Memory, Cache Locality, and why Arrays are Fast (Data Structures and Optimization)

Summary

This video script delves into the world of data structures, focusing on arrays and their optimization. It explains arrays as a contiguous block of memory, beneficial for fast access and iteration. The script also explores CPU caches, including L1, L2, and L3, and how they work in tandem with prefetching to enhance performance. It touches on the limitations of arrays, such as slow search times and the inefficiency of inserting or removing elements from the middle. The video promises further exploration of advanced data structures like hash tables, which are built on the foundation of arrays.

Takeaways

• 📚 The video introduces a new series on data structures and optimization, starting with arrays.
• 🔍 Understanding the internal workings of arrays is crucial for performance optimization.
• 🗃 Arrays are a way to store multiple items at once, accessible by their index, typically zero-indexed.
• 💾 Arrays use contiguous memory, meaning all elements are stored together in a single block of memory.
• 🏢 Memory is divided into slots, each with an address, allowing for direct access to any byte.
• 🔄 The CPU uses caches (L1, L2, L3) to store frequently accessed data quickly, reducing access time.
• 🔮 Prefetching is a technique where the CPU predicts future data needs and loads it into cache preemptively.
• 🚀 Caches are faster than main memory, and a cache hit is much quicker than a cache miss, which requires fetching data from main memory.
• 🔍 Operations on arrays are efficient due to their contiguous nature, which aligns well with CPU cache optimization.
• 🚧 Dynamic arrays can grow by allocating more memory initially and tracking the array's end, maintaining contiguous memory allocation.
• 🛑 While arrays are fast for certain operations, finding an element or inserting/removing from the middle or start can be slow and inefficient.

Q & A

What is the main topic of the video series?

The main topic of the video series is data structures and optimization, starting with an in-depth discussion on arrays.

Why is understanding what happens under the hood important for performance?

Understanding what happens under the hood is important for performance because it allows developers to make informed decisions about data structures and algorithms that can optimize their code execution speed.

What is an array and what is its basic property?

An array is a data structure used to store several items at once. Its basic property is the ability to look up individual elements by their index, typically starting with index zero.

What does 'contiguous memory' mean in the context of arrays?

In the context of arrays, 'contiguous memory' means that the memory allocated for the array is all together in one block with no gaps between the elements.

How does memory allocation work in terms of variable storage?

Memory allocation for a variable involves reserving a specific amount of space in memory, either on the stack or heap, based on the variable's data type and size.

What are the two strategies mentioned to save time when retrieving data?

The two strategies mentioned are: 1) Checking out the entire book instead of just a chapter to quickly access other chapters from the same book, and 2) Predicting the next data request based on current patterns and prefetching it.

What are the roles of L1, L2, and L3 caches in a CPU?

L1, L2, and L3 caches are levels of built-in memory in a CPU that store data to speed up access. The CPU checks these caches in order (from L1 to L3) when looking for data, with each level being slower but larger than the previous one.

Why are contiguous chunks of memory beneficial for CPU operations?

Contiguous chunks of memory are beneficial for CPU operations because they allow for faster access and processing. The CPU can efficiently iterate over or access elements in a contiguous block without incurring additional memory access costs.

What is prefetching and how does it relate to CPU operations?

Prefetching is a technique where the CPU predicts future memory access patterns and loads data into the cache before it is explicitly requested. This helps to reduce latency and improve performance by having the data readily available when needed.

What are the limitations of arrays when it comes to finding, inserting, or removing elements?

Arrays have limitations in finding elements as it requires checking each element one by one. Inserting or removing elements from anywhere except the end is also inefficient, as it may require shifting elements to maintain the array's order, which can be time-consuming for large arrays.

How do dynamic arrays accommodate more items?

Dynamic arrays accommodate more items by allocating more memory than initially needed and keeping track of the array's end. This allows the array to grow without the need for re-allocation and copying of the entire array.

Why are arrays foundational to understanding more advanced data structures?

Arrays are foundational because many advanced data structures, such as hash tables, are often implemented using a combination of arrays and other structures like linked lists. Understanding arrays helps in grasping the basic principles that are extended in more complex data structures.

Outlines

00:00

🚀 Introduction to Data Structures and Arrays

This paragraph introduces a new series on data structures and optimization, focusing on arrays. It emphasizes the importance of understanding how arrays work for better performance in programming. Arrays are described as a way to store multiple items efficiently, with the ability to access elements by their index. The explanation delves into the concept of contiguous memory allocation in arrays, which is crucial for performance. It also sets the stage for discussing how computers optimize memory access through caching mechanisms.

05:02

💡 Understanding Memory and CPU Caching

This paragraph explores the inner workings of memory and CPU caching to explain why certain operations are faster than others. It uses an analogy of a library assistant to illustrate the concept of caching, where checking out an entire book (cache) can save time when multiple chapters are needed. The paragraph then explains the hierarchical structure of CPU caches (L1, L2, L3) and how they work to speed up memory access. It also introduces the concept of prefetching, where the CPU predicts and loads data before it's explicitly requested, based on patterns of memory access.

Keywords

💡Data Structures

Data structures are specialized formats for organizing, storing, and manipulating data. They are fundamental to computer science and software development. In the video, data structures are introduced as a series of topics that will be explored for optimization purposes, starting with arrays. The script mentions that understanding arrays and their properties is crucial for performance, indicating their importance in the data structures series.

💡Arrays

An array is a data structure that stores a collection of elements, typically of the same type, in a contiguous block of memory. The script explains arrays as a way to store multiple items at once, emphasizing their property of being indexed for quick access. Arrays are central to the video's theme of optimization and performance because of their contiguous nature, which aligns with how CPUs efficiently access memory.

💡Indexing

Indexing refers to the method of accessing elements in an array using numerical indices. The script explains that arrays are zero-indexed, meaning the first element is accessed with index zero. This concept is essential for understanding how arrays facilitate quick data retrieval, which is a key point in the video's discussion on performance.

💡Contiguous Memory

Contiguous memory describes a block of memory where all the allocated space is in a single, unbroken sequence. The script uses the analogy of a 'big lump' of memory to explain how arrays are stored in a way that is beneficial for performance. CPUs can efficiently access contiguous memory, which is why arrays are fast for certain operations.

💡Cache

A cache is a small, fast memory storage used to store copies of frequently accessed data from main memory. The script discusses L1, L2, and L3 caches, which are levels of cache memory built into CPUs. Caches are relevant to the video's theme as they play a significant role in optimizing data access speed, illustrating the concept of prefetching and cache lines.

💡Prefetching

Prefetching is a technique where a system predicts and loads data into cache before it is explicitly requested. The script uses the analogy of predicting what a person will want to watch next on TV to explain how CPUs use prefetching to improve performance. This concept ties into the video's focus on optimization by showing how data can be accessed more quickly.

💡Dynamic Arrays

Dynamic arrays are arrays that can resize to accommodate a changing number of elements. The script mentions that dynamic arrays are implemented by allocating more memory than needed and tracking the array's end. This concept is important in the video as it shows how arrays can adapt to varying data sizes, which is a consideration in optimization.

💡Performance

Performance in the context of the video refers to the efficiency and speed of data operations, particularly how quickly data can be accessed and manipulated. The script discusses various aspects that affect performance, such as cache usage, prefetching, and the contiguous nature of arrays, all of which are central to the video's theme of optimization.

💡CPU

CPU, or Central Processing Unit, is the primary component of a computer that performs the basic arithmetic, logic, controlling, and input/output (I/O) operations. The script mentions the CPU in relation to caches and prefetching, highlighting its role in optimizing data access and processing speed, which is a key aspect of the video's exploration of data structures and optimization.

💡Optimization

Optimization in the video refers to the process of making data structures and algorithms run more efficiently or use fewer resources. The script discusses optimization in the context of understanding and improving the performance of arrays, caches, and prefetching, which are all techniques used to optimize data access and processing.

Highlights

Starting a new series on data structures and optimization with a focus on arrays.

Understanding arrays' inner workings is crucial for performance.

Arrays allow for the storage of multiple items at once.

Arrays are typically zero-indexed, enabling individual element access via index.

Memory is contiguous in arrays, meaning all elements are stored together.

Explains the concept of contiguous memory and its advantages.

Computer memory is divided into addressable slots for byte storage.

CPUs have built-in memory in the form of L1, L2, and L3 caches for faster data access.

Caches work by checking for data in a sequence from L1 to L3 before main memory.

Cache hits are much faster than accessing data from main memory.

CPU prefetching predicts and loads data before it's requested, enhancing performance.

Dynamic arrays can grow by allocating extra memory and tracking the end.

Arrays are contiguous, making operations like iteration very efficient.

Accessing random elements in an array is fast due to direct address calculation.

Appending or removing items from the end of an array is efficient.

Finding, inserting, or removing items from the middle or start of an array is inefficient.

Advanced data structures like hash tables are built upon the foundation of arrays.

Upcoming topics will include linked lists and their relationship with arrays.

Transcripts

why does the code on the top run 10

times faster than the code on the bottom

watch this video and find out today

we're starting a new series on data

structures and

optimization and we'll start by talking

about arrays

or the array data structure having an

understanding of what's happening under

the hood is super important for

performance

so we'll be going into depth on what

arrays are the cool things your computer

does to make things faster

we'll talk about why arrays are fast and

when they're not and if you stick around

to the end we'll talk about how this

fits into what's coming up next

what are arrays to put simply they're a

way of storing several items at once

typically in code you'll have a

situation like this where you want to

store some random

crap i might want to declare some items

like

float prices equals 199 299 etc etc

this is the c plus syntax or in

javascript it'll look something like

const price equals 199 299

you get the you get the idea now here in

the code

prices is my array and i've got three

items in the array

and generally the property of arrays is

that you can look up individual elements

in the array by their index

typically arrays are zero indexed

meaning the first element starts with

index zero

so if i want to refer to the first

element its price is at zero

and then the second is prices at one and

so on what does this have to do with

memory

so now when i talk about arrays i'm

going to be talking about them

in the sense of c plus or c sharp or a

language like that where they're the

exact same type of items be it an array

of floats

integers or complex structs and the

memory is contiguous

so what's a contiguous array when we're

talking about a contiguous array what we

mean is that the memory for the array is

all together in one big lump

if you're not quite sure what that means

recall how memory works

now this is a simplified view of how

memory works on your computer

you've got this giant block of data i'll

draw this big rectangle that represents

memory on your computer

and it's divided up into billions and

billions of these slots that fit a

single byte

each slot has an address which is

incrementing from one to the next

in the same way that houses on streets

have addresses which means that every

byte in memory

is addressable by its address when you

allocate a variable what you're doing is

allocating space for your variable

somewhere in memory be it on the stack

or heap for example

if i'm allocating space for a single

32-bit float

that's 32 bits or 4 bytes so we get this

little block of memory here

so a contiguous block of memory would

mean that let's say i allocate a big

chunk of memory

it would mean that all of the bytes for

the memory i requested are consecutive

with no gaps between them

and non-contiguous would mean that it's

fragmented between different places and

memory

so maybe a little here and a little

there with spaces in between

it's the difference between having a

coal cookie or a fragmented one

all good so far let's talk about some of

the cool things your computer

does for you but to do that we're going

to take a step back

and walk through a real world problem

let's say that you're my assistant

i work on big important things and i ask

you to look up something for me let's

say it's a chapter in a book

so you head to the library look up the

book copy the chapter

and bring it back to me job done then i

ask you for something else

maybe the next chapter in general if

your job is to head to the library and

get crap for me

how can you save some time there's two

easy strategies you can employ

the first is instead of just copying the

chapter i want

you could have just checked out the

entire book that way

once you get back to the office if i ask

you for something else and it happens to

be in the same book

well job done you get it back to me in a

fraction of the time

this is what the l1 l2 l3 caches are for

another thing you can do is try to

predict what i will want next

if you can see that i'm binge watching

seasons of rick and morty

and i'm on season 2 you can predict i'll

need season 3 really soon

and get it before i even ask this is

prefetching

the l123 caches when you go to buy a

computer

for example let me head over to the

apple website and i'll just click on the

macbook pro

option i don't actually own one of these

they're super expensive and i'm super

cheap

but i like looking at them anyway here

in the tech specs section you can find

mention of the size of the l3 cache

over here on the amd website i can find

mention of the l1 and l2

caches as well so what are these and how

do they work

most modern cpus come with a bit of

built-in memory in the form of these

caches

and there's often an l1 and an l2 cache

and usually an l3 cache as well

this is basically super ultra fast

memory that the cpu can use to save

things

when you do a read from memory you don't

just pull a single byte or whatever it

is that you asked for from memory

what actually happens is a whole

sequence of operations

starting at the cpu it goes and checks

the l1 cache

then the l2 cache then finally the l3

cache

looking for the data you're requesting

each of these is successfully costlier

to fetch from

but also each of these is successfully

bigger and of course

they're all way way faster than getting

it from main memory

and if at one of these stages you get a

cache hit like let's say the data was in

l1

already or maybe it missed l1 but you

hit l2

great you return the data and move on

with your life if you get a cache miss

that means that you have to reach all

the way out to main memory

which is pretty costly on the order of

at least 100 times more costly than

having it immediately available

at that point instead of just pulling in

that small bit of data you asked

it pulls in what's called a cash line

which is 64 bytes

which is why on subsequent requests you

may get a cash hit

you see the whole 64 bytes was cash

somewhere and so

you don't have to request it

specifically now but wait there's more

remember i mentioned that you might also

try to predict what

i'm going to watch next based on what

i'm watching now well

guess what the cpu does for you there's

a prefetcher unit that fills that exact

same role

it lives sort of between the cpu and the

caches looking at what you request from

memory

the exact details of how any given

hardware prefetch is implemented

is totally vendor specific and obviously

complex

but the gist of it is that if your

memory accesses follow an easy

recognizable pattern

for example you're iterating over the

array one by one

or with a constant stride that works too

then what happens is the hardware can

pull memory into the cache that you

haven't specifically requested yet and

when you do use it

cache it what does any of this have to

do with arrays

if anything we're almost there but first

one last quick tangent dynamic arrays

these are arrays that can grow to

accommodate more items

and these are just implemented really

simply by allocating more memory than

you needed to begin with

and keeping track of where the end of

the array is

that's all there's still contiguous

chunks of memory and we'll be talking

about dynamic arrays at this point

they're practically the same thing for

our purposes okay again what does this

have to do with arrays

arrays are contiguous chunks of memory

cpus love operating on contiguous chunks

of memory

which is why operations like say

iterating over a list

they're super fast pretty much can't

give the cpu a better scenario

accessing elements randomly is also

pretty fast

accessing a random element just involves

a memory read since you can calculate

the address trivially from the start of

the array

although you'll probably incur cash miss

but that's not a big deal

and appending items to an array assuming

that you have space

or removing them from the end of an

array is super fast

it should be somewhat obvious that it

just involves copying or removing a

single thing

so what sucks it's not particularly

difficult to run into scenarios where

arrays are pretty bad

finding an element in an array is slow

since you kind of have to check every

element one by one

this might not be a big deal when you

have a small array but imagine you have

billions

you want some way to do it faster so

finding sucks

also inserting or removing items from

anywhere except the end

it gets progressively slower and slower

the closer you are to the start of the

array

and it's not hard to see why here's your

array as a big rectangle and i'll just

go ahead and dump a bunch of numbers in

there

and now you want to remove the second

last item well that's not the end of the

world

you simply copy the last item into that

spot and then mark the array as being a

little bit smaller

job done but if you have to do an

operation at the beginning

you can kind of see where this is going

let's say you have to remove the first

item

well this is going to suck because i

have to move every single item in the

array

over by one how do we make this better

this is where more advanced data

structures come in

but it's not actually possible to

understand more advanced ones without a

solid basis in arrays

funnily enough they're foundational for

example

hash tables these are often implemented

as a combination

of arrays and linked lists so yeah you

might be able to understand what a hash

table does

but not how it does it anyway we'll

follow up this with linked lists in the

future

so stay tuned for that hope you enjoyed

this and learned something in the

process

cheers