cumsum = torch.empty(
+        batch, nheads, nchunks, chunk_size, device=dA_cumsum.device, dtype=torch.float32
+    )
+    grid_dx = lambda META: (
+        triton.cdiv(chunk_size, META["BLOCK_SIZE_M"])
+        * triton.cdiv(headdim, META["BLOCK_SIZE_N"]),
+        batch * nchunks,
+        nheads,
+    )
+    with torch.cuda.device(x.device.index):
+        _chunk_state_bwd_dx_kernel[grid_dx](
+            x,
+            B,
+            dstates,
+            dt,
+            dA_cumsum,
+            dx,
+            ddt,
+            ddA_cumsum,
+            chunk_size,
+            headdim,
+            dstate,
+            batch,
+            seqlen,
+            nheads // ngroups,
+            x.stride(0),
+            x.stride(1),
+            x.stride(2),
+            x.stride(3),
+            B.stride(0),
+            B.stride(1),
+            B.stride(2),
+            B.stride(-1),
+            dstates.stride(0),
+            dstates.stride(1),
+            dstates.stride(2),
+            dstates.stride(3),
+            dstates.stride(4),
+            dt.stride(0),
+            dt.stride(2),
+            dt.stride(1),
+            dt.stride(3),
+            dA_cumsum.stride(0),
+            dA_cumsum.stride(2),
+            dA_cumsum.stride(1),
+            dA_cumsum.stride(3),
+            dx.stride(0),
+            dx.stride(1),
+            dx.stride(2),
+            dx.stride(3),
+            ddt.stride(0),
+            ddt.stride(2),
+            ddt.stride(1),
+            ddt.stride(3),
+            ddA_cumsum.stride(0),
+            ddA_cumsum.stride(2),
+            ddA_cumsum.stride(1),
+            ddA_cumsum.stride(3),
+            BLOCK_SIZE_DSTATE=max(triton.next_power_of_2(dstate), 16),
+        )
+    return dx, ddt.to(dt.dtype), ddA_cumsum.to(dA_cumsum.dtype)
+
+
+def _chunk_state_bwd_db(x, dt, dA_cumsum, dstates, seq_idx=None, B=None, ngroups=1):
+    batch, seqlen, nheads, headdim = x.shape
+    _, _, nchunks, chunk_size = dt.shape
+    dstate = dstates.shape[-1]
+    assert dt.shape == (batch, nheads, nchunks, chunk_size)
+    assert dA_cumsum.shape == dt.shape
+    assert dstates.shape == (batch, nchunks, nheads, headdim, dstate)
+    if seq_idx is not None:
+        assert seq_idx.shape == (batch, seqlen)
+    if B is not None:
+        assert B.shape == (batch, seqlen, ngroups, dstate)
+        B_strides = (B.stride(0), B.stride(1), B.stride(2), B.stride(3))
+        # Use torch.empty since the Triton kernel will call init_to_zero
+        ddA_cumsum = torch.empty(
+            batch, nheads, nchunks, chunk_size, device=x.device, dtype=torch.float32
+        )
+        ddA_cumsum_strides = (
+            ddA_cumsum.stride(0),
+            ddA_cumsum.stride(2),
+            ddA_cumsum.stride(1),
+            ddA_cumsum.stride(3),
+        )
+    else:
+        B_strides = (0, 0, 0, 0)
+        ddA_cumsum = None
+        ddA_cumsum_strides = (0, 0, 0, 0)
+    nheads_ngroups_ratio = nheads // ngroups
+    sm_count = torch.cuda.get_device_properties(x.device).multi_processor_count
+    nheads_per_program = max(
+        min(math.ceil(batch * nchunks * nheads / sm_count), nheads_ngroups_ratio), 1
+    )
+    nsplits = triton.cdiv(nheads_ngroups_ratio, nheads_per_program)
+    dB = torch.empty(
+        batch, seqlen, nsplits, ngroups, dstate, device=x.device, dtype=torch.float32
+    )
+    grid_db = lambda META: (
+        triton.cdiv(chunk_size, META["BLOCK_SIZE_M"])
+        * triton.cdiv(dstate, META["BLOCK_SIZE_N"]),
+        batch * nchunks,
+        nsplits * ngroups,
+    )
+    with torch.cuda.device(x.device.index):
+        _chunk_state_bwd_db_kernel[grid_db](
+            x,
+            dstates,
+            B,
+            dt,
+            dA_cumsum,
+            seq_idx,
+            dB,
+            ddA_cumsum,
+            chunk_size,
+            dstate,
+            headdim,
+            batch,
+            seqlen,
+            nheads,
+            nheads_per_program,
+            ngroups,
+            x.stride(0),
+            x.stride(1),
+            x.stride(2),
+            x.stride(3),
+            dstates.stride(0),
+            dstates.stride(1),
+            dstates.stride(2),
+            dstates.stride(3),
+            dstates.stride(4),
+            *B_strides,
+            dt.stride(0),
+            dt.stride(2),
+            dt.stride(1),
+            dt.stride(3),
+            dA_cumsum.stride(0),
+            dA_cumsum.stride(2),
+            dA_cumsum.stride(1),
+            dA_cumsum.stride(3),
+            *(
+                (seq_idx.stride(0), seq_idx.stride(1))
+                if seq_idx is not None
+                else (0, 0)
+            ),
+            dB.stride(0),
+            dB.stride(1),
+            dB.stride(2),
+            dB.stride(3),
+            dB.stride(4),
+            *ddA_cumsum_strides,
+            HAS_DDA_CS=ddA_cumsum is not None,
+            HAS_SEQ_IDX=seq_idx is not None,
+            BLOCK_SIZE_K=max(triton.next_power_of_2(headdim), 16),
+        )
+    dB = dB.sum(2)
+    if ddA_cumsum is not None:
+        # The first element of ddA_cumsum is always zero, since that dA_cumsum does not contribute
+        # to the state of the chunk.
+        # torch.cumsum(ddA_cumsum[..., 1:], dim=-1, out=ddA_cumsum[..., 1:])
+        # But it's easier to just do the cumsum for all elements, the result will be the same.
+        torch.cumsum(ddA_cumsum, dim=-1, out=ddA_cumsum)
+    return dB if B is None else (dB, ddA_cumsum)
+
+
+def _chunk_state_bwd_ddAcs_stable(B, x, dt, dA_cumsum, dstates, seq_idx=None):
+    batch, seqlen, nheads, headdim = x.shape
+    _, _, nchunks, chunk_size = dt.shape
+    _, _, ngroups, dstate = B.shape
+    assert nheads % ngroups == 0
+    assert B.shape == (batch, seqlen, ngroups, dstate)
+    assert dt.shape == (batch, nheads, nchunks, chunk_size)
+    assert dA_cumsum.shape == dt.shape
+    assert dstates.shape == (batch, nchunks, nheads, headdim, dstate)
+    if seq_idx is not None:
+        assert seq_idx.shape == (batch, seqlen)
+    # Use torch.empty since the Triton kernel will call init_to_zero
+    ddA_cumsum = torch.empty(
+        batch, nheads, nchunks, chunk_size, device=x.device, dtype=torch.float32
+    )
+    grid_ddtcs = lambda META: (
+        triton.cdiv(chunk_size, META["BLOCK_SIZE_M"])
+        * triton.cdiv(headdim, META["BLOCK_SIZE_N"]),
+        batch * nchunks,
+        nheads,
+    )
+    with torch.cuda.device(x.device.index):
+        _chunk_state_bwd_ddAcs_stable_kernel[grid_ddtcs](
+            x,
+            B,
+            dstates,
+            dt,
+            dA_cumsum,
+            seq_idx,
+            ddA_cumsum,
+            chunk_size,
+            headdim,
+            dstate,
+            batch,
+            seqlen,
+            nheads // ngroups,
+            x.stride(0),
+            x.stride(1),
+            x.stride(2),
+            x.stride(3),
+            B.stride(0),
+            B.stride(1),
+            B.stride(2),
+            B.stride(-1),
+            dstates.stride(0),
+            dstates.stride(1),
+            dstates.stride(2),
+            dstates.stride(3),
+            dstates.stride(4),
+            dt.stride(0),
+            dt.stride(2),
+            dt.stride(1),
+            dt.stride(3),
+            dA_cumsum.stride(0),
+            dA_cumsum.stride(2),
+            dA_cumsum.stride(1),
+            dA_cumsum.stride(3),
+            *(
+                (seq_idx.stride(0), seq_idx.stride(1))
+                if seq_idx is not None
+                else (0, 0)
+            ),
+            ddA_cumsum.stride(0),
+            ddA_cumsum.stride(2),
+            ddA_cumsum.stride(1),
+            ddA_cumsum.stride(3),
+            HAS_SEQ_IDX=seq_idx is not None,
+            BLOCK_SIZE_M=max(triton.next_power_of_2(chunk_size), 16),
+            BLOCK_SIZE_DSTATE=max(triton.next_power_of_2(dstate), 16),
+        )
+    torch.cumsum(ddA_cumsum[..., 1:], dim=-1, out=ddA_cumsum[..., 1:])
+    return ddA_cumsum
+
+
+def chunk_state_varlen(B, x, dt, dA_cumsum, cu_seqlens, chunk_states):
+    total_seqlen, nheads, headdim = x.shape
+    _, nchunks, chunk_size = dt.shape
+    _, ngroups, dstate = B.shape
+    batch = cu_seqlens.shape[0] - 1
+    cu_seqlens = cu_seqlens.contiguous()
+    assert nheads % ngroups == 0
+    assert B.shape == (total_seqlen, ngroups, dstate)
+    assert dt.shape == (nheads, nchunks, chunk_size)
+    assert dA_cumsum.shape == dt.shape
+    assert chunk_states.shape == (nchunks, nheads, headdim, dstate)
+    states = torch.empty(
+        batch,
+        nheads,
+        headdim,
+        dstate,
+        dtype=chunk_states.dtype,
+        device=chunk_states.device,
+    )
+    grid = lambda META: (
+        triton.cdiv(headdim, META["BLOCK_SIZE_M"])
+        * triton.cdiv(dstate, META["BLOCK_SIZE_N"]),
+        batch,
+        nheads,
+    )
+    with torch.cuda.device(x.device.index):
+        _chunk_state_varlen_kernel[grid](
+            x,
+            B,
+            dt,
+            dA_cumsum,
+            chunk_states,
+            cu_seqlens,
+            states,
+            headdim,
+            dstate,
+            chunk_size,
+            total_seqlen,
+            nheads // ngroups,
+            x.stride(0),
+            x.stride(1),
+            x.stride(2),
+            B.stride(0),
+            B.stride(1),
+            B.stride(2),
+            dt.stride(1),
+            dt.stride(0),
+            dt.stride(2),
+            dA_cumsum.stride(1),
+            dA_cumsum.stride(0),
+            dA_cumsum.stride(2),
+            chunk_states.stride(0),
+            chunk_states.stride(1),
+            chunk_states.stride(2),
+            chunk_states.stride(3),
+            states.stride(0),
+            states.stride(1),
+            states.stride(2),
+            states.stride(3),
+        )
+    return states
+
+
+class ChunkStateFn(torch.autograd.Function):
+
+    @staticmethod
+    def forward(ctx, B, x, dt, dA_cumsum, states_in_fp32=True):
+        batch, seqlen, nheads, headdim = x.shape
+        _, _, nchunks, chunk_size = dt.shape
+        assert seqlen <= nchunks * chunk_size
+        _, _, ngroups, dstate = B.shape
+        assert B.shape == (batch, seqlen, ngroups, dstate)
+        assert dt.shape == (batch, nheads, nchunks, chunk_size)
+        assert dA_cumsum.shape == (batch, nheads, nchunks, chunk_size)
+        if B.stride(-1) != 1:
+            B = B.contiguous()
+        if (
+            x.stride(-1) != 1 and x.stride(1) != 1
+        ):  # Either M or K dimension should be contiguous
+            x = x.contiguous()
+        states = _chunk_state_fwd(B, x, dt, dA_cumsum, states_in_fp32=states_in_fp32)
+        ctx.save_for_backward(B, x, dt, dA_cumsum)
+        return states
+
+    @staticmethod
+    def backward(ctx, dstates):
+        B, x, dt, dA_cumsum = ctx.saved_tensors
+        batch, seqlen, nheads, headdim = x.shape
+        _, _, nchunks, chunk_size = dt.shape
+        _, _, ngroups, dstate = B.shape
+        assert dstates.shape == (batch, nchunks, nheads, headdim, dstate)
+        if dstates.stride(-1) != 1:
+            dstates = dstates.contiguous()
+        dx, ddt, ddA_cumsum = _chunk_state_bwd_dx(B, x, dt, dA_cumsum, dstates)
+        dB = _chunk_state_bwd_db(x, dt, dA_cumsum, dstates, ngroups=ngroups)
+        dB = dB.to(B.dtype)
+        return dB, dx, ddt, ddA_cumsum, None
+
+
+def chunk_state(B, x, dt, dA_cumsum, states_in_fp32=True):
+    """
+    Argument:
+        B: (batch, seqlen, ngroups, headdim)
+        x: (batch, seqlen, nheads, headdim)
+        dt: (batch, nheads, nchunks, chunk_size)
+        dA_cumsum: (batch, nheads, nchunks, chunk_size)
+    Return:
+        states: (batch, nchunks, nheads, headdim, dstate)
+    """
+    return ChunkStateFn.apply(B, x, dt, dA_cumsum, states_in_fp32)
+
+
+def chunk_state_ref(B, x, dt, dA_cumsum):
+    """
+    Argument:
+        B: (batch, seqlen, ngroups, headdim)
+        x: (batch, seqlen, nheads, headdim)
+        dt: (batch, nheads, nchunks, chunk_size)
+        dA_cumsum: (batch, nheads, nchunks, chunk_size)
+    Return:
+        states: (batch, nchunks, nheads, headdim, dstate)
+    """
+    # Check constraints.
+    batch, seqlen, nheads, headdim = x.shape
+    dstate = B.shape[-1]
+    _, _, nchunks, chunk_size = dt.shape
+    assert seqlen <= nchunks * chunk_size
+    assert x.shape == (batch, seqlen, nheads, headdim)
+    assert dt.shape == (batch, nheads, nchunks, chunk_size)
+    ngroups = B.shape[2]
+    assert nheads % ngroups == 0
+    assert B.shape == (batch, seqlen, ngroups, dstate)
+    B = repeat(B, "b l g d -> b l (g h) d", h=nheads // ngroups)
+    assert dA_cumsum.shape == (batch, nheads, nchunks, chunk_size)
+    if seqlen < nchunks * chunk_size:
+        x = F.pad(x, (0, 0, 0, 0, 0, nchunks * chunk_size - seqlen))
+        B = F.pad(B, (0, 0, 0, 0, 0, nchunks * chunk_size - seqlen))
+    x = rearrange(x, "b (c l) h p -> b c l h p", l=chunk_size)
+    B = rearrange(B, "b (c l) ... -> b c l ...", l=chunk_size)
+    decay_states = torch.exp((dA_cumsum[:, :, :, -1:] - dA_cumsum))
+    return torch.einsum(
+        "bclhn,bhcl,bhcl,bclhp->bchpn",
+        B.to(x.dtype),
+        decay_states.to(x.dtype),
+        dt.to(x.dtype),
+        x,
+    )