PROLOG | NAME | SYNOPSIS | DESCRIPTION | APPLICATION USAGE | RATIONALE | FUTURE DIRECTIONS | SEE ALSO | COPYRIGHT

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

PROLOG         top

       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         top

       complex.h — complex arithmetic

SYNOPSIS         top

       #include <complex.h>

DESCRIPTION         top

       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.

       _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         top

       Values are interpreted as radians, not degrees.

RATIONALE         top

       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         top

       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         top

       The System Interfaces volume of POSIX.1‐2008, cabs(3p), cacos(3p),
       cacosh(3p), carg(3p), casin(3p), casinh(3p), catan(3p), catanh(3p),
       ccos(3p), ccosh(3p), cexp(3p), cimag(3p), clog(3p), conj(3p),
       cpow(3p), cproj(3p), creal(3p), csin(3p), csinh(3p), csqrt(3p),
       ctan(3p), ctanh(3p)

COPYRIGHT         top

       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 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.kernel.org/doc/man-pages/reporting_bugs.html .

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

Pages that refer to this page: float.h(0p)tgmath.h(0p)cabs(3p)cacos(3p)cacosh(3p)carg(3p)casin(3p)casinh(3p)catan(3p)catanh(3p)ccos(3p)ccosh(3p)cexp(3p)cimag(3p)clog(3p)conj(3p)cpow(3p)cproj(3p)creal(3p)csin(3p)csinh(3p)csqrt(3p)ctan(3p)ctanh(3p)