PI generator (update)


This is an update of an earlier version. In this version the string containing the approximated pi value is created directly from the iteration of the generator. This way the program is simplified and can be used with Python2 and Python3 ...

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# a generator to approximate pi to n decimals
# tested with Python 2.5.4 and Python 3.1.1  by vegaseat

def pi_generate():
    generator to approximate pi
    returns a single digit of pi each time iterated
    q, r, t, k, m, x = 1, 0, 1, 1, 3, 3
    while True:
        if 4 * q + r - t < m * t:
            yield m
            q, r, t, k, m, x = \
            (10*q, 10*(r-m*t), t, k, (10*(3*q+r))//t - 10*m, x)
            q, r, t, k, m, x = \
            (q*k, (2*q+r)*x, t*x, k+1, (q*(7*k+2)+r*x)//(t*x), x+2)

# number of decimal digits desired
# used 56 here to make it display well, n can be much higher
n = 56
pi_str = ""
for ix, v in enumerate(pi_generate()):
    #print(v)  # test
    if ix > n:
    pi_str += str(v)

# use string slicing to insert the missing period at index 1
pi_str = pi_str[0] + '.' + pi_str[1:]

print( "pi approx. to %d decimals (below it is published pi):" % n )
print( pi_str )

# published pi value
pi_pub = "3.14159265358979323846264338327950288419716939937510582097"
print( pi_pub )

"""my result -->
pi approx. to 56 decimals (below it is published pi):
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