# (C) P. H. Welch, 20031 Paradigms of Parallelism Chapter 2.

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(C) P. H. Welch, 20031 Paradigms of Parallelism Chapter 2

(C) P. H. Welch, 20032 Geometric(90%) Algorithmic(70%) Farming(99%) ??? + mixtures of the above Levels of efficiency that should be obtained Paradigms of Parallelism

(C) P. H. Welch, 20033 Fox’s Wall specification A large pile of bricks One bricklayer – OK! Three bricklayers??? need organizing

(C) P. H. Welch, 20034 Geometric Distribution Task partitioned geometrically amongst workers For the main, each worker works away independently But needs to interact with neighbouring workers when working on boundaries of allotted task

(C) P. H. Welch, 20035 Geometric Distribution Green can work fastest (no half bricks to cut) Red works as fast as it can Blue is an apprentice (and slow)

(C) P. H. Welch, 20036 Geometric Distribution Green can work fastest (but is now held up!) Red works as fast as it can Blue is an apprentice (and slow)

(C) P. H. Welch, 20037 Algorithmic (Pipeline) Distribution Functional distribution of tasks to workers Need to interact with neighbouring workers continually (to input data and pass on results) Like geometric distribution but work area is all boundary

(C) P. H. Welch, 20038 Pipeline Distribution Some workers idle at the beginning and end All workers busy when “pipe” is full Must work at pace of slowest element in the “pipe”

(C) P. H. Welch, 20039 Pipeline Distribution Some workers idle at the beginning and end All workers busy when “pipe” is full Must work at pace of slowest element in the “pipe”

(C) P. H. Welch, 200310 Pipeline Distribution Some workers idle at the beginning and end All workers busy when “pipe” is full Must work at pace of slowest element in the “pipe”

(C) P. H. Welch, 200311 Pipeline Distribution Some workers idle at the beginning and end All workers busy when “pipe” is full Must work at pace of slowest element in the “pipe”

(C) P. H. Welch, 200312 Pipeline Distribution Some workers idle at the beginning and end All workers busy when “pipe” is full Must work at pace of slowest element in the “pipe”

(C) P. H. Welch, 200313 Pipeline Distribution Some workers idle at the beginning and end All workers busy when “pipe” is full Must work at pace of slowest element in the “pipe”

(C) P. H. Welch, 200314 Farming Distribution Each worker gets work from a single source (“farmer”) Each worker sends completed work to a single “harvester” Each worker’s work is not dependent on any particular other worker Each worker’s rate of work may be different

(C) P. H. Welch, 200315 Farming Distribution All workers always busy Work at your own pace Your work must not be (tightly) dependent on other work

(C) P. H. Welch, 200316 All workers always busy Work at your own pace Your work must not be (tightly) dependent on other work Farming Distribution

(C) P. H. Welch, 200317 All workers always busy Work at your own pace Your work must not be (tightly) dependent on other work Farming Distribution

(C) P. H. Welch, 200318 Take n particles with different masses and initial positions and velocities in 3-space. Assume some inter-particle forces (e.g., gravity). Display their movements. n-Body Problem

(C) P. H. Welch, 200319 C0C0 C2C2 C1C1 CiCi C i+1 C i+2 C n-1 C3C3 (position velocity) Each cell knows all constants (e.g. the masses of all particles). Cell C i knows the current position and velocity of particle i (its variables ). Geometric Distribution

(C) P. H. Welch, 200320 C0C0 C2C2 C1C1 CiCi C i+1 C i+2 C n-1 C3C3 (position velocity) Each cell knows all constants (e.g. the masses of all particles). Cell C i knows the current position and velocity of particle i (its variables ). graphics Geometric Distribution

(C) P. H. Welch, 200321 pump end.marker end.marker end.marker end.marker Sort Pump

(C) P. H. Welch, 200322 cell end.marker end.marker flow through the cell one at a time. The cell hangs on to the largest item is sees – passing smaller ones out. When the end.marker arrives, the cell finally outputs what it was holding (followed by the end.marker ). Sort Cell

(C) P. H. Welch, 200323 Rate of input of unsorted items. Cell cycle time. Inter-cell transfer rate. (n-1) This starts out with up to n items. With (n-1) separate (silicon) cells, its rate of output of sorted items is:- minimum This performance is independent of n. Pipeline Distribution

(C) P. H. Welch, 200324 (0,2) (-2,0)(2,0) (0,-2) c Z 0 = c Z i+1 = Z i + c Given c, find first |M such that |Z M | > 2. Give up is M = 511. Mandelbrot

(C) P. H. Welch, 200325 Colour the point c according to the value of M such that:- M 0 511 some colour spectrum whiteblack Mandelbrot

(C) P. H. Welch, 200326 work packets results farmer worker harvester worker Standard Process Farming

(C) P. H. Welch, 200327 Work Packet (x, y) a point in the complex plane a horizontal resolution n number of points to colour Results (x,y)(x + n.a,y) Computer the Mandelbrot number M for each of these points. Mandelbrot

(C) P. H. Welch, 200328 in.workin.result buffer prompter out.work work catch mux out.result worker Farm Worker Harness * omitted from the last worker! * * * omitted from the first worker! * *