Add outer/inner loop info

diff --git a/openpower/sv/cookbook/remap_matrix.mdwn b/openpower/sv/cookbook/remap_matrix.mdwn
index 406fda611bf3235f1537902c23b2ad590b790835..d6fb053b5ab6ea3bb2409f55d3dcf7b9470762f6 100644 (file)
--- a/openpower/sv/cookbook/remap_matrix.mdwn
+++ b/openpower/sv/cookbook/remap_matrix.mdwn
@@ -39,21 +39,8 @@ Matrix X has 2 rows, 3 columns (2x3), and matrix Y has 3 rows, 2 columns.
 To determine the final dimensions of the resultant matrix Z, take the number
 of rows from matrix X (2) and number of columns from matrix Y (2).
 
 To determine the final dimensions of the resultant matrix Z, take the number
 of rows from matrix X (2) and number of columns from matrix Y (2).
 

-For the algorithm, assign indeces to matrices as follows:
-
-    Index | 0 1 2 3 4 5 |
-    Mat X | 1 2 3 3 4 5 |
-
-    Index | 0 1 2 3  4  5 |
-    Mat Y | 6 7 8 9 10 11 |
-
-    Index |  0  1   2   3 |
-    Mat Z | 52 58 100 112 |
-
-(Start with the first row, then assign index left-to-right, top-to-bottom.)
-

 The method usually taught in linear algebra course to students is the
 The method usually taught in linear algebra course to students is the

-following:
+following (outer product):

 
 1. Start with the first row of the first matrix, and first column of the
 second matrix.
 
 1. Start with the first row of the first matrix, and first column of the
 second matrix.


@@ -89,7 +76,73 @@ Calculations:
     | 3 4 5 | * |  8  9 |   | 100 112 |
                 | 10 11 |
 
     | 3 4 5 | * |  8  9 |   | 100 112 |
                 | 10 11 |
 

+For the algorithm, assign indeces to matrices as follows:
+
+    Index | 0 1 2 3 4 5 |
+    Mat X | 1 2 3 3 4 5 |
+
+    Index | 0 1 2 3  4  5 |
+    Mat Y | 6 7 8 9 10 11 |
+
+    Index |  0  1   2   3 |
+    Mat Z | 52 58 100 112 |
+
+(Start with the first row, then assign index left-to-right, top-to-bottom.)
+
+Index list:
+
+    Mat X | Mat Y | Mat Z
+      0   |   0   |   0
+      1   |   2   |   0
+      2   |   4   |   0
+      0   |   1   |   1
+      1   |   3   |   1
+      2   |   5   |   1
+      3   |   0   |   2
+      4   |   2   |   2
+      5   |   4   |   2
+      3   |   1   |   3
+      4   |   3   |   3
+      5   |   5   |   3
+
+
+The issue with this algorithm is that the result matrix element is the same
+for three consecutive operations, and where each element is stored in CPU
+registers, the same register will be written to three times and thus causing
+consistent stalling.
+
+## Inner Product
+
+A slight modification to the order of the loops in the algorithm massively
+reduces the chance of read-after-write hazards, as the result matrix
+element (and thus register) changes with every multiply-add operation.
+
+The code:
+
+    for i in range(mat_X_num_rows):
+        for j in range(0, mat_X_num_cols): # or mat_Y_num_rows
+            for k in range(0, mat_Y_num_cols):
+                mat_Z[i][k] += mat_X[i][j] * mat_Y[j][k]

 
 

+Index list:
+
+    Mat X | Mat Y | Mat Z
+      0   |   0   |   0
+      0   |   1   |   1
+      3   |   0   |   2
+      3   |   1   |   3
+      1   |   2   |   0
+      1   |   3   |   1
+      4   |   2   |   2
+      4   |   3   |   3
+      2   |   4   |   0
+      2   |   5   |   1
+      5   |   4   |   2
+      5   |   5   |   3
+
+The index for the result matrix changes with every operation, and thus the
+consecutive multiply-add instruction doesn't depend on the previous write
+register.

 
 ## Appendix
 
 
 ## Appendix