Faster Transpose 2D (apache#16104)

* 2d transpose naive

* omp pragma

* omp pragma unroll

* blocksize

* make it 2d tile

* loop peeling

* better loop peeling

* redundancy

* removed bool

* removing excess for loops, memory save

* fix internal forloop

* remove commented code, lint fix

* Trigger notification

* explain params, indent fix, explain blocksize

* fix p,n and reduce for loop computation j+a,i+b

* kernel

* gpu thread 1

* remove gpu implementation

* fix internal for loop

* unittest to catch the previous error

* optimizations

* microsoft cpp doesn't support omp collapse

src/operator/tensor/matrix_op-inl.h

@@ -257,6 +257,51 @@ struct TransposeParam : public dmlc::Parameter<TransposeParam> {
   }
 };
 
+
+/*!
+ * \brief This function performs transpose operation on a 2D matrix by utilizing the L1 cache
+ * \param in  input tensor
+ * \param out output tensor
+ * \param row shape of dim 0 of input
+ * \param col shape of dim 1 of input
+ */
+template<typename DType>
+MSHADOW_XINLINE void Transpose2D(const DType *in, DType *out, index_t row, index_t col) {
+  // ensure cache line hits and prevent cache miss for any configuration
+  // L1 cache size to be utilized = 32kb = 2^15
+  // Largest size of a single unit of any dtype <= 8 byte = 2^3
+  // Number of elements - (2^15/2^3) = 2^12
+  // Block-size - 2^6 v 2^6 (64 v 64)
+
+  // But we could leverage unrolling of for loops (for parallelization)
+  // Block-size - 2^5 v 2^5 (32 v 32) with potential 4 pragma for loop unrolled
+  // blocksize * blocksize * num_threads = cache_size / dtype_size
+  // Instead of explicit unroll, let compiler figure out optimal unroll factor
+  index_t blocksize = 32;
+
+  // collapse 2 parallelizes 2 for loops
+  // inner 2 for loops aren't parallelized to prevent cache miss
+
+  // Microsoft Visual C++ compiler does not support omp collapse
+  #ifdef _MSC_VER
+    #pragma omp parallel for
+  #else
+    #pragma omp parallel for collapse(2)
+  #endif  // _MSC_VER
+
+  for (index_t i = 0; i < row; i += blocksize) {
+    for (index_t j = 0; j < col; j += blocksize) {
+      // transpose the block
+      for (index_t a = j; (a < blocksize + j) && (a < col); ++a) {
+        for (index_t b = i; (b < blocksize + i) && (b < row); ++b) {
+          out[a * row + b] = in[b * col + a];
+        }
+      }
+    }
+  }
+}
+
+
 template<typename xpu>
 void TransposeImpl(RunContext ctx,
                    const TBlob& src,
@@ -285,8 +330,13 @@ void TransposeImpl(RunContext ctx,
      case 2: {
       mshadow::Tensor<xpu, 2, DType> in = src.FlatTo2D<xpu, DType>(s);
       mshadow::Tensor<xpu, 2, DType> out = ret.FlatTo2D<xpu, DType>(s);
+
       if (axes[0] == 1 && axes[1] == 0) {
-        out = in.T();
+        if (ctx.get_ctx().dev_mask() == cpu::kDevMask) {
+          Transpose2D<DType>(in.dptr_, out.dptr_, in.shape_[0], in.shape_[1]);
+        } else {
+          out = in.T();
+        }
       } else {
         Copy(out, in, s);
       }

tests/python/unittest/test_operator.py

@@ -2874,6 +2874,13 @@ def test_transpose():
             assert_allclose(np.transpose(x.asnumpy()), y.asnumpy())
 
 
+@with_seed()
+def test_larger_transpose():
+    x = mx.nd.random.normal(shape=(50,51))
+    y = mx.nd.transpose(x)
+    assert_allclose(np.transpose(x.asnumpy()), y.asnumpy())
+
+
 @with_seed()
 def test_expand_dims():
     for ndim in range(1, 6):