CA HW1
3220104929 240918
- MTTF (Mean Time to Failure)
- MTTR (Mean Time to Repair)
- MTBF (Mean Time Between Failures) = MTTF+ MTTR
- Availability = (MTTF) / (MTTF+MTTR)
- 反映能用的时间占总时间的多少
1
a
由阿姆达尔定律，0.8 x 0.5 + 0.2 = 0.6，即所需时间为原来的0.6倍，为了频率也应降为原来的0.6倍
b
Capacitive load不变，电压和频率变为原来的0.6倍，核心变为2个，所以现在的能耗为原来的 2 x 0.6^2 x 0.6 = 0.432 倍
c
设 \(x\) 为电压达到 voltage floor 时得可并行比例，则有 1 - \(x\) + (1/2)\(x\) = 0.3
得 \(x\) = 1.4
很明显，双核情况下得电压不可能达到 voltage floor
d
假设任务全部都可并行，则电压值与频率均变为原来的 0.5 倍
则能耗为原来的 2 x 0.5^2 x 0.5 = 0.25 倍
2
MTTF = total # hours all computers work / # computers failed
Let \(x\) be the average amount of time the system runs until 1/3 of all computers fail
MTTF of each computer = 30 =10000\(x\) / (10000 x 1/3)
得 x = 10 days
即 MTTF of the system = 10 days
3
Briefly explain the meaning of Moore's Law.
摩尔定律是一个经验定律，其预测计算机处理器的性能每 18 个月就能翻一倍，同时价格降低一半
4
Briefly explain the meaning of Amdahl's Law.
阿姆达尔定律也是一个经验定律，用于估计一个计算任务由部分优化所带来的整体优化效果，这种优化手段通常为并行计算，下附其公式： $$ Speed_up = \frac{1}{1-p+p/n} $$ 其中，\(p\) 为可优化部分占整体的比例，\(n\) 为优化力度（就是 \(p\) 能被加快多少倍）
5
Briefly explain what parts are included in the ISA.
- 指令格式
- 寻址模式
- 数据类型
- 寄存器
- 中断与异常处理
- I/O
6
PPT上面的例题，fans 和 power supply 似乎有一个没算，是不是 fans 坏掉不会导致 failure
failure rate of the system = 10 * 1/1000000 + 1/500000 + 1/200000 + 1/200000 + 1/1000000 = 23/1000000
MTTF of the system = 1/failure rate of the system = 43478 hours
7
speedup = 1/(0.5 * 0.1 + 0.5) = 1.82
8
if decrease the CPI of FSQRT to 1.5
0.02 * (20-1.5) = 0.37 cycle
else
0.25 * (4*2) = 0.5 cycle
后者减少的 cycle 更多，故后者优化更好