Making Computations Execute Very Quickly

transcript

Making ComputationsExecute Very Quickly

Dr Russel Winder

email: russel@winder.org.uktwitter: @russel_winder

Web: http://www.russel.org.uk

Python is slow…

…at computation.

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.

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.

What is the value of ?

Well that's easy, it's…

Exactly.

It's simples. Александр Орлов 2009

Albeit irrational.

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.

π4=∫0

1+ x2dx

One possible algorithm

● Use quadrature to estimate the value of the integral which is the area under the curve.–

π=4n∑i=1

1+(i−0.5n

With n = 3 not much to do, but potentially lots of error. Use n = 107 or n = 109?

Embarrassingly parallel.

Chapel

Because addition is commutative andassociative, expression can be

decomposed into sums of partial sums.

a + b + c + d + e + f

( a + b ) + ( c + d ) + ( e + f )

Scatter Gather—

map reduce

data parallel

Chapel

The Python data modeland its GIL make Python

unsuitable for parallel computation.

PyPy and NumPy do not help,nor does Cython, Numba, etc., as much as they perhaps should.

Native code, e.g. C++, D, Chapel,are the way forward forCPU-bound components of a

Python-based system.

And then there isOpenCL and OpenGL,

soon to be replaced by Vulkan.

Making ComputationsExecute Very Quickly

Dr Russel Winder

email: russel@winder.org.uktwitter: @russel_winder

Web: http://www.russel.org.uk

Making Computations Execute Very Quickly

Technology