Add utility to test whether a value is a square triangular number

Author: kgryte

lib/node_modules/@stdlib/assert/is-square-triangular-number/README.md

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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.
+
+-->
+
+# isSquareTriangularNumber
+
+> Test if a value is a square [triangular number][@stdlib/assert/is-triangular-number].
+
+<section class="intro">
+
+A **square triangular number** is an integer value which is both a [square number][@stdlib/assert/is-square-number] and a [triangular number][@stdlib/assert/is-triangular-number].
+
+[Triangular numbers][@stdlib/assert/is-triangular-number] can be computed using the following formula
+
+<!-- <equation class="equation" label="eq:triangular_number" align="center" raw="T_n = \frac{n(n+1)}{2}" alt="Triangular number formula."> -->
+
+<div class="equation" align="center" data-raw-text="T_n = \frac{n(n+1)}{2}" data-equation="eq:triangular_number">
+    <img src="" alt="Triangular number formula.">
+    <br>
+</div>
+
+<!-- </equation> -->
+
+for `n >= 0`.
+
+By analogy with the square root of `x`, one can define the positive triangular root of `x` such that `T_n = x`
+
+<!-- <equation class="equation" label="eq:triangular_root" align="center" raw="n = \frac{\sqrt{8x+1} - 1}{2}" alt="Triangular root formula."> -->
+
+<div class="equation" align="center" data-raw-text="n = \frac{\sqrt{8x+1} - 1}{2}" data-equation="eq:triangular_root">
+    <img src="" alt="Triangular root formula.">
+    <br>
+</div>
+
+<!-- </equation> -->
+
+Accordingly, an integer `x` is a [triangular number][@stdlib/assert/is-triangular-number] **if and only** if `8x+1` is a [square number][@stdlib/assert/is-square-number].
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var isSquareTriangularNumber = require( '@stdlib/assert/is-square-triangular-number' );
+```
+
+#### isSquareTriangularNumber( value )
+
+Tests if a `value` is a square [triangular number][@stdlib/assert/is-triangular-number].
+
+<!-- eslint-disable no-new-wrappers -->
+
+```javascript
+var Number = require( '@stdlib/number/ctor' );
+
+var bool = isSquareTriangularNumber( 36.0 );
+// returns true
+
+bool = isSquareTriangularNumber( new Number( 36.0 ) );
+// returns true
+
+bool = isSquareTriangularNumber( 3.14 );
+// returns false
+
+bool = isSquareTriangularNumber( -5.0 );
+// returns false
+
+bool = isSquareTriangularNumber( NaN );
+// returns false
+
+bool = isSquareTriangularNumber( null );
+// returns false
+```
+
+#### isSquareTriangularNumber.isPrimitive( value )
+
+Tests if a `value` is a primitive square [triangular number][@stdlib/assert/is-triangular-number].
+
+<!-- eslint-disable no-new-wrappers -->
+
+```javascript
+var Number = require( '@stdlib/number/ctor' );
+
+var bool = isSquareTriangularNumber.isPrimitive( 36.0 );
+// returns true
+
+bool = isSquareTriangularNumber.isPrimitive( new Number( 36.0 ) );
+// returns false
+```
+
+#### isSquareTriangularNumber.isObject( value )
+
+Tests if a `value` is a `Number` object having a value which is a square [triangular number][@stdlib/assert/is-triangular-number].
+
+<!-- eslint-disable no-new-wrappers -->
+
+```javascript
+var Number = require( '@stdlib/number/ctor' );
+
+var bool = isSquareTriangularNumber.isObject( 36.0 );
+// returns false
+
+bool = isSquareTriangularNumber.isObject( new Number( 36.0 ) );
+// returns true
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Return values are not reliable for numbers greater than `1125899906842624`.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint-disable no-new-wrappers -->
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Number = require( '@stdlib/number/ctor' );
+var isSquareTriangularNumber = require( '@stdlib/assert/is-square-triangular-number' );
+
+var bool = isSquareTriangularNumber( 36.0 );
+// returns true
+
+bool = isSquareTriangularNumber( new Number( 36.0 ) );
+// returns true
+
+bool = isSquareTriangularNumber( 0.0 );
+// returns true
+
+bool = isSquareTriangularNumber( 1.0 );
+// returns true
+
+bool = isSquareTriangularNumber( 3.14 );
+// returns false
+
+bool = isSquareTriangularNumber( -5.0 );
+// returns false
+
+bool = isSquareTriangularNumber( NaN );
+// returns false
+
+bool = isSquareTriangularNumber( '0.5' );
+// returns false
+
+bool = isSquareTriangularNumber( null );
+// returns false
+```
+
+</section>
+
+<!-- /.examples -->
+
+<section class="links">
+
+[@stdlib/assert/is-square-number]: https://github.com/stdlib-js/stdlib
+
+[@stdlib/assert/is-triangular-number]: https://github.com/stdlib-js/stdlib
+
+</section>
+
+<!-- /.links -->