From fc87c009806dcc98867f6b58efe29b042aa01dee Mon Sep 17 00:00:00 2001 From: littleblack111 Date: Mon, 18 May 2026 23:10:59 +0800 Subject: node: update --- node_modules/fraction.js/LICENSE | 21 - node_modules/fraction.js/README.md | 466 ---------------- node_modules/fraction.js/bigfraction.js | 899 ------------------------------ node_modules/fraction.js/fraction.cjs | 904 ------------------------------- node_modules/fraction.js/fraction.d.ts | 60 -- node_modules/fraction.js/fraction.js | 891 ------------------------------ node_modules/fraction.js/fraction.min.js | 18 - node_modules/fraction.js/package.json | 55 -- 8 files changed, 3314 deletions(-) delete mode 100644 node_modules/fraction.js/LICENSE delete mode 100644 node_modules/fraction.js/README.md delete mode 100644 node_modules/fraction.js/bigfraction.js delete mode 100644 node_modules/fraction.js/fraction.cjs delete mode 100644 node_modules/fraction.js/fraction.d.ts delete mode 100644 node_modules/fraction.js/fraction.js delete mode 100644 node_modules/fraction.js/fraction.min.js delete mode 100644 node_modules/fraction.js/package.json (limited to 'node_modules/fraction.js') diff --git a/node_modules/fraction.js/LICENSE b/node_modules/fraction.js/LICENSE deleted file mode 100644 index 6dd5328f..00000000 --- a/node_modules/fraction.js/LICENSE +++ /dev/null @@ -1,21 +0,0 @@ -MIT License - -Copyright (c) 2023 Robert Eisele - -Permission is hereby granted, free of charge, to any person obtaining a copy -of this software and associated documentation files (the "Software"), to deal -in the Software without restriction, including without limitation the rights -to use, copy, modify, merge, publish, distribute, sublicense, and/or sell -copies of the Software, and to permit persons to whom the Software is -furnished to do so, subject to the following conditions: - -The above copyright notice and this permission notice shall be included in all -copies or substantial portions of the Software. - -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE -AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE -SOFTWARE. diff --git a/node_modules/fraction.js/README.md b/node_modules/fraction.js/README.md deleted file mode 100644 index 7d3f31a4..00000000 --- a/node_modules/fraction.js/README.md +++ /dev/null @@ -1,466 +0,0 @@ -# Fraction.js - ℚ in JavaScript - -[![NPM Package](https://img.shields.io/npm/v/fraction.js.svg?style=flat)](https://npmjs.org/package/fraction.js "View this project on npm") -[![MIT license](http://img.shields.io/badge/license-MIT-brightgreen.svg)](http://opensource.org/licenses/MIT) - - -Tired of inprecise numbers represented by doubles, which have to store rational and irrational numbers like PI or sqrt(2) the same way? Obviously the following problem is preventable: - -```javascript -1 / 98 * 98 // = 0.9999999999999999 -``` - -If you need more precision or just want a fraction as a result, just include *Fraction.js*: - -```javascript -var Fraction = require('fraction.js'); -// or -import Fraction from 'fraction.js'; -``` - -and give it a trial: - -```javascript -Fraction(1).div(98).mul(98) // = 1 -``` - -Internally, numbers are represented as *numerator / denominator*, which adds just a little overhead. However, the library is written with performance and accuracy in mind, which makes it the perfect basis for [Polynomial.js](https://github.com/infusion/Polynomial.js) and [Math.js](https://github.com/josdejong/mathjs). - -Convert decimal to fraction -=== -The simplest job for fraction.js is to get a fraction out of a decimal: -```javascript -var x = new Fraction(1.88); -var res = x.toFraction(true); // String "1 22/25" -``` - -Examples / Motivation -=== -A simple example might be - -```javascript -var f = new Fraction("9.4'31'"); // 9.4313131313131... -f.mul([-4, 3]).mod("4.'8'"); // 4.88888888888888... -``` -The result is - -```javascript -console.log(f.toFraction()); // -4154 / 1485 -``` -You could of course also access the sign (s), numerator (n) and denominator (d) on your own: -```javascript -f.s * f.n / f.d = -1 * 4154 / 1485 = -2.797306... -``` - -If you would try to calculate it yourself, you would come up with something like: - -```javascript -(9.4313131 * (-4 / 3)) % 4.888888 = -2.797308133... -``` - -Quite okay, but yea - not as accurate as it could be. - - -Laplace Probability -=== -Simple example. What's the probability of throwing a 3, and 1 or 4, and 2 or 4 or 6 with a fair dice? - -P({3}): -```javascript -var p = new Fraction([3].length, 6).toString(); // 0.1(6) -``` - -P({1, 4}): -```javascript -var p = new Fraction([1, 4].length, 6).toString(); // 0.(3) -``` - -P({2, 4, 6}): -```javascript -var p = new Fraction([2, 4, 6].length, 6).toString(); // 0.5 -``` - -Convert degrees/minutes/seconds to precise rational representation: -=== - -57+45/60+17/3600 -```javascript -var deg = 57; // 57° -var min = 45; // 45 Minutes -var sec = 17; // 17 Seconds - -new Fraction(deg).add(min, 60).add(sec, 3600).toString() // -> 57.7547(2) -``` - - -Rational approximation of irrational numbers -=== - -Now it's getting messy ;d To approximate a number like *sqrt(5) - 2* with a numerator and denominator, you can reformat the equation as follows: *pow(n / d + 2, 2) = 5*. - -Then the following algorithm will generate the rational number besides the binary representation. - -```javascript -var x = "/", s = ""; - -var a = new Fraction(0), - b = new Fraction(1); -for (var n = 0; n <= 10; n++) { - - var c = a.add(b).div(2); - - console.log(n + "\t" + a + "\t" + b + "\t" + c + "\t" + x); - - if (c.add(2).pow(2) < 5) { - a = c; - x = "1"; - } else { - b = c; - x = "0"; - } - s+= x; -} -console.log(s) -``` - -The result is - -``` -n a[n] b[n] c[n] x[n] -0 0/1 1/1 1/2 / -1 0/1 1/2 1/4 0 -2 0/1 1/4 1/8 0 -3 1/8 1/4 3/16 1 -4 3/16 1/4 7/32 1 -5 7/32 1/4 15/64 1 -6 15/64 1/4 31/128 1 -7 15/64 31/128 61/256 0 -8 15/64 61/256 121/512 0 -9 15/64 121/512 241/1024 0 -10 241/1024 121/512 483/2048 1 -``` -Thus the approximation after 11 iterations of the bisection method is *483 / 2048* and the binary representation is 0.00111100011 (see [WolframAlpha](http://www.wolframalpha.com/input/?i=sqrt%285%29-2+binary)) - - -I published another example on how to approximate PI with fraction.js on my [blog](http://www.xarg.org/2014/03/precise-calculations-in-javascript/) (Still not the best idea to approximate irrational numbers, but it illustrates the capabilities of Fraction.js perfectly). - - -Get the exact fractional part of a number ---- -```javascript -var f = new Fraction("-6.(3416)"); -console.log("" + f.mod(1).abs()); // 0.(3416) -``` - -Mathematical correct modulo ---- -The behaviour on negative congruences is different to most modulo implementations in computer science. Even the *mod()* function of Fraction.js behaves in the typical way. To solve the problem of having the mathematical correct modulo with Fraction.js you could come up with this: - -```javascript -var a = -1; -var b = 10.99; - -console.log(new Fraction(a) - .mod(b)); // Not correct, usual Modulo - -console.log(new Fraction(a) - .mod(b).add(b).mod(b)); // Correct! Mathematical Modulo -``` - -fmod() impreciseness circumvented ---- -It turns out that Fraction.js outperforms almost any fmod() implementation, including JavaScript itself, [php.js](http://phpjs.org/functions/fmod/), C++, Python, Java and even Wolframalpha due to the fact that numbers like 0.05, 0.1, ... are infinite decimal in base 2. - -The equation *fmod(4.55, 0.05)* gives *0.04999999999999957*, wolframalpha says *1/20*. The correct answer should be **zero**, as 0.05 divides 4.55 without any remainder. - - -Parser -=== - -Any function (see below) as well as the constructor of the *Fraction* class parses its input and reduce it to the smallest term. - -You can pass either Arrays, Objects, Integers, Doubles or Strings. - -Arrays / Objects ---- -```javascript -new Fraction(numerator, denominator); -new Fraction([numerator, denominator]); -new Fraction({n: numerator, d: denominator}); -``` - -Integers ---- -```javascript -new Fraction(123); -``` - -Doubles ---- -```javascript -new Fraction(55.4); -``` - -**Note:** If you pass a double as it is, Fraction.js will perform a number analysis based on Farey Sequences. If you concern performance, cache Fraction.js objects and pass arrays/objects. - -The method is really precise, but too large exact numbers, like 1234567.9991829 will result in a wrong approximation. If you want to keep the number as it is, convert it to a string, as the string parser will not perform any further observations. If you have problems with the approximation, in the file `examples/approx.js` is a different approximation algorithm, which might work better in some more specific use-cases. - - -Strings ---- -```javascript -new Fraction("123.45"); -new Fraction("123/45"); // A rational number represented as two decimals, separated by a slash -new Fraction("123:45"); // A rational number represented as two decimals, separated by a colon -new Fraction("4 123/45"); // A rational number represented as a whole number and a fraction -new Fraction("123.'456'"); // Note the quotes, see below! -new Fraction("123.(456)"); // Note the brackets, see below! -new Fraction("123.45'6'"); // Note the quotes, see below! -new Fraction("123.45(6)"); // Note the brackets, see below! -``` - -Two arguments ---- -```javascript -new Fraction(3, 2); // 3/2 = 1.5 -``` - -Repeating decimal places ---- -*Fraction.js* can easily handle repeating decimal places. For example *1/3* is *0.3333...*. There is only one repeating digit. As you can see in the examples above, you can pass a number like *1/3* as "0.'3'" or "0.(3)", which are synonym. There are no tests to parse something like 0.166666666 to 1/6! If you really want to handle this number, wrap around brackets on your own with the function below for example: 0.1(66666666) - -Assume you want to divide 123.32 / 33.6(567). [WolframAlpha](http://www.wolframalpha.com/input/?i=123.32+%2F+%2812453%2F370%29) states that you'll get a period of 1776 digits. *Fraction.js* comes to the same result. Give it a try: - -```javascript -var f = new Fraction("123.32"); -console.log("Bam: " + f.div("33.6(567)")); -``` - -To automatically make a number like "0.123123123" to something more Fraction.js friendly like "0.(123)", I hacked this little brute force algorithm in a 10 minutes. Improvements are welcome... - -```javascript -function formatDecimal(str) { - - var comma, pre, offset, pad, times, repeat; - - if (-1 === (comma = str.indexOf("."))) - return str; - - pre = str.substr(0, comma + 1); - str = str.substr(comma + 1); - - for (var i = 0; i < str.length; i++) { - - offset = str.substr(0, i); - - for (var j = 0; j < 5; j++) { - - pad = str.substr(i, j + 1); - - times = Math.ceil((str.length - offset.length) / pad.length); - - repeat = new Array(times + 1).join(pad); // Silly String.repeat hack - - if (0 === (offset + repeat).indexOf(str)) { - return pre + offset + "(" + pad + ")"; - } - } - } - return null; -} - -var f, x = formatDecimal("13.0123123123"); // = 13.0(123) -if (x !== null) { - f = new Fraction(x); -} -``` - -Attributes -=== - -The Fraction object allows direct access to the numerator, denominator and sign attributes. It is ensured that only the sign-attribute holds sign information so that a sign comparison is only necessary against this attribute. - -```javascript -var f = new Fraction('-1/2'); -console.log(f.n); // Numerator: 1 -console.log(f.d); // Denominator: 2 -console.log(f.s); // Sign: -1 -``` - - -Functions -=== - -Fraction abs() ---- -Returns the actual number without any sign information - -Fraction neg() ---- -Returns the actual number with flipped sign in order to get the additive inverse - -Fraction add(n) ---- -Returns the sum of the actual number and the parameter n - -Fraction sub(n) ---- -Returns the difference of the actual number and the parameter n - -Fraction mul(n) ---- -Returns the product of the actual number and the parameter n - -Fraction div(n) ---- -Returns the quotient of the actual number and the parameter n - -Fraction pow(exp) ---- -Returns the power of the actual number, raised to an possible rational exponent. If the result becomes non-rational the function returns `null`. - -Fraction mod(n) ---- -Returns the modulus (rest of the division) of the actual object and n (this % n). It's a much more precise [fmod()](#fmod-impreciseness-circumvented) if you like. Please note that *mod()* is just like the modulo operator of most programming languages. If you want a mathematical correct modulo, see [here](#mathematical-correct-modulo). - -Fraction mod() ---- -Returns the modulus (rest of the division) of the actual object (numerator mod denominator) - -Fraction gcd(n) ---- -Returns the fractional greatest common divisor - -Fraction lcm(n) ---- -Returns the fractional least common multiple - -Fraction ceil([places=0-16]) ---- -Returns the ceiling of a rational number with Math.ceil - -Fraction floor([places=0-16]) ---- -Returns the floor of a rational number with Math.floor - -Fraction round([places=0-16]) ---- -Returns the rational number rounded with Math.round - -Fraction roundTo(multiple) ---- -Rounds a fraction to the closest multiple of another fraction. - -Fraction inverse() ---- -Returns the multiplicative inverse of the actual number (n / d becomes d / n) in order to get the reciprocal - -Fraction simplify([eps=0.001]) ---- -Simplifies the rational number under a certain error threshold. Ex. `0.333` will be `1/3` with `eps=0.001` - -boolean equals(n) ---- -Check if two numbers are equal - -int compare(n) ---- -Compare two numbers. -``` -result < 0: n is greater than actual number -result > 0: n is smaller than actual number -result = 0: n is equal to the actual number -``` - -boolean divisible(n) ---- -Check if two numbers are divisible (n divides this) - -double valueOf() ---- -Returns a decimal representation of the fraction - -String toString([decimalPlaces=15]) ---- -Generates an exact string representation of the actual object. For repeated decimal places all digits are collected within brackets, like `1/3 = "0.(3)"`. For all other numbers, up to `decimalPlaces` significant digits are collected - which includes trailing zeros if the number is getting truncated. However, `1/2 = "0.5"` without trailing zeros of course. - -**Note:** As `valueOf()` and `toString()` are provided, `toString()` is only called implicitly in a real string context. Using the plus-operator like `"123" + new Fraction` will call valueOf(), because JavaScript tries to combine two primitives first and concatenates them later, as string will be the more dominant type. `alert(new Fraction)` or `String(new Fraction)` on the other hand will do what you expect. If you really want to have control, you should call `toString()` or `valueOf()` explicitly! - -String toLatex(excludeWhole=false) ---- -Generates an exact LaTeX representation of the actual object. You can see a [live demo](http://www.xarg.org/2014/03/precise-calculations-in-javascript/) on my blog. - -The optional boolean parameter indicates if you want to exclude the whole part. "1 1/3" instead of "4/3" - -String toFraction(excludeWhole=false) ---- -Gets a string representation of the fraction - -The optional boolean parameter indicates if you want to exclude the whole part. "1 1/3" instead of "4/3" - -Array toContinued() ---- -Gets an array of the fraction represented as a continued fraction. The first element always contains the whole part. - -```javascript -var f = new Fraction('88/33'); -var c = f.toContinued(); // [2, 1, 2] -``` - -Fraction clone() ---- -Creates a copy of the actual Fraction object - - -Exceptions -=== -If a really hard error occurs (parsing error, division by zero), *fraction.js* throws exceptions! Please make sure you handle them correctly. - - - -Installation -=== -Installing fraction.js is as easy as cloning this repo or use the following command: - -``` -npm install fraction.js -``` - -Using Fraction.js with the browser -=== -```html - - -``` - -Using Fraction.js with TypeScript -=== -```js -import Fraction from "fraction.js"; -console.log(Fraction("123/456")); -``` - -Coding Style -=== -As every library I publish, fraction.js is also built to be as small as possible after compressing it with Google Closure Compiler in advanced mode. Thus the coding style orientates a little on maxing-out the compression rate. Please make sure you keep this style if you plan to extend the library. - - -Precision -=== -Fraction.js tries to circumvent floating point errors, by having an internal representation of numerator and denominator. As it relies on JavaScript, there is also a limit. The biggest number representable is `Number.MAX_SAFE_INTEGER / 1` and the smallest is `-1 / Number.MAX_SAFE_INTEGER`, with `Number.MAX_SAFE_INTEGER=9007199254740991`. If this is not enough, there is `bigfraction.js` shipped experimentally, which relies on `BigInt` and should become the new Fraction.js eventually. - -Testing -=== -If you plan to enhance the library, make sure you add test cases and all the previous tests are passing. You can test the library with - -``` -npm test -``` - - -Copyright and licensing -=== -Copyright (c) 2023, [Robert Eisele](https://raw.org/) -Licensed under the MIT license. diff --git a/node_modules/fraction.js/bigfraction.js b/node_modules/fraction.js/bigfraction.js deleted file mode 100644 index 038ca05b..00000000 --- a/node_modules/fraction.js/bigfraction.js +++ /dev/null @@ -1,899 +0,0 @@ -/** - * @license Fraction.js v4.2.1 20/08/2023 - * https://www.xarg.org/2014/03/rational-numbers-in-javascript/ - * - * Copyright (c) 2023, Robert Eisele (robert@raw.org) - * Dual licensed under the MIT or GPL Version 2 licenses. - **/ - - -/** - * - * This class offers the possibility to calculate fractions. - * You can pass a fraction in different formats. Either as array, as double, as string or as an integer. - * - * Array/Object form - * [ 0 => , 1 => ] - * [ n => , d => ] - * - * Integer form - * - Single integer value - * - * Double form - * - Single double value - * - * String form - * 123.456 - a simple double - * 123/456 - a string fraction - * 123.'456' - a double with repeating decimal places - * 123.(456) - synonym - * 123.45'6' - a double with repeating last place - * 123.45(6) - synonym - * - * Example: - * - * let f = new Fraction("9.4'31'"); - * f.mul([-4, 3]).div(4.9); - * - */ - -(function(root) { - - "use strict"; - - // Set Identity function to downgrade BigInt to Number if needed - if (typeof BigInt === 'undefined') BigInt = function(n) { if (isNaN(n)) throw new Error(""); return n; }; - - const C_ONE = BigInt(1); - const C_ZERO = BigInt(0); - const C_TEN = BigInt(10); - const C_TWO = BigInt(2); - const C_FIVE = BigInt(5); - - // Maximum search depth for cyclic rational numbers. 2000 should be more than enough. - // Example: 1/7 = 0.(142857) has 6 repeating decimal places. - // If MAX_CYCLE_LEN gets reduced, long cycles will not be detected and toString() only gets the first 10 digits - const MAX_CYCLE_LEN = 2000; - - // Parsed data to avoid calling "new" all the time - const P = { - "s": C_ONE, - "n": C_ZERO, - "d": C_ONE - }; - - function assign(n, s) { - - try { - n = BigInt(n); - } catch (e) { - throw InvalidParameter(); - } - return n * s; - } - - // Creates a new Fraction internally without the need of the bulky constructor - function newFraction(n, d) { - - if (d === C_ZERO) { - throw DivisionByZero(); - } - - const f = Object.create(Fraction.prototype); - f["s"] = n < C_ZERO ? -C_ONE : C_ONE; - - n = n < C_ZERO ? -n : n; - - const a = gcd(n, d); - - f["n"] = n / a; - f["d"] = d / a; - return f; - } - - function factorize(num) { - - const factors = {}; - - let n = num; - let i = C_TWO; - let s = C_FIVE - C_ONE; - - while (s <= n) { - - while (n % i === C_ZERO) { - n/= i; - factors[i] = (factors[i] || C_ZERO) + C_ONE; - } - s+= C_ONE + C_TWO * i++; - } - - if (n !== num) { - if (n > 1) - factors[n] = (factors[n] || C_ZERO) + C_ONE; - } else { - factors[num] = (factors[num] || C_ZERO) + C_ONE; - } - return factors; - } - - const parse = function(p1, p2) { - - let n = C_ZERO, d = C_ONE, s = C_ONE; - - if (p1 === undefined || p1 === null) { - /* void */ - } else if (p2 !== undefined) { - n = BigInt(p1); - d = BigInt(p2); - s = n * d; - - if (n % C_ONE !== C_ZERO || d % C_ONE !== C_ZERO) { - throw NonIntegerParameter(); - } - - } else if (typeof p1 === "object") { - if ("d" in p1 && "n" in p1) { - n = BigInt(p1["n"]); - d = BigInt(p1["d"]); - if ("s" in p1) - n*= BigInt(p1["s"]); - } else if (0 in p1) { - n = BigInt(p1[0]); - if (1 in p1) - d = BigInt(p1[1]); - } else if (p1 instanceof BigInt) { - n = BigInt(p1); - } else { - throw InvalidParameter(); - } - s = n * d; - } else if (typeof p1 === "bigint") { - n = p1; - s = p1; - d = C_ONE; - } else if (typeof p1 === "number") { - - if (isNaN(p1)) { - throw InvalidParameter(); - } - - if (p1 < 0) { - s = -C_ONE; - p1 = -p1; - } - - if (p1 % 1 === 0) { - n = BigInt(p1); - } else if (p1 > 0) { // check for != 0, scale would become NaN (log(0)), which converges really slow - - let z = 1; - - let A = 0, B = 1; - let C = 1, D = 1; - - let N = 10000000; - - if (p1 >= 1) { - z = 10 ** Math.floor(1 + Math.log10(p1)); - p1/= z; - } - - // Using Farey Sequences - - while (B <= N && D <= N) { - let M = (A + C) / (B + D); - - if (p1 === M) { - if (B + D <= N) { - n = A + C; - d = B + D; - } else if (D > B) { - n = C; - d = D; - } else { - n = A; - d = B; - } - break; - - } else { - - if (p1 > M) { - A+= C; - B+= D; - } else { - C+= A; - D+= B; - } - - if (B > N) { - n = C; - d = D; - } else { - n = A; - d = B; - } - } - } - n = BigInt(n) * BigInt(z); - d = BigInt(d); - - } - - } else if (typeof p1 === "string") { - - let ndx = 0; - - let v = C_ZERO, w = C_ZERO, x = C_ZERO, y = C_ONE, z = C_ONE; - - let match = p1.match(/\d+|./g); - - if (match === null) - throw InvalidParameter(); - - if (match[ndx] === '-') {// Check for minus sign at the beginning - s = -C_ONE; - ndx++; - } else if (match[ndx] === '+') {// Check for plus sign at the beginning - ndx++; - } - - if (match.length === ndx + 1) { // Check if it's just a simple number "1234" - w = assign(match[ndx++], s); - } else if (match[ndx + 1] === '.' || match[ndx] === '.') { // Check if it's a decimal number - - if (match[ndx] !== '.') { // Handle 0.5 and .5 - v = assign(match[ndx++], s); - } - ndx++; - - // Check for decimal places - if (ndx + 1 === match.length || match[ndx + 1] === '(' && match[ndx + 3] === ')' || match[ndx + 1] === "'" && match[ndx + 3] === "'") { - w = assign(match[ndx], s); - y = C_TEN ** BigInt(match[ndx].length); - ndx++; - } - - // Check for repeating places - if (match[ndx] === '(' && match[ndx + 2] === ')' || match[ndx] === "'" && match[ndx + 2] === "'") { - x = assign(match[ndx + 1], s); - z = C_TEN ** BigInt(match[ndx + 1].length) - C_ONE; - ndx+= 3; - } - - } else if (match[ndx + 1] === '/' || match[ndx + 1] === ':') { // Check for a simple fraction "123/456" or "123:456" - w = assign(match[ndx], s); - y = assign(match[ndx + 2], C_ONE); - ndx+= 3; - } else if (match[ndx + 3] === '/' && match[ndx + 1] === ' ') { // Check for a complex fraction "123 1/2" - v = assign(match[ndx], s); - w = assign(match[ndx + 2], s); - y = assign(match[ndx + 4], C_ONE); - ndx+= 5; - } - - if (match.length <= ndx) { // Check for more tokens on the stack - d = y * z; - s = /* void */ - n = x + d * v + z * w; - } else { - throw InvalidParameter(); - } - - } else { - throw InvalidParameter(); - } - - if (d === C_ZERO) { - throw DivisionByZero(); - } - - P["s"] = s < C_ZERO ? -C_ONE : C_ONE; - P["n"] = n < C_ZERO ? -n : n; - P["d"] = d < C_ZERO ? -d : d; - }; - - function modpow(b, e, m) { - - let r = C_ONE; - for (; e > C_ZERO; b = (b * b) % m, e >>= C_ONE) { - - if (e & C_ONE) { - r = (r * b) % m; - } - } - return r; - } - - function cycleLen(n, d) { - - for (; d % C_TWO === C_ZERO; - d/= C_TWO) { - } - - for (; d % C_FIVE === C_ZERO; - d/= C_FIVE) { - } - - if (d === C_ONE) // Catch non-cyclic numbers - return C_ZERO; - - // If we would like to compute really large numbers quicker, we could make use of Fermat's little theorem: - // 10^(d-1) % d == 1 - // However, we don't need such large numbers and MAX_CYCLE_LEN should be the capstone, - // as we want to translate the numbers to strings. - - let rem = C_TEN % d; - let t = 1; - - for (; rem !== C_ONE; t++) { - rem = rem * C_TEN % d; - - if (t > MAX_CYCLE_LEN) - return C_ZERO; // Returning 0 here means that we don't print it as a cyclic number. It's likely that the answer is `d-1` - } - return BigInt(t); - } - - function cycleStart(n, d, len) { - - let rem1 = C_ONE; - let rem2 = modpow(C_TEN, len, d); - - for (let t = 0; t < 300; t++) { // s < ~log10(Number.MAX_VALUE) - // Solve 10^s == 10^(s+t) (mod d) - - if (rem1 === rem2) - return BigInt(t); - - rem1 = rem1 * C_TEN % d; - rem2 = rem2 * C_TEN % d; - } - return 0; - } - - function gcd(a, b) { - - if (!a) - return b; - if (!b) - return a; - - while (1) { - a%= b; - if (!a) - return b; - b%= a; - if (!b) - return a; - } - } - - /** - * Module constructor - * - * @constructor - * @param {number|Fraction=} a - * @param {number=} b - */ - function Fraction(a, b) { - - parse(a, b); - - if (this instanceof Fraction) { - a = gcd(P["d"], P["n"]); // Abuse a - this["s"] = P["s"]; - this["n"] = P["n"] / a; - this["d"] = P["d"] / a; - } else { - return newFraction(P['s'] * P['n'], P['d']); - } - } - - var DivisionByZero = function() {return new Error("Division by Zero");}; - var InvalidParameter = function() {return new Error("Invalid argument");}; - var NonIntegerParameter = function() {return new Error("Parameters must be integer");}; - - Fraction.prototype = { - - "s": C_ONE, - "n": C_ZERO, - "d": C_ONE, - - /** - * Calculates the absolute value - * - * Ex: new Fraction(-4).abs() => 4 - **/ - "abs": function() { - - return newFraction(this["n"], this["d"]); - }, - - /** - * Inverts the sign of the current fraction - * - * Ex: new Fraction(-4).neg() => 4 - **/ - "neg": function() { - - return newFraction(-this["s"] * this["n"], this["d"]); - }, - - /** - * Adds two rational numbers - * - * Ex: new Fraction({n: 2, d: 3}).add("14.9") => 467 / 30 - **/ - "add": function(a, b) { - - parse(a, b); - return newFraction( - this["s"] * this["n"] * P["d"] + P["s"] * this["d"] * P["n"], - this["d"] * P["d"] - ); - }, - - /** - * Subtracts two rational numbers - * - * Ex: new Fraction({n: 2, d: 3}).add("14.9") => -427 / 30 - **/ - "sub": function(a, b) { - - parse(a, b); - return newFraction( - this["s"] * this["n"] * P["d"] - P["s"] * this["d"] * P["n"], - this["d"] * P["d"] - ); - }, - - /** - * Multiplies two rational numbers - * - * Ex: new Fraction("-17.(345)").mul(3) => 5776 / 111 - **/ - "mul": function(a, b) { - - parse(a, b); - return newFraction( - this["s"] * P["s"] * this["n"] * P["n"], - this["d"] * P["d"] - ); - }, - - /** - * Divides two rational numbers - * - * Ex: new Fraction("-17.(345)").inverse().div(3) - **/ - "div": function(a, b) { - - parse(a, b); - return newFraction( - this["s"] * P["s"] * this["n"] * P["d"], - this["d"] * P["n"] - ); - }, - - /** - * Clones the actual object - * - * Ex: new Fraction("-17.(345)").clone() - **/ - "clone": function() { - return newFraction(this['s'] * this['n'], this['d']); - }, - - /** - * Calculates the modulo of two rational numbers - a more precise fmod - * - * Ex: new Fraction('4.(3)').mod([7, 8]) => (13/3) % (7/8) = (5/6) - **/ - "mod": function(a, b) { - - if (a === undefined) { - return newFraction(this["s"] * this["n"] % this["d"], C_ONE); - } - - parse(a, b); - if (0 === P["n"] && 0 === this["d"]) { - throw DivisionByZero(); - } - - /* - * First silly attempt, kinda slow - * - return that["sub"]({ - "n": num["n"] * Math.floor((this.n / this.d) / (num.n / num.d)), - "d": num["d"], - "s": this["s"] - });*/ - - /* - * New attempt: a1 / b1 = a2 / b2 * q + r - * => b2 * a1 = a2 * b1 * q + b1 * b2 * r - * => (b2 * a1 % a2 * b1) / (b1 * b2) - */ - return newFraction( - this["s"] * (P["d"] * this["n"]) % (P["n"] * this["d"]), - P["d"] * this["d"] - ); - }, - - /** - * Calculates the fractional gcd of two rational numbers - * - * Ex: new Fraction(5,8).gcd(3,7) => 1/56 - */ - "gcd": function(a, b) { - - parse(a, b); - - // gcd(a / b, c / d) = gcd(a, c) / lcm(b, d) - - return newFraction(gcd(P["n"], this["n"]) * gcd(P["d"], this["d"]), P["d"] * this["d"]); - }, - - /** - * Calculates the fractional lcm of two rational numbers - * - * Ex: new Fraction(5,8).lcm(3,7) => 15 - */ - "lcm": function(a, b) { - - parse(a, b); - - // lcm(a / b, c / d) = lcm(a, c) / gcd(b, d) - - if (P["n"] === C_ZERO && this["n"] === C_ZERO) { - return newFraction(C_ZERO, C_ONE); - } - return newFraction(P["n"] * this["n"], gcd(P["n"], this["n"]) * gcd(P["d"], this["d"])); - }, - - /** - * Gets the inverse of the fraction, means numerator and denominator are exchanged - * - * Ex: new Fraction([-3, 4]).inverse() => -4 / 3 - **/ - "inverse": function() { - return newFraction(this["s"] * this["d"], this["n"]); - }, - - /** - * Calculates the fraction to some integer exponent - * - * Ex: new Fraction(-1,2).pow(-3) => -8 - */ - "pow": function(a, b) { - - parse(a, b); - - // Trivial case when exp is an integer - - if (P['d'] === C_ONE) { - - if (P['s'] < C_ZERO) { - return newFraction((this['s'] * this["d"]) ** P['n'], this["n"] ** P['n']); - } else { - return newFraction((this['s'] * this["n"]) ** P['n'], this["d"] ** P['n']); - } - } - - // Negative roots become complex - // (-a/b)^(c/d) = x - // <=> (-1)^(c/d) * (a/b)^(c/d) = x - // <=> (cos(pi) + i*sin(pi))^(c/d) * (a/b)^(c/d) = x - // <=> (cos(c*pi/d) + i*sin(c*pi/d)) * (a/b)^(c/d) = x # DeMoivre's formula - // From which follows that only for c=0 the root is non-complex - if (this['s'] < C_ZERO) return null; - - // Now prime factor n and d - let N = factorize(this['n']); - let D = factorize(this['d']); - - // Exponentiate and take root for n and d individually - let n = C_ONE; - let d = C_ONE; - for (let k in N) { - if (k === '1') continue; - if (k === '0') { - n = C_ZERO; - break; - } - N[k]*= P['n']; - - if (N[k] % P['d'] === C_ZERO) { - N[k]/= P['d']; - } else return null; - n*= BigInt(k) ** N[k]; - } - - for (let k in D) { - if (k === '1') continue; - D[k]*= P['n']; - - if (D[k] % P['d'] === C_ZERO) { - D[k]/= P['d']; - } else return null; - d*= BigInt(k) ** D[k]; - } - - if (P['s'] < C_ZERO) { - return newFraction(d, n); - } - return newFraction(n, d); - }, - - /** - * Check if two rational numbers are the same - * - * Ex: new Fraction(19.6).equals([98, 5]); - **/ - "equals": function(a, b) { - - parse(a, b); - return this["s"] * this["n"] * P["d"] === P["s"] * P["n"] * this["d"]; // Same as compare() === 0 - }, - - /** - * Check if two rational numbers are the same - * - * Ex: new Fraction(19.6).equals([98, 5]); - **/ - "compare": function(a, b) { - - parse(a, b); - let t = (this["s"] * this["n"] * P["d"] - P["s"] * P["n"] * this["d"]); - - return (C_ZERO < t) - (t < C_ZERO); - }, - - /** - * Calculates the ceil of a rational number - * - * Ex: new Fraction('4.(3)').ceil() => (5 / 1) - **/ - "ceil": function(places) { - - places = C_TEN ** BigInt(places || 0); - - return newFraction(this["s"] * places * this["n"] / this["d"] + - (places * this["n"] % this["d"] > C_ZERO && this["s"] >= C_ZERO ? C_ONE : C_ZERO), - places); - }, - - /** - * Calculates the floor of a rational number - * - * Ex: new Fraction('4.(3)').floor() => (4 / 1) - **/ - "floor": function(places) { - - places = C_TEN ** BigInt(places || 0); - - return newFraction(this["s"] * places * this["n"] / this["d"] - - (places * this["n"] % this["d"] > C_ZERO && this["s"] < C_ZERO ? C_ONE : C_ZERO), - places); - }, - - /** - * Rounds a rational numbers - * - * Ex: new Fraction('4.(3)').round() => (4 / 1) - **/ - "round": function(places) { - - places = C_TEN ** BigInt(places || 0); - - /* Derivation: - - s >= 0: - round(n / d) = trunc(n / d) + (n % d) / d >= 0.5 ? 1 : 0 - = trunc(n / d) + 2(n % d) >= d ? 1 : 0 - s < 0: - round(n / d) =-trunc(n / d) - (n % d) / d > 0.5 ? 1 : 0 - =-trunc(n / d) - 2(n % d) > d ? 1 : 0 - - =>: - - round(s * n / d) = s * trunc(n / d) + s * (C + 2(n % d) > d ? 1 : 0) - where C = s >= 0 ? 1 : 0, to fix the >= for the positve case. - */ - - return newFraction(this["s"] * places * this["n"] / this["d"] + - this["s"] * ((this["s"] >= C_ZERO ? C_ONE : C_ZERO) + C_TWO * (places * this["n"] % this["d"]) > this["d"] ? C_ONE : C_ZERO), - places); - }, - - /** - * Check if two rational numbers are divisible - * - * Ex: new Fraction(19.6).divisible(1.5); - */ - "divisible": function(a, b) { - - parse(a, b); - return !(!(P["n"] * this["d"]) || ((this["n"] * P["d"]) % (P["n"] * this["d"]))); - }, - - /** - * Returns a decimal representation of the fraction - * - * Ex: new Fraction("100.'91823'").valueOf() => 100.91823918239183 - **/ - 'valueOf': function() { - // Best we can do so far - return Number(this["s"] * this["n"]) / Number(this["d"]); - }, - - /** - * Creates a string representation of a fraction with all digits - * - * Ex: new Fraction("100.'91823'").toString() => "100.(91823)" - **/ - 'toString': function(dec) { - - let N = this["n"]; - let D = this["d"]; - - function trunc(x) { - return typeof x === 'bigint' ? x : Math.floor(x); - } - - dec = dec || 15; // 15 = decimal places when no repetition - - let cycLen = cycleLen(N, D); // Cycle length - let cycOff = cycleStart(N, D, cycLen); // Cycle start - - let str = this['s'] < C_ZERO ? "-" : ""; - - // Append integer part - str+= trunc(N / D); - - N%= D; - N*= C_TEN; - - if (N) - str+= "."; - - if (cycLen) { - - for (let i = cycOff; i--;) { - str+= trunc(N / D); - N%= D; - N*= C_TEN; - } - str+= "("; - for (let i = cycLen; i--;) { - str+= trunc(N / D); - N%= D; - N*= C_TEN; - } - str+= ")"; - } else { - for (let i = dec; N && i--;) { - str+= trunc(N / D); - N%= D; - N*= C_TEN; - } - } - return str; - }, - - /** - * Returns a string-fraction representation of a Fraction object - * - * Ex: new Fraction("1.'3'").toFraction() => "4 1/3" - **/ - 'toFraction': function(excludeWhole) { - - let n = this["n"]; - let d = this["d"]; - let str = this['s'] < C_ZERO ? "-" : ""; - - if (d === C_ONE) { - str+= n; - } else { - let whole = n / d; - if (excludeWhole && whole > C_ZERO) { - str+= whole; - str+= " "; - n%= d; - } - - str+= n; - str+= '/'; - str+= d; - } - return str; - }, - - /** - * Returns a latex representation of a Fraction object - * - * Ex: new Fraction("1.'3'").toLatex() => "\frac{4}{3}" - **/ - 'toLatex': function(excludeWhole) { - - let n = this["n"]; - let d = this["d"]; - let str = this['s'] < C_ZERO ? "-" : ""; - - if (d === C_ONE) { - str+= n; - } else { - let whole = n / d; - if (excludeWhole && whole > C_ZERO) { - str+= whole; - n%= d; - } - - str+= "\\frac{"; - str+= n; - str+= '}{'; - str+= d; - str+= '}'; - } - return str; - }, - - /** - * Returns an array of continued fraction elements - * - * Ex: new Fraction("7/8").toContinued() => [0,1,7] - */ - 'toContinued': function() { - - let a = this['n']; - let b = this['d']; - let res = []; - - do { - res.push(a / b); - let t = a % b; - a = b; - b = t; - } while (a !== C_ONE); - - return res; - }, - - "simplify": function(eps) { - - eps = eps || 0.001; - - const thisABS = this['abs'](); - const cont = thisABS['toContinued'](); - - for (let i = 1; i < cont.length; i++) { - - let s = newFraction(cont[i - 1], C_ONE); - for (let k = i - 2; k >= 0; k--) { - s = s['inverse']()['add'](cont[k]); - } - - if (Math.abs(s['sub'](thisABS).valueOf()) < eps) { - return s['mul'](this['s']); - } - } - return this; - } - }; - - if (typeof define === "function" && define["amd"]) { - define([], function() { - return Fraction; - }); - } else if (typeof exports === "object") { - Object.defineProperty(exports, "__esModule", { 'value': true }); - Fraction['default'] = Fraction; - Fraction['Fraction'] = Fraction; - module['exports'] = Fraction; - } else { - root['Fraction'] = Fraction; - } - -})(this); diff --git a/node_modules/fraction.js/fraction.cjs b/node_modules/fraction.js/fraction.cjs deleted file mode 100644 index 0a10d8c9..00000000 --- a/node_modules/fraction.js/fraction.cjs +++ /dev/null @@ -1,904 +0,0 @@ -/** - * @license Fraction.js v4.3.7 31/08/2023 - * https://www.xarg.org/2014/03/rational-numbers-in-javascript/ - * - * Copyright (c) 2023, Robert Eisele (robert@raw.org) - * Dual licensed under the MIT or GPL Version 2 licenses. - **/ - - -/** - * - * This class offers the possibility to calculate fractions. - * You can pass a fraction in different formats. Either as array, as double, as string or as an integer. - * - * Array/Object form - * [ 0 => , 1 => ] - * [ n => , d => ] - * - * Integer form - * - Single integer value - * - * Double form - * - Single double value - * - * String form - * 123.456 - a simple double - * 123/456 - a string fraction - * 123.'456' - a double with repeating decimal places - * 123.(456) - synonym - * 123.45'6' - a double with repeating last place - * 123.45(6) - synonym - * - * Example: - * - * var f = new Fraction("9.4'31'"); - * f.mul([-4, 3]).div(4.9); - * - */ - -(function(root) { - - "use strict"; - - // Maximum search depth for cyclic rational numbers. 2000 should be more than enough. - // Example: 1/7 = 0.(142857) has 6 repeating decimal places. - // If MAX_CYCLE_LEN gets reduced, long cycles will not be detected and toString() only gets the first 10 digits - var MAX_CYCLE_LEN = 2000; - - // Parsed data to avoid calling "new" all the time - var P = { - "s": 1, - "n": 0, - "d": 1 - }; - - function assign(n, s) { - - if (isNaN(n = parseInt(n, 10))) { - throw InvalidParameter(); - } - return n * s; - } - - // Creates a new Fraction internally without the need of the bulky constructor - function newFraction(n, d) { - - if (d === 0) { - throw DivisionByZero(); - } - - var f = Object.create(Fraction.prototype); - f["s"] = n < 0 ? -1 : 1; - - n = n < 0 ? -n : n; - - var a = gcd(n, d); - - f["n"] = n / a; - f["d"] = d / a; - return f; - } - - function factorize(num) { - - var factors = {}; - - var n = num; - var i = 2; - var s = 4; - - while (s <= n) { - - while (n % i === 0) { - n/= i; - factors[i] = (factors[i] || 0) + 1; - } - s+= 1 + 2 * i++; - } - - if (n !== num) { - if (n > 1) - factors[n] = (factors[n] || 0) + 1; - } else { - factors[num] = (factors[num] || 0) + 1; - } - return factors; - } - - var parse = function(p1, p2) { - - var n = 0, d = 1, s = 1; - var v = 0, w = 0, x = 0, y = 1, z = 1; - - var A = 0, B = 1; - var C = 1, D = 1; - - var N = 10000000; - var M; - - if (p1 === undefined || p1 === null) { - /* void */ - } else if (p2 !== undefined) { - n = p1; - d = p2; - s = n * d; - - if (n % 1 !== 0 || d % 1 !== 0) { - throw NonIntegerParameter(); - } - - } else - switch (typeof p1) { - - case "object": - { - if ("d" in p1 && "n" in p1) { - n = p1["n"]; - d = p1["d"]; - if ("s" in p1) - n*= p1["s"]; - } else if (0 in p1) { - n = p1[0]; - if (1 in p1) - d = p1[1]; - } else { - throw InvalidParameter(); - } - s = n * d; - break; - } - case "number": - { - if (p1 < 0) { - s = p1; - p1 = -p1; - } - - if (p1 % 1 === 0) { - n = p1; - } else if (p1 > 0) { // check for != 0, scale would become NaN (log(0)), which converges really slow - - if (p1 >= 1) { - z = Math.pow(10, Math.floor(1 + Math.log(p1) / Math.LN10)); - p1/= z; - } - - // Using Farey Sequences - // http://www.johndcook.com/blog/2010/10/20/best-rational-approximation/ - - while (B <= N && D <= N) { - M = (A + C) / (B + D); - - if (p1 === M) { - if (B + D <= N) { - n = A + C; - d = B + D; - } else if (D > B) { - n = C; - d = D; - } else { - n = A; - d = B; - } - break; - - } else { - - if (p1 > M) { - A+= C; - B+= D; - } else { - C+= A; - D+= B; - } - - if (B > N) { - n = C; - d = D; - } else { - n = A; - d = B; - } - } - } - n*= z; - } else if (isNaN(p1) || isNaN(p2)) { - d = n = NaN; - } - break; - } - case "string": - { - B = p1.match(/\d+|./g); - - if (B === null) - throw InvalidParameter(); - - if (B[A] === '-') {// Check for minus sign at the beginning - s = -1; - A++; - } else if (B[A] === '+') {// Check for plus sign at the beginning - A++; - } - - if (B.length === A + 1) { // Check if it's just a simple number "1234" - w = assign(B[A++], s); - } else if (B[A + 1] === '.' || B[A] === '.') { // Check if it's a decimal number - - if (B[A] !== '.') { // Handle 0.5 and .5 - v = assign(B[A++], s); - } - A++; - - // Check for decimal places - if (A + 1 === B.length || B[A + 1] === '(' && B[A + 3] === ')' || B[A + 1] === "'" && B[A + 3] === "'") { - w = assign(B[A], s); - y = Math.pow(10, B[A].length); - A++; - } - - // Check for repeating places - if (B[A] === '(' && B[A + 2] === ')' || B[A] === "'" && B[A + 2] === "'") { - x = assign(B[A + 1], s); - z = Math.pow(10, B[A + 1].length) - 1; - A+= 3; - } - - } else if (B[A + 1] === '/' || B[A + 1] === ':') { // Check for a simple fraction "123/456" or "123:456" - w = assign(B[A], s); - y = assign(B[A + 2], 1); - A+= 3; - } else if (B[A + 3] === '/' && B[A + 1] === ' ') { // Check for a complex fraction "123 1/2" - v = assign(B[A], s); - w = assign(B[A + 2], s); - y = assign(B[A + 4], 1); - A+= 5; - } - - if (B.length <= A) { // Check for more tokens on the stack - d = y * z; - s = /* void */ - n = x + d * v + z * w; - break; - } - - /* Fall through on error */ - } - default: - throw InvalidParameter(); - } - - if (d === 0) { - throw DivisionByZero(); - } - - P["s"] = s < 0 ? -1 : 1; - P["n"] = Math.abs(n); - P["d"] = Math.abs(d); - }; - - function modpow(b, e, m) { - - var r = 1; - for (; e > 0; b = (b * b) % m, e >>= 1) { - - if (e & 1) { - r = (r * b) % m; - } - } - return r; - } - - - function cycleLen(n, d) { - - for (; d % 2 === 0; - d/= 2) { - } - - for (; d % 5 === 0; - d/= 5) { - } - - if (d === 1) // Catch non-cyclic numbers - return 0; - - // If we would like to compute really large numbers quicker, we could make use of Fermat's little theorem: - // 10^(d-1) % d == 1 - // However, we don't need such large numbers and MAX_CYCLE_LEN should be the capstone, - // as we want to translate the numbers to strings. - - var rem = 10 % d; - var t = 1; - - for (; rem !== 1; t++) { - rem = rem * 10 % d; - - if (t > MAX_CYCLE_LEN) - return 0; // Returning 0 here means that we don't print it as a cyclic number. It's likely that the answer is `d-1` - } - return t; - } - - - function cycleStart(n, d, len) { - - var rem1 = 1; - var rem2 = modpow(10, len, d); - - for (var t = 0; t < 300; t++) { // s < ~log10(Number.MAX_VALUE) - // Solve 10^s == 10^(s+t) (mod d) - - if (rem1 === rem2) - return t; - - rem1 = rem1 * 10 % d; - rem2 = rem2 * 10 % d; - } - return 0; - } - - function gcd(a, b) { - - if (!a) - return b; - if (!b) - return a; - - while (1) { - a%= b; - if (!a) - return b; - b%= a; - if (!b) - return a; - } - }; - - /** - * Module constructor - * - * @constructor - * @param {number|Fraction=} a - * @param {number=} b - */ - function Fraction(a, b) { - - parse(a, b); - - if (this instanceof Fraction) { - a = gcd(P["d"], P["n"]); // Abuse variable a - this["s"] = P["s"]; - this["n"] = P["n"] / a; - this["d"] = P["d"] / a; - } else { - return newFraction(P['s'] * P['n'], P['d']); - } - } - - var DivisionByZero = function() { return new Error("Division by Zero"); }; - var InvalidParameter = function() { return new Error("Invalid argument"); }; - var NonIntegerParameter = function() { return new Error("Parameters must be integer"); }; - - Fraction.prototype = { - - "s": 1, - "n": 0, - "d": 1, - - /** - * Calculates the absolute value - * - * Ex: new Fraction(-4).abs() => 4 - **/ - "abs": function() { - - return newFraction(this["n"], this["d"]); - }, - - /** - * Inverts the sign of the current fraction - * - * Ex: new Fraction(-4).neg() => 4 - **/ - "neg": function() { - - return newFraction(-this["s"] * this["n"], this["d"]); - }, - - /** - * Adds two rational numbers - * - * Ex: new Fraction({n: 2, d: 3}).add("14.9") => 467 / 30 - **/ - "add": function(a, b) { - - parse(a, b); - return newFraction( - this["s"] * this["n"] * P["d"] + P["s"] * this["d"] * P["n"], - this["d"] * P["d"] - ); - }, - - /** - * Subtracts two rational numbers - * - * Ex: new Fraction({n: 2, d: 3}).add("14.9") => -427 / 30 - **/ - "sub": function(a, b) { - - parse(a, b); - return newFraction( - this["s"] * this["n"] * P["d"] - P["s"] * this["d"] * P["n"], - this["d"] * P["d"] - ); - }, - - /** - * Multiplies two rational numbers - * - * Ex: new Fraction("-17.(345)").mul(3) => 5776 / 111 - **/ - "mul": function(a, b) { - - parse(a, b); - return newFraction( - this["s"] * P["s"] * this["n"] * P["n"], - this["d"] * P["d"] - ); - }, - - /** - * Divides two rational numbers - * - * Ex: new Fraction("-17.(345)").inverse().div(3) - **/ - "div": function(a, b) { - - parse(a, b); - return newFraction( - this["s"] * P["s"] * this["n"] * P["d"], - this["d"] * P["n"] - ); - }, - - /** - * Clones the actual object - * - * Ex: new Fraction("-17.(345)").clone() - **/ - "clone": function() { - return newFraction(this['s'] * this['n'], this['d']); - }, - - /** - * Calculates the modulo of two rational numbers - a more precise fmod - * - * Ex: new Fraction('4.(3)').mod([7, 8]) => (13/3) % (7/8) = (5/6) - **/ - "mod": function(a, b) { - - if (isNaN(this['n']) || isNaN(this['d'])) { - return new Fraction(NaN); - } - - if (a === undefined) { - return newFraction(this["s"] * this["n"] % this["d"], 1); - } - - parse(a, b); - if (0 === P["n"] && 0 === this["d"]) { - throw DivisionByZero(); - } - - /* - * First silly attempt, kinda slow - * - return that["sub"]({ - "n": num["n"] * Math.floor((this.n / this.d) / (num.n / num.d)), - "d": num["d"], - "s": this["s"] - });*/ - - /* - * New attempt: a1 / b1 = a2 / b2 * q + r - * => b2 * a1 = a2 * b1 * q + b1 * b2 * r - * => (b2 * a1 % a2 * b1) / (b1 * b2) - */ - return newFraction( - this["s"] * (P["d"] * this["n"]) % (P["n"] * this["d"]), - P["d"] * this["d"] - ); - }, - - /** - * Calculates the fractional gcd of two rational numbers - * - * Ex: new Fraction(5,8).gcd(3,7) => 1/56 - */ - "gcd": function(a, b) { - - parse(a, b); - - // gcd(a / b, c / d) = gcd(a, c) / lcm(b, d) - - return newFraction(gcd(P["n"], this["n"]) * gcd(P["d"], this["d"]), P["d"] * this["d"]); - }, - - /** - * Calculates the fractional lcm of two rational numbers - * - * Ex: new Fraction(5,8).lcm(3,7) => 15 - */ - "lcm": function(a, b) { - - parse(a, b); - - // lcm(a / b, c / d) = lcm(a, c) / gcd(b, d) - - if (P["n"] === 0 && this["n"] === 0) { - return newFraction(0, 1); - } - return newFraction(P["n"] * this["n"], gcd(P["n"], this["n"]) * gcd(P["d"], this["d"])); - }, - - /** - * Calculates the ceil of a rational number - * - * Ex: new Fraction('4.(3)').ceil() => (5 / 1) - **/ - "ceil": function(places) { - - places = Math.pow(10, places || 0); - - if (isNaN(this["n"]) || isNaN(this["d"])) { - return new Fraction(NaN); - } - return newFraction(Math.ceil(places * this["s"] * this["n"] / this["d"]), places); - }, - - /** - * Calculates the floor of a rational number - * - * Ex: new Fraction('4.(3)').floor() => (4 / 1) - **/ - "floor": function(places) { - - places = Math.pow(10, places || 0); - - if (isNaN(this["n"]) || isNaN(this["d"])) { - return new Fraction(NaN); - } - return newFraction(Math.floor(places * this["s"] * this["n"] / this["d"]), places); - }, - - /** - * Rounds a rational numbers - * - * Ex: new Fraction('4.(3)').round() => (4 / 1) - **/ - "round": function(places) { - - places = Math.pow(10, places || 0); - - if (isNaN(this["n"]) || isNaN(this["d"])) { - return new Fraction(NaN); - } - return newFraction(Math.round(places * this["s"] * this["n"] / this["d"]), places); - }, - - /** - * Rounds a rational number to a multiple of another rational number - * - * Ex: new Fraction('0.9').roundTo("1/8") => 7 / 8 - **/ - "roundTo": function(a, b) { - - /* - k * x/y ≤ a/b < (k+1) * x/y - ⇔ k ≤ a/b / (x/y) < (k+1) - ⇔ k = floor(a/b * y/x) - */ - - parse(a, b); - - return newFraction(this['s'] * Math.round(this['n'] * P['d'] / (this['d'] * P['n'])) * P['n'], P['d']); - }, - - /** - * Gets the inverse of the fraction, means numerator and denominator are exchanged - * - * Ex: new Fraction([-3, 4]).inverse() => -4 / 3 - **/ - "inverse": function() { - - return newFraction(this["s"] * this["d"], this["n"]); - }, - - /** - * Calculates the fraction to some rational exponent, if possible - * - * Ex: new Fraction(-1,2).pow(-3) => -8 - */ - "pow": function(a, b) { - - parse(a, b); - - // Trivial case when exp is an integer - - if (P['d'] === 1) { - - if (P['s'] < 0) { - return newFraction(Math.pow(this['s'] * this["d"], P['n']), Math.pow(this["n"], P['n'])); - } else { - return newFraction(Math.pow(this['s'] * this["n"], P['n']), Math.pow(this["d"], P['n'])); - } - } - - // Negative roots become complex - // (-a/b)^(c/d) = x - // <=> (-1)^(c/d) * (a/b)^(c/d) = x - // <=> (cos(pi) + i*sin(pi))^(c/d) * (a/b)^(c/d) = x # rotate 1 by 180° - // <=> (cos(c*pi/d) + i*sin(c*pi/d)) * (a/b)^(c/d) = x # DeMoivre's formula in Q ( https://proofwiki.org/wiki/De_Moivre%27s_Formula/Rational_Index ) - // From which follows that only for c=0 the root is non-complex. c/d is a reduced fraction, so that sin(c/dpi)=0 occurs for d=1, which is handled by our trivial case. - if (this['s'] < 0) return null; - - // Now prime factor n and d - var N = factorize(this['n']); - var D = factorize(this['d']); - - // Exponentiate and take root for n and d individually - var n = 1; - var d = 1; - for (var k in N) { - if (k === '1') continue; - if (k === '0') { - n = 0; - break; - } - N[k]*= P['n']; - - if (N[k] % P['d'] === 0) { - N[k]/= P['d']; - } else return null; - n*= Math.pow(k, N[k]); - } - - for (var k in D) { - if (k === '1') continue; - D[k]*= P['n']; - - if (D[k] % P['d'] === 0) { - D[k]/= P['d']; - } else return null; - d*= Math.pow(k, D[k]); - } - - if (P['s'] < 0) { - return newFraction(d, n); - } - return newFraction(n, d); - }, - - /** - * Check if two rational numbers are the same - * - * Ex: new Fraction(19.6).equals([98, 5]); - **/ - "equals": function(a, b) { - - parse(a, b); - return this["s"] * this["n"] * P["d"] === P["s"] * P["n"] * this["d"]; // Same as compare() === 0 - }, - - /** - * Check if two rational numbers are the same - * - * Ex: new Fraction(19.6).equals([98, 5]); - **/ - "compare": function(a, b) { - - parse(a, b); - var t = (this["s"] * this["n"] * P["d"] - P["s"] * P["n"] * this["d"]); - return (0 < t) - (t < 0); - }, - - "simplify": function(eps) { - - if (isNaN(this['n']) || isNaN(this['d'])) { - return this; - } - - eps = eps || 0.001; - - var thisABS = this['abs'](); - var cont = thisABS['toContinued'](); - - for (var i = 1; i < cont.length; i++) { - - var s = newFraction(cont[i - 1], 1); - for (var k = i - 2; k >= 0; k--) { - s = s['inverse']()['add'](cont[k]); - } - - if (Math.abs(s['sub'](thisABS).valueOf()) < eps) { - return s['mul'](this['s']); - } - } - return this; - }, - - /** - * Check if two rational numbers are divisible - * - * Ex: new Fraction(19.6).divisible(1.5); - */ - "divisible": function(a, b) { - - parse(a, b); - return !(!(P["n"] * this["d"]) || ((this["n"] * P["d"]) % (P["n"] * this["d"]))); - }, - - /** - * Returns a decimal representation of the fraction - * - * Ex: new Fraction("100.'91823'").valueOf() => 100.91823918239183 - **/ - 'valueOf': function() { - - return this["s"] * this["n"] / this["d"]; - }, - - /** - * Returns a string-fraction representation of a Fraction object - * - * Ex: new Fraction("1.'3'").toFraction(true) => "4 1/3" - **/ - 'toFraction': function(excludeWhole) { - - var whole, str = ""; - var n = this["n"]; - var d = this["d"]; - if (this["s"] < 0) { - str+= '-'; - } - - if (d === 1) { - str+= n; - } else { - - if (excludeWhole && (whole = Math.floor(n / d)) > 0) { - str+= whole; - str+= " "; - n%= d; - } - - str+= n; - str+= '/'; - str+= d; - } - return str; - }, - - /** - * Returns a latex representation of a Fraction object - * - * Ex: new Fraction("1.'3'").toLatex() => "\frac{4}{3}" - **/ - 'toLatex': function(excludeWhole) { - - var whole, str = ""; - var n = this["n"]; - var d = this["d"]; - if (this["s"] < 0) { - str+= '-'; - } - - if (d === 1) { - str+= n; - } else { - - if (excludeWhole && (whole = Math.floor(n / d)) > 0) { - str+= whole; - n%= d; - } - - str+= "\\frac{"; - str+= n; - str+= '}{'; - str+= d; - str+= '}'; - } - return str; - }, - - /** - * Returns an array of continued fraction elements - * - * Ex: new Fraction("7/8").toContinued() => [0,1,7] - */ - 'toContinued': function() { - - var t; - var a = this['n']; - var b = this['d']; - var res = []; - - if (isNaN(a) || isNaN(b)) { - return res; - } - - do { - res.push(Math.floor(a / b)); - t = a % b; - a = b; - b = t; - } while (a !== 1); - - return res; - }, - - /** - * Creates a string representation of a fraction with all digits - * - * Ex: new Fraction("100.'91823'").toString() => "100.(91823)" - **/ - 'toString': function(dec) { - - var N = this["n"]; - var D = this["d"]; - - if (isNaN(N) || isNaN(D)) { - return "NaN"; - } - - dec = dec || 15; // 15 = decimal places when no repetation - - var cycLen = cycleLen(N, D); // Cycle length - var cycOff = cycleStart(N, D, cycLen); // Cycle start - - var str = this['s'] < 0 ? "-" : ""; - - str+= N / D | 0; - - N%= D; - N*= 10; - - if (N) - str+= "."; - - if (cycLen) { - - for (var i = cycOff; i--;) { - str+= N / D | 0; - N%= D; - N*= 10; - } - str+= "("; - for (var i = cycLen; i--;) { - str+= N / D | 0; - N%= D; - N*= 10; - } - str+= ")"; - } else { - for (var i = dec; N && i--;) { - str+= N / D | 0; - N%= D; - N*= 10; - } - } - return str; - } - }; - - if (typeof exports === "object") { - Object.defineProperty(exports, "__esModule", { 'value': true }); - exports['default'] = Fraction; - module['exports'] = Fraction; - } else { - root['Fraction'] = Fraction; - } - -})(this); diff --git a/node_modules/fraction.js/fraction.d.ts b/node_modules/fraction.js/fraction.d.ts deleted file mode 100644 index e62cfe1b..00000000 --- a/node_modules/fraction.js/fraction.d.ts +++ /dev/null @@ -1,60 +0,0 @@ -declare module 'Fraction'; - -export interface NumeratorDenominator { - n: number; - d: number; -} - -type FractionConstructor = { - (fraction: Fraction): Fraction; - (num: number | string): Fraction; - (numerator: number, denominator: number): Fraction; - (numbers: [number | string, number | string]): Fraction; - (fraction: NumeratorDenominator): Fraction; - (firstValue: Fraction | number | string | [number | string, number | string] | NumeratorDenominator, secondValue?: number): Fraction; -}; - -export default class Fraction { - constructor (fraction: Fraction); - constructor (num: number | string); - constructor (numerator: number, denominator: number); - constructor (numbers: [number | string, number | string]); - constructor (fraction: NumeratorDenominator); - constructor (firstValue: Fraction | number | string | [number | string, number | string] | NumeratorDenominator, secondValue?: number); - - s: number; - n: number; - d: number; - - abs(): Fraction; - neg(): Fraction; - - add: FractionConstructor; - sub: FractionConstructor; - mul: FractionConstructor; - div: FractionConstructor; - pow: FractionConstructor; - gcd: FractionConstructor; - lcm: FractionConstructor; - - mod(n?: number | string | Fraction): Fraction; - - ceil(places?: number): Fraction; - floor(places?: number): Fraction; - round(places?: number): Fraction; - - inverse(): Fraction; - - simplify(eps?: number): Fraction; - - equals(n: number | string | Fraction): boolean; - compare(n: number | string | Fraction): number; - divisible(n: number | string | Fraction): boolean; - - valueOf(): number; - toString(decimalPlaces?: number): string; - toLatex(excludeWhole?: boolean): string; - toFraction(excludeWhole?: boolean): string; - toContinued(): number[]; - clone(): Fraction; -} diff --git a/node_modules/fraction.js/fraction.js b/node_modules/fraction.js/fraction.js deleted file mode 100644 index b9780e08..00000000 --- a/node_modules/fraction.js/fraction.js +++ /dev/null @@ -1,891 +0,0 @@ -/** - * @license Fraction.js v4.3.7 31/08/2023 - * https://www.xarg.org/2014/03/rational-numbers-in-javascript/ - * - * Copyright (c) 2023, Robert Eisele (robert@raw.org) - * Dual licensed under the MIT or GPL Version 2 licenses. - **/ - - -/** - * - * This class offers the possibility to calculate fractions. - * You can pass a fraction in different formats. Either as array, as double, as string or as an integer. - * - * Array/Object form - * [ 0 => , 1 => ] - * [ n => , d => ] - * - * Integer form - * - Single integer value - * - * Double form - * - Single double value - * - * String form - * 123.456 - a simple double - * 123/456 - a string fraction - * 123.'456' - a double with repeating decimal places - * 123.(456) - synonym - * 123.45'6' - a double with repeating last place - * 123.45(6) - synonym - * - * Example: - * - * var f = new Fraction("9.4'31'"); - * f.mul([-4, 3]).div(4.9); - * - */ - - -// Maximum search depth for cyclic rational numbers. 2000 should be more than enough. -// Example: 1/7 = 0.(142857) has 6 repeating decimal places. -// If MAX_CYCLE_LEN gets reduced, long cycles will not be detected and toString() only gets the first 10 digits -var MAX_CYCLE_LEN = 2000; - -// Parsed data to avoid calling "new" all the time -var P = { - "s": 1, - "n": 0, - "d": 1 -}; - -function assign(n, s) { - - if (isNaN(n = parseInt(n, 10))) { - throw InvalidParameter(); - } - return n * s; -} - -// Creates a new Fraction internally without the need of the bulky constructor -function newFraction(n, d) { - - if (d === 0) { - throw DivisionByZero(); - } - - var f = Object.create(Fraction.prototype); - f["s"] = n < 0 ? -1 : 1; - - n = n < 0 ? -n : n; - - var a = gcd(n, d); - - f["n"] = n / a; - f["d"] = d / a; - return f; -} - -function factorize(num) { - - var factors = {}; - - var n = num; - var i = 2; - var s = 4; - - while (s <= n) { - - while (n % i === 0) { - n/= i; - factors[i] = (factors[i] || 0) + 1; - } - s+= 1 + 2 * i++; - } - - if (n !== num) { - if (n > 1) - factors[n] = (factors[n] || 0) + 1; - } else { - factors[num] = (factors[num] || 0) + 1; - } - return factors; -} - -var parse = function(p1, p2) { - - var n = 0, d = 1, s = 1; - var v = 0, w = 0, x = 0, y = 1, z = 1; - - var A = 0, B = 1; - var C = 1, D = 1; - - var N = 10000000; - var M; - - if (p1 === undefined || p1 === null) { - /* void */ - } else if (p2 !== undefined) { - n = p1; - d = p2; - s = n * d; - - if (n % 1 !== 0 || d % 1 !== 0) { - throw NonIntegerParameter(); - } - - } else - switch (typeof p1) { - - case "object": - { - if ("d" in p1 && "n" in p1) { - n = p1["n"]; - d = p1["d"]; - if ("s" in p1) - n*= p1["s"]; - } else if (0 in p1) { - n = p1[0]; - if (1 in p1) - d = p1[1]; - } else { - throw InvalidParameter(); - } - s = n * d; - break; - } - case "number": - { - if (p1 < 0) { - s = p1; - p1 = -p1; - } - - if (p1 % 1 === 0) { - n = p1; - } else if (p1 > 0) { // check for != 0, scale would become NaN (log(0)), which converges really slow - - if (p1 >= 1) { - z = Math.pow(10, Math.floor(1 + Math.log(p1) / Math.LN10)); - p1/= z; - } - - // Using Farey Sequences - // http://www.johndcook.com/blog/2010/10/20/best-rational-approximation/ - - while (B <= N && D <= N) { - M = (A + C) / (B + D); - - if (p1 === M) { - if (B + D <= N) { - n = A + C; - d = B + D; - } else if (D > B) { - n = C; - d = D; - } else { - n = A; - d = B; - } - break; - - } else { - - if (p1 > M) { - A+= C; - B+= D; - } else { - C+= A; - D+= B; - } - - if (B > N) { - n = C; - d = D; - } else { - n = A; - d = B; - } - } - } - n*= z; - } else if (isNaN(p1) || isNaN(p2)) { - d = n = NaN; - } - break; - } - case "string": - { - B = p1.match(/\d+|./g); - - if (B === null) - throw InvalidParameter(); - - if (B[A] === '-') {// Check for minus sign at the beginning - s = -1; - A++; - } else if (B[A] === '+') {// Check for plus sign at the beginning - A++; - } - - if (B.length === A + 1) { // Check if it's just a simple number "1234" - w = assign(B[A++], s); - } else if (B[A + 1] === '.' || B[A] === '.') { // Check if it's a decimal number - - if (B[A] !== '.') { // Handle 0.5 and .5 - v = assign(B[A++], s); - } - A++; - - // Check for decimal places - if (A + 1 === B.length || B[A + 1] === '(' && B[A + 3] === ')' || B[A + 1] === "'" && B[A + 3] === "'") { - w = assign(B[A], s); - y = Math.pow(10, B[A].length); - A++; - } - - // Check for repeating places - if (B[A] === '(' && B[A + 2] === ')' || B[A] === "'" && B[A + 2] === "'") { - x = assign(B[A + 1], s); - z = Math.pow(10, B[A + 1].length) - 1; - A+= 3; - } - - } else if (B[A + 1] === '/' || B[A + 1] === ':') { // Check for a simple fraction "123/456" or "123:456" - w = assign(B[A], s); - y = assign(B[A + 2], 1); - A+= 3; - } else if (B[A + 3] === '/' && B[A + 1] === ' ') { // Check for a complex fraction "123 1/2" - v = assign(B[A], s); - w = assign(B[A + 2], s); - y = assign(B[A + 4], 1); - A+= 5; - } - - if (B.length <= A) { // Check for more tokens on the stack - d = y * z; - s = /* void */ - n = x + d * v + z * w; - break; - } - - /* Fall through on error */ - } - default: - throw InvalidParameter(); - } - - if (d === 0) { - throw DivisionByZero(); - } - - P["s"] = s < 0 ? -1 : 1; - P["n"] = Math.abs(n); - P["d"] = Math.abs(d); -}; - -function modpow(b, e, m) { - - var r = 1; - for (; e > 0; b = (b * b) % m, e >>= 1) { - - if (e & 1) { - r = (r * b) % m; - } - } - return r; -} - - -function cycleLen(n, d) { - - for (; d % 2 === 0; - d/= 2) { - } - - for (; d % 5 === 0; - d/= 5) { - } - - if (d === 1) // Catch non-cyclic numbers - return 0; - - // If we would like to compute really large numbers quicker, we could make use of Fermat's little theorem: - // 10^(d-1) % d == 1 - // However, we don't need such large numbers and MAX_CYCLE_LEN should be the capstone, - // as we want to translate the numbers to strings. - - var rem = 10 % d; - var t = 1; - - for (; rem !== 1; t++) { - rem = rem * 10 % d; - - if (t > MAX_CYCLE_LEN) - return 0; // Returning 0 here means that we don't print it as a cyclic number. It's likely that the answer is `d-1` - } - return t; -} - - -function cycleStart(n, d, len) { - - var rem1 = 1; - var rem2 = modpow(10, len, d); - - for (var t = 0; t < 300; t++) { // s < ~log10(Number.MAX_VALUE) - // Solve 10^s == 10^(s+t) (mod d) - - if (rem1 === rem2) - return t; - - rem1 = rem1 * 10 % d; - rem2 = rem2 * 10 % d; - } - return 0; -} - -function gcd(a, b) { - - if (!a) - return b; - if (!b) - return a; - - while (1) { - a%= b; - if (!a) - return b; - b%= a; - if (!b) - return a; - } -}; - -/** - * Module constructor - * - * @constructor - * @param {number|Fraction=} a - * @param {number=} b - */ -export default function Fraction(a, b) { - - parse(a, b); - - if (this instanceof Fraction) { - a = gcd(P["d"], P["n"]); // Abuse variable a - this["s"] = P["s"]; - this["n"] = P["n"] / a; - this["d"] = P["d"] / a; - } else { - return newFraction(P['s'] * P['n'], P['d']); - } -} - -var DivisionByZero = function() { return new Error("Division by Zero"); }; -var InvalidParameter = function() { return new Error("Invalid argument"); }; -var NonIntegerParameter = function() { return new Error("Parameters must be integer"); }; - -Fraction.prototype = { - - "s": 1, - "n": 0, - "d": 1, - - /** - * Calculates the absolute value - * - * Ex: new Fraction(-4).abs() => 4 - **/ - "abs": function() { - - return newFraction(this["n"], this["d"]); - }, - - /** - * Inverts the sign of the current fraction - * - * Ex: new Fraction(-4).neg() => 4 - **/ - "neg": function() { - - return newFraction(-this["s"] * this["n"], this["d"]); - }, - - /** - * Adds two rational numbers - * - * Ex: new Fraction({n: 2, d: 3}).add("14.9") => 467 / 30 - **/ - "add": function(a, b) { - - parse(a, b); - return newFraction( - this["s"] * this["n"] * P["d"] + P["s"] * this["d"] * P["n"], - this["d"] * P["d"] - ); - }, - - /** - * Subtracts two rational numbers - * - * Ex: new Fraction({n: 2, d: 3}).add("14.9") => -427 / 30 - **/ - "sub": function(a, b) { - - parse(a, b); - return newFraction( - this["s"] * this["n"] * P["d"] - P["s"] * this["d"] * P["n"], - this["d"] * P["d"] - ); - }, - - /** - * Multiplies two rational numbers - * - * Ex: new Fraction("-17.(345)").mul(3) => 5776 / 111 - **/ - "mul": function(a, b) { - - parse(a, b); - return newFraction( - this["s"] * P["s"] * this["n"] * P["n"], - this["d"] * P["d"] - ); - }, - - /** - * Divides two rational numbers - * - * Ex: new Fraction("-17.(345)").inverse().div(3) - **/ - "div": function(a, b) { - - parse(a, b); - return newFraction( - this["s"] * P["s"] * this["n"] * P["d"], - this["d"] * P["n"] - ); - }, - - /** - * Clones the actual object - * - * Ex: new Fraction("-17.(345)").clone() - **/ - "clone": function() { - return newFraction(this['s'] * this['n'], this['d']); - }, - - /** - * Calculates the modulo of two rational numbers - a more precise fmod - * - * Ex: new Fraction('4.(3)').mod([7, 8]) => (13/3) % (7/8) = (5/6) - **/ - "mod": function(a, b) { - - if (isNaN(this['n']) || isNaN(this['d'])) { - return new Fraction(NaN); - } - - if (a === undefined) { - return newFraction(this["s"] * this["n"] % this["d"], 1); - } - - parse(a, b); - if (0 === P["n"] && 0 === this["d"]) { - throw DivisionByZero(); - } - - /* - * First silly attempt, kinda slow - * - return that["sub"]({ - "n": num["n"] * Math.floor((this.n / this.d) / (num.n / num.d)), - "d": num["d"], - "s": this["s"] - });*/ - - /* - * New attempt: a1 / b1 = a2 / b2 * q + r - * => b2 * a1 = a2 * b1 * q + b1 * b2 * r - * => (b2 * a1 % a2 * b1) / (b1 * b2) - */ - return newFraction( - this["s"] * (P["d"] * this["n"]) % (P["n"] * this["d"]), - P["d"] * this["d"] - ); - }, - - /** - * Calculates the fractional gcd of two rational numbers - * - * Ex: new Fraction(5,8).gcd(3,7) => 1/56 - */ - "gcd": function(a, b) { - - parse(a, b); - - // gcd(a / b, c / d) = gcd(a, c) / lcm(b, d) - - return newFraction(gcd(P["n"], this["n"]) * gcd(P["d"], this["d"]), P["d"] * this["d"]); - }, - - /** - * Calculates the fractional lcm of two rational numbers - * - * Ex: new Fraction(5,8).lcm(3,7) => 15 - */ - "lcm": function(a, b) { - - parse(a, b); - - // lcm(a / b, c / d) = lcm(a, c) / gcd(b, d) - - if (P["n"] === 0 && this["n"] === 0) { - return newFraction(0, 1); - } - return newFraction(P["n"] * this["n"], gcd(P["n"], this["n"]) * gcd(P["d"], this["d"])); - }, - - /** - * Calculates the ceil of a rational number - * - * Ex: new Fraction('4.(3)').ceil() => (5 / 1) - **/ - "ceil": function(places) { - - places = Math.pow(10, places || 0); - - if (isNaN(this["n"]) || isNaN(this["d"])) { - return new Fraction(NaN); - } - return newFraction(Math.ceil(places * this["s"] * this["n"] / this["d"]), places); - }, - - /** - * Calculates the floor of a rational number - * - * Ex: new Fraction('4.(3)').floor() => (4 / 1) - **/ - "floor": function(places) { - - places = Math.pow(10, places || 0); - - if (isNaN(this["n"]) || isNaN(this["d"])) { - return new Fraction(NaN); - } - return newFraction(Math.floor(places * this["s"] * this["n"] / this["d"]), places); - }, - - /** - * Rounds a rational number - * - * Ex: new Fraction('4.(3)').round() => (4 / 1) - **/ - "round": function(places) { - - places = Math.pow(10, places || 0); - - if (isNaN(this["n"]) || isNaN(this["d"])) { - return new Fraction(NaN); - } - return newFraction(Math.round(places * this["s"] * this["n"] / this["d"]), places); - }, - - /** - * Rounds a rational number to a multiple of another rational number - * - * Ex: new Fraction('0.9').roundTo("1/8") => 7 / 8 - **/ - "roundTo": function(a, b) { - - /* - k * x/y ≤ a/b < (k+1) * x/y - ⇔ k ≤ a/b / (x/y) < (k+1) - ⇔ k = floor(a/b * y/x) - */ - - parse(a, b); - - return newFraction(this['s'] * Math.round(this['n'] * P['d'] / (this['d'] * P['n'])) * P['n'], P['d']); - }, - - /** - * Gets the inverse of the fraction, means numerator and denominator are exchanged - * - * Ex: new Fraction([-3, 4]).inverse() => -4 / 3 - **/ - "inverse": function() { - - return newFraction(this["s"] * this["d"], this["n"]); - }, - - /** - * Calculates the fraction to some rational exponent, if possible - * - * Ex: new Fraction(-1,2).pow(-3) => -8 - */ - "pow": function(a, b) { - - parse(a, b); - - // Trivial case when exp is an integer - - if (P['d'] === 1) { - - if (P['s'] < 0) { - return newFraction(Math.pow(this['s'] * this["d"], P['n']), Math.pow(this["n"], P['n'])); - } else { - return newFraction(Math.pow(this['s'] * this["n"], P['n']), Math.pow(this["d"], P['n'])); - } - } - - // Negative roots become complex - // (-a/b)^(c/d) = x - // <=> (-1)^(c/d) * (a/b)^(c/d) = x - // <=> (cos(pi) + i*sin(pi))^(c/d) * (a/b)^(c/d) = x # rotate 1 by 180° - // <=> (cos(c*pi/d) + i*sin(c*pi/d)) * (a/b)^(c/d) = x # DeMoivre's formula in Q ( https://proofwiki.org/wiki/De_Moivre%27s_Formula/Rational_Index ) - // From which follows that only for c=0 the root is non-complex. c/d is a reduced fraction, so that sin(c/dpi)=0 occurs for d=1, which is handled by our trivial case. - if (this['s'] < 0) return null; - - // Now prime factor n and d - var N = factorize(this['n']); - var D = factorize(this['d']); - - // Exponentiate and take root for n and d individually - var n = 1; - var d = 1; - for (var k in N) { - if (k === '1') continue; - if (k === '0') { - n = 0; - break; - } - N[k]*= P['n']; - - if (N[k] % P['d'] === 0) { - N[k]/= P['d']; - } else return null; - n*= Math.pow(k, N[k]); - } - - for (var k in D) { - if (k === '1') continue; - D[k]*= P['n']; - - if (D[k] % P['d'] === 0) { - D[k]/= P['d']; - } else return null; - d*= Math.pow(k, D[k]); - } - - if (P['s'] < 0) { - return newFraction(d, n); - } - return newFraction(n, d); - }, - - /** - * Check if two rational numbers are the same - * - * Ex: new Fraction(19.6).equals([98, 5]); - **/ - "equals": function(a, b) { - - parse(a, b); - return this["s"] * this["n"] * P["d"] === P["s"] * P["n"] * this["d"]; // Same as compare() === 0 - }, - - /** - * Check if two rational numbers are the same - * - * Ex: new Fraction(19.6).equals([98, 5]); - **/ - "compare": function(a, b) { - - parse(a, b); - var t = (this["s"] * this["n"] * P["d"] - P["s"] * P["n"] * this["d"]); - return (0 < t) - (t < 0); - }, - - "simplify": function(eps) { - - if (isNaN(this['n']) || isNaN(this['d'])) { - return this; - } - - eps = eps || 0.001; - - var thisABS = this['abs'](); - var cont = thisABS['toContinued'](); - - for (var i = 1; i < cont.length; i++) { - - var s = newFraction(cont[i - 1], 1); - for (var k = i - 2; k >= 0; k--) { - s = s['inverse']()['add'](cont[k]); - } - - if (Math.abs(s['sub'](thisABS).valueOf()) < eps) { - return s['mul'](this['s']); - } - } - return this; - }, - - /** - * Check if two rational numbers are divisible - * - * Ex: new Fraction(19.6).divisible(1.5); - */ - "divisible": function(a, b) { - - parse(a, b); - return !(!(P["n"] * this["d"]) || ((this["n"] * P["d"]) % (P["n"] * this["d"]))); - }, - - /** - * Returns a decimal representation of the fraction - * - * Ex: new Fraction("100.'91823'").valueOf() => 100.91823918239183 - **/ - 'valueOf': function() { - - return this["s"] * this["n"] / this["d"]; - }, - - /** - * Returns a string-fraction representation of a Fraction object - * - * Ex: new Fraction("1.'3'").toFraction(true) => "4 1/3" - **/ - 'toFraction': function(excludeWhole) { - - var whole, str = ""; - var n = this["n"]; - var d = this["d"]; - if (this["s"] < 0) { - str+= '-'; - } - - if (d === 1) { - str+= n; - } else { - - if (excludeWhole && (whole = Math.floor(n / d)) > 0) { - str+= whole; - str+= " "; - n%= d; - } - - str+= n; - str+= '/'; - str+= d; - } - return str; - }, - - /** - * Returns a latex representation of a Fraction object - * - * Ex: new Fraction("1.'3'").toLatex() => "\frac{4}{3}" - **/ - 'toLatex': function(excludeWhole) { - - var whole, str = ""; - var n = this["n"]; - var d = this["d"]; - if (this["s"] < 0) { - str+= '-'; - } - - if (d === 1) { - str+= n; - } else { - - if (excludeWhole && (whole = Math.floor(n / d)) > 0) { - str+= whole; - n%= d; - } - - str+= "\\frac{"; - str+= n; - str+= '}{'; - str+= d; - str+= '}'; - } - return str; - }, - - /** - * Returns an array of continued fraction elements - * - * Ex: new Fraction("7/8").toContinued() => [0,1,7] - */ - 'toContinued': function() { - - var t; - var a = this['n']; - var b = this['d']; - var res = []; - - if (isNaN(a) || isNaN(b)) { - return res; - } - - do { - res.push(Math.floor(a / b)); - t = a % b; - a = b; - b = t; - } while (a !== 1); - - return res; - }, - - /** - * Creates a string representation of a fraction with all digits - * - * Ex: new Fraction("100.'91823'").toString() => "100.(91823)" - **/ - 'toString': function(dec) { - - var N = this["n"]; - var D = this["d"]; - - if (isNaN(N) || isNaN(D)) { - return "NaN"; - } - - dec = dec || 15; // 15 = decimal places when no repetation - - var cycLen = cycleLen(N, D); // Cycle length - var cycOff = cycleStart(N, D, cycLen); // Cycle start - - var str = this['s'] < 0 ? "-" : ""; - - str+= N / D | 0; - - N%= D; - N*= 10; - - if (N) - str+= "."; - - if (cycLen) { - - for (var i = cycOff; i--;) { - str+= N / D | 0; - N%= D; - N*= 10; - } - str+= "("; - for (var i = cycLen; i--;) { - str+= N / D | 0; - N%= D; - N*= 10; - } - str+= ")"; - } else { - for (var i = dec; N && i--;) { - str+= N / D | 0; - N%= D; - N*= 10; - } - } - return str; - } -}; diff --git a/node_modules/fraction.js/fraction.min.js b/node_modules/fraction.js/fraction.min.js deleted file mode 100644 index 1cfa1516..00000000 --- a/node_modules/fraction.js/fraction.min.js +++ /dev/null @@ -1,18 +0,0 @@ -/* -Fraction.js v4.3.7 31/08/2023 -https://www.xarg.org/2014/03/rational-numbers-in-javascript/ - -Copyright (c) 2023, Robert Eisele (robert@raw.org) -Dual licensed under the MIT or GPL Version 2 licenses. -*/ -(function(B){function x(){return Error("Invalid argument")}function z(){return Error("Division by Zero")}function n(a,c){var b=0,d=1,f=1,l=0,k=0,t=0,y=1,u=1,g=0,h=1,v=1,q=1;if(void 0!==a&&null!==a)if(void 0!==c){if(b=a,d=c,f=b*d,0!==b%1||0!==d%1)throw Error("Parameters must be integer");}else switch(typeof a){case "object":if("d"in a&&"n"in a)b=a.n,d=a.d,"s"in a&&(b*=a.s);else if(0 in a)b=a[0],1 in a&&(d=a[1]);else throw x();f=b*d;break;case "number":0>a&&(f=a,a=-a);if(0===a%1)b=a;else if(0=h&&1E7>=q;)if(b=(g+v)/(h+q),a===b){1E7>=h+q?(b=g+v,d=h+q):q>h?(b=v,d=q):(b=g,d=h);break}else a>b?(g+=v,h+=q):(v+=g,q+=h),1E7f?-1:1;e.n=Math.abs(b);e.d=Math.abs(d)}function r(a,c){if(isNaN(a=parseInt(a,10)))throw x();return a*c} -function m(a,c){if(0===c)throw z();var b=Object.create(p.prototype);b.s=0>a?-1:1;a=0>a?-a:a;var d=w(a,c);b.n=a/d;b.d=c/d;return b}function A(a){for(var c={},b=a,d=2,f=4;f<=b;){for(;0===b%d;)b/=d,c[d]=(c[d]||0)+1;f+=1+2*d++}b!==a?1e.s?m(Math.pow(this.s*this.d,e.n),Math.pow(this.n,e.n)):m(Math.pow(this.s*this.n,e.n),Math.pow(this.d, -e.n));if(0>this.s)return null;var b=A(this.n),d=A(this.d),f=1,l=1,k;for(k in b)if("1"!==k){if("0"===k){f=0;break}b[k]*=e.n;if(0===b[k]%e.d)b[k]/=e.d;else return null;f*=Math.pow(k,b[k])}for(k in d)if("1"!==k){d[k]*=e.n;if(0===d[k]%e.d)d[k]/=e.d;else return null;l*=Math.pow(k,d[k])}return 0>e.s?m(l,f):m(f,l)},equals:function(a,c){n(a,c);return this.s*this.n*e.d===e.s*e.n*this.d},compare:function(a,c){n(a,c);var b=this.s*this.n*e.d-e.s*e.n*this.d;return(0b)},simplify:function(a){if(isNaN(this.n)|| -isNaN(this.d))return this;a=a||.001;for(var c=this.abs(),b=c.toContinued(),d=1;dthis.s&&(b+="-");1===f?b+=d:(a&&0<(c=Math.floor(d/f))&&(b=b+c+" ",d%=f),b=b+d+"/",b+=f);return b}, -toLatex:function(a){var c,b="",d=this.n,f=this.d;0>this.s&&(b+="-");1===f?b+=d:(a&&0<(c=Math.floor(d/f))&&(b+=c,d%=f),b=b+"\\frac{"+d+"}{"+f,b+="}");return b},toContinued:function(){var a=this.n,c=this.d,b=[];if(isNaN(a)||isNaN(c))return b;do{b.push(Math.floor(a/c));var d=a%c;a=c;c=d}while(1!==a);return b},toString:function(a){var c=this.n,b=this.d;if(isNaN(c)||isNaN(b))return"NaN";var d;a:{for(d=b;0===d%2;d/=2);for(;0===d%5;d/=5);if(1===d)d=0;else{for(var f=10%d,l=1;1!==f;l++)if(f=10*f%d,2E3>=1)k&1&&(t=t*l%b);l=t;for(k=0;300>k;k++){if(f===l){l=k;break a}f=10*f%b;l=10*l%b}l=0}f=0>this.s?"-":"";f+=c/b|0;(c=c%b*10)&&(f+=".");if(d){for(a=l;a--;)f+=c/b|0,c%=b,c*=10;f+="(";for(a=d;a--;)f+=c/b|0,c%=b,c*=10;f+=")"}else for(a=a||15;c&&a--;)f+=c/b|0,c%=b,c*=10;return f}};"object"===typeof exports?(Object.defineProperty(exports,"__esModule",{value:!0}),exports["default"]=p,module.exports=p):B.Fraction=p})(this); \ No newline at end of file diff --git a/node_modules/fraction.js/package.json b/node_modules/fraction.js/package.json deleted file mode 100644 index 085d287c..00000000 --- a/node_modules/fraction.js/package.json +++ /dev/null @@ -1,55 +0,0 @@ -{ - "name": "fraction.js", - "title": "fraction.js", - "version": "4.3.7", - "homepage": "https://www.xarg.org/2014/03/rational-numbers-in-javascript/", - "bugs": "https://github.com/rawify/Fraction.js/issues", - "description": "A rational number library", - "keywords": [ - "math", - "fraction", - "rational", - "rationals", - "number", - "parser", - "rational numbers" - ], - "author": { - "name": "Robert Eisele", - "email": "robert@raw.org", - "url": "https://raw.org/" - }, - "type": "module", - "main": "fraction.cjs", - "exports": { - ".": { - "import": "./fraction.js", - "require": "./fraction.cjs", - "types": "./fraction.d.ts" - } - }, - "types": "./fraction.d.ts", - "private": false, - "readmeFilename": "README.md", - "directories": { - "example": "examples" - }, - "license": "MIT", - "repository": { - "type": "git", - "url": "git://github.com/rawify/Fraction.js.git" - }, - "funding": { - "type": "patreon", - "url": "https://github.com/sponsors/rawify" - }, - "engines": { - "node": "*" - }, - "scripts": { - "test": "mocha tests/*.js" - }, - "devDependencies": { - "mocha": "*" - } -} -- cgit v1.2.3