feat: add constants/float16/fourth-root-eps

lib/node_modules/@stdlib/constants/float16/fourth-root-eps/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 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.
+
+-->
+
+# FLOAT16_FOURTH_ROOT_EPS
+
+> [Fourth root][nth-root] of [half-precision floating-point epsilon][@stdlib/constants/float16/eps].
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var FLOAT16_FOURTH_ROOT_EPS = require( '@stdlib/constants/float16/fourth-root-eps' );
+```
+
+#### FLOAT16_FOURTH_ROOT_EPS
+
+[Fourth root][nth-root] of [half-precision floating-point epsilon][@stdlib/constants/float16/eps].
+
+```javascript
+var bool = ( FLOAT16_FOURTH_ROOT_EPS === 0.1767766952966369 );
+// returns true
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var FLOAT16_FOURTH_ROOT_EPS = require( '@stdlib/constants/float16/fourth-root-eps' );
+
+var out = FLOAT16_FOURTH_ROOT_EPS;
+// returns 0.1767766952966369
+```
+
+</section>
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[nth-root]: https://en.wikipedia.org/wiki/Nth_root
+[@stdlib/constants/float16/eps]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/constants/float16/eps
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/constants/float16/fourth-root-eps/docs/repl.txt

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+
+{{alias}}
+    Fourth root of half-precision floating-point epsilon.
+
+    Examples
+    --------
+    > {{alias}}
+    0.1767766952966369
+
+    See Also
+    --------

lib/node_modules/@stdlib/constants/float16/fourth-root-eps/docs/types/index.d.ts

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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.
+*/
+
+// TypeScript Version: 4.1
+
+/**
+* Fourth root of half-precision floating-point epsilon.
+*
+* @example
+* var eps = FLOAT16_FOURTH_ROOT_EPS;
+* // returns 0.1767766952966369
+*/
+declare const FLOAT16_FOURTH_ROOT_EPS: number;
+
+
+// EXPORTS //
+
+export = FLOAT16_FOURTH_ROOT_EPS;

lib/node_modules/@stdlib/constants/float16/fourth-root-eps/docs/types/test.ts

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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.
+*/
+
+import FLOAT16_FOURTH_ROOT_EPS = require( './index' );
+
+
+// TESTS //
+
+// The export is a number...
+{
+	// eslint-disable-next-line @typescript-eslint/no-unused-expressions
+	FLOAT16_FOURTH_ROOT_EPS; // $ExpectType number
+}

lib/node_modules/@stdlib/constants/float16/fourth-root-eps/examples/index.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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';
+
+var FLOAT16_FOURTH_ROOT_EPS = require( './../lib' );
+
+console.log( FLOAT16_FOURTH_ROOT_EPS );
+// => 0.1767766952966369

lib/node_modules/@stdlib/constants/float16/fourth-root-eps/lib/index.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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';
+
+/**
+* Fourth root of half-precision floating-point epsilon.
+*
+* @module @stdlib/constants/float16/fourth-root-eps
+* @type {number}
+*
+* @example
+* var FLOAT16_FOURTH_ROOT_EPS = require( '@stdlib/constants/float16/fourth-root-eps' );
+* // returns 0.1767766952966369
+*/
+
+
+// MAIN //
+
+/**
+* Fourth root of half-precision floating-point epsilon.
+*
+* ```tex
+* \sqrt{\sqrt{\frac{1}{2^{10}}}}
+* ```
+*
+* @constant
+* @type {number}
+* @default 0.1767766952966369
+* @see [IEEE 754]{@link https://en.wikipedia.org/wiki/IEEE_754-1985}
+* @see [Half-precision floating-point format]{@link https://en.wikipedia.org/wiki/Half-precision_floating-point_format}
+*/
+var FLOAT16_FOURTH_ROOT_EPS = 0.1767766952966369;
+
+
+// EXPORTS //
+
+module.exports = FLOAT16_FOURTH_ROOT_EPS;

lib/node_modules/@stdlib/constants/float16/fourth-root-eps/package.json

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+{
+  "name": "@stdlib/constants/float16/fourth-root-eps",
+  "version": "0.0.0",
+  "description": "Fourth root of half-precision floating-point epsilon.",
+  "license": "Apache-2.0",
+  "author": {
+    "name": "The Stdlib Authors",
+    "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+  },
+  "contributors": [
+    {
+      "name": "The Stdlib Authors",
+      "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+    }
+  ],
+  "main": "./lib",
+  "directories": {
+    "doc": "./docs",
+    "example": "./examples",
+    "lib": "./lib",
+    "test": "./test"
+  },
+  "types": "./docs/types",
+  "scripts": {},
+  "homepage": "https://github.com/stdlib-js/stdlib",
+  "repository": {
+    "type": "git",
+    "url": "git://github.com/stdlib-js/stdlib.git"
+  },
+  "bugs": {
+    "url": "https://github.com/stdlib-js/stdlib/issues"
+  },
+  "dependencies": {},
+  "devDependencies": {},
+  "engines": {
+    "node": ">=0.10.0",
+    "npm": ">2.7.0"
+  },
+  "os": [
+    "aix",
+    "darwin",
+    "freebsd",
+    "linux",
+    "macos",
+    "openbsd",
+    "sunos",
+    "win32",
+    "windows"
+  ],
+  "keywords": [
+    "stdlib",
+    "stdmath",
+    "constant",
+    "const",
+    "mathematics",
+    "math",
+    "double",
+    "dbl",
+    "floating-point",
+    "float",
+    "float16",
+    "16bit",
+    "16-bit",
+    "ieee754",
+    "epsilon",
+    "eps",
+    "number",
+    "sqrt",
+    "fourth",
+    "root"
+  ]
+}

lib/node_modules/@stdlib/constants/float16/fourth-root-eps/test/test.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 tape = require( 'tape' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var sqrt = require( '@stdlib/math/base/special/sqrt' );
+var FLOAT16_FOURTH_ROOT_EPS = require( './../lib' );
+
+
+// TESTS //
+
+tape( 'main export is a number', function test( t ) {
+	t.ok( true, __filename );
+	t.strictEqual( typeof FLOAT16_FOURTH_ROOT_EPS, 'number', 'main export is a number' );
+	t.end();
+});
+
+tape( 'the exported value equals the fourth root of the difference between one and the smallest value greater than one which is representable as a double (2**-10)', function test( t ) {
+	var expected = sqrt( sqrt( pow( 2, -10 ) ) );
+	t.equal( FLOAT16_FOURTH_ROOT_EPS, expected, 'equals sqrt( sqrt(2**-10) )' );
+	t.end();
+});