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

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

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

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(C) P. H. Welch, 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

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

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

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(C) P. H. Welch, 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

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(C) P. H. Welch, 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”

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(C) P. H. Welch, 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”

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(C) P. H. Welch, 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”

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(C) P. H. Welch, 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”

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(C) P. H. Welch, 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”

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(C) P. H. Welch, 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”

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(C) P. H. Welch, 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

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

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

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

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(C) P. H. Welch, 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

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(C) P. H. Welch, 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

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(C) P. H. Welch, 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

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

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(C) P. H. Welch, 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

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(C) P. H. Welch, 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

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(C) P. H. Welch, (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

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

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

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(C) P. H. Welch, 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

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(C) P. H. Welch, 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! * *

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