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### 5.9 Complex Numbers

ISO C99 supports complex floating data types, and as an extension GCC supports them in C89 mode and in C++, and 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 GNU libc), 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 DWARF2 debug info format can represent this, so use of DWARF2 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.