COMPLEX(3) | Library Functions Manual | COMPLEX(3) |
complex
— complex
floating-point functions
#include
<complex.h>
The header file complex.h provides function prototypes and macros for working with complex floating-point values. The functions conform to the ISO/IEC 9899:2011 standard. In particular, arguments with infinite real or imaginary parts are regarded as infinities, even if the other part is a NaN.
complex.h defines the macro complex for use as a type specifier, and the macro I to be the imaginary unit, which can be used to construct complex floating-point numbers from two real floating-point numbers. For example:
#include <complex.h> double complex z = 1.0 + 1.0 * I; // z = 1 + i
Note however that certain complex values cannot be initialized using this technique, because I is actually a complex value. For example:
double complex z = 0.0 + INFINITY * I;
does not produce the result that one might expect; because of the promotion rules, it is evaluated like this:
0.0 + INFINITY * I = 0.0 + inf*(0.0,1.0) = 0.0 + (inf,0.0)*(0.0,1.0) = 0.0 + (inf*0.0 - 1.0*0.0, inf*1.0 + 0.0*0.0) = 0.0 + (NaN - 0.0, inf + 0.0) = 0.0 + (NaN, inf) = (0.0, 0.0) + (NaN, inf) = (0.0 + NaN, 0.0 + inf) = (NaN, inf)
For this reason, and to allow the initialization of complex objects with static or thread storage duration, C11 introduced the following 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)
These produce a complex number with real part having the converted value x and imaginary part y.
Each of the functions that use complex floating-point values are provided in single, double, and extended precision; the double precision prototypes are listed here. The man pages for the individual functions provide more details on their use, special cases, and prototypes for their single and extended precision versions.
The double-precision functions defined in complex.h are:
double
creal
(double
complex z)
double
cimag
(double
complex z)
creal
()
and
cimag
()
take a complex floating-point number and return its real and imaginary part,
respectively, as real floating-point numbers.
double
cabs
(double
complex z)
double
carg
(double
complex z)
cabs
()
and
carg
()
take a complex floating-point number and return its norm and argument (phase
angle), respectively, as real floating-point numbers. They are used to
convert between rectangular and polar coordinates, and are fully specified
in terms of real functions:
cabs(x + iy) = hypot(x,y) carg(x + iy) = atan2(y,x)
double complex
conj
(double
complex z)
conj
()
takes a complex floating-point number and returns its complex conjugate.
double complex
cproj
(double
complex z)
cproj
()
takes a complex floating-point number and returns its projection onto the
Riemann sphere, as defined in the C standard. For non-infinite inputs, the
return value is equal to the input value.
double complex
csqrt
(double
complex z)
csqrt
()
takes a complex floating-point number and returns its square root, with a
branch cut on the negative real axis.
double complex
cexp
(double
complex z)
double complex
clog
(double
complex z)
cexp
()
and
clog
()
take a complex floating-point number and return its base-e exponential and
logarithm, respectively. clog
() has a branch cut on
the negative real axis.
double complex
cpow
(double
complex z, double complex w)
cpow
()
takes two complex floating-point numbers, and returns the first raised to
the power of the second, with a branch cut for the first parameter along the
negative real axis.
double complex
csin
(double
complex z)
double complex
ccos
(double
complex z)
double complex
ctan
(double
complex z)
csin
(),
ccos
(),
and
ctan
()
take a complex floating-point number and return its sine, cosine, and
tangent, respectively.
double complex
casin
(double
complex z)
double complex
cacos
(double
complex z)
double complex
catan
(double
complex z)
casin
(),
cacos
(),
and
catan
()
take a complex floating-point number and return its inverse sine, cosine,
and tangent, respectively.
casin
()
and
cacos
()
have branch cuts outside the interval [-1, 1] on the real axis, and
catan
()
has a branch cut outside the interval [-i, i] on the imaginary axis.
double complex
csinh
(double
complex z)
double complex
ccosh
(double
complex z)
double complex
ctanh
(double
complex z)
csinh
(),
ccosh
(),
and
ctanh
()
take a complex floating-point number and return its hyperbolic sine, cosine,
and tangent, respectively.
double complex
casinh
(double
complex z)
double complex
cacosh
(double
complex z)
double complex
catanh
(double
complex z)
casinh
(),
cacosh
(),
and
catanh
()
take a complex floating-point number and return its inverse hyperbolic sine,
cosine, and tangent, respectively.
casinh
()
has a branch cut outside the interval [-i, i] on the imaginary axis.
cacosh
()
has a branch cut at values less than 1 on the real axis.
catanh
()
has a branch cut outside the interval [-1, 1] on the real axis.
Note that the complex math functions are not, in general, equivalent to their real counterparts for inputs on the real axis. For example, csqrt(-1 + 0i) is 0 + i, whereas sqrt(-1) is NaN.
cabs(3), cacos(3), cacosh(3), carg(3), casin(3), casinh(3), catan(3), catanh(3), ccos(3), ccosh(3), cexp(3), cimag(3), clog(3), conj(3), cpow(3), cproj(3), creal(3), csin(3), csinh(3), csqrt(3), ctan(3), ctanh(3), math(3)
The <complex.h> functions conform to ISO/IEC 9899:2011.
August 16, 2012 | macOS 14.6 |