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.1‐2017
       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() cerfc()   cexpm1() clog10()   clog2() 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(0P)