The Memory HierarchyCache, Main Memory, and Virtual Memory

Lecture for CPSC 5155Edward Bosworth, Ph.D.

Computer Science DepartmentColumbus State University

The Simple View of Memory

• The simplest view of memory is that presented at the ISA (Instruction Set Architecture) level. At this level, memory is a monolithic addressable unit. This view suffices for all programming uses.

The Multi-Level View of Memory

• Real memory has at least three levels, each of which can be elaborated further.

• The fact that most cache memories are now multi-level does not change the basic design issues.

The More Realistic View

Generic Primary / Secondary Memory

• In each case, we have a fast primary memory backed by a bigger secondary memory.

• The “actors” in the two cases are as follows:• Technology Primary Secondary Block• Cache Memory SRAM CacheDRAM Main Cache Line

Memory• Virtual Memory DRAM Main Disk Page

Memory Memory• Access Time TP TS

(Primary (Secondary)Time) Time)

Effective Access Time

• Effective Access Time:TE = h TP + (1 – h) TS, where h (the primary hit rate) is the fraction of memory accesses satisfied by the primary memory; 0.0 h 1.0.

• This can be extended to multi-level caches and mixed memory with cache and virtual memory.

Examples: Cache Memory• Suppose a single cache fronting a main memory, which

has 80 nanosecond access time.• Suppose the cache memory has access time 10

nanoseconds.• If the hit rate is 90%, then

TE = 0.9 10.0 + (1 – 0.9) 80.0= 0.9 10.0 + 0.1 80.0 = 9.0 + 8.0 = 17.0 ns.

• If the hit rate is 99%, thenTE = 0.99 10.0 + (1 – 0.99) 80.0

= 0.99 10.0 + 0.01 80.0 = 9.9 + 0.8 = 10.7 ns.

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Memory Technology Static RAM (SRAM)

0.5ns – 2.5ns, $2000 – $5000 per GB Dynamic RAM (DRAM)

50ns – 70ns, $20 – $75 per GB Magnetic disk

5ms – 20ms, $0.20 – $2 per GB Ideal memory

Access time of SRAM Capacity and cost/GB of disk

§5.1 Introduction

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Principle of Locality Programs access a small proportion of

their address space at any time Temporal locality

Items accessed recently are likely to be accessed again soon

e.g., instructions in a loop, induction variables Spatial locality

Items near those accessed recently are likely to be accessed soon

E.g., sequential instruction access, array data

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Taking Advantage of Locality Memory hierarchy Store everything on disk Copy recently accessed (and nearby)

items from disk to smaller DRAM memory Main memory

Copy more recently accessed (and nearby) items from DRAM to smaller SRAM memory Cache memory attached to CPU

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Memory Hierarchy Levels Block (aka line): unit of copying

May be multiple words If accessed data is present in

upper level Hit: access satisfied by upper level

Hit ratio: hits/accesses If accessed data is absent

Miss: block copied from lower level Time taken: miss penalty Miss ratio: misses/accesses

= 1 – hit ratio Then accessed data supplied from

upper level

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Cache Memory Cache memory

The level of the memory hierarchy closest to the CPU

Given accesses X1, …, Xn–1, Xn

§5.2 The Basics of C

aches

How do we know if the data is present?

Where do we look?

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Direct Mapped Cache Location determined by address Direct mapped: only one choice

(Block address) modulo (#Blocks in cache)

#Blocks is a power of 2

Use low-order address bits

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Tags and Valid Bits How do we know which particular block is

stored in a cache location? Store block address as well as the data Actually, only need the high-order bits Called the tag

What if there is no data in a location? Valid bit: 1 = present, 0 = not present Initially 0

The Dirty Bit

• In some contexts, it is important to mark the primary memory if the data have been changed since being copied from the secondary memory.

• For historical reasons, this bit is called the “dirty bit”, denoted D.

• If D = 0, the block does not need to be written back to secondary memory prior to being replaced. This is an efficiency consideration.

The Cache Line Tag

• The primary and secondary memories are divided into equally sized blocks.

• Suppose a cache line size M = 2m bytes. This would be the size of a primary memory block.

• In an n-bit address, the lower m bits would be the offset in the block and (n – m) bits would identify the block.

• The upper (n – m) bits are the block address.

The Direct Mapped Cache

• Suppose that the direct mapped cache has K = 2k cache lines.

• The full memory address can be divided as:

• The lower k bits of the block address always determine the cache line.

• For this reason, these bits are not part of the tag.

Bits n – k – m k mCache View Tag Line OffsetAddress View Block Address Offset

Simple Example from the Text

• In this next example, each cache line holds only one entry. There are 8 = 23 cache lines.

• Consider 5 bit addresses.n = 5, k = 3, m = 0 (1 = 20).

• The tag thus has 2 bits.• NOTE: The number of entries in a cache

line and also the number of lines in the cache must both be a power of 2. Otherwise, the addressing is impossible.

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Cache Example 8-blocks, 1 word/block, direct mapped Initial state

Index V Tag Data000 N001 N010 N011 N100 N101 N110 N111 N

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Cache Example

Index V Tag Data000 N001 N010 N011 N100 N101 N110 Y 10 Mem[10110]111 N

Word addr Binary addr Hit/miss Cache block22 10 110 Miss 110

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Cache Example

Index V Tag Data000 N001 N010 Y 11 Mem[11010]011 N100 N101 N110 Y 10 Mem[10110]111 N

Word addr Binary addr Hit/miss Cache block26 11 010 Miss 010

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Cache Example

Index V Tag Data000 N001 N010 Y 11 Mem[11010]011 N100 N101 N110 Y 10 Mem[10110]111 N

Word addr Binary addr Hit/miss Cache block22 10 110 Hit 11026 11 010 Hit 010

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Cache Example

Index V Tag Data000 Y 10 Mem[10000]001 N010 Y 11 Mem[11010]011 Y 00 Mem[00011]100 N101 N110 Y 10 Mem[10110]111 N

Word addr Binary addr Hit/miss Cache block16 10 000 Miss 0003 00 011 Miss 01116 10 000 Hit 000

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Cache Example

Index V Tag Data000 Y 10 Mem[10000]001 N010 Y 10 Mem[10010]011 Y 00 Mem[00011]100 N101 N110 Y 10 Mem[10110]111 N

Word addr Binary addr Hit/miss Cache block18 10 010 Miss 010

Another Direct-Mapped Cache• Assume a byte-addressable memory with

32-bit addresses.• Assume 256 cache lines. As 256 = 28, 8 bits of

the address are used to select the cache line.• Assume each cache line holds 16 bytes. As

16 = 24, 4 bits of the address are used to specify the offset within the cache line.

• The main memory is divided into blocks of size 16 bytes, each the size of a cache line.

Fields in the Memory Address• Divide the 32–bit address into three fields: a 20–bit

explicit tag, an 8–bit line number, and a 4–bit offset within the cache line.

• Consider the address 0x00AB7129. It would haveTag = 0x00AB7Line = 0x12 Block Address = 0x00AB12Offset = 0x9

Bits 31 – 12 11 – 4 3 – 0Cache View Tag Line OffsetAddress View Block Address Offset

Associative Caches

• In a direct-mapped cache, each memory block from the main memory can be mapped into exactly one location in the cache.

• Other cache organizations allow some flexibility in memory block placement.

• One option for flexible placement is called an associative cache, based on content addressable memory.

Associative Memory

• In associative memory, the contents of the memory are searched in one memory cycle.

• Consider an array of 256 entries, indexed from 0 to 255 (or 0x0 to 0xFF).

• Standard search strategies require either 128 tries (unordered) or 8 tries (binary search).

• In content addressable memory, only one search is required.

Associative Search• Associative memory would find the item in

one search. Think of the control circuitry as “broadcasting” the data value to all memory cells at the same time. If one of the memory cells has the value, it raises a Boolean flag and the item is found.

• Some associative memories allow duplicate values and resolve multiple matches. Cache designs do not allow duplicate values.

The Associative Match

• This shows a single word in a 4-bit content addressable memory and the circuit to generate the match signal (asserted low).

The Associative Cache

• Again, a 32-bit address with 16-byte cache lines (4 bits for offset in cache).

• The number of cache lines is not important for address handling in associative caches.

• The address will divide as follows:28 bits for the cache tag, and4 bits for the offset in the cache line.

• The cache tags will be stored in associative memory connected to the cache..

The Associative Cache Line

• A cache line in this arrangement would have the following format for our sample address.

• Here we assume that the CPU has not written to the cache line, so the dirty bit is D = 0.

D bit V Bit Tag 16 indexed entries0 1 0x00AB712 M[0xAB7120] … M[0xAB712F]

Set Associative Cache

• An N–way set–associative cache uses direct mapping, but allows a set of N memory blocks to be stored in the line. This allows some of the flexibility of a fully associative cache, without the complexity of a large associative memory for searching the cache.

• Suppose a 4-way set-associative cache with16 bytes per memory block. Each cache line has 4 sets of 16, or 64 bytes.

Sample 2-way Set Associative

• Consider addresses 0xCD4128 and 0xAB7129. Each would be stored in cache line 0x12. Set 0 of this cache line would have one block, and set 1 would have the other.

Set 0 Set 1D V Tag Contents D V Tag Contents

1 1 0xCD4 M[0xCD4120] toM[0xCD412F]

0 1 0xAB7 M[0xAB7120] to M[0xAB712F]

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Associative Caches Fully associative

Allow a given block to go in any cache entry Requires all entries to be searched at once Comparator per entry (expensive)

n-way set associative Each set contains n entries Block number determines which set

(Block number) modulo (#Sets in cache) Search all entries in a given set at once n comparators (less expensive)

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Spectrum of Associativity For a cache with 8 entries

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Associativity Example Compare 4-block caches

Direct mapped, 2-way set associative,fully associative

Block access sequence: 0, 8, 0, 6, 8

Direct mappedBlock

addressCache index

Hit/miss Cache content after access0 1 2 3

0 0 miss Mem[0]8 0 miss Mem[8]0 0 miss Mem[0]6 2 miss Mem[0] Mem[6]8 0 miss Mem[8] Mem[6]

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Associativity Example 2-way set associative

Block address

Cache index

Hit/miss Cache content after accessSet 0 Set 1

0 0 miss Mem[0]8 0 miss Mem[0] Mem[8]0 0 hit Mem[0] Mem[8]6 0 miss Mem[0] Mem[6]8 0 miss Mem[8] Mem[6]

Fully associativeBlock

addressHit/miss Cache content after access

0 miss Mem[0]8 miss Mem[0] Mem[8]0 hit Mem[0] Mem[8]6 miss Mem[0] Mem[8] Mem[6]8 hit Mem[0] Mem[8] Mem[6]

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How Much Associativity Increased associativity decreases miss

rate But with diminishing returns

Simulation of a system with 64KBD-cache, 16-word blocks, SPEC2000 1-way: 10.3% 2-way: 8.6% 4-way: 8.3% 8-way: 8.1%

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Set Associative Cache Organization