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* @license Apache-2.0
*
* Copyright (c) 2020 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var isInteger = require( '@stdlib/assert/is-integer' ).isObject;
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var floor = require( '@stdlib/math/base/special/floor' );
// MAIN //
/**
* Tests if a value is a number object having a value which is a square triangular number.
*
* ## Notes
*
* - Return values are not reliable for numbers greater than `1125899906842624`.
*
* @param {*} value - value to test
* @returns {boolean} boolean indicating if a value is a number object having a value which is a square triangular number
*
* @example
* var bool = isSquareTriangularNumber( 36.0 );
* // returns false
*
* @example
* var bool = isSquareTriangularNumber( new Number( 36.0 ) );
* // returns true
*/
function isSquareTriangularNumber( value ) {
var n;
var x;
if ( !isInteger( value ) ) {
return false;
}
// Test if a square number:
x = value.valueOf();
n = floor( sqrt( x ) + 0.5 );
if ( n*n !== x ) {
return false;
}
// Test if a triangular number:
x = ( 8.0*x ) + 1.0;
n = floor( sqrt( x ) + 0.5 );
return n*n === x;
}
// EXPORTS //
module.exports = isSquareTriangularNumber;
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