From: Andrey Miroshnikov <andrey@technepisteme.xyz>
Date: Tue, 17 Oct 2023 15:56:11 +0000 (+0000)
Subject: Add outer/inner loop info
X-Git-Url: https://git.libre-soc.org/?a=commitdiff_plain;h=9006971fe6c4e95560706918af19a4e42707a9d9;p=libreriscv.git

Add outer/inner loop info
---

diff --git a/openpower/sv/cookbook/remap_matrix.mdwn b/openpower/sv/cookbook/remap_matrix.mdwn
index 406fda611..d6fb053b5 100644
--- 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).
 
-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
-following:
+following (outer product):
 
 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 |
 
+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