Chapter 1¶
1 Performance¶
- Define: Performance = 1 / Execution Time
Example
\[
Performance_x / Performance_y = Execution\ time_y / Execution\ time_x = n
\]
2 Quantitative approaches¶
2.1 CPU Performance¶
\[
CPU\ Execution\ Time = CPU\ Clock\ Cycles \times Clock\ Period
\]
\[
CPU\ Execution\ Time = \frac{CPU\ Clock\ Cycles}{Clock\ Rate}
\]
2.2 CPU Clocking¶
- Operation of digital hardware governed by a constant-rate clock
Note
2.3 CPU Time¶
\[
\begin{aligned}
CPU\ Time&= CPU\ Clock \ Cycles\times Clock\ Cycle\ Time\\
\ \\
&=\frac{CPU\ Clock\ Cycles}{Clock\ Rate}
\end{aligned}
\]
- Performance improved by
- Reducing number of clock cycles
- Increasing clock rate
- Hardware designer must often trade off clock rate against cycle count
Example
2.4 Instruction Count and CPI¶
- Instruction count
- Determined by program, ISA and compiler
- CPI
- Determined by CPU hardware
- If different instructions have different CPI
- Average CPI affected by instruction mix
-
\[ CPU\ CLock \ Cycles=Instructions for a Program \times Average\ Clock\ Cycles\ Per\ Instruction \]
-
\[ \begin{aligned} CPU\ Time&=Instruction \ Count\times CPI\times Clock\\ &=\frac{Instruction\ Count\times CPI}{Clock\ Rate} \end{aligned} \]
-
\[ \begin{aligned} Weighted\ average\ CPI&=\frac{Clock\ Cycles}{Instruction\ Count}\\&=\sum^n_{i=1}(CPI_i\times \frac{Instruction\ Count_i}{Instruction\ Count}) \end{aligned} \]
Example
2.5 Summary¶
\[
CPU \ Time = \frac{Instructions}{Program}\times \frac{Clock\ cycles}{Instruction}\times \frac{Seconds}{Clock\ cycle}
\]
- Performance depends on
- Algorithm:affects IC（总指令数）, possibly CPI
- Programming language: affects IC, CPI
- Compiler: affects IC, CPI
- Instruction set architecture: affects IC, CPI, \(T_c\)（时钟周期）
2.6 Amdahl's Law（阿姆达尔定律）¶
\[
Improved\ Eexcution\ Time=\frac{Affected\ Execution\ Time}{Amount\ of\ Improvement}+Unaffected\ Execution\ Time
\]
- Affected Execution Time：表示能通过加速模式得到改善的执行时间部分。
- Amount of Improvement：表示在加速模式下的性能提升量。
- Unaffected Execution Time：表示无法通过加速模式改进的执行时间部分。