#define cproj( z )
(4) (since C99)1-3) Computes the projection of z on the Riemann sphere.
Type-generic macro: if
z
has type
long double complex,
long double imaginary, or
long double,
cprojl
is called. If
z
has type
float complex,
float imaginary, or
float,
cprojf
is called. If
z
has type
double complex,
double imaginary,
double, or any integer type,
cproj
is called.
For most z, cproj(z)==z, but all complex infinities, even the numbers where one component is infinite and the other is NaN, become positive real infinity, INFINITY+0.0*I or INFINITY-0.0*I. The sign of the imaginary (zero) component is the sign of cimag(z).
The projection of z on the Riemann sphere.
This function is fully specified for all possible inputs and is not subject to any errors described in math_errhandling
[edit] NotesThe cproj function helps model the Riemann sphere by mapping all infinities to one (give or take the sign of the imaginary zero), and should be used just before any operation, especially comparisons, that might give spurious results for any of the other infinities.
#include <stdio.h>
#include <complex.h>
#include <math.h>
int main(void)
{
double complex z1 = cproj(1 + 2*I);
printf("cproj(1+2i) = %.1f%+.1fi\n", creal(z1),cimag(z1));
double complex z2 = cproj(INFINITY+2.0*I);
printf("cproj(Inf+2i) = %.1f%+.1fi\n", creal(z2),cimag(z2));
double complex z3 = cproj(INFINITY-2.0*I);
printf("cproj(Inf-2i) = %.1f%+.1fi\n", creal(z3),cimag(z3));
}
Output:
cproj(1+2i) = 1.0+2.0i cproj(Inf+2i) = inf+0.0i cproj(Inf-2i) = inf-0.0i[edit] References
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