Parallelism

Can we make it faster?

Apr 20, 2023

The RAM model

The RAM (Random Access Machine) model of computation assumes:

There is a single processing unit There is an arbitrarily large amount of memory Accessing any arbitrarily chosen (i.e. random) memory location takes unit

time

This simple model is very useful guide for algorithm design For maximum efficiency, “tuning” to the particular hardware is required

The RAM model breaks down when the assumptions are violated If an array is so large that only a portion of it fits in memory (the rest is on

disk), very different sorting algorithms should be used

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Approaches to parallelism The basic question is, do the processing units share

memory, or do they send messages to one another? A thread consists of a single flow of control, a program

counter, a call stack, and a small amount of thread-specific data Threads share memory, and communicate by reading and

writing to that memory This is thread-based or shared-memory parallel processing Java “out of the box” is thread-based

A process is a thread that has its own private memory Threads (sometimes called actors) send messages to one

another This is message-passing parallel processing

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The PRAM model An obvious extension to the RAM model is the Parallel Random

Access model, which assumes: There are multiple processing units There is an arbitrarily large amount of memory Accessing any memory location takes unit time

The third assumption is “good enough” for many in-memory sequential programs, but not good enough for parallel programs

If the processing units share memory, then complicated and expensive synchronization mechanisms must be used

If the processing units do not share memory, then each has its own (fast) local memory, and communicates with other processes by sending messages to them (much slower--especially if over a network!)

Bottom line: Because there seems to be no way to meet the unit time assumption, the PRAM model is seriously broken!

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The CTA model

The Candidate Type Architecture model makes these assumptions: There are P standard sequential processors, each with its own

local memory One of the processors may be acting as “controller,” doing things like

initialization and synchronization Processors can access non-local memory over a

communication network Non-local memory is between 100 times and 10000 times slower to

access than local memory (based on common architectures) A processor can make only a very small number (maybe 1 or

2) of simultaneous non-local memory accesses

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Consequences of CTA

The CTA model does not specify how many processors are available The programmer does not need to plan for some specific

number of processors More processors may cause the code to execute somewhat

more quickly The CTA modes does specify a huge discrepancy

between local and non-local memory access The programmer should minimize the number of non-local

memory accesses

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Costs of parallelism

It would be great if having N processors meant our programs would run N times as fast, but...

There is overhead involved in setting up the parallelism, which we don’t need to pay for a sequential program

There are parts of any program that cannot be parallelized Some processors will be idle because there is nothing for them to

do Processors have to contend for the same resources, such as

memory, and may have to wait for one another

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Overhead

Overhead is any cost incurred by the parallel algorithm but not by the corresponding sequential algorithm

Communication among threads and processes (a single thread has no other threads with which to communicate)

Synchronization is when one thread or process has to wait for results or events from another thread or process

Contention for a shared resource, such as memory Java’s synchronized is used to wait for a lock to become free

Extra computation to combine the results of the various threads or processes

Extra memory may be needed to give each thread or process the memory required to do its job

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Amdahl’s law

Some proportion P of a program can be made to run in parallel, while the remaining (1 - P) must remain sequential

If there are N processors, then the computation can be done in (1 - P) + P/N time

The maximum speedup is then 1 . (1 - P) + P/N

As N goes to infinity, the maximum speedup is 1/(1 - P)

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If P = 75%, what is the maximum speedup that can be achieved? (Remember, P is the proportion of the program than can be made to run in parallel.)

A. 2xB. 4xC. 8xD. 75xE. Depends on overhead

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2x 4x 8x75x

Depends on overh

ead

0% 0% 0%0%0%

Consequences of Amdahl’s law If 75% of a process can be parallelized, and there are four

processors, then the possible speedup is1 / ((1 - 0.75) + 0.75/4) = 2.286

But with 40 processors--ten times as many--the speedup is only1 / ((1 - 0.75) + 0.75/40) = 3.721

This has led many people (including Amdahl) to conclude that having lots of processors won’t help very much

However.... For many problems, as the data set gets larger,

The inherently sequential part of the program remains (fairly) constant Thus, the sequential proportion P becomes smaller So: The greater the volume of data, the more speedup we can get

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Idle time

Idle time results when There is a load imbalance--one process may have much less

work to do than another A process must wait for access to memory or some other

shared resource Data is registers is most quickly accessed Data in a cache is next most quickly accessed

A level 1 cache is the fastest, but also the smallest A level 2 cache is larger, but slower Memory--RAM--is much slower Disk access is very much slower

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Dependencies

A dependency is when one thread or process requires the result of another thread or process Example: (a + b) * (c + d)

The additions can be done in parallel The multiplication must wait for the results of the additions Of course, at this level, the hardware itself handles the parallelism

Threads or processors that depend on results from other threads or processors must wait for those results

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Parallelism in Java

Java uses the shared memory model There are various competing Java packages (such as Akka and

Kilim) to support message passing, but nothing yet in the official Java release

The programming language Erlang has developed the message passing approach

Scala is a Java competitor that supports both approaches Scala’s message passing is based on Erlang

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Concurrency in Java, I

Java Concurrency in Practice, by Brian Goetz, is the book to have if you need to do much concurrent programming in Java

The following 11 points are from his summary of basic principles

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1. It’s the mutable state, stupid!2. Make fields final unless they need to be mutable.3. Immutable objects are automatically thread-safe.4. Encapsulation makes it practical to manage the complexity.5. Guard each mutable variable with a lock.

Concurrency in Java, II

6. Guard all variables in an invariant with the same lock.

7. Hold locks for the duration of compound actions.

8. A program that accesses a mutable variable from multiple threads without synchronization is a broken program.

9. Don’t rely on clever reasoning about why you don’t need to synchronize.

10. Include thread safety in the design process—or explicitly document that your class in not thread-safe.

11. Document your synchronization policy.

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Models of concurrency

Shared memory model—as in Java. Actors

An actor is a lightweight thread with its own private memory Actors can send messages to one another Messages are received in an actor’s “mailbox” (a queue) Actors can monitor the health of other actors

STM, Software Transactional Memory A copy is made of the input data to a function The function is computed The input data is compared to the current values of that data

If nothing has changed, the function result is stored If the input data has changed, the result is discarded and the function is tried

again with the new data

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Functional programming In functional programming (FP):

A function is a value It can be assigned to variables It can be passed as an argument to another function It can be returned as the result of a function call There are much briefer ways of writing a literal function

Scala example: a => 101 * a A function acts like a function in mathematics

If you call it with the same arguments, you will get the same result. Every time. Guaranteed.

Functions have no side effects Immutable values are strongly emphasized over mutable values

Some languages, such as Haskell, don’t allow mutable values at all Computation proceeds by the application of functions, not by changing the

state of mutable variables

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Why functional programming?

Here are the three most important reasons that functional programming is better for concurrency than imperative programming: Immutable values are automatically thread safe Immutable values are automatically thread safe Immutable values are automatically thread safe

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Why not functional programming? Functional languages—Lisp, Haskell, ML, OCaml—have long

been regarded as only for ivory-tower academics Functional languages are “weird” (meaning: unfamiliar)

What’s happening now? Moore’s law has ended

Instead of getting faster processors, we’re now getting more of them Consequently, parallelism, and concurrency, have become much

more important After about ten years, CIS 120 is once again starting with

OCaml Python has gotten more functional Other languages are getting more functional Microsoft is starting to promote F# (based on ML?) Java 8 will have some functional features Scala is a hybrid object/functional language based on Java,

and is freely available now

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The End