Chapter 1 Computer Abstractions and Technology

1.1 Intro

Determines both the number of source-level statements and the number of I/O operations executed
Not in this class

Design for Moore’s Law
- integrated circuit resources double every 18–24 months
Use abstraction to simplify design
- lower-level details are hidden to offer a simpler model at higher levels
Make the common case fast
- Making the common case fast will tend to enhance performance better than optimizing the rare case
Performance via parallelism
Performance via pipelining
Performance via prediction
- it can be faster on average to guess and start working rather than wait until you know for sure
Hierarchy of memories
- cache, main memory, secondary memory
Dependability via redundancy
- we make systems dependable by including redundant components that can take over when a failure occurs and to help detect failures

c o s t p e r d i e = \frac{c o s t p e r w a f e r}{d i e s p e r w a f e r \times y e l d}

d i e s p e r w a f e r \approx \frac{w a f e r a r e a}{d i e a r e a}

y i e l d = \frac{1}{(1 + d e f e c t s p e r a r e a \times d i e a r e a / 2)^{2}}

Nonlinear relation to area and defect rate
- Wafer cost and area are fixed.
- Defect rate determined by manufacturing process
- Die area determined by architecture and circuit design

Response time(aka execution time): the time between the start and completion of a task
throughput(aka bandwidth): the total amount of work done in a given time

$p e r f o r m a n c e = \frac{1}{e x e c u t i o n t i m e}$
Computer X is
$n$ times faster than Y.

$\frac{p e r f o r m a n c e_{X}}{p e r f o r m a n c e_{Y}} = \frac{e x e c u t i o n t i m e_{Y}}{e x e c u t i o n t i m e_{X}} = n$

Response time, elapsed time or wall clock time
- Total time to complete a task
- System performance
CPU(execution) time
- The actual time the CPU spends computing a task
- Comprise user CPU time and system CPU time.
- CPU performance
Operation of digital hardware governed by a constant-rate CPU clock
- Clock period(週期): duration of a clock cycle
  - time per cycle
- Clock frequency(頻率): cycles per second
  - Hz
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C P U t i m e = C P U c l o c k c y c l e s \times c l o c k c y c l e t i m e = \frac{C P U c l o c k c y c l e s}{c l o c k r a t e}

Performance improved by
- Reduce number pof clock cycles
- Increase clock rate
- Hardware designer must trade off clock rate against clock cycle

c l o c k c y c l e s = i n s t r u c t i o n c o u n t \times C P I

C P U t i m e = i n s t r u c t i o n c o u n t \times C P I t i m e s c l o c k c y c l e t i m e = \frac{i n s t r u c t i o n c o u n t \times C P I}{c l o c k r a t e}

Instruction count for a program
- Determined by program, ISA and compiler
Clock cycles per instruction (CPI)
- Determined by CPU hardware
- If different instructions have different CPI, average CPI is affected by instruction mix.

If different instruction classes take different number of cycles

$c l o c k c y c l e s = \sum_{i = 1}^{n} (C P I_{i} \times i n s t r u c t i o n c o u n t_{i})$
Weighted average CPI

$C P I = \frac{c l o c k / c y c l e s}{i n s t r u c t i o n c o u n t} = \sum_{i = 1}^{n} (C P I_{i} \times \frac{i n s t r u c t i o n c o u n t_{i}}{i n s t r u c t i o n c o u n t})$

C P U t i m e = \frac{i n s t r u c t i o n s}{p r o g r a m} \times \frac{c l o c k c y c l e s}{i n s t r u c t i o n s} \times \frac{s e c o n d s}{c l o c k c y c l e}

Performance depends on
- Algorithm: affects instruction count (IC), possibly CPI
- Programming language: affects IC, CPI
- Compiler: affects IC, CPI
- Instruction set architecture: affects IC, CPI, clock rate

Admahl's Law

$T_{i m p r o v e d} = \frac{T_{a d d e c t e d}}{i m p r o v e m e n t f a c t o r} + T_{u n a f f e c t e d}$
collary: make the common case fast

MIPS (millions of instructions per second) does not account for
- Differences in ISAs between computers
- Differences in complexity between instructions
  
  $M I P S = \frac{i n s t r u c t i o n c o u n t}{e x e c u t i o n t i m e \times 10^{6}} = \frac{i n s t r u c t i o n c o u n t}{\frac{i n s t r u c t i o n c o u n t \times C P I}{c l o c k r a t e} \times 10^{6}} = \frac{c l o c k r a t e}{C P I \times 10^{6}}$
CPI varies between programs on a given CPU. CPI varies between programs on a given CPU.