From afdc384bb78d1ae7938eb0d5f15ba785863d4043 Mon Sep 17 00:00:00 2001 From: Andrey Miroshnikov Date: Tue, 17 Oct 2023 08:59:28 +0000 Subject: [PATCH] Adding initial notes for matrix remap example --- openpower/sv/cookbook/remap_matrix.mdwn | 79 +++++++++++++++++++++++++ 1 file changed, 79 insertions(+) create mode 100644 openpower/sv/cookbook/remap_matrix.mdwn diff --git a/openpower/sv/cookbook/remap_matrix.mdwn b/openpower/sv/cookbook/remap_matrix.mdwn new file mode 100644 index 000000000..6542e8491 --- /dev/null +++ b/openpower/sv/cookbook/remap_matrix.mdwn @@ -0,0 +1,79 @@ +# SVP64/Vector+1 REMAP Worked Example: Matrix Multiply + +TODO: Include screenshots + +One of the most powerful and versatile modes of the REMAP engine (a part of +the SVP64/Vector+1 feature set) is the ability to perform matrix +multiplication with all elements within a scalar register file. + +This is done by converting the index used to iterate over the operand and +result matrices to the actual index inside the scalar register file. + +## Worked example - manual (conventional method) + +The matrix multiply looks like this: + + mat_X * mat_Y = mat_Z + +When multiplying non-square matrices (rows != columns), to determine the +dimension of the result when matrix X has `a` rows and `b` columns and matrix +Y has `b` rows and `c` columns: + + X_axb * Y_bxc = Z_axc + +The result matrix will have number of rows of the first matrix, and number of +columns of the second matrix. + + +For this example, the following values will be used for the operand matrices X +and Y, result Z shown for completeness. + + X =| 1 2 3 | Y = | 6 7 | Z = | 52 58 | + | 3 4 5 | | 8 9 | | 100 112 | + | 10 11 | + +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 | + +The method usually taught in linear algebra course to students is the following: + +1. Start with the first row of the first matrix, and first column of the second matrix. +2. Multiply each element in the row by each element in the column, and sum the result. +3. Store result in the first row, first column entry. + +Equation: (TODO) + + A(i, j) * B(j, k) = C(i, k) + +Calculations: + + | 1 2 3 | | 6 7 | = | (1*6 + 2*8 + 3*10) (1*7 + 2*9 3*11) | + | 3 4 5 | * | 8 9 | | (3*6 + 4*8 + 5*10) (3*7 + 4*9 5*11) | + | 10 11 | + + | 1 2 3 | | 6 7 | = | ( 6 + 16 + 30) ( 7 + 18 + 33) | + | 3 4 5 | * | 8 9 | | (18 + 32 + 50) (21 + 36 + 55) | + | 10 11 | + + | 1 2 3 | | 6 7 | = | 52 58 | + | 3 4 5 | * | 8 9 | | 100 112 | + | 10 11 | + +## Appendix + +### Links + +- [Online matrix calculator](https://matrix.reshish.com/multCalculation.php) +- [LibreSOC matrix multiply REMAP]() -- 2.30.2