### Cost

Your company would like to estimate cost of an IC manufacturing project. You will be using wafers of diameter 30cm with 1.2 defects per cm^{2} at a cost per processed wafer of $5000 each. Each die has a size of 25mm x 25mm using a process with α=4. For the purposes of this problem, ignore completely bad wafers, and the costs and failures during testing and packaging.

#### Approximate dies per wafer

What is the approximate number of dies per wafer considering only the ratio of wafer area to die area?

What is the approximate number of dies per wafer including the estimate of partial dies lost along the perimeter?

#### Actual dies per wafer

What is the actual maximum number of dies per wafer? Show us how you get this number.

#### Yield

What is the yield?

Approximately how many good dies per wafer? This is an expected average, include decimal places.

#### Cost

What is the total cost per good die?

### Algorithm Speedup

A naïve ray tracing algorithm spends 5% of its time on I/O, 95% of its time doing ray intersection computation, and negligible time traversing data structures.

A smarter ray tracer uses more complex data structures to do fewer ray intersections. The resulting program spends 30% of its time on I/O, 60% of its time traversing data structures and only 10% on intersection computations.

Assuming the I/O time doesn't change, what is the speedup of the smarter ray tracer relative to the naïve one?

### Parallel Speedup

Consider an algorithm that is to be parallelized using message passing. The algorithm will be broken into three phases, A: *partition and distribute work*, B: *compute*, and C: *collect results*. The variables you can control are the number of processors, p, and the number of partitions, w ≥ p. The other factor (which you cannot control) is the size of the problem, n. Given constants K_{A}, K_{B} and K_{C}, the times for these three phases are

- Time(A) = K
_{A}w - Time(B) = K
_{B}n/p - Time(C) = K
_{C}n

Where the serial algorithm ran in time

- Time(S) = (K
_{B}+ K_{C}) n

#### Speedup

What is the speedup of the parallel algorithm?

#### Amdahl's Law

In terms of the Amdahlâ€™s law speedup equation, what is the fraction enhanced, fraction unenhanced, and enhanced speedup? Note that this should be algebraically equivalent to your answer above.

#### Optimization

What is the optimal choice for w and p?