Calculate Pi using Monte Carlo

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Calculate Pi using Monte Carlo

• Stuart Brorson

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Drunken dart player

• Player throws darts at dartboard of unit radius.
• Dartboard sits inside of square frame.
• Hes drunk, so darts can hit anywhere in side of
  frame.
• Hits inside/ hits outside pi/4 provides way
  to calculate Pi!
• Convergence rate?

3
Serial MATLAB code

• xmin -1 xmax 1 ymin -1 ymax 1
• samples 5000000
• hits 0
• for i1samples
• hits hits monteCarloTrial(xmin, xmax, ymin,
  ymax)
• end
• ratio hits/samples
• piestimate 4ratio

• function t monteCarloTrial(xmin, xmax, ymin,
  ymax)x rand()(xmax-xmin) xminy
  rand()(ymax-ymin) yminif (xx yy) lt 1
  t1 inside circleelse t0 outside
  circleend

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Exercise parallelize using Star-P

• Whats best way to parallelize a Monte Carlo
  algorithm?
• How to do it using Star-P?
• What can go wrong?
• Can you express this algorithm using
  data-parallel methods?