0.1浮大于0.1双大。我希望它是假的 [英] 0.1 float is greater than 0.1 double. I expected it to be false

问题描述

让：

double d = 0.1;
float f = 0.1;

宜恩pression

should the expression

(f > d)

收益真正或假？

根据经验，答案是真正。不过，我希望它是假。

Empirically, the answer is true. However, I expected it to be false.

由于 0.1 不能在二进制psented完全重新$ P $，而双有 15 到 16 小数precision的数字，浮动只有 7 。于是，他们俩都小于 0.1 ，而双更接近 0.1 。

As 0.1 cannot be perfectly represented in binary, while double has 15 to 16 decimal digits of precision, and float has only 7. So, they both are less than 0.1, while the double is more close to 0.1.

我需要一个确切的解释真正。

I need an exact explanation for the true.

推荐答案

我想说转换双击到<$ C $时，答案取决于舍入模式C>浮动。 浮动已24的二进制的precision和位双有53二，0.1是：

I'd say the answer depends on the rounding mode when converting the double to float. float has 24 binary bits of precision, and double has 53. In binary, 0.1 is:

0.1₁₀ = 0.0001100110011001100110011001100110011001100110011…₂
             ^        ^         ^   ^ 
             1       10        20  24

因此​​，如果我们圆的最多的在第24位，我们会得到

So if we round up at the 24th digit, we'll get

0.1₁₀ ~ 0.000110011001100110011001101

比的精确值，在53个数字越precise近似更大

which is greater than the exact value and the more precise approximation at 53 digits.

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