add a half simd gemm fallback (#2046)

* add a half simd gemm fallback

* nit

mlx/backend/cpu/CMakeLists.txt

@@ -74,8 +74,8 @@ target_sources(
 if(MLX_BUILD_ACCELERATE)
   target_sources(mlx PRIVATE ${CMAKE_CURRENT_SOURCE_DIR}/gemms/bnns.cpp)
 else()
-  target_sources(mlx PRIVATE ${CMAKE_CURRENT_SOURCE_DIR}/gemms/no_fp16.cpp
+  target_sources(mlx PRIVATE ${CMAKE_CURRENT_SOURCE_DIR}/gemms/simd_fp16.cpp
-                             ${CMAKE_CURRENT_SOURCE_DIR}/gemms/no_bf16.cpp)
+                             ${CMAKE_CURRENT_SOURCE_DIR}/gemms/simd_bf16.cpp)
 endif()
 
 if(IOS)

mlx/backend/cpu/gemms/no_bf16.cpp

@@ -1,27 +0,0 @@
-// Copyright © 2025 Apple Inc.
-
-#include "mlx/backend/cpu/gemm.h"
-
-namespace mlx::core {
-
-template <>
-void matmul<bfloat16_t>(
-    const bfloat16_t*,
-    const bfloat16_t*,
-    bfloat16_t*,
-    bool,
-    bool,
-    size_t,
-    size_t,
-    size_t,
-    float,
-    float,
-    size_t,
-    const Shape&,
-    const Strides&,
-    const Shape&,
-    const Strides&) {
-  throw std::runtime_error("[Matmul::eval_cpu] bfloat16 not supported.");
-}
-
-} // namespace mlx::core

mlx/backend/cpu/gemms/no_fp16.cpp

@@ -1,27 +0,0 @@
-// Copyright © 2025 Apple Inc.
-
-#include "mlx/backend/cpu/gemm.h"
-
-namespace mlx::core {
-
-template <>
-void matmul<float16_t>(
-    const float16_t*,
-    const float16_t*,
-    float16_t*,
-    bool,
-    bool,
-    size_t,
-    size_t,
-    size_t,
-    float,
-    float,
-    size_t,
-    const Shape&,
-    const Strides&,
-    const Shape&,
-    const Strides&) {
-  throw std::runtime_error("[Matmul::eval_cpu] float16 not supported.");
-}
-
-} // namespace mlx::core

mlx/backend/cpu/gemms/simd_bf16.cpp

@@ -0,0 +1,45 @@
+// Copyright © 2025 Apple Inc.
+
+#include "mlx/backend/common/utils.h"
+#include "mlx/backend/cpu/gemm.h"
+#include "mlx/backend/cpu/gemms/simd_gemm.h"
+
+namespace mlx::core {
+
+template <>
+void matmul<bfloat16_t>(
+    const bfloat16_t* a,
+    const bfloat16_t* b,
+    bfloat16_t* out,
+    bool a_transposed,
+    bool b_transposed,
+    size_t lda,
+    size_t ldb,
+    size_t ldc,
+    float alpha,
+    float beta,
+    size_t batch_size,
+    const Shape& a_shape,
+    const Strides& a_strides,
+    const Shape& b_shape,
+    const Strides& b_strides) {
+  auto ndim = a_shape.size();
+  size_t M = a_shape[ndim - 2];
+  size_t N = b_shape[ndim - 1];
+  size_t K = a_shape[ndim - 1];
+  for (int i = 0; i < batch_size; ++i) {
+    simd_gemm<bfloat16_t, float>(
+        a + elem_to_loc(M * K * i, a_shape, a_strides),
+        b + elem_to_loc(K * N * i, b_shape, b_strides),
+        out + M * N * i,
+        a_transposed,
+        b_transposed,
+        M,
+        N,
+        K,
+        alpha,
+        beta);
+  }
+}
+
+} // namespace mlx::core

mlx/backend/cpu/gemms/simd_fp16.cpp

@@ -0,0 +1,45 @@
+// Copyright © 2025 Apple Inc.
+
+#include "mlx/backend/common/utils.h"
+#include "mlx/backend/cpu/gemm.h"
+#include "mlx/backend/cpu/gemms/simd_gemm.h"
+
+namespace mlx::core {
+
+template <>
+void matmul<float16_t>(
+    const float16_t* a,
+    const float16_t* b,
+    float16_t* out,
+    bool a_transposed,
+    bool b_transposed,
+    size_t lda,
+    size_t ldb,
+    size_t ldc,
+    float alpha,
+    float beta,
+    size_t batch_size,
+    const Shape& a_shape,
+    const Strides& a_strides,
+    const Shape& b_shape,
+    const Strides& b_strides) {
+  auto ndim = a_shape.size();
+  size_t M = a_shape[ndim - 2];
+  size_t N = b_shape[ndim - 1];
+  size_t K = a_shape[ndim - 1];
+  for (int i = 0; i < batch_size; ++i) {
+    simd_gemm<float16_t, float>(
+        a + elem_to_loc(M * K * i, a_shape, a_strides),
+        b + elem_to_loc(K * N * i, b_shape, b_strides),
+        out + M * N * i,
+        a_transposed,
+        b_transposed,
+        M,
+        N,
+        K,
+        alpha,
+        beta);
+  }
+}
+
+} // namespace mlx::core

mlx/backend/cpu/gemms/simd_gemm.h

@@ -0,0 +1,139 @@
+// Copyright © 2025 Apple Inc.
+#pragma once
+
+#include "mlx/backend/cpu/simd/simd.h"
+
+namespace mlx::core {
+
+inline int ceildiv(int a, int b) {
+  return (a + b - 1) / b;
+}
+
+template <int block_size, typename T, typename AccT>
+void load_block(
+    const T* in,
+    AccT* out,
+    int M,
+    int N,
+    int i,
+    int j,
+    bool transpose) {
+  if (transpose) {
+    for (int ii = 0; ii < block_size && i * block_size + ii < M; ++ii) {
+      for (int jj = 0; jj < block_size && j * block_size + jj < N; ++jj) {
+        out[jj * block_size + ii] =
+            in[(i * block_size + ii) * N + j * block_size + jj];
+      }
+    }
+  } else {
+    for (int ii = 0; ii < block_size && i * block_size + ii < M; ++ii) {
+      for (int jj = 0; jj < block_size && j * block_size + jj < N; ++jj) {
+        out[ii * block_size + jj] =
+            in[(i * block_size + ii) * N + j * block_size + jj];
+      }
+    }
+  }
+}
+
+template <typename T, typename AccT>
+void simd_gemm(
+    const T* a,
+    const T* b,
+    T* c,
+    bool a_trans,
+    bool b_trans,
+    int M,
+    int N,
+    int K,
+    float alpha,
+    float beta) {
+  constexpr int block_size = 16;
+  constexpr int simd_size = simd::max_size<AccT>;
+  static_assert(
+      (block_size % simd_size) == 0,
+      "Block size must be divisible by SIMD size");
+
+  int last_k_block_size = K - block_size * (K / block_size);
+  int last_k_simd_block = (last_k_block_size / simd_size) * simd_size;
+  for (int i = 0; i < ceildiv(M, block_size); i++) {
+    for (int j = 0; j < ceildiv(N, block_size); j++) {
+      AccT c_block[block_size * block_size] = {0.0};
+      AccT a_block[block_size * block_size];
+      AccT b_block[block_size * block_size];
+
+      int k = 0;
+      for (; k < K / block_size; k++) {
+        // Load a and b blocks
+        if (a_trans) {
+          load_block<block_size>(a, a_block, K, M, k, i, true);
+        } else {
+          load_block<block_size>(a, a_block, M, K, i, k, false);
+        }
+        if (b_trans) {
+          load_block<block_size>(b, b_block, N, K, j, k, false);
+        } else {
+          load_block<block_size>(b, b_block, K, N, k, j, true);
+        }
+
+        // Multiply and accumulate
+        for (int ii = 0; ii < block_size && i * block_size + ii < M; ++ii) {
+          for (int jj = 0; jj < block_size && j * block_size + jj < N; ++jj) {
+            for (int kk = 0; kk < block_size; kk += simd_size) {
+              auto av =
+                  simd::load<AccT, simd_size>(a_block + ii * block_size + kk);
+              auto bv =
+                  simd::load<AccT, simd_size>(b_block + jj * block_size + kk);
+              c_block[ii * block_size + jj] += simd::sum(av * bv);
+            }
+          }
+        }
+      }
+      if (last_k_block_size) {
+        // Load a and b blocks
+        if (a_trans) {
+          load_block<block_size>(a, a_block, K, M, k, i, true);
+        } else {
+          load_block<block_size>(a, a_block, M, K, i, k, false);
+        }
+        if (b_trans) {
+          load_block<block_size>(b, b_block, N, K, j, k, false);
+        } else {
+          load_block<block_size>(b, b_block, K, N, k, j, true);
+        }
+
+        // Multiply and accumulate
+        for (int ii = 0; ii < block_size && i * block_size + ii < M; ++ii) {
+          for (int jj = 0; jj < block_size && j * block_size + jj < N; ++jj) {
+            int kk = 0;
+            for (; kk < last_k_simd_block; kk += simd_size) {
+              auto av =
+                  simd::load<AccT, simd_size>(a_block + ii * block_size + kk);
+              auto bv =
+                  simd::load<AccT, simd_size>(b_block + jj * block_size + kk);
+              c_block[ii * block_size + jj] += simd::sum(av * bv);
+            }
+            for (; kk < last_k_block_size; ++kk) {
+              c_block[ii * block_size + jj] +=
+                  a_block[ii * block_size + kk] * b_block[jj * block_size + kk];
+            }
+          }
+        }
+      }
+
+      // Store
+      for (int ii = 0; ii < block_size && i * block_size + ii < M; ++ii) {
+        for (int jj = 0; jj < block_size && j * block_size + jj < N; ++jj) {
+          auto c_idx = (i * block_size + ii) * N + j * block_size + jj;
+          if (beta != 0) {
+            c[c_idx] = static_cast<T>(
+                alpha * c_block[ii * block_size + jj] + beta * c[c_idx]);
+          } else {
+            c[c_idx] = static_cast<T>(alpha * c_block[ii * block_size + jj]);
+          }
+        }
+      }
+    }
+  }
+}
+
+} // namespace mlx::core

python/tests/test_blas.py

@@ -12,7 +12,7 @@ import numpy as np
 class TestBlas(mlx_tests.MLXTestCase):
     @property
     def dtypes(self):
-        return ["float32", "float16"] if mx.metal.is_available() else ["float32"]
+        return ["float32", "float16"]
 
     def __gemm_test(
         self,