iOS——实现复数
作为这个问题的后续行动：
我正在实现一个计算器应用程序使用 Apple 的复数支持 当我注意到如果使用该支持进行计算时，最终会得到以下结果：
(1+i)^2=1.2246063538223773e-16 + 2i
当然，正确的恒等式是 ( 1+i)^2=2i。这是一个更普遍现象的具体示例——如果舍入误差将本应为零的部分舍入为稍微非零的部分，那么舍入误差可能会非常烦人。
关于如何处理这个问题的建议？我可以用其他方式实现复数的整数幂，但一般问题仍然存在，而且我的解决方案本身可能会导致其他不一致。
As a follow-up to this question:
I was in the process of implementing a calculator app using Apple's complex number support when I noticed that if one calculates using that support, one ends up with the following:
(1+i)^2=1.2246063538223773e-16 + 2i
Of course the correct identity is (1+i)^2=2i. This is a specific example of a more general phenomenon -- roundoff errors can be really annoying if they round a part that is supposed to be zero to something that is slightly nonzero.
Suggestions on how to deal with this? I could implement integer powers of complex numbers in other ways, but the general problem will remain, and my solution could itself cause other inconsistencies.
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正如您所注意到的，这是浮点的标准舍入误差问题。 @Howard 指出，您可能应该在显示之前将双精度结果舍入到浮点范围内。
我通常也使用
FLT_EPSILON来帮助我处理此类事情。有了这些，您可能会喜欢这样的函数（未经测试），
正如他们所说，复杂的版本留给读者作为练习：D
As you note, this is as standard rounding error issue with floating points. A @Howard notes, you should likely round your double results back into the float range before displaying.
I typically use
FLT_EPSILONto help me with these kinds of things as well.With those, you might like a function like this (untested)
The complex version is left as an exercise for the reader as they say :D