Faster complex matmul (#2571)

mlx/backend/cpu/gemms/cblas.cpp

@@ -88,4 +88,47 @@ void matmul<double>(
   }
 }
 
+template <>
+void matmul<complex64_t>(
+    const complex64_t* a,
+    const complex64_t* b,
+    complex64_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];
+  auto calpha = static_cast<complex64_t>(alpha);
+  auto cbeta = static_cast<complex64_t>(beta);
+
+  for (int i = 0; i < batch_size; ++i) {
+    cblas_cgemm(
+        CblasRowMajor,
+        a_transposed ? CblasTrans : CblasNoTrans, // transA
+        b_transposed ? CblasTrans : CblasNoTrans, // transB
+        M,
+        N,
+        K,
+        &calpha,
+        a + elem_to_loc(M * K * i, a_shape, a_strides),
+        lda,
+        b + elem_to_loc(K * N * i, b_shape, b_strides),
+        ldb,
+        &cbeta,
+        out + M * N * i,
+        ldc);
+  }
+}
+
 } // namespace mlx::core