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complex.h(0P)		   POSIX Programmer's Manual		 complex.h(0P)

       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 _Com‐
		   plex, with the value of the imaginary unit (that is, a num‐
		   ber i such that i2=−1).

       imaginary   Expands to _Imaginary.

		   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.

       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  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

       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

       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 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 .

       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‐ .

IEEE/The Open Group		     2013			 complex.h(0P)

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