在32位平台上编译时和运行时之间双倍增不同 [英] Double multiplication differs between compile time and runtime in 32 bit platform

问题描述

我编译和32位和64位平台上运行下面的程序：

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;
}

而在64位的结果被预期（的值是相同的，并出射code是非零）在32位似乎还有在编译时计算出的值之间的差别不大，右手侧的比较，和左侧在运行时计算

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.

这是在编译器错误或有一个合理的解释？

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

编辑：这是从不同，为什么比较double和float导致意想不到的结果，因为这里所有的值都是双

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允许中间计算在更大precision（重点矿山）完成。

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

（IEEE-754：2008）一个语言标准也应定义，并且需要实现来提供，属性，允许和禁止的值变化的优化，单独地或共同地，对于一个块这些优化可能包括，但并非如此。限于：[...] 的前pression评价更广泛的中间结果使用

(IEEE-754:2008) "A language standard should also define, and require implementations to provide, attributes that allow and disallow value-changing optimizations, separately or collectively, for a block. These optimizations might include, but are not limited to: [...] Use of wider intermediate results in expression evaluation."

在您的情况下，例如在IA-32，双值可以存储在具有更大precision（80位而不是64）的的x87 FPU寄存器。所以，你实际上是比较双precision完成对双扩展precision做了乘法的乘积。

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，在x64那里的结果是 1 （不使用的x87 FPU上交所来代替），加入 GCC 选项 -mfpmath = 387 来使用的x87使我的机器上的结果改变 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.

如果你不知道这是否也是用C允许的，它是：

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

（C99，6.3.1.p8）浮操作数和浮动前pressions的结果的值可被重新psented更大precision和范围比由类型所要求$ P $ ;

(C99, 6.3.1.p8) "The values of floating operands and of the results of floating expressions may be represented in greater precision and range than that required by the type;"

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