aphrodite-engine/kernels/quantization/marlin/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/extension.h>

 #include <ATen/cuda/CUDAContext.h>
 #include <c10/cuda/CUDAGuard.h>
 #include <cuda.h>
 #include <cuda_fp16.h>
 #include <cuda_runtime.h>
 
 #include <iostream>
 
 template <typename T> inline std::string str(T x) { return std::to_string(x); }
 
 namespace marlin {
 
 constexpr int ceildiv(int a, int b) { return (a + b - 1) / b; }
 
 #if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 800
 
 // Instances of `Vec` are used to organize groups of >>registers<<, as needed
 // for instance as inputs to tensor core operations. Consequently, all
 // corresponding index accesses must be compile-time constants, which is why we
 // extensively use `#pragma unroll` throughout the kernel code to guarantee
 // this.
 template <typename T, int n> struct Vec {
   T elems[n];
   __device__ T &operator[](int i) { return elems[i]; }
 };
 
 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
 
 // Predicated asynchronous global->shared copy; used for inputs A where we apply
 // predication to handle batchsizes that are not multiples of 16.
 __device__ inline void cp_async4_pred(void *smem_ptr, const void *glob_ptr,
                                       bool pred = true) {
   const int BYTES = 16;
   uint32_t smem = static_cast<uint32_t>(__cvta_generic_to_shared(smem_ptr));
   asm volatile("{\n"
                "   .reg .pred p;\n"
                "   setp.ne.b32 p, %0, 0;\n"
                "   @p cp.async.cg.shared.global [%1], [%2], %3;\n"
                "}\n" ::"r"((int)pred),
                "r"(smem), "l"(glob_ptr), "n"(BYTES));
 }
 
 // Asynchronous global->shared copy with a cache hint indicating that the values
 // may be evicted immediately; used for quantized weights B, which are only
 // accessed precisely once and should thus not pollute the L2 cache which we
 // need for inputs A and outputs C.

 // Async global->shared copy
 __device__ inline void cp_async4(void *smem_ptr, const void *glob_ptr) {
   const int BYTES = 16;
   uint32_t smem = static_cast<uint32_t>(__cvta_generic_to_shared(smem_ptr));
      asm volatile("{\n"
                   "   cp.async.cg.shared.global [%0], [%1], %2;\n"
                   "}\n" ::"r"(smem), "l"(glob_ptr), "n"(BYTES));
  }
 
 // Async copy fence.
 __device__ inline void cp_async_fence() {
   asm volatile("cp.async.commit_group;\n" ::);
 }
 
 // Wait until at most `n` async copy stages are still pending.
 template <int n> __device__ inline void cp_async_wait() {
   asm volatile("cp.async.wait_group %0;\n" ::"n"(n));
 }
 
 // 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);
 }
 
 // Wait until barrier reaches `count`, then lock for current threadblock.
 __device__ inline void barrier_acquire(int *lock, int count) {
   if (threadIdx.x == 0) {
     int state = -1;
     do
       // Guarantee that subsequent writes by this threadblock will be visible
       // globally.
       asm volatile("ld.global.acquire.gpu.b32 %0, [%1];\n"
                    : "=r"(state)
                    : "l"(lock));
     while (state != count);
   }
   __syncthreads();
 }
 
 // Release barrier and increment visitation count.
 __device__ inline void barrier_release(int *lock, bool reset = false) {
   __syncthreads();
   if (threadIdx.x == 0) {
     if (reset) {
       lock[0] = 0;
       return;
     }
     int val = 1;
     // Make sure that all writes since acquiring this barrier are visible
     // globally, while releasing the barrier.
     asm volatile("fence.acq_rel.gpu;\n");
     asm volatile("red.relaxed.gpu.global.add.s32 [%0], %1;\n"
                  :
                  : "l"(lock), "r"(val));
   }
 }
 
 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 (group_blocks != -1 && 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 (group_blocks != -1) {
       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
 
 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::tile_size == 0,
               "size_k = " + str(size_k) +
                   " is not divisible by tile_size = " + str(marlin::tile_size));
   TORCH_CHECK((size_k / marlin::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::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::tile_size == 0,
               "b_q_weight.size(1) = " + str(b_q_weight.size(1)) +
                   " is not divisible by tile_size = " + str(marlin::tile_size));
 
   int actual_size_n =
       (b_q_weight.size(1) / marlin::tile_size) * marlin::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::min_thread_n == 0,
       "size_n = " + str(size_n) +
           ", is not divisible by min_thread_n = " + str(marlin::min_thread_n));
   int min_workspace_size = (size_n / marlin::min_thread_n) * marlin::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::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::max_par);
 
   return c;
 }