| Types and the imaginary constant | |||||||||||||||||||||||||||||||
|
| ||||||||||||||||||||||||||||||
| Manipulation | |||||||||||||||||||||||||||||||
| Power and exponential functions | |||||||||||||||||||||||||||||||
| Trigonometric functions | |||||||||||||||||||||||||||||||
| Hyperbolic functions | |||||||||||||||||||||||||||||||
Defined in header <complex.h> | ||
| (1) | (since C99) | |
| (2) | (since C99) | |
| (3) | (since C99) | |
Defined in header <tgmath.h> | ||
#define cproj( z ) | (4) | (since C99) |
z on the Riemann sphere.z has typelongdoublecomplex,longdoubleimaginary, orlongdouble,cprojl is called. Ifz has typefloatcomplex,floatimaginary, orfloat,cprojf is called. Ifz has typedoublecomplex,doubleimaginary,double, or any integer type,cproj is called.For mostz,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 orINFINITY-0.0*I. The sign of the imaginary (zero) component is the sign ofcimag(z).
Contents |
| z | - | complex argument |
The projection ofz on the Riemann sphere.
This function is fully specified for all possible inputs and is not subject to any errors described inmath_errhandling
Thecproj 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){doublecomplex z1= cproj(1+2*I);printf("cproj(1+2i) = %.1f%+.1fi\n",creal(z1),cimag(z1)); doublecomplex z2= cproj(INFINITY+2.0*I);printf("cproj(Inf+2i) = %.1f%+.1fi\n",creal(z2),cimag(z2)); doublecomplex z3= cproj(INFINITY-2.0*I);printf("cproj(Inf-2i) = %.1f%+.1fi\n",creal(z3),cimag(z3));}
Output:
cproj(1+2i) = 1.0+2.0icproj(Inf+2i) = inf+0.0icproj(Inf-2i) = inf-0.0i
C++ documentation forproj |
