iOS — implementing complex numbers

Question

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.

Answer 1

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_EPSILON to help me with these kinds of things as well.

#define fequal(a,b) (fabs((a) - (b)) < FLT_EPSILON)
#define fequalzero(a) (fabs(a) < FLT_EPSILON)

With those, you might like a function like this (untested)

inline void froundzero(a) { if (fequalzero(a)) a = 0; }

The complex version is left as an exercise for the reader as they say :D