COMPLEX_NUMBERS
Complex Numbers in C Programming


COMPLEX_NUMBERS is a C program which demonstrates very briefly some of the features of using complex numbers in a C program.

The first issue is how to declare a complex variable, including the choice of single precision or double precision, whether the variable is a scalar, vector, or array, and whether the variable is initialized with a value, or assigned one.

A second issue concerns the question of how a complex variable is to be printed out.

Another issue concerns how a complex variable is to operated on by the arithmetic operators of addition, subtraction, multiplication, division, and exponentiation.

The language also provides a number of intrinsic functions that can be applied to a complex variable. The names of these functions can sometimes be easy to forget. Moreover, it is occasionally true that there may be a selection of functions with similar names (say, "exp", "cexp" and "dcexp") which may or may not produce the desired results.

Another issue concerns the details of double precision calculation. Even a single accidental use of a single precision function name in a double precision computation can result in the loss of half the digits of accuracy. Thus, it sometimes really matters whether you use "cmplx" or "dcmplx" to assign values to a double precision complex variable.

An unusual feature of the implementation of complex numbers in C is that a complex number can be defined by a statement like

z = a + b * I;
where I is predefined; but I is actually implemented via a macro, and is not a numeric value. It needs to be multiplied by a number to be meaningful (this is how it determines the precision it will use, for instance). So you cannot set the imaginary unit by
a = I;
Instead, you would have to write
a = 1 * I;

Another issue concerns the mistakes that can be made, which will evoke no warning from the compiler, but which will produce incorrect results. Here I am thinking, in particular, of the fact that if z is float complex or double complex, you should compute its exponential with the expression cexp(z); however, no compiler warning will occur if you use the expression exp(z); however, these two expressions are not equivalent, and will yield different results.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

COMPLEX_NUMBERS is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BLAS1_C, a C library which contains basic linear algebra routines for vector-vector operations, using single precision complex arithmetic;

BLAS1_Z, a C library which contains basic linear algebra routines for vector-vector operations, using double precision complex arithmetic.

C4_COMPLEX_LIB, a C library which defines a single precision complex variable or "C4" as a structure, and implements certain corresponding elementary functions.

C4LIB, a C library which implements certain elementary functions for "C4" or single precision complex variables;

C8_COMPLEX_LIB, a C library which defines a double precision complex variable or "C8" as a structure, and implements certain corresponding elementary functions.

C8LIB, a C library which implements certain elementary functions for "C8" or double precision complex variables;

Source Code:

Examples and Tests:

You can go up one level to the C source codes.


Last revised on 12 November 2010.