complex.h(3)               POSIX Programmer's Manual              complex.h(3)



PROLOG
       This manual page is part of the POSIX Programmer's Manual.  The OS
       implementation of this interface may differ (consult the corresponding
       OS manual page for details of OS behavior), or the interface may not be
       implemented on OS.

NAME
       complex.h -- complex arithmetic

SYNOPSIS
       #include <complex.h>

DESCRIPTION
       The functionality described on this reference page is aligned with the
       ISO C standard. Any conflict between the requirements described here
       and the ISO C standard is unintentional. This volume of POSIX.1-2017
       defers to the ISO C standard.

       The <complex.h> header shall define the following macros:

       complex     Expands to _Complex.

       _Complex_I  Expands to a constant expression of type const float
                   _Complex, with the value of the imaginary unit (that is, a
                   number _i such that _i2=-1).

       imaginary   Expands to _Imaginary.

       _Imaginary_I
                   Expands to a constant expression of type const float
                   _Imaginary with the value of the imaginary unit.

       I           Expands to either _Imaginary_I or _Complex_I. If
                   _Imaginary_I is not defined, I expands to _Complex_I.

       The macros imaginary and _Imaginary_I shall be defined if and only if
       the implementation supports imaginary types.

       An application may undefine and then, perhaps, redefine the complex,
       imaginary, and I macros.

       The following shall be declared as functions and may also be defined as
       macros. Function prototypes shall be provided.


           double               cabs(double complex);
           float                cabsf(float complex);
           long double          cabsl(long double complex);
           double complex       cacos(double complex);
           float complex        cacosf(float complex);
           double complex       cacosh(double complex);
           float complex        cacoshf(float complex);
           long double complex  cacoshl(long double complex);
           long double complex  cacosl(long double complex);
           double               carg(double complex);
           float                cargf(float complex);
           long double          cargl(long double complex);
           double complex       casin(double complex);
           float complex        casinf(float complex);
           double complex       casinh(double complex);
           float complex        casinhf(float complex);
           long double complex  casinhl(long double complex);
           long double complex  casinl(long double complex);
           double complex       catan(double complex);
           float complex        catanf(float complex);
           double complex       catanh(double complex);
           float complex        catanhf(float complex);
           long double complex  catanhl(long double complex);
           long double complex  catanl(long double complex);
           double complex       ccos(double complex);
           float complex        ccosf(float complex);
           double complex       ccosh(double complex);
           float complex        ccoshf(float complex);
           long double complex  ccoshl(long double complex);
           long double complex  ccosl(long double complex);
           double complex       cexp(double complex);
           float complex        cexpf(float complex);
           long double complex  cexpl(long double complex);
           double               cimag(double complex);
           float                cimagf(float complex);
           long double          cimagl(long double complex);
           double complex       clog(double complex);
           float complex        clogf(float complex);
           long double complex  clogl(long double complex);
           double complex       conj(double complex);
           float complex        conjf(float complex);
           long double complex  conjl(long double complex);
           double complex       cpow(double complex, double complex);
           float complex        cpowf(float complex, float complex);
           long double complex  cpowl(long double complex, long double complex);
           double complex       cproj(double complex);
           float complex        cprojf(float complex);
           long double complex  cprojl(long double complex);
           double               creal(double complex);
           float                crealf(float complex);
           long double          creall(long double complex);
           double complex       csin(double complex);
           float complex        csinf(float complex);
           double complex       csinh(double complex);
           float complex        csinhf(float complex);
           long double complex  csinhl(long double complex);
           long double complex  csinl(long double complex);
           double complex       csqrt(double complex);
           float complex        csqrtf(float complex);
           long double complex  csqrtl(long double complex);
           double complex       ctan(double complex);
           float complex        ctanf(float complex);
           double complex       ctanh(double complex);
           float complex        ctanhf(float complex);
           long double complex  ctanhl(long double complex);
           long double complex  ctanl(long double complex);

       The following sections are informative.

APPLICATION USAGE
       Values are interpreted as radians, not degrees.

RATIONALE
       The choice of _I instead of _i for the imaginary unit concedes to the
       widespread use of the identifier _i for other purposes. The application
       can use a different identifier, say _j, for the imaginary unit by
       following the inclusion of the <complex.h> header with:


           #undef I
           #define j _Imaginary_I

       An _I suffix to designate imaginary constants is not required, as
       multiplication by _I provides a sufficiently convenient and more
       generally useful notation for imaginary terms. The corresponding real
       type for the imaginary unit is float, so that use of _I for algorithmic
       or notational convenience will not result in widening types.

       On systems with imaginary types, the application has the ability to
       control whether use of the macro I introduces an imaginary type, by
       explicitly defining I to be _Imaginary_I or _Complex_I. Disallowing
       imaginary types is useful for some applications intended to run on
       implementations without support for such types.

       The macro _Imaginary_I provides a test for whether imaginary types are
       supported.

       The cis() function (cos(_x) + _I*sin(_x)) was considered but rejected
       because its implementation is easy and straightforward, even though
       some implementations could compute sine and cosine more efficiently in
       tandem.

FUTURE DIRECTIONS
       The following function names and the same names suffixed with _f or _l
       are reserved for future use, and may be added to the declarations in
       the <complex.h> header.


              cerf()    cexpm1()   clog2()
              cerfc()   clog10()   clgamma()
              cexp2()   clog1p()   ctgamma()

SEE ALSO
       The System Interfaces volume of POSIX.1-2017, cabs(), cacos(),
       cacosh(), carg(), casin(), casinh(), catan(), catanh(), ccos(),
       ccosh(), cexp(), cimag(), clog(), conj(), cpow(), cproj(), creal(),
       csin(), csinh(), csqrt(), ctan(), ctanh()

COPYRIGHT
       Portions of this text are reprinted and reproduced in electronic form
       from IEEE Std 1003.1-2017, Standard for Information Technology --
       Portable Operating System Interface (POSIX), The Open Group Base
       Specifications Issue 7, 2018 Edition, Copyright (C) 2018 by the
       Institute of Electrical and Electronics Engineers, Inc and The Open
       Group.  In the event of any discrepancy between this version and the
       original IEEE and The Open Group Standard, the original IEEE and The
       Open Group Standard is the referee document. The original Standard can
       be obtained online at http://www.opengroup.org/unix/online.html .

       Any typographical or formatting errors that appear in this page are
       most likely to have been introduced during the conversion of the source
       files to man page format. To report such errors, see
       https://www.kernel.org/doc/man-pages/reporting_bugs.html .



IEEE/The Open Group                  2017                         complex.h(3)
