Complex integer division

["Joseph S. Myers" <jsm28 at cam dot ac dot uk>]

GCC supports complex integer types as an extension (whereas C99 only 
allows complex floating point types).

How ought division of such numbers to work?  That is, when can / and %
applied to such numbers yield undefined behavior, and exactly which values
should the results have?  Presumably (a/b)*b + a%b equals a, as for normal
integer division, and the algebraic value of a%b divided by b should have
real and imaginary parts both strictly between 1 and -1 (or some similar
constraint), but is there a more precise specification?  For normal
integer division, C99 precisely defines the results.

PR c/2995, though it claims to be a problem with casts, in fact reflects a 
problem with how GCC handles complex integer division: using the normal 
mathematical formulas without regard for how C integers behave.  A simple 
testcase which will divide by zero but clearly shouldn't is:

	int
	main (void)
	{
	  _Complex int x = 1;
	  x = x / 65536;
	  return 0;
	}

I don't think this is a reasonable way to do complex integer division; the 
only corner case for normal integer division that causes problems is the 
most negative integer modulo -1 (which ought to be 0 rather than an 
exception), and making a lot of cases simply not work for dividing complex 
integers seems bad.  (C99 in fact requires that for floating point 
division the usual mathematical formulas - the only way GCC supports - 
should not be used by default because of undue overflow and underflow; 
CX_LIMITED_RANGE defaults to "off".)

Suggestions on the right way to fix this?

-- 
Joseph S. Myers
jsm28@cam.ac.uk