sqrt1pm1

Compute sqrt( 1 + x ) - 1.

Installation

npm install @stdlib/math-base-special-sqrt1pm1

Usage

var sqrt1pm1 = require( '@stdlib/math-base-special-sqrt1pm1' );

sqrt1pm1( x )

Computes sqrt( 1 + x ) - 1 more accurately for small x.

var v = sqrt1pm1( 3.0 );
// returns 1.0

v = sqrt1pm1( 0.5 );
// returns ~0.225

v = sqrt1pm1( 0.02 );
// returns ~0.01

v = sqrt1pm1( -0.5 );
// returns ~-0.293

v = sqrt1pm1( -1.1 );
// returns NaN

v = sqrt1pm1( NaN );
// returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var sqrt1pm1 = require( '@stdlib/math-base-special-sqrt1pm1' );

var x;
var i;

for ( i = 0; i < 100; i++ ) {
    x = round( randu() * 100.0 );
    console.log( 'sqrt(1+%d) - 1 = %d', x, sqrt1pm1( x ) );
}

C APIs

Usage

#include "stdlib/math/base/special/sqrt1pm1.h"

stdlib_base_sqrt1pm1( x )

Computes sqrt( 1 + x ) - 1 more accurately for small x.

double out = stdlib_base_sqrt1pm1( 3.0 );
// returns 1.0

out = stdlib_base_sqrt1pm1( 0.5 );
// returns ~0.225

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_sqrt1pm1( const double x );

Examples

#include "stdlib/math/base/special/sqrt1pm1.h"
#include <stdlib.h>
#include <stdio.h>

int main( void ) {
    double x;
    double v;
    int i;
    
    for ( i = 0; i < 100; i++ ) {
        x = ( (double)rand() / (double)RAND_MAX ) * 100.0;
        v = stdlib_base_sqrt1pm1( x );
        printf( "sqrt(1+%lf) - 1 = %lf\n", x, v );
    }
}

See Also

• @stdlib/math-base/special/sqrt: compute the principal square root of a double-precision floating-point number.

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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Copyright

Copyright © 2016-2024. The Stdlib Authors.