x*x != x*x在自动变量中？

Question

如何通过将x * x存储在"auto变量“中来更改它？我认为应该是相同的，而且我的测试表明类型、大小和值显然都是的。

但即使是x * x == (xx = x * x)也是假的。搞什么鬼?

(注:我知道IEEE 754和浮动和双工以及它们的常见问题，但这个问题让我感到困惑。)

#include <iostream>
#include <cmath>
#include <typeinfo>
#include <iomanip>
using namespace std;

int main() {
    auto x = sqrt(11);
    auto xx = x * x;
    cout << boolalpha << fixed << setprecision(130);
    cout << "   xx == 11           " << (   xx == 11          ) << endl;
    cout << "x * x == 11           " << (x * x == 11          ) << endl;
    cout << "x * x == xx           " << (x * x == xx          ) << endl;
    cout << "x * x == (xx = x * x) " << (x * x == (xx = x * x)) << endl;
    cout << "x * x == x * x        " << (x * x == x * x       ) << endl;
    cout << "types        " << typeid(xx).name() << " " << typeid(x * x).name() << endl;
    cout << "sizeofs      " << sizeof(xx) << " " << sizeof(x * x) << endl;
    cout << "xx           " << xx    << endl;
    cout << "x * x        " << x * x << endl;
}

这是输出：

   xx == 11           true
x * x == 11           false
x * x == xx           false
x * x == (xx = x * x) false
x * x == x * x        true
types        d d
sizeofs      8 8
xx           11.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
x * x        11.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

按此编制：

C:\Stefan\code\leetcode>g++ test4.cpp -static-libstdc++ -std=c++11 -o a.exe

C:\Stefan\code\leetcode>g++ --version
g++ (GCC) 4.8.1
Copyright (C) 2013 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Answer 1

这是双打通常不精确的现象。您没有提到您的硬件，但是在x86 (32位英特尔)上，计算过程中使用的临时程序是10字节长的双倍。x * x将是其中之一，而xx = x * x将被存储到一个8字节的双倍，然后加载回FPU进行比较。

如果打开优化或构建64位可执行文件，可能会得到不同的结果。