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129 lines
4.0 KiB
129 lines
4.0 KiB
2 months ago
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# frac
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Rational approximation to a floating point number with bounded denominator.
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Uses the [Mediant Method](https://en.wikipedia.org/wiki/Mediant_method).
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This module also provides an implementation of the continued fraction method as
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described by Aberth in "A method for exact computation with rational numbers".
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The algorithm is used in <a href="http://sheetjs.com">SheetJS Libraries</a> to
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replicate fraction formats.
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## Installation
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### JS
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With [`npm`](https://www.npmjs.org/package/frac):
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```bash
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$ npm install frac
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```
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In the browser:
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```html
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<script src="frac.js"></script>
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```
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The script will manipulate `module.exports` if available . This is not always
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desirable. To prevent the behavior, define `DO_NOT_EXPORT_FRAC`
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### Python
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From [`PyPI`](https://pypi.python.org/pypi/frac):
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```bash
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$ pip install frac
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```
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## Usage
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In all cases, the relevant function takes 3 arguments:
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- `x` the number we wish to approximate
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- `D` the maximum denominator
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- `mixed` if true, return a mixed fraction; if false, improper
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The return value is an array of the form `[quot, num, den]` where `quot==0`
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for improper fractions. `quot <= x` for mixed fractions, which may lead to some
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unexpected results when rendering negative numbers.
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### JS
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The exported `frac` function implements the Mediant method.
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`frac.cont` implements the Aberth algorithm
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For example:
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```js
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> // var frac = require('frac'); // uncomment this line if in node
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> frac(1.3, 9); // [ 0, 9, 7 ] // 1.3 ~ 9/7
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> frac(1.3, 9, true); // [ 1, 2, 7 ] // 1.3 ~ 1 + 2/7
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> frac(-1.3, 9); // [ 0, -9, 7 ] // -1.3 ~ -9/7
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> frac(-1.3, 9, true); // [ -2, 5, 7 ] // -1.3 ~ -2 + 5/7
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> frac.cont(1.3, 9); // [ 0, 4, 3 ] // 1.3 ~ 4/3
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> frac.cont(1.3, 9, true); // [ 1, 1, 3 ] // 1.3 ~ 1 + 1/3
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> frac.cont(-1.3, 9); // [ 0, -4, 3 ] // -1.3 ~ -4/3
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> frac.cont(-1.3, 9, true); // [ -2, 2, 3 ] // -1.3 ~ -2 + 2/3
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```
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### Python
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`frac.med` implements Mediant method.
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`frac.cont` implements Aberth algorithm.
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For example:
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```py
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>>> import frac
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>>> frac.med(1.3, 9) ## [ 0, 9, 7 ] ## 1.3 ~ 9/7
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>>> frac.med(1.3, 9, True) ## [ 1, 2, 7 ] ## 1.3 ~ 1 + 2/7
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>>> frac.med(-1.3, 9) ## [ 0, -9, 7 ] ## -1.3 ~ -9/7
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>>> frac.med(-1.3, 9, True) ## [ -2, 5, 7 ] ## -1.3 ~ -2 + 5/7
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>>> frac.cont(1.3, 9) ## [ 0, 4, 3 ] ## 1.3 ~ 4/3
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>>> frac.cont(1.3, 9, True) ## [ 1, 1, 3 ] ## 1.3 ~ 1 + 1/3
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>>> frac.cont(-1.3, 9) ## [ 0, -4, 3 ] ## -1.3 ~ -4/3
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>>> frac.cont(-1.3, 9, True) ## [ -2, 2, 3 ] ## -1.3 ~ -2 + 2/3
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```
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## Testing
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The test TSV baselines in the `test_files` directory have four columns:
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- Column A contains the raw values
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- Column B format "Up to one digit (1/4)" (`denominator = 9`)
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- Column C format "Up to two digits (21/25)" (`denominator = 99`)
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- Column D format "Up to three digits (312/943)" (`denominator = 999`)
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`make test` will run the node-based tests.
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`make pytest` will run the python tests against the system Python version.
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`make pypytest` will run the python tests against `pypy` if installed
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## License
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Please consult the attached LICENSE file for details. All rights not explicitly
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granted by the Apache 2.0 License are reserved by the Original Author.
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## Badges
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[](https://saucelabs.com/u/frac)
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[](https://travis-ci.org/SheetJS/frac)
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[](https://coveralls.io/r/SheetJS/frac?branch=master)
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[](https://npmjs.org/package/frac)
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[](https://david-dm.org/sheetjs/frac)
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[](https://ghit.me/repo/sheetjs/js-xlsx)
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[](https://github.com/SheetJS/frac)
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