2018-10-24 15:15:50 +00:00
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#!/usr/bin/python3
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import math
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2018-10-25 11:49:36 +00:00
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import cmath
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2018-10-24 15:15:50 +00:00
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def bailey_borwein_plouffe_pi(n):
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2018-10-24 15:48:09 +00:00
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"""
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See https://en.wikipedia.org/wiki/Approximations_of_%CF%80#Efficient_methods
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"""
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2018-10-24 15:15:50 +00:00
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result = 0
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for k in range(n):
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result += (1/16)**k * ( 4/(8*k + 1) - 2/(8*k + 4) - 1/(8*k + 5) - 1/(8*k + 6))
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return result
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if( __name__ == "__main__"):
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assert bailey_borwein_plouffe_pi(1000) == math.pi
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2018-10-24 15:46:55 +00:00
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# Please note that the ``is`` operator checks wether the
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# two references are the same object, basically by comparing
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# their pointers.
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#
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# The ``==`` operator accesses the ``__eq__`` method of the
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# object that *compares* the other object to itself.
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#
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# Because ``a/b`` **cannot** return the same object as ``math.pi``,
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# the latter was created when the module ``math`` was initialized,
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# this will **always** evaluate to False.
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2018-10-25 11:49:36 +00:00
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# As it turns out there is also the ``float.as_integer_ratio``.
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# Now I kind of assume that this exercise aims torward this crap.
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# You can use this method to construct two integers that are a
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# fractional representation of the float.
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#
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# I doubt very much that there is a use case for this crap.
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# There is the built-in module ``decimal`` that provides
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# a proper way of dealing with floating point arithmetics,
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# rounding and precision.
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a,b = math.pi.as_integer_ratio()
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assert a/b == math.pi
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