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.1-2024 defers to the ISO C standard.

Implementations shall not define the macro __STDC_NO_COMPLEX__, except for profile implementations that define _POSIX_SUBPROFILE (see 2.1.5.1 Subprofiling Considerations) in <unistd.h>, which may define __STDC_NO_COMPLEX__ and, if they do so, need not provide this header nor support any of its facilities.

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. ^[MXC] Implementations that support the IEC 60559 Complex Floating-Point option shall define the macros imaginary and _Imaginary_I, and the macro I shall expand to _Imaginary_I.

An application may undefine and then, perhaps, redefine the complex, imaginary, and I macros.

The following shall be defined as macros.

double complex       CMPLX(double x, double y);
float complex        CMPLXF(float x, float y);
long double complex  CMPLXL(long double x, long double y);

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);

APPLICATION USAGE

The <complex.h> header is optional in the ISO C standard but is mandated by POSIX.1-2024. Note however that subprofiles can choose to make this header optional (see 2.1.5.1 Subprofiling Considerations), and therefore application portability to subprofile implementations would benefit from checking whether __STDC_NO_COMPLEX__ is defined before inclusion of <complex.h>.

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 CMPLX, 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.

Issue 8

Austin Group Defect 1302 is applied, aligning this header with the ISO/IEC 9899:2018 standard.