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node_modules/frac/LICENSE

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+Copyright (C) 2012-present   SheetJS
+
+   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.

node_modules/frac/README.md

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+# frac
+
+Rational approximation to a floating point number with bounded denominator.
+
+Uses the [Mediant Method](https://en.wikipedia.org/wiki/Mediant_method).
+
+This module also provides an implementation of the continued fraction method as
+described by Aberth in "A method for exact computation with rational numbers".
+The algorithm is used in <a href="http://sheetjs.com">SheetJS Libraries</a> to
+replicate fraction formats.
+
+## Installation
+
+### JS
+
+With [`npm`](https://www.npmjs.org/package/frac):
+
+```bash
+$ npm install frac
+```
+
+In the browser:
+
+```html
+<script src="frac.js"></script>
+```
+
+The script will manipulate `module.exports` if available .  This is not always
+desirable.  To prevent the behavior, define `DO_NOT_EXPORT_FRAC`
+
+### Python
+
+From [`PyPI`](https://pypi.python.org/pypi/frac):
+
+```bash
+$ pip install frac
+```
+
+## Usage
+
+In all cases, the relevant function takes 3 arguments:
+
+ - `x` the number we wish to approximate
+ - `D` the maximum denominator
+ - `mixed` if true, return a mixed fraction; if false, improper
+
+The return value is an array of the form `[quot, num, den]` where `quot==0`
+for improper fractions.  `quot <= x` for mixed fractions, which may lead to some
+unexpected results when rendering negative numbers.
+
+### JS
+
+The exported `frac` function implements the Mediant method.
+
+`frac.cont` implements the Aberth algorithm
+
+For example:
+
+```js
+> // var frac = require('frac'); // uncomment this line if in node
+> frac(1.3, 9);              // [  0,  9, 7 ] //  1.3 ~       9/7
+> frac(1.3, 9, true);        // [  1,  2, 7 ] //  1.3 ~  1 +  2/7
+> frac(-1.3, 9);             // [  0, -9, 7 ] // -1.3 ~      -9/7
+> frac(-1.3, 9, true);       // [ -2,  5, 7 ] // -1.3 ~ -2 +  5/7
+
+> frac.cont(1.3, 9);         // [  0,  4, 3 ] //  1.3 ~       4/3
+> frac.cont(1.3, 9, true);   // [  1,  1, 3 ] //  1.3 ~  1 +  1/3
+> frac.cont(-1.3, 9);        // [  0, -4, 3 ] // -1.3 ~      -4/3
+> frac.cont(-1.3, 9, true);  // [ -2,  2, 3 ] // -1.3 ~ -2 +  2/3
+```
+
+
+### Python
+
+`frac.med` implements Mediant method.
+
+`frac.cont` implements Aberth algorithm.
+
+For example:
+
+```py
+>>> import frac
+>>> frac.med(1.3, 9)         ## [  0,  9, 7 ] ##  1.3 ~       9/7
+>>> frac.med(1.3, 9, True)   ## [  1,  2, 7 ] ##  1.3 ~  1 +  2/7
+>>> frac.med(-1.3, 9)        ## [  0, -9, 7 ] ## -1.3 ~      -9/7
+>>> frac.med(-1.3, 9, True)  ## [ -2,  5, 7 ] ## -1.3 ~ -2 +  5/7
+
+>>> frac.cont(1.3, 9)        ## [  0,  4, 3 ] ##  1.3 ~       4/3
+>>> frac.cont(1.3, 9, True)  ## [  1,  1, 3 ] ##  1.3 ~  1 +  1/3
+>>> frac.cont(-1.3, 9)       ## [  0, -4, 3 ] ## -1.3 ~      -4/3
+>>> frac.cont(-1.3, 9, True) ## [ -2,  2, 3 ] ## -1.3 ~ -2 +  2/3
+```
+
+## Testing
+
+The test TSV baselines in the `test_files` directory have four columns:
+
+- Column A contains the raw values
+- Column B format "Up to one digit (1/4)" (`denominator = 9`)
+- Column C format "Up to two digits (21/25)" (`denominator = 99`)
+- Column D format "Up to three digits (312/943)" (`denominator = 999`)
+
+`make test` will run the node-based tests.
+
+`make pytest` will run the python tests against the system Python version.
+
+`make pypytest` will run the python tests against `pypy` if installed
+
+## License
+
+Please consult the attached LICENSE file for details.  All rights not explicitly
+granted by the Apache 2.0 License are reserved by the Original Author.
+
+## Badges
+
+[![Build Status](https://saucelabs.com/browser-matrix/frac.svg)](https://saucelabs.com/u/frac)
+
+[![Build Status](https://travis-ci.org/SheetJS/frac.svg?branch=master)](https://travis-ci.org/SheetJS/frac)
+
+[![Coverage Status](http://img.shields.io/coveralls/SheetJS/frac/master.svg)](https://coveralls.io/r/SheetJS/frac?branch=master)
+
+[![NPM Downloads](https://img.shields.io/npm/dt/frac.svg)](https://npmjs.org/package/frac)
+
+[![Dependencies Status](https://david-dm.org/sheetjs/frac/status.svg)](https://david-dm.org/sheetjs/frac)
+
+[![ghit.me](https://ghit.me/badge.svg?repo=sheetjs/js-xlsx)](https://ghit.me/repo/sheetjs/js-xlsx)
+
+[![Analytics](https://ga-beacon.appspot.com/UA-36810333-1/SheetJS/frac?pixel)](https://github.com/SheetJS/frac)

node_modules/frac/dist/LICENSE

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+Copyright (C) 2012-present   SheetJS
+
+   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.

node_modules/frac/dist/frac.js

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+/* frac.js (C) 2012-present SheetJS -- http://sheetjs.com */
+var frac = function frac(x, D, mixed) {
+  var n1 = Math.floor(x), d1 = 1;
+  var n2 = n1+1, d2 = 1;
+  if(x !== n1) while(d1 <= D && d2 <= D) {
+    var m = (n1 + n2) / (d1 + d2);
+    if(x === m) {
+      if(d1 + d2 <= D) { d1+=d2; n1+=n2; d2=D+1; }
+      else if(d1 > d2) d2=D+1;
+      else d1=D+1;
+      break;
+    }
+    else if(x < m) { n2 = n1+n2; d2 = d1+d2; }
+    else { n1 = n1+n2; d1 = d1+d2; }
+  }
+  if(d1 > D) { d1 = d2; n1 = n2; }
+  if(!mixed) return [0, n1, d1];
+  var q = Math.floor(n1/d1);
+  return [q, n1 - q*d1, d1];
+};
+frac.cont = function cont(x, D, mixed) {
+  var sgn = x < 0 ? -1 : 1;
+  var B = x * sgn;
+  var P_2 = 0, P_1 = 1, P = 0;
+  var Q_2 = 1, Q_1 = 0, Q = 0;
+  var A = Math.floor(B);
+  while(Q_1 < D) {
+    A = Math.floor(B);
+    P = A * P_1 + P_2;
+    Q = A * Q_1 + Q_2;
+    if((B - A) < 0.00000005) break;
+    B = 1 / (B - A);
+    P_2 = P_1; P_1 = P;
+    Q_2 = Q_1; Q_1 = Q;
+  }
+  if(Q > D) { if(Q_1 > D) { Q = Q_2; P = P_2; } else { Q = Q_1; P = P_1; } }
+  if(!mixed) return [0, sgn * P, Q];
+  var q = Math.floor(sgn * P/Q);
+  return [q, sgn*P - q*Q, Q];
+};
+// eslint-disable-next-line no-undef
+if(typeof module !== 'undefined' && typeof DO_NOT_EXPORT_FRAC === 'undefined') module.exports = frac;

node_modules/frac/dist/frac.min.js

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+/* frac.js (C) 2012-present SheetJS -- http://sheetjs.com */
+var frac=function frac(x,D,mixed){var n1=Math.floor(x),d1=1;var n2=n1+1,d2=1;if(x!==n1)while(d1<=D&&d2<=D){var m=(n1+n2)/(d1+d2);if(x===m){if(d1+d2<=D){d1+=d2;n1+=n2;d2=D+1}else if(d1>d2)d2=D+1;else d1=D+1;break}else if(x<m){n2=n1+n2;d2=d1+d2}else{n1=n1+n2;d1=d1+d2}}if(d1>D){d1=d2;n1=n2}if(!mixed)return[0,n1,d1];var q=Math.floor(n1/d1);return[q,n1-q*d1,d1]};frac.cont=function cont(x,D,mixed){var sgn=x<0?-1:1;var B=x*sgn;var P_2=0,P_1=1,P=0;var Q_2=1,Q_1=0,Q=0;var A=Math.floor(B);while(Q_1<D){A=Math.floor(B);P=A*P_1+P_2;Q=A*Q_1+Q_2;if(B-A<5e-8)break;B=1/(B-A);P_2=P_1;P_1=P;Q_2=Q_1;Q_1=Q}if(Q>D){if(Q_1>D){Q=Q_2;P=P_2}else{Q=Q_1;P=P_1}}if(!mixed)return[0,sgn*P,Q];var q=Math.floor(sgn*P/Q);return[q,sgn*P-q*Q,Q]};if(typeof module!=="undefined"&&typeof DO_NOT_EXPORT_FRAC==="undefined")module.exports=frac;

node_modules/frac/dist/frac.min.map

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node_modules/frac/frac.js

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+/* frac.js (C) 2012-present SheetJS -- http://sheetjs.com */
+var frac = function frac(x, D, mixed) {
+  var n1 = Math.floor(x), d1 = 1;
+  var n2 = n1+1, d2 = 1;
+  if(x !== n1) while(d1 <= D && d2 <= D) {
+    var m = (n1 + n2) / (d1 + d2);
+    if(x === m) {
+      if(d1 + d2 <= D) { d1+=d2; n1+=n2; d2=D+1; }
+      else if(d1 > d2) d2=D+1;
+      else d1=D+1;
+      break;
+    }
+    else if(x < m) { n2 = n1+n2; d2 = d1+d2; }
+    else { n1 = n1+n2; d1 = d1+d2; }
+  }
+  if(d1 > D) { d1 = d2; n1 = n2; }
+  if(!mixed) return [0, n1, d1];
+  var q = Math.floor(n1/d1);
+  return [q, n1 - q*d1, d1];
+};
+frac.cont = function cont(x, D, mixed) {
+  var sgn = x < 0 ? -1 : 1;
+  var B = x * sgn;
+  var P_2 = 0, P_1 = 1, P = 0;
+  var Q_2 = 1, Q_1 = 0, Q = 0;
+  var A = Math.floor(B);
+  while(Q_1 < D) {
+    A = Math.floor(B);
+    P = A * P_1 + P_2;
+    Q = A * Q_1 + Q_2;
+    if((B - A) < 0.00000005) break;
+    B = 1 / (B - A);
+    P_2 = P_1; P_1 = P;
+    Q_2 = Q_1; Q_1 = Q;
+  }
+  if(Q > D) { if(Q_1 > D) { Q = Q_2; P = P_2; } else { Q = Q_1; P = P_1; } }
+  if(!mixed) return [0, sgn * P, Q];
+  var q = Math.floor(sgn * P/Q);
+  return [q, sgn*P - q*Q, Q];
+};
+// eslint-disable-next-line no-undef
+if(typeof module !== 'undefined' && typeof DO_NOT_EXPORT_FRAC === 'undefined') module.exports = frac;

node_modules/frac/package.json

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+{
+  "name": "frac",
+  "version": "1.1.2",
+  "author": "SheetJS",
+  "description": "Rational approximation with bounded denominator",
+  "keywords": [ "math", "fraction", "rational", "approximation" ],
+  "main": "./frac",
+  "types": "types",
+  "dependencies": {},
+  "devDependencies": {
+    "voc": "~1.1.0",
+    "mocha": "~2.5.3",
+    "blanket": "~1.2.3",
+    "codepage": "~1.10.0",
+    "@sheetjs/uglify-js": "~2.7.3",
+    "@types/node": "^8.0.7",
+    "dtslint": "^0.1.2",
+    "typescript": "2.2.0"
+  },
+  "repository": { "type":"git", "url":"git://github.com/SheetJS/frac.git" },
+  "scripts": {
+    "test": "make test",
+    "build": "make",
+    "lint": "make fullint",
+    "dtslint": "dtslint types"
+  },
+  "config": {
+    "blanket": {
+      "pattern": "frac.js"
+    }
+  },
+  "homepage": "http://sheetjs.com/opensource",
+  "bugs": { "url": "https://github.com/SheetJS/frac/issues" },
+  "license": "Apache-2.0",
+  "engines": { "node": ">=0.8" }
+}

node_modules/frac/types/index.d.ts

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+/* frac.js (C) 2012-present SheetJS -- http://sheetjs.com */
+// TypeScript Version: 2.2
+
+export interface Frac$Module {
+	(x: number, D: number, mixed?: boolean): [number, number, number];
+	cont(x: number, D: number, mixed?: boolean): [number, number, number];
+}
+export const frac: Frac$Module;
+export default frac;

node_modules/frac/types/tsconfig.json

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+{
+    "compilerOptions": {
+        "module": "commonjs",
+        "lib": [ "es5" ],
+        "noImplicitAny": true,
+        "noImplicitThis": true,
+        "strictNullChecks": false,
+        "baseUrl": ".",
+        "paths": { "frac": ["."] },
+        "types": [],
+        "noEmit": true,
+        "forceConsistentCasingInFileNames": true
+    }
+}

node_modules/frac/types/tslint.json

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+{
+	"extends": "dtslint/dtslint.json",
+	"rules": {
+		"whitespace": false,
+		"no-sparse-arrays": false,
+		"only-arrow-functions": false,
+		"no-consecutive-blank-lines": false,
+		"prefer-conditional-expression": false,
+		"one-variable-per-declaration": false
+	}
+}