浮点加法和乘法是否关联?
我在添加三个浮点值并将它们与 1 进行比较时遇到问题.
I had a problem when I was adding three floating point values and comparing them to 1.
cout << ((0.7 + 0.2 + 0.1)==1)<<endl; //output is 0
cout << ((0.7 + 0.1 + 0.2)==1)<<endl; //output is 1
为什么这些值会不同?
推荐答案
浮点加法不一定是关联的.如果您更改添加的顺序，这可能会改变结果.
Floating point addition is not necessarily associative. If you change the order in which you add things up, this can change the result.
关于该主题的标准论文是 每个计算机科学家应该做的了解浮点运算.它给出了以下示例:
The standard paper on the subject is What Every Computer Scientist Should Know about Floating Point Arithmetic. It gives the following example:
另一个灰色区域涉及括号的解释.由于舍入误差，代数的结合定律不一定适用于浮点数.例如，当 x = 1e30、y = -1e30 和 z = 1 时，表达式 (x+y)+z 与 x+(y+z) 的答案完全不同(前者为 1，后者为 0).
Another grey area concerns the interpretation of parentheses. Due to roundoff errors, the associative laws of algebra do not necessarily hold for floating-point numbers. For example, the expression (x+y)+z has a totally different answer than x+(y+z) when x = 1e30, y = -1e30 and z = 1 (it is 1 in the former case, 0 in the latter).
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