慶應義塾大学
2016年度 春学期
コンピューター・アーキテクチャ
Computer Architecture
第7回 6月27日
Lecture 7, June 27: Memory: Caching and Memory Hierarchy
RIP,
Gene Amdahl. He was 92, and had been living with Alzheimer's for
several years. He passed away 2015/11/10.
Next Lectures
No lecture next Thursday! I will be here this Thursday and next Monday, but not next Thursday.
I lied to you! Do you know what lies I told? That's today's topic...
Outline of This Lecture
- Fast!
- Review: Processor Performance Equation
- Principle of Caching
- Manipulating Bitfields
- Basic Fixed-Block Size Cache Organizations:
Four Questions
- Cache Performance
- Six Cache Optimizations
- Okay, Why?
- Final Thoughts: The Full Memory Hierarchy
- Homework
Fast!
The five-stage pipeline we discussed last week is far from the only
way to divide the work in a pipeline. The Intel Prescott
microprocessor (which went into production in Feb. 2004) had
a thirty stage pipeline! Filling that pipeline takes some
serious time, so every branch is a problem.
Review: Processor Performance Equation
In the first lecture we saw the processor performance
equation:
| CPU time = |
(seconds
)/
program
|
= |
(Instructions
)/
program
|
× |
(Clock cycles
)/
Instruction
|
× |
(Seconds
)/
Clock cycle
|
All three terms are actually interdependent. We know that the last
term in that equation is the inverse of clock speed, and that clock
speed goes up as you deepen the pipeline (assuming a good pipeline
design). The first term depends on the instruction set design; after
the last three lectures, you should have a better feel for what that
involves, but it will rarely vary by more than a factor of two or so
between architectures. The interesting term for this lecture is the
middle one: what is the average clock cycles per instruction,
or CPI?
Principle of Caching
Cache: a safe place for hiding or storing things.
Webster's New World Dictionary of the American Language, Second
College Edition (1976)
A cache, in computer terms, is usually a "nearby" place where a
copy of "far away" data is kept. This caching behavior is done
for a fundamental reason: performance. There are many common types of
caches:
- DNS (Internet name server) caches
- Web caches
- File system caches
- CPU caches
In this lecture, we are primarily concerned with the last of these.
This is the point where I admit that last week I told a white lie: in
the MEM stage of the pipeline, results came back from memory in
one clock cycle. In reality, they don't. We need to discuss cache
hits and cache misses, hit time and miss
penalty.
With those values, we can determine the actual average CPI and
expected execution time for a program.
Manipulating Bitfields
We have now reached the point where it is imperative that you be
able to extract and manipulate individual bitfields from
larger words. I did some chalk board exercises last week,
today it's your turn.
Basic Fixed-Block Size Cache Organizations: Four Questions
Cache Performance
Above, we alluded to the change in system performance based on memory
latency. The figure above and Fig. 5.28 in the text give a hint as to
the typical latencies of some important memories:
- Register: 250psec, 1 clock cycle
- L1 cache: 1nsec, 1 to 4 clock cycles
- L2 cache: a few nsec, 7-23 clock cycles
- Main memory: 30-50nsec, 50-100 clock cycles!
This list should make it extremely clear that a cache miss
results in a very large miss penalty. The average memory
access time then becomes:
| Avg. memory access time | = |
Hit time +
Miss rate × Miss penalty
|
Let's review the MIPS pipeline that we saw last week:
In our simple model of its performance, we assumed memory could be
accessed in one clock cycle, but obviously that's not true. If the
pipeline stalls here waiting on main memory, worst case, performance
could drop by a factor of one hundred!
Fortunately, many processors support out of order execution,
which allows other instructions to complete while a load is waiting on
memory, provided that there is no data hazard.
It's obvious from that high miss penalty that cache hit rates must
exceed 90%, indeed, usually are above 95%. Even a small improvement
in cache hit rate can make a large improvement in system
performance.
Six Basic Optimizations
- Larger block size to reduce miss rate
- Larger caches to reduce miss rate
- Higher associativity to reduce miss rate
- Multilevel caches to reduce miss penalty
- Giving priority to read misses over writes to reduce miss
penalty
- Avoiding address translation during indexing of the cache to
reduce hit time
Okay, Why?
So far, we have taken it as more or less given that caches are
desirable. But what are the technological factors that force us to
use multiple levels of memory? Why not just use the fastest type for
all memory?
The principle reason is that there is a direct tradeoff between size
and performance: it's always easier to look through a small number of
things than a large number of things when you're looking for
something. In computer chips, it's also not possible to fit all of
the RAM we would like to have into the same chip with the CPU, in
general-purpose systems; you likely have a couple of dozen memory
chips in your laptop.
In standard computer technology, too, we have the distinction
of DRAM versus SRAM. DRAM is slower, but much denser,
and is therefore much cheaper. SRAM is faster and more expensive.
SRAM is generally used for on-chip caches. The capacity of DRAM is
roughly 4-8 times that of SRAM, while SRAM is 8-16 times faster and
8-16 times more expensive.
An SRAM cell typically requires six transistors, while a DRAM cell
requires only one. DRAMs are often read in bursts that fill
at least one cache block.
Whereas, in DRAM circuits, a single bit of memory requires only a
single transistor:
Final Thoughts: The Full Memory Hierarchy
We have talked about "main memory" and "cache memory", but in reality
memory is a hierarchy with a number of levels:
- Registers
- L1 (on-chip) cache
- L2 (on-chip) cache
- L3 (off-chip) cache
- Main memory
- Hard disk
- Tape
Ideally one would desire an indefinitely large memory capacity such
that any particular...word would be immediately available...We
are...forced to recognize the possibility of constructing a hierarchy
of memories, each of which has greater capacity than the preceding but
which is less quickly accessible.
A.W. Burks, H.H. Goldstine, and J. von Neumann,
Preliminary Discussion of the Logical Design of an Electronic
Computing Instrument (1946)
理想とは言えば、無限の容量を備え、いかなる語にも瞬時にアクセスできるよ
うな記憶装置が欲しい。しかし、現実には記憶装置をいくつかの階層にわけて
構成せざるをえない、この記憶階層とは、下の階層に行くほど容量が大きくな
るが、アクセスにはより時間がかかるような仕組みである。準備
A.W. Burks, H.H. Goldstine, and J. von Neumann,
Preliminary Discussion of the Logical Design of an Electronic
Computing Instrument (1946)
宿題
Homework
This week's homework (submit via SFS):
- Clearly we need more practice with hexadecimal notation and bit
fields. Assuming the above example of the AMD Opteron processor,
with 40-bit physical addresses, identify
the tag, index, and block offset of the
following addresses:
- 0x1000
- 0x1004
- 0x1044
- 0x1049
- 0x81231000
- 0xA1239004
- 0xA1239913
- Assume a system with a 1GHz system clock, only one level of cache,
and that L1 access is 1 clock cycle and main memory is 50 clock cycles.
- Plot the average memory access time as a function of
cache hit rate. Graph 0.1-1.0 and 0.9-1.0 as two separate graphs.
- Plot the expected completion time for one billion instructions
as a function of cache hit rate. Graph 0.1-1.0 and 0.9-1.0 as two separate graphs.
- At what cache hit ratio does average memory access time
double, compared to the average access time with 100% hit
ratio?
Or, in 日本語:
- 授業中で扱った40bitの物理アドレスを持つOpteron AMD processorの場合において，以下のアドレスのタグ，インデックス，ブロックオフセットを計算しなさい．
- 0x1000
- 0x1004
- 0x1044
- 0x1049
- 0x81231000
- 0xA1239004
- 0xA1239913
- 1GHzのシステムクロックでキャッシュをL1キャッシュのみ持つシステムで，L1キャッシュへのアクセスは1クロック，メインメモリへのアクセスには50クロックかかるとする．
- メモリアクセスタイムを，ヒットレートの関数でグラフを描きなさい．0.1-1.0, 0.9-1.0をに分けて二枚のグラフを描いて下さい。
- 10億命令を実行するのに必要な時間をヒットレートの関数で描きなさい．
- ヒットレートが100%のときと比較して、ヒットレートがいくつのときに平均のメモリーアクセスタイムは倍になりますか。
Next Lecture
No lecture next week! Will (probably) be rescheduled for Nov. 19.
Next lecture:
第9回 11月19日
Lecture 8, November 19: Memory: Virtual Memory （仮想記録）
Readings for next time:
- Follow-up from this lecture:
- P-H: 7.1-7.3
- H-P: Appendix C.1, C.2 and C.3, Section 5.3
- For next time:
Additional Information
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