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Python script to compute Pi with arctan's formula.
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#! /usr/local/bin/python3.6 | |
""" | |
Computation of Pi with arctan's formula | |
Formulas: 1: Machin | |
2: Klingenstierna | |
3: Euler | |
4: Euler(2) | |
5: Gauss | |
6: Stormer | |
7: Stormer(2) | |
8: Takano | |
""" | |
import math | |
import sys | |
import time | |
class CalcPiArctan: | |
FORMULA = [ | |
"Machin", "Klingenstierna", "Euler", "Euler2", | |
"Gauss", "Stormer", "Stormer2", "Takano" | |
] # Formula names | |
KK = [ # Coefficients | |
[ 16, 1, 5, -4, 1, 239 ], # 1: Machin | |
[ 32, 1, 10, -4, 1, 239, -16, 1, 515 ], # 2: Klingenstierna | |
[ 20, 1, 7, 8, 3, 79 ], # 3: Euler | |
[ 16, 1, 5, -4, 1, 70, 4, 1, 99 ], # 4: Euler(2) | |
[ 48, 1, 18, 32, 1, 57, -20, 1, 239 ], # 5: Gauss | |
[ 24, 1, 8, 8, 1, 57, 4, 1, 239 ], # 6: Stormer | |
[176, 1, 57, 28, 1, 239, -48, 1, 682, 96, 1, 12943], # 7: Stormer(2) | |
[ 48, 1, 49, 128, 1, 57, -20, 1, 239, 48, 1, 110443] # 8: Takano | |
] | |
# File name | |
FILE_PRE = "PI_" # Prefix | |
FILE_EXT = ".txt" # Extension | |
# Output strings | |
STR_TITLE = "** Pi Computation by Arctan method **" | |
STR_FORMULA = " Formula = [ {:s} ]" | |
STR_DIGITS = " Digits = {:d}" | |
STR_TIME = " Time = {:f} seconds" | |
# Multi-digit computation | |
MAX_DIGITS = 100000000 # 8-digits per 1 item | |
def __init__(self, x, y): | |
self.fname = self.FILE_PRE + self.FORMULA[x - 1] + self.FILE_EXT | |
print("\n[ Output file :", self.fname, "]\n") | |
self.formula = self.FORMULA[x - 1] | |
self.ks = int(len(self.KK[x-1]) / 3) | |
self.kk = self.KK[x - 1] | |
self.l = y | |
self.l1 = int(self.l / 8) + 1 | |
self.n = [] | |
for i in range(0, self.ks): | |
n = self.l / (math.log10(self.kk[i * 3 + 2]) \ | |
- math.log10(self.kk[i * 3 + 1])) + 1 | |
self.n.append(int(n / 2) + 1) | |
def compute(self): | |
""" Computation and display """ | |
try: | |
t0 = time.time() | |
a = [[0 for _ in range(self.l1 + 2)] for _ in range(self.ks)] | |
q = [[0 for _ in range(self.l1 + 2)] for _ in range(self.ks)] | |
sk = [[0 for _ in range(self.l1 + 2)] for _ in range(self.ks)] | |
s = [0 for _ in range(self.l1 + 2)] | |
for i in range(self.ks): | |
a[i][0] = self.kk[i * 3] * self.kk[i * 3 + 2] | |
if self.kk[i * 3] < 0: | |
a[i][0] *= -1 | |
if self.kk[i * 3 + 1] != 1: | |
a[i] = self.__long_div(a[i], self.kk[i * 3 + 1]) | |
for i in range(self.ks): | |
for k in range(1, self.n[i] + 1): | |
a[i] = self.__long_div(a[i], self.kk[i * 3 + 2]) | |
a[i] = self.__long_div(a[i], self.kk[i * 3 + 2]) | |
if self.kk[i * 3 + 1] != 1: | |
a[i] = self.__long_mul(a[i], self.kk[i * 3 + 1]) | |
a[i] = self.__long_mul(a[i], self.kk[i * 3 + 1]) | |
q[i] = self.__long_div(a[i], 2 * k - 1) | |
if k % 2 == 0: | |
sk[i] = self.__long_sub(sk[i], q[i]) | |
else: | |
sk[i] = self.__long_add(sk[i], q[i]) | |
for i in range(self.ks): | |
if self.kk[i * 3] >= 0: | |
s = self.__long_add(s, sk[i]) | |
else: | |
s = self.__long_sub(s, sk[i]) | |
t1 = time.time() | |
tt = t1 - t0 | |
self.__display(tt, s) | |
except Exception as e: | |
raise | |
def __long_add(self, a, b): | |
""" Computation of long + long | |
:param list a | |
:param list b | |
:return list z | |
""" | |
try: | |
z = [0 for _ in range(self.l1 + 2)] | |
cr = 0 | |
for i in reversed(range(self.l1 + 2)): | |
z[i] = a[i] + b[i] + cr | |
if z[i] < self.MAX_DIGITS: | |
cr = 0 | |
else: | |
z[i] -= self.MAX_DIGITS | |
cr = 1 | |
return z | |
except Exception as e: | |
raise | |
def __long_sub(self, a, b): | |
""" Computation of long - long | |
:param list a | |
:param list b | |
:return list z | |
""" | |
try: | |
z = [0 for _ in range(self.l1 + 2)] | |
br = 0 | |
for i in reversed(range(self.l1 + 2)): | |
z[i] = a[i] - b[i] - br | |
if z[i] >= 0: | |
br = 0 | |
else: | |
z[i] += self.MAX_DIGITS | |
br = 1 | |
return z | |
except Exception as e: | |
raise | |
def __long_mul(self, a, b): | |
""" Computation of long * short | |
:param list a | |
:param list b | |
:return list z | |
""" | |
try: | |
z = [0 for _ in range(self.l1 + 2)] | |
cr = 0 | |
for i in reversed(range(self.l1 + 2)): | |
w = a[i] | |
z[i] = (w * b + cr) % self.MAX_DIGITS | |
cr = int((w * b + cr) / self.MAX_DIGITS) | |
return z | |
except Exception as e: | |
raise | |
def __long_div(self, a, b): | |
""" Computation of long / short | |
:param list a | |
:param list b | |
:return list z | |
""" | |
try: | |
z = [0 for _ in range(self.l1 + 2)] | |
r = 0 | |
for i in range(self.l1 + 2): | |
w = a[i] | |
z[i] = int((w + r) / b) | |
r = ((w + r) % b) * self.MAX_DIGITS | |
return z | |
except Exception as e: | |
raise | |
def __display(self, tt, s): | |
""" Display | |
:param float tt: elapsed time | |
:param list s: result of calculation | |
""" | |
try: | |
print(self.STR_TITLE) | |
print(self.STR_FORMULA.format(self.formula)) | |
print(self.STR_DIGITS.format(self.l)) | |
print(self.STR_TIME.format(tt)) | |
out_file = open(self.fname, "w") | |
out_file.write(self.STR_TITLE) | |
out_file.write("\n") | |
out_file.write(self.STR_FORMULA.format(self.formula)) | |
out_file.write("\n") | |
out_file.write(self.STR_DIGITS.format(self.l)) | |
out_file.write("\n") | |
out_file.write(self.STR_TIME.format(tt)) | |
out_file.write("\n\n {:d}.\n".format(s[0])) | |
for i in range(1, self.l1): | |
if i % 10 == 1: | |
out_file.write("{:08d}:".format((i - 1) * 8 + 1)) | |
out_file.write(" {:08d}".format(s[i])) | |
if i % 10 == 0: | |
out_file.write("\n") | |
out_file.close | |
except Exception as e: | |
raise | |
if __name__ == '__main__': | |
try: | |
print("1:Machin, 2:Klingenstierna, 3:Euler, 4:Euler(2)") | |
print("5:Gauss, 6:Stormer, 7:Stormer(2), 8:Takano : ", end="") | |
f = int(input()) | |
if f < 1 or f > 8: | |
f = 1 | |
print("Please input number of Pi Decimal-Digits : ", end="") | |
n = int(input()) | |
obj = CalcPiArctan(f, n) | |
obj.compute() | |
except Exception as e: | |
print("EXCEPTION!", e.args, file=sys.stderr) | |
sys.exit(1) |
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