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2. Consider the following piece of C code: for (j=2;j<=1000;j++) D[j] = D[j-1]+D[j-2]; The RISC-V code corresponding to the above fragment is: li x5, 8000 add x12, x10, x5 addi x11, x10, 16 LOOP: fld f0, -16(x11) fld f1, -8(x11) fadd.d f2, f0, f1 fsd f2, 0(x11) addi x11, x11, 8 ble x11, x12, LOOP The latency of an instruction is the number of cycles that must come between that instruction and an instruction using the result. Assume floating point instructions have the following associated latencies (in cycles): fadd.d fld fsd 4 6 1 2.1 How many cycles does it take to execute this code? 2.2 Re-order the code to reduce stalls. Now, how many cycles does it take to execute this code? (Hint: You can remove additional stalls by changing the offset on the fsd instruction.) 2.3 When an instruction in a later iteration of a loop depends upon a data value produced in an earlier iteration of the same loop, we say that there is a loop-carried dependence between iterations of the loop. Identify the loop-carried dependences in the above code. Identify the dependent program variable and assembly-level registers. You can ignore the loop induction variable j. 2.4 Rewrite the code by using registers to carry the data between iterations of the loop (as opposed to storing and re-loading the data from main memory). Show where this code stalls and calculate the number of cycles required to execute. Note that for this problem you will need to use the assembler pseudo-instruction "fmv.d rd, rs1", which writes the value of floating-point register rs1 into floating-point register rd. Assume that fmv.d executes in a single cycle
Sri K.
Q: Consider a drilling machine in a factory. It could be in one of three different states: G, in which it is working normally (making good parts); B in which it is working but producing bad parts; or D, in which it is under repair (down") and not making parts. Transitions can occur at times 0, 30 seconds, 60 seconds, etc. Assume that all transitions are governed by Bernoulli distributions. That is, each time at which a transition can occur it occurs with a probability determined by the origin and destination state, and not dependent on how long the system was in the origin state. When it is working or making bad parts, the machine performs an operation in exactly 30 seconds. Assume that when it is in one of these states and it changes state, it changes state before it makes the next part and that the change takes no time. That is, when it goes from G to B, it makes one bad part; and when it goes from G to D, it does not make a part. When the machine is making good parts, it could go to the bad part state or it could go to the downstate. The mean time until it leaves the good state is 20 minutes. When it leaves G, it goes to D 90% of the time and it goes to B 10% of the time. After it reaches the bad state, it stays in that state until it produces an average of 30 parts, and then it always goes to D. After the machine enters D, it stays there for a random length of time whose mean is 3 minutes, and then it always goes to G. Part 1: What are the probabilities of going from each state to each other state in one operation time? (Please answer with 3 decimals) (pij is the probability of going from state j to state I.) The solution will be released after this problem is finished. You will need the solution to complete the rest of the problem. pGG = pGB = pGD = pBG = pBB = pBD = pDG = pDB = pDD = Part 2 What is the steady-state probability of being in each state? (Please answer with 3 decimals) P(G) = P(B) = P(D) = Part 3 What is the production rate of good parts in parts/min? (Please answer with 3 decimals) = What is the production rate of bad parts in parts/min? (Please answer with 3 decimals) = The yield is the number of good parts produced divided by the total number of parts produced (or the production rate of good parts divided by the total production rate). What is the yield? (Please answer with 3 decimals) =
A shop in a manufacturing plant makes three gears that fit together to become part of the gear shift mechanism for a forklift. Each part must be a specific diameter within specific tolerances. The three parts, when put together to slip into the gearbox, must also meet an overall diameter within a specific tolerance. To solve this problem, you must understand the relationship between standard deviation and process sigma (1 sigma = 1 standard deviation). You must also depict the relationship between standard deviation and % distribution. Part | Nominal (inches) | Tolerances (inches) ---|---|--- 1 | 1.750 | ± 0.042 2 | 2.000 | ± 0.060 3 | 1.250 | ± 0.030 "Nominal" is the intended or target diameter of the part. "Tolerance" is the amount of variation that is considered acceptable. For example, Part 1 should have a diameter of 1.750 inches but the part will be considered acceptable if its diameter is as small as 1.705 inches or as large as 1.795 inches. Samples for the three parts were taken: Part 1 1.74831 1.75740 1.75134 1.73316 1.75134 1.71498 1.75437 1.73619 1.73922 1.73619 1.74528 1.74831 1.76346 1.74528 1.76952 1.70892 1.75134 1.71195 1.74831 1.77861 1.75740 1.73619 1.74225 1.74528 1.73922 1.74528 1.74992 1.74225 1.74528 1.74124 1.74831 1.77861 1.75740 1.73619 1.74225 1.74528 1.73922 1.73922 1.74528 1.73619 1.74528 1.74225 1.73922 1.74528 1.73619 1.74528 1.74225 1.73922 1.74528 1.73922 1.74528 1.74225 1.73922 1.74528 1.73922 1.74528 1.74225 1.73922 1.74528 1.73922 1.74528 1.74225 1.73922 1.74528 1.73922 1.74528 1.74225 1.73922 1.74528 1.73922 1.74528 1.74225 1.73922 1.74528 1.73922 1.74528 1.74225 1.73922 1.74528 1.73922 1.74528 1.74225 1.73922 1.74528 1.73922 1.74528 1.74225 1.73922 1.74528 1.73922 1.74528 1.74225 1.73922 1.74528 1.73922 1.74528 1.74225 1.73922 1.74528 1.73922 1.74528 1.74225 1.73922 1.74528 1.73922 1.74528 1.74225 1.73922 1.74528 1.73922 1.74528 1.74225 1.73922 1.74528 1.73922 1.74528 1.74225 1.73922 1.74528 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