C8_COMPLEX_LIB
A Double Precision Complex Arithmetic Utility Library

C8_COMPLEX_LIB is a C library which contains routines for "C8" or "double precision complex" arithmetic.

The original C specification did not include support for complex numbers. Until the later C99 specification added such support, it was common for programmers to develop their own complex arithmetic libraries. Despite the fact that these routines are now generally obsolete, the procedures involved can still be instructive and useful, including the use of structures for the data type and the development of a variety of functions to carry out the necessary arithmetic operations.

To use the structures and functions of this library, it is necessary that the user's source code invoke the include file:

        # include "c8_complex_lib.h"
      

This package defines a double precision complex number as a C struct whose components are doubles:

        struct c8_complex
        {
          double real;
          double imag;
        };
      

To declare a variable c you could use a statement like:

        struct c8_complex c;
      

The declaration can include an initialization:

        struct c8_complex c = { 1.0, 2.0 };
      

The value of a variable c declared as struct c8_complex may be examined or changed by accessing the components of the struct. Thus, the initialization above could be carried out at run time by the commands:

        c.real = 1.0;
        c.imag = 2.0;
      

In the common case when pointers are used, we declare

        struct *c8_complex c;
      

        c = ( struct c8_complex *) malloc ( sizeof ( struct c8_complex ) );
      

        c->real = 1.0;
        c->imag = 2.0;
      

        free ( c );
      

Licensing:

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

Languages:

C8_COMPLEX_LIB is available in a C version and a C++ version.

Related Programs:

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.

C8LIB, a C library which implements certain elementary functions for "C8" or double precision complex variables using the C99 standard "double complex" datatype.

COMPLEX_NUMBERS, a C program which demonstrates some simple features involved in the use of complex numbers in C programming.

I4LIB, a C library which contains many utility routines, using "I4" or "single precision integer" arithmetic.

I8LIB, a C library which contains many utility routines, using "I8" or "double precision integer" arithmetic.

R4LIB, a C library which contains many utility routines, using "R4" or "single precision real" arithmetic.

R8LIB, a C library which contains many utility routines, using "R8" or "double precision real" arithmetic.

Source Code:

• c8_complex_lib.c, the source code;
• c8_complex_lib.h, the include file.

Examples and Tests:

• c8_complex_lib_test.c, the calling program;
• c8_complex_lib_test.txt, the output file.

List of Routines:

• C8_ABS returns the absolute value of a C8.
• C8_ACOS evaluates the inverse cosine of a C8.
• C8_ACOSH evaluates the inverse hyperbolic cosine of a C8.
• C8_ADD adds two C8's.
• C8_ARG returns the argument of a C8.
• C8_ASIN evaluates the inverse sine of a C8.
• C8_ASINH evaluates the inverse hyperbolic sine of a C8.
• C8_ATAN evaluates the inverse tangent of a C8.
• C8_ATANH evaluates the inverse hyperbolic tangent of a C8.
• C8_CONJ conjugates a C8.
• C8_COPY copies a C8.
• C8_COS evaluates the cosine of a C8.
• C8_COSH evaluates the hyperbolic cosine of a C8.
• C8_CUBE_ROOT computes the principal cube root of a C8.
• C8_DIV divides two C8's.
• C8_DIV_R8 divides a C8 by an R8.
• C8_EXP exponentiates a C8.
• C8_I returns the value of I as a C8
• C8_IMAG returns the imaginary part of a C8.
• C8_INV inverts a C8.
• C8_LOG evaluates the logarithm of a C8.
• C8_MAG returns the magnitude of a C8.
• C8_MUL multiplies two C8's.
• C8_NEG negates a C8.
• C8_NORMAL_01 returns a unit pseudonormal C8.
• C8_ONE returns the value of 1 as a C8
• C8_REAL returns the real part of a C8.
• C8_SIN evaluates the sine of a C8.
• C8_SINH evaluates the hyperbolic sine of a C8.
• C8_SQRT computes a square root of a C8.
• C8_SUB subtracts two C8's.
• C8_SWAP swaps two C8's.
• C8_TAN evaluates the tangent of a C8.
• C8_TANH evaluates the hyperbolic tangent of a C8.
• C8_TO_CARTESIAN converts a C8 from Cartesian to polar form.
• C8_TO_POLAR converts a C8 from Cartesian to polar form.
• C8_UNIFORM_01 returns a unit pseudorandom C8.
• C8_ZERO returns the value of 0 as a C8
• CARTESIAN_TO_C8 converts a Cartesian form to a C8.
• POLAR_TO_C8 converts a polar form to a C8.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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