Revert changes to MatrixTransposeMatrixMultiply.

This change while algebraically equivalent was causing non-trivial
changes in the numbers being reported by ceres and in some cases
they got worse.

Also fix a small header include in parallel_for_test.cc which
was discovered as part of testing this patch.

Change-Id: I8c8d61538819f0b25af6059fa75ad068fc22f5e4
diff --git a/internal/ceres/benchmarks/macbook-pro-2014-small_blas_gemm_benchmark.json b/internal/ceres/benchmarks/macbook-pro-2014-small_blas_gemm_benchmark.json
index dda3d1f..0c67c43 100644
--- a/internal/ceres/benchmarks/macbook-pro-2014-small_blas_gemm_benchmark.json
+++ b/internal/ceres/benchmarks/macbook-pro-2014-small_blas_gemm_benchmark.json
@@ -1,6 +1,6 @@
 {
   "context": {
-    "date": "2018-02-25 15:01:29",
+    "date": "2018-02-28 19:43:04",
     "num_cpus": 8,
     "mhz_per_cpu": 2200,
     "cpu_scaling_enabled": false,
@@ -9,2158 +9,2158 @@
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       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/6/10/2",
-      "iterations": 3320841,
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       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/6/10/4",
-      "iterations": 2595438,
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/6/10/6",
-      "iterations": 1901048,
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       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/6/10/8",
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       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/6/12/6",
-      "iterations": 1699041,
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+      "iterations": 1000000,
+      "real_time": 5.0361730399890803e+02,
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/6/12/8",
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       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/6/15/6",
-      "iterations": 1454845,
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/6/15/8",
-      "iterations": 1690588,
-      "real_time": 4.0958818113106776e+02,
-      "cpu_time": 4.0942500479121969e+02,
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/2/2",
-      "iterations": 11031440,
-      "real_time": 6.5554157024771769e+01,
-      "cpu_time": 6.5520457891264968e+01,
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       "time_unit": "ns"
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/2/4",
-      "iterations": 9025387,
-      "real_time": 7.9776080069881658e+01,
-      "cpu_time": 7.9611766232295039e+01,
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       "time_unit": "ns"
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/2/6",
-      "iterations": 6950305,
-      "real_time": 1.0042530103821075e+02,
-      "cpu_time": 1.0040710443642280e+02,
+      "iterations": 6497424,
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+      "cpu_time": 1.0755647161089711e+02,
       "time_unit": "ns"
     },
     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/2/8",
-      "iterations": 7750479,
-      "real_time": 9.2724468376972212e+01,
-      "cpu_time": 9.2359323855981700e+01,
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       "time_unit": "ns"
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/4/2",
-      "iterations": 6325568,
-      "real_time": 1.1790369006234678e+02,
-      "cpu_time": 1.1779131929337998e+02,
+      "iterations": 9029229,
+      "real_time": 7.9354870277396074e+01,
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       "time_unit": "ns"
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/4/4",
-      "iterations": 5399068,
-      "real_time": 1.3595422061298001e+02,
-      "cpu_time": 1.3584918730417584e+02,
+      "iterations": 5264385,
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       "time_unit": "ns"
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/4/6",
-      "iterations": 3507928,
-      "real_time": 1.9749404777928154e+02,
-      "cpu_time": 1.9739259186620586e+02,
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       "time_unit": "ns"
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/4/8",
-      "iterations": 4200067,
-      "real_time": 1.7134937180691117e+02,
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       "time_unit": "ns"
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/5/2",
-      "iterations": 3795087,
-      "real_time": 1.6795350276303446e+02,
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       "time_unit": "ns"
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/5/4",
-      "iterations": 3927311,
-      "real_time": 1.7862383165866763e+02,
-      "cpu_time": 1.7855575990798138e+02,
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       "time_unit": "ns"
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/5/6",
-      "iterations": 3291887,
-      "real_time": 2.1772611665457177e+02,
-      "cpu_time": 2.1768517570622586e+02,
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       "time_unit": "ns"
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/5/8",
-      "iterations": 3392969,
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       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/8/2",
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       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/8/4",
-      "iterations": 2434131,
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       "time_unit": "ns"
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       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/12/2",
-      "iterations": 2069800,
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       "time_unit": "ns"
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       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/12/4",
-      "iterations": 1819978,
-      "real_time": 3.8383968815841575e+02,
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       "time_unit": "ns"
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       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/12/6",
-      "iterations": 1389082,
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       "time_unit": "ns"
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       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/12/8",
-      "iterations": 1455504,
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       "time_unit": "ns"
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       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/15/4",
-      "iterations": 1374112,
-      "real_time": 4.8682727903993663e+02,
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       "time_unit": "ns"
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     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/15/6",
-      "iterations": 1079964,
-      "real_time": 6.4053175021590130e+02,
-      "cpu_time": 6.3993984984682413e+02,
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+      "real_time": 6.8780457096420480e+02,
+      "cpu_time": 6.8775161830781997e+02,
       "time_unit": "ns"
     },
     {
       "name": "BM_MatrixTransposeMatrixMultiplyDynamic/8/15/8",
-      "iterations": 1148388,
-      "real_time": 5.4868444198163991e+02,
-      "cpu_time": 5.4819364187018891e+02,
+      "iterations": 765931,
+      "real_time": 9.2770876097494795e+02,
+      "cpu_time": 9.2749477433345874e+02,
       "time_unit": "ns"
     }
   ]
diff --git a/internal/ceres/parallel_for_test.cc b/internal/ceres/parallel_for_test.cc
index 2f44460..a3cf2dc 100644
--- a/internal/ceres/parallel_for_test.cc
+++ b/internal/ceres/parallel_for_test.cc
@@ -35,6 +35,7 @@
 
 #include "ceres/parallel_for.h"
 
+#include <cmath>
 #include <vector>
 
 #include "ceres/context_impl.h"
diff --git a/internal/ceres/small_blas.h b/internal/ceres/small_blas.h
index 2d050d3..264ac53 100644
--- a/internal/ceres/small_blas.h
+++ b/internal/ceres/small_blas.h
@@ -221,27 +221,22 @@
   DCHECK_LE(start_row_c + NUM_ROW_C, row_stride_c);
   DCHECK_LE(start_col_c + NUM_COL_C, col_stride_c);
 
-  if (kOperation == 0) {
-    std::fill(C, C + NUM_ROW_C * NUM_COL_C, 0.0);
-  }
-
-  // Evaluate C op A' * B
-  // as the sum of rank one outer products of the rows of A and B.
-  for (int r = 0; r < NUM_ROW_A; ++r) {
-    double* c_row = C + start_row_c * col_stride_c;
-    for (int i = 0; i < NUM_COL_A; ++i) {
-      const double a_value = A[i];
-      for (int j = 0; j < NUM_COL_B; ++j) {
-        if (kOperation >= 0) {
-          c_row[start_col_c + j] += a_value * B[j];
-        } else {
-          c_row[start_col_c + j] -= a_value * B[j];
-        }
+  for (int row = 0; row < NUM_ROW_C; ++row) {
+    for (int col = 0; col < NUM_COL_C; ++col) {
+      double tmp = 0.0;
+      for (int k = 0; k < NUM_ROW_A; ++k) {
+        tmp += A[k * NUM_COL_A + row] * B[k * NUM_COL_B + col];
       }
-      c_row += col_stride_c;
+
+      const int index = (row + start_row_c) * col_stride_c + start_col_c + col;
+      if (kOperation > 0) {
+        C[index]+= tmp;
+      } else if (kOperation < 0) {
+        C[index]-= tmp;
+      } else {
+        C[index]= tmp;
+      }
     }
-    A += NUM_COL_A;
-    B += NUM_COL_B;
   }
 }