4. (20%) Apply Gram-Schmidt Orthonormalization process to the vectors น1 = (1, 1,1),u2 = (1,0, -1),u3 = (2,1, -1) with respect to the stan- dard inner product.

5. (20%) . Find an orthogonal matrix Q so that QTAQ is a diagonal matrix.

1.1 Using the average instruction mix information for the program SPEC2000fp, find the percentage of all memory accesses (both data and instruction) that are for reads. Assume that two- thirds of data transfers are loads.

1.2 Compute the effective CPI for MIPS. Average the instruction frequencies for SPEC2000int and SPEC2000fp to obtain the instruction mix.

1.3 Consider an architecture that is similar to MIPS except that it supports update addressing for data transfer instructions. If we run SPEC2000int using this architecture, some percentage of the data transfer instructions will be able to make use of the new instructions, and for each instruction changed, one arithmetic instruction can be eliminated. If 25% of the data transfer instructions can be changed, which will be faster for SPEC2000int, the modified MIPS architecture or the unmodified architecture? How much faster? (Assume that both architectures have CPI values as given in the above table and that the modified architecture has its cycle time increased by 20% in order to accommodate the new instructions.)

2.1 Using C1 on both Il and 12, how much faster can the makers of I1 claim Il is compared to I2?

2.2 Which computer and compiler would you purchase if all other criteria are identical, including cost?

3.1 What will the speedup be if both improvements are made?

3.2 You are going to change the program described in Problem 3 so that the percentages are not 20%, 50%, and 30% anymore. Assuming that none of the new percentages is O, what sort of program would result in a tie with regard to speedup (i.e., the same speedup) between the two individual improvements? Provide both a formula and some examples.

4.1 We have a program of 1000 instructions in the format of "Iw, add, 1w, add, .. ." The add instruction depends (and only depends) on the 1w instruction right before it. The 1w instruction also depends (and only depends) on the add instruction right before it. If the program is executed on the pipelined datapath of Figure 1, what would be the actual CPI?

4.2 What would be the actual CPI for the program in Problen 4.1 without forwarding?

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