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NAME

       complex.h - complex arithmetic

SYNOPSIS

       #include <complex.h>

DESCRIPTION

       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 i**2=-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 IEEE Std 1003.1-2001, 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, 2003 Edition, Standard for Information Technology
       -- Portable Operating System Interface (POSIX),  The  Open  Group  Base
       Specifications  Issue  6,  Copyright  (C) 2001-2003 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 .