def my_square(n): x = 1.0 while 1: if x * x >= n: x=(x * x + (x - 1) * (x - 1)) / 2 for i in range(0,10): j = n / x x = (j + x) / 2 print '%.30f' % x break else: x = x + 1
↑小数点下30桁まで計算できる
↓誤差が出ないバージョン。小数点以下100桁まで。
UNTIL = 100
def f(n):
xn = 0
while xn * xn < n:
xn += 1
return len(str(xn))
def g(s, p):
return s[:p] + '.' + s[p:]
def sq(n):
a, b = 5*n, 5
res = ''
sz = 0
cnt = 0
while sz <= UNTIL:
if a >= b:
a, b = a-b, b+10
cnt += 1
else:
a, b = a*100, (b/10)*100 + b%10
res += str(cnt)
sz += 1
cnt = 0
return g(res, f(n))
print sq(2)
print sq(10000)
# 初心者が書いたもの
# coding:utf-8 c = raw_input( "平方根を求めたい数値を入力: " ) x = int( c ) a = float(0) t = 1 n = 0 while t > a: k = float(10**n) n += 1 while a**2 > x: a = a - 1/k while a**2 < x: a = a +1/k t = a + 1 print "+-" + str(a) if a**2 == x: break
↓分数を使ったもの
#!/usr/bin/python
# -*- coding: utf-8 -*-
from fractions import Fraction
from decimal import Decimal, getcontext
from operator import truediv
from functools import reduce
getcontext().prec = 50
ZERO = Fraction('0/1')
ONE = Fraction('1/1')
HALF = Fraction('1/2')
def my_sqrt(num):
'''
ニュートン法で平方根を求める。
'''
if not 0 < num <= 10000:
return 'Not implemented...'
p = Fraction(num).limit_denominator()
x0 = ZERO
x1 = HALF * (ONE + p)
for _ in range(12):
x0 = x1
x1 = HALF * (x0 + p / x0)
x = str(x1)
if '/' in x:
return reduce(truediv, map(Decimal, x.split('/')))
else:
return '{0:30}'.format(x)
print(my_sqrt(0))
print(my_sqrt(1))
print(my_sqrt(2))
print(my_sqrt(3))
print(my_sqrt(10))
print(my_sqrt(100))
print(my_sqrt(0.0001))
print(my_sqrt(10000))