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       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.


       complex.h — complex arithmetic


       #include <complex.h>


       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 _Complex, with the value
                   of the imaginary unit (that is, a number i such that i2=−1).

       imaginary   Expands to _Imaginary.

                   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

       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.


       Values are interpreted as radians, not degrees.


       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.


       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()


       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()


       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  Electrical  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 .

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