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feat: add math/iter/sequences/tribonacci
PR-URL: #1393 Closes: #1331 Reviewed-by: Philipp Burckhardt <pburckhardt@outlook.com>
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‎lib/node_modules/@stdlib/math/iter/sequences/tribonacci/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2024 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# iterTribonacciSeq
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> Create an iterator which generates a [tribonacci sequence][tribonacci-number].
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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The [Tribonacci numbers][tribonacci-number] are the integer sequence
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<!-- <equation class="equation" label="eq:tribonacci_sequence" align="center" raw="0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, \ldots" alt="Tribonacci sequence"> -->
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```math
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0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, \ldots
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```
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<!-- <div class="equation" align="center" data-raw-text="0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, \ldots" data-equation="eq:tribonacci_sequence">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@3249a68fb57cd71148f87ef3b2774be70a04d80a/lib/node_modules/@stdlib/math/base/special/tribonacci/docs/img/equation_tribonacci_sequence.svg" alt="Tribonacci sequence">
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<br>
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</div> -->
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<!-- </equation> -->
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The sequence is defined by the recurrence relation
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<!-- <equation class="equation" label="eq:tribonacci_recurrence_relation" align="center" raw="F_n = F_{n-1} + F_{n-2} + F_{n-3}" alt="Tribonacci sequence recurrence relation"> -->
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```math
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F_n = F_{n-1} + F_{n-2} + F_{n-3}
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```
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<!-- <div class="equation" align="center" data-raw-text="F_n = F_{n-1} + F_{n-2} + F_{n-3}" data-equation="eq:tribonacci_recurrence_relation">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@3249a68fb57cd71148f87ef3b2774be70a04d80a/lib/node_modules/@stdlib/math/base/special/tribonacci/docs/img/equation_tribonacci_recurrence_relation.svg" alt="Tribonacci sequence recurrence relation">
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<br>
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</div> -->
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<!-- </equation> -->
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with seed values `F_0 = 0`, `F_1 = 0`, and `F_2 = 1`.
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</section>
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<!-- /.intro -->
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<!-- Package usage documentation. -->
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<section class="usage">
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## Usage
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```javascript
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var iterTribonacciSeq = require( '@stdlib/math/iter/sequences/tribonacci' );
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```
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#### iterTribonacciSeq( \[options] )
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Returns an iterator which generates a [Tribonacci sequence][tribonacci-number].
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```javascript
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var it = iterTribonacciSeq();
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// returns <Object>
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var v = it.next().value;
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// returns 0
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v = it.next().value;
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// returns 0
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v = it.next().value;
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// returns 1
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// ...
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```
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The returned iterator protocol-compliant object has the following properties:
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- **next**: function which returns an iterator protocol-compliant object containing the next iterated value (if one exists) assigned to a `value` property and a `done` property having a `boolean` value indicating whether the iterator is finished.
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- **return**: function which closes an iterator and returns a single (optional) argument in an iterator protocol-compliant object.
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The function supports the following `options`:
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- **iter**: number of iterations. Default: `64`.
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The returned iterator can only generate the first `64` [Tribonacci numbers][tribonacci-number], as larger [Tribonacci numbers][tribonacci-number] cannot be safely represented in [double-precision floating-point format][ieee754]. By default, the function returns an iterator which generates all `64` numbers. To limit the number of iterations, set the `iter` option.
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```javascript
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var opts = {
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'iter': 3
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};
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var it = iterTribonacciSeq( opts );
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// returns <Object>
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var v = it.next().value;
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// returns 0
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v = it.next().value;
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// returns 0
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v = it.next().value;
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// returns 1
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var bool = it.next().done;
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// returns true
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```
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</section>
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<!-- /.usage -->
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<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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## Notes
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- If an environment supports `Symbol.iterator`, the returned iterator is iterable.
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</section>
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<!-- /.notes -->
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<!-- Package usage examples. -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var iterTribonacciSeq = require( '@stdlib/math/iter/sequences/tribonacci' );
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// Create an iterator:
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var it = iterTribonacciSeq();
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// Perform manual iteration...
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var v;
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while ( true ) {
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v = it.next();
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if ( v.done ) {
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break;
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}
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console.log( v.value );
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}
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```
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</section>
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<!-- /.examples -->
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<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="references">
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</section>
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<!-- /.references -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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* * *
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## See Also
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- <span class="package-name">[`@stdlib/math/base/special/tribonacci`][@stdlib/math/base/special/tribonacci]</span><span class="delimiter">: </span><span class="description">compute the nth Tribonacci number.</span>
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- <span class="package-name">[`@stdlib/math/base/special/fibonacci`][@stdlib/math/base/special/fibonacci]</span><span class="delimiter">: </span><span class="description">compute the nth Fibonacci number.</span>
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- <span class="package-name">[`@stdlib/math/iter/sequences/lucas`][@stdlib/math/iter/sequences/lucas]</span><span class="delimiter">: </span><span class="description">create an iterator which generates a Lucas sequence.</span>
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[tribonacci-number]: https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Tribonacci_numbers
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[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985
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<!-- <related-links> -->
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[@stdlib/math/base/special/tribonacci]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/tribonacci
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[@stdlib/math/iter/sequences/lucas]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/iter/sequences/lucas
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[@stdlib/math/base/special/fibonacci]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/fibonacci
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/math/iter/sequences/tribonacci/benchmark/benchmark.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var isIteratorLike = require( '@stdlib/assert/is-iterator-like' );
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var pkg = require( './../package.json' ).name;
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var iterTribonacciSeq = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var iter;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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iter = iterTribonacciSeq();
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if ( typeof iter !== 'object' ) {
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b.fail( 'should return an object' );
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}
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}
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b.toc();
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if ( !isIteratorLike( iter ) ) {
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b.fail( 'should return an iterator protocol-compliant object' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+'::iteration', function benchmark( b ) {
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var iter;
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var z;
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var i;
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iter = iterTribonacciSeq();
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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z = iter.next().value;
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if ( isnan( z ) ) {
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b.fail( 'should not be NaN' );
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}
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}
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b.toc();
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if ( isnan( z ) ) {
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b.fail( 'should not be NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

‎lib/node_modules/@stdlib/math/iter/sequences/tribonacci/docs/img/equation_tribonacci_recurrence_relation.svg

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