6.10 Complex Numbers

ISO C99 supports complex floating data types, and as an extension GCC supports them in C90 mode and in C++. GCC also supports complex integer data types which are not part of ISO C99. You can declare complex types using the keyword _Complex. As an extension, the older GNU keyword __complex__ is also supported.

For example, ‘_Complex double x;’ declares x as a variable whose real part and imaginary part are both of type double. ‘_Complex short int y;’ declares y to have real and imaginary parts of type short int; this is not likely to be useful, but it shows that the set of complex types is complete.

To write a constant with a complex data type, use the suffix ‘i’ or ‘j’ (either one; they are equivalent). For example, 2.5fi has type _Complex float and 3i has type _Complex int. Such a constant always has a pure imaginary value, but you can form any complex value you like by adding one to a real constant. This is a GNU extension; if you have an ISO C99 conforming C library (such as the GNU C Library), and want to construct complex constants of floating type, you should include <complex.h> and use the macros I or _Complex_I instead.

To extract the real part of a complex-valued expression exp, write __real__ exp. Likewise, use __imag__ to extract the imaginary part. This is a GNU extension; for values of floating type, you should use the ISO C99 functions crealf, creal, creall, cimagf, cimag and cimagl, declared in <complex.h> and also provided as built-in functions by GCC.

The operator ‘~’ performs complex conjugation when used on a value with a complex type. This is a GNU extension; for values of floating type, you should use the ISO C99 functions conjf, conj and conjl, declared in <complex.h> and also provided as built-in functions by GCC.

GCC can allocate complex automatic variables in a noncontiguous fashion; it's even possible for the real part to be in a register while the imaginary part is on the stack (or vice versa). Only the DWARF 2 debug info format can represent this, so use of DWARF 2 is recommended. If you are using the stabs debug info format, GCC describes a noncontiguous complex variable as if it were two separate variables of noncomplex type. If the variable's actual name is foo, the two fictitious variables are named foo$real and foo$imag. You can examine and set these two fictitious variables with your debugger.