How to work with complex numbers in C?

How can I work with complex numbers in C? I see there is a complex.h header file, but it doesn't give me much information about how to use it. How to access real and imaginary parts in an efficient way? Is there native functions to get module and phase?

Solution 1:

This code will help you, and it's fairly self-explanatory:

#include <stdio.h>      /* Standard Library of Input and Output */
#include <complex.h>    /* Standard Library of Complex Numbers */

int main() {

    double complex z1 = 1.0 + 3.0 * I;
    double complex z2 = 1.0 - 4.0 * I;

    printf("Working with complex numbers:\n\v");

    printf("Starting values: Z1 = %.2f + %.2fi\tZ2 = %.2f %+.2fi\n", creal(z1), cimag(z1), creal(z2), cimag(z2));

    double complex sum = z1 + z2;
    printf("The sum: Z1 + Z2 = %.2f %+.2fi\n", creal(sum), cimag(sum));

    double complex difference = z1 - z2;
    printf("The difference: Z1 - Z2 = %.2f %+.2fi\n", creal(difference), cimag(difference));

    double complex product = z1 * z2;
    printf("The product: Z1 x Z2 = %.2f %+.2fi\n", creal(product), cimag(product));

    double complex quotient = z1 / z2;
    printf("The quotient: Z1 / Z2 = %.2f %+.2fi\n", creal(quotient), cimag(quotient));

    double complex conjugate = conj(z1);
    printf("The conjugate of Z1 = %.2f %+.2fi\n", creal(conjugate), cimag(conjugate));

    return 0;
}

  with:

creal(z1): get the real part (for float crealf(z1), for long double creall(z1))

cimag(z1): get the imaginary part (for float cimagf(z1), for long double cimagl(z1))

Another important point to remember when working with complex numbers is that functions like cos(), exp() and sqrt() must be replaced with their complex forms, e.g. ccos(), cexp(), csqrt().

Solution 2:

Complex types are in the C language since C99 standard (-std=c99 option of GCC). Some compilers may implement complex types even in more earlier modes, but this is non-standard and non-portable extension (e.g. IBM XL, GCC, may be intel,... ).

You can start from http://en.wikipedia.org/wiki/Complex.h - it gives a description of functions from complex.h

This manual http://pubs.opengroup.org/onlinepubs/009604499/basedefs/complex.h.html also gives some info about macros.

To declare a complex variable, use

  double _Complex  a;        // use c* functions without suffix

or

  float _Complex   b;        // use c*f functions - with f suffix
  long double _Complex c;    // use c*l functions - with l suffix

To give a value into complex, use _Complex_I macro from complex.h:

  float _Complex d = 2.0f + 2.0f*_Complex_I;

(actually there can be some problems here with (0,-0i) numbers and NaNs in single half of complex)

Module is cabs(a)/cabsl(c)/cabsf(b); Real part is creal(a), Imaginary is cimag(a). carg(a) is for complex argument.

To directly access (read/write) real an imag part you may use this unportable GCC-extension:

 __real__ a = 1.4;
 __imag__ a = 2.0;
 float b = __real__ a;