问题描述
我听说由于内部使用二进制浮点，所以像0.1 + 0.2这样的浮点运算可能会产生像0.30000000000000004这样的舍入误差.
I heard that floating point arithmetic like 0.1 + 0.2 may yield rounding error like 0.30000000000000004 due to binary floating point being used internally.
但是，如果我在C ++中的任何浮点数上添加0，是否可以保证产生相同的值而不会出现舍入错误?我不知道浮点算术如何工作以及何时出现舍入错误.
But if I add a 0 to any floating point number in C++, does it guarantee to produce the same value without any rounding error? I have no idea how floating point arithmetic works and when rounding error appears.
推荐答案
如果 C ++实现支持IEEE754数学，则可以保证.IEEE754标准具有精确的数学运算定义，因此C ++并未定义其自己的规则.但是IEEE754支持不是强制性的.
If the C++ implementation supports IEEE754 math, then it is guaranteed. The IEEE754 standard has precise definitions of mathematical operations, so C++ doesn't define its own rules. But IEEE754 support is not mandatory.
x + 0.0 == x 对于任何数字(*)都是正确的，因为IEEE754保证加法，减法，乘法和除法精确到最后一位.
x + 0.0 == x is true for any number (*) because IEEE754 guarantees that addition, subtraction, multiplication and division are precise to the last bit.
(*)当x不是数字(NaN)时， x + 0.0 也是NaN，但在IEEE754中为 NaN！= NaN .
(*) When x is Not a Number (NaN), x+0.0 is also NaN, but NaN != NaN in IEEE754.
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