如何在Python中获得更精确的十进制值 [英] How can I get more exact decimal values in Python

问题描述

from math import sqrt


a=1e-8
b=10
c=1e-8

x1 = ((-b)-sqrt((b**2)-(4*a*c)))/(2*a)
x2 = ((-b)+sqrt((b**2)-(4*a*c)))/(2*a)

print 'x1 = {}'.format(x1)
print 'x2 = {}'.format(x2)

print (4*a*c)
print (sqrt(b**2-4*a*c))
print b**2
print 2*a

当我运行程序时，将返回:

When I run the program, this returns:

x1 = -1e+09
x2 = 0.0

4e-16
10.0
100.0
2e-08

我需要的是x2等于-1e-9.

What I need is for x2 to be equal to -1e-9.

问题似乎出在

sqrt((b**2)-(4*a*c))

结果是10，显然是因为4 *(10 ^ -8)*(10 ^ -8)几乎等于0，并且被python认为是0.

as it gives 10 as a result, obviously because 4*(10^-8)*(10^-8) is almost equal to 0, and is considered 0 by python.

结果是:

sqrt((b**2)-(4*a*c)) = sqrt(b**2) = sqrt(10**2) = 10

任何帮助将不胜感激

推荐答案

使用十进制模块:

from decimal import Decimal
a = Decimal('1E-8')
b = 10
c = Decimal('1E-8')
x1 = ((-b)-((b**2)-(4*a*c)).sqrt())/(2*a)
x2 = ((-b)+((b**2)-(4*a*c)).sqrt())/(2*a)
print 'x1 = {}'.format(x1)
print 'x2 = {}'.format(x2)

产生

x1 = -999999999.999999999000000000
x2 = -1.0000000000E-9

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