digital-filter-designer/math.min.js

/**
 * math.js
 * https://github.com/josdejong/mathjs
 *
 * Math.js is an extensive math library for JavaScript and Node.js,
 * It features real and complex numbers, units, matrices, a large set of
 * mathematical functions, and a flexible expression parser.
 *
 * @version 7.1.0
 * @date    2020-07-13
 *
 * @license
 * Copyright (C) 2013-2020 Jos de Jong <wjosdejong@gmail.com>
 *
 * Licensed under the Apache License, Version 2.0 (the "License"); you may not
 * use this file except in compliance with the License. You may obtain a copy
 * of the License at
 *
 * https://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
 * License for the specific language governing permissions and limitations under
 * the License.
 */
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    /**
     * @license Complex.js v2.0.11 11/02/2016
     *
     * Copyright (c) 2016, Robert Eisele (robert@xarg.org)
     * Dual licensed under the MIT or GPL Version 2 licenses.
     **/
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    /**
     * @license Fraction.js v4.0.12 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(){"use strict";var d={s:1,n:0,d:1};function e(t){function e(){var e=Error.apply(this,arguments);e.name=this.name=t,this.stack=e.stack,this.message=e.message}function r(){}return r.prototype=Error.prototype,e.prototype=new r,e}var y=f.DivisionByZero=e("DivisionByZero"),t=f.InvalidParameter=e("InvalidParameter");function g(e,t){return isNaN(e=parseInt(e,10))&&v(),e*t}function v(){throw new t}var n=function(e,t){var r,n=0,i=1,a=1,o=0,s=0,u=0,c=1,f=1,l=0,p=1,m=1,h=1;if(null!=e)if(void 0!==t)a=(n=e)*(i=t);else switch(typeof e){case"object":"d"in e&&"n"in e?(n=e.n,i=e.d,"s"in e&&(n*=e.s)):0 in e?(n=e[0],1 in e&&(i=e[1])):v(),a=n*i;break;case"number":if(e<0&&(e=-(a=e)),e%1==0)n=e;else if(0<e){for(1<=e&&(e/=f=Math.pow(10,Math.floor(1+Math.log(e)/Math.LN10)));p<=1e7&&h<=1e7;){if(e===(r=(l+m)/(p+h))){i=p+h<=1e7?(n=l+m,p+h):p<h?(n=m,h):(n=l,p);break}r<e?(l+=m,p+=h):(m+=l,h+=p),i=1e7<p?(n=m,h):(n=l,p)}n*=f}else(isNaN(e)||isNaN(t))&&(i=n=NaN);break;case"string":if(null===(p=e.match(/\d+|./g))&&v(),"-"===p[l]?(a=-1,l++):"+"===p[l]&&l++,p.length===l+1?s=g(p[l++],a):"."===p[l+1]||"."===p[l]?("."!==p[l]&&(o=g(p[l++],a)),(++l+1===p.length||"("===p[l+1]&&")"===p[l+3]||"'"===p[l+1]&&"'"===p[l+3])&&(s=g(p[l],a),c=Math.pow(10,p[l].length),l++),("("===p[l]&&")"===p[l+2]||"'"===p[l]&&"'"===p[l+2])&&(u=g(p[l+1],a),f=Math.pow(10,p[l+1].length)-1,l+=3)):"/"===p[l+1]||":"===p[l+1]?(s=g(p[l],a),c=g(p[l+2],1),l+=3):"/"===p[l+3]&&" "===p[l+1]&&(o=g(p[l],a),s=g(p[l+2],a),c=g(p[l+4],1),l+=5),p.length<=l){a=n=u+(i=c*f)*o+f*s;break}default:v()}if(0===i)throw new y;d.s=a<0?-1:1,d.n=Math.abs(n),d.d=Math.abs(i)};function u(e,t,r){for(var n=1,i=function(e,t,r){for(var n=1;0<t;e=e*e%r,t>>=1)1&t&&(n=n*e%r);return n}(10,r,t),a=0;a<300;a++){if(n===i)return a;n=10*n%t,i=10*i%t}return 0}function c(e,t){if(!e)return t;if(!t)return e;for(;;){if(!(e%=t))return t;if(!(t%=e))return e}}function f(e,t){if(!(this instanceof f))return new f(e,t);n(e,t),e=f.REDUCE?c(d.d,d.n):1,this.s=d.s,this.n=d.n/e,this.d=d.d/e}f.REDUCE=1,f.prototype={s:1,n:0,d:1,abs:function(){return new f(this.n,this.d)},neg:function(){return new f(-this.s*this.n,this.d)},add:function(e,t){return n(e,t),new f(this.s*this.n*d.d+d.s*this.d*d.n,this.d*d.d)},sub:function(e,t){return n(e,t),new f(this.s*this.n*d.d-d.s*this.d*d.n,this.d*d.d)},mul:function(e,t){return n(e,t),new f(this.s*d.s*this.n*d.n,this.d*d.d)},div:function(e,t){return n(e,t),new f(this.s*d.s*this.n*d.d,this.d*d.n)},clone:function(){return new f(this)},mod:function(e,t){return isNaN(this.n)||isNaN(this.d)?new f(NaN):void 0===e?new f(this.s*this.n%this.d,1):(n(e,t),0===d.n&&0===this.d&&f(0,0),new f(this.s*(d.d*this.n)%(d.n*this.d),d.d*this.d))},gcd:function(e,t){return n(e,t),new f(c(d.n,this.n)*c(d.d,this.d),d.d*this.d)},lcm:function(e,t){return n(e,t),0===d.n&&0===this.n?new f:new f(d.n*this.n,c(d.n,this.n)*c(d.d,this.d))},ceil:function(e){return e=Math.pow(10,e||0),isNaN(this.n)||isNaN(this.d)?new f(NaN):new f(Math.ceil(e*this.s*this.n/this.d),e)},floor:function(e){return e=Math.pow(10,e||0),isNaN(this.n)||isNaN(this.d)?new f(NaN):new f(Math.floor(e*this.s*this.n/this.d),e)},round:function(e){return e=Math.pow(10,e||0),isNaN(this.n)||isNaN(this.d)?new f(NaN):new f(Math.round(e*this.s*this.n/this.d),e)},inverse:function(){return new f(this.s*this.d,this.n)},pow:function(e){return e<0?new f(Math.pow(this.s*this.d,-e),Math.pow(this.n,-e)):new f(Math.pow(this.s*this.n,e),Math.pow(this.d,e))},equals:function(e,t){return n(e,t),this.s*this.n*d.d==d.s*d.n*this.d},compare:function(e,t){n(e,t);var r=this.s*this.n*d.d-d.s*d.n*this.d;return(0<r)-(r<0)},simplify:function(e){if(isNaN(this.n)||isNaN(this.d))return this;var t=this.abs().toContinued();e=e||.001;for(var r=0;r<t.length;r++){var n=function e(t){return 1===t.length?new f(t[0]):e(t.slice(1)).inverse().add(t[0])}(t.slice(0,r+1));if(n.sub(this.abs()).abs().valueOf()<e)return n.mul(this.s)}return this},divisible:function(e,t){return n(e,t),!(!(d.n*this.d)||this.n*d.d%(d.n*this.d))},valueOf:function(){return this.s*this.n/this.d},toFraction:function(e){var t,r="",n=this.n,i=this.d;
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