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| from time import time
from mpmath import *
precision = 50
mp.dps = precision
mp.pretty = True
sqrt_3 = sqrt(3)
base_9_list = []
base_10_list = []
def bbp_fraction(integer, n):
numerator = mpf(16)*sqrt_3*(integer+1)
denominator = mpf(9)**(integer-n+1)*mpf(3)*(mpf(16)*(integer**2+integer)+mpf(3))
return fmod(numerator/denominator, 1)
def base_9_fraction(integer, k):
numerator = base_9_list[integer] * mpf(10)**(k-1)
denominator = mpf(9)**integer
return fmod(numerator/denominator, 1)
def kappa_n(n, epsilon):
numerator = n*log(9) - 2*log(2) - 0.5*log(3) - log(epsilon)
denominator = log(9)
return ceil(numerator / denominator)
def kappa_k(k, epsilon):
numerator = k*log(10) - log(epsilon)
denominator = log(9)
return ceil(numerator / denominator)
class Processor:
def __init__(self, base):
self.base = base
def epsilon(self, sum_fraction):
return 1 - fmod(self.base*sum_fraction, 1)
def digit(self, sum_fraction):
return int(floor(self.base*sum_fraction))
def print(self):
base_list = eval('base_%s_list' % self.base)
number_of_lines = int(ceil((len(base_list)-1) / 10))
print('Pi in base %s to %s decimal places.\n\n' %(self.base, len(base_list)-1))
print('%s. ' % base_list[0])
for i in range(number_of_lines):
if i == number_of_lines - 1:
sub_list = base_list[1+i*10:]
else:
sub_list = base_list[1+i*10:1+(i+1)*10]
sub_list_string = ' '.join(map(str, sub_list))
print(' ' + sub_list_string + '\n')
def main():
P1 = Processor(9)
P2 = Processor(10)
t1 = time()
for i in range(precision):
j = 0
sum_fraction = mpf(0)
while True:
sum_fraction += bbp_fraction(j, i)
sum_fraction = fmod(sum_fraction, 1)
epsilon = P1.epsilon(sum_fraction)
kappa = kappa_n(i, epsilon)
if kappa <= j:
base_9_list.append(P1.digit(sum_fraction))
break
j += 1
t2 = time()
P1.print()
print('Time taken: %.4f seconds.\n\n' %(t2 - t1))
t3 = time()
for i in range(precision):
j = 0
sum_fraction = mpf(0)
out_of_range = False
while True:
if j == precision:
out_of_range = True
break
sum_fraction += base_9_fraction(j, i)
sum_fraction = fmod(sum_fraction, 1)
epsilon = P2.epsilon(sum_fraction)
kappa = kappa_k(i, epsilon)
if kappa <= j:
base_10_list.append(P2.digit(sum_fraction))
break
j += 1
if out_of_range:
break
t4 = time()
P2.print()
print('Time taken: %.4f seconds.\n\n' %(t4 - t3))
if __name__ == '__main__':
main()
|