Memory, Cache Locality, and why Arrays are Fast (Data Structures and Optimization)
Summary
TLDRThis 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
🚀 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.
💡 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.
Mindmap
Keywords
💡Data Structures
💡Arrays
💡Indexing
💡Contiguous Memory
💡Cache
💡Prefetching
💡Dynamic Arrays
💡Performance
💡CPU
💡Optimization
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
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