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maths/pi_generator.py
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@ -3,60 +3,53 @@ def calculate_pi(limit: int) -> str:
https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80
Leibniz Formula for Pi
The Leibniz formula is the special case arctan 1 = 1/4 Pi .
The Leibniz formula is the special case arctan(1) = pi / 4.
Leibniz's formula converges extremely slowly: it exhibits sublinear convergence.
Convergence (https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80#Convergence)
We cannot try to prove against an interrupted, uncompleted generation.
https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80#Unusual_behaviour
The errors can in fact be predicted;
but those calculations also approach infinity for accuracy.
The errors can in fact be predicted, but those calculations also approach infinity
for accuracy.
Our output will always be a string since we can defintely store all digits in there.
For simplicity' sake, let's just compare against known values and since our outpit
is a string, we need to convert to float.
Our output will be a string so that we can definitely store all digits.
>>> import math
>>> float(calculate_pi(15)) == math.pi
True
Since we cannot predict errors or interrupt any infinite alternating
series generation since they approach infinity,
or interrupt any alternating series, we are going to need math.isclose()
Since we cannot predict errors or interrupt any infinite alternating series
generation since they approach infinity, or interrupt any alternating series, we'll
need math.isclose()
>>> math.isclose(float(calculate_pi(50)), math.pi)
True
>>> math.isclose(float(calculate_pi(100)), math.pi)
True
Since math.pi-constant contains only 16 digits, here some test with preknown values:
Since math.pi contains only 16 digits, here are some tests with known values:
>>> calculate_pi(50)
'3.14159265358979323846264338327950288419716939937510'
>>> calculate_pi(80)
'3.14159265358979323846264338327950288419716939937510582097494459230781640628620899'
To apply the Leibniz formula for calculating pi,
the variables q, r, t, k, n, and l are used for the iteration process.
"""
# Variables used for the iteration process
q = 1
r = 0
t = 1
k = 1
n = 3
l = 3
decimal = limit
counter = 0
result = ""
"""
We will avoid using yield since we otherwise get a Generator-Object,
which we can't just compare against anything. We would have to make a list out of it
after the generation, so we will just stick to plain return logic:
"""
# We can't compare against anything if we make a generator,
# so we'll stick with plain return logic
while counter != decimal + 1:
if 4 * q + r - t < n * t:
result += str(n)