02.Performance Evaluation and Metrics

Pipeline CPI = Ideal pipeline CPI + Structural Stalls + Data Hazard Stalls Ideal pipeline CPI: measure of the maximum performance attainable by the implementation

Performance Evaluation and Metrics

$IC=\text{\# instructions}$

$CPI=\frac{\text{CC}}{\text{IC}}=\frac{\text{clock cycle}}{\text{\# instructions}}$

$MIPS=\frac{\text{clock frequency}}{CP{I}^{\ast }10^6}$

Ahmdal’s law , this doesn’t tell anything on the performance of the CPU still depends on its frequency.

$\text{SPEED UP}=SU=\frac{1}{1-\text{(fraction enhanced)}+(\frac{\text{fraction enhanced}}{S{U}_{\text{fraction enhanced}}})}$

To sum up, Amdahl’s law states that, for a fixed problem, the upper limit of speedup is determined by the serial fraction of the code → strong scaling

Gustafson law revises it:

$S{U}_{GUS}=\frac{1}{\text{sequential}+\frac{\text{parallel}}{N}}$

$X$ is $n$ times faster than $Y$ means:

$\frac{\mathrm{Performance}(X)}{\mathrm{Performance}(Y)}=\frac{\mathrm{Exe}(Y)}{\mathrm{Exe}(X)}$

The $\text{CPU time}$ can be computed like this:

so, $X$ is $n$ times faster than $Y$ means:

$\frac{EX{E}_{CP{U}_1}}{EX{E}_{CP{U}_2}}=\left(\frac{I{C}_1\ast CP{I}_1}{F_1}\right)\ast \left(\frac{F_2}{I{C}_2\ast CP{I}_2}\right)$

Floating-point operations per second (FLOPS) is a measure of compute performance used to quantify the number of floating-point operations a core, machine, or system is capable of in a one second.

$\text{Pipeline Speedup}=\frac{\text{Pipeline Depth}}{\text{1 + Pipe Stall Cycles per Instruction due to Branches}}$

$\text{Pipeline Speedup}=\frac{\text{Pipeline Depth}}{\text{1 + Branch Frequency * Branch Penalty}}$