cproj(), cprojf(), cprojl() — Calculate the projection

Standards

Standards / Extensions C or C++ Dependencies
C99
Single UNIX Specification, Version 3
 both
z/OS® V1R7 a compiler that is designed  to support C99

Format

#include <complex.h>

double complex cproj(double complex z);
float complex cprojf(float complex z);
long double complex cprojl(long double complex z);

General description

The cproj() family of functions compute a projection of z onto the Riemann sphere: z projects to z except that all complex infinities (even those with one infinite part and one NaN part) project to positive infinity on the real axis. If z has an infinite part, then cproj(z) is equivalent to:

INFINITY +I * copysign(0.0, cimag(z))

Note: The following table shows the viable formats for these functions. See IEEE binary floating-point for more information about IEEE Binary Floating-Point.
Function Hex IEEE
cproj X X
cprojf X X
cprojl X X

Returned value

The cproj() family of functions return the value of the projection onto the Riemann sphere.

For a variable z of complex type, z == creal(z) + cimag(z)*I.

Special behavior for hex: On hexadecimal floating point mode, cproj(z) family of functions always returns z .

Example

#include <complex.h>
#include <stdio.h>

/*
 * Illustrates complex function cproj().  
 *
 * NOTE:        When compiled in HEX(FLOAT), cproj(z) should
 *              always return z
 */


#define INFINITEL 1.0L/0.0L   /* An infinite number */

void InitReal ( long double complex *z, long double RealPart)
{
  union LongDoubleComplexMap {
     long double complex w;
     long double ldarray[2];
  }z1;

  z1.w = *z;
  z1.ldarray[0] = RealPart;
  *z = z1.w;
}


main() {

  long double complex z,w;
  z = 2.5 + I*(-3.999);

  printf("Ilustrates function cproj() ");

  #ifdef _BFP_
    printf ("(IEEE mode)");
  #else
    printf ("(HFP mode)");
  #endif

  printf("\n\n z = %Lf + I*%Lf\n\n",creall(z), cimagl(z));
  w = cprojl(z);
  printf(" cproj(z) = %Lf + I*%Lf\n",creall(w), cimagl(w));


  printf(" Initializing z(real) with infinity ...\n");
  InitReal(z,INFINITEL);
  printf(" z = %Lf + %Lf*I\n",creall(z),cimagl(z));


  w = cprojl(z);
  printf(" cproj(z) = %Lf + %Lf*I\n",creall(w),cimagl(w));
}


Output

Ilustrates function cproj() (IEEE mode)

 z = 2.500000 + I*-3.999000

 cproj(z) = 2.500000 + I*-3.999000
 Initializing z(real) with infinity ...
 z = INF + -3.999000*I
 cproj(z) = INF + -0.000000*I

Related information