Python数组中的浮点精度 [英] Floating point precision in Python array

问题描述

对于这个非常简单而愚蠢的问题，我深表歉意.但是，为什么在这两种情况下显示的精度有所不同?

I apologize for the really simple and dumb question; however, why is there a difference in precision displayed for these two cases?

1)

>> test = numpy.array([0.22])
>> test2 = test[0] * 2
>> test2
0.44

2)

>> test = numpy.array([0.24])
>> test2 = test[0] * 2
>> test2
0.47999999999999998

我在64位linux上使用python2.6.6. 预先感谢您的帮助.

I'm using python2.6.6 on 64-bit linux. Thank you in advance for your help.

这似乎也适用于python中的列表

This also hold seems to hold for a list in python

>>> t = [0.22]
>>> t
[0.22]

>>> t = [0.24]
>>> t
[0.23999999999999999]

推荐答案

因为它们是不同的数字，并且不同的数字具有不同的舍入效果.

Because they are different numbers and different numbers have different rounding effects.

(实际上，右侧的所有相关问题"都将解释舍入效应本身的原因.)

(Practically any of the Related questions down the right-hand side will explain the cause of the rounding effects themselves.)

好的，更严肃的答案.看来numpy对数组中的数字执行了一些转换或计算:

Okay, more serious answer. It appears that numpy performs some transformation or calculation on the numbers in an array:

>>> t = numpy.array([0.22])
>>> t[0]
0.22


>>> t = numpy.array([0.24])
>>> t[0]
0.23999999999999999

Python不会自动执行此操作:

whereas Python doesn't automatically do this:

>>> t = 0.22
>>> t
0.22

>>> t = 0.24
>>> t
0.24

舍入误差小于float的numpy的"eps"值，这意味着应将其视为相等(实际上是):

The rounding error is less than numpy's "eps" value for float, which implies that it should be treated as equal (and in fact, it is):

>>> abs(numpy.array([0.24])[0] - 0.24) < numpy.finfo(float).eps
True

>>> numpy.array([0.24])[0] == 0.24
True

但是Python将其显示为'0.24'而不是numpy的原因不是因为Python的默认float.__repr__方法使用了较低的精度(这是IIRC，这是最近的更改):

But the reason that Python displays it as '0.24' and numpy doesn't is because Python's default float.__repr__ method uses lower precision (which, IIRC, was a pretty recent change):

>>> str(numpy.array([0.24])[0])
0.24

>>> '%0.17f' % 0.24
'0.23999999999999999'

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