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complex.h(0P)              POSIX Programmer's Manual             complex.h(0P)
PROLOG
       This  manual  page is part of the POSIX Programmer's Manual.  The Linux
       implementation of this interface may differ (consult the  corresponding
       Linux  manual page for details of Linux behavior), or the interface may
       not be implemented on Linux.
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.1-2008
       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 _Com-
                   plex, with the value of the imaginary unit (that is, a num-
                   ber i such that i2=-1).
       imaginary   Expands to _Imaginary.
       _Imaginary_I
                   Expands to a constant expression of type const float _Imag-
                   inary with the value of the imaginary unit.
       I           Expands to either _Imaginary_I or  _Complex_I.  If  _Imagi-
                   nary_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  fol-
       lowing 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 multi-
       plication 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  nota-
       tional 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.1-2008,  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, 2013 Edition, Standard for Information Technology
       -- Portable Operating System Interface (POSIX),  The  Open  Group  Base
       Specifications Issue 7, Copyright (C) 2013 by the Institute of Electri-
       cal and Electronics Engineers,  Inc  and  The  Open  Group.   (This  is
       POSIX.1-2008  with  the  2013  Technical Corrigendum 1 applied.) 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.unix.org/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.ker-
       nel.org/doc/man-pages/reporting_bugs.html .
IEEE/The Open Group                  2013                        complex.h(0P)