Lua笔记--number的存储

Lua 笔记--number的存储

Lua语言里面的数字类型是number，没有像C/C++里面那样多种多样，如果是这样的话，那么在计算机内数字就应该是按照浮点数存储的，而浮点数存储不是有不确定性吗？不会出现类似1+2=2.9999999999的错误吗？

这个问题在Roberto Ierusalimschy的《Programming In Lua》一书中进行了说明

Some people fear that even a simple increment or comparison can go weird with floating-point numbers. Reality, however, is not like that. Virtually all plat-forms nowadays follow the IEEE 754 standard for floating-point representation.Following this standard, the only possible source of errors is a representation error, which happens when a number cannot be exactly represented. An operation rounds its result only if that result has no exact representation. Any operation with a result that has an exact representation must give that exact result.

The fact is that any integer up to $2^{53}$ (approximately $10^{16}$ ) has an exact representation as a double-precision floating-point number. When you use a double to represent an integer, there is no rounding error at all, unless the number has an absolute value greater than $2^{53}$ . In particular, a Lua number can represent any 32-bit integer without rounding problems.

小于$2^{{53}$的整数都是可以用浮点数精确存储的，所以不存在$1+2\neq3$的问题。可为什么小于$2}{53}$的整数就可以精确存储呢？这里面需要了解浮点数在计算机内部到底是如何存储的，有一个标准叫IEEE754 ，它规定了浮点数是如何存储的，可以看看我写的对IEEE 754的理解(文末链接) 。

简单地说，双精度浮点数能存储的有效位数最大是53，这里的位数是指化成二进制之后的位数，如果位数大于53，则存在不精确存储。而53位最多可以存储的整数即为$2^{53}$ ,至于不精确存储具体发生在那些时候，可以参考本人写的文章。

对IEEE754标准的理解