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311 What are the advantages of a larger computer word size Are there disadvantages If so, what are the disadvantages Advantages: Easy to represent large numbers Easy to address large memory space Disadvantages: Memory use is likely to be less bit-efficient when numbers are small Processors and supporting hardware are more expensive 312 Assume that cache memory has an access time of 10 nanoseconds, while main memory has an access time of 100 nanoseconds If the hit rate of the cache is 70 (ie, 70% of the time, the value needed is already in the cache), what is the average access time to memory 70 * ( 10ns ) + 30 * ( 100ns ) = 37ns average access time 313 Assume our 1GHz computer, which averages 3 cycles per instruction, is connected to the Internet via a 10 Mbit connection (ie.

private static void sort(int[] a, int p, int q) { if (q - p < 2) { return; } if (q - p < 8) { insertionSort(a, p, q); return; } int m = partition(a, p, q); sort(a, p, m); sort(a, m+1, q); } // steps 2 & 3 // step 4

This requires a generalization of the insertion sort:

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, the line speed allows 10 million bits to pass every second) From the time the computer receives the first bit, how many instructions can the computer execute while waiting for a single 8-bit character to arrive 8 bits * 1 sec/10,000,000 bits = 0000008 sec/character 1Billion cycles/sec * 1 instruction/3 cycles * 0000008 sec/character = 267 instr/char 314 What complexity does DMA present to the management of cache memory DMA directly updates main memory, or directly reads from main memory If the CPU takes advantage of cache memory to accelerate reads and writes, a cache coherency can develop The CPU may be reading memory location x via a cached copy that has been changed in main memory via a DMA transfer The cached value is, therefore, stale.

public static void insertionSort(int[] a, int p, int q) { for (int i = p+1; i < q; i++) { int ai = a[i], j; for (j = i; j > 0 && a[j-1] > ai; j--) { a[j] = a[j-1]; } a[j] = ai; } }

Likewise, if DMA is being used to write values from main memory to a device, and values the CPU has written to cache memory have not yet been flushed to main memory, stale or incorrect values may be written..

14.29 14.30 14.31

The heap sort is not always preferred over the quick sort because it is slower in the average case. The heap sort is not always preferred over the merge sort because it is not stable. The postcondition of heapify (Algorithm 14.9 on page 266) establishes the loop invariant in step 3. That guarantees that the root s0 is the maximum element of the subsequence. Step 5 inserts that maximum at the end of the subsequence. So when the loop at step 4 is finished, the sequence will be sorted. The heapify algorithm restores the heap property to the complete segment ss by applying the heapifyDown() method from its root. The Las Vegas sort has complexity O(n n ). There are n! different permutations of a deck of n cards. Shuffling them is equivalent to selecting one permutation at random. Only one of the n! permutations leaves the cards in order. So the expected number of random shuffles required before the correct one occurs is n!/2. Then each permutation takes n 1 comparisons to see if it is the correct one. So the total complexity is O(n n!/2). By Stirling s Formula (page 325), O(n n!/2) = O(n!) = O(2 n ).

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3.15 Discuss the concept of a memory hierarchy whereby memory closer to the CPU is faster, more expensive, and smaller than memory at the next level. Arrange the different types of memory we have discussed in such a hierarchy. The smallest, fastest, most expensive memory locations are the registers on the CPU. Adjacent to the CPU are cache memories that are smaller, faster and more expensive than main memory, but larger, slower, and less expensive than the set of registers. The next level in the memory hierarchy is main memory, which modern machines have in some abundance, often measured in gigabytes. After main memory, the next level in the memory hierarchy is mass storage, today almost always on magnetic disk drives. Such memory is more expansive, less expensive per byte, and slower than main memory. Beyond magnetic disks, optical disk memory today represents the next step in the memory hierarchy, with lower costs, higher densities, and slower speeds.

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