32位平台的编译时间和运行时间之间的双乘法不同

问题描述

我正在32位和64位平台中编译和运行以下程序：

I'm compiling and running the following program in 32 and 64 bit platforms:

int main()
{
  double y = 8.34214e08;
  double z = 1.25823e45;

  return y * z == 8.34214e08 * 1.25823e45;
}

虽然在64位结果是预期的（值相同，退出代码非零）在32位似乎在编译时计算的值之间有一点差异，右侧的比较，左侧在运行时计算。

While in 64bit the result is the expected (the values are the same and the exit code is non-zero) in 32bit seems there is a little difference between the value calculated at compile time, the right hand side of the comparison, and the left side computed at runtime.

这是编译器中的错误还是有逻辑解释？

Is this a bug in the compiler or there is a logical explanation?

编辑：这不同于因为这里所有的值都是双倍的。

this is different from Why comparing double and float leads to unexpected result? because here all the values are double.

推荐答案

IEEE-754允许以更高的精度（强调我的）完成中间计算。

IEEE-754 allows intermediate computations to be done in a greater precision (emphasis mine).

在您的情况下，例如在IA-32上，双精度值可以更精确地存储在x87 FPU寄存器中（80位而不是64位） 。所以你实际上是将双重精度乘法与双倍扩展精度乘法相比较。

In your case for example on a IA-32, the double values could be stored in the x87 FPU registers with greater precision (80-bit instead of 64). So you are actually comparing a multiplication done on double precision with a multiplication done on double-extended precision.

例如，x64上的结果是 1 （不使用x87 FPU，因为使用SSE），添加 gcc 选项 -mfpmath = 387 使用x87使结果更改为我的机器上的 0 。

For example, on x64 where the result is 1 (the x87 FPU is not used as SSE is used instead), adding gcc option -mfpmath=387 to use the x87 makes the result change to 0 on my machine.

如果你想知道这是否也被C允许，它是：

And if you wonder if that is also allowed by C, it is:

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