Making Computations Execute Very Quickly

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Copyright © 2015 Russel Winder 4 CPU Bound vs I/O Bound 1/2 — ● Python is entirely fine for essentially I/O bound activity: ● Managing user interfaces via native code widgets (Qt, GTK, Wx, ) … ● Managing networking activity. Common theme here, the use of an event loop.

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Copyright © 2015 Russel Winder 5 CPU Bound vs I/O Bound 2/2 — ● Python uses hardware floating point, but via the Python heap. ● Python uses hardware integers for small integer values, but via the Python heap. Result: non-trivial numerical activity is slow.

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Copyright © 2015 Russel Winder 15 Approximating  ● What is it's value represented as a floating point number? ● We can only obtain an approximation. ● A plethora of possible algorithms to choose from, a popular one is to employ the following integral equation. π 4 =∫ 0 1 1 1+x2 dx

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Copyright © 2015 Russel Winder 16 One possible algorithm ● Use quadrature to estimate the value of the integral which is the area under the curve. – π= 4 n ∑ i=1 n 1 1+( i−0.5 n ) 2 With n = 3 not much to do, but potentially lots of error. Use n = 107 or n = 109? Embarrassingly parallel.

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