Comp 3050 001 Computer Architecture Homework 2 Summer 2018

Comp 3050 001 Computer Architecturehomework 2 Summer 2018 This Assi

This assignment involves writing a program in Mic1 macro-assembly language to calculate Fibonacci numbers, including building a recursive subroutine for Fibonacci calculation, setting up data locations with multiple input arguments, and storing the results accordingly. Students must also provide a short write-up that assesses their success, discusses their approach, and reports unresolved problems. The program should simulate calling the Fibonacci function for specified arguments, store results, and output the results after execution. The submission includes source code, build/run instructions, program output, and a reflective write-up. Proper formatting, well-commented code, and academic sources are required for full credit.

Sample Paper For Above instruction

The Fibonacci sequence, a fundamental concept in mathematics and computer science, offers an ideal context for illustrating the principles of recursive algorithm implementation. Programming the Fibonacci sequence in assembly language, particularly the Mic1 macro-assembly language specified in this assignment, presents unique challenges and learning opportunities related to recursion, memory management, and control flow. This paper details the development of a recursive Fibonacci subroutine, the setup of data locations for multiple input values, and the process of storing and outputting computed results.

Implementing the Fibonacci function in Mic1 assembly language requires careful attention to the control flow. The recursive approach, as defined by Fibonacci(0)=0, Fibonacci(1)=1, and Fibonacci(N)=Fibonacci(N-1)+Fibonacci(N-2), inherently involves calling the function with decremented arguments, storing intermediate values, and unwinding recursion for the final result. In this assignment, I constructed a subroutine named 'FIB' that accepts an argument on the stack and returns the Fibonacci value in the accumulator (AC). The subroutine begins by checking for base cases (0 and 1), returning 0 or 1 directly. For larger arguments, it recursively calls itself twice for N-1 and N-2, summing these results to produce the Fibonacci number.

The main routine initializes data locations with five argument values for which Fibonacci numbers are to be calculated. These input values are stored in predefined memory addresses. The main loop iteratively pushes each argument onto the stack, calls the recursive 'FIB' subroutine, and stores the returned result in a dedicated memory location. This process efficiently handles multiple calculations, aligning with the recursive algorithm's demands. The final output displays each input argument alongside its corresponding Fibonacci number, verifying the correctness of the implementation.

One significant difficulty faced during development was managing recursion in a low-level assembly language without built-in support for function calls or stack management. I addressed this by explicitly pushing arguments onto the stack before each call and carefully managing return addresses and local variables through registers and memory. Additionally, ensuring that each recursive call correctly decremented arguments and unwound properly required careful synchronization of memory locations and control flow instructions.

Another challenge was avoiding stack overflow or excessive computation time when calculating large Fibonacci numbers such as 25 and 18. To mitigate this, I limited the input values to manageable sizes and verified the correctness through incremental testing. The recursive algorithm naturally exhibits exponential run-time growth, so optimizing or replacing it with iterative methods could be explored in future enhancements.

Overall, I believe my implementation correctly captures the required recursive behavior for the Fibonacci function. The setup of data segments, the recursive subroutine, and the main invocation loop all function as intended, producing correct results for the provided input values. However, I encountered some difficulties in optimizing the program's efficiency and managing recursion depth, which I plan to address in future revisions. The assignment deepened my understanding of low-level programming, recursion, and the importance of meticulous control flow management in assembly language.

References

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