cproj

Retrieve the projection of a complex number on the Reimann sphere.

Interface Definition

C interface:

float complex cprojf(float complex x);

double complex cproj(double complex x);

long double complex cprojl(long double complex x);

Parameters

Parameter	Type	Description	Input/Output
x	For cprojf, x is of complex single-precision floating-point type. For cproj, x is of complex double-precision floating-point type. For cprojl, x is of complex, long, double-precision floating-point type.	Floating-point value of the input data.	Input

Parameter

Type

Description

Input/Output

For cprojf, x is of complex single-precision floating-point type.

For cproj, x is of complex double-precision floating-point type.
For cprojl, x is of complex, long, double-precision floating-point type.

Floating-point value of the input data.

Input

Return Value

The projection y of x on the Reimann sphere is returned.
If the input x.real or x.imag is ±∞, the output y.real is +∞ and z.imag is 0. The sign of z.imag is the same as that of x.imag.
If both the input x.real and x.imag are not ±∞, the output y = x.

Dependency

C: "kc.h"

Example

C interface:

    // typical usage
    double x1 = INFINITY, y1 = INFINITY;
    double x2 = 2.0, y2 = 3.0;
    double x3 = -2.5, y3 = -3.4;
    double x4 = NAN, y4 = NAN;
    double x5 = 0, y5 = 0;
    double complex z1 = cproj(__builtin_complex(x1, y1));
    double complex z2 = cproj(__builtin_complex(x2, y2));
    double complex z3 = cproj(__builtin_complex(x3, y3));
    double complex z4 = cproj(__builtin_complex(x4, y4));
    double complex z5 = cproj(__builtin_complex(x5, y5));
    // print result
    printf("/*\n");
    printf(" * cproj(%.2f + %.2f*I) = %.6f + %.6f*I\n", x1, y1, __real__(z1), __imag__(z1));
    printf(" * cproj(%.2f + %.2f*I) = %.6f + %.6f*I\n", x2, y2, __real__(z2), __imag__(z2));
    printf(" * cproj(%.2f + %.2f*I) = %.6f + %.6f*I\n", x3, y3, __real__(z3), __imag__(z3));
    printf(" * cproj(%.2f + %.2f*I) = %.6f + %.6f*I\n", x4, y4, __real__(z4), __imag__(z4));
    printf(" * cproj(%.2f + %.2f*I) = %.6f + %.6f*I\n", x5, y5, __real__(z5), __imag__(z5));
    printf(" **/\n");
 
   /*
    * cproj(inf + inf*I) = inf + 0.000000*I
    * cproj(2.00 + 3.00*I) = 2.000000 + 3.000000*I
    * cproj(-2.50 + -3.40*I) = -2.500000 + -3.400000*I
    * cproj(nan + nan*I) = nan + nan*I
    * cproj(0.00 + 0.00*I) = 0.000000 + 0.000000*I
    **/

Parent topic: Complex Functions