cabsf, cabs, cabsl

Defined in header <complex.h>
float       cabsf( float complex z );
(1) (since C99)
double      cabs( double complex z );
(2) (since C99)
long double cabsl( long double complex z );
(3) (since C99)
Defined in header <tgmath.h>
#define fabs( z )
(4) (since C99)
1-3) Computes the complex absolute value (also known as norm, modulus, or magnitude) of z.
4) Type-generic macro: if z has type long double complex or long double imaginary, cabsl is called. If z has type float complex or float imaginary, cabsf is called. If z has type double complex or double imaginary, cabs is called. For real and integer types, the corresponding version of fabs is called.


z - complex argument

Return value

If no errors occur, returns the absolute value (norm, magnitude) of z.

Errors and special cases are handled as if the function is implemented as hypot(creal(z), cimag(z)).


#include <stdio.h>
#include <complex.h>
int main(void)
    double complex z = 1.0 + 1.0*I;
    printf("%.1f%+.1fi cartesian is rho=%f theta=%f polar\n",
           creal(z), cimag(z), cabs(z), carg(z));


1.0+1.0i cartesian is rho=1.414214 theta=0.785398 polar


  • C11 standard (ISO/IEC 9899:2011):
    • The cabs functions (p: 195)
    • 7.25 Type-generic math <tgmath.h> (p: 373-375)
    • G.7 Type-generic math <tgmath.h> (p: 545)
  • C99 standard (ISO/IEC 9899:1999):
    • The cabs functions (p: 177)
    • 7.22 Type-generic math <tgmath.h> (p: 335-337)
    • G.7 Type-generic math <tgmath.h> (p: 480)

See also

computes the phase angle of a complex number
computes absolute value of an integral value (\(\small{|x|}\)|x|)
computes absolute value of a floating-point value (\(\small{|x|}\)|x|)
computes square root of the sum of the squares of two given numbers (\(\scriptsize{\sqrt{x^2+y^2} }\)x2
C++ documentation for abs

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