The 20th-anniversary rerelease of Grease slid into multiplexes earlier this year, and we’re still hopelessly devoted to Olivia Newton-John. To be sure, the Aussie-bred 49-year-old has a few tiny lines around her Pacific-blue eyes, but her flawless complexion and the bright smile that made wholesome hot in the halls of Rydell High still radiate youth. “Olivia looks better now than she did then,” says Grease producer Allan Carr. “You can’t believe her chronological age in comparison to how she looks.”
But she has learned a lot in the last two decades. A high-profile spokeswoman for breast cancer awareness, Newton-John, a survivor of the disease who was diagnosed and treated in 1992, says that her experience has “affected me on every level. I think it has made me appreciate the day, no matter what the day is.” Though she tries to stick to a diet of mainly tofu, veggies and rice, she has relaxed her once-obsessive ways. “I think if you’re fanatical, you don’t enjoy life,” she says. “I’ll eat red meat on occasion if my body tells me I need it. I was vegetarian for a number of years, and I got very weak on it. It obviously wasn’t right for my body.”
Some things that are right include sunblock and eye cream. And the 5’6″ Newton-John, whose first album in four years, the country-flavored Back with a Heart, comes out this month, soaps up her fine features twice a day. “I had pimples into my 20s,” she says, “and I still get them occasionally. No matter how tired I am, or how late it is, I’ll always wash my face before going to bed.”
Divorced since 1995 from actor Matt Lattanzi, Newton-John lives with daughter Chloe, 12, on the beach in Malibu, where she runs daily through the nearby hills with her three dogs to keep her figure trim. But she credits nature for keeping her young. “I think it’s just genetics,” she says. “My mom [Irene, 84, a former corporate publicist] still looks good.” With the big five-o looming in September, she says, “The way I’m looking at it is, ‘Wow, I got to 50, and I feel good and I look reasonably good.’ ” And with Sandy-style exuberance, she adds, “I’m going to party around the world!”
When Caleb and Liam Nelson were just 5 and 3 years old, the brothers wanted to do something to help their 2-year-old sister, Sophie. They knew she had something wrong with her that meant she had to see a lot of doctors, so they worked with their parents to start a lemonade stand to raise money to help find a cure for her condition.
“We scrambled to throw it together,” says their dad, David Nelson, 37. “But we didn’t have any lemonade. We did have sweet tea though, and that’s Sophie’s favorite, so we did a sweet tea stand.”
The family made $125 from that first sweet tea stand that was set up on their front lawn in Mint Hill, North Carolina, in 2016.
“Sophie has NF,” Caleb tells PEOPLE. “We try to raise money so that doctors can try to figure out how to make a medicine to cure kids with NF.”
Sophie, now 5, was diagnosed with neurofibromatosis (or NF) when she was just a 2 years old. The genetic disease causes tumors to grow all over the body – inside and out. Sophie Nelson looks like most other girls her age, but if you look closely, you’ll see she has more than 20 birthmarks all over her face and body.
Sophie’s pediatrician initially thought the birthmarks were tumors. Now they know they’re birthmarks and they’re continuing to monitor Sophie for tumors.
“We knew nothing about anything and we cried for two days,” she says. “All we had was this black and white the pamphlet with a little bit of information so we Googled it.”
They learned that Sophie can basically develop a tumor anywhere there is a nerve ending — and some of the tumors can be dangerous, even potentially deadly.
For now, Sophie’s parents consider themselves lucky. “She’s only 5 so we don’t really know what it will mean,” says David. “Right now there are things that can make her life a little difficult but nothing super scary. The tumors are generally not cancerous, but they can be. We have friends with NF kids who didn’t make it to 10.”
Right now, the family is focused on awareness and they’ve found a fun way to get all three of their kids and other families across the country involved.
It started when Caleb came home from school with the Guinness World Records book as his reading assignment when he was in the first grade.
“He said ‘Sweet Tea for Sophie’ should have a word record,” David recalls. “And what else can we say but sure?”
That first year, friends and family hosted 40 stands in seven states raising $7,000. But they didn’t set a record.
“It took Guinness a year to get back to us and it turns out they’re really not interested in this type of world record,” David says while laughing.
“Our goal now is to have a sweet tea stand in every zip code I think we have about 43,000 to go and that’s the fun of it. As we fill in the map, that means that awareness about NF is spreading across the country – that’s the new mission,” David tells PEOPLE.
In the two years since they started, they’ve raised more than $16,000 from neighborhood sweet tea stands with all the money going to the Children’s Tumor Foundation. This May 19, they’re once again asking people across the country to host “Sweet Tea for Sophie” stands.
Caleb says, “Sweet Tea for Sophie is really important to us because it helps our sister. We want our sister to be healed and we don’t want her to have NF anymore…we love her.”
Adds Shanna, “We can’t make any promises to Sophie about what her future holds, but we can make sure she is surrounded by love and then we’ll face everything else as it comes.”
We studied how to write a fast matrix-multiplication algorithm on an abstract machine with a 2-level memory hierarchy, and then on the RS6000/590. We did this in order to illustrate several more general points:
To get full speed out of the architecture, one must exploit parallelism, pipelining, and locality. These are ubiquitous issues at all levels of parallel computing, not just the very low level of the RS6000/590 CPU and cache. We will see them throughout the semester.
Since it is a challenge, one should try to use a higher level building block (such as IBM's ESSL library) that has already dealt with these issues and hidden them from the user. We will discuss many other such building blocks, at different levels of abstraction, during the semester.
Using such a higher level building block effectively often requires reorganizing existing algorithms or designing new ones. We will illustrate this later with the example of Gaussian elimination, which is very natural to express in term of saxpys or matrix-vector products, but takes some effort to reorganize to use matrix-matrix multiplication.
Just as it is difficult to juggle parallelism, pipelining and locality, it is also a challenge to reorganize algorithms in the way just suggested. We cannot yet expect compilers to do this automatically for us in all cases (although a great deal of work has been done on dense linear algebra computations in particular). Building software tools (such as compilers, libraries, and run-time systems) to aid parallelization is an active research area, which we will discuss at length during the semester. Building these tools requires a knowledge of low-level architectural details, such as we discussed for the RS6000/590.
If your goal is to parallelize your code as with as little effort as possible, you would want to use an appropriate parallelization tool that hides low-level details. But since few effective tools are currently available, you cannot yet avoid knowing some low-level details, if you hope to get good performance. Since very few people are equally knowledgeable about all the topics needed to successfully parallelize a large application (namely the application area itself, the mathematics of algorithms, and computer science), it is often effective to work in interdisciplinary teams, consisting of applications scientists, mathematicians and computer scientists. A good team member is an expert in one topic shares a common language with other team members, and appreciates the challenges and opportunities at other levels. One goal of this course is to give you the experience of working in such interdisciplinary teams.
This explains our detailed look at the RS6000 architecture. We will not look at other architectures in nearly as much detail, but just at those parts which help us write good parallel code.
A block diagram of a "generic parallel computer" with p processors is shown below. We will expand on this basic picture as time goes on, but for now imagine each processor Proc_i executing some program, sometimes referring to data stored in its own memory Mem_i, and sometimes communicating with other processors over the Interconnection Network. This picture is sufficiently abstract to include the case where the entire parallel computer resides in one "processor" (as is the case with the dual floating point units in the RS6000/590) where the parallel computer sits in one room (the IBM SP-2 -- which consists of multiple RS6000s -- or most other commercial parallel computers), or where the parallel computer consists of computers spread across continents, and the interconnection network is the Internet, telephone system, or some other network.
There are three standard functions any parallel architecture must provide. We will discuss particular implementations of these functions later.
Synchronization, such as getting processors to ``agree'' on the value of a variable, or a time at which to start or stop.
A programming model is the interface provided to the user by the programming language, compiler, libraries, run-time system, or anything else that the user directly "programs". Not surprisingly, any programming model must provide a way for the user to express parallelism, communication, and synchronization in his or her algorithm.
Historically, people usually designed a parallel architecture, and then a programming model to match it. In other words, the programming model expressed parallelism, communication and synchronization in a way closely tied to the details of the architecture. As a result, when the machine became obsolete and new ones were built, all the programs written for it became obsolete as well, and users had to start from scratch. This did not exactly encourage widespread adoption of parallel programming.
In the meantime, people have realized that it is possible and valuable to build programming models independently of architectures, to let people build up useful bodies of software that survive generations of machine architectures. This implies that we will view the systems we program as consisting of layers, with the programming model at the top, the machine at the bottom, and the compiler, libraries, and so on providing a mapping from the programming model to the machine, that hides machine details.
For example, Connection Machine Fortran (CMF) was orginally designed for the Thinking Machines CM-2, and provided a programming model (called data parallelism below) closely suited to the CM-2 architecture. In particular, the CM-2 essentially required every processor to execute the same instruction at the same time, a very limited form of parallelism (called SIMD below). The next generation CM5 was later designed to permit much more flexible parallelism (called MIMD below), but the CMF compiler was modified to continue to run CMF programs on the new architecture. So the programming model provided to the user (CMF) remained the same, but the mapping to the machine (the way the compiler generated code) changed significantly.
So the great benefit one gets for separating machines from programming models is the ability to write programs that run portably across several machines. The potential drawback is loss of performance, depending on how well the programming model can be mapped to a particular architecture. Not all programming models map equally well to all architectures, and there are many hard research questions left on to best implement these mappings. Therefore, existing compilers, libraries, and run-time systems are often incomplete, buggy, inefficient, or some combination of the three. Caveat programmor. When we study programming models later, we will spend some of our time on how these mappings work, so we can predict whether one parallel program is more efficient than another one for solving the same problem.
The following sections are organized as follows. First, we will discuss some standard ways in which parallel architectures provide parallelism, communication, and synchronization. Second, we will very briefly do the same for our programming models, pointing out how the programming models have "natural" architectures for which they were originally developed, even though they can be mapped to others. Subsequent lectures will look at these programming models in great detail. Third, we will present standard ways to measure the performance of parallel programs. Finally, we will discuss a set of sample applications called Sharks and Fish, that we will use to illustrate all these programming models.
The two main styles of parallelism are SIMD and MIMD, or single-instruction-multiple-data and multiple-instruction-multiple-data. This is old terminology, dating to Flynn's taxonomy of parallel machines in the 1960s. SIMD means performing the same operation (e.g. single instruction) on multiple pieces of data in parallel, and MIMD means performing arbitrary operations (e.g. multiple instructions) on different data at the same time. In the SIMD case, one can think of the generic parallel processor in the figure above as being augmented by another control processor, which at every cycle sends a common instruction to each Proc_i to execute. Examples of SIMD parallelism include the vector operations on a single processor Cray T-90 and earlier Cray vector machines; the Thinking Machines CM-2; and a single pipelined floating point unit in the RS6000/590, where the adder and multiplier must operate in a pipeline controlled by a single fused-multipy-add instruction. Examples of MIMD parallelism include almost every commercial parallel machine, where each processor may also be programmed as a standard sequential machine, running sequential jobs. Note that a particular machine can exhibit both SIMD and MIMD parallelism at different levels, such as a multiprocessor Cray T90. MIMD parallel is more flexible and more common than SIMD parallelism, which now usually appears within individual floating point or memory units.
In order to discuss communication, we must first discuss how an architecture names the different memory locations to which instructions must refer. Neither humans nor machines can communicate without a common set of names upon which they agree. Recall that the memory of a conventional (nonparallel) computer consists of a sequence of words, each of which is named by its unique address, an integer. A typical computer instruction will look like "load r1, 37", which says to load the word stored at memory address 37 into register r1. Examining the figure of a generic parallel computer above, we see that there are multiple memories Mem_i. The two major ways to name the memory locations of these multiple memories are called shared memory and distributed memory. With shared memory, each word in each memory has a unique address which all processors agree on. Therefore, if Proc_1 and Proc_3 both execute the instruction "load r1, 37", the same data from one location in one Mem_i will be fetched into register r1 of Proc_1 and register r1 of Proc_3. With distributed memory, Proc_1 would fetch location 37 of Mem_1 and Proc_3 would fetch location 37 of Mem_3. Therefore, to communicate on a shared memory machine, Proc_1 and Proc_3 merely need to load and store into a common address, such as 37. On a distributed memory machine, explicit messages must be sent over the communication network, and be processed differently than simple loads and stores.
On the market one can find both successful shared memory machines (click here for examples) and successful distributed memory machines (e.g. IBM SP-2, Intel Paragon, along with networks of workstations). Roughly speaking, shared memory machines offer faster communication than distributed memory machines, and they naturally support a programming model (also called shared memory) which is often easier to program than the programming model natural to distributed memory machines (called message passing). However, shared memory machines are harder to build (or at least more expensive per processor) than distributed memory machines, for large numbers of processors (more than 32, say, although this number is growing).
An important property of communication is its cost, which is essential to understanding the performance of a parallel program. Suppose we want to send n words of data from one processor to another. The simplest model that we will use for the time required by this operation is
We consider sending n words at a time because on most machines the memory hierarchy dictates that it is most efficient to send groups of adjacent words (such as a cache line) all at once. Latency (in units of seconds) measure the time to send an "empty" message. Bandwidth (in units of words/second) measures the rate at which words pass through the interconnection network. The form of this formula should be familiar: recall that the time to process n words by a pipeline of s stages, each stage taking t seconds, is
Thus, the intercommunication network works like a pipeline, "pumping" data through it at a rate given by bandwidth, and with a delay given by the latency for the first word in the message to make it across the network.
To give an order-of-magnitude feeling for the cost of communication, let us change units to measure latency and bandwidth in cycles and words per cycle, respectively. Recall that a cycle in the basic unit of time in which a computer does one operation, such as an add. On shared memory machines, where communication is fastest, latency may be hundreds of cycles. At the other extreme, a distributed memory machine consisting of a network of workstations running PVM over an Ethernet, latency may be O(10^5) cycles (this includes both hardware and software delays). In other words, in one communication the processor could instead of done anywhere from 10^2 to 10^5 other useful operations. The time per word (reciprocal of bandwidth) is typically much lower than the latency (O(10) to O(1000) MBytes/second), so it is often much more efficient to send one large message than many small one. We will see that the difference between a good parallel algorithm and a bad one is often the amount of communication they perform.
Some shared memory machines are constructed out of clusters of smaller shared memory machines. In this case, it is often faster to access memory located with the cluster, than memory in another cluster. Such machines are called NUMA machines, for NonUniform Memory Access, and require (at least) two latencies and two bandwidths (for nearby and remote memory) to model communication accurately.
Synchronization refers to the need for two or more processors to agree on a time or a value of some data. The three most common manifestations of synchronization (or lack of it) are mutual exclusion, barriers, and memory consistency. We discuss each briefly.
Mutual exclusion refers permitting just one processor access to a particular memory location at a time. To illustrate the need for such a facility, suppose we want to compute the sum s of p numbers x_i, where Proc_i has computed x_i. The "obvious" algorithm is for each processor to fetch s from the processor that owns it (say Proc_0), add x_i to s, and store s back in Proc_0. Depending on the order in which each processor accesses s on Proc_0, the answer could range from the true sum to any partial sum of the x_i. For example, suppose that we only want to add x_1 and x_2. Here are two unintended possibilities for the execution (the time axis is vertical, and we indicate the time at which each processor executes each instruction.
The loads and stores of s involve communication with Proc_0. The final value of s stored in Proc_0 is x_2, since this is the last value stored in s. If the two stores are reverse in time, the final value of s would be x_1. This is called a race condition, because the final value of s depends on the nondeterministic condition of whether Proc_1 or Proc_2 is slightly ahead of the other.
Mutual exclusion provide a mechanism to avoid race conditions, by allowing just one processor exclusive access to a variable. This is often implemented by providing a "test&set" instruction, which sets a particular word to a particular value, while fetching the old value, all without other processors being able to interfere. Later when we discuss programming models we will show how to solve the problem of adding numbers using the test&set instruction.
Barriers involve each processor waiting at the same point in the program for all the others to "catch up", before proceeding. This is necessary to make sure a parallel job on which all the processor had been cooperating is indeed finished. Barrier can be implemented in software using the test&set instruction above, but some architectures (like the CM-5) have special hardware for this.
Memory consistency refers to a problem on shared memory machines with caches. Suppose processors Proc_1 and Proc_2 both read memory location 37 into their caches. The purpose of caches is to eliminate the need to access slow memory when accessing commonly used data, like location 37. After reading and using location 37, suppose Proc_1 and Proc_2 then try to store new, different values into it. How will the differing views of memory held by Proc_1 and Proc_2 be reconciled? Which value will eventually make it back into main memory at location 37? Insisting that each processor have the same view of all memory locations at the same time, so that location 37 has a single value across the machine, seems very reasonable. This is called sequential memory consistency, because it is the same way memory looks on a sequential machine. But it is expensive to implement, because all writes must hit main memory, and update all other caches in the machine rather than just update the local cache. This expense has led some shared memory machine to offer weak(er) memory consistency models, which leave it to the user to program in such a way that these problems cannot occur. We discuss this later when we discuss programming models.
We give a very brief overview of our 4 major programming models for this course, how they let the user express parallelism, communication and synchronization, and how they map to particular architectures. Subsequence lectures will discuss these models in great detail.
Data parallelism means applying the same operation, of set of operations, to all the elements of a data structure. This model evolved historically from SIMD architectures. The simplest examples are array operations like C = A+B, where A, B and C are arrays, and each each entry may be added in parallel. Data parallelism generalizes to more complex operations like global sums, and to more complex data structure like linked lists. Communication is implicit, meaning that if a statement like C=A+B requires communication, because elements of the arrays A, B and C are stored on different processors, this is done invisibly for the user. Synchronization is also implicit, since each statement completes execution before the next one begins. Our main data parallel programming language will be Connection Machine Fortran (or CM Fortran, or simply CMF). A CMF manual is available in Volume 2 of the class reference material, or by typing cmview while logged in to rodin. CMF is quite similar to the more recently emerging standard High Performance Fortran, or HPF, which many manufacturers are supporting. We will use the sequential programming language Matlab (which runs on all workstations across campus) to prototype data-parallel codes, since it many similar to CMF in many ways. In addition to Matlab's own on-line help facility, a mini-manual is located in Volume 4 of the class reference material, or here. The recent sequential language Fortran 90 updates Fortran 77 to have similar array operations, as well as recursion, structures, limited pointers, and other more modern programming language features.
Message Passing means running p independent sequential programs, written in sequential languages like C or Fortran, and communicating by calling subroutines like send(data,destination_proc) and receive(data,source_proc) to send data from one processor (source_proc) to another (destination_proc). In addition to send and receive, there are usually subroutines for computing global sums, barrier synchronization, etc. Since it is inconvenient to maintain p different program texts for p processors (since p will vary from machine to machine), there is usually a single program text executing on all processors. But since the program can branch based on the processor number (MY_PROC) of the processor on which it executes,
different processors can run completely independently. This is called SPMD programming (single program multiple data). This programming model is natural for MIMD distributed memory machines, and is supported on the CM-5 in the message-passing library CMMD (not really an acronym). See Volume 1 of the class reference material for documentation. Two similar but more portable message passing libraries are PVM and MPI. Message-passing is the "assembly language programming" of parallel computing, often resulting in long, complicated, and error-prone programs. But it is also the most portable, since PVM and MPI do run (or will run) on all almost all platforms.
Shared memory programming with threads Shared memory programming with threads is a natural programming model for shared memory machines. There is a single program text, which initially starts executing on one processor. This program may execute a statment like "spawn(proc,0)", which will cause some other processor to execute subroutine proc with argument 0. Subroutine proc can "see" all the variables it can normally see according to the scoping rules of the serial language. The main program which spawned proc can later wait for proc to finish with a barrier statement, go on to spawn other parallel subroutine calls, etc. We will use two such programming models this semester. The first is C augmented with Solaris threads, running on a Sparc multiprocessor. The second is pSather, a parallel object oriented language designed and implemented locally at ICSI . A manual is also located in Volume 4 of the class reference material.
Split-C is a locally designed and implemented language which augments C with just enough parallel constructs to expose the basic parallelism provided by the machine. It includes features of data parallelism, message passing, and shared memory. Originally implemented for the CM-5, it has been ported to many machines, including all the platforms we will use this semester. A manual is located in Volume 4 of the class reference material.
In addition to the major programming languages listed above, we will mention other languages, libraries and run-time systems throughout the course.
The following is a list of ways we will use to measure the performance of a parallel program. We will use these criteria to measure the difference between a good parallel program and a bad one, or (See also section 4.1 of the book by Kumar et al, or click here for a gentler introduction.
Throughout these notes we will use p to denote the number of parallel processors available, and n to denote the problem size. For example, in the case of matrix multiplication, n may denote the dimension of the matrix. It would also be reasonable to measure problem size by the amount of input data, which would be the square of the matrix dimension for matrix multiplication. So it is important to be specific when defining n.
T(p,n) is the time to solve a problem of size n on p processors. Sometimes we omit n and write T(p).
T(1,n) or T(1) is the serial or sequential time, using the best serial algorithm. The best serial algorithm may not be the parallel algorithm with p set to 1, since the parallel algorithm may have unnecessary overheads.
Speedup(p) = T(1)/T(p) measures how much faster you go on p processors than 1 processor. A "speedup plot" is Speedup(p) plotted versus p. If you use a poor serial algorithm, T(1) and so Speedup(p) will be artificially large, and your parallel algorithm will look artificially good. (See the paper "Misleading Performance Reporting in the Supercomputing Field" by Bailey in Volume 6 of the class reference material.
Efficiency(p) = Speedup(p)/p. An "efficiency plot" is Efficiency(p) plotted versus p. A good algorithm will have an efficiency near 1.
It is a ``pseudo theorem'' that Speedup(p) <= p, or Efficiency(p) <= 1, because in principle one processor can simulate the actions of p processors in at most p times as much time, by taking one step of each of the p serial programs making up the parallel program, in a round robin fashion. This idea is due to Brent. Actually, we can sometimes get "superlinear speedup", i.e. Speedup(p)>p, if either
the algorithm is nondeterministic, and a different path is taken in the parallel algorithm than the serial algorithm (this happens in search problems and symbolic computing)
the problem is too large for one processor without hitting a slower level in memory hierarchy (eg paging or ``thrashing'') Our pseudo-theorem implies that if we plot the straight line "Speedup(p)=p" through the origin on a speedup plot, this will bound the true speedup from above, and the quality of the parallel implementation can be measured by how close our algorithm gets to this ``perfect speedup curve''.
Perfect speedup is seldom attainable. Instead, we often try to design "scalable algorithms", where Efficiency(p) is bounded away from 0 as p grows. This means that we are guaranteed to get some benefit proportional to the size of the machine, as we use more and more processors.
A common variation on these performance measures is as follows: Since people often buy a larger machine to run a larger problem, not just the same problem faster, we let problem size n(p) grow with p, to measure the ``scaled speedup'' T(1,n(p))/T(p,n(p)) and ``scaled efficiency'' T(1,n(p))/(T(p,n(p))*p). For example, we may let n(p) grow so that the amount of memory used be a constant per processor, no matter what p is. In the case of matrix multiplication C = A*B, this means the the matrix dimension N for p processors would satisfy 3*N^2 = n(p) = p*M, where M is the amount of memory used per processor.
Amdahl's law gives a simple bound on how much speedup we can expect: suppose a problem spends fraction f<1 of its time doing work than can be parallelized, and fraction s=1-f doing serial work, which cannot be parallelized. Then T(p) = T(1)*f/p + T(1)*s, and Speedup(p) = T(1)/T(p) = 1/(f/p+s) <= 1/s, no matter how big p is. Efficiency(p) = 1/(f+s*p) goes to 0 as p increases. In other words, speedup is bounded by 1/s, and in fact increasing p past s/f can't increase speed by more than a factor of two.
Amdahl's law teaches us this lesson: We need to make sure there are no serial bottleneck (the s part) in codes if we hope to have a scalable algorithm. For example, even if only s=1% of a program is serial, the speedup is limited to 100, and so it is not worth using a machine with more than 100 processors. As we will see, this means we need to measure performance carefully (profiling) to identify serial bottlenecks. The assignments will discuss how to profile programs accurately.
This is a collection of 6 successively more difficult parallel programming problems, designed to illustrate many parallel programming problems and techniques. It is basically a simulation of "particles" moving around and interacting subject to certain rules, which are not entirely physical but instructive and amusing. Some of the problems are discrete (the sharks and fish can only occupy a discrete set of positions), and some are continuous (the sharks and fish can be anywhere). We have working implementations of many of these problem in 6 programming models, 5 of which are parallel, to illustrate different ways the same algorithm is expressed in different parallel programming models. You will have programming assignments involving modifying some of these implementations. The 6 languages are
The ocean may either be discrete, where sharks and fish are constrained to move from one grid point to a neighboring grid point, or the ocean may be continuous.
These three kinds of forces are parallelized in different ways: The external force can be computed independently for each fish, and will be the easiest force to parallelize. Forces which only depend on the nearest neighbors, or very close neighbors, require relatively little cooperation between processors and are next easiest to parallelize. Forces which depend on all other fish, like gravity, require the cleverest algorithms to compute efficiently (in serial or parallel).
A shark eats any fish it "collides" with, and dies if it does not eat for too long. Here are the rules for the 6 different sharks and fish problems in brief, with more details available here.
Sharks and Fish 2. Fish alone move continuously subject to gravitational attraction and Newton's laws.
Sharks and Fish 5. Sharks and Fish both move randomly on a square grid, with at most one fish or shark per grid point, including rules for fish attracting sharks, eating, breeding and dying.
The following software for these problems exists. It can be seen by clicking on the x's below. In each case you will see a directory of source code for each problem. In the case of the Matlab code, the routine fishXinit.m is an initialization program, to be run first to set up the problem (where X varies from 1 to 5), and fishX.m is the main Matlab solution routine.