Python十进制.十进制精度与Wolfram alpha不匹配 [英] Python decimal.Decimal precision doesn't match wolfram alpha's

问题描述

我有以下python代码:

I have the following python code:

In [1]: import decimal

In [2]: decimal.getcontext().prec = 80

In [3]: (1-decimal.Decimal('0.002'))**5
Out[3]: Decimal('0.990039920079968')

不应该匹配0.99003992007996799440405766290496103465557098388671875 根据此 http ://www.wolframalpha.com/input/?i = SetPrecision％5B％281 +-+ 0.002％29％5E5％2C + 80％5D 吗?

Shouldn't it match 0.99003992007996799440405766290496103465557098388671875 according to this http://www.wolframalpha.com/input/?i=SetPrecision%5B%281+-+0.002%29%5E5%2C+80%5D ?

推荐答案

Wolfram alpha在这里实际上是错误的.

Wolfram alpha is actually wrong here.

(1 - 0.002) ** 5

恰好是0.990039920079968.

您可以通过简单地评估.之后是否有15位数字与5 * 3匹配来验证这一点，其中3是表达式(1 - 0.002)中.之后的位数.根据定义，第15位之后不能有任何数字.

You can verify that by simply assessing that there are 15 digits after the ., which matches 5 * 3, 3 being the number of digits after the . in the expression (1 - 0.002). There couldn't be any digit after the 15th by definition.

多挖一点给我带来了一些有趣的东西:

A little more digging got me something interesting:

此符号Decimal('0.002')使用此 exact 值创建实际的小数.使用Decimal(0.002)十进制是由浮点数而不是字符串构成的，从而产生了不精确性.使用此表示法是原始公式:

This notation Decimal('0.002') creates an actual decimal with this exact value. Using Decimal(0.002) the decimal is made from a float rather than a string, creating an imprecision. Using this notation is the original formula :

(1-decimal.Decimal(0.002))**5

返回Decimal('0.99003992007996799979349352807411754897106595345737537649055432859002826694496107'，它实际上是.之后的80位数字，但与Wolfram alpha值不同.

Returns Decimal('0.99003992007996799979349352807411754897106595345737537649055432859002826694496107' which is indeed 80 digits long after the ., but different from the wolfram alpha value.

这可能是由于python和Wolfram alpha浮点表示形式之间的精度差异所致，这进一步表明Wolfram alpha在使用SetPrecision时正在使用浮点数.

This is probably caused by a difference of precision between python and wolfram alpha floating point representation, and is a further indication that wolfram alpha is using floats when SetPrecision is used.

Nota :直接要求结果返回正确的值(请参见

Nota: directly asking for the result returns the correct value (see http://www.wolframalpha.com/input/?i=%281+-+0.002%29%5E5).

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