Question

Ordered structures Consider a list Λ deployed to implement a Stack Abstract Data Type.

1. Given the code below, identify the cycle in which each event takes place. Assume that the first instruction is fetched in Cycle t, therefore all other cycles will be expressed as Cycle t+n, where n is an integer representing the offset from the initial cycle. Remember the number of cycles for floating point operations - there are four ADD stages, seven MULTIPLY stages, and one DIVIDE stage that must iterate for a total of 25 cycles. Assume no forwarding, but operands being committed in the WB stage can also be delivered to an instruction in the ID stage. Also assume no dynamic scheduling, instructions must issue in the listing order. (HINT: If you find this difficult, it may help to draw a timeline.)
ADD.D FO, F2, F4
MUL.D F6, FO, F2
DIV.D F6, F6, F6
ADD.D F8, F2, F6

Events:
a. In what cycle is the DIV.D instruction fetched?
b. In what cycle is the product of FO and F2 completed?
c. In what cycle is the product of FO and F2 committed to F6?
d. In what cycle does the ADD.D F8, F2, F6 instruction issue?1. Let the head of Λ correspond to the topmost position of the Stack. Implement the body of operations push(el, Λ ) and pop(Λ) (let return element be held in variable topmost ) using list construction operations. In both cases a) we assume that appropriate preconditions exist, and b) we can refer to Λ′ as the state of the list upon successful termination of one of its operations. 2. Let the last element of Λ correspond to the topmost position of the Stack. Implement the body of both operations as above. When applicable, use control flow statements in your answer.

Answer 1

The question includes cycle-by-cycle pipeline analysis in a computer architecture context and implementation of a stack ADT in computer science. Calculating cycle times requires understanding the stages of instruction pipeline, while stack operations involve the use of list manipulation.

Step-by-step explanation:

The student has presented a two-part question. The first part deals with a cycle-by-cycle analysis of instructions in a pipeline assuming no forwarding and no dynamic scheduling. This question belongs to computer architecture, a subject matter often discussed in computer science and engineering courses.

For the first part, the cycle-by-cycle analysis requires understanding of the basic stages of an instruction pipeline: Instruction Fetch (IF), Instruction Decode (ID), Execute (EX), Memory access (MEM), and Write Back (WB). Given that we have a pipeline with a specific number of stages for arithmetic operations (ADD, MUL, DIV), cycle times can be calculated accordingly. To aid with visual representation, a timeline diagram is often useful, which is not provided here.

The second part of the question requires the implementation of push and pop operations for a stack using a list. In computer science, specifically in data structures, the stack abstract data type (ADT) is a collection that is processed with Last-In-First-Out (LIFO) order. The push operation adds an element to the top of the stack, while the pop operation removes the element from the top. This can be implemented in two ways based on whether the head or the tail of the list represents the top of the stack, which alters the complexity of these operations.