The Open Group Base Specifications Issue 7
IEEE Std 1003.1-2008, 2016 Edition
Copyright © 2001-2016 The IEEE and The Open Group

#### NAME

> complex.h - complex arithmetic

#### SYNOPSIS

> `#include <complex.h>`

#### DESCRIPTION

> [CX] 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 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() cerfc() cexp2() | cexpm1() clog10() clog1p() | clog2() clgamma() ctgamma()

#### SEE ALSO

> XSH cabs, cacos, cacosh, carg, casin, casinh, catan, catanh, ccos, ccosh, cexp, cimag, clog, conj, cpow, cproj, creal, csin, csinh, csqrt, ctan, ctanh

#### CHANGE HISTORY

> First released in Issue 6. Included for alignment with the ISO/IEC 9899:1999 standard.

End of informative text.

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