# cabs2

Compute the squared absolute value of a double-precision complex floating-point number.

The absolute value of a complex number is defined as

which corresponds to the length of a vector from the origin to a complex value plotted in the complex plane.

## Usage

var cabs2 = require( '@stdlib/math/base/special/cabs2' );


#### cabs2( z )

Computes the squared absolute value of a double-precision complex floating-point number.

var Complex128 = require( '@stdlib/complex/float64' );

var y = cabs2( new Complex128( 5.0, 3.0 ) );
// returns 34.0


## Notes

• Be careful to avoid overflow and underflow.
• Depending on the environment, this function may have better performance than computing the absolute value of a complex number and then squaring. Hence, where appropriate, consider using cabs2() over cabs().

## Examples

var Complex128 = require( '@stdlib/complex/float64' );
var discreteUniform = require( '@stdlib/random/base/discrete-uniform' ).factory;
var cabs2 = require( '@stdlib/math/base/special/cabs2' );

// Create a PRNG to generate uniformly distributed pseudorandom integers:
var rand = discreteUniform( -50, 50 );

// Compute the squared absolute value for a set of random numbers...
var z;
var i;
for ( i = 0; i < 100; i++ ) {
z = new Complex128( rand(), rand() );
console.log( 'cabs2(%s) = %d', z.toString(), cabs2( z ) );
}


## C APIs

### Usage

#include "stdlib/math/base/special/cabs2.h"


#### stdlib_base_cabs2( z )

Computes the squared absolute value of a double-precision complex floating-point number.

#include <complex.h>

double y = stdlib_base_cabs2( 5.0+3.0*I );
// returns 34.0


The function accepts the following arguments:

• z: [in] double complex input value.
double stdlib_base_cabs2( const double complex z );


### Examples

#include "stdlib/math/base/special/cabs2.h"
#include <stdio.h>
#include <complex.h>

int main() {
double complex x[] = { 3.14+1.0*I, -3.14-1.0*I, 0.0+0.0*I, 0.0/0.0+0.0/0.0*I };

double complex v;
double y;
int i;
for ( i = 0; i < 4; i++ ) {
v = x[ i ];
y = stdlib_base_cabs2( v );
printf( "f(%lf + %lf) = %lf\n", creal( v ), cimag( v ), y );
}
}