added factorial module

24_10_22_faktorialis/node_modules/complex.js/LICENSE

@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2024 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.

24_10_22_faktorialis/node_modules/complex.js/README.md

@@ -0,0 +1,336 @@
+# Complex.js - ℂ in JavaScript
+
+[![NPM Package](https://img.shields.io/npm/v/complex.js.svg?style=flat)](https://npmjs.org/package/complex.js "View this project on npm")
+[![MIT license](http://img.shields.io/badge/license-MIT-brightgreen.svg)](http://opensource.org/licenses/MIT)
+
+Complex.js is a well tested JavaScript library to work with [complex number arithmetic](https://raw.org/book/analysis/complex-numbers/) in JavaScript. It implements every elementary complex number manipulation function and the API is intentionally similar to [Fraction.js](https://github.com/rawify/Fraction.js). Furthermore, it's the basis of [Polynomial.js](https://github.com/infusion/Polynomial.js) and [Math.js](https://github.com/josdejong/mathjs).
+
+
+## Examples
+
+
+```js
+let Complex = require('complex.js');
+
+let c = new Complex("99.3+8i");
+c.mul({re: 3, im: 9}).div(4.9).sub(3, 2);
+```
+
+A classical use case for complex numbers is solving quadratic equations `ax² + bx + c = 0` for all `a, b, c ∈ ℝ`:
+
+```js
+
+function quadraticRoot(a, b, c) {
+  let sqrt = Complex(b * b - 4 * a * c).sqrt()
+  let x1 = Complex(-b).add(sqrt).div(2 * a)
+  let x2 = Complex(-b).sub(sqrt).div(2 * a)
+  return {x1, x2}
+}
+
+// quadraticRoot(1, 4, 5) -> -2 ± i
+```
+
+For cubic roots have a look at [RootFinder](https://github.com/rawify/RootFinder.js) which uses Complex.js.
+
+## Parser
+
+
+Any function (see below) as well as the constructor of the *Complex* class parses its input like this.
+
+You can pass either Objects, Doubles or Strings.
+
+### Objects
+
+```javascript
+new Complex({re: real, im: imaginary});
+new Complex({arg: angle, abs: radius});
+new Complex({phi: angle, r: radius});
+new Complex([real, imaginary]); // Vector/Array syntax
+```
+If there are other attributes on the passed object, they're not getting preserved and have to be merged manually.
+
+### Doubles
+
+```javascript
+new Complex(55.4);
+```
+
+### Strings
+
+```javascript
+new Complex("123.45");
+new Complex("15+3i");
+new Complex("i");
+```
+
+### Two arguments
+
+```javascript
+new Complex(3, 2); // 3+2i
+```
+
+## Attributes
+
+
+Every complex number object exposes its real and imaginary part as attribute `re` and `im`:
+
+```javascript
+let c = new Complex(3, 2);
+
+console.log("Real part:", c.re); // 3
+console.log("Imaginary part:", c.im); // 2
+```
+
+## Functions
+
+
+Complex sign()
+---
+Returns the complex sign, defined as the complex number normalized by it's absolute value
+
+Complex add(n)
+---
+Adds another complex number
+
+Complex sub(n)
+---
+Subtracts another complex number
+
+Complex mul(n)
+---
+Multiplies the number with another complex number
+
+Complex div(n)
+---
+Divides the number by another complex number
+
+Complex pow(exp)
+---
+Returns the number raised to the complex exponent (Note: `Complex.ZERO.pow(0) = Complex.ONE` by convention)
+
+Complex sqrt()
+---
+Returns the complex square root of the number
+
+Complex exp(n)
+---
+Returns `e^n` with complex exponent `n`.
+
+Complex log()
+---
+Returns the natural logarithm (base `E`) of the actual complex number
+
+_Note:_ The logarithm to a different base can be calculated with `z.log().div(Math.log(base))`.
+
+double abs()
+---
+Calculates the magnitude of the complex number
+
+double arg()
+---
+Calculates the angle of the complex number
+
+Complex inverse()
+---
+Calculates the multiplicative inverse of the complex number (1 / z)
+
+Complex conjugate()
+---
+Calculates the conjugate of the complex number (multiplies the imaginary part with -1)
+
+Complex neg()
+---
+Negates the number (multiplies both the real and imaginary part with -1) in order to get the additive inverse
+
+Complex floor([places=0])
+---
+Floors the complex number parts towards zero
+
+Complex ceil([places=0])
+---
+Ceils the complex number parts off zero
+
+Complex round([places=0])
+---
+Rounds the complex number parts
+
+boolean equals(n)
+---
+Checks if both numbers are exactly the same, if both numbers are infinite they
+are considered **not** equal.
+
+boolean isNaN()
+---
+Checks if the given number is not a number
+
+boolean isFinite()
+---
+Checks if the given number is finite
+
+Complex clone()
+---
+Returns a new Complex instance with the same real and imaginary properties
+
+Array toVector()
+---
+Returns a Vector of the actual complex number with two components
+
+String toString()
+---
+Returns a string representation of the actual number. As of v1.9.0 the output is a bit more human readable
+
+```javascript
+new Complex(1, 2).toString(); // 1 + 2i
+new Complex(0, 1).toString(); // i
+new Complex(9, 0).toString(); // 9
+new Complex(1, 1).toString(); // 1 + i
+```
+
+double valueOf()
+---
+Returns the real part of the number if imaginary part is zero. Otherwise `null`
+
+
+## Trigonometric functions
+
+The following trigonometric functions are defined on Complex.js:
+
+| Trig | Arcus | Hyperbolic | Area-Hyperbolic |
+|------|-------|------------|------------------|
+| sin()  | asin()  | sinh()       | asinh()            |
+| cos()  | acos()  | cosh()       | acosh()            |
+| tan()  | atan()  | tanh()       | atanh()            |
+| cot()  | acot()  | coth()       | acoth()            |
+| sec()  | asec()  | sech()       | asech()            |
+| csc()  | acsc()  | csch()       | acsch()            |
+
+
+## Geometric Equivalence
+
+
+Complex numbers can also be seen as a vector in the 2D space. Here is a simple overview of basic operations and how to implement them with complex.js:
+
+New vector
+---
+```js
+let v1 = new Complex(1, 0);
+let v2 = new Complex(1, 1);
+```
+
+Scale vector
+---
+```js
+scale(v1, factor):= v1.mul(factor)
+```
+
+Vector norm
+---
+```js
+norm(v):= v.abs()
+```
+
+Translate vector
+---
+```js
+translate(v1, v2):= v1.add(v2)
+```
+
+Rotate vector around center
+---
+```js
+rotate(v, angle):= v.mul({abs: 1, arg: angle})
+```
+
+Rotate vector around a point
+---
+```js
+rotate(v, p, angle):= v.sub(p).mul({abs: 1, arg: angle}).add(p)
+```
+
+Distance to another vector
+---
+```js
+distance(v1, v2):= v1.sub(v2).abs()
+```
+
+## Constants
+
+
+Complex.ZERO
+---
+A complex zero value (south pole on the Riemann Sphere)
+
+Complex.ONE
+---
+A complex one instance
+
+Complex.INFINITY
+---
+A complex infinity value (north pole on the Riemann Sphere)
+
+Complex.NAN
+---
+A complex NaN value (not on the Riemann Sphere)
+
+Complex.I
+---
+An imaginary number i instance
+
+Complex.PI
+---
+A complex PI instance
+
+Complex.E
+---
+A complex euler number instance
+
+Complex.EPSILON
+---
+A small epsilon value used for `equals()` comparison in order to circumvent double imprecision.
+
+
+## Installation
+
+Installing complex.js is as easy as cloning this repo or use one of the following command:
+
+
+```bash
+npm install complex.js
+```
+
+## Using Complex.js with the browser
+
+```html
+<script src="complex.min.js"></script>
+<script>
+    console.log(Complex("4+3i"));
+</script>
+```
+
+
+
+## Coding Style
+
+As every library I publish, Complex.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.
+
+## Building the library
+
+After cloning the Git repository run:
+
+```
+npm install
+npm run build
+```
+
+## Run a test
+
+Testing the source against the shipped test suite is as easy as
+
+```
+npm run test
+```
+
+## Copyright and Licensing
+
+Copyright (c) 2024, [Robert Eisele](https://raw.org/)
+Licensed under the MIT license.

24_10_22_faktorialis/node_modules/complex.js/complex.d.ts

@@ -0,0 +1,323 @@
+type AValue =
+  | Complex
+  | { im: number; re: number }
+  | { abs: number; arg: number }
+  | { r: number; phi: number }
+  | [number, number]
+  | string
+  | number
+  | null
+  | undefined;
+type BValue = number | undefined;
+
+export function Complex(a: AValue, b?: BValue): Complex;
+
+export default Complex;
+
+/**
+ *
+ * This class allows the manipulation of complex numbers.
+ * You can pass a complex number in different formats. Either as object, double, string or two integer parameters.
+ *
+ * Object form
+ * { re: <real>, im: <imaginary> }
+ * { arg: <angle>, abs: <radius> }
+ * { phi: <angle>, r: <radius> }
+ *
+ * Array / Vector form
+ * [ real, imaginary ]
+ *
+ * Double form
+ * 99.3 - Single double value
+ *
+ * String form
+ * '23.1337' - Simple real number
+ * '15+3i' - a simple complex number
+ * '3-i' - a simple complex number
+ *
+ * Example:
+ *
+ * var c = new Complex('99.3+8i');
+ * c.mul({r: 3, i: 9}).div(4.9).sub(3, 2);
+ *
+ */
+export class Complex {
+  re: number;
+  im: number;
+
+  constructor(a: AValue, b?: BValue);
+
+  /**
+   * Calculates the sign of a complex number, which is a normalized complex
+   *
+   */
+  sign(): Complex;
+  /**
+   * Adds two complex numbers
+   *
+   */
+  add(a: AValue, b?: BValue): Complex;
+  /**
+   * Subtracts two complex numbers
+   *
+   */
+  sub(a: AValue, b?: BValue): Complex;
+  /**
+   * Multiplies two complex numbers
+   *
+   */
+  mul(a: AValue, b?: BValue): Complex;
+  /**
+   * Divides two complex numbers
+   *
+   */
+  div(a: AValue, b?: BValue): Complex;
+  /**
+   * Calculate the power of two complex numbers
+   *
+   */
+  pow(a: AValue, b?: BValue): Complex;
+  /**
+   * Calculate the complex square root
+   *
+   */
+  sqrt(): Complex;
+  /**
+   * Calculate the complex exponent
+   *
+   */
+  exp(): Complex;
+  /**
+   * Calculate the complex exponent and subtracts one.
+   *
+   * This may be more accurate than `Complex(x).exp().sub(1)` if
+   * `x` is small.
+   *
+   */
+  expm1(): Complex;
+  /**
+   * Calculate the natural log
+   *
+   */
+  log(): Complex;
+  /**
+   * Calculate the magnitude of the complex number
+   *
+   */
+  abs(): number;
+  /**
+   * Calculate the angle of the complex number
+   *
+   */
+  arg(): number;
+  /**
+   * Calculate the sine of the complex number
+   *
+   */
+  sin(): Complex;
+  /**
+   * Calculate the cosine
+   *
+   */
+  cos(): Complex;
+  /**
+   * Calculate the tangent
+   *
+   */
+  tan(): Complex;
+  /**
+   * Calculate the cotangent
+   *
+   */
+  cot(): Complex;
+  /**
+   * Calculate the secant
+   *
+   */
+  sec(): Complex;
+  /**
+   * Calculate the cosecans
+   *
+   */
+  csc(): Complex;
+  /**
+   * Calculate the complex arcus sinus
+   *
+   */
+  asin(): Complex;
+  /**
+   * Calculate the complex arcus cosinus
+   *
+   */
+  acos(): Complex;
+  /**
+   * Calculate the complex arcus tangent
+   *
+   */
+  atan(): Complex;
+  /**
+   * Calculate the complex arcus cotangent
+   *
+   */
+  acot(): Complex;
+  /**
+   * Calculate the complex arcus secant
+   *
+   */
+  asec(): Complex;
+  /**
+   * Calculate the complex arcus cosecans
+   *
+   */
+  acsc(): Complex;
+  /**
+   * Calculate the complex sinh
+   *
+   */
+  sinh(): Complex;
+  /**
+   * Calculate the complex cosh
+   *
+   */
+  cosh(): Complex;
+  /**
+   * Calculate the complex tanh
+   *
+   */
+  tanh(): Complex;
+  /**
+   * Calculate the complex coth
+   *
+   */
+  coth(): Complex;
+  /**
+   * Calculate the complex coth
+   *
+   */
+  csch(): Complex;
+  /**
+   * Calculate the complex sech
+   *
+   */
+  sech(): Complex;
+  /**
+   * Calculate the complex asinh
+   *
+   */
+  asinh(): Complex;
+  /**
+   * Calculate the complex acosh
+   *
+   */
+  acosh(): Complex;
+  /**
+   * Calculate the complex atanh
+   *
+   */
+  atanh(): Complex;
+  /**
+   * Calculate the complex acoth
+   *
+   */
+  acoth(): Complex;
+  /**
+   * Calculate the complex acsch
+   *
+   */
+  acsch(): Complex;
+  /**
+   * Calculate the complex asech
+   *
+   */
+  asech(): Complex;
+  /**
+   * Calculate the complex inverse 1/z
+   *
+   */
+  inverse(): Complex;
+  /**
+   * Returns the complex conjugate
+   *
+   */
+  conjugate(): Complex;
+  /**
+   * Gets the negated complex number
+   *
+   */
+  neg(): Complex;
+  /**
+   * Ceils the actual complex number
+   *
+   */
+  ceil(places: number): Complex;
+  /**
+   * Floors the actual complex number
+   *
+   */
+  floor(places: number): Complex;
+  /**
+   * Ceils the actual complex number
+   *
+   */
+  round(places: number): Complex;
+  /**
+   * Compares two complex numbers
+   *
+   * **Note:** new Complex(Infinity).equals(Infinity) === false
+   *
+   */
+  equals(a: AValue, b?: BValue): boolean;
+  /**
+   * Clones the actual object
+   *
+   */
+  clone(): Complex;
+  /**
+   * Gets a string of the actual complex number
+   *
+   */
+  toString(): string;
+  /**
+   * Returns the actual number as a vector
+   *
+   */
+  toVector(): number[];
+  /**
+   * Returns the actual real value of the current object
+   *
+   * @returns {number|null}
+   */
+  valueOf(): number | null;
+  /**
+   * Determines whether a complex number is not on the Riemann sphere.
+   *
+   */
+  isNaN(): boolean;
+  /**
+   * Determines whether or not a complex number is at the zero pole of the
+   * Riemann sphere.
+   *
+   */
+  isZero(): boolean;
+  /**
+   * Determines whether a complex number is not at the infinity pole of the
+   * Riemann sphere.
+   *
+   */
+  isFinite(): boolean;
+  /**
+   * Determines whether or not a complex number is at the infinity pole of the
+   * Riemann sphere.
+   *
+   */
+  isInfinite(): boolean;
+
+  static ZERO: Complex;
+  static ONE: Complex;
+  static I: Complex;
+  static PI: Complex;
+  static E: Complex;
+  static INFINITY: Complex;
+  static NAN: Complex;
+  static EPSILON: number;
+}

24_10_22_faktorialis/node_modules/complex.js/dist/complex.min.js

@@ -0,0 +1,25 @@
+/*
+Complex.js v2.3.0 10/10/2024
+https://raw.org/article/complex-numbers-in-javascript/
+
+Copyright (c) 2024, Robert Eisele (https://raw.org/)
+Licensed under the MIT license.
+*/
+'use strict';(function(n){function l(){throw SyntaxError("Invalid Param");}function m(a,b){var c=Math.abs(a),e=Math.abs(b);if(0===a)return Math.log(e);if(0===b)return Math.log(c);if(3E3>c&&3E3>e)return.5*Math.log(a*a+b*b);a/=2;b/=2;return.5*Math.log(a*a+b*b)+Math.LN2}function d(a,b){if(!(this instanceof d))return new d(a,b);var c={re:0,im:0};if(void 0===a||null===a)c.re=c.im=0;else if(void 0!==b)c.re=a,c.im=b;else switch(typeof a){case "object":"im"in a&&"re"in a?(c.re=a.re,c.im=a.im):"abs"in a&&
+"arg"in a?!Number.isFinite(a.abs)&&Number.isFinite(a.arg)?c=d.INFINITY:(c.re=a.abs*Math.cos(a.arg),c.im=a.abs*Math.sin(a.arg)):"r"in a&&"phi"in a?!Number.isFinite(a.r)&&Number.isFinite(a.phi)?c=d.INFINITY:(c.re=a.r*Math.cos(a.phi),c.im=a.r*Math.sin(a.phi)):2===a.length?(c.re=a[0],c.im=a[1]):l();break;case "string":c.im=c.re=0;a=a.replace(/_/g,"").match(/\d+\.?\d*e[+-]?\d+|\d+\.?\d*|\.\d+|./g);b=1;var e=0;null===a&&l();for(var f=0;f<a.length;f++){var h=a[f];" "!==h&&"\t"!==h&&"\n"!==h&&("+"===h?b++:
+"-"===h?e++:("i"===h||"I"===h?(0===b+e&&l()," "===a[f+1]||isNaN(a[f+1])?c.im+=parseFloat((e%2?"-":"")+"1"):(c.im+=parseFloat((e%2?"-":"")+a[f+1]),f++)):((0===b+e||isNaN(h))&&l(),"i"===a[f+1]||"I"===a[f+1]?(c.im+=parseFloat((e%2?"-":"")+h),f++):c.re+=parseFloat((e%2?"-":"")+h)),b=e=0))}0<b+e&&l();break;case "number":c.im=0;c.re=a;break;default:l()}this.re=c.re;this.im=c.im}var g=Math.cosh||function(a){return 1E-9>Math.abs(a)?1-a:.5*(Math.exp(a)+Math.exp(-a))},k=Math.sinh||function(a){return 1E-9>Math.abs(a)?
+a:.5*(Math.exp(a)-Math.exp(-a))};d.prototype={re:0,im:0,sign:function(){var a=this.abs();return new d(this.re/a,this.im/a)},add:function(a,b){a=new d(a,b);return this.isInfinite()&&a.isInfinite()?d.NAN:this.isInfinite()||a.isInfinite()?d.INFINITY:new d(this.re+a.re,this.im+a.im)},sub:function(a,b){a=new d(a,b);return this.isInfinite()&&a.isInfinite()?d.NAN:this.isInfinite()||a.isInfinite()?d.INFINITY:new d(this.re-a.re,this.im-a.im)},mul:function(a,b){a=new d(a,b);return this.isInfinite()&&a.isZero()||
+this.isZero()&&a.isInfinite()?d.NAN:this.isInfinite()||a.isInfinite()?d.INFINITY:0===a.im&&0===this.im?new d(this.re*a.re,0):new d(this.re*a.re-this.im*a.im,this.re*a.im+this.im*a.re)},div:function(a,b){var c=new d(a,b);if(this.isZero()&&c.isZero()||this.isInfinite()&&c.isInfinite())return d.NAN;if(this.isInfinite()||c.isZero())return d.INFINITY;if(this.isZero()||c.isInfinite())return d.ZERO;a=this.re;b=this.im;var e=c.re,f=c.im;if(0===f)return new d(a/e,b/e);if(Math.abs(e)<Math.abs(f))return c=e/
+f,e=e*c+f,new d((a*c+b)/e,(b*c-a)/e);c=f/e;e=f*c+e;return new d((a+b*c)/e,(b-a*c)/e)},pow:function(a,b){var c=new d(a,b);a=this.re;b=this.im;if(c.isZero())return d.ONE;if(0===c.im){if(0===b&&0<a)return new d(Math.pow(a,c.re),0);if(0===a)switch((c.re%4+4)%4){case 0:return new d(Math.pow(b,c.re),0);case 1:return new d(0,Math.pow(b,c.re));case 2:return new d(-Math.pow(b,c.re),0);case 3:return new d(0,-Math.pow(b,c.re))}}if(0===a&&0===b&&0<c.re&&0<=c.im)return d.ZERO;var e=Math.atan2(b,a);b=m(a,b);a=
+Math.exp(c.re*b-c.im*e);b=c.im*b+c.re*e;return new d(a*Math.cos(b),a*Math.sin(b))},sqrt:function(){var a=this.re,b=this.im,c=this.abs();if(0<=a){if(0===b)return new d(Math.sqrt(a),0);var e=.5*Math.sqrt(2*(c+a))}else e=Math.abs(b)/Math.sqrt(2*(c-a));a=0>=a?.5*Math.sqrt(2*(c-a)):Math.abs(b)/Math.sqrt(2*(c+a));return new d(e,0>b?-a:a)},exp:function(){var a=Math.exp(this.re);return new d(a*Math.cos(this.im),a*Math.sin(this.im))},expm1:function(){var a=this.re,b=this.im,c=Math.expm1(a)*Math.cos(b);var e=
+Math.PI/4;-e>b||b>e?e=Math.cos(b)-1:(e=b*b,e*=e*(e*(e*(e*(e*(e*(e/20922789888E3-1/87178291200)+1/479001600)-1/3628800)+1/40320)-1/720)+1/24)-.5);return new d(c+e,Math.exp(a)*Math.sin(b))},log:function(){var a=this.re,b=this.im;return new d(m(a,b),Math.atan2(b,a))},abs:function(){var a=this.re;var b=this.im,c=Math.abs(a),e=Math.abs(b);3E3>c&&3E3>e?a=Math.sqrt(c*c+e*e):(c<e?(c=e,e=a/b):e=b/a,a=c*Math.sqrt(1+e*e));return a},arg:function(){return Math.atan2(this.im,this.re)},sin:function(){var a=this.re,
+b=this.im;return new d(Math.sin(a)*g(b),Math.cos(a)*k(b))},cos:function(){var a=this.re,b=this.im;return new d(Math.cos(a)*g(b),-Math.sin(a)*k(b))},tan:function(){var a=2*this.re,b=2*this.im,c=Math.cos(a)+g(b);return new d(Math.sin(a)/c,k(b)/c)},cot:function(){var a=2*this.re,b=2*this.im,c=Math.cos(a)-g(b);return new d(-Math.sin(a)/c,k(b)/c)},sec:function(){var a=this.re,b=this.im,c=.5*g(2*b)+.5*Math.cos(2*a);return new d(Math.cos(a)*g(b)/c,Math.sin(a)*k(b)/c)},csc:function(){var a=this.re,b=this.im,
+c=.5*g(2*b)-.5*Math.cos(2*a);return new d(Math.sin(a)*g(b)/c,-Math.cos(a)*k(b)/c)},asin:function(){var a=this.re,b=this.im,c=(new d(b*b-a*a+1,-2*a*b)).sqrt();a=(new d(c.re-b,c.im+a)).log();return new d(a.im,-a.re)},acos:function(){var a=this.re,b=this.im,c=(new d(b*b-a*a+1,-2*a*b)).sqrt();a=(new d(c.re-b,c.im+a)).log();return new d(Math.PI/2-a.im,a.re)},atan:function(){var a=this.re,b=this.im;if(0===a){if(1===b)return new d(0,Infinity);if(-1===b)return new d(0,-Infinity)}var c=a*a+(1-b)*(1-b);a=(new d((1-
+b*b-a*a)/c,-2*a/c)).log();return new d(-.5*a.im,.5*a.re)},acot:function(){var a=this.re,b=this.im;if(0===b)return new d(Math.atan2(1,a),0);var c=a*a+b*b;return 0!==c?(new d(a/c,-b/c)).atan():(new d(0!==a?a/0:0,0!==b?-b/0:0)).atan()},asec:function(){var a=this.re,b=this.im;if(0===a&&0===b)return new d(0,Infinity);var c=a*a+b*b;return 0!==c?(new d(a/c,-b/c)).acos():(new d(0!==a?a/0:0,0!==b?-b/0:0)).acos()},acsc:function(){var a=this.re,b=this.im;if(0===a&&0===b)return new d(Math.PI/2,Infinity);var c=
+a*a+b*b;return 0!==c?(new d(a/c,-b/c)).asin():(new d(0!==a?a/0:0,0!==b?-b/0:0)).asin()},sinh:function(){var a=this.re,b=this.im;return new d(k(a)*Math.cos(b),g(a)*Math.sin(b))},cosh:function(){var a=this.re,b=this.im;return new d(g(a)*Math.cos(b),k(a)*Math.sin(b))},tanh:function(){var a=2*this.re,b=2*this.im,c=g(a)+Math.cos(b);return new d(k(a)/c,Math.sin(b)/c)},coth:function(){var a=2*this.re,b=2*this.im,c=g(a)-Math.cos(b);return new d(k(a)/c,-Math.sin(b)/c)},csch:function(){var a=this.re,b=this.im,
+c=Math.cos(2*b)-g(2*a);return new d(-2*k(a)*Math.cos(b)/c,2*g(a)*Math.sin(b)/c)},sech:function(){var a=this.re,b=this.im,c=Math.cos(2*b)+g(2*a);return new d(2*g(a)*Math.cos(b)/c,-2*k(a)*Math.sin(b)/c)},asinh:function(){var a=this.im;this.im=-this.re;this.re=a;var b=this.asin();this.re=-this.im;this.im=a;a=b.re;b.re=-b.im;b.im=a;return b},acosh:function(){var a=this.acos();if(0>=a.im){var b=a.re;a.re=-a.im;a.im=b}else b=a.im,a.im=-a.re,a.re=b;return a},atanh:function(){var a=this.re,b=this.im,c=1<
+a&&0===b,e=1-a,f=1+a,h=e*e+b*b;a=0!==h?new d((f*e-b*b)/h,(b*e+f*b)/h):new d(-1!==a?a/0:0,0!==b?b/0:0);b=a.re;a.re=m(a.re,a.im)/2;a.im=Math.atan2(a.im,b)/2;c&&(a.im=-a.im);return a},acoth:function(){var a=this.re,b=this.im;if(0===a&&0===b)return new d(0,Math.PI/2);var c=a*a+b*b;return 0!==c?(new d(a/c,-b/c)).atanh():(new d(0!==a?a/0:0,0!==b?-b/0:0)).atanh()},acsch:function(){var a=this.re,b=this.im;if(0===b)return new d(0!==a?Math.log(a+Math.sqrt(a*a+1)):Infinity,0);var c=a*a+b*b;return 0!==c?(new d(a/
+c,-b/c)).asinh():(new d(0!==a?a/0:0,0!==b?-b/0:0)).asinh()},asech:function(){var a=this.re,b=this.im;if(this.isZero())return d.INFINITY;var c=a*a+b*b;return 0!==c?(new d(a/c,-b/c)).acosh():(new d(0!==a?a/0:0,0!==b?-b/0:0)).acosh()},inverse:function(){if(this.isZero())return d.INFINITY;if(this.isInfinite())return d.ZERO;var a=this.re,b=this.im,c=a*a+b*b;return new d(a/c,-b/c)},conjugate:function(){return new d(this.re,-this.im)},neg:function(){return new d(-this.re,-this.im)},ceil:function(a){a=Math.pow(10,
+a||0);return new d(Math.ceil(this.re*a)/a,Math.ceil(this.im*a)/a)},floor:function(a){a=Math.pow(10,a||0);return new d(Math.floor(this.re*a)/a,Math.floor(this.im*a)/a)},round:function(a){a=Math.pow(10,a||0);return new d(Math.round(this.re*a)/a,Math.round(this.im*a)/a)},equals:function(a,b){a=new d(a,b);return Math.abs(a.re-this.re)<=d.EPSILON&&Math.abs(a.im-this.im)<=d.EPSILON},clone:function(){return new d(this.re,this.im)},toString:function(){var a=this.re,b=this.im,c="";if(this.isNaN())return"NaN";
+if(this.isInfinite())return"Infinity";Math.abs(a)<d.EPSILON&&(a=0);Math.abs(b)<d.EPSILON&&(b=0);if(0===b)return c+a;0!==a?(c=c+a+" ",0>b?(b=-b,c+="-"):c+="+",c+=" "):0>b&&(b=-b,c+="-");1!==b&&(c+=b);return c+"i"},toVector:function(){return[this.re,this.im]},valueOf:function(){return 0===this.im?this.re:null},isNaN:function(){return isNaN(this.re)||isNaN(this.im)},isZero:function(){return 0===this.im&&0===this.re},isFinite:function(){return isFinite(this.re)&&isFinite(this.im)},isInfinite:function(){return!(this.isNaN()||
+this.isFinite())}};d.ZERO=new d(0,0);d.ONE=new d(1,0);d.I=new d(0,1);d.PI=new d(Math.PI,0);d.E=new d(Math.E,0);d.INFINITY=new d(Infinity,Infinity);d.NAN=new d(NaN,NaN);d.EPSILON=1E-15;"function"===typeof define&&define.amd?define([],function(){return d}):"object"===typeof exports?(Object.defineProperty(d,"__esModule",{value:!0}),d["default"]=d,d.Complex=d,module.exports=d):n.Complex=d})(this);

24_10_22_faktorialis/node_modules/complex.js/examples/gamma.js

@@ -0,0 +1,33 @@
+/*
+ * A gamma function implementation based on Lanczos Approximation
+ * https://en.wikipedia.org/wiki/Lanczos_approximation
+ */
+
+var Complex = require('complex.js');
+
+var P = [
+  Complex(0.99999999999980993),
+  Complex(676.5203681218851), Complex(-1259.1392167224028), Complex(771.32342877765313),
+  Complex(-176.61502916214059), Complex(12.507343278686905), Complex(-0.13857109526572012),
+  Complex(9.9843695780195716e-6), Complex(1.5056327351493116e-7)
+];
+
+var SQRT2PI = Complex(Math.sqrt(2 * Math.PI));
+
+function gamma(z) {
+
+  z = z.sub(1);
+
+  var x = P[0];
+  var t = z.add(7.5);
+  for (var i = 1; i < P.length; i++) {
+    x = x.add(P[i].div(z.add(i)));
+  }
+  return SQRT2PI.mul(t.pow(z.add(0.5))).mul(t.neg().exp()).mul(x);
+}
+
+var fac = 1;
+for (var i = 1; i <= 10; i++) {
+  console.log(fac, gamma(Complex(i)));
+  fac *= i;
+}

24_10_22_faktorialis/node_modules/complex.js/package.json

@@ -0,0 +1,60 @@
+{
+    "name": "complex.js",
+    "title": "Complex.js",
+    "version": "2.3.0",
+    "homepage": "https://raw.org/article/complex-numbers-in-javascript/",
+    "bugs": "https://github.com/rawify/Complex.js/issues",
+    "description": "A complex numbers library",
+    "keywords": [
+        "complex numbers",
+        "math",
+        "complex",
+        "number",
+        "calculus",
+        "parser",
+        "arithmetic"
+    ],
+    "private": false,
+    "main": "./dist/complex.js",
+    "module": "./dist/complex.mjs",
+    "types": "./complex.d.ts",
+    "browser": "./dist/complex.min.js",
+    "unpkg": "./dist/complex.min.js",
+    "readmeFilename": "README.md",
+    "exports": {
+        ".": {
+            "types": "./complex.d.ts",
+            "require": "./dist/complex.js",
+            "import": "./dist/complex.mjs"
+        }
+    },
+    "repository": {
+        "type": "git",
+        "url": "git@github.com:rawify/Complex.js.git"
+    },
+    "funding": {
+        "type": "github",
+        "url": "https://github.com/sponsors/rawify"
+    },
+    "author": {
+        "name": "Robert Eisele",
+        "email": "robert@raw.org",
+        "url": "https://raw.org/"
+    },
+    "license": "MIT",
+    "engines": {
+        "node": "*"
+    },
+    "directories": {
+        "example": "examples",
+        "test": "tests"
+    },
+    "scripts": {
+        "build": "crude-build Complex",
+        "test": "mocha tests/*.js"
+    },
+    "devDependencies": {
+        "crude-build": "^0.1.1",
+        "mocha": "*"
+    }
+}