Intial Commit
This commit is contained in:
valki
9
nodered/rootfs/data/node_modules/fraction.js/.idea/Fraction.js.iml
generated
vendored
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9
nodered/rootfs/data/node_modules/fraction.js/.idea/Fraction.js.iml
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4
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4
nodered/rootfs/data/node_modules/fraction.js/.idea/misc.xml
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8
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6
nodered/rootfs/data/node_modules/fraction.js/.idea/vcs.xml
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6
nodered/rootfs/data/node_modules/fraction.js/.idea/vcs.xml
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373
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generated
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373
nodered/rootfs/data/node_modules/fraction.js/.idea/workspace.xml
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|
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4
nodered/rootfs/data/node_modules/fraction.js/.travis.yml
generated
vendored
Normal file
4
nodered/rootfs/data/node_modules/fraction.js/.travis.yml
generated
vendored
Normal file
@@ -0,0 +1,4 @@
|
||||
language: node_js
|
||||
node_js:
|
||||
- "stable"
|
||||
script: npm test
|
||||
489
nodered/rootfs/data/node_modules/fraction.js/README.md
generated
vendored
Normal file
489
nodered/rootfs/data/node_modules/fraction.js/README.md
generated
vendored
Normal file
@@ -0,0 +1,489 @@
|
||||
# Fraction.js - ℚ in JavaSript
|
||||
|
||||
[](https://npmjs.org/package/fraction.js "View this project on npm")
|
||||
[](https://travis-ci.org/infusion/Fraction.js)
|
||||
[](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, have a look at *Fraction.js*:
|
||||
|
||||
```javascript
|
||||
var Fraction = require('fraction.js');
|
||||
|
||||
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 in mind and outperforms any other implementation, as you can see [here](http://jsperf.com/convert-a-rational-number-to-a-babylonian-fractions/28). This basic data-type 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 = new Fraction(a).add(b).div(2);
|
||||
|
||||
console.log(n + "\t" + a.n + "/" + a.d + "\t" + b.n + "/" + b.d + "\t" + c.n + "/" + c.d + "\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()); // Same as: Math.abs(f - parseInt(f, 10));
|
||||
```
|
||||
|
||||
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 comparision 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 integer exponent.
|
||||
*Note:* Rational exponents are planned, but would slow down the function a lot, because of a kinda slow root finding algorithm, whether the result will become irrational. So for now, only integer exponents are implemented.
|
||||
|
||||
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 will. 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])
|
||||
---
|
||||
Returns the ceiling of a rational number (rounded up)
|
||||
|
||||
Fraction floor([places=0])
|
||||
---
|
||||
Returns the floor of a rational number (rounded down)
|
||||
|
||||
Fraction round([places=0])
|
||||
---
|
||||
Returns the rational number rounded (normal round)
|
||||
|
||||
Fraction inverse()
|
||||
---
|
||||
Returns the multiplicative inverse of the actual number (n / d becomes d / n) in order to get the reciprocal
|
||||
|
||||
boolean equals(n)
|
||||
---
|
||||
Check if two numbers are equal
|
||||
|
||||
boolean 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()
|
||||
---
|
||||
Generates an exact string representation of the actual object, including repeating decimal places of any length.
|
||||
|
||||
**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
|
||||
|
||||
Options
|
||||
===
|
||||
|
||||
The library should work without configuring anything. However, there is one global option:
|
||||
|
||||
```javascript
|
||||
Fraction.REDUCE = <true|false>
|
||||
```
|
||||
|
||||
It tells Fraction.js whether to reduce the fraction or not.
|
||||
|
||||
```javascript
|
||||
// Normal behavior
|
||||
var f = Fraction(3, 6);
|
||||
console.log(f); // 1/2
|
||||
|
||||
// Disable fraction reduction
|
||||
Fraction.REDUCE = false;
|
||||
var g = Fraction(3, 6);
|
||||
console.log(g); // 3/6
|
||||
|
||||
// Back to normal behavior
|
||||
Fraction.REDUCE = true;
|
||||
var h = Fraction(g);
|
||||
console.log(h); // 1/2
|
||||
```
|
||||
|
||||
|
||||
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 one of the following commands:
|
||||
|
||||
```
|
||||
bower install fraction.js
|
||||
```
|
||||
or
|
||||
|
||||
```
|
||||
npm install --save fraction.js
|
||||
```
|
||||
|
||||
Using Fraction.js with the browser
|
||||
===
|
||||
```html
|
||||
<script src="fraction.js"></script>
|
||||
<script>
|
||||
console.log(Fraction("123/456"));
|
||||
</script>
|
||||
```
|
||||
|
||||
Using Fraction.js with require.js
|
||||
===
|
||||
```html
|
||||
<script src="require.js"></script>
|
||||
<script>
|
||||
requirejs(['fraction.js'],
|
||||
function(Fraction) {
|
||||
console.log(Fraction("123/456"));
|
||||
});
|
||||
</script>
|
||||
```
|
||||
|
||||
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`.
|
||||
|
||||
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) 2015, Robert Eisele (robert@xarg.org)
|
||||
Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
31
nodered/rootfs/data/node_modules/fraction.js/bower.json
generated
vendored
Normal file
31
nodered/rootfs/data/node_modules/fraction.js/bower.json
generated
vendored
Normal file
@@ -0,0 +1,31 @@
|
||||
{
|
||||
"name": "fraction.js",
|
||||
"main": "fraction.js",
|
||||
"version": "4.0.0",
|
||||
"homepage": "http://www.xarg.org/2014/03/rational-numbers-in-javascript/",
|
||||
"description": "A rational number library",
|
||||
"keywords": [
|
||||
"math", "fraction", "rational", "number", "parser", "rational numbers"
|
||||
],
|
||||
"moduleType": [
|
||||
"amd",
|
||||
"globals",
|
||||
"node"
|
||||
],
|
||||
"authors": [
|
||||
"Robert Eisele <robert@xarg.org> (http://www.xarg.org/)"
|
||||
],
|
||||
"license": [
|
||||
"MIT",
|
||||
"GPL"
|
||||
],
|
||||
"repository": {
|
||||
"type": "git",
|
||||
"url": "git://github.com/infusion/Fraction.js.git"
|
||||
},
|
||||
"ignore": [
|
||||
"tests",
|
||||
".travis.yml",
|
||||
"package.json"
|
||||
]
|
||||
}
|
||||
53
nodered/rootfs/data/node_modules/fraction.js/examples/approx.js
generated
vendored
Normal file
53
nodered/rootfs/data/node_modules/fraction.js/examples/approx.js
generated
vendored
Normal file
@@ -0,0 +1,53 @@
|
||||
/**
|
||||
* @license Fraction.js v2.7.0 01/06/2015
|
||||
* http://www.xarg.org/2014/03/rational-numbers-in-javascript/
|
||||
*
|
||||
* Copyright (c) 2015, Robert Eisele (robert@xarg.org)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
**/
|
||||
|
||||
// Another rational approximation, not using Farey Sequences but Binary Search using the mediant
|
||||
function approximate(p, precision) {
|
||||
|
||||
var num1 = Math.floor(p);
|
||||
var den1 = 1;
|
||||
|
||||
var num2 = num1 + 1;
|
||||
var den2 = 1;
|
||||
|
||||
if (p !== num1) {
|
||||
|
||||
while (den1 <= precision && den2 <= precision) {
|
||||
|
||||
var m = (num1 + num2) / (den1 + den2);
|
||||
|
||||
if (p === m) {
|
||||
|
||||
if (den1 + den2 <= precision) {
|
||||
den1 += den2;
|
||||
num1 += num2;
|
||||
den2 = precision + 1;
|
||||
} else if (den1 > den2) {
|
||||
den2 = precision + 1;
|
||||
} else {
|
||||
den1 = precision + 1;
|
||||
}
|
||||
break;
|
||||
|
||||
} else if (p < m) {
|
||||
num2 += num1;
|
||||
den2 += den1;
|
||||
} else {
|
||||
num1 += num2;
|
||||
den1 += den2;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
if (den1 > precision) {
|
||||
den1 = den2;
|
||||
num1 = num2;
|
||||
}
|
||||
return new Fraction(num1, den1);
|
||||
}
|
||||
|
||||
23
nodered/rootfs/data/node_modules/fraction.js/examples/egyptian.js
generated
vendored
Normal file
23
nodered/rootfs/data/node_modules/fraction.js/examples/egyptian.js
generated
vendored
Normal file
@@ -0,0 +1,23 @@
|
||||
/**
|
||||
* @license Fraction.js v2.7.0 01/06/2015
|
||||
* http://www.xarg.org/2014/03/rational-numbers-in-javascript/
|
||||
*
|
||||
* Copyright (c) 2015, Robert Eisele (robert@xarg.org)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
**/
|
||||
|
||||
// Based on http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptian.html
|
||||
function egyptian(a, b) {
|
||||
|
||||
var res = [];
|
||||
|
||||
do {
|
||||
var t = Math.ceil(b / a);
|
||||
var x = new Fraction(a, b).sub(1, t);
|
||||
res.push(t);
|
||||
a = x.n;
|
||||
b = x.d;
|
||||
} while (a !== 0);
|
||||
return res;
|
||||
}
|
||||
console.log("1 / " + egyptian(521, 1050).join(" + 1 / "));
|
||||
112
nodered/rootfs/data/node_modules/fraction.js/examples/hesse-convergence.js
generated
vendored
Normal file
112
nodered/rootfs/data/node_modules/fraction.js/examples/hesse-convergence.js
generated
vendored
Normal file
@@ -0,0 +1,112 @@
|
||||
/**
|
||||
* @license Fraction.js v2.4.1 01/06/2015
|
||||
* http://www.xarg.org/2014/03/rational-numbers-in-javascript/
|
||||
*
|
||||
* Copyright (c) 2015, Robert Eisele (robert@xarg.org)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
**/
|
||||
|
||||
var Fraction = require('../fraction.min.js');
|
||||
|
||||
/*
|
||||
We have the polynom f(x) = 1/3x_1^2 + x_2^2 + x_1 * x_2 + 3
|
||||
|
||||
The gradient of f(x):
|
||||
|
||||
grad(x) = | x_1^2+x_2 |
|
||||
| 2x_2+x_1 |
|
||||
|
||||
And thus the Hesse-Matrix H:
|
||||
| 2x_1 1 |
|
||||
| 1 2 |
|
||||
|
||||
The inverse Hesse-Matrix H^-1 is
|
||||
| -2 / (1-4x_1) 1 / (1 - 4x_1) |
|
||||
| 1 / (1 - 4x_1) -2x_1 / (1 - 4x_1) |
|
||||
|
||||
We now want to find lim ->oo x[n], with the starting element of (3 2)^T
|
||||
|
||||
*/
|
||||
|
||||
// Get the Hesse Matrix
|
||||
function H(x) {
|
||||
|
||||
var z = new Fraction(1).sub(new Fraction(4).mul(x[0]));
|
||||
|
||||
return [
|
||||
new Fraction(-2).div(z),
|
||||
new Fraction(1).div(z),
|
||||
new Fraction(1).div(z),
|
||||
new Fraction(-2).mul(x[0]).div(z),
|
||||
];
|
||||
}
|
||||
|
||||
// Get the gradient of f(x)
|
||||
function grad(x) {
|
||||
|
||||
return [
|
||||
new Fraction(x[0]).mul(x[0]).add(x[1]),
|
||||
new Fraction(2).mul(x[1]).add(x[0])
|
||||
];
|
||||
}
|
||||
|
||||
// A simple matrix multiplication helper
|
||||
function matrMult(m, v) {
|
||||
|
||||
return [
|
||||
new Fraction(m[0]).mul(v[0]).add(new Fraction(m[1]).mul(v[1])),
|
||||
new Fraction(m[2]).mul(v[0]).add(new Fraction(m[3]).mul(v[1]))
|
||||
];
|
||||
}
|
||||
|
||||
// A simple vector subtraction helper
|
||||
function vecSub(a, b) {
|
||||
|
||||
return [
|
||||
new Fraction(a[0]).sub(b[0]),
|
||||
new Fraction(a[1]).sub(b[1])
|
||||
];
|
||||
}
|
||||
|
||||
// Main function, gets a vector and the actual index
|
||||
function run(V, j) {
|
||||
|
||||
var t = H(V);
|
||||
//console.log("H(X)");
|
||||
for (var i in t) {
|
||||
|
||||
// console.log(t[i].toFraction());
|
||||
}
|
||||
|
||||
var s = grad(V);
|
||||
//console.log("vf(X)");
|
||||
for (var i in s) {
|
||||
|
||||
// console.log(s[i].toFraction());
|
||||
}
|
||||
|
||||
//console.log("multiplikation");
|
||||
var r = matrMult(t, s);
|
||||
for (var i in r) {
|
||||
|
||||
// console.log(r[i].toFraction());
|
||||
}
|
||||
|
||||
var R = (vecSub(V, r));
|
||||
|
||||
console.log("X"+j);
|
||||
console.log(R[0].toFraction(), "= "+R[0].valueOf());
|
||||
console.log(R[1].toFraction(), "= "+R[1].valueOf());
|
||||
console.log("\n");
|
||||
|
||||
return R;
|
||||
}
|
||||
|
||||
|
||||
// Set the starting vector
|
||||
var v = [3, 2];
|
||||
|
||||
for (var i = 0; i < 15; i++) {
|
||||
|
||||
v = run(v, i);
|
||||
}
|
||||
68
nodered/rootfs/data/node_modules/fraction.js/examples/integrate.js
generated
vendored
Normal file
68
nodered/rootfs/data/node_modules/fraction.js/examples/integrate.js
generated
vendored
Normal file
@@ -0,0 +1,68 @@
|
||||
/**
|
||||
* @license Fraction.js v2.7.0 01/06/2015
|
||||
* http://www.xarg.org/2014/03/rational-numbers-in-javascript/
|
||||
*
|
||||
* Copyright (c) 2015, Robert Eisele (robert@xarg.org)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
**/
|
||||
|
||||
// NOTE: This is a nice example, but a stable version of this is served with Polynomial.js:
|
||||
// https://github.com/infusion/Polynomial.js
|
||||
|
||||
var Fraction = require('../fraction.min.js');
|
||||
|
||||
function integrate(poly) {
|
||||
|
||||
poly = poly.replace(/\s+/g, "");
|
||||
|
||||
var regex = /(\([+-]?[0-9/]+\)|[+-]?[0-9/]+)x(?:\^(\([+-]?[0-9/]+\)|[+-]?[0-9]+))?/g;
|
||||
var arr;
|
||||
var res = {};
|
||||
while (null !== (arr = regex.exec(poly))) {
|
||||
|
||||
var a = (arr[1] || "1").replace("(", "").replace(")", "").split("/");
|
||||
var b = (arr[2] || "1").replace("(", "").replace(")", "").split("/");
|
||||
|
||||
var exp = new Fraction(b).add(1);
|
||||
var key = "" + exp;
|
||||
|
||||
if (res[key] !== undefined) {
|
||||
res[key] = {x: new Fraction(a).div(exp).add(res[key].x), e: exp};
|
||||
} else {
|
||||
res[key] = {x: new Fraction(a).div(exp), e: exp};
|
||||
}
|
||||
}
|
||||
|
||||
var str = "";
|
||||
var c = 0;
|
||||
for (var i in res) {
|
||||
if (res[i].x.s !== -1 && c > 0) {
|
||||
str += ("+");
|
||||
} else if (res[i].x.s === -1) {
|
||||
str += ("-");
|
||||
}
|
||||
if (res[i].x.n / res[i].x.d !== 1) {
|
||||
if (res[i].x.d !== 1) {
|
||||
str += ("" + res[i].x.n + "/" + res[i].x.d + "");
|
||||
} else {
|
||||
str += ("" + res[i].x.n);
|
||||
}
|
||||
}
|
||||
str += ("x");
|
||||
if (res[i].e.n / res[i].e.d !== 1) {
|
||||
str += ("^");
|
||||
if (res[i].e.d !== 1) {
|
||||
str += ("(" + res[i].e.n + "/" + res[i].e.d + ")");
|
||||
} else {
|
||||
str += ("" + res[i].e.n);
|
||||
}
|
||||
}
|
||||
c++;
|
||||
}
|
||||
return str;
|
||||
}
|
||||
|
||||
var poly = "-2/3x^3-2x^2+3x+8x^3-1/3x^(4/8)";
|
||||
|
||||
console.log("f(x): " + poly);
|
||||
console.log("F(x): " + integrate(poly));
|
||||
797
nodered/rootfs/data/node_modules/fraction.js/fraction.js
generated
vendored
Normal file
797
nodered/rootfs/data/node_modules/fraction.js/fraction.js
generated
vendored
Normal file
@@ -0,0 +1,797 @@
|
||||
/**
|
||||
* @license Fraction.js v4.0.0 09/09/2015
|
||||
* http://www.xarg.org/2014/03/rational-numbers-in-javascript/
|
||||
*
|
||||
* Copyright (c) 2015, Robert Eisele (robert@xarg.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 => <nominator>, 1 => <denominator> ]
|
||||
* [ n => <nominator>, d => <denominator> ]
|
||||
*
|
||||
* 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 createError(name) {
|
||||
var errorConstructor = function() {
|
||||
var temp = Error.apply(this, arguments);
|
||||
temp.name = this.name = name;
|
||||
this.stack = temp.stack;
|
||||
this.message = temp.message;
|
||||
}
|
||||
|
||||
var IntermediateInheritor = function() {};
|
||||
IntermediateInheritor.prototype = Error.prototype;
|
||||
errorConstructor.prototype = new IntermediateInheritor();
|
||||
|
||||
return errorConstructor;
|
||||
}
|
||||
|
||||
var DivisionByZero = Fraction['DivisionByZero'] = createError('DivisionByZero');
|
||||
var InvalidParameter = Fraction['InvalidParameter'] = createError('InvalidParameter');
|
||||
|
||||
function assign(n, s) {
|
||||
|
||||
if (isNaN(n = parseInt(n, 10))) {
|
||||
throwInvalidParam();
|
||||
}
|
||||
return n * s;
|
||||
}
|
||||
|
||||
function throwInvalidParam() {
|
||||
throw new InvalidParameter();
|
||||
}
|
||||
|
||||
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;
|
||||
} 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 {
|
||||
throwInvalidParam();
|
||||
}
|
||||
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[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:
|
||||
throwInvalidParam();
|
||||
}
|
||||
|
||||
if (d === 0) {
|
||||
throw new DivisionByZero();
|
||||
}
|
||||
|
||||
P["s"] = s < 0 ? -1 : 1;
|
||||
P["n"] = Math.abs(n);
|
||||
P["d"] = Math.abs(d);
|
||||
};
|
||||
|
||||
var modpow = function(b, e, m) {
|
||||
|
||||
for (var r = 1; e > 0; b = (b * b) % m, e >>= 1) {
|
||||
|
||||
if (e & 1) {
|
||||
r = (r * b) % m;
|
||||
}
|
||||
}
|
||||
return r;
|
||||
};
|
||||
|
||||
var cycleLen = function(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;
|
||||
|
||||
for (var t = 1; 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;
|
||||
};
|
||||
|
||||
var cycleStart = function(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;
|
||||
};
|
||||
|
||||
var gcd = function(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) {
|
||||
|
||||
if (!(this instanceof Fraction)) {
|
||||
return new Fraction(a, b);
|
||||
}
|
||||
|
||||
parse(a, b);
|
||||
|
||||
if (Fraction['REDUCE']) {
|
||||
a = gcd(P["d"], P["n"]); // Abuse a
|
||||
} else {
|
||||
a = 1;
|
||||
}
|
||||
|
||||
this["s"] = P["s"];
|
||||
this["n"] = P["n"] / a;
|
||||
this["d"] = P["d"] / a;
|
||||
}
|
||||
|
||||
/**
|
||||
* Boolean global variable to be able to disable automatic reduction of the fraction
|
||||
*
|
||||
*/
|
||||
Fraction['REDUCE'] = 1;
|
||||
|
||||
Fraction.prototype = {
|
||||
|
||||
"s": 1,
|
||||
"n": 0,
|
||||
"d": 1,
|
||||
|
||||
/**
|
||||
* Calculates the absolute value
|
||||
*
|
||||
* Ex: new Fraction(-4).abs() => 4
|
||||
**/
|
||||
"abs": function() {
|
||||
|
||||
return new Fraction(this["n"], this["d"]);
|
||||
},
|
||||
|
||||
/**
|
||||
* Inverts the sign of the current fraction
|
||||
*
|
||||
* Ex: new Fraction(-4).neg() => 4
|
||||
**/
|
||||
"neg": function() {
|
||||
|
||||
return new Fraction(-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 new Fraction(
|
||||
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 new Fraction(
|
||||
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 new Fraction(
|
||||
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 new Fraction(
|
||||
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 new Fraction(this);
|
||||
},
|
||||
|
||||
/**
|
||||
* 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 new Fraction(this["s"] * this["n"] % this["d"], 1);
|
||||
}
|
||||
|
||||
parse(a, b);
|
||||
if (0 === P["n"] && 0 === this["d"]) {
|
||||
Fraction(0, 0); // 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 new Fraction(
|
||||
(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 new Fraction(gcd(P["n"], this["n"]), P["d"] * this["d"] / gcd(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 new Fraction;
|
||||
}
|
||||
return new Fraction(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 new Fraction(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 new Fraction(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 new Fraction(Math.round(places * this["s"] * this["n"] / this["d"]), places);
|
||||
},
|
||||
|
||||
/**
|
||||
* Gets the inverse of the fraction, means numerator and denumerator are exchanged
|
||||
*
|
||||
* Ex: new Fraction([-3, 4]).inverse() => -4 / 3
|
||||
**/
|
||||
"inverse": function() {
|
||||
|
||||
return new Fraction(this["s"] * this["d"], this["n"]);
|
||||
},
|
||||
|
||||
/**
|
||||
* Calculates the fraction to some integer exponent
|
||||
*
|
||||
* Ex: new Fraction(-1,2).pow(-3) => -8
|
||||
*/
|
||||
"pow": function(m) {
|
||||
|
||||
if (m < 0) {
|
||||
return new Fraction(Math.pow(this['s'] * this["d"],-m), Math.pow(this["n"],-m));
|
||||
} else {
|
||||
return new Fraction(Math.pow(this['s'] * this["n"], m), Math.pow(this["d"], m));
|
||||
}
|
||||
},
|
||||
|
||||
/**
|
||||
* 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);
|
||||
},
|
||||
|
||||
/**
|
||||
* 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() => "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 = [];
|
||||
|
||||
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() {
|
||||
|
||||
var g;
|
||||
var N = this["n"];
|
||||
var D = this["d"];
|
||||
|
||||
if (isNaN(N) || isNaN(D)) {
|
||||
return "NaN";
|
||||
}
|
||||
|
||||
if (!Fraction['REDUCE']) {
|
||||
g = gcd(N, D);
|
||||
N/= g;
|
||||
D/= g;
|
||||
}
|
||||
|
||||
var p = String(N).split(""); // Numerator chars
|
||||
var t = 0; // Tmp var
|
||||
|
||||
var ret = [~this["s"] ? "" : "-", "", ""]; // Return array, [0] is zero sign, [1] before comma, [2] after
|
||||
var zeros = ""; // Collection variable for zeros
|
||||
|
||||
var cycLen = cycleLen(N, D); // Cycle length
|
||||
var cycOff = cycleStart(N, D, cycLen); // Cycle start
|
||||
|
||||
var j = -1;
|
||||
var n = 1; // str index
|
||||
|
||||
// rough estimate to fill zeros
|
||||
var length = 15 + cycLen + cycOff + p.length; // 15 = decimal places when no repitation
|
||||
|
||||
for (var i = 0; i < length; i++, t*= 10) {
|
||||
|
||||
if (i < p.length) {
|
||||
t+= Number(p[i]);
|
||||
} else {
|
||||
n = 2;
|
||||
j++; // Start now => after comma
|
||||
}
|
||||
|
||||
if (cycLen > 0) { // If we have a repeating part
|
||||
if (j === cycOff) {
|
||||
ret[n]+= zeros + "(";
|
||||
zeros = "";
|
||||
} else if (j === cycLen + cycOff) {
|
||||
ret[n]+= zeros + ")";
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
if (t >= D) {
|
||||
ret[n]+= zeros + ((t / D) | 0); // Flush zeros, Add current digit
|
||||
zeros = "";
|
||||
t = t % D;
|
||||
} else if (n > 1) { // Add zeros to the zero buffer
|
||||
zeros+= "0";
|
||||
} else if (ret[n]) { // If before comma, add zero only if already something was added
|
||||
ret[n]+= "0";
|
||||
}
|
||||
}
|
||||
|
||||
// If it's empty, it's a leading zero only
|
||||
ret[0]+= ret[1] || "0";
|
||||
|
||||
// If there is something after the comma, add the comma sign
|
||||
if (ret[2]) {
|
||||
return ret[0] + "." + ret[2];
|
||||
}
|
||||
return ret[0];
|
||||
}
|
||||
};
|
||||
|
||||
if (typeof define === "function" && define["amd"]) {
|
||||
define([], function() {
|
||||
return Fraction;
|
||||
});
|
||||
} else if (typeof exports === "object") {
|
||||
module["exports"] = Fraction;
|
||||
} else {
|
||||
root['Fraction'] = Fraction;
|
||||
}
|
||||
|
||||
})(this);
|
||||
17
nodered/rootfs/data/node_modules/fraction.js/fraction.min.js
generated
vendored
Normal file
17
nodered/rootfs/data/node_modules/fraction.js/fraction.min.js
generated
vendored
Normal file
@@ -0,0 +1,17 @@
|
||||
/*
|
||||
Fraction.js v4.0.0 09/09/2015
|
||||
http://www.xarg.org/2014/03/rational-numbers-in-javascript/
|
||||
|
||||
Copyright (c) 2015, Robert Eisele (robert@xarg.org)
|
||||
Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
*/
|
||||
(function(w){function q(a,c){if(!a)return c;if(!c)return a;for(;;){a%=c;if(!a)return c;c%=a;if(!c)return a}}function x(a){for(;0===a%2;a/=2);for(;0===a%5;a/=5);if(1===a)return 0;for(var c=10%a,d=1;1!==c;d++)if(c=10*c%a,2E3<d)return 0;return d}function k(a,c){var d=0,l=1,e=1,k=0,m=0,n=0,h=1,r=1,f=0,g=1,q=1,t=1;if(void 0!==a&&null!==a)if(void 0!==c)d=a,l=c,e=d*l;else switch(typeof a){case "object":if("d"in a&&"n"in a)d=a.n,l=a.d,"s"in a&&(d*=a.s);else if(0 in a)d=a[0],1 in a&&(l=a[1]);else throw new u;
|
||||
e=d*l;break;case "number":0>a&&(e=a,a=-a);if(0===a%1)d=a;else if(0<a){1<=a&&(r=Math.pow(10,Math.floor(1+Math.log(a)/Math.LN10)),a/=r);for(;1E7>=g&&1E7>=t;)if(d=(f+q)/(g+t),a===d){1E7>=g+t?(d=f+q,l=g+t):t>g?(d=q,l=t):(d=f,l=g);break}else a>d?(f+=q,g+=t):(q+=f,t+=g),1E7<g?(d=q,l=t):(d=f,l=g);d*=r}else if(isNaN(a)||isNaN(c))l=d=NaN;break;case "string":g=a.match(/\d+|./g);"-"===g[f]?(e=-1,f++):"+"===g[f]&&f++;if(g.length===f+1)m=p(g[f++],e);else if("."===g[f+1]||"."===g[f]){"."!==g[f]&&(k=p(g[f++],e));
|
||||
f++;if(f+1===g.length||"("===g[f+1]&&")"===g[f+3]||"'"===g[f+1]&&"'"===g[f+3])m=p(g[f],e),h=Math.pow(10,g[f].length),f++;if("("===g[f]&&")"===g[f+2]||"'"===g[f]&&"'"===g[f+2])n=p(g[f+1],e),r=Math.pow(10,g[f+1].length)-1,f+=3}else"/"===g[f+1]||":"===g[f+1]?(m=p(g[f],e),h=p(g[f+2],1),f+=3):"/"===g[f+3]&&" "===g[f+1]&&(k=p(g[f],e),m=p(g[f+2],e),h=p(g[f+4],1),f+=5);if(g.length<=f){l=h*r;e=d=n+l*k+r*m;break}default:throw new u;}if(0===l)throw new y;b.s=0>e?-1:1;b.n=Math.abs(d);b.d=Math.abs(l)}function v(a){function c(){}
|
||||
function d(){var c=Error.apply(this,arguments);c.name=this.name=a;this.stack=c.stack;this.message=c.message}c.prototype=Error.prototype;d.prototype=new c;return d}function p(a,c){if(isNaN(a=parseInt(a,10)))throw new u;return a*c}function e(a,c){if(!(this instanceof e))return new e(a,c);k(a,c);a=e.REDUCE?q(b.d,b.n):1;this.s=b.s;this.n=b.n/a;this.d=b.d/a}var b={s:1,n:0,d:1},y=e.DivisionByZero=v("DivisionByZero"),u=e.InvalidParameter=v("InvalidParameter");e.REDUCE=1;e.prototype={s:1,n:0,d:1,abs:function(){return new e(this.n,
|
||||
this.d)},neg:function(){return new e(-this.s*this.n,this.d)},add:function(a,c){k(a,c);return new e(this.s*this.n*b.d+b.s*this.d*b.n,this.d*b.d)},sub:function(a,c){k(a,c);return new e(this.s*this.n*b.d-b.s*this.d*b.n,this.d*b.d)},mul:function(a,c){k(a,c);return new e(this.s*b.s*this.n*b.n,this.d*b.d)},div:function(a,c){k(a,c);return new e(this.s*b.s*this.n*b.d,this.d*b.n)},clone:function(){return new e(this)},mod:function(a,c){if(isNaN(this.n)||isNaN(this.d))return new e(NaN);if(void 0===a)return new e(this.s*
|
||||
this.n%this.d,1);k(a,c);0===b.n&&0===this.d&&e(0,0);return new e(this.s*b.d*this.n%(b.n*this.d),b.d*this.d)},gcd:function(a,c){k(a,c);return new e(q(b.n,this.n),b.d*this.d/q(b.d,this.d))},lcm:function(a,c){k(a,c);return 0===b.n&&0===this.n?new e:new e(b.n*this.n/q(b.n,this.n),q(b.d,this.d))},ceil:function(a){a=Math.pow(10,a||0);return isNaN(this.n)||isNaN(this.d)?new e(NaN):new e(Math.ceil(a*this.s*this.n/this.d),a)},floor:function(a){a=Math.pow(10,a||0);return isNaN(this.n)||isNaN(this.d)?new e(NaN):
|
||||
new e(Math.floor(a*this.s*this.n/this.d),a)},round:function(a){a=Math.pow(10,a||0);return isNaN(this.n)||isNaN(this.d)?new e(NaN):new e(Math.round(a*this.s*this.n/this.d),a)},inverse:function(){return new e(this.s*this.d,this.n)},pow:function(a){return 0>a?new e(Math.pow(this.s*this.d,-a),Math.pow(this.n,-a)):new e(Math.pow(this.s*this.n,a),Math.pow(this.d,a))},equals:function(a,c){k(a,c);return this.s*this.n*b.d===b.s*b.n*this.d},compare:function(a,c){k(a,c);var d=this.s*this.n*b.d-b.s*b.n*this.d;
|
||||
return(0<d)-(0>d)},divisible:function(a,c){k(a,c);return!(!(b.n*this.d)||this.n*b.d%(b.n*this.d))},valueOf:function(){return this.s*this.n/this.d},toFraction:function(a){var c,d="",e=this.n,b=this.d;0>this.s&&(d+="-");1===b?d+=e:(a&&0<(c=Math.floor(e/b))&&(d=d+c+" ",e%=b),d=d+e+"/",d+=b);return d},toLatex:function(a){var c,d="",e=this.n,b=this.d;0>this.s&&(d+="-");1===b?d+=e:(a&&0<(c=Math.floor(e/b))&&(d+=c,e%=b),d=d+"\\frac{"+e+"}{"+b,d+="}");return d},toContinued:function(){var a,c=this.n,d=this.d,
|
||||
e=[];do e.push(Math.floor(c/d)),a=c%d,c=d,d=a;while(1!==c);return e},toString:function(){var a,c=this.n,d=this.d;if(isNaN(c)||isNaN(d))return"NaN";e.REDUCE||(a=q(c,d),c/=a,d/=a);a=String(c).split("");var c=0,b=[~this.s?"":"-","",""],k="",p=x(d),m;a:{m=1;var n;n=p;for(var h=10,r=1;0<n;h=h*h%d,n>>=1)n&1&&(r=r*h%d);n=r;for(h=0;300>h;h++){if(m===n){m=h;break a}m=10*m%d;n=10*n%d}m=0}n=-1;for(var h=1,r=15+p+m+a.length,f=0;f<r;f++,c*=10){f<a.length?c+=Number(a[f]):(h=2,n++);if(0<p)if(n===m)b[h]+=k+"(",k=
|
||||
"";else if(n===p+m){b[h]+=k+")";break}c>=d?(b[h]+=k+(c/d|0),k="",c%=d):1<h?k+="0":b[h]&&(b[h]+="0")}b[0]+=b[1]||"0";return b[2]?b[0]+"."+b[2]:b[0]}};"function"===typeof define&&define.amd?define([],function(){return e}):"object"===typeof exports?module.exports=e:w.Fraction=e})(this);
|
||||
68
nodered/rootfs/data/node_modules/fraction.js/package.json
generated
vendored
Normal file
68
nodered/rootfs/data/node_modules/fraction.js/package.json
generated
vendored
Normal file
@@ -0,0 +1,68 @@
|
||||
{
|
||||
"_from": "fraction.js@4.0.0",
|
||||
"_id": "fraction.js@4.0.0",
|
||||
"_inBundle": false,
|
||||
"_integrity": "sha1-c5dOL4tR73CVNtYkzJB4Liu2EnQ=",
|
||||
"_location": "/fraction.js",
|
||||
"_phantomChildren": {},
|
||||
"_requested": {
|
||||
"type": "version",
|
||||
"registry": true,
|
||||
"raw": "fraction.js@4.0.0",
|
||||
"name": "fraction.js",
|
||||
"escapedName": "fraction.js",
|
||||
"rawSpec": "4.0.0",
|
||||
"saveSpec": null,
|
||||
"fetchSpec": "4.0.0"
|
||||
},
|
||||
"_requiredBy": [
|
||||
"/mathjs"
|
||||
],
|
||||
"_resolved": "https://registry.npmjs.org/fraction.js/-/fraction.js-4.0.0.tgz",
|
||||
"_shasum": "73974e2f8b51ef709536d624cc90782e2bb61274",
|
||||
"_spec": "fraction.js@4.0.0",
|
||||
"_where": "/data/node_modules/mathjs",
|
||||
"author": {
|
||||
"name": "Robert Eisele",
|
||||
"email": "robert@xarg.org",
|
||||
"url": "http://www.xarg.org/"
|
||||
},
|
||||
"bugs": {
|
||||
"url": "https://github.com/infusion/Fraction.js/issues"
|
||||
},
|
||||
"bundleDependencies": false,
|
||||
"deprecated": false,
|
||||
"description": "A rational number library",
|
||||
"devDependencies": {
|
||||
"mocha": "*"
|
||||
},
|
||||
"directories": {
|
||||
"example": "examples"
|
||||
},
|
||||
"engines": {
|
||||
"node": "*"
|
||||
},
|
||||
"homepage": "http://www.xarg.org/2014/03/rational-numbers-in-javascript/",
|
||||
"keywords": [
|
||||
"math",
|
||||
"fraction",
|
||||
"rational",
|
||||
"rationals",
|
||||
"number",
|
||||
"parser",
|
||||
"rational numbers"
|
||||
],
|
||||
"license": "MIT OR GPL-2.0",
|
||||
"main": "fraction",
|
||||
"name": "fraction.js",
|
||||
"private": false,
|
||||
"repository": {
|
||||
"type": "git",
|
||||
"url": "git://github.com/infusion/Fraction.js.git"
|
||||
},
|
||||
"scripts": {
|
||||
"test": "mocha tests/*.js"
|
||||
},
|
||||
"title": "fraction.js",
|
||||
"version": "4.0.0"
|
||||
}
|
||||
1448
nodered/rootfs/data/node_modules/fraction.js/tests/fraction.test.js
generated
vendored
Normal file
1448
nodered/rootfs/data/node_modules/fraction.js/tests/fraction.test.js
generated
vendored
Normal file
@@ -0,0 +1,1448 @@
|
||||
var assert = require('assert');
|
||||
|
||||
var Fraction = require('../fraction');
|
||||
|
||||
var tests = [{
|
||||
set: "foo",
|
||||
expectError: Fraction.InvalidParameter
|
||||
}, {
|
||||
set: " 123",
|
||||
expectError: Fraction.InvalidParameter
|
||||
}, {
|
||||
set: 0,
|
||||
expect: 0
|
||||
}, {
|
||||
set: .2,
|
||||
expect: "0.2"
|
||||
}, {
|
||||
set: .333,
|
||||
expect: "0.333"
|
||||
}, {
|
||||
set: 1.1,
|
||||
expect: "1.1"
|
||||
}, {
|
||||
set: 1.2,
|
||||
expect: "1.2"
|
||||
}, {
|
||||
set: 1.3,
|
||||
expect: "1.3"
|
||||
}, {
|
||||
set: 1.4,
|
||||
expect: "1.4"
|
||||
}, {
|
||||
set: 1.5,
|
||||
expect: "1.5"
|
||||
}, {
|
||||
set: 2.555,
|
||||
expect: "2.555"
|
||||
}, {
|
||||
set: " - ",
|
||||
expectError: Fraction.InvalidParameter
|
||||
}, {
|
||||
set: ".5",
|
||||
expect: "0.5"
|
||||
}, {
|
||||
set: "-.5",
|
||||
expect: "-0.5"
|
||||
}, {
|
||||
set: "123",
|
||||
expect: "123"
|
||||
}, {
|
||||
set: "-123",
|
||||
expect: "-123"
|
||||
}, {
|
||||
set: "123.4",
|
||||
expect: "123.4"
|
||||
}, {
|
||||
set: "-123.4",
|
||||
expect: "-123.4"
|
||||
}, {
|
||||
set: "123.",
|
||||
expect: "123"
|
||||
}, {
|
||||
set: "-123.",
|
||||
expect: "-123"
|
||||
}, {
|
||||
set: "123.4(56)",
|
||||
expect: "123.4(56)"
|
||||
}, {
|
||||
set: "-123.4(56)",
|
||||
expect: "-123.4(56)"
|
||||
}, {
|
||||
set: "123.(4)",
|
||||
expect: "123.(4)"
|
||||
}, {
|
||||
set: "-123.(4)",
|
||||
expect: "-123.(4)"
|
||||
}, {
|
||||
set: "0/0",
|
||||
expectError: Fraction.DivisionByZero
|
||||
}, {
|
||||
set: "9/0",
|
||||
expectError: Fraction.DivisionByZero
|
||||
}, {
|
||||
label: "0/1+0/1",
|
||||
set: "0/1",
|
||||
param: "0/1",
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "1/9+0/1",
|
||||
set: "1/9",
|
||||
param: "0/1",
|
||||
expect: "0.(1)"
|
||||
}, {
|
||||
set: "123/456",
|
||||
expect: "0.269(736842105263157894)"
|
||||
}, {
|
||||
set: "-123/456",
|
||||
expect: "-0.269(736842105263157894)"
|
||||
}, {
|
||||
set: "19 123/456",
|
||||
expect: "19.269(736842105263157894)"
|
||||
}, {
|
||||
set: "-19 123/456",
|
||||
expect: "-19.269(736842105263157894)"
|
||||
}, {
|
||||
set: "123.(22)123",
|
||||
expectError: Fraction.InvalidParameter
|
||||
}, {
|
||||
set: "+33.3(3)",
|
||||
expect: "33.(3)"
|
||||
}, {
|
||||
set: "3.'09009'",
|
||||
expect: "3.(09009)"
|
||||
}, {
|
||||
set: "123.(((",
|
||||
expectError: Fraction.InvalidParameter
|
||||
}, {
|
||||
set: "123.((",
|
||||
expectError: Fraction.InvalidParameter
|
||||
}, {
|
||||
set: "123.()",
|
||||
expectError: Fraction.InvalidParameter
|
||||
}, {
|
||||
set: null,
|
||||
expect: "0" // I would say it's just fine
|
||||
}, {
|
||||
set: [22, 7],
|
||||
expect: '3.(142857)' // We got Pi! - almost ;o
|
||||
}, {
|
||||
set: "355/113",
|
||||
expect: "3.(1415929203539823008849557522123893805309734513274336283185840707964601769911504424778761061946902654867256637168)" // Yay, a better PI
|
||||
}, {
|
||||
set: "3 1/7",
|
||||
expect: '3.(142857)'
|
||||
}, {
|
||||
set: [36, -36],
|
||||
expect: "-1"
|
||||
}, {
|
||||
set: "9/12",
|
||||
expect: "0.75"
|
||||
}, {
|
||||
set: "0.09(33)",
|
||||
expect: "0.09(3)"
|
||||
}, {
|
||||
set: 1 / 2,
|
||||
expect: "0.5"
|
||||
}, {
|
||||
set: 1 / 3,
|
||||
expect: "0.(3)"
|
||||
}, {
|
||||
set: "0.'3'",
|
||||
expect: "0.(3)"
|
||||
}, {
|
||||
set: "0.00002",
|
||||
expect: "0.00002"
|
||||
}, {
|
||||
set: 7 / 8,
|
||||
expect: "0.875"
|
||||
}, {
|
||||
set: 0.003,
|
||||
expect: "0.003"
|
||||
}, {
|
||||
set: 4,
|
||||
expect: "4"
|
||||
}, {
|
||||
set: -99,
|
||||
expect: "-99"
|
||||
}, {
|
||||
set: "-92332.1192",
|
||||
expect: "-92332.1192"
|
||||
}, {
|
||||
set: '88.92933(12111)',
|
||||
expect: "88.92933(12111)"
|
||||
}, {
|
||||
set: '-192322.823(123)',
|
||||
expect: "-192322.8(231)"
|
||||
}, {
|
||||
label: "-99.12 % 0.09(34)",
|
||||
set: '-99.12',
|
||||
fn: "mod",
|
||||
param: "0.09(34)",
|
||||
expect: "-0.07(95)"
|
||||
}, {
|
||||
label: "0.4 / 0.1",
|
||||
set: .4,
|
||||
fn: "div",
|
||||
param: ".1",
|
||||
expect: "4"
|
||||
}, {
|
||||
label: "1 / -.1",
|
||||
set: 1,
|
||||
fn: "div",
|
||||
param: "-.1",
|
||||
expect: "-10"
|
||||
}, {
|
||||
label: "1 - (-1)",
|
||||
set: 1,
|
||||
fn: "sub",
|
||||
param: "-1",
|
||||
expect: "2"
|
||||
}, {
|
||||
label: "1 + (-1)",
|
||||
set: 1,
|
||||
fn: "add",
|
||||
param: "-1",
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "-187 % 12",
|
||||
set: '-187',
|
||||
fn: "mod",
|
||||
param: "12",
|
||||
expect: "-7"
|
||||
}, {
|
||||
label: "Negate by 99 * -1",
|
||||
set: '99',
|
||||
fn: "mul",
|
||||
param: "-1",
|
||||
expect: "-99"
|
||||
}, {
|
||||
set: [20,-5],
|
||||
expect: "-4",
|
||||
fn: "toFraction",
|
||||
param: true
|
||||
}, {
|
||||
set: [-10,-7],
|
||||
expect: "1 3/7",
|
||||
fn: "toFraction",
|
||||
param: true
|
||||
}, {
|
||||
set: [21,-6],
|
||||
expect: "-3 1/2",
|
||||
fn: "toFraction",
|
||||
param: true
|
||||
}, {
|
||||
set: "10/78",
|
||||
expect: "5/39",
|
||||
fn: "toFraction",
|
||||
param: true
|
||||
}, {
|
||||
set: "0/91",
|
||||
expect: "0",
|
||||
fn: "toFraction",
|
||||
param: true
|
||||
}, {
|
||||
set: "-0/287",
|
||||
expect: "0",
|
||||
fn: "toFraction",
|
||||
param: true
|
||||
}, {
|
||||
set: "-5/20",
|
||||
expect: "-1/4",
|
||||
fn: "toFraction",
|
||||
param: true
|
||||
}, {
|
||||
set: "42/9",
|
||||
expect: "4 2/3",
|
||||
fn: "toFraction",
|
||||
param: true
|
||||
}, {
|
||||
set: "71/23",
|
||||
expect: "3 2/23",
|
||||
fn: "toFraction",
|
||||
param: true
|
||||
}, {
|
||||
set: "6/3",
|
||||
expect: "2",
|
||||
fn: "toFraction",
|
||||
param: true
|
||||
}, {
|
||||
set: "28/4",
|
||||
expect: "7",
|
||||
fn: "toFraction",
|
||||
param: true
|
||||
}, {
|
||||
set: "105/35",
|
||||
expect: "3",
|
||||
fn: "toFraction",
|
||||
param: true
|
||||
}, {
|
||||
set: "4/6",
|
||||
expect: "2/3",
|
||||
fn: "toFraction",
|
||||
param: true
|
||||
}, {
|
||||
label: "99.(9) + 66",
|
||||
set: '99.(999999)',
|
||||
fn: "add",
|
||||
param: "66",
|
||||
expect: "166"
|
||||
}, {
|
||||
label: "-82.124 / 66.(3)",
|
||||
set: '-82.124',
|
||||
fn: "div",
|
||||
param: "66.(3)",
|
||||
expect: "-1.238(050251256281407035175879396984924623115577889447236180904522613065326633165829145728643216080402010)"
|
||||
}, {
|
||||
label: "100 - .91",
|
||||
set: '100',
|
||||
fn: "sub",
|
||||
param: ".91",
|
||||
expect: "99.09"
|
||||
}, {
|
||||
label: "381.(33411) % 11.119(356)",
|
||||
set: '381.(33411)',
|
||||
fn: "mod",
|
||||
param: "11.119(356)",
|
||||
expect: "3.275(997225017295217)"
|
||||
}, {
|
||||
label: "13/26 mod 1",
|
||||
set: '13/26',
|
||||
fn: "mod",
|
||||
param: "1.000",
|
||||
expect: "0.5"
|
||||
}, {
|
||||
label: "381.(33411) % 1", // Extract fraction part of a number
|
||||
set: '381.(33411)',
|
||||
fn: "mod",
|
||||
param: "1",
|
||||
expect: "0.(33411)"
|
||||
}, {
|
||||
label: "-222/3",
|
||||
set: {
|
||||
n: 3,
|
||||
d: 222,
|
||||
s: -1
|
||||
},
|
||||
fn: "inverse",
|
||||
param: null,
|
||||
expect: "-74"
|
||||
}, {
|
||||
label: "inverse",
|
||||
set: 1 / 2,
|
||||
fn: "inverse",
|
||||
param: null,
|
||||
expect: "2"
|
||||
}, {
|
||||
label: "abs(-222/3)",
|
||||
set: {
|
||||
n: -222,
|
||||
d: 3
|
||||
},
|
||||
fn: "abs",
|
||||
param: null,
|
||||
expect: "74"
|
||||
}, {
|
||||
label: "9 % -2",
|
||||
set: 9,
|
||||
fn: "mod",
|
||||
param: "-2",
|
||||
expect: "1"
|
||||
}, {
|
||||
label: "-9 % 2",
|
||||
set: '-9',
|
||||
fn: "mod",
|
||||
param: "-2",
|
||||
expect: "-1"
|
||||
}, {
|
||||
label: "1 / 195312500",
|
||||
set: '1',
|
||||
fn: "div",
|
||||
param: "195312500",
|
||||
expect: "0.00000000512"
|
||||
}, {
|
||||
label: "10 / 0",
|
||||
set: 10,
|
||||
fn: "div",
|
||||
param: 0,
|
||||
expectError: Fraction.DivisionByZero
|
||||
}, {
|
||||
label: "-3 / 4",
|
||||
set: [-3, 4],
|
||||
fn: "inverse",
|
||||
param: null,
|
||||
expect: "-1.(3)"
|
||||
}, {
|
||||
label: "-19.6",
|
||||
set: [-98, 5],
|
||||
fn: "equals",
|
||||
param: '-19.6',
|
||||
expect: "true" // actually, we get a real bool but we call toString() in the test below
|
||||
}, {
|
||||
label: "-19.6",
|
||||
set: [98, -5],
|
||||
fn: "equals",
|
||||
param: '-19.6',
|
||||
expect: "true"
|
||||
}, {
|
||||
label: "99/88",
|
||||
set: [99, 88],
|
||||
fn: "equals",
|
||||
param: [88, 99],
|
||||
expect: "false"
|
||||
}, {
|
||||
label: "99/88",
|
||||
set: [99, -88],
|
||||
fn: "equals",
|
||||
param: [9, 8],
|
||||
expect: "false"
|
||||
}, {
|
||||
label: "12.5",
|
||||
set: 12.5,
|
||||
fn: "add",
|
||||
param: 0,
|
||||
expect: "12.5"
|
||||
}, {
|
||||
label: "0/1 -> 1/0",
|
||||
set: 0,
|
||||
fn: "inverse",
|
||||
param: null,
|
||||
expectError: Fraction.DivisionByZero
|
||||
}, {
|
||||
label: "abs(-100.25)",
|
||||
set: -100.25,
|
||||
fn: "abs",
|
||||
param: null,
|
||||
expect: "100.25"
|
||||
}, {
|
||||
label: "0.022222222",
|
||||
set: '0.0(22222222)',
|
||||
fn: "abs",
|
||||
param: null,
|
||||
expect: "0.0(2)"
|
||||
}, {
|
||||
label: "1.5 | 100.5",
|
||||
set: 100.5,
|
||||
fn: "divisible",
|
||||
param: '1.5',
|
||||
expect: "true"
|
||||
}, {
|
||||
label: "1.5 | 100.6",
|
||||
set: 100.6,
|
||||
fn: "divisible",
|
||||
param: 1.6,
|
||||
expect: "false"
|
||||
}, {
|
||||
label: "(1/6) | (2/3)", // == 4
|
||||
set: [2, 3],
|
||||
fn: "divisible",
|
||||
param: [1, 6],
|
||||
expect: "true"
|
||||
}, {
|
||||
label: "(1/6) | (2/5)",
|
||||
set: [2, 5],
|
||||
fn: "divisible",
|
||||
param: [1, 6],
|
||||
expect: "false"
|
||||
}, {
|
||||
label: "0 | (2/5)",
|
||||
set: [2, 5],
|
||||
fn: "divisible",
|
||||
param: 0,
|
||||
expect: "false"
|
||||
}, {
|
||||
label: "6 | 0",
|
||||
set: 0,
|
||||
fn: "divisible",
|
||||
param: 6,
|
||||
expect: "true"
|
||||
}, {
|
||||
label: "fmod(4.55, 0.05)", // http://phpjs.org/functions/fmod/ (comment section)
|
||||
set: 4.55,
|
||||
fn: "mod",
|
||||
param: 0.05,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "fmod(99.12, 0.4)",
|
||||
set: 99.12,
|
||||
fn: "mod",
|
||||
param: "0.4",
|
||||
expect: "0.32"
|
||||
}, {
|
||||
label: "fmod(fmod(1.0,0.1))", // http://stackoverflow.com/questions/4218961/why-fmod1-0-0-1-1
|
||||
set: 1.0,
|
||||
fn: "mod",
|
||||
param: 0.1,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "bignum",
|
||||
set: [5385020324, 1673196525],
|
||||
fn: "add",
|
||||
param: 0,
|
||||
expect: "3.(218402765927331817761216065160068390651241640607638723132060054929889362518249313241909822876305579226564554334106090735515960983722459021960973771446244188201382978607369507894477607763379738073505740755707103802405996510182807127214180653405313521076073236525518124656635896372065439234641011461579505730804694326029633608042545988433725679653799185364671971213901487154953301137175144443955858681932177692037700114157241630656625945359287666462252543824760812242303694719901477203940523364402755976319039988443676692431571957753139608032594975655952907265331548545978482712901881026796897035152520412986155347172980771042421331827712228842932840779118878459301127224131666183086293464540873344211613157635502500221843336663635492549209065563891247024912390372075390247418784233967973367623387814530633214170702392535748303684768888699431168134896765937282830538988837548536027469935129108638329260216459031911986549219016576669019797300858008894083735919783840096129771725410438561602917505461589456743582467098418101244861239476934725285781955589466694595244871190489712498058170423226285388083745870796617868902160193047257255091418505067717613147684489722449070948195998673855720564564285118868508288349451359277715449474771052372344605485001231400477597812366960300733352288070285108917495510576678970810078630781282551372738477328597129377853566842663625541536431292791502779388093696883574390641290627829865950743592418111195874017249707113753418774282955195594850999346893814520682201392929620147280666866075400198431562006740361835260206508019134213776830548939850326308799)"
|
||||
}, {
|
||||
label: "ceil(0.4)",
|
||||
set: 0.4,
|
||||
fn: "ceil",
|
||||
param: null,
|
||||
expect: "1"
|
||||
}, {
|
||||
label: "ceil(0.5)",
|
||||
set: 0.5,
|
||||
fn: "ceil",
|
||||
param: null,
|
||||
expect: "1"
|
||||
}, {
|
||||
label: "ceil(0.23, 2)",
|
||||
set: 0.23,
|
||||
fn: "ceil",
|
||||
param: 2,
|
||||
expect: "0.23"
|
||||
}, {
|
||||
label: "ceil(0.6)",
|
||||
set: 0.6,
|
||||
fn: "ceil",
|
||||
param: null,
|
||||
expect: "1"
|
||||
}, {
|
||||
label: "ceil(-0.4)",
|
||||
set: -0.4,
|
||||
fn: "ceil",
|
||||
param: null,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "ceil(-0.5)",
|
||||
set: -0.5,
|
||||
fn: "ceil",
|
||||
param: null,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "ceil(-0.6)",
|
||||
set: -0.6,
|
||||
fn: "ceil",
|
||||
param: null,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "floor(0.4)",
|
||||
set: 0.4,
|
||||
fn: "floor",
|
||||
param: null,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "floor(0.4, 1)",
|
||||
set: 0.4,
|
||||
fn: "floor",
|
||||
param: 1,
|
||||
expect: "0.4"
|
||||
}, {
|
||||
label: "floor(0.5)",
|
||||
set: 0.5,
|
||||
fn: "floor",
|
||||
param: null,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "floor(0.6)",
|
||||
set: 0.6,
|
||||
fn: "floor",
|
||||
param: null,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "floor(-0.4)",
|
||||
set: -0.4,
|
||||
fn: "floor",
|
||||
param: null,
|
||||
expect: "-1"
|
||||
}, {
|
||||
label: "floor(-0.5)",
|
||||
set: -0.5,
|
||||
fn: "floor",
|
||||
param: null,
|
||||
expect: "-1"
|
||||
}, {
|
||||
label: "floor(-0.6)",
|
||||
set: -0.6,
|
||||
fn: "floor",
|
||||
param: null,
|
||||
expect: "-1"
|
||||
}, {
|
||||
label: "round(0.4)",
|
||||
set: 0.4,
|
||||
fn: "round",
|
||||
param: null,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "round(0.5)",
|
||||
set: 0.5,
|
||||
fn: "round",
|
||||
param: null,
|
||||
expect: "1"
|
||||
}, {
|
||||
label: "round(0.5, 1)",
|
||||
set: 0.5,
|
||||
fn: "round",
|
||||
param: 1,
|
||||
expect: "0.5"
|
||||
}, {
|
||||
label: "round(0.6)",
|
||||
set: 0.6,
|
||||
fn: "round",
|
||||
param: null,
|
||||
expect: "1"
|
||||
}, {
|
||||
label: "round(-0.4)",
|
||||
set: -0.4,
|
||||
fn: "round",
|
||||
param: null,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "round(-0.5)",
|
||||
set: -0.5,
|
||||
fn: "round",
|
||||
param: null,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "round(-0.6)",
|
||||
set: -0.6,
|
||||
fn: "round",
|
||||
param: null,
|
||||
expect: "-1"
|
||||
}, {
|
||||
label: "17402216385200408/5539306332998545",
|
||||
set: [17402216385200408, 5539306332998545],
|
||||
fn: "add",
|
||||
param: 0,
|
||||
expect: "3.14158765358987"
|
||||
}, {
|
||||
label: "99+1",
|
||||
set: [99, 1],
|
||||
fn: "add",
|
||||
param: 1,
|
||||
expect: "100"
|
||||
}, {
|
||||
label: "gcd(5/8, 3/7)",
|
||||
set: [5, 8],
|
||||
fn: "gcd",
|
||||
param: [3, 7],
|
||||
expect: "0.017(857142)" // == 1/56
|
||||
}, {
|
||||
label: "gcd(52, 39)",
|
||||
set: 52,
|
||||
fn: "gcd",
|
||||
param: 39,
|
||||
expect: "13"
|
||||
}, {
|
||||
label: "gcd(51357, 3819)",
|
||||
set: 51357,
|
||||
fn: "gcd",
|
||||
param: 3819,
|
||||
expect: "57"
|
||||
}, {
|
||||
label: "gcd(841, 299)",
|
||||
set: 841,
|
||||
fn: "gcd",
|
||||
param: 299,
|
||||
expect: "1"
|
||||
}, {
|
||||
label: "gcd(2/3, 7/5)",
|
||||
set: [2, 3],
|
||||
fn: "gcd",
|
||||
param: [7, 5],
|
||||
expect: "0.0(6)" // == 1/15
|
||||
}, {
|
||||
label: "lcm(-3, 3)",
|
||||
set: -3,
|
||||
fn: "lcm",
|
||||
param: 3,
|
||||
expect: "3"
|
||||
}, {
|
||||
label: "lcm(3,-3)",
|
||||
set: 3,
|
||||
fn: "lcm",
|
||||
param: -3,
|
||||
expect: "3"
|
||||
}, {
|
||||
label: "lcm(0,3)",
|
||||
set: 0,
|
||||
fn: "lcm",
|
||||
param: 3,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "lcm(3, 0)",
|
||||
set: 3,
|
||||
fn: "lcm",
|
||||
param: 0,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "lcm(0, 0)",
|
||||
set: 0,
|
||||
fn: "lcm",
|
||||
param: 0,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "lcm(200, 333)",
|
||||
set: 200,
|
||||
fn: "lcm",
|
||||
param: 333, expect: "66600"},
|
||||
{
|
||||
label: "1 + -1",
|
||||
set: 1,
|
||||
fn: "add",
|
||||
param: -1,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "3/10+3/14",
|
||||
set: "3/10",
|
||||
fn: "add",
|
||||
param: "3/14",
|
||||
expect: "0.5(142857)"
|
||||
}, {
|
||||
label: "3/10-3/14",
|
||||
set: "3/10",
|
||||
fn: "sub",
|
||||
param: "3/14",
|
||||
expect: "0.0(857142)"
|
||||
}, {
|
||||
label: "3/10*3/14",
|
||||
set: "3/10",
|
||||
fn: "mul",
|
||||
param: "3/14",
|
||||
expect: "0.06(428571)"
|
||||
}, {
|
||||
label: "3/10 / 3/14",
|
||||
set: "3/10",
|
||||
fn: "div",
|
||||
param: "3/14",
|
||||
expect: "1.4"
|
||||
}, {
|
||||
label: "1-2",
|
||||
set: "1",
|
||||
fn: "sub",
|
||||
param: "2",
|
||||
expect: "-1"
|
||||
}, {
|
||||
label: "1--1",
|
||||
set: "1",
|
||||
fn: "sub",
|
||||
param: "-1",
|
||||
expect: "2"
|
||||
}, {
|
||||
label: "0/1*1/3",
|
||||
set: "0/1",
|
||||
fn: "mul",
|
||||
param: "1/3",
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "3/10 * 8/12",
|
||||
set: "3/10",
|
||||
fn: "mul",
|
||||
param: "8/12",
|
||||
expect: "0.2"
|
||||
}, {
|
||||
label: ".5+5",
|
||||
set: ".5",
|
||||
fn: "add",
|
||||
param: 5, expect: "5.5"},
|
||||
{
|
||||
label: "10/12-5/60",
|
||||
set: "10/12",
|
||||
fn: "sub",
|
||||
param: "5/60",
|
||||
expect: "0.75"
|
||||
}, {
|
||||
label: "10/15 / 3/4",
|
||||
set: "10/15",
|
||||
fn: "div",
|
||||
param: "3/4",
|
||||
expect: "0.(8)"
|
||||
}, {
|
||||
label: "1/4 + 3/8",
|
||||
set: "1/4",
|
||||
fn: "add",
|
||||
param: "3/8",
|
||||
expect: "0.625"
|
||||
}, {
|
||||
label: "2-1/3",
|
||||
set: "2",
|
||||
fn: "sub",
|
||||
param: "1/3",
|
||||
expect: "1.(6)"
|
||||
}, {
|
||||
label: "5*6",
|
||||
set: "5",
|
||||
fn: "mul",
|
||||
param: 6,
|
||||
expect: "30"
|
||||
}, {
|
||||
label: "1/2-1/5",
|
||||
set: "1/2",
|
||||
fn: "sub",
|
||||
param: "1/5",
|
||||
expect: "0.3"
|
||||
}, {
|
||||
label: "1/2-5",
|
||||
set: "1/2",
|
||||
fn: "add",
|
||||
param: -5,
|
||||
expect: "-4.5"
|
||||
}, {
|
||||
label: "1*-1",
|
||||
set: "1",
|
||||
fn: "mul",
|
||||
param: -1,
|
||||
expect: "-1"
|
||||
}, {
|
||||
label: "5/10",
|
||||
set: 5.0,
|
||||
fn: "div",
|
||||
param: 10,
|
||||
expect: "0.5"
|
||||
}, {
|
||||
label: "1/-1",
|
||||
set: "1",
|
||||
fn: "div",
|
||||
param: -1,
|
||||
expect: "-1"
|
||||
}, {
|
||||
label: "4/5 + 13/2",
|
||||
set: "4/5",
|
||||
fn: "add",
|
||||
param: "13/2",
|
||||
expect: "7.3"
|
||||
}, {
|
||||
label: "4/5 + 61/2",
|
||||
set: "4/5",
|
||||
fn: "add",
|
||||
param: "61/2",
|
||||
expect: "31.3"
|
||||
}, {
|
||||
label: "0.8 + 6.5",
|
||||
set: "0.8",
|
||||
fn: "add",
|
||||
param: "6.5",
|
||||
expect: "7.3"
|
||||
}, {
|
||||
label: "2/7 inverse",
|
||||
set: "2/7",
|
||||
fn: "inverse",
|
||||
param: null,
|
||||
expect: "3.5"
|
||||
}, {
|
||||
label: "neg 1/3",
|
||||
set: "1/3",
|
||||
fn: "neg",
|
||||
param: null,
|
||||
expect: "-0.(3)"
|
||||
}, {
|
||||
label: "1/2+1/3",
|
||||
set: "1/2",
|
||||
fn: "add",
|
||||
param: "1/3",
|
||||
expect: "0.8(3)"
|
||||
}, {
|
||||
label: "1/2+3",
|
||||
set: ".5",
|
||||
fn: "add",
|
||||
param: 3,
|
||||
expect: "3.5"
|
||||
}, {
|
||||
label: "1/2+3.14",
|
||||
set: "1/2",
|
||||
fn: "add",
|
||||
param: "3.14",
|
||||
expect: "3.64"
|
||||
}, {
|
||||
label: "3.5 < 4.1",
|
||||
set: 3.5,
|
||||
fn: "compare",
|
||||
param: 4.1,
|
||||
expect: "-1"
|
||||
}, {
|
||||
label: "3.5 > 4.1",
|
||||
set: 4.1,
|
||||
fn: "compare",
|
||||
param: 3.1,
|
||||
expect: "1"
|
||||
}, {
|
||||
label: "-3.5 > -4.1",
|
||||
set: -3.5,
|
||||
fn: "compare",
|
||||
param: -4.1,
|
||||
expect: "1"
|
||||
}, {
|
||||
label: "-3.5 > -4.1",
|
||||
set: -4.1,
|
||||
fn: "compare",
|
||||
param: -3.5,
|
||||
expect: "-1"
|
||||
}, {
|
||||
label: "4.3 == 4.3",
|
||||
set: 4.3,
|
||||
fn: "compare",
|
||||
param: 4.3,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "-4.3 == -4.3",
|
||||
set: -4.3,
|
||||
fn: "compare",
|
||||
param: -4.3,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "-4.3 < 4.3",
|
||||
set: -4.3,
|
||||
fn: "compare",
|
||||
param: 4.3,
|
||||
expect: "-1"
|
||||
}, {
|
||||
label: "4.3 == -4.3",
|
||||
set: 4.3,
|
||||
fn: "compare",
|
||||
param: -4.3,
|
||||
expect: "1"
|
||||
}, {
|
||||
label: "-0.5^-3",
|
||||
set: -0.5,
|
||||
fn: "pow",
|
||||
param: -3,
|
||||
expect: "-8"
|
||||
}, {
|
||||
label: "",
|
||||
set: -3,
|
||||
fn: "pow",
|
||||
param: -3,
|
||||
expect: "-0.(037)"
|
||||
}, {
|
||||
label: "-3",
|
||||
set: -3,
|
||||
fn: "pow",
|
||||
param: 2,
|
||||
expect: "9"
|
||||
}, {
|
||||
label: "-3",
|
||||
set: -3,
|
||||
fn: "pow",
|
||||
param: 3,
|
||||
expect: "-27"
|
||||
}, {
|
||||
label: "0^0",
|
||||
set: 0,
|
||||
fn: "pow",
|
||||
param: 0,
|
||||
expect: "1"
|
||||
}, {
|
||||
label: "2/3^7",
|
||||
set: [2, 3],
|
||||
fn: "pow",
|
||||
param: 7,
|
||||
expect: "0.(058527663465935070873342478280749885688157293095564700502972107910379515317786922725194330132601737540009144947416552354823959762231367169638774577046181984453589391860996799268404206675811614083219021490626428898033836305441243712848651120256)"
|
||||
}, {
|
||||
label: "-0.6^4",
|
||||
set: -0.6,
|
||||
fn: "pow",
|
||||
param: 4,
|
||||
expect: "0.1296"
|
||||
}, {
|
||||
label: "8128371:12394 - 8128371/12394",
|
||||
set: "8128371:12394",
|
||||
fn: "sub",
|
||||
param: "8128371/12394",
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "3/4 + 1/4",
|
||||
set: "3/4",
|
||||
fn: "add",
|
||||
param: "1/4",
|
||||
expect: "1"
|
||||
}, {
|
||||
label: "1/10 + 2/10",
|
||||
set: "1/10",
|
||||
fn: "add",
|
||||
param: "2/10",
|
||||
expect: "0.3"
|
||||
}, {
|
||||
label: "5/10 + 2/10",
|
||||
set: "5/10",
|
||||
fn: "add",
|
||||
param: "2/10",
|
||||
expect: "0.7"
|
||||
}, {
|
||||
label: "18/10 + 2/10",
|
||||
set: "18/10",
|
||||
fn: "add",
|
||||
param: "2/10",
|
||||
expect: "2"
|
||||
}, {
|
||||
label: "1/3 + 1/6",
|
||||
set: "1/3",
|
||||
fn: "add",
|
||||
param: "1/6",
|
||||
expect: "0.5"
|
||||
}, {
|
||||
label: "1/3 + 2/6",
|
||||
set: "1/3",
|
||||
fn: "add",
|
||||
param: "2/6",
|
||||
expect: "0.(6)"
|
||||
}, {
|
||||
label: "3/4 / 1/4",
|
||||
set: "3/4",
|
||||
fn: "div",
|
||||
param: "1/4",
|
||||
expect: "3"
|
||||
}, {
|
||||
label: "1/10 / 2/10",
|
||||
set: "1/10",
|
||||
fn: "div",
|
||||
param: "2/10",
|
||||
expect: "0.5"
|
||||
}, {
|
||||
label: "5/10 / 2/10",
|
||||
set: "5/10",
|
||||
fn: "div",
|
||||
param: "2/10",
|
||||
expect: "2.5"
|
||||
}, {
|
||||
label: "18/10 / 2/10",
|
||||
set: "18/10",
|
||||
fn: "div",
|
||||
param: "2/10",
|
||||
expect: "9"
|
||||
}, {
|
||||
label: "1/3 / 1/6",
|
||||
set: "1/3",
|
||||
fn: "div",
|
||||
param: "1/6",
|
||||
expect: "2"
|
||||
}, {
|
||||
label: "1/3 / 2/6",
|
||||
set: "1/3",
|
||||
fn: "div",
|
||||
param: "2/6",
|
||||
expect: "1"
|
||||
}, {
|
||||
label: "3/4 * 1/4",
|
||||
set: "3/4",
|
||||
fn: "mul",
|
||||
param: "1/4",
|
||||
expect: "0.1875"
|
||||
}, {
|
||||
label: "1/10 * 2/10",
|
||||
set: "1/10",
|
||||
fn: "mul",
|
||||
param: "2/10",
|
||||
expect: "0.02"
|
||||
}, {
|
||||
label: "5/10 * 2/10",
|
||||
set: "5/10",
|
||||
fn: "mul",
|
||||
param: "2/10",
|
||||
expect: "0.1"
|
||||
}, {
|
||||
label: "18/10 * 2/10",
|
||||
set: "18/10",
|
||||
fn: "mul",
|
||||
param: "2/10",
|
||||
expect: "0.36"
|
||||
}, {
|
||||
label: "1/3 * 1/6",
|
||||
set: "1/3",
|
||||
fn: "mul",
|
||||
param: "1/6",
|
||||
expect: "0.0(5)"
|
||||
}, {
|
||||
label: "1/3 * 2/6",
|
||||
set: "1/3",
|
||||
fn: "mul",
|
||||
param: "2/6",
|
||||
expect: "0.(1)"
|
||||
}, {
|
||||
label: "5/4 - 1/4",
|
||||
set: "5/4",
|
||||
fn: "sub",
|
||||
param: "1/4",
|
||||
expect: "1"
|
||||
}, {
|
||||
label: "5/10 - 2/10",
|
||||
set: "5/10",
|
||||
fn: "sub",
|
||||
param: "2/10",
|
||||
expect: "0.3"
|
||||
}, {
|
||||
label: "9/10 - 2/10",
|
||||
set: "9/10",
|
||||
fn: "sub",
|
||||
param: "2/10",
|
||||
expect: "0.7"
|
||||
}, {
|
||||
label: "22/10 - 2/10",
|
||||
set: "22/10",
|
||||
fn: "sub",
|
||||
param: "2/10",
|
||||
expect: "2"
|
||||
}, {
|
||||
label: "2/3 - 1/6",
|
||||
set: "2/3",
|
||||
fn: "sub",
|
||||
param: "1/6",
|
||||
expect: "0.5"
|
||||
}, {
|
||||
label: "3/3 - 2/6",
|
||||
set: "3/3",
|
||||
fn: "sub",
|
||||
param: "2/6",
|
||||
expect: "0.(6)"
|
||||
}, {
|
||||
label: "0.006999999999999999",
|
||||
set: 0.006999999999999999,
|
||||
fn: "add",
|
||||
param: 0,
|
||||
expect: "0.007"
|
||||
}, {
|
||||
label: "1/7 - 1",
|
||||
set: 1 / 7,
|
||||
fn: "add",
|
||||
param: -1,
|
||||
expect: "-0.(857142)"
|
||||
}, {
|
||||
label: "0.0065 + 0.0005",
|
||||
set: 0.0065,
|
||||
fn: "add",
|
||||
param: 0.0005,
|
||||
expect: "0.007"
|
||||
}, {
|
||||
label: "6.5/.5",
|
||||
set: 6.5,
|
||||
fn: "div",
|
||||
param: .5,
|
||||
expect: "13"
|
||||
}, {
|
||||
label: "0.999999999999999999999999999",
|
||||
set: 0.999999999999999999999999999,
|
||||
fn: "sub",
|
||||
param: 1,
|
||||
expect: "0"
|
||||
}, {
|
||||
label: "0.5833333333333334",
|
||||
set: 0.5833333333333334,
|
||||
fn: "add",
|
||||
param: 0,
|
||||
expect: "0.58(3)"
|
||||
}, {
|
||||
label: "1.75/3",
|
||||
set: 1.75 / 3,
|
||||
fn: "add",
|
||||
param: 0,
|
||||
expect: "0.58(3)"
|
||||
}, {
|
||||
label: "3.3333333333333",
|
||||
set: 3.3333333333333,
|
||||
fn: "add",
|
||||
param: 0,
|
||||
expect: "3.(3)"
|
||||
}, {
|
||||
label: "4.285714285714285714285714",
|
||||
set: 4.285714285714285714285714,
|
||||
fn: "add",
|
||||
param: 0,
|
||||
expect: "4.(285714)"
|
||||
}, {
|
||||
label: "-4",
|
||||
set: -4,
|
||||
fn: "neg",
|
||||
param: 0,
|
||||
expect: "4"
|
||||
}, {
|
||||
label: "4",
|
||||
set: 4,
|
||||
fn: "neg",
|
||||
param: 0,
|
||||
expect: "-4"
|
||||
}, {
|
||||
label: "0",
|
||||
set: 0,
|
||||
fn: "neg",
|
||||
param: 0,
|
||||
expect: "0"
|
||||
}
|
||||
];
|
||||
|
||||
describe('Fraction', function() {
|
||||
for (var i = 0; i < tests.length; i++) {
|
||||
|
||||
(function(i) {
|
||||
var action;
|
||||
|
||||
if (tests[i].fn) {
|
||||
action = function() {
|
||||
return new Fraction(tests[i].set)[tests[i].fn](tests[i].param).toString();
|
||||
};
|
||||
} else {
|
||||
action = function() {
|
||||
return new Fraction(tests[i].set).toString();
|
||||
};
|
||||
}
|
||||
|
||||
it(String(tests[i].label || tests[i].set), function() {
|
||||
if(tests[i].expectError) {
|
||||
assert.throws(action, tests[i].expectError);
|
||||
} else {
|
||||
assert.equal(action(), tests[i].expect);
|
||||
}
|
||||
});
|
||||
|
||||
})(i);
|
||||
}
|
||||
});
|
||||
|
||||
describe('JSON', function() {
|
||||
|
||||
it("Should be possible to stringify the object", function() {
|
||||
|
||||
assert.equal('{"s":1,"n":14623,"d":330}', JSON.stringify(new Fraction("44.3(12)")));
|
||||
|
||||
assert.equal('{"s":-1,"n":2,"d":1}', JSON.stringify(new Fraction(-1 / 2).inverse()));
|
||||
|
||||
});
|
||||
});
|
||||
|
||||
describe('Arguments', function() {
|
||||
|
||||
it("Should be possible to use different kind of params", function() {
|
||||
|
||||
// String
|
||||
var fraction = new Fraction("0.1");
|
||||
assert.equal("1/10", fraction.n + "/" + fraction.d);
|
||||
|
||||
var fraction = new Fraction("6234/6460");
|
||||
assert.equal("3117/3230", fraction.n + "/" + fraction.d);
|
||||
|
||||
// Two params
|
||||
var fraction = new Fraction(1, 2);
|
||||
assert.equal("1/2", fraction.n + "/" + fraction.d);
|
||||
|
||||
// Object
|
||||
var fraction = new Fraction({n: 1, d: 3});
|
||||
assert.equal("1/3", fraction.n + "/" + fraction.d);
|
||||
|
||||
// Array
|
||||
var fraction = new Fraction([1, 4]);
|
||||
assert.equal("1/4", fraction.n + "/" + fraction.d);
|
||||
});
|
||||
});
|
||||
|
||||
describe('fractions', function() {
|
||||
|
||||
it("Should pass 0.08 = 2/25", function() {
|
||||
|
||||
var fraction = new Fraction("0.08");
|
||||
assert.equal("2/25", fraction.n + "/" + fraction.d);
|
||||
});
|
||||
|
||||
it("Should pass 0.200 = 1/5", function() {
|
||||
|
||||
var fraction = new Fraction("0.200");
|
||||
assert.equal("1/5", fraction.n + "/" + fraction.d);
|
||||
});
|
||||
|
||||
it("Should pass 0.125 = 1/8", function() {
|
||||
|
||||
var fraction = new Fraction("0.125");
|
||||
assert.equal("1/8", fraction.n + "/" + fraction.d);
|
||||
});
|
||||
|
||||
it("Should pass 8.36 = 209/25", function() {
|
||||
|
||||
var fraction = new Fraction(8.36);
|
||||
assert.equal("209/25", fraction.n + "/" + fraction.d);
|
||||
});
|
||||
|
||||
});
|
||||
|
||||
describe('constructors', function() {
|
||||
|
||||
it("Should pass 0.08 = 2/25", function() {
|
||||
|
||||
var tmp = new Fraction({d: 4, n: 2, s: -1});
|
||||
assert.equal("-1/2", tmp.s * tmp.n + "/" + tmp.d);
|
||||
|
||||
var tmp = new Fraction(-88.3);
|
||||
assert.equal("-883/10", tmp.s * tmp.n + "/" + tmp.d);
|
||||
|
||||
var tmp = new Fraction(-88.3).clone();
|
||||
assert.equal("-883/10", tmp.s * tmp.n + "/" + tmp.d);
|
||||
|
||||
var tmp = new Fraction("123.'3'");
|
||||
assert.equal("370/3", tmp.s * tmp.n + "/" + tmp.d);
|
||||
|
||||
var tmp = new Fraction("123.'3'").clone();
|
||||
assert.equal("370/3", tmp.s * tmp.n + "/" + tmp.d);
|
||||
|
||||
var tmp = new Fraction([-1023461776, 334639305]);
|
||||
tmp = tmp.add([4, 25]);
|
||||
assert.equal("-4849597436/1673196525", tmp.s * tmp.n + "/" + tmp.d);
|
||||
});
|
||||
});
|
||||
|
||||
describe('Latex Output', function() {
|
||||
|
||||
it("Should pass 123.'3' = \\frac{370}{3}", function() {
|
||||
|
||||
var tmp = new Fraction("123.'3'");
|
||||
assert.equal("\\frac{370}{3}", tmp.toLatex());
|
||||
});
|
||||
|
||||
it("Should pass 1.'3' = \\frac{4}{3}", function() {
|
||||
|
||||
var tmp = new Fraction("1.'3'");
|
||||
assert.equal("\\frac{4}{3}", tmp.toLatex());
|
||||
});
|
||||
|
||||
it("Should pass -1.0000000000 = -1", function() {
|
||||
|
||||
var tmp = new Fraction("-1.0000000000");
|
||||
assert.equal('-1', tmp.toLatex());
|
||||
});
|
||||
|
||||
it("Should pass -0.0000000000 = 0", function() {
|
||||
|
||||
var tmp = new Fraction("-0.0000000000");
|
||||
assert.equal('0', tmp.toLatex());
|
||||
});
|
||||
});
|
||||
|
||||
describe('Fraction Output', function() {
|
||||
|
||||
it("Should pass 123.'3' = 123 1/3", function() {
|
||||
|
||||
var tmp = new Fraction("123.'3'");
|
||||
assert.equal('370/3', tmp.toFraction());
|
||||
});
|
||||
|
||||
it("Should pass 1.'3' = 1 1/3", function() {
|
||||
|
||||
var tmp = new Fraction("1.'3'");
|
||||
assert.equal('4/3', tmp.toFraction());
|
||||
});
|
||||
|
||||
it("Should pass -1.0000000000 = -1", function() {
|
||||
|
||||
var tmp = new Fraction("-1.0000000000");
|
||||
assert.equal('-1', tmp.toFraction());
|
||||
});
|
||||
|
||||
it("Should pass -0.0000000000 = 0", function() {
|
||||
|
||||
var tmp = new Fraction("-0.0000000000");
|
||||
assert.equal('0', tmp.toFraction());
|
||||
});
|
||||
|
||||
it("Should pass 1/-99/293 = -1/29007", function() {
|
||||
|
||||
var tmp = new Fraction(-99).inverse().div(293);
|
||||
assert.equal('-1/29007', tmp.toFraction());
|
||||
});
|
||||
|
||||
it('Should work with large calculations', function() {
|
||||
var x = Fraction(1123875);
|
||||
var y = Fraction(1238750184);
|
||||
var z = Fraction(1657134);
|
||||
var r = Fraction(77344464613500, 92063);
|
||||
assert.equal(x.mul(y).div(z).toFraction(), r.toFraction());
|
||||
});
|
||||
});
|
||||
|
||||
describe('Fraction toContined', function() {
|
||||
|
||||
it("Should pass 415/93", function() {
|
||||
|
||||
var tmp = new Fraction(415, 93);
|
||||
assert.equal('4,2,6,7', tmp.toContinued().toString());
|
||||
});
|
||||
|
||||
it("Should pass 0/2", function() {
|
||||
|
||||
var tmp = new Fraction(0, 2);
|
||||
assert.equal('0', tmp.toContinued().toString());
|
||||
});
|
||||
|
||||
it("Should pass 1/7", function() {
|
||||
|
||||
var tmp = new Fraction(1, 7);
|
||||
assert.equal('0,7', tmp.toContinued().toString());
|
||||
});
|
||||
|
||||
it("Should pass 23/88", function() {
|
||||
|
||||
var tmp = new Fraction('23/88');
|
||||
assert.equal('0,3,1,4,1,3', tmp.toContinued().toString());
|
||||
});
|
||||
|
||||
it("Should pass 1/99", function() {
|
||||
|
||||
var tmp = new Fraction('1/99');
|
||||
assert.equal('0,99', tmp.toContinued().toString());
|
||||
});
|
||||
|
||||
it("Should pass 1768/99", function() {
|
||||
|
||||
var tmp = new Fraction('1768/99');
|
||||
assert.equal('17,1,6,14', tmp.toContinued().toString());
|
||||
});
|
||||
|
||||
it("Should pass 1768/99", function() {
|
||||
|
||||
var tmp = new Fraction('7/8');
|
||||
assert.equal('0,1,7', tmp.toContinued().toString());
|
||||
});
|
||||
|
||||
});
|
||||
|
||||
describe('Fraction NaN', function() {
|
||||
|
||||
for (var i in Fraction.prototype) {
|
||||
|
||||
(function(i) {
|
||||
|
||||
if (Fraction.prototype[i] instanceof Function)
|
||||
switch (i) {
|
||||
case 'toFraction':
|
||||
case 'toContinued':
|
||||
case 'toLatex':
|
||||
case 'valueOf':
|
||||
case 'divisible':
|
||||
case 'compare':
|
||||
case 'equals':
|
||||
break;
|
||||
case 'toString':
|
||||
it("Should pass " + i, function() {
|
||||
var x = Fraction(NaN)[i]();
|
||||
|
||||
assert.equal('NaN', x);
|
||||
});
|
||||
break;
|
||||
case 'add':
|
||||
case 'sub':
|
||||
case 'mul':
|
||||
case 'div':
|
||||
case 'pow':
|
||||
case "gcd":
|
||||
case 'lcm':
|
||||
case 'equals':
|
||||
it("Should pass " + i, function() {
|
||||
var x = Fraction(NaN)[i](NaN);
|
||||
|
||||
assert.equal('NaN NaN', x.d + " " + x.d);
|
||||
});
|
||||
break;
|
||||
|
||||
default:
|
||||
it("Should pass " + i, function() {
|
||||
|
||||
var x = Fraction(NaN)[i]();
|
||||
|
||||
assert.equal('NaN NaN', x.d + " " + x.d);
|
||||
});
|
||||
}
|
||||
|
||||
})(i);
|
||||
}
|
||||
});
|
||||
Reference in New Issue
Block a user