32位平台的编译时间和运行时间之间的双乘法不同 [英] Double multiplication differs between compile time and runtime in 32 bit platform

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).

（IEEE-754：2008）语言标准还应该定义并要求实现提供允许和禁止价值的属性，这些优化可能包括但不限于：[...] 在表达式评估中使用更广泛的中间结果。

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:

（C99，6.3.1.p8）浮动操作数的值浮动表达式的结果可能会以比类型所要求的更高的精度和范围表示;

(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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