time-to-botec

README.md (5413B)

---

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 @license Apache-2.0
 
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 See the License for the specific language governing permissions and
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 # continued-fraction
 
 > [Continued fraction][continued-fraction] approximation.
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var continuedFraction = require( '@stdlib/math/base/tools/continued-fraction' );
 ```
 
 #### continuedFraction( generator\[, options ] )
 
 Evaluates the continued fraction described by the supplied `generator` argument. `generator` can be either a function which returns an array with two elements, the `a` and `b` terms of the fraction, or an ES6 [Generator object][es6-generator]. By default, the function computes
 
 <!-- <equation class="equation" label="eq:continued_fraction_a" align="center" raw="\frac{a_1}{b_1+\frac{a_2}{b_2+\frac{a_3}{b_3+\frac{a_4}{b_4}+\ldots}}}" alt="Continued fraction without leading b_0 term"> -->
 
 <div class="equation" align="center" data-raw-text="\frac{a_1}{b_1+\frac{a_2}{b_2+\frac{a_3}{b_3+\frac{a_4}{b_4}+\ldots}}}" data-equation="eq:continued_fraction_a">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/tools/continued-fraction/docs/img/equation_continued_fraction_a.svg" alt="Continued fraction without leading b_0 term">
     <br>
 </div>
 
 <!-- </equation> -->
 
 Using an ES6 [Generator object][es6-generator]:
 
 <!-- eslint-disable no-restricted-syntax -->
 
 ```javascript
 // Continued fraction for (e-1)^(-1):
 var gen = generator();
 var out = continuedFraction( gen );
 // returns ~0.582
 
 function* generator() {
     var i = 0;
     while ( true ) {
         i += 1;
         yield [ i, i ];
     }
 }
 ```
 
 Alternatively, one can use a closure to achieve the same goal:
 
 ```javascript
 // Continued fraction for (e-1)^(-1):
 var gen = generator();
 var out = continuedFraction( gen );
 // returns ~0.582
 
 function generator() {
     var i = 0;
     return gen;
 
     function gen() {
         i += 1;
         return [ i, i ];
     }
 }
 ```
 
 The function accepts the following `options`:
 
 -   **maxIter**: `integer` denoting the maximum number of times the supplied generator object will be called. Default: `1000000`.
 -   **tolerance**: `number` primitive specifying the used tolerance to assess convergence. Default: `2.22e-16`.
 -   **keep**: `boolean` primitive indicating whether to keep the `b0` term in the continued fraction. Default: `false`.
 
 To evaluate
 
 <!-- <equation class="equation" label="eq:continued_fraction_b" align="center" raw="b_0 + \frac{a_1}{b_1+\frac{a_2}{b_2+\frac{a_3}{b_3+\frac{a_4}{b_4}+\ldots}}}" alt="Continued fraction with leading b_0 term"> -->
 
 <div class="equation" align="center" data-raw-text="b_0 + \frac{a_1}{b_1+\frac{a_2}{b_2+\frac{a_3}{b_3+\frac{a_4}{b_4}+\ldots}}}" data-equation="eq:continued_fraction_b">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/tools/continued-fraction/docs/img/equation_continued_fraction_b.svg" alt="Continued fraction with leading b_0 term">
     <br>
 </div>
 
 <!-- </equation> -->
 
 set the `keep` option to `true`.
 
 ```javascript
 var out = continuedFraction( generator(), {
     'keep': true
 });
 // returns ~1.718
 
 function generator() {
     var i = 0;
     return gen;
 
     function gen() {
         i += 1;
         return [ i, i ];
     }
 }
 ```
 
 To change the maximum number of iterations, set the `maxIter` option.
 
 ```javascript
 var out = continuedFraction( generator(), {
     'maxIter': 10
 });
 // returns ~0.582
 
 function generator() {
     var i = 0;
     return gen;
 
     function gen() {
         i += 1;
         return [ i, i ];
     }
 }
 ```
 
 The default tolerance of `2.22e-16` to assess convergence can be changed via the `tolerance` option.
 
 ```javascript
 var out = continuedFraction( generator(), {
     'tolerance': 1e-1
 });
 // returns ~0.579
 
 function generator() {
     var i = 0;
     return gen;
 
     function gen() {
         i += 1;
         return [ i, i ];
     }
 }
 ```
 
 </section>
 
 <!-- /.usage -->
 
 <section class="examples">
 
 ## Examples
 
 <!-- eslint-disable no-restricted-syntax -->
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 var continuedFraction = require( '@stdlib/math/base/tools/continued-fraction' );
 var out;
 
 function* generator() {
     while ( true ) {
         yield [ 1, 1 ];
     }
 }
 
 function closure() {
     var ones = [ 1, 1 ];
     return gen;
 
     function gen() {
         return ones;
     }
 }
 
 out = continuedFraction( generator(), {
     'keep': true
 });
 console.log( 'Golden ratio (generator): %d,', out );
 
 out = continuedFraction( closure(), {
     'keep': true
 });
 console.log( 'Golden ratio (closure): %d', out );
 ```
 
 </section>
 
 <!-- /.examples -->
 
 <section class="links">
 
 [continued-fraction]: https://en.wikipedia.org/wiki/Continued_fraction
 
 [es6-generator]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Statements/function*
 
 </section>
 
 <!-- /.links -->