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214 Assignment2_EE675_shreyas_prashant.tex
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+\documentclass[a4paper,12pt]{article}
+\usepackage[utf8]{inputenc}
+\usepackage{amsmath}
+\usepackage{graphicx}
+\usepackage{float}
+%opening
+
+\begin{document}
+\title{\textbf{Assignment 2 : EE675 Microprocessor Applications in Power Electronics}}
+ \author{Shreyas Shyamsunder \\ 113300025 \\
+ Prashant Rupapara \\ 11307R008 \\
+ \textbf{Group 10} \\}
+ \date{Oct 09,2012}
+ \maketitle
+
+\maketitle
+\begin{enumerate}
+ \item
+ \begin{flushleft}
+ This question requires us to make 4 subroutines for getting and setting the required element in a matrix. The value of array
+ address is placed in ARO, i in R0 and j in R1. i and j are the indexes required for accessing the corresponding element in
+ the matrix. This question is dealt in 4 parts.
+ \begin{enumerate}
+ \item
+ \begin{flushleft}
+ $getnum\_2$ subroutine accepts the value of i and j in R0 and R1 for a two dimensional matrix and places the array element in R0. Even though the
+ array is two dimensional, it is stored in contiguous memory locations.The appropriate element needs to be indexed after
+ the initial offset of the array header is taken care of. The index of the element can be calculated as
+ \begin{align}
+ index = (j*R0)+R1+4+R0 \nonumber
+ \end{align}
+ \begin{flushleft}
+ where j is the number of columns in the matrix which is stored in the 4th memory location from the base address of the
+ array. Once the index is known the corresponding element can be acccessed and placed in R0. If the value placed in R0
+ and R1 is more than the maximum allowable(which is placed in the array header), then the appropriate error bit is set.
+ This error check is done at the beginning of the subroutine.
+ \end{flushleft}
+ \end{flushleft}
+ \item
+ \begin{flushleft}
+ $getnum\_1$ subroutine accepts the value of i in R0 for a one dimensional matrix and places the array element in R0.
+ It does not matter whether the matrix is a row matrix or a column matrix, it will be stored in the same way in memory. This
+ subroutine does not check whether matrix is one dimensional or not. It is assumed that the user has taken care
+ of that problem. It was not mentioned in the question to tackle this issue. The appropriate element needs to be accessed
+ appropriate element needs to be indexed after accounting for the offset due to the header. The index of the element can be
+ calculated as
+ \begin{align}
+ index = R0+4 \nonumber
+ \end{align}
+ \begin{flushleft}
+ where j is the number of columns in the matrix which is stored in the 4th memory location from the base address of the
+ array. Once the index is known the corresponding element can be acccessed and placed in R0. If the value placed in R0
+ is more than the maximum allowable number of columns or rows(which is placed in the array header), then the appropriate
+ error bit is set.This error check is done at the beginning of the subroutine. The value of R0 is checked with both the
+ row or column entries in the header. This is done because the matrix could either be a row or a column matrix. As
+ mentioned above it is assumed that atleast one of these values is 0, this subroutine does not address the issue when both
+ number of rows as well as columns is a finite number in the header(denoting a 2 dimensional matrix).
+ \end{flushleft}
+ \end{flushleft}
+ \item
+ \begin{flushleft}
+ $setnum\_2$ subroutine accepts the value of i,j and the data in R0,R1 and R3 respectively and stores R3 in the
+ corresponding position in the matrix. The appropriate index is calculated same as for the getnum\_2.
+ \begin{align}
+ index = (j*R0)+R1+4+R0 \nonumber
+ \end{align}
+ \begin{flushleft}
+ where j is the number of columns in the matrix which is stored in the 4th memory location from the base address of the
+ array. Once the index is known the value in R3 is placed in the corresponding matrix location. The error check is same
+ as the one for getnum\_2.
+ This error check is done at the beginning of the subroutine.
+ \end{flushleft}
+ \end{flushleft}
+ \item
+ \begin{flushleft}
+ $setnum\_1$ subroutine accepts the value of i adn data in R0 and R3 and stores R3 in the corresponding position in the
+ matrix. The appropriate index is calculated same as for the getnum\_1.
+ \begin{align}
+ index = R0+4 \nonumber
+ \end{align}
+ \begin{flushleft}
+ Once the index is known the value in R3 is placed in the corresponding matrix location. The error check is same
+ as the one for getnum\_1.
+ This error check is done at the beginning of the subroutine.
+ \end{flushleft}
+ \end{flushleft}
+
+ \end{enumerate}
+ \end{flushleft}
+
+
+ \begin{flushleft}
+ The above subroutines were successfully tested with the TMS320VC33 board. All the subroutines are made global and stored in
+ the file asubs.asm.
+ \end{flushleft}
+ \item
+ \begin{flushleft}
+ In this question we are required to perform arithmetic operations on the matrix. It is assumed that the matrices are already
+ stored in memory locations. This question is dealt in 4 parts.
+ \begin{enumerate}
+ \item
+ \begin{flushleft}
+ $mmult\ $ This subroutine accepts the starting addresses of the two matrices in AR0 and AR1 respectively and calculates
+ C = A*B. However first the dimension check is done. Two matrices can be multiplied if the number of columns of the
+ first matrix is equal to the number of rows of the second matrix. This check is performed first as all the values is
+ known(placed in the matrix header). If this is satisfied, the dimensions of the new matrix is written in the appropriate
+ header position for C(given be base address AR2).
+ \end{flushleft}
+ \begin{flushleft}
+ Our subroutine uses the previous subroutines getnum\_2 and setnum\_2(written for question 1) to access and place the
+ element in the corresponding positions in the matrix respectively.
+ \end{flushleft}
+ \begin{flushleft}
+ We know that a particular element in C can be given as
+ \end{flushleft}
+ \begin{align}
+ C[i,k] = \sum^{J}_{j=0} A(i,j)*B(j,k) \nonumber
+ \end{align}
+ \begin{flushleft}
+ where J is the number of columns of matrix1 or number of rows of matrix2.
+ \end{flushleft}
+ \begin{flushleft}
+ In our subroutine, we have generated the appropriate indexes for the three matrices using loops. We have made use of
+ the conditional branch instructions to get the appropriate values of i,j and k. These values are then passed onto
+ the subroutines to get the value of the matrix element. This is multiplied and accumulated and then stored into the
+ index of the matrix C using the setnum\_2 subroutine.
+ \end{flushleft}
+ \item
+ \begin{flushleft}
+ $madd $ This subroutine performs the operation C = A+B where the base addresses for A,B and C are stored in AR0, AR1
+ and AR2 respectively.Our subroutine first performs the check for dimensions. Two matrices can be added or subtractd only
+ if their dimensions match. This check is performed and the appropriate error bit is set at the beginning of the subroutine.
+ We know that
+ \end{flushleft}
+ \begin{align}
+ C[i,j] = A(i,j)+B(i,j) \nonumber
+ \end{align}
+ In our subroutine, we have used a loop to calculated sum of each corresponding element of A and B. The result is stored
+ in the appropriate address using AR2.
+ \item
+ \begin{flushleft}
+ $msub $ This subroutine performs the operation C = A-B where the base addresses for A,B and C are stored in AR0, AR1
+ and AR2 respectively.Our subroutine first performs the check for dimensions.The check for dimensions is performed
+ and the appropriate error bit is set.
+ We know that
+ \end{flushleft}
+ \begin{align}
+ C[i,j] = A(i,j)-B(i,j) \nonumber
+ \end{align}
+ \begin{flushleft}
+ In our subroutine, we have used a loop to calculated difference of each corresponding element of A and B. The result is stored
+ in the appropriate address using AR2. (Please note that matrix elements are stored in contiguous memory locations).
+
+ \end{flushleft}
+ \item
+ \begin{flushleft}
+ $mneg $ This subroutine performs the operation C = -A where the base addresses for A and C are stored in AR0
+ and AR2 respectively.Our subroutine first performs the check for dimensions.The check for dimensions is performed
+ and the appropriate error bit is set.
+ We know that
+ \end{flushleft}
+ \begin{align}
+ C[i,j] = -A(i,j) \nonumber
+ \end{align}
+ \begin{flushleft}
+ In our subroutine, we have used a loop to calculated difference of each corresponding element of C. The instruction negf
+ is used to negate. The result is stored in the appropriate address using AR2. (Please note that matrix elements are stored
+ in contiguous memory locations).
+
+ \end{flushleft}
+ \item
+ \begin{flushleft}
+ $mtrn $ This subroutine performs the operation $C = A^T$ where the base addresses for A and C are stored in AR0
+ and AR2 respectively.Our subroutine first performs the check for dimensions.The check for dimensions is performed
+ and the appropriate error bit is set.
+ We know that
+ \end{flushleft}
+ \begin{align}
+ C[i,j] = A(j,i) \nonumber
+ \end{align}
+ \begin{flushleft}
+ The logic for calculating the transpose is as follows. (pseudo code)
+ \end{flushleft}
+ \begin{flushleft}
+ IR0 = 4 \nonumber \\
+ for(R1=0,R1$<$(number of columns+1),R1++) \\
+ \{\\
+ IR1 = R1 + 4 \\
+ for(R2=0,R2$<$(number of rows+1),R2++) \\
+ \{\\
+ C[IR0]=A[IR1] \\
+ IR1 = R1+R5+4 \\
+ IR0 = IR0 + 1 \\
+ \}\\
+ \}\\
+ \end{flushleft}
+
+
+ \end{enumerate}
+
+ \begin{flushleft}
+ The above subroutines were successfully compiled and checked on the TMS320VC33 board. The main calling program initializes
+ the required matrices. Also all the operations were performed on floating point numbers with appropriate checks for overfow
+ and underflow. This was done by monitoring the v bit and the UF bit in the status register.
+ \end{flushleft}
+
+
+ \end{flushleft}
+ \end{enumerate}
+
+
+
+
+\end{document}
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