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cabs2f

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

The absolute value of a complex number is defined as

$$|a + bi| = \sqrt{a^2 + b^2}$$

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

Usage

var cabs2f = require( '@stdlib/math/base/special/cabs2f' );

cabs2f( z )

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

var Complex64 = require( '@stdlib/complex/float32/ctor' );

var y = cabs2f( new Complex64( 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 cabs2f() over cabsf().

Examples

var Complex64 = require( '@stdlib/complex/float32/ctor' );
var discreteUniform = require( '@stdlib/random/base/discrete-uniform' ).factory;
var cabs2f = require( '@stdlib/math/base/special/cabs2f' );

// 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 Complex64( rand(), rand() );
    console.log( 'cabs2f(%s) = %d', z.toString(), cabs2f( z ) );
}

C APIs

Usage

#include "stdlib/math/base/special/cabs2f.h"

stdlib_base_cabs2f( z )

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

#include "stdlib/complex/float32/ctor.h"

stdlib_complex64_t z = stdlib_complex64( 5.0f, 3.0f );

float y = stdlib_base_cabs2f( z );
// returns 34.0f

The function accepts the following arguments:

  • z: [in] stdlib_complex64_t input value.
float stdlib_base_cabs2f( const stdlib_complex64_t z );

Examples

#include "stdlib/math/base/special/cabs2f.h"
#include "stdlib/complex/float32/ctor.h"
#include "stdlib/complex/float32/reim.h"
#include <stdio.h>

int main( void ) {
    const stdlib_complex64_t x[] = {
        stdlib_complex64( 3.14f, 1.0f ),
        stdlib_complex64( -3.14f, -1.0f ),
        stdlib_complex64( 0.0f, 0.0f ),
        stdlib_complex64( 0.0f/0.0f, 0.0f/0.0f )
    };

    stdlib_complex64_t v;
    float re;
    float im;
    float y;
    int i;
    for ( i = 0; i < 4; i++ ) {
        v = x[ i ];
        y = stdlib_base_cabs2f( v );
        stdlib_complex64_reim( v, &re, &im );
        printf( "f(%f + %fi) = %f\n", re, im, y );
    }
}

See Also