6.11 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.

The ISO C++14 library also defines the ‘i’ suffix, so C++14 code that includes the ‘<complex>’ header cannot use ‘i’ for the GNU extension. The ‘j’ suffix still has the GNU meaning.

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 debug info format can represent this, so use of DWARF 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.