marlin/dense/marlin_cuda_kernel.cu

/*
 * Modified by Neural Magic
 * Copyright (C) Marlin.2024 Elias Frantar
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *         http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

#include <torch/all.h>

#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <cuda.h>
#include <cuda_fp16.h>
#include <cuda_runtime.h>

#include <iostream>

#include "common/base.h"

#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 800
  #include "common/mem.h"
#endif

template <typename T>
inline std::string str(T x) {
  return std::to_string(x);
}

namespace marlin_dense {

#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 800

using I4 = Vec<int, 4>;
// Matrix fragments for tensor core instructions; their precise layout is
// documented here:
// https://docs.nvidia.com/cuda/parallel-thread-execution/index.html#matrix-fragments-for-mma-m16n8k16-with-floating-point-type
using FragA = Vec<half2, 4>;
using FragB = Vec<half2, 2>;
using FragC = Vec<float, 4>;
using FragS = Vec<half2, 1>;  // quantization scales

// m16n8k16 tensor core mma instruction with fp16 inputs and fp32
// output/accumulation.
__device__ inline void mma(const FragA& a_frag, const FragB& frag_b,
                           FragC& frag_c) {
  const uint32_t* a = reinterpret_cast<const uint32_t*>(&a_frag);
  const uint32_t* b = reinterpret_cast<const uint32_t*>(&frag_b);
  float* c = reinterpret_cast<float*>(&frag_c);
  asm volatile(
      "mma.sync.aligned.m16n8k16.row.col.f32.f16.f16.f32 "
      "{%0,%1,%2,%3}, {%4,%5,%6,%7}, {%8,%9}, {%10,%11,%12,%13};\n"
      : "=f"(c[0]), "=f"(c[1]), "=f"(c[2]), "=f"(c[3])
      : "r"(a[0]), "r"(a[1]), "r"(a[2]), "r"(a[3]), "r"(b[0]), "r"(b[1]),
        "f"(c[0]), "f"(c[1]), "f"(c[2]), "f"(c[3]));
}

// Instruction for loading a full 16x16 matrix fragment of operand A from shared
// memory, directly in tensor core layout.
__device__ inline void ldsm4(FragA& frag_a, const void* smem_ptr) {
  uint32_t* a = reinterpret_cast<uint32_t*>(&frag_a);
  uint32_t smem = static_cast<uint32_t>(__cvta_generic_to_shared(smem_ptr));
  asm volatile("ldmatrix.sync.aligned.m8n8.x4.shared.b16 {%0,%1,%2,%3}, [%4];\n"
               : "=r"(a[0]), "=r"(a[1]), "=r"(a[2]), "=r"(a[3])
               : "r"(smem));
}

// Lookup-table based 3-input logical operation; explicitly used for
// dequantization as the compiler does not seem to automatically recognize it in
// all cases.
template <int lut>
__device__ inline int lop3(int a, int b, int c) {
  int res;
  asm volatile("lop3.b32 %0, %1, %2, %3, %4;\n"
               : "=r"(res)
               : "r"(a), "r"(b), "r"(c), "n"(lut));
  return res;
}

// Efficiently dequantize an int32 value into a full B-fragment of 4 fp16
// values. We mostly follow the strategy in the link below, with some small
// changes:
// https://github.com/NVIDIA/FasterTransformer/blob/main/src/fastertransformer/cutlass_extensions/include/cutlass_extensions/interleaved_numeric_conversion.h
__device__ inline FragB dequant(int q) {
  const int LO = 0x000f000f;
  const int HI = 0x00f000f0;
  const int EX = 0x64006400;
  // Guarantee that the `(a & b) | c` operations are LOP3s.
  int lo = lop3<(0xf0 & 0xcc) | 0xaa>(q, LO, EX);
  int hi = lop3<(0xf0 & 0xcc) | 0xaa>(q, HI, EX);
  // We want signed int4 outputs, hence we fuse the `-8` symmetric zero point
  // directly into `SUB` and `ADD`.
  const int SUB = 0x64086408;
  const int MUL = 0x2c002c00;
  const int ADD = 0xd480d480;
  FragB frag_b;
  frag_b[0] = __hsub2(*reinterpret_cast<half2*>(&lo),
                      *reinterpret_cast<const half2*>(&SUB));
  frag_b[1] = __hfma2(*reinterpret_cast<half2*>(&hi),
                      *reinterpret_cast<const half2*>(&MUL),
                      *reinterpret_cast<const half2*>(&ADD));
  return frag_b;
}

// Multiply dequantized values by the corresponding quantization scale; used
// only for grouped quantization.
__device__ inline void scale(FragB& frag_b, FragS& frag_s, int i) {
  half2 s = __half2half2(reinterpret_cast<__half*>(&frag_s)[i]);
  frag_b[0] = __hmul2(frag_b[0], s);
  frag_b[1] = __hmul2(frag_b[1], s);
}

template <const int threads,          // number of threads in a threadblock
          const int thread_m_blocks,  // number of 16x16 blocks in the m
                                      // dimension (batchsize) of the
                                      // threadblock
          const int thread_n_blocks,  // same for n dimension (output)
          const int thread_k_blocks,  // same for k dimension (reduction)
          const int stages,  // number of stages for the async global->shared
                             // fetch pipeline
          const int group_blocks = -1  // number of consecutive 16x16 blocks
                                       // with a separate quantization scale
          >
__global__ void Marlin(
    const int4* __restrict__ A,  // fp16 input matrix of shape mxk
    const int4* __restrict__ B,  // 4bit quantized weight matrix of shape kxn
    int4* __restrict__ C,        // fp16 output buffer of shape mxn
    const int4* __restrict__ s,  // fp16 quantization scales of shape
                                 // (k/groupsize)xn
    int prob_m,                  // batch dimension m
    int prob_n,                  // output dimension n
    int prob_k,                  // reduction dimension k
    int* locks  // extra global storage for barrier synchronization
) {
  // Each threadblock processes one "stripe" of the B matrix with (roughly) the
  // same size, which might involve multiple column "slices" (of width 16 *
  // `thread_n_blocks`). Stripes are defined as shown in the 3x3 matrix 5 SM
  // example:
  //   0 1 3
  //   0 2 3
  //   1 2 4
  // While this kind of partitioning makes things somewhat more complicated, it
  // ensures good utilization of all SMs for many kinds of shape and GPU
  // configurations, while requiring as few slow global cross-threadblock
  // reductions as possible.

  // For larger GEMMs we run multiple batchsize 64 versions in parallel for a
  // better partitioning with less reductions
  int parallel = 1;
  if (prob_m > 16 * thread_m_blocks) {
    parallel = prob_m / (16 * thread_m_blocks);
    prob_m = 16 * thread_m_blocks;
  }

  int k_tiles = prob_k / 16 / thread_k_blocks;
  int n_tiles = prob_n / 16 / thread_n_blocks;
  int iters = ceildiv(k_tiles * n_tiles * parallel, gridDim.x);
  // Ensure that the number of tiles in each stripe is a multiple of the
  // groupsize; this avoids an annoying special case where a stripe starts in
  // the middle of group.
  if (group_blocks != -1)
    iters = (group_blocks / thread_k_blocks) *
            ceildiv(iters, (group_blocks / thread_k_blocks));

  int slice_row = (iters * blockIdx.x) % k_tiles;
  int slice_col_par = (iters * blockIdx.x) / k_tiles;
  int slice_col = slice_col_par;
  int slice_iters;  // number of threadblock tiles in the current slice
  int slice_count =
      0;          // total number of active threadblocks in the current slice
  int slice_idx;  // index of threadblock in current slice; numbered bottom to
                  // top

  // We can easily implement parallel problem execution by just remapping
  // indices and advancing global pointers
  if (slice_col_par >= n_tiles) {
    A += (slice_col_par / n_tiles) * 16 * thread_m_blocks * prob_k / 8;
    C += (slice_col_par / n_tiles) * 16 * thread_m_blocks * prob_n / 8;
    locks += (slice_col_par / n_tiles) * n_tiles;
    slice_col = slice_col_par % n_tiles;
  }

  // Compute all information about the current slice which is required for
  // synchronization.
  auto init_slice = [&]() {
    slice_iters =
        iters * (blockIdx.x + 1) - (k_tiles * slice_col_par + slice_row);
    if (slice_iters < 0 || slice_col_par >= n_tiles * parallel) slice_iters = 0;
    if (slice_iters == 0) return;
    if (slice_row + slice_iters > k_tiles) slice_iters = k_tiles - slice_row;
    slice_count = 1;
    slice_idx = 0;
    int col_first = iters * ceildiv(k_tiles * slice_col_par, iters);
    if (col_first <= k_tiles * (slice_col_par + 1)) {
      int col_off = col_first - k_tiles * slice_col_par;
      slice_count = ceildiv(k_tiles - col_off, iters);
      if (col_off > 0) slice_count++;
      int delta_first = iters * blockIdx.x - col_first;
      if (delta_first < 0 || (col_off == 0 && delta_first == 0))
        slice_idx = slice_count - 1;
      else {
        slice_idx = slice_count - 1 - delta_first / iters;
        if (col_off > 0) slice_idx--;
      }
    }
    if (slice_col == n_tiles) {
      A += 16 * thread_m_blocks * prob_k / 8;
      C += 16 * thread_m_blocks * prob_n / 8;
      locks += n_tiles;
      slice_col = 0;
    }
  };
  init_slice();

  int a_gl_stride = prob_k / 8;  // stride of the A matrix in global memory
  // We typically use `constexpr` to indicate that this value is a compile-time
  // constant
  constexpr int a_sh_stride =
      16 * thread_k_blocks / 8;  // stride of an A matrix tile in shared memory
  constexpr int a_gl_rd_delta_o =
      16 * thread_k_blocks /
      8;  // delta between subsequent A tiles in global memory
  int a_gl_rd_delta_i =
      a_gl_stride *
      (threads / a_gl_rd_delta_o);  // between subsequent accesses within a tile
  constexpr int a_sh_wr_delta =
      a_sh_stride *
      (threads / a_gl_rd_delta_o);  // between shared memory writes
  constexpr int a_sh_rd_delta_o =
      2 * ((threads / 32) /
           (thread_n_blocks / 4));  // between shared memory tile reads
  constexpr int a_sh_rd_delta_i =
      a_sh_stride * 16;  // within a shared memory tile
  constexpr int a_sh_stage =
      a_sh_stride * (16 * thread_m_blocks);  // overall size of a tile
  constexpr int a_sh_wr_iters =
      ceildiv(a_sh_stage,
              a_sh_wr_delta);  // number of shared write iterations for a tile

  int b_gl_stride = 16 * prob_n / 32;
  constexpr int b_sh_stride = 32 * thread_n_blocks / 4;
  int b_gl_rd_delta_o = b_gl_stride * thread_k_blocks;
  int b_gl_rd_delta_i = b_gl_stride * (threads / b_sh_stride);
  constexpr int b_sh_wr_delta = threads;
  constexpr int b_sh_rd_delta = threads;
  constexpr int b_sh_stage = b_sh_stride * thread_k_blocks;
  constexpr int b_sh_wr_iters = b_sh_stage / b_sh_wr_delta;

  int s_gl_stride = prob_n / 8;
  constexpr int s_sh_stride = 16 * thread_n_blocks / 8;
  constexpr int s_sh_stage = s_sh_stride;
  int s_gl_rd_delta = s_gl_stride;

  // Global A read index of current thread.
  int a_gl_rd = a_gl_stride * (threadIdx.x / a_gl_rd_delta_o) +
                (threadIdx.x % a_gl_rd_delta_o);
  a_gl_rd += a_gl_rd_delta_o * slice_row;
  // Shared write index of current thread.
  int a_sh_wr = a_sh_stride * (threadIdx.x / a_gl_rd_delta_o) +
                (threadIdx.x % a_gl_rd_delta_o);
  // Shared read index.
  int a_sh_rd =
      a_sh_stride * ((threadIdx.x % 32) % 16) + (threadIdx.x % 32) / 16;
  a_sh_rd += 2 * ((threadIdx.x / 32) / (thread_n_blocks / 4));

  int b_gl_rd =
      b_gl_stride * (threadIdx.x / b_sh_stride) + (threadIdx.x % b_sh_stride);
  b_gl_rd += b_sh_stride * slice_col;
  b_gl_rd += b_gl_rd_delta_o * slice_row;
  int b_sh_wr = threadIdx.x;
  int b_sh_rd = threadIdx.x;

  int s_gl_rd = s_gl_stride * ((thread_k_blocks * slice_row) / group_blocks) +
                s_sh_stride * slice_col + threadIdx.x;
  int s_sh_wr = threadIdx.x;
  int s_sh_rd;
  // We use a different scale layout for grouped and column-wise quantization as
  // we scale a `half2` tile in column-major layout in the former and in
  // row-major in the latter case.
  if (group_blocks != -1)
    s_sh_rd = 8 * ((threadIdx.x / 32) % (thread_n_blocks / 4)) +
              (threadIdx.x % 32) / 4;
  else
    s_sh_rd = 8 * ((threadIdx.x / 32) % (thread_n_blocks / 4)) +
              (threadIdx.x % 32) % 4;

  // Precompute which thread should not read memory in which iterations; this is
  // needed if there are more threads than required for a certain tilesize or
  // when the batchsize is not a multiple of 16.
  bool a_sh_wr_pred[a_sh_wr_iters];
  #pragma unroll
  for (int i = 0; i < a_sh_wr_iters; i++)
    a_sh_wr_pred[i] = a_sh_wr_delta * i + a_sh_wr < a_sh_stride * prob_m;
  bool s_sh_wr_pred = threadIdx.x < s_sh_stride;

  // To ensure that writing and reading A tiles to/from shared memory, the
  // latter in fragment format, is fully bank conflict free, we need to use a
  // rather fancy XOR-based layout. The key here is that neither reads nor
  // writes of the 16-byte `int4` blocks of 8 consecutive threads involve the
  // same shared memory banks. Further, it seems (based on NSight-Compute) that
  // each warp must also write a consecutive memory segment?
  auto transform_a = [&](int i) {
    int row = i / a_gl_rd_delta_o;
    return a_gl_rd_delta_o * row + (i % a_gl_rd_delta_o) ^ row;
  };
  // Since the computation of this remapping is non-trivial and, due to our main
  // loop unrolls, all shared memory accesses are static, we simply precompute
  // both transformed reads and writes.
  int a_sh_wr_trans[a_sh_wr_iters];
  #pragma unroll
  for (int i = 0; i < a_sh_wr_iters; i++)
    a_sh_wr_trans[i] = transform_a(a_sh_wr_delta * i + a_sh_wr);
  int a_sh_rd_trans[b_sh_wr_iters][thread_m_blocks];
  #pragma unroll
  for (int i = 0; i < b_sh_wr_iters; i++) {
  #pragma unroll
    for (int j = 0; j < thread_m_blocks; j++)
      a_sh_rd_trans[i][j] =
          transform_a(a_sh_rd_delta_o * i + a_sh_rd_delta_i * j + a_sh_rd);
  }

  // Since B-accesses have non-constant stride they have to be computed at
  // runtime; we break dependencies between subsequent accesses with a tile by
  // maintining multiple pointers (we have enough registers), a tiny
  // optimization.
  const int4* B_ptr[b_sh_wr_iters];
  #pragma unroll
  for (int i = 0; i < b_sh_wr_iters; i++)
    B_ptr[i] = B + b_gl_rd_delta_i * i + b_gl_rd;

  extern __shared__ int4 sh[];
  // Shared memory storage for global fetch pipelines.
  int4* sh_a = sh;
  int4* sh_b = sh_a + (stages * a_sh_stage);
  int4* sh_s = sh_b + (stages * b_sh_stage);
  // Register storage for double buffer of shared memory reads.
  FragA frag_a[2][thread_m_blocks];
  I4 frag_b_quant[2];
  FragC frag_c[thread_m_blocks][4][2];
  FragS frag_s[2][4];

  // Zero accumulators.
  auto zero_accums = [&]() {
  #pragma unroll
    for (int i = 0; i < thread_m_blocks * 4 * 2 * 4; i++)
      reinterpret_cast<float*>(frag_c)[i] = 0;
  };

  // Asynchronously fetch the next A, B and s tile from global to the next
  // shared memory pipeline location.
  auto fetch_to_shared = [&](int pipe, int a_off, bool pred = true) {
    if (pred) {
      int4* sh_a_stage = sh_a + a_sh_stage * pipe;
  #pragma unroll
      for (int i = 0; i < a_sh_wr_iters; i++) {
        cp_async4_pred(
            &sh_a_stage[a_sh_wr_trans[i]],
            &A[a_gl_rd_delta_i * i + a_gl_rd + a_gl_rd_delta_o * a_off],
            a_sh_wr_pred[i]);
      }
      int4* sh_b_stage = sh_b + b_sh_stage * pipe;
  #pragma unroll
      for (int i = 0; i < b_sh_wr_iters; i++) {
        cp_async4(&sh_b_stage[b_sh_wr_delta * i + b_sh_wr], B_ptr[i]);
        B_ptr[i] += b_gl_rd_delta_o;
      }
      // Only fetch scales if this tile starts a new group
      if constexpr (group_blocks != -1) {
        // This assumes group_blocks >= thread_k_blocks
        // and would need to be modified to support smaller groups.
        static_assert(group_blocks >= thread_k_blocks);
        if (pipe % (group_blocks / thread_k_blocks) == 0) {
          int4* sh_s_stage = sh_s + s_sh_stage * pipe;
          if (s_sh_wr_pred) cp_async4(&sh_s_stage[s_sh_wr], &s[s_gl_rd]);
          s_gl_rd += s_gl_rd_delta;
        }
      }
    }
    // Insert a fence even when we are winding down the pipeline to ensure that
    // waiting is also correct at this point.
    cp_async_fence();
  };

  // Wait until the next thread tile has been loaded to shared memory.
  auto wait_for_stage = [&]() {
    // We only have `stages - 2` active fetches since we are double buffering
    // and can only issue the next fetch when it is guaranteed that the previous
    // shared memory load is fully complete (as it may otherwise be
    // overwritten).
    cp_async_wait<stages - 2>();
    __syncthreads();
  };

  // Load the next sub-tile from the current location in the shared memory pipe
  // into the current register buffer.
  auto fetch_to_registers = [&](int k, int pipe) {
    // It may seem inefficient that we reload the groups for every sub-tile;
    // however, this does not seem to be a significant bottleneck, while some
    // theoretically better attempts have lead to bad instruction ordering by
    // the compiler and correspondingly a noticeable drop in performance.
    if constexpr (group_blocks != -1) {
      // This assumes group_blocks >= thread_k_blocks
      // and would need to be modified to support smaller groups.
      static_assert(group_blocks >= thread_k_blocks);
      int4* sh_s_stage =
          sh_s + s_sh_stage * ((group_blocks / thread_k_blocks) *
                               (pipe / (group_blocks / thread_k_blocks)));
      reinterpret_cast<int4*>(&frag_s[k % 2])[0] = sh_s_stage[s_sh_rd];
    }
    int4* sh_a_stage = sh_a + a_sh_stage * pipe;
  #pragma unroll
    for (int i = 0; i < thread_m_blocks; i++)
      ldsm4(frag_a[k % 2][i], &sh_a_stage[a_sh_rd_trans[k % b_sh_wr_iters][i]]);
    int4* sh_b_stage = sh_b + b_sh_stage * pipe;
    frag_b_quant[k % 2] = *reinterpret_cast<I4*>(
        &sh_b_stage[b_sh_rd_delta * (k % b_sh_wr_iters) + b_sh_rd]);
  };

  // Execute the actual tensor core matmul of a sub-tile.
  auto matmul = [&](int k) {
  // We have the m dimension as the inner loop in order to encourage overlapping
  // dequantization and matmul operations.
  #pragma unroll
    for (int j = 0; j < 4; j++) {
      int b_quant = frag_b_quant[k % 2][j];
      int b_quant_shift = b_quant >> 8;
      FragB frag_b0 = dequant(b_quant);
      // If there are no groups, we can just scale the final output once and can
      // avoid doing so for each weight.
      if (group_blocks != -1) scale(frag_b0, frag_s[k % 2][j], 0);
      FragB frag_b1 = dequant(b_quant_shift);
      if (group_blocks != -1) scale(frag_b1, frag_s[k % 2][j], 1);
  #pragma unroll
      for (int i = 0; i < thread_m_blocks; i++) {
        mma(frag_a[k % 2][i], frag_b0, frag_c[i][j][0]);
        mma(frag_a[k % 2][i], frag_b1, frag_c[i][j][1]);
      }
    }
  };

  // Since we slice across the k dimension of a tile in order to increase the
  // number of warps while keeping the n dimension of a tile reasonable, we have
  // multiple warps that accumulate their partial sums of the same output
  // location; which we have to reduce over in the end. We do in shared memory.
  auto thread_block_reduce = [&]() {
    constexpr int red_off = threads / b_sh_stride / 2;
    if (red_off >= 1) {
      int red_idx = threadIdx.x / b_sh_stride;
      constexpr int red_sh_stride = b_sh_stride * 4 * 2;
      constexpr int red_sh_delta = b_sh_stride;
      int red_sh_rd = red_sh_stride * (threadIdx.x / b_sh_stride) +
                      (threadIdx.x % b_sh_stride);

      // Parallel logarithmic shared memory reduction. We make sure to avoid any
      // unnecessary read or write iterations, e.g., for two warps we write only
      // once by warp 1 and read only once by warp 0.

  #pragma unroll
      for (int m_block = 0; m_block < thread_m_blocks; m_block++) {
  #pragma unroll
        for (int i = red_off; i > 0; i /= 2) {
          if (i <= red_idx && red_idx < 2 * i) {
  #pragma unroll
            for (int j = 0; j < 4 * 2; j++) {
              int red_sh_wr =
                  red_sh_delta * j + (red_sh_rd - red_sh_stride * i);
              if (i < red_off) {
                float* c_rd =
                    reinterpret_cast<float*>(&sh[red_sh_delta * j + red_sh_rd]);
                float* c_wr = reinterpret_cast<float*>(&sh[red_sh_wr]);
  #pragma unroll
                for (int k = 0; k < 4; k++)
                  reinterpret_cast<FragC*>(frag_c)[4 * 2 * m_block + j][k] +=
                      c_rd[k] + c_wr[k];
              }
              sh[red_sh_wr] =
                  reinterpret_cast<int4*>(&frag_c)[4 * 2 * m_block + j];
            }
          }
          __syncthreads();
        }
        if (red_idx == 0) {
  #pragma unroll
          for (int i = 0; i < 4 * 2; i++) {
            float* c_rd =
                reinterpret_cast<float*>(&sh[red_sh_delta * i + red_sh_rd]);
  #pragma unroll
            for (int j = 0; j < 4; j++)
              reinterpret_cast<FragC*>(frag_c)[4 * 2 * m_block + i][j] +=
                  c_rd[j];
          }
        }
        __syncthreads();
      }
    }
  };

  // Since multiple threadblocks may process parts of the same column slice, we
  // finally have to globally reduce over the results. As the striped
  // partitioning minimizes the number of such reductions and our outputs are
  // usually rather small, we perform this reduction serially in L2 cache.
  auto global_reduce = [&](bool first = false, bool last = false) {
    // We are very careful here to reduce directly in the output buffer to
    // maximize L2 cache utilization in this step. To do this, we write out
    // results in FP16 (but still reduce with FP32 compute).
    constexpr int active_threads = 32 * thread_n_blocks / 4;
    if (threadIdx.x < active_threads) {
      int c_gl_stride = prob_n / 8;
      int c_gl_wr_delta_o = 8 * c_gl_stride;
      int c_gl_wr_delta_i = 4 * (active_threads / 32);
      int c_gl_wr = c_gl_stride * ((threadIdx.x % 32) / 4) +
                    4 * (threadIdx.x / 32) + threadIdx.x % 4;
      c_gl_wr += (2 * thread_n_blocks) * slice_col;
      constexpr int c_sh_wr_delta = active_threads;
      int c_sh_wr = threadIdx.x;

      int row = (threadIdx.x % 32) / 4;

      if (!first) {
  // Interestingly, doing direct global accesses here really seems to mess up
  // the compiler and lead to slowdowns, hence we also use async-copies even
  // though these fetches are not actually asynchronous.
  #pragma unroll
        for (int i = 0; i < thread_m_blocks * 4; i++) {
          cp_async4_pred(
              &sh[c_sh_wr + c_sh_wr_delta * i],
              &C[c_gl_wr + c_gl_wr_delta_o * (i / 2) +
                 c_gl_wr_delta_i * (i % 2)],
              i < (thread_m_blocks - 1) * 4 || 8 * (i / 2) + row < prob_m);
        }
        cp_async_fence();
        cp_async_wait<0>();
      }

  #pragma unroll
      for (int i = 0; i < thread_m_blocks * 4; i++) {
        if (i < (thread_m_blocks - 1) * 4 || 8 * (i / 2) + row < prob_m) {
          if (!first) {
            int4 c_red = sh[c_sh_wr + i * c_sh_wr_delta];
  #pragma unroll
            for (int j = 0; j < 2 * 4; j++) {
              reinterpret_cast<float*>(
                  &frag_c)[4 * 2 * 4 * (i / 4) + 4 * j + (i % 4)] +=
                  __half2float(reinterpret_cast<__half*>(&c_red)[j]);
            }
          }
          if (!last) {
            int4 c;
  #pragma unroll
            for (int j = 0; j < 2 * 4; j++) {
              reinterpret_cast<__half*>(&c)[j] =
                  __float2half(reinterpret_cast<float*>(
                      &frag_c)[4 * 2 * 4 * (i / 4) + 4 * j + (i % 4)]);
            }
            C[c_gl_wr + c_gl_wr_delta_o * (i / 2) + c_gl_wr_delta_i * (i % 2)] =
                c;
          }
        }
      }
    }
  };

  // Write out the reduce final result in the correct layout. We only actually
  // reshuffle matrix fragments in this step, the reduction above is performed
  // in fragment layout.
  auto write_result = [&]() {
    int c_gl_stride = prob_n / 8;
    constexpr int c_sh_stride = 2 * thread_n_blocks + 1;
    int c_gl_wr_delta = c_gl_stride * (threads / (2 * thread_n_blocks));
    constexpr int c_sh_rd_delta =
        c_sh_stride * (threads / (2 * thread_n_blocks));

    int c_gl_wr = c_gl_stride * (threadIdx.x / (2 * thread_n_blocks)) +
                  (threadIdx.x % (2 * thread_n_blocks));
    c_gl_wr += (2 * thread_n_blocks) * slice_col;
    int c_sh_wr =
        (4 * c_sh_stride) * ((threadIdx.x % 32) / 4) + (threadIdx.x % 32) % 4;
    c_sh_wr += 32 * (threadIdx.x / 32);
    int c_sh_rd = c_sh_stride * (threadIdx.x / (2 * thread_n_blocks)) +
                  (threadIdx.x % (2 * thread_n_blocks));

    int c_gl_wr_end = c_gl_stride * prob_m;

    // We first reorder in shared memory to guarantee the most efficient final
    // global write patterns
    auto write = [&](int idx, float c0, float c1, FragS& s) {
      half2 res = __halves2half2(__float2half(c0), __float2half(c1));
      if (group_blocks ==
          -1)  // for per-column quantization we finally apply the scale here
        res = __hmul2(res, s[0]);
      ((half2*)sh)[idx] = res;
    };
    if (threadIdx.x / 32 < thread_n_blocks / 4) {
  #pragma unroll
      for (int i = 0; i < thread_m_blocks; i++) {
  #pragma unroll
        for (int j = 0; j < 4; j++) {
          int wr = c_sh_wr + 8 * j;
          write(wr + (4 * c_sh_stride) * 0 + 0, frag_c[i][j][0][0],
                frag_c[i][j][0][1], frag_s[j / 2][2 * (j % 2) + 0]);
          write(wr + (4 * c_sh_stride) * 8 + 0, frag_c[i][j][0][2],
                frag_c[i][j][0][3], frag_s[j / 2][2 * (j % 2) + 0]);
          write(wr + (4 * c_sh_stride) * 0 + 4, frag_c[i][j][1][0],
                frag_c[i][j][1][1], frag_s[j / 2][2 * (j % 2) + 1]);
          write(wr + (4 * c_sh_stride) * 8 + 4, frag_c[i][j][1][2],
                frag_c[i][j][1][3], frag_s[j / 2][2 * (j % 2) + 1]);
        }
        c_sh_wr += 16 * (4 * c_sh_stride);
      }
    }
    __syncthreads();

  #pragma unroll
    for (int i = 0;
         i < ceildiv(16 * thread_m_blocks, threads / (2 * thread_n_blocks));
         i++) {
      if (c_gl_wr < c_gl_wr_end) {
        C[c_gl_wr] = sh[c_sh_rd];
        c_gl_wr += c_gl_wr_delta;
        c_sh_rd += c_sh_rd_delta;
      }
    }
  };

  // Start global fetch and register load pipelines.
  auto start_pipes = [&]() {
  #pragma unroll
    for (int i = 0; i < stages - 1; i++) fetch_to_shared(i, i, i < slice_iters);
    zero_accums();
    wait_for_stage();
    fetch_to_registers(0, 0);
    a_gl_rd += a_gl_rd_delta_o * (stages - 1);
  };
  start_pipes();

  // Main loop.
  while (slice_iters) {
  // We unroll over both the global fetch and the register load pipeline to
  // ensure all shared memory accesses are static. Note that both pipelines have
  // even length meaning that the next iteration will always start at index 0.
  #pragma unroll
    for (int pipe = 0; pipe < stages;) {
  #pragma unroll
      for (int k = 0; k < b_sh_wr_iters; k++) {
        fetch_to_registers(k + 1, pipe % stages);
        if (k == b_sh_wr_iters - 2) {
          fetch_to_shared((pipe + stages - 1) % stages, pipe,
                          slice_iters >= stages);
          pipe++;
          wait_for_stage();
        }
        matmul(k);
      }
      slice_iters--;
      if (slice_iters == 0) break;
    }
    a_gl_rd += a_gl_rd_delta_o * stages;

    // Process results and, if necessary, proceed to the next column slice.
    // While this pattern may not be the most readable, other ways of writing
    // the loop seemed to noticeably worse performance after compilation.
    if (slice_iters == 0) {
      cp_async_wait<0>();
      bool last = slice_idx == slice_count - 1;
      // For per-column scales, we only fetch them here in the final step before
      // write-out
      if (group_blocks == -1 && last) {
        if (s_sh_wr_pred) cp_async4(&sh_s[s_sh_wr], &s[s_gl_rd]);
        cp_async_fence();
      }
      thread_block_reduce();
      if (group_blocks == -1 && last) {
        cp_async_wait<0>();
        __syncthreads();
        if (threadIdx.x / 32 < thread_n_blocks / 4) {
          reinterpret_cast<int4*>(&frag_s)[0] = sh_s[s_sh_rd + 0];
          reinterpret_cast<int4*>(&frag_s)[1] = sh_s[s_sh_rd + 4];
        }
      }
      if (slice_count > 1) {  // only globally reduce if there is more than one
                              // block in a slice
        barrier_acquire(&locks[slice_col], slice_idx);
        global_reduce(slice_idx == 0, last);
        barrier_release(&locks[slice_col], last);
      }
      if (last)  // only the last block in a slice actually writes the result
        write_result();
      slice_row = 0;
      slice_col_par++;
      slice_col++;
      init_slice();
      if (slice_iters) {
        a_gl_rd = a_gl_stride * (threadIdx.x / a_gl_rd_delta_o) +
                  (threadIdx.x % a_gl_rd_delta_o);
  #pragma unroll
        for (int i = 0; i < b_sh_wr_iters; i++)
          B_ptr[i] += b_sh_stride - b_gl_rd_delta_o * k_tiles;
        if (slice_col == 0) {
  #pragma unroll
          for (int i = 0; i < b_sh_wr_iters; i++) B_ptr[i] -= b_gl_stride;
        }
        s_gl_rd = s_sh_stride * slice_col + threadIdx.x;
        start_pipes();
      }
    }
  }
}

#else

template <const int threads,          // number of threads in a threadblock
          const int thread_m_blocks,  // number of 16x16 blocks in the m
                                      // dimension (batchsize) of the
                                      // threadblock
          const int thread_n_blocks,  // same for n dimension (output)
          const int thread_k_blocks,  // same for k dimension (reduction)
          const int stages,  // number of stages for the async global->shared
                             // fetch pipeline
          const int group_blocks = -1  // number of consecutive 16x16 blocks
                                       // with a separate quantization scale
          >
__global__ void Marlin(
    const int4* __restrict__ A,  // fp16 input matrix of shape mxk
    const int4* __restrict__ B,  // 4bit quantized weight matrix of shape kxn
    int4* __restrict__ C,        // fp16 output buffer of shape mxn
    const int4* __restrict__ s,  // fp16 quantization scales of shape
                                 // (k/groupsize)xn
    int prob_m,                  // batch dimension m
    int prob_n,                  // output dimension n
    int prob_k,                  // reduction dimension k
    int* locks  // extra global storage for barrier synchronization
) {
  // Marlin is not implemented yet for SM < 8.0
  assert(false);
  return;
}

#endif

// 8 warps are a good choice since every SM has 4 schedulers and having more
// than 1 warp per schedule allows some more latency hiding. At the same time,
// we want relatively few warps to have many registers per warp and small tiles.
const int USER_THREADS =
    256;               // Note: This is only used with user-provided thread_k/n
const int STAGES = 4;  // 4 pipeline stages fit into shared memory
const int SHARED_MEM =
    96 * 1024;  // max shared memory on compute capability 8.6 (< 8.0)

static constexpr int min_thread_n = 64;
static constexpr int min_thread_k = 64;

static constexpr int tile_size = 16;
static constexpr int max_par = 16;

static constexpr int pack_factor_4bit =
    8;  // We have 8 4-bit vals inside a 32 bit

#define __CALL_IF(THREAD_M_BLOCKS, THREAD_N_BLOCKS, THREAD_K_BLOCKS,           \
                  GROUP_BLOCKS, NUM_THREADS)                                   \
  else if (thread_m_blocks == THREAD_M_BLOCKS &&                               \
           thread_n_blocks == THREAD_N_BLOCKS &&                               \
           thread_k_blocks == THREAD_K_BLOCKS &&                               \
           group_blocks == GROUP_BLOCKS && num_threads == NUM_THREADS) {       \
    cudaFuncSetAttribute(Marlin<NUM_THREADS, THREAD_M_BLOCKS, THREAD_N_BLOCKS, \
                                THREAD_K_BLOCKS, STAGES, GROUP_BLOCKS>,        \
                         cudaFuncAttributeMaxDynamicSharedMemorySize,          \
                         SHARED_MEM);                                          \
    Marlin<NUM_THREADS, THREAD_M_BLOCKS, THREAD_N_BLOCKS, THREAD_K_BLOCKS,     \
           STAGES, GROUP_BLOCKS><<<blocks, NUM_THREADS, SHARED_MEM, stream>>>( \
        A_ptr, B_ptr, C_ptr, s_ptr, prob_m, prob_n, prob_k, locks);            \
  }

typedef struct {
  int thread_k;
  int thread_n;
  int num_threads;
} thread_config_t;

thread_config_t small_batch_thread_configs[] = {
    // Ordered by priority

    // thread_k, thread_n, num_threads
    {128, 128, 256},  // Default
    {128, 64, 128},   // Reduce N 2X, same K
    {64, 256, 256},   // Reduce K 2X, increase N 2X
    {64, 128, 128},   // Reduce K 2X, same N
};

thread_config_t large_batch_thread_configs[] = {
    // Ordered by priority

    // thread_k, thread_n, num_threads
    {64, 256, 256},   // Default
    {128, 128, 256},  // Reduce N 2X, increase K 2X
    {64, 128, 128},   // Reduce N 2X, same K
    {128, 64, 128},   // Reduce N 4X, increase K 2X
};

bool is_valid_config(thread_config_t const& th_config, int prob_m, int prob_n,
                     int prob_k) {
  // Sanity
  if (th_config.thread_k == -1 || th_config.thread_n == -1 ||
      th_config.num_threads == -1) {
    return false;
  }

  // Verify K/N are divisible by thread K/N
  if (prob_k % th_config.thread_k != 0 || prob_n % th_config.thread_n != 0) {
    return false;
  }

  // thread_k can be only 128 or 64 (because it must be less than groupsize
  // which is 128)
  if (th_config.thread_k != 128 && th_config.thread_k != 64) {
    return false;
  }

  // Verify min for thread K/N
  if (th_config.thread_n < min_thread_n || th_config.thread_k < min_thread_k) {
    return false;
  }

  // num_threads must be at least 128 (= 4 warps)
  if (th_config.num_threads < 128) {
    return false;
  }

  return true;
}

thread_config_t determine_thread_config(int prob_m, int prob_n, int prob_k) {
  if (prob_m <= 16) {
    for (auto th_config : small_batch_thread_configs) {
      if (is_valid_config(th_config, prob_m, prob_n, prob_k)) {
        return th_config;
      }
    }

  } else {
    for (auto th_config : large_batch_thread_configs) {
      if (is_valid_config(th_config, prob_m, prob_n, prob_k)) {
        return th_config;
      }
    }
  }

  return thread_config_t{-1, -1, -1};
}

#define CALL_IF(N_BLOCKS, K_BLOCKS, NUM_THREADS)    \
  __CALL_IF(1, N_BLOCKS, K_BLOCKS, -1, NUM_THREADS) \
  __CALL_IF(1, N_BLOCKS, K_BLOCKS, 8, NUM_THREADS)  \
  __CALL_IF(1, N_BLOCKS, K_BLOCKS, -1, NUM_THREADS) \
  __CALL_IF(1, N_BLOCKS, K_BLOCKS, 8, NUM_THREADS)  \
  __CALL_IF(2, N_BLOCKS, K_BLOCKS, -1, NUM_THREADS) \
  __CALL_IF(2, N_BLOCKS, K_BLOCKS, 8, NUM_THREADS)  \
  __CALL_IF(3, N_BLOCKS, K_BLOCKS, -1, NUM_THREADS) \
  __CALL_IF(3, N_BLOCKS, K_BLOCKS, 8, NUM_THREADS)  \
  __CALL_IF(4, N_BLOCKS, K_BLOCKS, -1, NUM_THREADS) \
  __CALL_IF(4, N_BLOCKS, K_BLOCKS, 8, NUM_THREADS)

void marlin_cuda(const void* A, const void* B, void* C, void* s, int prob_m,
                 int prob_n, int prob_k, void* workspace, int groupsize = -1,
                 int dev = 0, cudaStream_t stream = 0, int thread_k = -1,
                 int thread_n = -1, int sms = -1, int max_par = 16) {
  int tot_m = prob_m;
  int tot_m_blocks = ceildiv(tot_m, 16);
  int pad = 16 * tot_m_blocks - tot_m;

  if (sms == -1)
    cudaDeviceGetAttribute(&sms, cudaDevAttrMultiProcessorCount, dev);

  // Set thread config
  thread_config_t th_config;
  if (thread_k != -1 && thread_n != -1) {
    // User-defined config
    th_config = thread_config_t{thread_k, thread_n, USER_THREADS};
  } else {
    // Auto config
    th_config = determine_thread_config(prob_m, prob_n, prob_k);
  }

  if (!is_valid_config(th_config, prob_m, prob_n, prob_k)) {
    throw std::runtime_error(
        "Invalid thread config: thread_k = " + str(th_config.thread_k) +
        ", thread_n = " + str(th_config.thread_n) +
        ", num_threads = " + str(th_config.num_threads) + " for MKN = [" +
        str(prob_m) + ", " + str(prob_k) + ", " + str(prob_n) + "]");
  }

  // Uncomment for debug
  // std::cout << "Using thread_config: thread_k = " + str(th_config.thread_k) +
  //                  ", thread_n = " + str(th_config.thread_n) +
  //                  ", num_threads = " + str(th_config.num_threads) + " for
  //                  MKN = [" + str(prob_m) +
  //                  ", " + str(prob_k) + ", " + str(prob_n) + "]\n";

  int num_threads = th_config.num_threads;
  thread_k = th_config.thread_k;
  thread_n = th_config.thread_n;

  int thread_k_blocks = thread_k / 16;
  int thread_n_blocks = thread_n / 16;
  int group_blocks = (groupsize == -1) ? -1 : groupsize / 16;
  int blocks = sms;

  if (prob_m == 0 || prob_n == 0 || prob_k == 0) {
    return;
  }

  TORCH_CHECK(prob_n % thread_n == 0, "prob_n = ", prob_n,
              " is not divisible by thread_n = ", thread_n);
  TORCH_CHECK(prob_k % thread_k == 0, "prob_k = ", prob_k,
              " is not divisible by thread_k = ", thread_k);
  if (group_blocks != -1) {
    TORCH_CHECK(prob_k % group_blocks == 0, "prob_k = ", prob_k,
                " is not divisible by group_blocks = ", group_blocks);
  }

  const int4* A_ptr = (const int4*)A;
  const int4* B_ptr = (const int4*)B;
  int4* C_ptr = (int4*)C;
  const int4* s_ptr = (const int4*)s;

  int* locks = (int*)workspace;

  for (int i = 0; i < tot_m_blocks; i += 4) {
    int thread_m_blocks = tot_m_blocks - i;
    prob_m = tot_m - 16 * i;
    int par = 1;
    if (thread_m_blocks > 4) {
      // Note that parallel > 1 currently only works for inputs without any
      // padding
      par = (16 * thread_m_blocks - pad) / 64;
      if (par > max_par) par = max_par;
      prob_m = 64 * par;
      i += 4 * (par - 1);
      thread_m_blocks = 4;
    }

    // For compilation speed, we only define the kernel configurations that have
    // seemed useful (in terms of performance) in our testing, however many more
    // are, in principle, possible.
    if (false) {
    }
    CALL_IF(8, 8, 256)
    CALL_IF(16, 4, 256)
    CALL_IF(8, 4, 128)
    CALL_IF(4, 8, 128)
    else {
      throw std::runtime_error("Unsupported shapes: MKN = [" + str(prob_m) +
                               ", " + str(prob_k) + ", " + str(prob_n) + "]" +
                               ", groupsize = " + str(groupsize) +
                               ", thread_m_blocks = " + str(thread_m_blocks) +
                               ", thread_n_blocks = " + str(thread_n_blocks) +
                               ", thread_k_blocks = " + str(thread_k_blocks));
    }

    A_ptr += 16 * thread_m_blocks * (prob_k / 8) * par;
    C_ptr += 16 * thread_m_blocks * (prob_n / 8) * par;
  }
}

}  // namespace marlin_dense

torch::Tensor marlin_gemm(torch::Tensor& a, torch::Tensor& b_q_weight,
                          torch::Tensor& b_scales, torch::Tensor& workspace,
                          int64_t size_m, int64_t size_n, int64_t size_k) {
  // Verify M
  TORCH_CHECK(size_m == a.size(0),
              "Shape mismatch: a.size(0) = " + str(a.size(0)) +
                  ", size_m = " + str(size_m));

  // Verify K
  TORCH_CHECK(size_k == a.size(1),
              "Shape mismatch: a.size(1) = " + str(a.size(1)) +
                  ", size_k = " + str(size_k));
  TORCH_CHECK(size_k % marlin_dense::tile_size == 0,
              "size_k = " + str(size_k) + " is not divisible by tile_size = " +
                  str(marlin_dense::tile_size));
  TORCH_CHECK((size_k / marlin_dense::tile_size) == b_q_weight.size(0),
              "Shape mismatch: b_q_weight.size(0) = " +
                  str(b_q_weight.size(0)) + ", size_k = " + str(size_k) +
                  ", tile_size = " + str(marlin_dense::tile_size));

  // Verify N
  TORCH_CHECK(b_scales.size(1) == size_n,
              "b_scales.size(1) = " + str(b_scales.size(1)) +
                  ", size_n = " + str(size_n));
  TORCH_CHECK(
      b_q_weight.size(1) % marlin_dense::tile_size == 0,
      "b_q_weight.size(1) = " + str(b_q_weight.size(1)) +
          " is not divisible by tile_size = " + str(marlin_dense::tile_size));

  int actual_size_n = (b_q_weight.size(1) / marlin_dense::tile_size) *
                      marlin_dense::pack_factor_4bit;
  TORCH_CHECK(
      size_n == actual_size_n,
      "size_n = " + str(size_n) + ", actual_size_n = " + str(actual_size_n));

  // Verify A device and strides
  TORCH_CHECK(a.device().is_cuda(), "A is not on GPU");
  TORCH_CHECK(a.is_contiguous(), "A is not contiguous");

  // Verify B device and strides
  TORCH_CHECK(b_q_weight.device().is_cuda(), "b_q_weight is not on GPU");
  TORCH_CHECK(b_q_weight.is_contiguous(), "b_q_weight is not contiguous");

  // Verify scales device and strides
  TORCH_CHECK(b_scales.device().is_cuda(), "b_scales is not on GPU");
  TORCH_CHECK(b_scales.is_contiguous(), "b_scales is not contiguous");

  // Alloc C matrix
  const at::cuda::OptionalCUDAGuard device_guard(device_of(a));
  auto options = torch::TensorOptions().dtype(a.dtype()).device(a.device());
  torch::Tensor c = torch::empty({size_m, size_n}, options);

  // thread_k: `k` size of a thread_tile in `weights` (can usually be left as
  // auto -1)
  int thread_k = -1;
  // thread_n: `n` size of a thread_tile in `weights` (can usually be left as
  // auto -1)
  int thread_n = -1;
  // sms: number of SMs to use for the kernel (can usually be left as auto -1)
  int sms = -1;

  // Detect groupsize
  if (b_scales.size(0) != 1) {
    TORCH_CHECK(size_k % b_scales.size(0) == 0,
                "size_k = " + str(size_k) +
                    ", is not divisible by b_scales.size(0) = " +
                    str(b_scales.size(0)));
  }
  int groupsize = b_scales.size(0) == 1 ? -1 : size_k / b_scales.size(0);

  // Verify groupsize
  TORCH_CHECK(groupsize == -1 || groupsize == 128,
              "Unexpected groupsize = " + str(groupsize));

  // Verify workspace size
  TORCH_CHECK(size_n % marlin_dense::min_thread_n == 0,
              "size_n = " + str(size_n) +
                  ", is not divisible by min_thread_n = " +
                  str(marlin_dense::min_thread_n));
  int min_workspace_size =
      (size_n / marlin_dense::min_thread_n) * marlin_dense::max_par;
  TORCH_CHECK(workspace.numel() >= min_workspace_size,
              "workspace.numel = " + str(workspace.numel()) +
                  " is below min_workspace_size = " + str(min_workspace_size));

  int dev = a.get_device();
  marlin_dense::marlin_cuda(a.data_ptr(), b_q_weight.data_ptr(), c.data_ptr(),
                            b_scales.data_ptr(), size_m, size_n, size_k,
                            workspace.data_ptr(), groupsize, dev,
                            at::cuda::getCurrentCUDAStream(dev), thread_k,
                            thread_n, sms, marlin_dense::max_par);

  return c;
}