Computer Memory and Data Access: Understanding Memory Architecture and Localities, Study notes of Data Structures and Algorithms

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Computer Memory

Data Structures and Algorithms

Warm Up

public int sum1(int n, int m, int[][] table) { int output = 0; for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { output += table[i][j]; } } return output; } public int sum2(int n, int m, int[][] table) { int output = 0; for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { output += table[j][i]; } } return output; } What do these two methods do? What is the big-Θ Θ(n*m)

Incorrect Assumptions

Accessing memory is a quick and constant-time operation

Sometimes accessing memory is cheaper and easier than at other times

Sometimes accessing memory is very slow

Lies!

Memory Architecture

CPU Register L1 Cache L2 Cache RAM Disk What is it? Typical Size Time The brain of the computer! 32 bits ≈free Extra memory to make accessing it faster 128KB 0.5 ns Extra memory to make accessing it faster 2MB 7 ns Working memory, what your programs need 8GB 100 ns Large, longtime storage 1 TB 8,000,000 ns

Memory Architecture

Takeaways:

• the more memory a layer can store, the slower it is (generally)
• accessing the disk is very slow

Computer Design Decisions

• Physics
  • Speed of light
  • Physical closeness to CPU
• Cost
  • “good enough” to achieve speed
  • Balance between speed and space

Locality

How does the OS minimize disk accesses?

Spatial Locality

Computers try to partition memory you are likely to use close by

• Arrays
• Fields

Temporal Locality

Computers assume the memory you have just accessed you will likely access again in the near

future

Leveraging Temporal Locality

When looking up address in “slow layer”

Once we load something into RAM or cache, keep it around or a while

• But these layers are smaller
  • When do we “evict” memory to make room?

Moving Memory

Amount of memory moved from disk to RAM

• Called a “ block ” or “ page ”
  • ≈4kb
  • Smallest unit of data on disk

Amount of memory moved from RAM to Cache

• called a “ cache line ”
  • ≈64 bytes

Operating System is the Memory Boss

• controls page and cache line size
• decides when to move data to cache or evict

Java and Memory

What happens when you use the “ new ”

keyword in Java?

• Your program asks the J ava V irtual

M achine for more memory from the

“heap”

• Pile of recently used memory
• If necessary the JVM asks Operating

System for more memory

• Hardware can only allocate in units of page
• If you want 100 bytes you get 4kb
• Each page is contiguous

What happens when you create a new array?

• Program asks JVM for one long, contiguous chunk of memory

What happens when you create a new object?

• Program asks the JVM for any random place in memory

What happens when you read an array index?

• Program asks JVM for the address, JVM hands off to OS
• OS checks the L1 caches, the L2 caches then RAM then disk to find it
• If data is found, OS loads it into caches to speed up future lookups

What happens when we open and read data from a

file?

• Files are always stored on disk, must make a disk access

Array v Linked List

Is iterating over an ArrayList faster than iterating over a LinkedList?

Answer:

LinkedList nodes can be stored in memory, which means the don’t have spatial locality. The

ArrayList is more likely to be stored in contiguous regions of memory, so it should be quicker to

access based on how the OS will load the data into our different memory layers.