scientific-programming-exer.../ex_03.py

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