quantized.h

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// Copyright © 2023-2024 Apple Inc.
 
#include <metal_simdgroup>
#include <metal_stdlib>
 
using namespace metal;
 
#define MLX_MTL_CONST static constant constexpr const
 
MLX_MTL_CONST int SIMD_SIZE = 32;
 
template <typename T, typename U, int values_per_thread, int bits>
inline U load_vector(const device T* x, thread U* x_thread) {
  static_assert(
      bits == 2 || bits == 4 || bits == 8,
      "Template undefined for bits not in {2, 4, 8}");
 
  U sum = 0;
 
  if (bits == 2) {
    for (int i = 0; i < values_per_thread; i += 4) {
      sum += x[i] + x[i + 1] + x[i + 2] + x[i + 3];
      x_thread[i] = x[i];
      x_thread[i + 1] = x[i + 1] / 4.0f;
      x_thread[i + 2] = x[i + 2] / 16.0f;
      x_thread[i + 3] = x[i + 3] / 64.0f;
    }
  }
 
  else if (bits == 4) {
    for (int i = 0; i < values_per_thread; i += 4) {
      sum += x[i] + x[i + 1] + x[i + 2] + x[i + 3];
      x_thread[i] = x[i];
      x_thread[i + 1] = x[i + 1] / 16.0f;
      x_thread[i + 2] = x[i + 2] / 256.0f;
      x_thread[i + 3] = x[i + 3] / 4096.0f;
    }
  }
 
  else if (bits == 8) {
    for (int i = 0; i < values_per_thread; i++) {
      sum += x[i];
      x_thread[i] = x[i];
    }
  }
 
  return sum;
}
 
template <typename T, typename U, int values_per_thread, int bits>
inline U load_vector_safe(const device T* x, thread U* x_thread, int N) {
  static_assert(
      bits == 2 || bits == 4 || bits == 8,
      "Template undefined for bits not in {2, 4, 8}");
 
  U sum = 0;
 
  if (bits == 2) {
    for (int i = 0; i < N; i += 4) {
      sum += x[i] + x[i + 1] + x[i + 2] + x[i + 3];
      x_thread[i] = x[i];
      x_thread[i + 1] = x[i + 1] / 4.0f;
      x_thread[i + 2] = x[i + 2] / 16.0f;
      x_thread[i + 3] = x[i + 3] / 64.0f;
    }
    for (int i = N; i < values_per_thread; i++) {
      x_thread[i] = 0;
    }
  }
 
  else if (bits == 4) {
    for (int i = 0; i < N; i += 4) {
      sum += x[i] + x[i + 1] + x[i + 2] + x[i + 3];
      x_thread[i] = x[i];
      x_thread[i + 1] = x[i + 1] / 16.0f;
      x_thread[i + 2] = x[i + 2] / 256.0f;
      x_thread[i + 3] = x[i + 3] / 4096.0f;
    }
    for (int i = N; i < values_per_thread; i++) {
      x_thread[i] = 0;
    }
  }
 
  else if (bits == 8) {
    for (int i = 0; i < N; i++) {
      sum += x[i];
      x_thread[i] = x[i];
    }
    for (int i = N; i < values_per_thread; i++) {
      x_thread[i] = 0;
    }
  }
 
  return sum;
}
 
template <typename U, int values_per_thread, int bits>
inline U qdot(
    const device uint8_t* w,
    const thread U* x_thread,
    U scale,
    U bias,
    U sum) {
  static_assert(
      bits == 2 || bits == 4 || bits == 8,
      "Template undefined for bits not in {2, 4, 8}");
 
  U accum = 0;
 
  if (bits == 2) {
    for (int i = 0; i < (values_per_thread / 4); i++) {
      accum +=
          (x_thread[4 * i] * (w[i] & 0x03) +
           x_thread[4 * i + 1] * (w[i] & 0x0c) +
           x_thread[4 * i + 2] * (w[i] & 0x30) +
           x_thread[4 * i + 3] * (w[i] & 0xc0));
    }
  }
 
  else if (bits == 4) {
    const device uint16_t* ws = (const device uint16_t*)w;
    for (int i = 0; i < (values_per_thread / 4); i++) {
      accum +=
          (x_thread[4 * i] * (ws[i] & 0x000f) +
           x_thread[4 * i + 1] * (ws[i] & 0x00f0) +
           x_thread[4 * i + 2] * (ws[i] & 0x0f00) +
           x_thread[4 * i + 3] * (ws[i] & 0xf000));
    }
  }
 
  else if (bits == 8) {
    for (int i = 0; i < values_per_thread; i++) {
      accum += x_thread[i] * w[i];
    }
  }
 
  return scale * accum + sum * bias;
}
 
template <typename U, int values_per_thread, int bits>
inline U qdot_safe(
    const device uint8_t* w,
    const thread U* x_thread,
    U scale,
    U bias,
    U sum,
    int N) {
  static_assert(
      bits == 2 || bits == 4 || bits == 8,
      "Template undefined for bits not in {2, 4, 8}");
 
  U accum = 0;
 
  if (bits == 2) {
    for (int i = 0; i < (N / 4); i++) {
      accum +=
          (x_thread[4 * i] * (w[i] & 0x03) +
           x_thread[4 * i + 1] * (w[i] & 0x0c) +
           x_thread[4 * i + 2] * (w[i] & 0x30) +
           x_thread[4 * i + 3] * (w[i] & 0xc0));
    }
  }
 
  else if (bits == 4) {
    const device uint16_t* ws = (const device uint16_t*)w;
    for (int i = 0; i < (N / 4); i++) {
      accum +=
          (x_thread[4 * i] * (ws[i] & 0x000f) +
           x_thread[4 * i + 1] * (ws[i] & 0x00f0) +
           x_thread[4 * i + 2] * (ws[i] & 0x0f00) +
           x_thread[4 * i + 3] * (ws[i] & 0xf000));
    }
  }
 
  else if (bits == 8) {
    for (int i = 0; i < N; i++) {
      accum += x_thread[i] * w[i];
    }
  }
 
  return scale * accum + sum * bias;
}
 
template <typename U, int values_per_thread, int bits>
inline void
qouter(const thread uint8_t* w, U x, U scale, U bias, thread U* result) {
  static_assert(
      bits == 2 || bits == 4 || bits == 8,
      "Template undefined for bits not in {2, 4, 8}");
 
  if (bits == 2) {
    U s[4] = {scale, scale / 4.0f, scale / 16.0f, scale / 64.0f};
    for (int i = 0; i < (values_per_thread / 4); i++) {
      result[4 * i] += x * (s[0] * (w[i] & 0x03) + bias);
      result[4 * i + 1] += x * (s[1] * (w[i] & 0x0c) + bias);
      result[4 * i + 2] += x * (s[2] * (w[i] & 0x30) + bias);
      result[4 * i + 3] += x * (s[3] * (w[i] & 0xc0) + bias);
    }
  }
 
  else if (bits == 4) {
    U s[2] = {scale, scale / 16.0f};
    for (int i = 0; i < (values_per_thread / 2); i++) {
      result[2 * i] += x * (s[0] * (w[i] & 0x0f) + bias);
      result[2 * i + 1] += x * (s[1] * (w[i] & 0xf0) + bias);
    }
  }
 
  else if (bits == 8) {
    for (int i = 0; i < values_per_thread; i++) {
      result[i] += x * (scale * w[i] + bias);
    }
  }
}
 
template <typename U, int N, int bits>
inline void
dequantize(const device uint8_t* w, U scale, U bias, threadgroup U* w_local) {
  static_assert(
      bits == 2 || bits == 4 || bits == 8,
      "Template undefined for bits not in {2, 4, 8}");
 
  if (bits == 2) {
    U s[4] = {
        scale,
        scale / static_cast<U>(4.0f),
        scale / static_cast<U>(16.0f),
        scale / static_cast<U>(64.0f)};
    for (int i = 0; i < (N / 4); i++) {
      w_local[4 * i] = s[0] * (w[i] & 0x03) + bias;
      w_local[4 * i + 1] = s[1] * (w[i] & 0x0c) + bias;
      w_local[4 * i + 2] = s[2] * (w[i] & 0x30) + bias;
      w_local[4 * i + 3] = s[3] * (w[i] & 0xc0) + bias;
    }
  }
 
  else if (bits == 4) {
    U s[2] = {scale, scale / static_cast<U>(16.0f)};
    for (int i = 0; i < (N / 2); i++) {
      w_local[2 * i] = s[0] * (w[i] & 0x0f) + bias;
      w_local[2 * i + 1] = s[1] * (w[i] & 0xf0) + bias;
    }
  }
 
  else if (bits == 8) {
    for (int i = 0; i < N; i++) {
      w_local[i] = scale * w[i] + bias;
    }
  }
}
 
template <
    typename T,
    short BROWS,
    short BCOLS,
    short dst_ld,
    short reduction_dim,
    short tgp_size,
    short group_size,
    short bits>
struct QuantizedBlockLoader {
  static_assert(
      BCOLS <= group_size,
      "The group size should be larger than the columns");
  static_assert(
      group_size % BCOLS == 0,
      "The group size should be divisible by the columns");
  static_assert(
      bits == 2 || bits == 4 || bits == 8,
      "Template undefined for bits not in {2, 4, 8}");
 
  MLX_MTL_CONST short pack_factor = 32 / bits;
  MLX_MTL_CONST short BCOLS_PACKED = BCOLS / pack_factor;
  MLX_MTL_CONST short n_reads =
      (BCOLS_PACKED * BROWS < tgp_size) ? 1 : (BCOLS_PACKED * BROWS) / tgp_size;
  MLX_MTL_CONST short group_steps = group_size / BCOLS;
 
  const int src_ld;
  const int tile_stride;
  short group_step_cnt;
  const int group_stride;
 
  const short thread_idx;
  const short bi;
  const short bj;
 
  threadgroup T* dst;
  const device uint32_t* src;
  const device T* scales;
  const device T* biases;
 
  QuantizedBlockLoader(
      const device uint32_t* src_,
      const device T* scales_,
      const device T* biases_,
      const int src_ld_,
      threadgroup T* dst_,
      ushort simd_group_id [[simdgroup_index_in_threadgroup]],
      ushort simd_lane_id [[thread_index_in_simdgroup]])
      : src_ld(src_ld_),
        tile_stride(
            reduction_dim ? BCOLS_PACKED : BROWS * src_ld / pack_factor),
        group_step_cnt(0),
        group_stride(BROWS * src_ld / group_size),
        thread_idx(simd_group_id * 32 + simd_lane_id),
        bi(n_reads * thread_idx / BCOLS_PACKED),
        bj((n_reads * thread_idx) % BCOLS_PACKED),
        dst(dst_ + bi * dst_ld + bj * pack_factor),
        src(src_ + bi * src_ld / pack_factor + bj),
        scales(scales_ + bi * src_ld / group_size),
        biases(biases_ + bi * src_ld / group_size) {}
 
  void load_unsafe() const {
    if (BCOLS_PACKED * BROWS < tgp_size && bi >= BROWS) {
      return;
    }
 
    T scale = *scales;
    T bias = *biases;
    for (int i = 0; i < n_reads; i++) {
      dequantize<T, pack_factor, bits>(
          (device uint8_t*)(src + i), scale, bias, dst + i * pack_factor);
    }
  }
 
  void load_safe(short2 src_tile_dim) const {
    if (BCOLS_PACKED * BROWS < tgp_size && bi >= BROWS) {
      return;
    }
 
    if (reduction_dim == 1 && bi >= src_tile_dim.y) {
      for (int i = 0; i < n_reads * pack_factor; i++) {
        dst[i] = T(0);
      }
      return;
    }
 
    if (reduction_dim == 0 && bi >= src_tile_dim.x) {
      for (int i = 0; i < n_reads * pack_factor; i++) {
        dst[i] = T(0);
      }
      return;
    }
 
    T scale = *scales;
    T bias = *biases;
    for (int i = 0; i < n_reads; i++) {
      dequantize<T, pack_factor, bits>(
          (device uint8_t*)(src + i), scale, bias, dst + i * pack_factor);
    }
  }
 
  void next() {
    src += tile_stride;
    if (reduction_dim == 1) {
      if (group_steps > 1) {
        group_step_cnt++;
        if (group_step_cnt == group_steps) {
          group_step_cnt = 0;
          scales++;
          biases++;
        }
      } else {
        scales++;
        biases++;
      }
    } else {
      scales += group_stride;
      biases += group_stride;
    }
  }
};
 
template <typename T, int group_size, int bits>
METAL_FUNC void qmv_fast_impl(
    const device uint32_t* w,
    const device T* scales,
    const device T* biases,
    const device T* x,
    device T* y,
    const constant int& in_vec_size,
    const constant int& out_vec_size,
    uint3 tid [[threadgroup_position_in_grid]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  constexpr int packs_per_thread = bits > 2 ? 2 : 1;
  constexpr int num_simdgroups = 2;
  constexpr int results_per_simdgroup = 4;
  constexpr int pack_factor = 32 / bits;
  constexpr int values_per_thread = pack_factor * packs_per_thread;
  constexpr int block_size = values_per_thread * SIMD_SIZE;
  constexpr int scale_step_per_thread = group_size / values_per_thread;
 
  typedef float U;
 
  thread U x_thread[values_per_thread];
  thread U result[results_per_simdgroup] = {0};
 
  // Adjust positions
  const int in_vec_size_w = in_vec_size / pack_factor;
  const int in_vec_size_g = in_vec_size / group_size;
  const int out_row = tid.x * (num_simdgroups * results_per_simdgroup) +
      simd_gid * results_per_simdgroup;
  w += out_row * in_vec_size_w + simd_lid * packs_per_thread;
  scales += out_row * in_vec_size_g + simd_lid / scale_step_per_thread;
  biases += out_row * in_vec_size_g + simd_lid / scale_step_per_thread;
  x += tid.y * in_vec_size + simd_lid * values_per_thread;
  y += tid.y * out_vec_size + out_row;
 
  for (int k = 0; k < in_vec_size; k += block_size) {
    U sum = load_vector<T, U, values_per_thread, bits>(x, x_thread);
 
    for (int row = 0; row < results_per_simdgroup; row++) {
      const device uint8_t* wl =
          (const device uint8_t*)(w + row * in_vec_size_w);
      const device T* sl = scales + row * in_vec_size_g;
      const device T* bl = biases + row * in_vec_size_g;
 
      U s = sl[0];
      U b = bl[0];
      result[row] += qdot<U, values_per_thread, bits>(wl, x_thread, s, b, sum);
    }
 
    w += block_size / pack_factor;
    scales += block_size / group_size;
    biases += block_size / group_size;
    x += block_size;
  }
 
  for (int row = 0; row < results_per_simdgroup; row++) {
    result[row] = simd_sum(result[row]);
    if (simd_lid == 0) {
      y[row] = static_cast<T>(result[row]);
    }
  }
}
 
template <typename T, int group_size, int bits>
METAL_FUNC void qmv_impl(
    const device uint32_t* w,
    const device T* scales,
    const device T* biases,
    const device T* x,
    device T* y,
    const constant int& in_vec_size,
    const constant int& out_vec_size,
    uint3 tid [[threadgroup_position_in_grid]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  constexpr int num_simdgroups = 2;
  constexpr int results_per_simdgroup = 4;
  constexpr int packs_per_thread = 1;
  constexpr int pack_factor = 32 / bits;
  constexpr int values_per_thread = pack_factor * packs_per_thread;
  constexpr int block_size = values_per_thread * SIMD_SIZE;
  constexpr int scale_step_per_thread = group_size / values_per_thread;
 
  typedef float U;
 
  thread U x_thread[values_per_thread];
  thread U result[results_per_simdgroup] = {0};
 
  // Adjust positions
  const int in_vec_size_w = in_vec_size / pack_factor;
  const int in_vec_size_g = in_vec_size / group_size;
  const int out_row = tid.x * (num_simdgroups * results_per_simdgroup) +
      simd_gid * results_per_simdgroup;
  const int used_out_row = min(out_vec_size - results_per_simdgroup, out_row);
 
  if (out_row >= out_vec_size) {
    return;
  }
 
  // In this case we need to properly guard all our reads because there isn't
  // even 1 tile in the matrix
  if (out_vec_size < (num_simdgroups * results_per_simdgroup)) {
    w += out_row * in_vec_size_w + simd_lid * packs_per_thread;
    scales += out_row * in_vec_size_g + simd_lid / scale_step_per_thread;
    biases += out_row * in_vec_size_g + simd_lid / scale_step_per_thread;
    x += tid.y * in_vec_size + simd_lid * values_per_thread;
    y += tid.y * out_vec_size + out_row;
 
    int k = 0;
    for (; k < in_vec_size - block_size; k += block_size) {
      U sum = load_vector<T, U, values_per_thread, bits>(x, x_thread);
 
      for (int row = 0; out_row + row < out_vec_size; row++) {
        const device uint8_t* wl =
            (const device uint8_t*)(w + row * in_vec_size_w);
        const device T* sl = scales + row * in_vec_size_g;
        const device T* bl = biases + row * in_vec_size_g;
 
        U s = sl[0];
        U b = bl[0];
        result[row] +=
            qdot<U, values_per_thread, bits>(wl, x_thread, s, b, sum);
      }
 
      w += block_size / pack_factor;
      scales += block_size / group_size;
      biases += block_size / group_size;
      x += block_size;
    }
    const int remaining = clamp(
        static_cast<int>(in_vec_size - k - simd_lid * values_per_thread),
        0,
        values_per_thread);
    U sum =
        load_vector_safe<T, U, values_per_thread, bits>(x, x_thread, remaining);
 
    for (int row = 0; out_row + row < out_vec_size; row++) {
      const device uint8_t* wl =
          (const device uint8_t*)(w + row * in_vec_size_w);
      const device T* sl = scales + row * in_vec_size_g;
      const device T* bl = biases + row * in_vec_size_g;
 
      U s = sl[0];
      U b = bl[0];
      result[row] += qdot<U, values_per_thread, bits>(wl, x_thread, s, b, sum);
    }
 
    for (int row = 0; out_row + row < out_vec_size; row++) {
      result[row] = simd_sum(result[row]);
      if (simd_lid == 0) {
        y[row] = static_cast<T>(result[row]);
      }
    }
  }
 
  // In this case the last tile is moved back to redo some output values
  else {
    w += used_out_row * in_vec_size_w + simd_lid * packs_per_thread;
    scales += used_out_row * in_vec_size_g + simd_lid / scale_step_per_thread;
    biases += used_out_row * in_vec_size_g + simd_lid / scale_step_per_thread;
    x += tid.y * in_vec_size + simd_lid * values_per_thread;
    y += tid.y * out_vec_size + used_out_row;
 
    int k = 0;
    for (; k < in_vec_size - block_size; k += block_size) {
      U sum = load_vector<T, U, values_per_thread, bits>(x, x_thread);
 
      for (int row = 0; row < results_per_simdgroup; row++) {
        const device uint8_t* wl =
            (const device uint8_t*)(w + row * in_vec_size_w);
        const device T* sl = scales + row * in_vec_size_g;
        const device T* bl = biases + row * in_vec_size_g;
 
        U s = sl[0];
        U b = bl[0];
        result[row] +=
            qdot<U, values_per_thread, bits>(wl, x_thread, s, b, sum);
      }
 
      w += block_size / pack_factor;
      scales += block_size / group_size;
      biases += block_size / group_size;
      x += block_size;
    }
    const int remaining = clamp(
        static_cast<int>(in_vec_size - k - simd_lid * values_per_thread),
        0,
        values_per_thread);
    U sum =
        load_vector_safe<T, U, values_per_thread, bits>(x, x_thread, remaining);
 
    for (int row = 0; row < results_per_simdgroup; row++) {
      const device uint8_t* wl =
          (const device uint8_t*)(w + row * in_vec_size_w);
      const device T* sl = scales + row * in_vec_size_g;
      const device T* bl = biases + row * in_vec_size_g;
 
      U s = sl[0];
      U b = bl[0];
      result[row] += qdot_safe<U, values_per_thread, bits>(
          wl, x_thread, s, b, sum, remaining);
    }
 
    for (int row = 0; row < results_per_simdgroup; row++) {
      result[row] = simd_sum(result[row]);
      if (simd_lid == 0) {
        y[row] = static_cast<T>(result[row]);
      }
    }
  }
}
 
template <typename T, const int group_size, const int bits>
METAL_FUNC void qvm_impl(
    const device T* x,
    const device uint32_t* w,
    const device T* scales,
    const device T* biases,
    device T* y,
    const constant int& in_vec_size,
    const constant int& out_vec_size,
    uint3 tid [[threadgroup_position_in_grid]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  constexpr int num_simdgroups = 2;
  constexpr int pack_factor = 32 / bits;
  constexpr int tn = 32 / pack_factor;
  constexpr int blocksize = SIMD_SIZE;
 
  typedef float U;
  typedef struct {
    uint32_t wi[tn];
  } vec_w;
 
  thread vec_w w_local;
  thread U result[tn * pack_factor] = {0};
  thread U scale = 1;
  thread U bias = 0;
  thread U x_local = 0;
 
  // Adjust positions
  const int out_vec_size_w = out_vec_size / pack_factor;
  const int out_vec_size_g = out_vec_size / group_size;
  int out_col =
      tid.x * (num_simdgroups * pack_factor * tn) + simd_gid * pack_factor * tn;
  w += out_col / pack_factor + simd_lid * out_vec_size_w;
  scales += out_col / group_size + simd_lid * out_vec_size_g;
  biases += out_col / group_size + simd_lid * out_vec_size_g;
  x += tid.y * in_vec_size + simd_lid;
  y += tid.y * out_vec_size + out_col;
 
  if (out_col >= out_vec_size) {
    return;
  }
 
  // Loop over in_vec in blocks of blocksize
  int remaining = in_vec_size % blocksize;
  if (remaining == 0) {
    for (int i = 0; i < in_vec_size; i += blocksize) {
      x_local = *x;
      scale = *scales;
      bias = *biases;
      w_local = *((device vec_w*)w);
 
      qouter<U, tn * pack_factor, bits>(
          (thread uint8_t*)&w_local, x_local, scale, bias, result);
 
      x += blocksize;
      scales += blocksize * out_vec_size_g;
      biases += blocksize * out_vec_size_g;
      w += blocksize * out_vec_size_w;
    }
  } else {
    for (int i = blocksize; i < in_vec_size; i += blocksize) {
      x_local = *x;
      scale = *scales;
      bias = *biases;
      w_local = *((device vec_w*)w);
 
      qouter<U, tn * pack_factor, bits>(
          (thread uint8_t*)&w_local, x_local, scale, bias, result);
 
      x += blocksize;
      scales += blocksize * out_vec_size_g;
      biases += blocksize * out_vec_size_g;
      w += blocksize * out_vec_size_w;
    }
    if (static_cast<int>(simd_lid) < remaining) {
      x_local = *x;
      scale = *scales;
      bias = *biases;
      w_local = *((device vec_w*)w);
    } else {
      x_local = 0;
      scale = 0;
      bias = 0;
    }
    qouter<U, tn * pack_factor, bits>(
        (thread uint8_t*)&w_local, x_local, scale, bias, result);
  }
 
// Accumulate in the simdgroup
#pragma clang loop unroll(full)
  for (int k = 0; k < tn * pack_factor; k++) {
    result[k] = simd_sum(result[k]);
  }
 
  // Store the result
  if (simd_lid == 0) {
#pragma clang loop unroll(full)
    for (int k = 0; k < tn * pack_factor; k++) {
      y[k] = static_cast<T>(result[k]);
    }
  }
}
 
template <
    typename T,
    const int group_size,
    const int bits,
    const bool aligned_N,
    const int BM = 32,
    const int BK = 32,
    const int BN = 32>
METAL_FUNC void qmm_t_impl(
    const device T* x,
    const device uint32_t* w,
    const device T* scales,
    const device T* biases,
    device T* y,
    threadgroup T* Xs,
    threadgroup T* Ws,
    const constant int& M,
    const constant int& N,
    const constant int& K,
    uint3 tid [[threadgroup_position_in_grid]],
    uint lid [[thread_index_in_threadgroup]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  static_assert(BK >= SIMD_SIZE, "BK should be larger than SIMD_SIZE");
  static_assert(BK % SIMD_SIZE == 0, "BK should be divisible by SIMD_SIZE");
 
  (void)lid;
 
  constexpr int WM = 2;
  constexpr int WN = 2;
  constexpr int pack_factor = 32 / bits;
  constexpr int BK_padded = (BK + 16 / sizeof(T));
 
  // Instantiate the appropriate BlockMMA and Loader
  using mma_t = mlx::steel::
      BlockMMA<T, T, BM, BN, BK, WM, WN, false, true, BK_padded, BK_padded>;
  using loader_x_t =
      mlx::steel::BlockLoader<T, BM, BK, BK_padded, 1, WM * WN * SIMD_SIZE>;
  using loader_w_t = QuantizedBlockLoader<
      T,
      BN,
      BK,
      BK_padded,
      1,
      WM * WN * SIMD_SIZE,
      group_size,
      bits>;
 
  // Set the block
  const int K_w = K / pack_factor;
  const int K_g = K / group_size;
  const int y_row = tid.y * BM;
  const int y_col = tid.x * BN;
 
  x += y_row * K;
  w += y_col * K_w;
  scales += y_col * K_g;
  biases += y_col * K_g;
  y += y_row * N + y_col;
 
  // Make the x loader and mma operation
  const short num_els = min(BM, M - y_row);
  const short num_outs = min(BN, N - y_col);
  loader_x_t loader_x(x, K, Xs, simd_gid, simd_lid);
  loader_w_t loader_w(w, scales, biases, K, Ws, simd_gid, simd_lid);
  mma_t mma_op(simd_gid, simd_lid);
 
  if (num_els < BM) {
    if (!aligned_N && num_outs < BN) {
      for (int k = 0; k < K; k += BK) {
        threadgroup_barrier(mem_flags::mem_threadgroup);
        loader_x.load_safe(short2(BK, num_els));
        loader_w.load_safe(short2(BK, num_outs));
        threadgroup_barrier(mem_flags::mem_threadgroup);
        mma_op.mma(Xs, Ws);
        loader_x.next();
        loader_w.next();
      }
    } else {
      for (int k = 0; k < K; k += BK) {
        threadgroup_barrier(mem_flags::mem_threadgroup);
        loader_x.load_safe(short2(BK, num_els));
        loader_w.load_unsafe();
        threadgroup_barrier(mem_flags::mem_threadgroup);
        mma_op.mma(Xs, Ws);
        loader_x.next();
        loader_w.next();
      }
    }
  } else {
    if (!aligned_N && num_outs < BN) {
      for (int k = 0; k < K; k += BK) {
        threadgroup_barrier(mem_flags::mem_threadgroup);
        loader_x.load_unsafe();
        loader_w.load_safe(short2(BK, num_outs));
        threadgroup_barrier(mem_flags::mem_threadgroup);
        mma_op.mma(Xs, Ws);
        loader_x.next();
        loader_w.next();
      }
    } else {
      for (int k = 0; k < K; k += BK) {
        threadgroup_barrier(mem_flags::mem_threadgroup);
        loader_x.load_unsafe();
        loader_w.load_unsafe();
        threadgroup_barrier(mem_flags::mem_threadgroup);
        mma_op.mma(Xs, Ws);
        loader_x.next();
        loader_w.next();
      }
    }
  }
 
  // Store results to device memory
  threadgroup_barrier(mem_flags::mem_threadgroup);
  if (num_els < BM || num_outs < BN) {
    mma_op.store_result_safe(y, N, short2(num_outs, num_els));
  } else {
    mma_op.store_result(y, N);
  }
}
 
template <
    typename T,
    const int group_size,
    const int bits,
    const int BM = 32,
    const int BK = 32,
    const int BN = 32>
METAL_FUNC void qmm_n_impl(
    const device T* x,
    const device uint32_t* w,
    const device T* scales,
    const device T* biases,
    device T* y,
    threadgroup T* Xs,
    threadgroup T* Ws,
    const constant int& M,
    const constant int& N,
    const constant int& K,
    uint3 tid [[threadgroup_position_in_grid]],
    uint lid [[thread_index_in_threadgroup]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  static_assert(BK >= SIMD_SIZE, "BK should be larger than SIMD_SIZE");
  static_assert(BK % SIMD_SIZE == 0, "BK should be divisible by SIMD_SIZE");
 
  (void)lid;
 
  constexpr int WM = 2;
  constexpr int WN = 2;
  constexpr int pack_factor = 32 / bits;
  constexpr int BK_padded = (BK + 16 / sizeof(T));
  constexpr int BN_padded = (BN + 16 / sizeof(T));
 
  // Instantiate the appropriate BlockMMA and Loader
  using mma_t = mlx::steel::
      BlockMMA<T, T, BM, BN, BK, WM, WN, false, false, BK_padded, BN_padded>;
  using loader_x_t = mlx::steel::
      BlockLoader<T, BM, BK, BK_padded, 1, WM * WN * SIMD_SIZE, 1, 4>;
  using loader_w_t = QuantizedBlockLoader<
      T,
      BK,
      BN,
      BN_padded,
      0,
      WM * WN * SIMD_SIZE,
      group_size,
      bits>;
 
  // Set the block
  const int y_row = tid.y * BM;
  const int y_col = tid.x * BN;
  x += y_row * K;
  w += y_col / pack_factor;
  scales += y_col / group_size;
  biases += y_col / group_size;
  y += y_row * N + y_col;
 
  // Make the x loader and mma operation
  const short num_els = min(BM, M - y_row);
  loader_x_t loader_x(x, K, Xs, simd_gid, simd_lid);
  loader_w_t loader_w(w, scales, biases, N, Ws, simd_gid, simd_lid);
  mma_t mma_op(simd_gid, simd_lid);
 
  if (num_els < BM) {
    if ((K % BK) != 0) {
      const int k_blocks = K / BK;
      for (int k = 0; k < k_blocks; k++) {
        threadgroup_barrier(mem_flags::mem_threadgroup);
        loader_x.load_safe(short2(BK, num_els));
        loader_w.load_unsafe();
        threadgroup_barrier(mem_flags::mem_threadgroup);
        mma_op.mma(Xs, Ws);
        loader_x.next();
        loader_w.next();
      }
      const short num_k = K - k_blocks * BK;
      threadgroup_barrier(mem_flags::mem_threadgroup);
      loader_x.load_safe(short2(num_k, num_els));
      loader_w.load_safe(short2(BN, num_k));
      threadgroup_barrier(mem_flags::mem_threadgroup);
      mma_op.mma(Xs, Ws);
    } else {
      for (int k = 0; k < K; k += BK) {
        threadgroup_barrier(mem_flags::mem_threadgroup);
        loader_x.load_safe(short2(BK, num_els));
        loader_w.load_unsafe();
        threadgroup_barrier(mem_flags::mem_threadgroup);
        mma_op.mma(Xs, Ws);
        loader_x.next();
        loader_w.next();
      }
    }
  } else {
    if ((K % BK) != 0) {
      const int k_blocks = K / BK;
      for (int k = 0; k < k_blocks; k++) {
        threadgroup_barrier(mem_flags::mem_threadgroup);
        loader_x.load_unsafe();
        loader_w.load_unsafe();
        threadgroup_barrier(mem_flags::mem_threadgroup);
        mma_op.mma(Xs, Ws);
        loader_x.next();
        loader_w.next();
      }
      const short num_k = K - k_blocks * BK;
      threadgroup_barrier(mem_flags::mem_threadgroup);
      loader_x.load_safe(short2(num_k, BM));
      loader_w.load_safe(short2(BN, num_k));
      threadgroup_barrier(mem_flags::mem_threadgroup);
      mma_op.mma(Xs, Ws);
    } else {
      for (int k = 0; k < K; k += BK) {
        threadgroup_barrier(mem_flags::mem_threadgroup);
        loader_x.load_unsafe();
        loader_w.load_unsafe();
        threadgroup_barrier(mem_flags::mem_threadgroup);
        mma_op.mma(Xs, Ws);
        loader_x.next();
        loader_w.next();
      }
    }
  }
 
  // Store results to device memory
  threadgroup_barrier(mem_flags::mem_threadgroup);
  if (num_els < BM) {
    mma_op.store_result_safe(y, N, short2(BN, num_els));
  } else {
    mma_op.store_result(y, N);
  }
}
 
template <typename T>
METAL_FUNC void adjust_matrix_offsets(
    const device T*& x,
    const device uint32_t*& w,
    const device T*& scales,
    const device T*& biases,
    const device uint32_t* lhs_indices,
    const device uint32_t* rhs_indices,
    device T*& y,
    int output_stride,
    const constant int& batch_ndims,
    const constant int* batch_shape,
    const constant size_t* lhs_strides,
    const constant size_t* rhs_strides,
    const constant int& x_batch_ndims,
    const constant int* x_shape,
    const constant size_t* x_strides,
    const constant int& w_batch_ndims,
    const constant int* w_shape,
    const constant size_t* w_strides,
    const constant size_t* s_strides,
    const constant size_t* b_strides,
    uint3 tid [[threadgroup_position_in_grid]]) {
  // Set the input/output matrices
  uint32_t x_idx;
  uint32_t w_idx;
  if (batch_ndims == 1) {
    x_idx = lhs_indices[tid.z * lhs_strides[0]];
    w_idx = rhs_indices[tid.z * rhs_strides[0]];
  } else {
    ulong2 idx = elem_to_loc_broadcast(
        tid.z, batch_shape, lhs_strides, rhs_strides, batch_ndims);
    x_idx = lhs_indices[idx.x];
    w_idx = rhs_indices[idx.y];
  }
  if (x_batch_ndims == 1) {
    x += x_idx * x_strides[0];
  } else {
    x += elem_to_loc(x_idx, x_shape, x_strides, x_batch_ndims);
  }
  if (w_batch_ndims == 1) {
    w += w_idx * w_strides[0];
    scales += w_idx * s_strides[0];
    biases += w_idx * b_strides[0];
  } else {
    ulong3 idx = elem_to_loc_broadcast(
        w_idx, w_shape, w_strides, s_strides, b_strides, w_batch_ndims);
    w += idx.x;
    scales += idx.y;
    biases += idx.z;
  }
  y += tid.z * output_stride;
}
 
template <typename T, int group_size, int bits>
[[kernel]] void qmv_fast(
    const device uint32_t* w [[buffer(0)]],
    const device T* scales [[buffer(1)]],
    const device T* biases [[buffer(2)]],
    const device T* x [[buffer(3)]],
    device T* y [[buffer(4)]],
    const constant int& in_vec_size [[buffer(5)]],
    const constant int& out_vec_size [[buffer(6)]],
    uint3 tid [[threadgroup_position_in_grid]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  qmv_fast_impl<T, group_size, bits>(
      w,
      scales,
      biases,
      x,
      y,
      in_vec_size,
      out_vec_size,
      tid,
      simd_gid,
      simd_lid);
}
 
template <typename T, const int group_size, const int bits>
[[kernel]] void qmv(
    const device uint32_t* w [[buffer(0)]],
    const device T* scales [[buffer(1)]],
    const device T* biases [[buffer(2)]],
    const device T* x [[buffer(3)]],
    device T* y [[buffer(4)]],
    const constant int& in_vec_size [[buffer(5)]],
    const constant int& out_vec_size [[buffer(6)]],
    uint3 tid [[threadgroup_position_in_grid]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  qmv_impl<T, group_size, bits>(
      w,
      scales,
      biases,
      x,
      y,
      in_vec_size,
      out_vec_size,
      tid,
      simd_gid,
      simd_lid);
}
 
template <typename T, const int group_size, const int bits>
[[kernel]] void qvm(
    const device T* x [[buffer(0)]],
    const device uint32_t* w [[buffer(1)]],
    const device T* scales [[buffer(2)]],
    const device T* biases [[buffer(3)]],
    device T* y [[buffer(4)]],
    const constant int& in_vec_size [[buffer(5)]],
    const constant int& out_vec_size [[buffer(6)]],
    uint3 tid [[threadgroup_position_in_grid]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  qvm_impl<T, group_size, bits>(
      x,
      w,
      scales,
      biases,
      y,
      in_vec_size,
      out_vec_size,
      tid,
      simd_gid,
      simd_lid);
}
 
template <
    typename T,
    const int group_size,
    const int bits,
    const bool aligned_N,
    const int BM = 32,
    const int BK = 32,
    const int BN = 32>
[[kernel]] void qmm_t(
    const device T* x [[buffer(0)]],
    const device uint32_t* w [[buffer(1)]],
    const device T* scales [[buffer(2)]],
    const device T* biases [[buffer(3)]],
    device T* y [[buffer(4)]],
    const constant int& M [[buffer(5)]],
    const constant int& N [[buffer(6)]],
    const constant int& K [[buffer(7)]],
    uint3 tid [[threadgroup_position_in_grid]],
    uint lid [[thread_index_in_threadgroup]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  (void)lid;
 
  constexpr int BK_padded = (BK + 16 / sizeof(T));
 
  threadgroup T Xs[BM * BK_padded];
  threadgroup T Ws[BN * BK_padded];
 
  qmm_t_impl<T, group_size, bits, aligned_N, BM, BK, BN>(
      x, w, scales, biases, y, Xs, Ws, M, N, K, tid, lid, simd_gid, simd_lid);
}
 
template <
    typename T,
    const int group_size,
    const int bits,
    const int BM = 32,
    const int BK = 32,
    const int BN = 32>
[[kernel]] void qmm_n(
    const device T* x [[buffer(0)]],
    const device uint32_t* w [[buffer(1)]],
    const device T* scales [[buffer(2)]],
    const device T* biases [[buffer(3)]],
    device T* y [[buffer(4)]],
    const constant int& M [[buffer(5)]],
    const constant int& N [[buffer(6)]],
    const constant int& K [[buffer(7)]],
    uint3 tid [[threadgroup_position_in_grid]],
    uint lid [[thread_index_in_threadgroup]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  (void)lid;
 
  constexpr int BK_padded = (BK + 16 / sizeof(T));
  constexpr int BN_padded = (BN + 16 / sizeof(T));
 
  threadgroup T Xs[BM * BK_padded];
  threadgroup T Ws[BK * BN_padded];
 
  qmm_n_impl<T, group_size, bits, BM, BK, BN>(
      x, w, scales, biases, y, Xs, Ws, M, N, K, tid, lid, simd_gid, simd_lid);
}
 
template <typename T, int group_size, int bits>
[[kernel]] void bs_qmv_fast(
    const device uint32_t* w [[buffer(0)]],
    const device T* scales [[buffer(1)]],
    const device T* biases [[buffer(2)]],
    const device T* x [[buffer(3)]],
    const device uint32_t* lhs_indices [[buffer(4)]],
    const device uint32_t* rhs_indices [[buffer(5)]],
    device T* y [[buffer(6)]],
    const constant int& in_vec_size [[buffer(7)]],
    const constant int& out_vec_size [[buffer(8)]],
    const constant int& batch_ndims [[buffer(9)]],
    const constant int* batch_shape [[buffer(10)]],
    const constant size_t* lhs_strides [[buffer(11)]],
    const constant size_t* rhs_strides [[buffer(12)]],
    const constant int& x_batch_ndims [[buffer(13)]],
    const constant int* x_shape [[buffer(14)]],
    const constant size_t* x_strides [[buffer(15)]],
    const constant int& w_batch_ndims [[buffer(16)]],
    const constant int* w_shape [[buffer(17)]],
    const constant size_t* w_strides [[buffer(18)]],
    const constant size_t* s_strides [[buffer(19)]],
    const constant size_t* b_strides [[buffer(20)]],
    uint3 tid [[threadgroup_position_in_grid]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  adjust_matrix_offsets<T>(
      x,
      w,
      scales,
      biases,
      lhs_indices,
      rhs_indices,
      y,
      out_vec_size,
      batch_ndims,
      batch_shape,
      lhs_strides,
      rhs_strides,
      x_batch_ndims,
      x_shape,
      x_strides,
      w_batch_ndims,
      w_shape,
      w_strides,
      s_strides,
      b_strides,
      tid);
  qmv_fast_impl<T, group_size, bits>(
      w,
      scales,
      biases,
      x,
      y,
      in_vec_size,
      out_vec_size,
      tid,
      simd_gid,
      simd_lid);
}
 
template <typename T, int group_size, int bits>
[[kernel]] void bs_qmv(
    const device uint32_t* w [[buffer(0)]],
    const device T* scales [[buffer(1)]],
    const device T* biases [[buffer(2)]],
    const device T* x [[buffer(3)]],
    const device uint32_t* lhs_indices [[buffer(4)]],
    const device uint32_t* rhs_indices [[buffer(5)]],
    device T* y [[buffer(6)]],
    const constant int& in_vec_size [[buffer(7)]],
    const constant int& out_vec_size [[buffer(8)]],
    const constant int& batch_ndims [[buffer(9)]],
    const constant int* batch_shape [[buffer(10)]],
    const constant size_t* lhs_strides [[buffer(11)]],
    const constant size_t* rhs_strides [[buffer(12)]],
    const constant int& x_batch_ndims [[buffer(13)]],
    const constant int* x_shape [[buffer(14)]],
    const constant size_t* x_strides [[buffer(15)]],
    const constant int& w_batch_ndims [[buffer(16)]],
    const constant int* w_shape [[buffer(17)]],
    const constant size_t* w_strides [[buffer(18)]],
    const constant size_t* s_strides [[buffer(19)]],
    const constant size_t* b_strides [[buffer(20)]],
    uint3 tid [[threadgroup_position_in_grid]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  adjust_matrix_offsets<T>(
      x,
      w,
      scales,
      biases,
      lhs_indices,
      rhs_indices,
      y,
      out_vec_size,
      batch_ndims,
      batch_shape,
      lhs_strides,
      rhs_strides,
      x_batch_ndims,
      x_shape,
      x_strides,
      w_batch_ndims,
      w_shape,
      w_strides,
      s_strides,
      b_strides,
      tid);
  qmv_impl<T, group_size, bits>(
      w,
      scales,
      biases,
      x,
      y,
      in_vec_size,
      out_vec_size,
      tid,
      simd_gid,
      simd_lid);
}
 
template <typename T, int group_size, int bits>
[[kernel]] void bs_qvm(
    const device T* x [[buffer(0)]],
    const device uint32_t* w [[buffer(1)]],
    const device T* scales [[buffer(2)]],
    const device T* biases [[buffer(3)]],
    const device uint32_t* lhs_indices [[buffer(4)]],
    const device uint32_t* rhs_indices [[buffer(5)]],
    device T* y [[buffer(6)]],
    const constant int& in_vec_size [[buffer(7)]],
    const constant int& out_vec_size [[buffer(8)]],
    const constant int& batch_ndims [[buffer(9)]],
    const constant int* batch_shape [[buffer(10)]],
    const constant size_t* lhs_strides [[buffer(11)]],
    const constant size_t* rhs_strides [[buffer(12)]],
    const constant int& x_batch_ndims [[buffer(13)]],
    const constant int* x_shape [[buffer(14)]],
    const constant size_t* x_strides [[buffer(15)]],
    const constant int& w_batch_ndims [[buffer(16)]],
    const constant int* w_shape [[buffer(17)]],
    const constant size_t* w_strides [[buffer(18)]],
    const constant size_t* s_strides [[buffer(19)]],
    const constant size_t* b_strides [[buffer(20)]],
    uint3 tid [[threadgroup_position_in_grid]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  adjust_matrix_offsets<T>(
      x,
      w,
      scales,
      biases,
      lhs_indices,
      rhs_indices,
      y,
      out_vec_size,
      batch_ndims,
      batch_shape,
      lhs_strides,
      rhs_strides,
      x_batch_ndims,
      x_shape,
      x_strides,
      w_batch_ndims,
      w_shape,
      w_strides,
      s_strides,
      b_strides,
      tid);
  qvm_impl<T, group_size, bits>(
      x,
      w,
      scales,
      biases,
      y,
      in_vec_size,
      out_vec_size,
      tid,
      simd_gid,
      simd_lid);
}
 
template <
    typename T,
    const int group_size,
    const int bits,
    const bool aligned_N,
    const int BM = 32,
    const int BK = 32,
    const int BN = 32>
[[kernel]] void bs_qmm_t(
    const device T* x [[buffer(0)]],
    const device uint32_t* w [[buffer(1)]],
    const device T* scales [[buffer(2)]],
    const device T* biases [[buffer(3)]],
    const device uint32_t* lhs_indices [[buffer(4)]],
    const device uint32_t* rhs_indices [[buffer(5)]],
    device T* y [[buffer(6)]],
    const constant int& M [[buffer(7)]],
    const constant int& N [[buffer(8)]],
    const constant int& K [[buffer(9)]],
    const constant int& batch_ndims [[buffer(10)]],
    const constant int* batch_shape [[buffer(11)]],
    const constant size_t* lhs_strides [[buffer(12)]],
    const constant size_t* rhs_strides [[buffer(13)]],
    const constant int& x_batch_ndims [[buffer(14)]],
    const constant int* x_shape [[buffer(15)]],
    const constant size_t* x_strides [[buffer(16)]],
    const constant int& w_batch_ndims [[buffer(17)]],
    const constant int* w_shape [[buffer(18)]],
    const constant size_t* w_strides [[buffer(19)]],
    const constant size_t* s_strides [[buffer(20)]],
    const constant size_t* b_strides [[buffer(21)]],
    uint3 tid [[threadgroup_position_in_grid]],
    uint lid [[thread_index_in_threadgroup]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  (void)lid;
 
  constexpr int BK_padded = (BK + 16 / sizeof(T));
 
  threadgroup T Xs[BM * BK_padded];
  threadgroup T Ws[BN * BK_padded];
 
  adjust_matrix_offsets<T>(
      x,
      w,
      scales,
      biases,
      lhs_indices,
      rhs_indices,
      y,
      M * N,
      batch_ndims,
      batch_shape,
      lhs_strides,
      rhs_strides,
      x_batch_ndims,
      x_shape,
      x_strides,
      w_batch_ndims,
      w_shape,
      w_strides,
      s_strides,
      b_strides,
      tid);
  qmm_t_impl<T, group_size, bits, aligned_N, BM, BK, BN>(
      x, w, scales, biases, y, Xs, Ws, M, N, K, tid, lid, simd_gid, simd_lid);
}
 
template <
    typename T,
    const int group_size,
    const int bits,
    const int BM = 32,
    const int BK = 32,
    const int BN = 32>
[[kernel]] void bs_qmm_n(
    const device T* x [[buffer(0)]],
    const device uint32_t* w [[buffer(1)]],
    const device T* scales [[buffer(2)]],
    const device T* biases [[buffer(3)]],
    const device uint32_t* lhs_indices [[buffer(4)]],
    const device uint32_t* rhs_indices [[buffer(5)]],
    device T* y [[buffer(6)]],
    const constant int& M [[buffer(7)]],
    const constant int& N [[buffer(8)]],
    const constant int& K [[buffer(9)]],
    const constant int& batch_ndims [[buffer(10)]],
    const constant int* batch_shape [[buffer(11)]],
    const constant size_t* lhs_strides [[buffer(12)]],
    const constant size_t* rhs_strides [[buffer(13)]],
    const constant int& x_batch_ndims [[buffer(14)]],
    const constant int* x_shape [[buffer(15)]],
    const constant size_t* x_strides [[buffer(16)]],
    const constant int& w_batch_ndims [[buffer(17)]],
    const constant int* w_shape [[buffer(18)]],
    const constant size_t* w_strides [[buffer(19)]],
    const constant size_t* s_strides [[buffer(20)]],
    const constant size_t* b_strides [[buffer(21)]],
    uint3 tid [[threadgroup_position_in_grid]],
    uint lid [[thread_index_in_threadgroup]],
    uint simd_gid [[simdgroup_index_in_threadgroup]],
    uint simd_lid [[thread_index_in_simdgroup]]) {
  (void)lid;
 
  constexpr int BK_padded = (BK + 16 / sizeof(T));
  constexpr int BN_padded = (BN + 16 / sizeof(T));
 
  threadgroup T Xs[BM * BK_padded];
  threadgroup T Ws[BK * BN_padded];
 
  adjust_matrix_offsets<T>(
      x,
      w,
      scales,
      biases,
      lhs_indices,
      rhs_indices,
      y,
      M * N,
      batch_ndims,
      batch_shape,
      lhs_strides,
      rhs_strides,
      x_batch_ndims,
      x_shape,
      x_strides,
      w_batch_ndims,
      w_shape,
      w_strides,
      s_strides,
      b_strides,
      tid);
  qmm_n_impl<T, group_size, bits, BM, BK, BN>(
      x, w, scales, biases, y, Xs, Ws, M, N, K, tid, lid, simd_gid, simd_lid);
}
 
template <typename T, const int group_size, const int bits>
[[kernel]] void affine_quantize(
    const device T* w [[buffer(0)]],
    device uint8_t* out [[buffer(1)]],
    device T* scales [[buffer(2)]],
    device T* biases [[buffer(3)]],
    uint2 index [[thread_position_in_grid]],
    uint2 grid_dim [[threads_per_grid]]) {
  constexpr T eps = T(1e-7);
  constexpr int simd_size = 32;
  constexpr int uint8_bits = 8;
  constexpr T n_bins = (1 << bits) - 1;
  constexpr int packs_per_int = uint8_bits / bits;
  constexpr int values_per_reduce = group_size / simd_size;
  constexpr int writes_per_reduce = packs_per_int / values_per_reduce;
  constexpr int writes_per_pack =
      writes_per_reduce > 1 ? 1 : values_per_reduce / packs_per_int;
 
  static_assert(
      group_size % simd_size == 0,
      "Group size must be divisible by simd size.");
 
  size_t offset = index.x + grid_dim.x * size_t(index.y);
  size_t in_index = offset * values_per_reduce;
  size_t out_index = offset * writes_per_pack;
 
  T w_thread[values_per_reduce];
  T w_min = Limits<T>::max;
  T w_max = 0;
 
#pragma clang loop unroll(full)
  for (int i = 0; i < values_per_reduce; i++) {
    T val = w[in_index + i];
    w_thread[i] = val;
    w_min = min(w_min, val);
    w_max = max(w_max, val);
  }
 
  w_min = simd_min(w_min);
  w_max = simd_max(w_max);
 
  T scale = max((w_max - w_min) / n_bins, eps);
  bool side = abs(w_min) > abs(w_max);
  scale = side ? scale : -scale;
  T edge = side ? w_min : w_max;
  T q0 = round(edge / scale);
  bool at_zero = q0 == 0.0f;
  scale = at_zero ? scale : edge / q0;
  T bias = at_zero ? T(0) : edge;
 
  // Write out the scales and biases
  size_t gindex = in_index / group_size;
  if (in_index % group_size == 0) {
    scales[gindex] = scale;
    biases[gindex] = bias;
  }
 
  uint8_t output = 0;
#pragma clang loop unroll(full)
  for (int i = 0; i < values_per_reduce; i++) {
    uint8_t val = min(round((w_thread[i] - bias) / scale), n_bins);
    if (bits == 8) {
      output = val;
    } else {
      output += val << (bits * (i % packs_per_int));
    }
 
    if (packs_per_int < values_per_reduce &&
        i % packs_per_int == packs_per_int - 1) {
      out[out_index + i / packs_per_int] = output;
      output = 0;
    } else {
#pragma clang loop unroll(full)
      for (int j = 0; j < writes_per_reduce - 1; j++) {
        uint8_t sval = simd_shuffle_down(val, j + 1);
        output += sval << (bits * (values_per_reduce + j + i));
      }
    }
  }
  if (writes_per_reduce > 0 && out_index % writes_per_reduce == 0) {
    out[out_index / writes_per_reduce] = output;
  }
}
 
template <typename T, const int group_size, const int bits>
[[kernel]] void affine_quantize_scales_biases(
    const device T* w [[buffer(0)]],
    const device T* scales [[buffer(1)]],
    const device T* biases [[buffer(2)]],
    device uint8_t* out [[buffer(3)]],
    uint2 index [[thread_position_in_grid]],
    uint2 grid_dim [[threads_per_grid]]) {
  constexpr int uint8_bits = 8;
  constexpr int packs_per_int = uint8_bits / bits;
  constexpr T n_bins = (1 << bits) - 1;
 
  size_t offset = index.x + grid_dim.x * size_t(index.y);
  size_t in_index = offset * packs_per_int;
  size_t gindex = in_index / group_size;
 
  T scale = scales[gindex];
  T bias = biases[gindex];
 
  uint8_t output = 0;
#pragma clang loop unroll(full)
  for (int i = 0; i < packs_per_int; i++) {
    uint8_t val = min(round((w[in_index + i] - bias) / scale), n_bins);
    if (bits == 8) {
      output = val;
    } else {
      output += val << (bits * i);
    }
  }
  out[offset] = output;
}
 
template <typename T, const int group_size, const int bits>
[[kernel]] void affine_dequantize(
    const device uint8_t* w [[buffer(0)]],
    const device T* scales [[buffer(1)]],
    const device T* biases [[buffer(2)]],
    device T* out [[buffer(3)]],
    uint2 index [[thread_position_in_grid]],
    uint2 grid_dim [[threads_per_grid]]) {
  constexpr int uint8_bits = 8;
  constexpr int packs_per_int = uint8_bits / bits;
 
  size_t offset = index.x + grid_dim.x * size_t(index.y);
  size_t oindex = offset * packs_per_int;
  size_t gindex = oindex / group_size;
  T scale = scales[gindex];
  T bias = biases[gindex];
  uint val = w[offset];
 
#pragma clang loop unroll(full)
  for (int i = 0; i < packs_per_int; i++) {
    uint8_t d;
    if (bits == 2) {
      d = (val >> (bits * i)) & 0x03;
    } else if (bits == 4) {
      d = (val >> (bits * i)) & 0x0f;
    } else if (bits == 8) {
      d = val;
    }
    out[oindex + i] = scale * d + bias;
  }
}