An initial quantized matmul implementation (#205)

* Add quantized matvec
* Add quantized matrix matrix with 2nd matrix transposed
* Add quantized matmul tests
* Add a slow cpu quantized matmul
* Add a slightly faster vectorized cpu version

benchmarks/python/comparative/bench_mlx.py

@@ -23,6 +23,16 @@ def none_or_list(x):
         return [int(xi) for xi in x.split(",")]
 
 
+def dtype_from_str(x):
+    if x == "":
+        return mx.float32
+    else:
+        dt = getattr(mx, x)
+        if not isinstance(dt, mx.Dtype):
+            raise ValueError(f"{x} is not an mlx dtype")
+        return dt
+
+
 def bench(f, *args):
     for i in range(10):
         f(*args)
@@ -49,6 +59,15 @@ def matmul(x, y):
     mx.eval(ys)
 
 
+def quant_matmul(x, w, s, b):
+    groups = x.shape[-1] // s.shape[-1]
+    width = 32 // (x.shape[-1] // w.shape[0])
+    ys = []
+    for i in range(10):
+        ys.append(mx.quantized_matmul(x, w, s, b, groups=groups, width=width))
+    mx.eval(ys)
+
+
 def conv1d(x, y):
     ys = []
     for i in range(10):
@@ -296,9 +315,7 @@ if __name__ == "__main__":
     parser.add_argument(
         "--fused", action="store_true", help="Use fused functions where possible"
     )
-    parser.add_argument(
-        "--dtype", choices=["float32", "float16", "bfloat16"], default="float32"
-    )
+    parser.add_argument("--dtype", type=dtype_from_str, default=[], action="append")
 
     args = parser.parse_args()
 
@@ -315,11 +332,15 @@ if __name__ == "__main__":
         mx.set_default_device(mx.cpu)
     else:
         mx.set_default_device(mx.gpu)
-    dtype = dict(float32=mx.float32, float16=mx.float16, bfloat16=mx.bfloat16)[
-        args.dtype
-    ]
+
+    types = args.dtype
+    if not types:
+        types = [mx.float32]
+    if len(types) < len(args.size):
+        types = types + [types[0]] * (len(args.size) - len(types))
+
     xs = []
-    for size in args.size:
+    for size, dtype in zip(args.size, types):
         xs.append(mx.random.normal(size).astype(dtype))
     for i, t in enumerate(args.transpose):
         if t is None:
@@ -335,6 +356,9 @@ if __name__ == "__main__":
     elif args.benchmark == "matmul":
         print(bench(matmul, *xs))
 
+    elif args.benchmark == "quant_matmul":
+        print(bench(quant_matmul, *xs))
+
     elif args.benchmark == "linear":
         print(bench(linear, *xs))
 

benchmarks/python/comparative/bench_torch.py

@@ -22,6 +22,16 @@ def none_or_list(x):
         return [int(xi) for xi in x.split(",")]
 
 
+def dtype_from_str(x):
+    if x == "":
+        return torch.float32
+    else:
+        dt = getattr(torch, x)
+        if not isinstance(dt, torch.dtype):
+            raise ValueError(f"{x} is not a torch dtype")
+        return dt
+
+
 def bench(f, *args):
     for i in range(10):
         f(*args)
@@ -312,7 +322,7 @@ if __name__ == "__main__":
     parser.add_argument(
         "--fused", action="store_true", help="Use fused functions where possible"
     )
-    parser.add_argument("--dtype", choices=["float32", "float16"], default="float32")
+    parser.add_argument("--dtype", type=dtype_from_str, default=[], action="append")
 
     args = parser.parse_args()
 
@@ -327,9 +337,15 @@ if __name__ == "__main__":
 
     torch.set_num_threads(1)
     device = "cpu" if args.cpu else "mps"
-    dtype = dict(float32=torch.float32, float16=torch.float16)[args.dtype]
+
+    types = args.dtype
+    if not types:
+        types = [torch.float32]
+    if len(types) < len(args.size):
+        types = types + [types[0]] * (len(args.size) - len(types))
+
     xs = []
-    for size in args.size:
+    for size, dtype in zip(args.size, types):
         xs.append(torch.randn(*size).to(device).to(dtype))
     for i, t in enumerate(args.transpose):
         if t is None:

mlx/backend/accelerate/CMakeLists.txt

@@ -4,6 +4,7 @@ target_sources(
   ${CMAKE_CURRENT_SOURCE_DIR}/conv.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/matmul.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/primitives.cpp
+  ${CMAKE_CURRENT_SOURCE_DIR}/quantized.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/reduce.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/softmax.cpp
 )

mlx/backend/accelerate/quantized.cpp

@@ -0,0 +1,107 @@
+// Copyright © 2023 Apple Inc.
+
+#include <cassert>
+
+#include <simd/vector.h>
+
+#include "mlx/primitives.h"
+
+namespace mlx::core {
+
+namespace {
+
+void _qmm_t_4_64(
+    float* result,
+    const float* x,
+    const uint32_t* w,
+    const float* scales,
+    const float* biases,
+    int M,
+    int N,
+    int K) {
+  constexpr int width = 4;
+  constexpr int groups = 64;
+  constexpr int bitmask = (1 << width) - 1;
+  constexpr int pack_factor = 32 / width;
+  constexpr int packs_in_group = groups / pack_factor;
+  const int Kg = K / groups;
+  const int Kw = K / pack_factor;
+
+  for (int m = 0; m < M; m++) {
+    const uint32_t* w_local = w;
+    const float* scales_local = scales;
+    const float* biases_local = biases;
+
+    for (int n = 0; n < N; n++) {
+      const simd_float16* x_local = (simd_float16*)x;
+      simd_float16 sum = 0;
+      for (int k = 0; k < K; k += groups) {
+        float scale = *scales_local++;
+        float bias = *biases_local++;
+
+        for (int kw = 0; kw < packs_in_group; kw += 2) {
+          // TODO: vectorize this properly
+          simd_uint16 wi;
+          for (int e = 0; e < 2; e++) {
+            uint32_t wii = *w_local++;
+            for (int p = 0; p < 8; p++) {
+              wi[e * 8 + p] = wii & bitmask;
+              wii >>= width;
+            }
+          }
+          simd_float16 wf = simd_float(wi);
+          wf *= scale;
+          wf += bias;
+
+          sum += (*x_local) * wf;
+          x_local++;
+        }
+      }
+
+      *result = simd_reduce_add(sum);
+      result++;
+    }
+
+    x += K;
+  }
+}
+
+} // namespace
+
+void QuantizedMatmul::eval_cpu(const std::vector<array>& inputs, array& out) {
+  assert(inputs.size() == 4);
+
+  auto& x = inputs[0];
+  auto& w = inputs[1];
+  auto& scales = inputs[2];
+  auto& biases = inputs[3];
+
+  if (w.strides()[0] != 1) {
+    throw std::runtime_error("The quantized weight should be transposed");
+  }
+
+  if (!x.flags().row_contiguous || !scales.flags().row_contiguous ||
+      !biases.flags().row_contiguous) {
+    throw std::runtime_error("x, scales and biases should be row contiguous.");
+  }
+
+  if (x.dtype() == float32 && width_ == 4 && groups_ == 64) {
+    out.set_data(allocator::malloc_or_wait(out.nbytes()));
+    int K = x.shape(-1);
+    int M = x.size() / K;
+    int N = w.shape(1);
+    _qmm_t_4_64(
+        out.data<float>(),
+        x.data<float>(),
+        w.data<uint32_t>(),
+        scales.data<float>(),
+        biases.data<float>(),
+        M,
+        N,
+        K);
+  } else {
+    eval(inputs, out);
+  }
+}
+
+} // namespace mlx::core

mlx/backend/common/CMakeLists.txt

@@ -8,6 +8,7 @@ target_sources(
   ${CMAKE_CURRENT_SOURCE_DIR}/erf.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/fft.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/primitives.cpp
+  ${CMAKE_CURRENT_SOURCE_DIR}/quantized.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/reduce.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/scan.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/softmax.cpp

mlx/backend/common/default_primitives.cpp

@@ -62,6 +62,7 @@ DEFAULT(NotEqual)
 DEFAULT(Pad)
 DEFAULT(Partition)
 DEFAULT(Power)
+DEFAULT(QuantizedMatmul)
 DEFAULT(RandomBits)
 DEFAULT(Reduce)
 DEFAULT(Reshape)

mlx/backend/common/quantized.cpp

@@ -0,0 +1,183 @@
+// Copyright © 2023 Apple Inc.
+
+#include <cassert>
+
+#include "mlx/primitives.h"
+
+namespace mlx::core {
+
+namespace {
+
+template <typename T, int width, int groups>
+void _qmm_t(
+    T* result,
+    const T* x,
+    const uint32_t* w,
+    const T* scales,
+    const T* biases,
+    int M,
+    int N,
+    int K) {
+  constexpr int bitmask = (1 << width) - 1;
+  constexpr int pack_factor = 32 / width;
+  constexpr int packs_in_group = groups / pack_factor;
+  const int Kg = K / groups;
+  const int Kw = K / pack_factor;
+
+  for (int m = 0; m < M; m++) {
+    const uint32_t* w_local = w;
+    const T* scales_local = scales;
+    const T* biases_local = biases;
+
+    for (int n = 0; n < N; n++) {
+      const T* x_local = x;
+      T sum = 0;
+      for (int k = 0; k < K; k += groups) {
+        T scale = *scales_local++;
+        T bias = *biases_local++;
+
+        for (int kw = 0; kw < packs_in_group; kw++) {
+          uint32_t wi = *w_local++;
+
+#pragma clang loop unroll(full)
+          for (int p = 0; p < pack_factor; p++) {
+            sum += (*x_local++) * (scale * static_cast<T>(wi & bitmask) + bias);
+            wi >>= width;
+          }
+        }
+      }
+      *result = sum;
+      result++;
+    }
+
+    x += K;
+  }
+}
+
+template <typename T>
+void _qmm_t_dispatch_typed(
+    T* result,
+    const T* x,
+    const uint32_t* w,
+    const T* scales,
+    const T* biases,
+    int M,
+    int N,
+    int K,
+    int width,
+    int groups) {
+  switch (width) {
+    case 2: {
+      switch (groups) {
+        case 64:
+          return _qmm_t<T, 2, 64>(result, x, w, scales, biases, M, N, K);
+        case 128:
+          return _qmm_t<T, 2, 128>(result, x, w, scales, biases, M, N, K);
+      }
+    }
+    case 4: {
+      switch (groups) {
+        case 64:
+          return _qmm_t<T, 4, 64>(result, x, w, scales, biases, M, N, K);
+        case 128:
+          return _qmm_t<T, 4, 128>(result, x, w, scales, biases, M, N, K);
+      }
+    }
+    case 8: {
+      switch (groups) {
+        case 64:
+          return _qmm_t<T, 8, 64>(result, x, w, scales, biases, M, N, K);
+        case 128:
+          return _qmm_t<T, 8, 128>(result, x, w, scales, biases, M, N, K);
+      }
+    }
+  }
+  std::ostringstream msg;
+  msg << "Quantization type not supported. Provided bit width=" << width
+      << " and groups=" << groups << ". The supported options are width in "
+      << "{2, 4, 8} and groups in {64, 128}.";
+  throw std::invalid_argument(msg.str());
+}
+
+void _qmm_t_dispatch(
+    array out,
+    const array& x,
+    const array& w,
+    const array& scales,
+    const array& biases,
+    int width,
+    int groups) {
+  int K = x.shape(-1);
+  int M = x.size() / K;
+  int N = w.shape(1);
+
+  switch (x.dtype()) {
+    case float32:
+      _qmm_t_dispatch_typed<float>(
+          out.data<float>(),
+          x.data<float>(),
+          w.data<uint32_t>(),
+          scales.data<float>(),
+          biases.data<float>(),
+          M,
+          N,
+          K,
+          width,
+          groups);
+      break;
+    case float16:
+      _qmm_t_dispatch_typed<float16_t>(
+          out.data<float16_t>(),
+          x.data<float16_t>(),
+          w.data<uint32_t>(),
+          scales.data<float16_t>(),
+          biases.data<float16_t>(),
+          M,
+          N,
+          K,
+          width,
+          groups);
+      break;
+    case bfloat16:
+      _qmm_t_dispatch_typed<bfloat16_t>(
+          out.data<bfloat16_t>(),
+          x.data<bfloat16_t>(),
+          w.data<uint32_t>(),
+          scales.data<bfloat16_t>(),
+          biases.data<bfloat16_t>(),
+          M,
+          N,
+          K,
+          width,
+          groups);
+      break;
+    default:
+      throw std::invalid_argument(
+          "[quantized_matmul] only floating types are supported");
+  }
+}
+
+} // namespace
+
+void QuantizedMatmul::eval(const std::vector<array>& inputs, array& out) {
+  assert(inputs.size() == 4);
+
+  auto& x = inputs[0];
+  auto& w = inputs[1];
+  auto& scales = inputs[2];
+  auto& biases = inputs[3];
+
+  if (w.strides()[0] != 1) {
+    throw std::runtime_error("The quantized weight should be transposed");
+  }
+
+  if (!x.flags().row_contiguous || !scales.flags().row_contiguous ||
+      !biases.flags().row_contiguous) {
+    throw std::runtime_error("x, scales and biases should be row contiguous.");
+  }
+
+  out.set_data(allocator::malloc_or_wait(out.nbytes()));
+  _qmm_t_dispatch(out, x, w, scales, biases, width_, groups_);
+}
+
+} // namespace mlx::core

mlx/backend/metal/CMakeLists.txt

@@ -10,6 +10,7 @@ target_sources(
   ${CMAKE_CURRENT_SOURCE_DIR}/matmul.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/metal.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/primitives.cpp
+  ${CMAKE_CURRENT_SOURCE_DIR}/quantized.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/scan.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/softmax.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/sort.cpp

mlx/backend/metal/kernels/CMakeLists.txt

@@ -18,6 +18,7 @@ set(
   "copy"
   "gemm"
   "gemv"
+  "quantized"
   "random"
   "reduce"
   "scan"

mlx/backend/metal/kernels/quantized.metal

@@ -0,0 +1,287 @@
+// Copyright © 2023 Apple Inc.
+
+#include <metal_stdlib>
+#include <metal_simdgroup>
+
+#include "mlx/backend/metal/kernels/bf16.h"
+#include "mlx/backend/metal/kernels/defines.h"
+#include "mlx/backend/metal/kernels/gemm/gemm.h"
+#include "mlx/backend/metal/kernels/utils.h"
+
+using namespace metal;
+
+#define MLX_MTL_CONST static constant constexpr const
+
+MLX_MTL_CONST int SIMD_SIZE = 32;
+
+template <typename T, const int BM, const int BN, const int groups, const int width>
+[[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 lid [[thread_index_in_threadgroup]],
+    uint simd_gid [[simdgroup_index_in_threadgroup]],
+    uint simd_lid [[thread_index_in_simdgroup]]) {
+
+  static_assert(BN == SIMD_SIZE, "qmv expects BN to be equal to SIMD_SIZE");
+
+  constexpr int bitmask = (1 << width) - 1;
+  constexpr int el_per_thread = 32 / width;
+  constexpr int colgroup = BN * el_per_thread;
+  constexpr int groups_per_block = colgroup / groups;
+  constexpr int simdgroups_fetching_vec = colgroup / SIMD_SIZE;
+
+  threadgroup T scales_block[BM * groups_per_block];
+  threadgroup T biases_block[BM * groups_per_block];
+  threadgroup T x_block[colgroup];
+
+  thread uint32_t w_local;
+  thread T result = 0;
+  thread T scale = 1;
+  thread T bias = 0;
+  thread T x_thread[el_per_thread];
+
+  // Adjust positions
+  const int in_vec_size_w = in_vec_size / el_per_thread;
+  const int in_vec_size_g = in_vec_size / groups;
+  int out_row = tid.y * BM + simd_gid;
+  w += out_row * in_vec_size_w;
+  scales += out_row * in_vec_size_g;
+  biases += out_row * in_vec_size_g;
+  x += tid.z * in_vec_size;
+  y += tid.z * out_vec_size;
+
+  // Loop over in_vec in blocks of colgroup
+  for (int i=0; i<in_vec_size; i+=colgroup) {
+    // Load the vec to shared memory
+    threadgroup_barrier(mem_flags::mem_threadgroup);
+    if (simd_gid < simdgroups_fetching_vec) {
+      x_block[lid] = x[lid + i];
+    }
+    if (simd_lid == 0) {
+      #pragma clang loop unroll(full)
+      for (int j=0; j<groups_per_block; j++) {
+        scales_block[simd_gid * groups_per_block + j] = scales[i / groups + j];
+      }
+      #pragma clang loop unroll(full)
+      for (int j=0; j<groups_per_block; j++) {
+        biases_block[simd_gid * groups_per_block + j] = biases[i / groups + j];
+      }
+    }
+    threadgroup_barrier(mem_flags::mem_threadgroup);
+
+    // Load in_vec, scale, bias to registers
+    #pragma clang loop unroll(full)
+    for (int j=0; j<el_per_thread; j++) {
+      x_thread[j] = x_block[simd_lid*el_per_thread + j];
+    }
+    scale = scales_block[simd_gid * groups_per_block + simd_lid * el_per_thread / groups];
+    bias = biases_block[simd_gid * groups_per_block + simd_lid * el_per_thread / groups];
+
+    // Load the matrix elements
+    w_local = w[i / el_per_thread + simd_lid];
+
+    // Do all the work.
+    #pragma clang loop unroll(full)
+    for (int k=0; k<el_per_thread; k++) {
+      result += (scale * static_cast<T>(w_local & bitmask) + bias) * x_thread[k];
+      w_local >>= width;
+    }
+  }
+
+  // Accumulate in the simdgroup
+  result = simd_sum(result);
+
+  // Store the result
+  if (simd_lid == 0) {
+    y[out_row] = result;
+  }
+}
+
+
+template <typename T, const int BM, const int BK, const int BN, const int groups, const int width>
+[[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]]) {
+
+  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");
+
+  const uint lidy = lid / SIMD_SIZE;
+
+  constexpr int WM = 2;
+  constexpr int WN = 2;
+  constexpr int bitmask = (1 << width) - 1;
+  constexpr int el_per_int = 32 / width;
+  constexpr int ints_per_block = BK / el_per_int;
+  constexpr int groups_per_block = (BK / groups > 0) ? (BK / groups) : 1;
+  constexpr int groups_per_simd = BN / (WM * WN);
+  constexpr int w_els_per_thread = (BN * BK / el_per_int) / (SIMD_SIZE * WM * WN);
+
+  // Using the kernel just as a type to instantiate the appropriate BlockMMA
+  // and constexpr size calculations
+  using mma_t = BlockMMA<T, BM, BN, BK, WM, WN, false, true>;
+  using loader_x_t = BlockLoader<T, BM, BK, BK, 4, WM * WN * SIMD_SIZE, false, true, 0>;
+
+  threadgroup T scales_block[BN * groups_per_block];
+  threadgroup T biases_block[BN * groups_per_block];
+  threadgroup T Xs[BM * BK];
+  threadgroup T Ws[BN * BK];
+
+  // Set the block
+  const int K_w = K / el_per_int;
+  const int K_g = K / groups;
+  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);
+  loader_x_t loader_x(x, K, Xs, simd_gid, simd_lid);
+  mma_t mma_op(simd_gid, simd_lid);
+
+  for (int k=0; k<K; k += BK) {
+    threadgroup_barrier(mem_flags::mem_threadgroup);
+    // Load the x tile
+    if (num_els < BM) {
+        loader_x.load_safe(short2(BK, num_els));
+    } else {
+        loader_x.load_unsafe();
+    }
+
+    // Load the scale and bias
+    if (simd_lid == 0) {
+      threadgroup T *scales_block_local = scales_block + lidy * groups_per_block * groups_per_simd;
+      threadgroup T *biases_block_local = biases_block + lidy * groups_per_block * groups_per_simd;
+      const device T *scales_local = scales + lidy * groups_per_simd * K_g + k / groups;
+      const device T *biases_local = biases + lidy * groups_per_simd * K_g + k / groups;
+      #pragma clang loop unroll(full)
+      for (int gs=0; gs<groups_per_simd; gs++) {
+        #pragma clang loop unroll(full)
+        for (int gc=0; gc<groups_per_block; gc++) {
+          scales_block_local[gc] = scales_local[gc];
+          biases_block_local[gc] = biases_local[gc];
+        }
+        scales_block_local += groups_per_block;
+        scales_local += K_g;
+        biases_block_local += groups_per_block;
+        biases_local += K_g;
+      }
+    }
+    threadgroup_barrier(mem_flags::mem_threadgroup);
+
+    // Load the w tile
+    {
+      for (int wo=0; wo<w_els_per_thread; wo++) {
+        int offset = lid * w_els_per_thread + wo;
+        int offset_row = offset / (BK / el_per_int);
+        int offset_col = offset % (BK / el_per_int);
+        const device uint32_t * w_local = w + offset_row * K_w + offset_col;
+        threadgroup T * Ws_local = Ws + offset_row * BK + offset_col * el_per_int;
+
+        uint32_t wi = *w_local;
+        T scale = scales_block[offset_row * groups_per_block + offset_col / (groups / el_per_int)];
+        T bias = biases_block[offset_row * groups_per_block + offset_col / (groups / el_per_int)];
+
+        #pragma clang loop unroll(full)
+        for (int t=0; t<el_per_int; t++) {
+          Ws_local[t] = scale * static_cast<T>(wi & bitmask) + bias;
+          wi >>= width;
+        }
+      }
+    }
+    threadgroup_barrier(mem_flags::mem_threadgroup);
+
+    // Multiply and accumulate threadgroup elements
+    mma_op.mma(Xs, Ws);
+
+    // Prepare for next iteration
+    loader_x.next();
+    w += ints_per_block;
+    // scales and biases cannot be advanced because they would have to be
+    // advanced every other iteration or sth.
+  }
+
+  // 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);
+  }
+}
+
+
+#define instantiate_qmv(name, itype, groups, width) \
+  template [[host_name("qmv_n_" #name "_groups_" #groups "_width_" #width)]] \
+  [[kernel]] void qmv<itype, 32, 32, groups, width>( \
+    const device uint32_t* w [[buffer(0)]], \
+    const device itype* scales [[buffer(1)]], \
+    const device itype* biases [[buffer(2)]], \
+    const device itype* x [[buffer(3)]], \
+    device itype* 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 lid [[thread_index_in_threadgroup]], \
+    uint simd_gid [[simdgroup_index_in_threadgroup]], \
+    uint simd_lid [[thread_index_in_simdgroup]]);
+
+#define instantiate_qmv_types(groups, width) \
+  instantiate_qmv(float32, float, groups, width) \
+  instantiate_qmv(float16, half, groups, width) \
+  instantiate_qmv(bfloat16, bfloat16_t, groups, width)
+
+instantiate_qmv_types(128, 2)
+instantiate_qmv_types(128, 4)
+instantiate_qmv_types(128, 8)
+instantiate_qmv_types( 64, 2)
+instantiate_qmv_types( 64, 4)
+instantiate_qmv_types( 64, 8)
+
+#define instantiate_qmm_t(name, itype, groups, width) \
+  template [[host_name("qmm_t_" #name "_groups_" #groups "_width_" #width)]] \
+  [[kernel]] void qmm_t<itype, 32, 64, 32, groups, width>( \
+      const device itype* x [[buffer(0)]], \
+      const device uint32_t* w [[buffer(1)]], \
+      const device itype* scales [[buffer(2)]], \
+      const device itype* biases [[buffer(3)]], \
+      device itype* 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]]);
+
+#define instantiate_qmm_t_types(groups, width) \
+  instantiate_qmm_t(float32, float, groups, width) \
+  instantiate_qmm_t(float16, half, groups, width) \
+  instantiate_qmm_t(bfloat16, bfloat16_t, groups, width)
+
+instantiate_qmm_t_types(128, 2)
+instantiate_qmm_t_types(128, 4)
+instantiate_qmm_t_types(128, 8)
+instantiate_qmm_t_types( 64, 2)
+instantiate_qmm_t_types( 64, 4)
+instantiate_qmm_t_types( 64, 8)

mlx/backend/metal/quantized.cpp

@@ -0,0 +1,123 @@
+// Copyright © 2023 Apple Inc.
+
+#include <cassert>
+#include <iostream>
+
+#include "mlx/backend/metal/copy.h"
+#include "mlx/backend/metal/device.h"
+#include "mlx/backend/metal/utils.h"
+#include "mlx/primitives.h"
+
+namespace mlx::core {
+
+void QuantizedMatmul::eval_gpu(const std::vector<array>& inputs, array& out) {
+  assert(inputs.size() == 4);
+
+  out.set_data(allocator::malloc_or_wait(out.nbytes()));
+  auto& s = stream();
+  auto& d = metal::device(s.device);
+
+  auto& x_pre = inputs[0];
+  auto& w_pre = inputs[1];
+  auto& scales_pre = inputs[2];
+  auto& biases_pre = inputs[3];
+
+  std::vector<array> copies;
+  auto check_transpose = [&copies, &s](const array& arr) {
+    auto stx = arr.strides()[arr.ndim() - 2];
+    auto sty = arr.strides()[arr.ndim() - 1];
+    if (stx == arr.shape(-1) && sty == 1) {
+      return std::make_tuple(false, stx, arr);
+    } else if (stx == 1 && sty == arr.shape(-2)) {
+      return std::make_tuple(true, sty, arr);
+    } else {
+      array arr_copy(arr.shape(), arr.dtype(), nullptr, {});
+      copy_gpu(arr, arr_copy, CopyType::General, s);
+      copies.push_back(arr_copy);
+      size_t stx = arr.shape(-1);
+      return std::make_tuple(false, stx, arr_copy);
+    }
+  };
+  auto [x_transposed, x_cols, x] = check_transpose(x_pre);
+  auto [w_transposed, w_cols, w] = check_transpose(w_pre);
+  auto [scales_transposed, scales_cols, scales] = check_transpose(scales_pre);
+  auto [biases_transposed, biases_cols, biases] = check_transpose(biases_pre);
+
+  if (!w_transposed) {
+    throw std::runtime_error("The quantized weight should be transposed.");
+  }
+
+  if (x_transposed || scales_transposed || biases_transposed) {
+    throw std::runtime_error("x, scales and biases should be row contiguous.");
+  }
+
+  int D = x.shape(-1);
+  int B = x.size() / D;
+
+  // Route to the qmv kernel
+  if (B == 1) {
+    std::ostringstream kname;
+    kname << "qmv_" << (w_transposed ? "n_" : "t_") << type_to_name(out)
+          << "_groups_" << groups_ << "_width_" << width_;
+
+    // Encode and dispatch kernel
+    auto compute_encoder = d.get_command_encoder(s.index);
+    auto kernel = d.get_kernel(kname.str());
+    compute_encoder->setComputePipelineState(kernel);
+
+    int O = w.size() / w_cols;
+
+    int bo = 32;
+    int bd = 32;
+    MTL::Size group_dims = MTL::Size(bd, bo, 1);
+    MTL::Size grid_dims = MTL::Size(1, O / bo, B);
+
+    set_array_buffer(compute_encoder, w, 0);
+    set_array_buffer(compute_encoder, scales, 1);
+    set_array_buffer(compute_encoder, biases, 2);
+    set_array_buffer(compute_encoder, x, 3);
+    set_array_buffer(compute_encoder, out, 4);
+    compute_encoder->setBytes(&D, sizeof(int), 5);
+    compute_encoder->setBytes(&O, sizeof(int), 6);
+
+    compute_encoder->dispatchThreadgroups(grid_dims, group_dims);
+  }
+
+  // Route to the qmm kernel
+  else {
+    std::ostringstream kname;
+    kname << "qmm_" << (w_transposed ? "t_" : "n_") << type_to_name(out)
+          << "_groups_" << groups_ << "_width_" << width_;
+
+    // Encode and dispatch kernel
+    auto compute_encoder = d.get_command_encoder(s.index);
+    auto kernel = d.get_kernel(kname.str());
+    compute_encoder->setComputePipelineState(kernel);
+
+    int O = w.size() / w_cols;
+
+    int wn = 2;
+    int wm = 2;
+    int bm = 32;
+    int bn = 32;
+    int bk = 64;
+    MTL::Size group_dims = MTL::Size(32, wn, wm);
+    MTL::Size grid_dims = MTL::Size(O / bn, (B + bm - 1) / bm, 1);
+
+    set_array_buffer(compute_encoder, x, 0);
+    set_array_buffer(compute_encoder, w, 1);
+    set_array_buffer(compute_encoder, scales, 2);
+    set_array_buffer(compute_encoder, biases, 3);
+    set_array_buffer(compute_encoder, out, 4);
+    compute_encoder->setBytes(&B, sizeof(int), 5);
+    compute_encoder->setBytes(&O, sizeof(int), 6);
+    compute_encoder->setBytes(&D, sizeof(int), 7);
+
+    compute_encoder->dispatchThreadgroups(grid_dims, group_dims);
+  }
+
+  d.get_command_buffer(s.index)->addCompletedHandler(
+      [copies](MTL::CommandBuffer*) mutable { copies.clear(); });
+}
+
+} // namespace mlx::core

mlx/backend/no_metal/primitives.cpp

@@ -58,6 +58,7 @@ NO_GPU(NotEqual)
 NO_GPU(Pad)
 NO_GPU(Partition)
 NO_GPU(Power)
+NO_GPU(QuantizedMatmul)
 NO_GPU(RandomBits)
 NO_GPU(Reduce)
 NO_GPU(Reshape)

mlx/ops.cpp

@@ -2564,4 +2564,75 @@ array conv2d(
       {in, wt});
 }
 
+array quantized_matmul(
+    const array& in_x,
+    const array& w,
+    const array& scales,
+    const array& biases,
+    int groups /* = 128 */,
+    int width /* = 4 */,
+    StreamOrDevice s /* = {} */) {
+  auto x = in_x;
+
+  if (w.dtype() != uint32) {
+    std::ostringstream msg;
+    msg << "[quantized_matmul] The weight matrix should be uint32 "
+        << "but received" << w.dtype();
+    throw std::invalid_argument(msg.str());
+  }
+  if (w.ndim() != 2) {
+    std::ostringstream msg;
+    msg << "[quantized_matmul] Batched quantized matmul is not supported for now "
+        << "received w with shape " << w.shape();
+    throw std::invalid_argument(msg.str());
+  }
+
+  // Keep x's batch dimensions to reshape it back after the matmul
+  auto original_shape = x.shape();
+  int x_inner_dims = original_shape.back();
+  original_shape.pop_back();
+
+  // Reshape x into a matrix if it isn't already one
+  if (x.ndim() != 2) {
+    x = reshape(x, {-1, x_inner_dims}, s);
+  }
+
+  int w_inner_dims = w.shape(0) * (32 / width);
+  if (w_inner_dims != x_inner_dims) {
+    std::ostringstream msg;
+    msg << "[quantized_matmul] Last dimension of first input with "
+        << "shape (..., " << x_inner_dims
+        << ") does not match the expanded first "
+        << "dimension of the quantized matrix " << w_inner_dims
+        << ", computed from shape " << w.shape() << " with groups=" << groups
+        << " and width=" << width;
+    throw std::invalid_argument(msg.str());
+  }
+
+  int n_groups = x_inner_dims / groups;
+  if (scales.shape(-1) != n_groups || biases.shape(-1) != n_groups) {
+    std::ostringstream msg;
+    msg << "[quantized_matmul] Scales and biases provided do not match the "
+        << "quantization arguments (groups=" << groups << ", width=" << width
+        << "). Expected shapes (" << w.shape(1) << ", " << x_inner_dims / groups
+        << "), but got scales.shape=" << scales.shape()
+        << " and biases.shape=" << biases.shape();
+    throw std::invalid_argument(msg.str());
+  }
+
+  auto out = array(
+      {x.shape(0), w.shape(1)},
+      x.dtype(),
+      std::make_unique<QuantizedMatmul>(to_stream(s), groups, width),
+      {x, w, scales, biases});
+
+  // If needed reshape x to the original batch shape
+  if (original_shape.size() != 1) {
+    original_shape.push_back(w.shape(1));
+    out = reshape(out, original_shape, s);
+  }
+
+  return out;
+}
+
 } // namespace mlx::core

mlx/ops.h

@@ -1028,4 +1028,14 @@ array load(std::shared_ptr<io::Reader> in_stream, StreamOrDevice s = {});
 /** Load array from file in .npy format */
 array load(const std::string& file, StreamOrDevice s = {});
 
+/** Quantized matmul multiplies x with a quantized matrix w*/
+array quantized_matmul(
+    const array& x,
+    const array& w,
+    const array& scales,
+    const array& biases,
+    int groups = 128,
+    int width = 4,
+    StreamOrDevice s = {});
+
 } // namespace mlx::core

mlx/primitives.cpp

@@ -1696,6 +1696,31 @@ std::pair<array, int> Power::vmap(
   return {power(a, b, stream()), to_ax};
 }
 
+std::pair<array, int> QuantizedMatmul::vmap(
+    const std::vector<array>& inputs,
+    const std::vector<int>& axes) {
+  throw std::runtime_error("QuantizedMatmul::vmap NYI");
+}
+
+std::vector<array> QuantizedMatmul::vjp(
+    const std::vector<array>& primals,
+    const array& cotan,
+    const std::vector<int>& argnums) {
+  throw std::runtime_error("QuantizedMatmul::vjp NYI");
+}
+
+array QuantizedMatmul::jvp(
+    const std::vector<array>& primals,
+    const std::vector<array>& tangents,
+    const std::vector<int>& argnums) {
+  throw std::runtime_error("QuantizedMatmul::vjp NYI");
+}
+
+bool QuantizedMatmul::is_equivalent(const Primitive& other) const {
+  const QuantizedMatmul& qm_other = static_cast<const QuantizedMatmul&>(other);
+  return groups_ == qm_other.groups_ && width_ == qm_other.width_;
+}
+
 std::pair<array, int> RandomBits::vmap(
     const std::vector<array>& inputs,
     const std::vector<int>& axes) {

mlx/primitives.h

@@ -1110,6 +1110,29 @@ class Power : public Primitive {
   void eval(const std::vector<array>& inputs, array& out);
 };
 
+class QuantizedMatmul : public Primitive {
+ public:
+  explicit QuantizedMatmul(Stream stream, int groups, int width)
+      : Primitive(stream), groups_(groups), width_(width){};
+
+  void eval_cpu(const std::vector<array>& inputs, array& out) override;
+  void eval_gpu(const std::vector<array>& inputs, array& out) override;
+
+  std::pair<array, int> vmap(
+      const std::vector<array>& inputs,
+      const std::vector<int>& axes) override;
+
+  DEFINE_GRADS()
+  DEFINE_PRINT(QuantizedMatmul)
+  bool is_equivalent(const Primitive& other) const override;
+
+ private:
+  int groups_;
+  int width_;
+
+  void eval(const std::vector<array>& inputs, array& out);
+};
+
 class RandomBits : public Primitive {
  public:
   explicit RandomBits(Stream stream, const std::vector<int>& shape, int width)

python/src/ops.cpp

@@ -2977,4 +2977,36 @@ void init_ops(py::module_& m) {
         Returns:
           result (array): An array of the same type as ``a`` rounded to the given number of decimals.
       )pbdoc");
+  m.def(
+      "quantized_matmul",
+      &quantized_matmul,
+      "x"_a,
+      "w"_a,
+      py::pos_only(),
+      "scales"_a,
+      "biases"_a,
+      "groups"_a = 128,
+      "width"_a = 4,
+      py::kw_only(),
+      "stream"_a = none,
+      R"pbdoc(
+        quantized_matmul(x: array, w: array, scales: array, biases: array, /, groups: int = 128, width: int = 4, *, stream: Union[None, Stream, Device] = None) -> array
+
+        Perform the matrix multiplication with the quantized matrix ``w``. The
+        quantization uses one floating point scale and bias per ``groups`` of
+        elements. Each element in ``w`` takes ``width`` bits and is packed in an
+        unsigned 32 bit integer.
+
+        Args:
+          x (array): Input array
+          w (array): Quantized matrix packed in unsigned integers
+          scales (array): The scales to use per ``groups`` elements of ``w``
+          biases (array): The biases to use per ``groups`` elements of ``w``
+          groups (int): The size of the group in ``w`` that shares a scale and
+                        bias. (default: 128)
+          width (int): The bitwidth of the elements in ``w``. (default: 4)
+
+        Returns:
+          result (array): The result of the multiplication of ``x`` with ``w``.
+      )pbdoc");
 }

python/tests/test_quantized.py

@@ -0,0 +1,112 @@
+# Copyright © 2023 Apple Inc.
+
+import unittest
+
+import mlx.core as mx
+import mlx_tests
+
+
+def select_bits(w, width, start):
+    shift_left = 32 - (start + width)
+    shift_right = shift_left + start
+    return (w * (2**shift_left)) // (2**shift_right)
+
+
+def dequantize(w, scales, biases, width):
+    w_full = mx.concatenate(
+        [select_bits(w, width, i)[..., None] for i in range(0, 32, width)], axis=-1
+    )
+    w_full = w_full.reshape(len(w), scales.shape[-1], -1)
+    w_full = scales[..., None] * w_full + biases[..., None]
+    w_full = w_full.reshape(len(w), -1)
+
+    return w_full
+
+
+def quantize(w, width, groups):
+    w = w.reshape(len(w), -1, groups)
+    w_max = w.max(-1, keepdims=True)
+    w_min = w.min(-1, keepdims=True)
+    delta = (w_max - w_min) / (2**width - 1)
+
+    w_int = mx.round((w - w_min) / delta).astype(mx.uint32)
+    scales = delta.squeeze(-1)
+    biases = w_min.squeeze(-1)
+
+    shifts = mx.array([2**i for i in range(0, 32, width)], dtype=mx.uint32)
+    w_int = w_int.reshape(len(w), -1, 32 // width)
+    w_int = w_int * shifts[None, None]
+    packed_w = w_int.sum(-1)
+
+    return packed_w, scales, biases
+
+
+class TestQuantized(mlx_tests.MLXTestCase):
+    def test_quantize_dequantize(self):
+        w = mx.random.normal(shape=(128, 128))
+        w_q, scales, biases = quantize(w, 4, 64)
+        w_hat = dequantize(w_q, scales, biases, 4)
+        w_hat2 = dequantize(*quantize(w_hat, 4, 64), 4)
+        self.assertLess((w_hat - w_hat2).abs().max(), 1e-6)
+
+    def test_qmm(self):
+        key = mx.random.key(0)
+        k1, k2 = mx.random.split(key)
+        for groups in [128, 64]:
+            for width in [2, 4, 8]:
+                for M in [8, 32, 33, 64]:
+                    for N in [512, 1024]:
+                        for K in [512, 1024]:
+                            with self.subTest(
+                                shape=(M, N, K), groups=groups, width=width
+                            ):
+                                x = mx.random.normal(shape=(M, K), key=k1)
+                                w = mx.random.normal(shape=(N, K), key=k2)
+                                w_q, scales, biases = quantize(w, width, groups)
+                                w_hat = dequantize(w_q, scales, biases, width)
+                                y_q = mx.quantized_matmul(
+                                    x, w_q.T, scales, biases, width=width, groups=groups
+                                )
+                                y_hat = x @ w_hat.T
+                                self.assertEqual(y_q.shape, y_hat.shape)
+                                self.assertLess((y_q - y_hat).abs().max(), 0.1)
+
+    def test_qmm_shapes(self):
+        key = mx.random.key(0)
+        k1, k2 = mx.random.split(key)
+        groups = 64
+        width = 4
+        w = mx.random.normal(shape=(32, 128), key=k2)
+        w_q, scales, biases = quantize(w, width, groups)
+        w_hat = dequantize(w_q, scales, biases, width)
+        for s in [(3, 128), (2, 1, 7, 128)]:
+            x = mx.random.normal(shape=(3, 128), key=k1)
+            y_q = mx.quantized_matmul(
+                x, w_q.T, scales, biases, width=width, groups=groups
+            )
+            y_hat = x @ w_hat.T
+            self.assertEqual(y_q.shape, y_hat.shape)
+            self.assertLess((y_q - y_hat).abs().max(), 0.1)
+
+    def test_qmv(self):
+        key = mx.random.key(0)
+        k1, k2 = mx.random.split(key)
+        for groups in [128, 64]:
+            for width in [2, 4, 8]:
+                for M in [512, 1024]:
+                    for N in [512, 1024]:
+                        # with self.subTest(shape=(M, N), groups=groups, width=width):
+                        x = mx.random.normal(shape=(1, N), key=k1)
+                        w = mx.random.normal(shape=(M, N), key=k2)
+                        w_q, scales, biases = quantize(w, width, groups)
+                        w_hat = dequantize(w_q, scales, biases, width)
+                        y_q = mx.quantized_matmul(
+                            x, w_q.T, scales, biases, width=width, groups=groups
+                        )
+                        y_hat = x @ w_hat.T
+                        self.assertEqual(y_q.shape, y_hat.shape)
+                        self.assertLess((y_q - y_hat).abs().max(), 0.1)
+
+
+if __name__ == "__main__":
+    unittest.main()