Parallelize tensor contraction over the inner dimension in cases where where one or both of the outer dimensions (m and n) are small but k is large. This speeds up individual matmul microbenchmarks by up to 85%.

Naming below is BM_Matmul_M_K_N_THREADS, measured on a 2-socket Intel Broadwell-based server.

Benchmark                          Base (ns)  New (ns) Improvement
------------------------------------------------------------------
BM_Matmul_1_80_13522_1                  387457    396013     -2.2%
BM_Matmul_1_80_13522_2                  406487    230789    +43.2%
BM_Matmul_1_80_13522_4                  395821    123211    +68.9%
BM_Matmul_1_80_13522_6                  391625     97002    +75.2%
BM_Matmul_1_80_13522_8                  408986    113828    +72.2%
BM_Matmul_1_80_13522_16                 399988     67600    +83.1%
BM_Matmul_1_80_13522_22                 411546     60044    +85.4%
BM_Matmul_1_80_13522_32                 393528     57312    +85.4%
BM_Matmul_1_80_13522_44                 390047     63525    +83.7%
BM_Matmul_1_80_13522_88                 387876     63592    +83.6%
BM_Matmul_1_1500_500_1                  245359    248119     -1.1%
BM_Matmul_1_1500_500_2                  401833    143271    +64.3%
BM_Matmul_1_1500_500_4                  210519    100231    +52.4%
BM_Matmul_1_1500_500_6                  251582     86575    +65.6%
BM_Matmul_1_1500_500_8                  211499     80444    +62.0%
BM_Matmul_3_250_512_1                    70297     68551     +2.5%
BM_Matmul_3_250_512_2                    70141     52450    +25.2%
BM_Matmul_3_250_512_4                    67872     58204    +14.2%
BM_Matmul_3_250_512_6                    71378     63340    +11.3%
BM_Matmul_3_250_512_8                    69595     41652    +40.2%
BM_Matmul_3_250_512_16                   72055     42549    +40.9%
BM_Matmul_3_250_512_22                   70158     54023    +23.0%
BM_Matmul_3_250_512_32                   71541     56042    +21.7%
BM_Matmul_3_250_512_44                   71843     57019    +20.6%
BM_Matmul_3_250_512_88                   69951     54045    +22.7%
BM_Matmul_3_1500_512_1                  369328    374284     -1.4%
BM_Matmul_3_1500_512_2                  428656    223603    +47.8%
BM_Matmul_3_1500_512_4                  205599    139508    +32.1%
BM_Matmul_3_1500_512_6                  214278    139071    +35.1%
BM_Matmul_3_1500_512_8                  184149    142338    +22.7%
BM_Matmul_3_1500_512_16                 156462    156983     -0.3%
BM_Matmul_3_1500_512_22                 163905    158259     +3.4%
BM_Matmul_3_1500_512_32                 155314    157662     -1.5%
BM_Matmul_3_1500_512_44                 235434    158657    +32.6%
BM_Matmul_3_1500_512_88                 156779    160275     -2.2%
BM_Matmul_1500_4_512_1                  363358    349528     +3.8%
BM_Matmul_1500_4_512_2                  303134    263319    +13.1%
BM_Matmul_1500_4_512_4                  176208    130086    +26.2%
BM_Matmul_1500_4_512_6                  148026    115449    +22.0%
BM_Matmul_1500_4_512_8                  131656     98421    +25.2%
BM_Matmul_1500_4_512_16                 134011     82861    +38.2%
BM_Matmul_1500_4_512_22                 134950     85685    +36.5%
BM_Matmul_1500_4_512_32                 133165     90081    +32.4%
BM_Matmul_1500_4_512_44                 133203     90644    +32.0%
BM_Matmul_1500_4_512_88                 134106    100566    +25.0%
BM_Matmul_4_1500_512_1                  439243    435058     +1.0%
BM_Matmul_4_1500_512_2                  451830    257032    +43.1%
BM_Matmul_4_1500_512_4                  276434    164513    +40.5%
BM_Matmul_4_1500_512_6                  182542    144827    +20.7%
BM_Matmul_4_1500_512_8                  179411    166256     +7.3%
BM_Matmul_4_1500_512_16                 158101    155560     +1.6%
BM_Matmul_4_1500_512_22                 152435    155448     -1.9%
BM_Matmul_4_1500_512_32                 155150    149538     +3.6%
BM_Matmul_4_1500_512_44                 193842    149777    +22.7%
BM_Matmul_4_1500_512_88                 149544    154468     -3.3%

1 files changed, 22 insertions, 3 deletions

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorContraction.h b/unsupported/Eigen/CXX11/src/Tensor/TensorContraction.h
index 3b22e43e7..ea17a897d 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorContraction.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorContraction.h
@@ -590,6 +590,25 @@ struct TensorContractionEvaluatorBase
 
     // zero out the result buffer (which must be of size at least m * n * sizeof(Scalar)
     this->m_device.memset(buffer, 0, m * n * sizeof(Scalar));
+    this->template evalGemmPartial<lhs_inner_dim_contiguous,
+                                   rhs_inner_dim_contiguous,
+                                   rhs_inner_dim_reordered, Alignment>(buffer,
+                                                                       0, k, 1);
+  }
+
+  template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>
+  EIGEN_DEVICE_FUNC void evalGemmPartial(Scalar* buffer, Index k_start, Index k_end, int num_threads) const {
+    // columns in left side, rows in right side
+    const Index k = this->m_k_size;
+
+    eigen_assert(k_end >= k_start && k_start >= 0 && k_end <= k);
+    const Index k_slice = k_end - k_start;
+
+    // rows in left side
+    const Index m = this->m_i_size;
+
+    // columns in right side
+    const Index n = this->m_j_size;
 
     // define mr, nr, and all of my data mapper types
     typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar;
@@ -620,7 +639,7 @@ struct TensorContractionEvaluatorBase
     typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper;
 
     // Declare GEBP packing and kernel structs
-    internal::gemm_pack_lhs<LhsScalar, Index, typename LhsMapper::SubMapper, mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing, ColMajor> pack_lhs;
+    internal::gemm_pack_lhs<LhsScalar, Index, typename LhsMapper::SubMapper, mr, Traits::LhsProgress,  typename Traits::LhsPacket4Packing, ColMajor> pack_lhs;
     internal::gemm_pack_rhs<RhsScalar, Index, typename RhsMapper::SubMapper, nr, ColMajor> pack_rhs;
 
     internal::gebp_kernel<LhsScalar, RhsScalar, Index, OutputMapper, mr, nr, false, false> gebp;
@@ -635,7 +654,7 @@ struct TensorContractionEvaluatorBase
     OutputMapper output(buffer, m);
 
     // Sizes of the blocks to load in cache. See the Goto paper for details.
-    internal::TensorContractionBlocking<LhsScalar, RhsScalar, Index, internal::ShardByCol> blocking(k, m, n, 1);
+    internal::TensorContractionBlocking<LhsScalar, RhsScalar, Index, internal::ShardByCol> blocking(k_slice, m, n, num_threads);
     const Index kc = blocking.kc();
     const Index mc = numext::mini(m, blocking.mc());
     const Index nc = numext::mini(n, blocking.nc());
@@ -648,7 +667,7 @@ struct TensorContractionEvaluatorBase
     for(Index i2=0; i2<m; i2+=mc)
     {
       const Index actual_mc = numext::mini(i2+mc,m)-i2;
-      for (Index k2 = 0; k2 < k; k2 += kc) {
+      for (Index k2 = k_start; k2 < k_end; k2 += kc) {
         // make sure we don't overshoot right edge of left matrix, then pack vertical panel
         const Index actual_kc = numext::mini(k2 + kc, k) - k2;
         pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc, 0, 0);