UNPKG

mathjs

Version:

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser and offers an integrated solution to work with numbers, big numbers, complex numbers, units, and matrices.

mathjs.org

josdejong/mathjs

28 lines • 432 kB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
/** * 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 3.1.2 * @date 2016-03-24 * * @license * Copyright (C) 2013-2016 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 * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the * License for the specific language governing permissions and limitations under * the License. */ !function(e,t){"object"==typeof exports&&"object"==typeof module?module.exports=t():"function"==typeof define&&define.amd?define([],t):"object"==typeof exports?exports.math=t():e.math=t()}(this,function(){return function(e){function t(n){if(r[n])return r[n].exports;var i=r[n]={exports:{},id:n,loaded:!1};return e[n].call(i.exports,i,i.exports,t),i.loaded=!0,i.exports}var r={};return t.m=e,t.c=r,t.p="",t(0)}([function(e,t,r){function n(e){var t=i.create(e);return t.create=n,t["import"](r(13)),t}var i=r(1);e.exports=n()},function(e,t,r){e.exports=r(2)},function(e,t,r){var n=r(3).isFactory,i=(r(3).deepExtend,r(4)),a=r(8),o=r(10),s=r(12);t.create=function(e){function t(e){if(!n(e))throw new Error("Factory object with properties `type`, `name`, and `factory` expected");var i,a=r.indexOf(e);return-1===a?(i=e.math===!0?e.factory(c.type,f,t,c.typed,c):e.factory(c.type,f,t,c.typed),r.push(e),u.push(i)):i=u[a],i}if("function"!=typeof Object.create)throw new Error("ES5 not supported by this JavaScript engine. Please load the es5-shim and es5-sham library for compatibility.");var r=[],u=[],c=a.mixin({});c.type={},c.expression={transform:Object.create(c)},c.typed=i.create(c.type);var f={epsilon:1e-12,matrix:"Matrix",number:"number",precision:64,predictable:!1};return c["import"]=t(o),c.config=t(s),e&&c.config(e),c}},function(e,t){"use strict";t.clone=function r(e){var t=typeof e;if("number"===t||"string"===t||"boolean"===t||null===e||void 0===e)return e;if("function"==typeof e.clone)return e.clone();if(Array.isArray(e))return e.map(function(e){return r(e)});if(e instanceof Number)return new Number(e.valueOf());if(e instanceof String)return new String(e.valueOf());if(e instanceof Boolean)return new Boolean(e.valueOf());if(e instanceof Date)return new Date(e.valueOf());if(e&&e.isBigNumber===!0)return e;if(e instanceof RegExp)throw new TypeError("Cannot clone "+e);var n={};for(var i in e)e.hasOwnProperty(i)&&(n[i]=r(e[i]));return n},t.extend=function(e,t){for(var r in t)t.hasOwnProperty(r)&&(e[r]=t[r]);return e},t.deepExtend=function n(e,t){if(Array.isArray(t))throw new TypeError("Arrays are not supported by deepExtend");for(var r in t)if(t.hasOwnProperty(r))if(t[r]&&t[r].constructor===Object)void 0===e[r]&&(e[r]={}),e[r].constructor===Object?n(e[r],t[r]):e[r]=t[r];else{if(Array.isArray(t[r]))throw new TypeError("Arrays are not supported by deepExtend");e[r]=t[r]}return e},t.deepEqual=function(e,r){var n,i,a;if(Array.isArray(e)){if(!Array.isArray(r))return!1;if(e.length!=r.length)return!1;for(i=0,a=e.length;a>i;i++)if(!t.deepEqual(e[i],r[i]))return!1;return!0}if(e instanceof Object){if(Array.isArray(r)||!(r instanceof Object))return!1;for(n in e)if(!t.deepEqual(e[n],r[n]))return!1;for(n in r)if(!t.deepEqual(e[n],r[n]))return!1;return!0}return typeof e==typeof r&&e==r},t.canDefineProperty=function(){try{if(Object.defineProperty)return Object.defineProperty({},"x",{get:function(){}}),!0}catch(e){}return!1},t.lazy=function(e,r,n){if(t.canDefineProperty()){var i,a=!0;Object.defineProperty(e,r,{get:function(){return a&&(i=n(),a=!1),i},set:function(e){i=e,a=!1},configurable:!0,enumerable:!0})}else e[r]=n()},t.traverse=function(e,t){var r=e;if(t)for(var n=t.split("."),i=0;i<n.length;i++){var a=n[i];a in r||(r[a]={}),r=r[a]}return r},t.isFactory=function(e){return e&&"function"==typeof e.factory}},function(e,t,r){var n=r(5),i=r(6).digits,a=function(){return a=n.create,n};t.create=function(e){var t=a();return t.types=[{name:"number",test:function(e){return"number"==typeof e}},{name:"Complex",test:function(e){return e&&e.isComplex}},{name:"BigNumber",test:function(e){return e&&e.isBigNumber}},{name:"Fraction",test:function(e){return e&&e.isFraction}},{name:"Unit",test:function(e){return e&&e.isUnit}},{name:"string",test:function(e){return"string"==typeof e}},{name:"Array",test:Array.isArray},{name:"Matrix",test:function(e){return e&&e.isMatrix}},{name:"DenseMatrix",test:function(e){return e&&e.isDenseMatrix}},{name:"SparseMatrix",test:function(e){return e&&e.isSparseMatrix}},{name:"ImmutableDenseMatrix",test:function(e){return e&&e.isImmutableDenseMatrix}},{name:"Range",test:function(e){return e&&e.isRange}},{name:"Index",test:function(e){return e&&e.isIndex}},{name:"boolean",test:function(e){return"boolean"==typeof e}},{name:"ResultSet",test:function(e){return e&&e.isResultSet}},{name:"Help",test:function(e){return e&&e.isHelp}},{name:"function",test:function(e){return"function"==typeof e}},{name:"Date",test:function(e){return e instanceof Date}},{name:"RegExp",test:function(e){return e instanceof RegExp}},{name:"Object",test:function(e){return"object"==typeof e}},{name:"null",test:function(e){return null===e}},{name:"undefined",test:function(e){return void 0===e}}],t.conversions=[{from:"number",to:"BigNumber",convert:function(t){if(i(t)>15)throw new TypeError("Cannot implicitly convert a number with >15 significant digits to BigNumber (value: "+t+"). Use function bignumber(x) to convert to BigNumber.");return new e.BigNumber(t)}},{from:"number",to:"Complex",convert:function(t){return new e.Complex(t,0)}},{from:"number",to:"string",convert:function(e){return e+""}},{from:"BigNumber",to:"Complex",convert:function(t){return new e.Complex(t.toNumber(),0)}},{from:"Fraction",to:"Complex",convert:function(t){return new e.Complex(t.valueOf(),0)}},{from:"number",to:"Fraction",convert:function(t){if(i(t)>15)throw new TypeError("Cannot implicitly convert a number with >15 significant digits to Fraction (value: "+t+"). Use function fraction(x) to convert to Fraction.");return new e.Fraction(t)}},{from:"string",to:"number",convert:function(e){var t=Number(e);if(isNaN(t))throw new Error('Cannot convert "'+e+'" to a number');return t}},{from:"boolean",to:"number",convert:function(e){return+e}},{from:"boolean",to:"BigNumber",convert:function(t){return new e.BigNumber(+t)}},{from:"boolean",to:"Fraction",convert:function(t){return new e.Fraction(+t)}},{from:"boolean",to:"string",convert:function(e){return+e}},{from:"null",to:"number",convert:function(){return 0}},{from:"null",to:"string",convert:function(){return"null"}},{from:"null",to:"BigNumber",convert:function(){return new e.BigNumber(0)}},{from:"null",to:"Fraction",convert:function(){return new e.Fraction(0)}},{from:"Array",to:"Matrix",convert:function(t){return new e.DenseMatrix(t)}},{from:"Matrix",to:"Array",convert:function(e){return e.valueOf()}}],t}},function(e,t,r){var n,i,a;!function(r){i=[],n=r,a="function"==typeof n?n.apply(t,i):n,!(void 0!==a&&(e.exports=a))}(function(){function e(){function t(e){for(var t,r=0;r<N.types.length;r++){var n=N.types[r];if(n.name===e){t=n.test;break}}if(!t){var i;for(r=0;r<N.types.length;r++)if(n=N.types[r],n.name.toLowerCase()==e.toLowerCase()){i=n.name;break}throw new Error('Unknown type "'+e+'"'+(i?'. Did you mean "'+i+'"?':""))}return t}function r(e){for(var t="",r=0;r<e.length;r++){var n=e[r];if(""!=n.name)if(""==t)t=n.name;else if(t!=n.name){var i=new Error("Function names do not match (expected: "+t+", actual: "+n.name+")");throw i.data={actual:n.name,expected:t},i}}return t}function n(e,t,r,n,i){var a,o=m(n),s=i?i.split(","):null,u=e||"unnamed",c=s&&d(s,"any"),f={fn:e,index:r,actual:n,expected:s};a=s?t>r&&!c?"Unexpected type of argument in function "+u+" (expected: "+s.join(" or ")+", actual: "+o+", index: "+r+")":"Too few arguments in function "+u+" (expected: "+s.join(" or ")+", index: "+r+")":"Too many arguments in function "+u+" (expected: "+r+", actual: "+t+")";var l=new TypeError(a);return l.data=f,l}function i(e){this.name=e||"refs",this.categories={}}function a(e,t){if("string"==typeof e){var r=e.trim(),n="..."===r.substr(0,3);if(n&&(r=r.substr(3)),""===r)this.types=["any"];else{this.types=r.split("|");for(var i=0;i<this.types.length;i++)this.types[i]=this.types[i].trim()}}else{if(!Array.isArray(e)){if(e instanceof a)return e.clone();throw new Error("String or Array expected")}this.types=e}this.conversions=[],this.varArgs=n||t||!1,this.anyType=-1!==this.types.indexOf("any")}function o(e,t){var r;if("string"==typeof e)r=""!==e?e.split(","):[];else{if(!Array.isArray(e))throw new Error("string or Array expected");r=e}this.params=new Array(r.length);for(var n=0;n<r.length;n++){var i=new a(r[n]);if(this.params[n]=i,n===r.length-1)this.varArgs=i.varArgs;else if(i.varArgs)throw new SyntaxError('Unexpected variable arguments operator "..."')}this.fn=t}function s(e,t,r){this.path=e||[],this.param=e[e.length-1]||null,this.signature=t||null,this.childs=r||[]}function u(e){var t,r,n={},i=[];for(var a in e)if(e.hasOwnProperty(a)){var s=e[a];if(t=new o(a,s),t.ignore())continue;var u=t.expand();for(r=0;r<u.length;r++){var c=u[r],f=c.toString(),l=n[f];if(l){var p=o.compare(c,l);if(0>p)n[f]=c;else if(0===p)throw new Error('Signature "'+f+'" is defined twice')}else n[f]=c}}for(f in n)n.hasOwnProperty(f)&&i.push(n[f]);for(i.sort(function(e,t){return o.compare(e,t)}),r=0;r<i.length;r++)if(t=i[r],t.varArgs)for(var h=t.params.length-1,m=t.params[h],g=0;g<m.types.length;){if(m.conversions[g])for(var v=m.types[g],y=0;y<i.length;y++){var x=i[y],b=x.params[h];if(x!==t&&b&&d(b.types,v)&&!b.conversions[h]){m.types.splice(g,1),m.conversions.splice(g,1),g--;break}}g++}return i}function c(e){for(var t={},r=0;r<e.length;r++){var n=e[r];if(n.fn&&!n.hasConversions()){var i=n.params.join(",");t[i]=n.fn}}return t}function f(e,t){var r,n,i,o=t.length,u=[];for(r=0;r<e.length;r++)n=e[r],n.params.length!==o||i||(i=n),void 0!=n.params[o]&&u.push(n);u.sort(function(e,t){return a.compare(e.params[o],t.params[o])});var c=[];for(r=0;r<u.length;r++){n=u[r];var l=n.params[o],p=c.filter(function(e){return e.param.overlapping(l)})[0];if(p){if(p.param.varArgs)throw new Error('Conflicting types "'+p.param+'" and "'+l+'"');p.signatures.push(n)}else c.push({param:l,signatures:[n]})}var h=new Array(c.length);for(r=0;r<c.length;r++){var m=c[r];h[r]=f(m.signatures,t.concat(m.param))}return new s(t,i,h)}function l(e){for(var t=[],r=0;e>r;r++)t[r]="arg"+r;return t}function p(e,t){var r=new i,a=u(t);if(0==a.length)throw new Error("No signatures provided");var o=f(a,[]),s=[],p=e||"",m=l(h(a));s.push("function "+p+"("+m.join(", ")+") {"),s.push(' "use strict";'),s.push(" var name = '"+p+"';"),s.push(o.toCode(r," ")),s.push("}");var d=[r.toCode(),"return "+s.join("\n")].join("\n"),g=new Function(r.name,"createError",d),v=g(r,n);return v.signatures=c(a),v}function h(e){for(var t=0,r=0;r<e.length;r++){var n=e[r].params.length;n>t&&(t=n)}return t}function m(e){for(var t,r=0;r<N.types.length;r++){var n=N.types[r];if("Object"===n.name)t=n;else if(n.test(e))return n.name}return t&&t.test(e)?t.name:"unknown"}function d(e,t){return-1!==e.indexOf(t)}function g(e,t){if(!e.signatures)throw new TypeError("Function is no typed-function");var r;if("string"==typeof t){r=t.split(",");for(var n=0;n<r.length;n++)r[n]=r[n].trim()}else{if(!Array.isArray(t))throw new TypeError("String array or a comma separated string expected");r=t}var i=r.join(","),a=e.signatures[i];if(a)return a;throw new TypeError("Signature not found (signature: "+(e.name||"unnamed")+"("+r.join(", ")+"))")}function v(e,t){var r=m(e);if(t===r)return e;for(var n=0;n<N.conversions.length;n++){var i=N.conversions[n];if(i.from===r&&i.to===t)return i.convert(e)}throw new Error("Cannot convert from "+r+" to "+t)}i.prototype.add=function(e,t){var r=t||"fn";this.categories[r]||(this.categories[r]=[]);var n=this.categories[r].indexOf(e);return-1==n&&(n=this.categories[r].length,this.categories[r].push(e)),r+n},i.prototype.toCode=function(){var e=[],t=this.name+".categories",r=this.categories;for(var n in r)if(r.hasOwnProperty(n))for(var i=r[n],a=0;a<i.length;a++)e.push("var "+n+a+" = "+t+"['"+n+"']["+a+"];");return e.join("\n")},a.compare=function(e,t){if(e.anyType)return 1;if(t.anyType)return-1;if(d(e.types,"Object"))return 1;if(d(t.types,"Object"))return-1;if(e.hasConversions()){if(t.hasConversions()){var r,n,i;for(r=0;r<e.conversions.length;r++)if(void 0!==e.conversions[r]){n=e.conversions[r];break}for(r=0;r<t.conversions.length;r++)if(void 0!==t.conversions[r]){i=t.conversions[r];break}return N.conversions.indexOf(n)-N.conversions.indexOf(i)}return 1}if(t.hasConversions())return-1;var a,o;for(r=0;r<N.types.length;r++)if(N.types[r].name===e.types[0]){a=r;break}for(r=0;r<N.types.length;r++)if(N.types[r].name===t.types[0]){o=r;break}return a-o},a.prototype.overlapping=function(e){for(var t=0;t<this.types.length;t++)if(d(e.types,this.types[t]))return!0;return!1},a.prototype.clone=function(){var e=new a(this.types.slice(),this.varArgs);return e.conversions=this.conversions.slice(),e},a.prototype.hasConversions=function(){return this.conversions.length>0},a.prototype.contains=function(e){for(var t=0;t<this.types.length;t++)if(e[this.types[t]])return!0;return!1},a.prototype.toString=function(e){for(var t=[],r={},n=0;n<this.types.length;n++){var i=this.conversions[n],a=e&&i?i.to:this.types[n];a in r||(r[a]=!0,t.push(a))}return(this.varArgs?"...":"")+t.join("|")},o.prototype.clone=function(){return new o(this.params.slice(),this.fn)},o.prototype.expand=function(){function e(r,n){if(n.length<r.params.length){var i,s,u,c=r.params[n.length];if(c.varArgs){for(s=c.clone(),i=0;i<N.conversions.length;i++)if(u=N.conversions[i],!d(c.types,u.from)&&d(c.types,u.to)){var f=s.types.length;s.types[f]=u.from,s.conversions[f]=u}e(r,n.concat(s))}else{for(i=0;i<c.types.length;i++)e(r,n.concat(new a(c.types[i])));for(i=0;i<N.conversions.length;i++)u=N.conversions[i],!d(c.types,u.from)&&d(c.types,u.to)&&(s=new a(u.from),s.conversions[0]=u,e(r,n.concat(s)))}}else t.push(new o(n,r.fn))}var t=[];return e(this,[]),t},o.compare=function(e,t){if(e.params.length>t.params.length)return 1;if(e.params.length<t.params.length)return-1;var r,n=e.params.length,i=0,o=0;for(r=0;n>r;r++)e.params[r].hasConversions()&&i++,t.params[r].hasConversions()&&o++;if(i>o)return 1;if(o>i)return-1;for(r=0;r<e.params.length;r++){var s=a.compare(e.params[r],t.params[r]);if(0!==s)return s}return 0},o.prototype.hasConversions=function(){for(var e=0;e<this.params.length;e++)if(this.params[e].hasConversions())return!0;return!1},o.prototype.ignore=function(){for(var e={},t=0;t<N.ignore.length;t++)e[N.ignore[t]]=!0;for(t=0;t<this.params.length;t++)if(this.params[t].contains(e))return!0;return!1},o.prototype.toCode=function(e,t){for(var r=[],n=new Array(this.params.length),i=0;i<this.params.length;i++){var a=this.params[i],o=a.conversions[0];a.varArgs?n[i]="varArgs":o?n[i]=e.add(o.convert,"convert")+"(arg"+i+")":n[i]="arg"+i}var s=this.fn?e.add(this.fn,"signature"):void 0;return s?t+"return "+s+"("+n.join(", ")+"); // signature: "+this.params.join(", "):r.join("\n")},o.prototype.toString=function(){return this.params.join(", ")},s.prototype.toCode=function(e,r,n){var i=[];if(this.param){var a=this.path.length-1,o=this.param.conversions[0],s="// type: "+(o?o.from+" (convert to "+o.to+")":this.param);if(this.param.varArgs)if(this.param.anyType)i.push(r+"if (arguments.length > "+a+") {"),i.push(r+" var varArgs = [];"),i.push(r+" for (var i = "+a+"; i < arguments.length; i++) {"),i.push(r+" varArgs.push(arguments[i]);"),i.push(r+" }"),i.push(this.signature.toCode(e,r+" ")),i.push(r+"}");else{for(var u=function(r,n){for(var i=[],a=0;a<r.length;a++)i[a]=e.add(t(r[a]),"test")+"("+n+")";return i.join(" || ")}.bind(this),c=this.param.types,f=[],l=0;l<c.length;l++)void 0===this.param.conversions[l]&&f.push(c[l]);i.push(r+"if ("+u(c,"arg"+a)+") { "+s),i.push(r+" var varArgs = [arg"+a+"];"),i.push(r+" for (var i = "+(a+1)+"; i < arguments.length; i++) {"),i.push(r+" if ("+u(f,"arguments[i]")+") {"),i.push(r+" varArgs.push(arguments[i]);");for(var l=0;l<c.length;l++){var p=this.param.conversions[l];if(p){var h=e.add(t(c[l]),"test"),m=e.add(p.convert,"convert");i.push(r+" }"),i.push(r+" else if ("+h+"(arguments[i])) {"),i.push(r+" varArgs.push("+m+"(arguments[i]));")}}i.push(r+" } else {"),i.push(r+" throw createError(name, arguments.length, i, arguments[i], '"+f.join(",")+"');"),i.push(r+" }"),i.push(r+" }"),i.push(this.signature.toCode(e,r+" ")),i.push(r+"}")}else if(this.param.anyType)i.push(r+"// type: any"),i.push(this._innerCode(e,r,n));else{var d=this.param.types[0],h="any"!==d?e.add(t(d),"test"):null;i.push(r+"if ("+h+"(arg"+a+")) { "+s),i.push(this._innerCode(e,r+" ",n)),i.push(r+"}")}}else i.push(this._innerCode(e,r,n));return i.join("\n")},s.prototype._innerCode=function(e,t,r){var n,i=[];this.signature&&(i.push(t+"if (arguments.length === "+this.path.length+") {"),i.push(this.signature.toCode(e,t+" ")),i.push(t+"}"));var a;for(n=0;n<this.childs.length;n++)if(this.childs[n].param.anyType){a=this.childs[n];break}for(n=0;n<this.childs.length;n++)i.push(this.childs[n].toCode(e,t,a));r&&!this.param.anyType&&i.push(r.toCode(e,t,a));var o=this._exceptions(e,t);return o&&i.push(o),i.join("\n")},s.prototype._exceptions=function(e,t){var r=this.path.length;if(0===this.childs.length)return[t+"if (arguments.length > "+r+") {",t+" throw createError(name, arguments.length, "+r+", arguments["+r+"]);",t+"}"].join("\n");for(var n={},i=[],a=0;a<this.childs.length;a++){var o=this.childs[a];if(o.param)for(var s=0;s<o.param.types.length;s++){var u=o.param.types[s];u in n||o.param.conversions[s]||(n[u]=!0,i.push(u))}}return t+"throw createError(name, arguments.length, "+r+", arguments["+r+"], '"+i.join(",")+"');"};var y=[{name:"number",test:function(e){return"number"==typeof e}},{name:"string",test:function(e){return"string"==typeof e}},{name:"boolean",test:function(e){return"boolean"==typeof e}},{name:"Function",test:function(e){return"function"==typeof e}},{name:"Array",test:Array.isArray},{name:"Date",test:function(e){return e instanceof Date}},{name:"RegExp",test:function(e){return e instanceof RegExp}},{name:"Object",test:function(e){return"object"==typeof e}},{name:"null",test:function(e){return null===e}},{name:"undefined",test:function(e){return void 0===e}}],x={},b=[],w=[],N={config:x,types:y,conversions:b,ignore:w};return N=p("typed",{Object:function(e){var t=[];for(var n in e)e.hasOwnProperty(n)&&t.push(e[n]);var i=r(t);return p(i,e)},"string, Object":p,"...Function":function(e){for(var t,n=r(e),i={},a=0;a<e.length;a++){var o=e[a];if("object"!=typeof o.signatures)throw t=new TypeError("Function is no typed-function (index: "+a+")"),t.data={index:a},t;for(var s in o.signatures)if(o.signatures.hasOwnProperty(s))if(i.hasOwnProperty(s)){if(o.signatures[s]!==i[s])throw t=new Error('Signature "'+s+'" is defined twice'),t.data={signature:s},t}else i[s]=o.signatures[s]}return p(n,i)}}),N.config=x,N.types=y,N.conversions=b,N.ignore=w,N.create=e,N.find=g,N.convert=v,N.addType=function(e){if(!e||"string"!=typeof e.name||"function"!=typeof e.test)throw new TypeError("Object with properties {name: string, test: function} expected");N.types.push(e)},N.addConversion=function(e){if(!e||"string"!=typeof e.from||"string"!=typeof e.to||"function"!=typeof e.convert)throw new TypeError("Object with properties {from: string, to: string, convert: function} expected");N.conversions.push(e)},N}return e()})},function(e,t,r){"use strict";var n=r(7);t.isNumber=function(e){return"number"==typeof e},t.isInteger=function(e){return isFinite(e)?e==Math.round(e):!1},t.sign=function(e){return e>0?1:0>e?-1:0},t.format=function(e,r){if("function"==typeof r)return r(e);if(e===1/0)return"Infinity";if(e===-(1/0))return"-Infinity";if(isNaN(e))return"NaN";var n="auto",i=void 0;switch(r&&(r.notation&&(n=r.notation),t.isNumber(r)?i=r:r.precision&&(i=r.precision)),n){case"fixed":return t.toFixed(e,i);case"exponential":return t.toExponential(e,i);case"engineering":return t.toEngineering(e,i);case"auto":return t.toPrecision(e,i,r&&r.exponential).replace(/((\.\d*?)(0+))($|e)/,function(){var e=arguments[2],t=arguments[4];return"."!==e?e+t:t});default:throw new Error('Unknown notation "'+n+'". Choose "auto", "exponential", or "fixed".')}},t.toExponential=function(e,t){return new n(e).toExponential(t)},t.toEngineering=function(e,t){return new n(e).toEngineering(t)},t.toFixed=function(e,t){return new n(e).toFixed(t)},t.toPrecision=function(e,t,r){return new n(e).toPrecision(t,r)},t.digits=function(e){return e.toExponential().replace(/e.*$/,"").replace(/^0\.?0*|\./,"").length},t.DBL_EPSILON=Number.EPSILON||2.220446049250313e-16,t.nearlyEqual=function(e,r,n){if(null==n)return e==r;if(e==r)return!0;if(isNaN(e)||isNaN(r))return!1;if(isFinite(e)&&isFinite(r)){var i=Math.abs(e-r);return i<t.DBL_EPSILON?!0:i<=Math.max(Math.abs(e),Math.abs(r))*n}return!1}},function(e,t){"use strict";function r(e){var t=String(e).toLowerCase().match(/^0*?(-?)(\d+\.?\d*)(e([+-]?\d+))?$/);if(!t)throw new SyntaxError("Invalid number");var r=t[1],n=t[2],i=parseFloat(t[4]||"0"),a=n.indexOf(".");i+=-1!==a?a-1:n.length-1,this.sign=r,this.coefficients=n.replace(".","").replace(/^0*/,function(e){return i-=e.length,""}).replace(/0*$/,"").split("").map(function(e){return parseInt(e)}),0===this.coefficients.length&&(this.coefficients.push(0),i++),this.exponent=i}function n(e){for(var t=[],r=0;e>r;r++)t.push(0);return t}r.prototype.toEngineering=function(e){var t=this.roundDigits(e),r=t.exponent,i=t.coefficients,a=r%3===0?r:0>r?r-3-r%3:r-r%3,o=r>=0?r:Math.abs(a);i.length-1<o&&(i=i.concat(n(o-(i.length-1))));for(var s=Math.abs(r-a),u=1,c="";--s>=0;)u++;var f=i.slice(u).join(""),l=f.match(/[1-9]/)?"."+f:"";return c=i.slice(0,u).join("")+l,c+="e"+(r>=0?"+":"")+a.toString(),t.sign+c},r.prototype.toFixed=function(e){var t=this.roundDigits(this.exponent+1+(e||0)),r=t.coefficients,i=t.exponent+1,a=i+(e||0);return r.length<a&&(r=r.concat(n(a-r.length))),0>i&&(r=n(-i+1).concat(r),i=1),e&&r.splice(i,0,0===i?"0.":"."),this.sign+r.join("")},r.prototype.toExponential=function(e){var t=e?this.roundDigits(e):this.clone(),r=t.coefficients,i=t.exponent;r.length<e&&(r=r.concat(n(e-r.length)));var a=r.shift();return this.sign+a+(r.length>0?"."+r.join(""):"")+"e"+(i>=0?"+":"")+i},r.prototype.toPrecision=function(e,t){var r=t&&void 0!==t.lower?t.lower:.001,i=t&&void 0!==t.upper?t.upper:1e5,a=Math.abs(Math.pow(10,this.exponent));if(r>a||a>=i)return this.toExponential(e);var o=e?this.roundDigits(e):this.clone(),s=o.coefficients,u=o.exponent;s.length<e&&(s=s.concat(n(e-s.length))),s=s.concat(n(u-s.length+1+(s.length<e?e-s.length:0))),s=n(-u).concat(s);var c=u>0?u:0;return c<s.length-1&&s.splice(c+1,0,"."),this.sign+s.join("")},r.prototype.clone=function(){var e=new r("0");return e.sign=this.sign,e.coefficients=this.coefficients.slice(0),e.exponent=this.exponent,e},r.prototype.roundDigits=function(e){for(var t=this.clone(),r=t.coefficients;0>=e;)r.unshift(0),t.exponent++,e++;if(r.length>e){var n=r.splice(e,r.length-e);if(n[0]>=5){var i=e-1;for(r[i]++;10===r[i];)r.pop(),0===i&&(r.unshift(0),t.exponent++,i++),i--,r[i]++}}return t},e.exports=r},function(e,t,r){var n=r(9);t.mixin=function(e){var t=new n;return e.on=t.on.bind(t),e.off=t.off.bind(t),e.once=t.once.bind(t),e.emit=t.emit.bind(t),e}},function(e,t){function r(){}r.prototype={on:function(e,t,r){var n=this.e||(this.e={});return(n[e]||(n[e]=[])).push({fn:t,ctx:r}),this},once:function(e,t,r){function n(){i.off(e,n),t.apply(r,arguments)}var i=this;return n._=t,this.on(e,n,r)},emit:function(e){var t=[].slice.call(arguments,1),r=((this.e||(this.e={}))[e]||[]).slice(),n=0,i=r.length;for(n;i>n;n++)r[n].fn.apply(r[n].ctx,t);return this},off:function(e,t){var r=this.e||(this.e={}),n=r[e],i=[];if(n&&t)for(var a=0,o=n.length;o>a;a++)n[a].fn!==t&&n[a].fn._!==t&&i.push(n[a]);return i.length?r[e]=i:delete r[e],this}},e.exports=r},function(e,t,r){"use strict";function n(e,t,r,n,u){function c(e,t){var r=arguments.length;if(1!=r&&2!=r)throw new s("import",r,1,2);if(t||(t={}),a(e))h(e,t);else if(Array.isArray(e))e.forEach(function(e){c(e,t)});else if("object"==typeof e){for(var n in e)if(e.hasOwnProperty(n)){var i=e[n];m(i)?f(n,i,t):a(e)?h(e,t):c(i,t)}}else if(!t.silent)throw new TypeError("Factory, Object, or Array expected")}function f(e,t,r){if(r.wrap&&"function"==typeof t&&(t=p(t)),d(u[e])&&d(t))return t=r.override?n(e,t.signatures):n(u[e],t),u[e]=t,l(e,t),void u.emit("import",e,function(){return t});if(void 0===u[e]||r.override)return u[e]=t,l(e,t),void u.emit("import",e,function(){return t});if(!r.silent)throw new Error('Cannot import "'+e+'": already exists')}function l(e,t){t&&"function"==typeof t.transform&&(u.expression.transform[e]=t.transform)}function p(e){var t=function(){for(var t=[],r=0,n=arguments.length;n>r;r++){var i=arguments[r];t[r]=i&&i.valueOf()}return e.apply(u,t)};return e.transform&&(t.transform=e.transform),t}function h(e,t){if("string"==typeof e.name){var a=e.name,s=e.path?o(u,e.path):u,c=s.hasOwnProperty(a)?s[a]:void 0,f=function(){var i=r(e);if(d(c)&&d(i))return t.override||(i=n(c,i)),i;if(void 0===c||t.override)return i;if(!t.silent)throw new Error('Cannot import "'+a+'": already exists')};e.lazy!==!1?i(s,a,f):s[a]=f(),u.emit("import",a,f,e.path)}else r(e)}function m(e){return"function"==typeof e||"number"==typeof e||"string"==typeof e||"boolean"==typeof e||null===e||e&&e.isUnit===!0||e&&e.isComplex===!0||e&&e.isBigNumber===!0||e&&e.isFraction===!0||e&&e.isMatrix===!0||e&&Array.isArray(e)===!0}function d(e){return"function"==typeof e&&"object"==typeof e.signatures}return c}var i=r(3).lazy,a=r(3).isFactory,o=r(3).traverse,s=(r(3).extend,r(11));t.math=!0,t.name="import",t.factory=n,t.lazy=!0},function(e,t){"use strict";function r(e,t,n,i){if(!(this instanceof r))throw new SyntaxError("Constructor must be called with the new operator");this.fn=e,this.count=t,this.min=n,this.max=i,this.message="Wrong number of arguments in function "+e+" ("+t+" provided, "+n+(void 0!=i?"-"+i:"")+" expected)",this.stack=(new Error).stack}r.prototype=new Error,r.prototype.constructor=Error,r.prototype.name="ArgumentsError",r.prototype.isArgumentsError=!0,e.exports=r},function(e,t,r){"use strict";function n(e,t,r,n,i){function a(e){if(e){var r=s.clone(t);o(e,"matrix",u),o(e,"number",c),s.deepExtend(t,e);var n=s.clone(t);return i.emit("config",n,r),n}return s.clone(t)}var u=["Matrix","Array"],c=["number","BigNumber","Fraction"];return a.MATRIX=u,a.NUMBER=c,a}function i(e,t){return-1!==e.indexOf(t)}function a(e,t){return e.map(function(e){return e.toLowerCase()}).indexOf(t.toLowerCase())}function o(e,t,r){if(void 0!==e[t]&&!i(r,e[t])){var n=a(r,e[t]);-1!==n?(console.warn('Warning: Wrong casing for configuration option "'+t+'", should be "'+r[n]+'" instead of "'+e[t]+'".'),e[t]=r[n]):console.warn('Warning: Unknown value "'+e[t]+'" for configuration option "'+t+'". Available options: '+r.map(JSON.stringify).join(", ")+".")}}var s=r(3);t.name="config",t.math=!0,t.factory=n},function(e,t,r){e.exports=[r(14),r(93),r(95),r(326),r(489),r(491)]},function(e,t,r){e.exports=[r(15),r(20),r(21),r(26),r(33),r(37),r(70),r(71),r(73),r(74)]},function(e,t,r){e.exports=[r(16),r(18)]},function(e,t,r){function n(e,t,r,n,a){var o=i.clone({precision:t.precision});return o.prototype.type="BigNumber",o.prototype.isBigNumber=!0,o.prototype.toJSON=function(){return{mathjs:"BigNumber",value:this.toString()}},o.fromJSON=function(e){return new o(e.value)},a.on("config",function(e,t){e.precision!==t.precision&&o.config({precision:e.precision})}),o}var i=r(17);t.name="BigNumber",t.path="type",t.factory=n,t.math=!0},function(e,t,r){var n;!function(i){"use strict";function a(e){var t,r,n,i=e.length-1,a="",o=e[0];if(i>0){for(a+=o,t=1;i>t;t++)n=e[t]+"",r=Re-n.length,r&&(a+=g(r)),a+=n;o=e[t],n=o+"",r=Re-n.length,r&&(a+=g(r))}else if(0===o)return"0";for(;o%10===0;)o/=10;return a+o}function o(e,t,r){if(e!==~~e||t>e||e>r)throw Error(_e+e)}function s(e,t,r,n){var i,a,o,s;for(a=e[0];a>=10;a/=10)--t;return--t<0?(t+=Re,i=0):(i=Math.ceil((t+1)/Re),t%=Re),a=Ce(10,Re-t),s=e[i]%a|0,null==n?3>t?(0==t?s=s/100|0:1==t&&(s=s/10|0),o=4>r&&99999==s||r>3&&49999==s||5e4==s||0==s):o=(4>r&&s+1==a||r>3&&s+1==a/2)&&(e[i+1]/a/100|0)==Ce(10,t-2)-1||(s==a/2||0==s)&&0==(e[i+1]/a/100|0):4>t?(0==t?s=s/1e3|0:1==t?s=s/100|0:2==t&&(s=s/10|0),o=(n||4>r)&&9999==s||!n&&r>3&&4999==s):o=((n||4>r)&&s+1==a||!n&&r>3&&s+1==a/2)&&(e[i+1]/a/1e3|0)==Ce(10,t-3)-1,o}function u(e,t,r){for(var n,i,a=[0],o=0,s=e.length;s>o;){for(i=a.length;i--;)a[i]*=t;for(a[0]+=xe.indexOf(e.charAt(o++)),n=0;n<a.length;n++)a[n]>r-1&&(void 0===a[n+1]&&(a[n+1]=0),a[n+1]+=a[n]/r|0,a[n]%=r)}return a.reverse()}function c(e,t){var r,n,i=t.d.length;32>i?(r=Math.ceil(i/3),n=Math.pow(4,-r).toString()):(r=16,n="2.3283064365386962890625e-10"),e.precision+=r,t=_(e,1,t.times(n),new e(1));for(var a=r;a--;){var o=t.times(t);t=o.times(o).minus(o).times(8).plus(1)}return e.precision-=r,t}function f(e,t,r,n){var i,a,o,s,u,c,f,l,p,h=e.constructor;e:if(null!=t){if(l=e.d,!l)return e;for(i=1,s=l[0];s>=10;s/=10)i++;if(a=t-i,0>a)a+=Re,o=t,f=l[p=0],u=f/Ce(10,i-o-1)%10|0;else if(p=Math.ceil((a+1)/Re),s=l.length,p>=s){if(!n)break e;for(;s++<=p;)l.push(0);f=u=0,i=1,a%=Re,o=a-Re+1}else{for(f=s=l[p],i=1;s>=10;s/=10)i++;a%=Re,o=a-Re+i,u=0>o?0:f/Ce(10,i-o-1)%10|0}if(n=n||0>t||void 0!==l[p+1]||(0>o?f:f%Ce(10,i-o-1)),c=4>r?(u||n)&&(0==r||r==(e.s<0?3:2)):u>5||5==u&&(4==r||n||6==r&&(a>0?o>0?f/Ce(10,i-o):0:l[p-1])%10&1||r==(e.s<0?8:7)),1>t||!l[0])return l.length=0,c?(t-=e.e+1,l[0]=Ce(10,(Re-t%Re)%Re),e.e=-t||0):l[0]=e.e=0,e;if(0==a?(l.length=p,s=1,p--):(l.length=p+1,s=Ce(10,Re-a),l[p]=o>0?(f/Ce(10,i-o)%Ce(10,o)|0)*s:0),c)for(;;){if(0==p){for(a=1,o=l[0];o>=10;o/=10)a++;for(o=l[0]+=s,s=1;o>=10;o/=10)s++;a!=s&&(e.e++,l[0]==Ie&&(l[0]=1));break}if(l[p]+=s,l[p]!=Ie)break;l[p--]=0,s=1}for(a=l.length;0===l[--a];)l.pop()}return Me&&(e.e>h.maxE?(e.d=null,e.e=NaN):e.e<h.minE&&(e.e=0,e.d=[0])),e}function l(e,t,r){if(!e.isFinite())return N(e);var n,i=e.e,o=a(e.d),s=o.length;return t?(r&&(n=r-s)>0?o=o.charAt(0)+"."+o.slice(1)+g(n):s>1&&(o=o.charAt(0)+"."+o.slice(1)),o=o+(e.e<0?"e":"e+")+e.e):0>i?(o="0."+g(-i-1)+o,r&&(n=r-s)>0&&(o+=g(n))):i>=s?(o+=g(i+1-s),r&&(n=r-i-1)>0&&(o=o+"."+g(n))):((n=i+1)<s&&(o=o.slice(0,n)+"."+o.slice(n)),r&&(n=r-s)>0&&(i+1===s&&(o+="."),o+=g(n))),o}function p(e,t){for(var r=1,n=e[0];n>=10;n/=10)r++;return r+t*Re-1}function h(e,t,r){if(t>Ue)throw Me=!0,r&&(e.precision=r),Error(Oe);return f(new e(be),t,1,!0)}function m(e,t,r){if(t>qe)throw Error(Oe);return f(new e(we),t,r,!0)}function d(e){var t=e.length-1,r=t*Re+1;if(t=e[t]){for(;t%10==0;t/=10)r--;for(t=e[0];t>=10;t/=10)r++}return r}function g(e){for(var t="";e--;)t+="0";return t}function v(e,t,r,n){var i,a=new e(1),o=Math.ceil(n/Re+4);for(Me=!1;;){if(r%2&&(a=a.times(t),C(a.d,o)&&(i=!0)),r=Te(r/2),0===r){r=a.d.length-1,i&&0===a.d[r]&&++a.d[r];break}t=t.times(t),C(t.d,o)}return Me=!0,a}function y(e){return 1&e.d[e.d.length-1]}function x(e,t,r){for(var n,i=new e(t[0]),a=0;++a<t.length;){if(n=new e(t[a]),!n.s){i=n;break}i[r](n)&&(i=n)}return i}function b(e,t){var r,n,i,o,u,c,l,p=0,h=0,m=0,d=e.constructor,g=d.rounding,v=d.precision;if(!e.d||!e.d[0]||e.e>17)return new d(e.d?e.d[0]?e.s<0?0:1/0:1:e.s?e.s<0?0:e:NaN);for(null==t?(Me=!1,l=v):l=t,c=new d(.03125);e.e>-2;)e=e.times(c),m+=5;for(n=Math.log(Ce(2,m))/Math.LN10*2+5|0,l+=n,r=o=u=new d(1),d.precision=l;;){if(o=f(o.times(e),l,1),r=r.times(++h),c=u.plus(je(o,r,l,1)),a(c.d).slice(0,l)===a(u.d).slice(0,l)){for(i=m;i--;)u=f(u.times(u),l,1);if(null!=t)return d.precision=v,u;if(!(3>p&&s(u.d,l-n,g,p)))return f(u,d.precision=v,g,Me=!0);d.precision=l+=10,r=o=c=new d(1),h=0,p++}u=c}}function w(e,t){var r,n,i,o,u,c,l,p,m,d,g,v=1,y=10,x=e,b=x.d,N=x.constructor,E=N.rounding,M=N.precision;if(x.s<0||!b||!b[0]||!x.e&&1==b[0]&&1==b.length)return new N(b&&!b[0]?-1/0:1!=x.s?NaN:b?0:x);if(null==t?(Me=!1,m=M):m=t,N.precision=m+=y,r=a(b),n=r.charAt(0),!(Math.abs(o=x.e)<15e14))return p=h(N,m+2,M).times(o+""),x=w(new N(n+"."+r.slice(1)),m-y).plus(p),N.precision=M,null==t?f(x,M,E,Me=!0):x;for(;7>n&&1!=n||1==n&&r.charAt(1)>3;)x=x.times(e),r=a(x.d),n=r.charAt(0),v++;for(o=x.e,n>1?(x=new N("0."+r),o++):x=new N(n+"."+r.slice(1)),d=x,l=u=x=je(x.minus(1),x.plus(1),m,1),g=f(x.times(x),m,1),i=3;;){if(u=f(u.times(g),m,1),p=l.plus(je(u,new N(i),m,1)),a(p.d).slice(0,m)===a(l.d).slice(0,m)){if(l=l.times(2), 0!==o&&(l=l.plus(h(N,m+2,M).times(o+""))),l=je(l,new N(v),m,1),null!=t)return N.precision=M,l;if(!s(l.d,m-y,E,c))return f(l,N.precision=M,E,Me=!0);N.precision=m+=y,p=u=x=je(d.minus(1),d.plus(1),m,1),g=f(x.times(x),m,1),i=c=1}l=p,i+=2}}function N(e){return String(e.s*e.s/0)}function E(e,t){var r,n,i;for((r=t.indexOf("."))>-1&&(t=t.replace(".","")),(n=t.search(/e/i))>0?(0>r&&(r=n),r+=+t.slice(n+1),t=t.substring(0,n)):0>r&&(r=t.length),n=0;48===t.charCodeAt(n);n++);for(i=t.length;48===t.charCodeAt(i-1);--i);if(t=t.slice(n,i)){if(i-=n,e.e=r=r-n-1,e.d=[],n=(r+1)%Re,0>r&&(n+=Re),i>n){for(n&&e.d.push(+t.slice(0,n)),i-=Re;i>n;)e.d.push(+t.slice(n,n+=Re));t=t.slice(n),n=Re-t.length}else n-=i;for(;n--;)t+="0";e.d.push(+t),Me&&(e.e>e.constructor.maxE?(e.d=null,e.e=NaN):e.e<e.constructor.minE&&(e.e=0,e.d=[0]))}else e.e=0,e.d=[0];return e}function M(e,t){var r,n,i,a,o,s,c,f,l;if("Infinity"===t||"NaN"===t)return+t||(e.s=NaN),e.e=NaN,e.d=null,e;if(ze.test(t))r=16,t=t.toLowerCase();else if(Se.test(t))r=2;else{if(!Be.test(t))throw Error(_e+t);r=8}for(a=t.search(/p/i),a>0?(c=+t.slice(a+1),t=t.substring(2,a)):t=t.slice(2),a=t.indexOf("."),o=a>=0,n=e.constructor,o&&(t=t.replace(".",""),s=t.length,a=s-a,i=v(n,new n(r),a,2*a)),f=u(t,r,Ie),l=f.length-1,a=l;0===f[a];--a)f.pop();return 0>a?new n(0*e.s):(e.e=p(f,l),e.d=f,Me=!1,o&&(e=je(e,i,4*s)),c&&(e=e.times(Math.abs(c)<54?Math.pow(2,c):Ne.pow(2,c))),Me=!0,e)}function A(e,t){var r,n=t.d.length;if(3>n)return _(e,2,t,t);r=1.4*Math.sqrt(n),r=r>16?16:0|r,t=t.times(Math.pow(5,-r)),t=_(e,2,t,t);for(var i,a=new e(5),o=new e(16),s=new e(20);r--;)i=t.times(t),t=t.times(a.plus(i.times(o.times(i).minus(s))));return t}function _(e,t,r,n,i){var a,o,s,u,c=1,f=e.precision,l=Math.ceil(f/Re);for(Me=!1,u=r.times(r),s=new e(n);;){if(o=je(s.times(u),new e(t++*t++),f,1),s=i?n.plus(o):n.minus(o),n=je(o.times(u),new e(t++*t++),f,1),o=s.plus(n),void 0!==o.d[l]){for(a=l;o.d[a]===s.d[a]&&a--;);if(-1==a)break}a=s,s=n,n=o,o=a,c++}return Me=!0,o.d.length=l+1,o}function O(e,t){var r,n=t.s<0,i=m(e,e.precision,1),a=i.times(.5);if(t=t.abs(),t.lte(a))return ge=n?4:1,t;if(r=t.divToInt(i),r.isZero())ge=n?3:2;else{if(t=t.minus(r.times(i)),t.lte(a))return ge=y(r)?n?2:3:n?4:1,t;ge=y(r)?n?1:4:n?3:2}return t.minus(i).abs()}function T(e,t,r,n){var i,a,s,c,f,p,h,m,d,g=e.constructor,v=void 0!==r;if(v?(o(r,1,ye),void 0===n?n=g.rounding:o(n,0,8)):(r=g.precision,n=g.rounding),e.isFinite()){for(h=l(e),s=h.indexOf("."),v?(i=2,16==t?r=4*r-3:8==t&&(r=3*r-2)):i=t,s>=0&&(h=h.replace(".",""),d=new g(1),d.e=h.length-s,d.d=u(l(d),10,i),d.e=d.d.length),m=u(h,10,i),a=f=m.length;0==m[--f];)m.pop();if(m[0]){if(0>s?a--:(e=new g(e),e.d=m,e.e=a,e=je(e,d,r,n,0,i),m=e.d,a=e.e,p=de),s=m[r],c=i/2,p=p||void 0!==m[r+1],p=4>n?(void 0!==s||p)&&(0===n||n===(e.s<0?3:2)):s>c||s===c&&(4===n||p||6===n&&1&m[r-1]||n===(e.s<0?8:7)),m.length=r,p)for(;++m[--r]>i-1;)m[r]=0,r||(++a,m.unshift(1));for(f=m.length;!m[f-1];--f);for(s=0,h="";f>s;s++)h+=xe.charAt(m[s]);if(v){if(f>1)if(16==t||8==t){for(s=16==t?4:3,--f;f%s;f++)h+="0";for(m=u(h,i,t),f=m.length;!m[f-1];--f);for(s=1,h="1.";f>s;s++)h+=xe.charAt(m[s])}else h=h.charAt(0)+"."+h.slice(1);h=h+(0>a?"p":"p+")+a}else if(0>a){for(;++a;)h="0"+h;h="0."+h}else if(++a>f)for(a-=f;a--;)h+="0";else f>a&&(h=h.slice(0,a)+"."+h.slice(a))}else h=v?"0p+0":"0";h=(16==t?"0x":2==t?"0b":8==t?"0o":"")+h}else h=N(e);return e.s<0?"-"+h:h}function C(e,t){return e.length>t?(e.length=t,!0):void 0}function S(e){return new this(e).abs()}function z(e){return new this(e).acos()}function B(e){return new this(e).acosh()}function k(e,t){return new this(e).plus(t)}function I(e){return new this(e).asin()}function R(e){return new this(e).asinh()}function P(e){return new this(e).atan()}function U(e){return new this(e).atanh()}function q(e,t){e=new this(e),t=new this(t);var r,n=this.precision,i=this.rounding,a=n+4;return e.s&&t.s?e.d||t.d?!t.d||e.isZero()?(r=t.s<0?m(this,n,i):new this(0),r.s=e.s):!e.d||t.isZero()?(r=m(this,a,1).times(.5),r.s=e.s):t.s<0?(this.precision=a,this.rounding=1,r=this.atan(je(e,t,a,1)),t=m(this,a,1),this.precision=n,this.rounding=i,r=e.s<0?r.minus(t):r.plus(t)):r=this.atan(je(e,t,a,1)):(r=m(this,a,1).times(t.s>0?.25:.75),r.s=e.s):r=new this(NaN),r}function L(e){return new this(e).cbrt()}function j(e){return f(e=new this(e),e.e+1,2)}function F(e){if(!e||"object"!=typeof e)throw Error(Ae+"Object expected");var t,r,n,i=["precision",1,ye,"rounding",0,8,"toExpNeg",-ve,0,"toExpPos",0,ve,"maxE",0,ve,"minE",-ve,0,"modulo",0,9];for(t=0;t<i.length;t+=3)if(void 0!==(n=e[r=i[t]])){if(!(Te(n)===n&&n>=i[t+1]&&n<=i[t+2]))throw Error(_e+r+": "+n);this[r]=n}if(e.hasOwnProperty(r="crypto"))if(void 0===(n=e[r]))this[r]=n;else{if(n!==!0&&n!==!1&&0!==n&&1!==n)throw Error(_e+r+": "+n);this[r]=!(!n||!Ee||!Ee.getRandomValues&&!Ee.randomBytes)}return this}function $(e){return new this(e).cos()}function D(e){return new this(e).cosh()}function G(e){function t(e){var r,n,i,a=this;if(!(a instanceof t))return new t(e);if(a.constructor=t,e instanceof t)return a.s=e.s,a.e=e.e,void(a.d=(e=e.d)?e.slice():e);if(i=typeof e,"number"===i){if(0===e)return a.s=0>1/e?-1:1,a.e=0,void(a.d=[0]);if(0>e?(e=-e,a.s=-1):a.s=1,e===~~e&&1e7>e){for(r=0,n=e;n>=10;n/=10)r++;return a.e=r,void(a.d=[e])}return 0*e!==0?(e||(a.s=NaN),a.e=NaN,void(a.d=null)):E(a,e.toString())}if("string"!==i)throw Error(_e+e);return 45===e.charCodeAt(0)?(e=e.slice(1),a.s=-1):a.s=1,ke.test(e)?E(a,e):M(a,e)}var r,n,i;if(t.prototype=Le,t.ROUND_UP=0,t.ROUND_DOWN=1,t.ROUND_CEIL=2,t.ROUND_FLOOR=3,t.ROUND_HALF_UP=4,t.ROUND_HALF_DOWN=5,t.ROUND_HALF_EVEN=6,t.ROUND_HALF_CEIL=7,t.ROUND_HALF_FLOOR=8,t.EUCLID=9,t.config=F,t.clone=G,t.abs=S,t.acos=z,t.acosh=B,t.add=k,t.asin=I,t.asinh=R,t.atan=P,t.atanh=U,t.atan2=q,t.cbrt=L,t.ceil=j,t.cos=$,t.cosh=D,t.div=H,t.exp=V,t.floor=Z,t.fromJSON=W,t.hypot=Y,t.ln=X,t.log=J,t.log10=K,t.log2=Q,t.max=ee,t.min=te,t.mod=re,t.mul=ne,t.pow=ie,t.random=ae,t.round=oe,t.sign=se,t.sin=ue,t.sinh=ce,t.sqrt=fe,t.sub=le,t.tan=pe,t.tanh=he,t.trunc=me,void 0===e&&(e={}),e)for(i=["precision","rounding","toExpNeg","toExpPos","maxE","minE","modulo","crypto"],r=0;r<i.length;)e.hasOwnProperty(n=i[r++])||(e[n]=this[n]);return t.config(e),t}function H(e,t){return new this(e).div(t)}function V(e){return new this(e).exp()}function Z(e){return f(e=new this(e),e.e+1,3)}function W(e){var t,r,n,i;if("string"!=typeof e||!e)throw Error(_e+e);if(n=e.length,i=xe.indexOf(e.charAt(0)),1===n)return new this(i>81?[-1/0,1/0,NaN][i-82]:i>40?-(i-41):i);if(64&i)r=16&i,t=r?(7&i)-3:(15&i)-7,n=1;else{if(2===n)return i=88*i+xe.indexOf(e.charAt(1)),new this(i>=2816?-(i-2816)-41:i+41);if(r=32&i,!(31&i))return e=u(e.slice(1),88,10).join(""),new this(r?"-"+e:e);t=15&i,n=t+1,t=1===t?xe.indexOf(e.charAt(1)):2===t?88*xe.indexOf(e.charAt(1))+xe.indexOf(e.charAt(2)):+u(e.slice(1,n),88,10).join(""),16&i&&(t=-t)}return e=u(e.slice(n),88,10).join(""),t=t-e.length+1,e=e+"e"+t,new this(r?"-"+e:e)}function Y(){var e,t,r=new this(0);for(Me=!1,e=0;e<arguments.length;)if(t=new this(arguments[e++]),t.d)r.d&&(r=r.plus(t.times(t)));else{if(t.s)return Me=!0,new this(1/0);r=t}return Me=!0,r.sqrt()}function X(e){return new this(e).ln()}function J(e,t){return new this(e).log(t)}function Q(e){return new this(e).log(2)}function K(e){return new this(e).log(10)}function ee(){return x(this,arguments,"lt")}function te(){return x(this,arguments,"gt")}function re(e,t){return new this(e).mod(t)}function ne(e,t){return new this(e).mul(t)}function ie(e,t){return new this(e).pow(t)}function ae(e){var t,r,n,i,a=0,s=new this(1),u=[];if(void 0===e?e=this.precision:o(e,1,ye),n=Math.ceil(e/Re),this.crypto===!1)for(;n>a;)u[a++]=1e7*Math.random()|0;else if(Ee&&Ee.getRandomValues)for(t=Ee.getRandomValues(new Uint32Array(n));n>a;)i=t[a],i>=429e7?t[a]=Ee.getRandomValues(new Uint32Array(1))[0]:u[a++]=i%1e7;else if(Ee&&Ee.randomBytes){for(t=Ee.randomBytes(n*=4);n>a;)i=t[a]+(t[a+1]<<8)+(t[a+2]<<16)+((127&t[a+3])<<24),i>=214e7?Ee.randomBytes(4).copy(t,a):(u.push(i%1e7),a+=4);a=n/4}else{if(this.crypto)throw Error(Ae+"crypto unavailable");for(;n>a;)u[a++]=1e7*Math.random()|0}for(n=u[--a],e%=Re,n&&e&&(i=Ce(10,Re-e),u[a]=(n/i|0)*i);0===u[a];a--)u.pop();if(0>a)r=0,u=[0];else{for(r=-1;0===u[0];r-=Re)u.shift();for(n=1,i=u[0];i>=10;i/=10)n++;Re>n&&(r-=Re-n)}return s.e=r,s.d=u,s}function oe(e){return f(e=new this(e),e.e+1,this.rounding)}function se(e){return e=new this(e),e.d?e.d[0]?e.s:0*e.s:e.s||NaN}function ue(e){return new this(e).sin()}function ce(e){return new this(e).sinh()}function fe(e){return new this(e).sqrt()}function le(e,t){return new this(e).sub(t)}function pe(e){return new this(e).tan()}function he(e){return new this(e).tanh()}function me(e){return f(e=new this(e),e.e+1,1)}var de,ge,ve=9e15,ye=1e9,xe="0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ!#$%()*+,-./:;=?@[]^_`{|}~",be="2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058",we="3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789",Ne={precision:20,rounding:4,modulo:1,toExpNeg:-7,toExpPos:21,minE:-ve,maxE:ve,crypto:void 0},Ee="undefined"!=typeof crypto?crypto:null,Me=!0,Ae="[DecimalError] ",_e=Ae+"Invalid argument: ",Oe=Ae+"Precision limit exceeded",Te=Math.floor,Ce=Math.pow,Se=/^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$/i,ze=/^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$/i,Be=/^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$/i,ke=/^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,Ie=1e7,Re=7,Pe=9007199254740991,Ue=be.length-1,qe=we.length-1,Le={};Le.absoluteValue=Le.abs=function(){var e=new this.constructor(this);return e.s<0&&(e.s=1),f(e)},Le.ceil=function(){return f(new this.constructor(this),this.e+1,2)},Le.comparedTo=Le.cmp=function(e){var t,r,n,i,a=this,o=a.d,s=(e=new a.constructor(e)).d,u=a.s,c=e.s;if(!o||!s)return u&&c?u!==c?u:o===s?0:!o^0>u?1:-1:NaN;if(!o[0]||!s[0])return o[0]?u:s[0]?-c:0;if(u!==c)return u;if(a.e!==e.e)return a.e>e.e^0>u?1:-1;for(n=o.length,i=s.length,t=0,r=i>n?n:i;r>t;++t)if(o[t]!==s[t])return o[t]>s[t]^0>u?1:-1;return n===i?0:n>i^0>u?1:-1},Le.cosine=Le.cos=function(){var e,t,r=this,n=r.constructor;return r.d?r.d[0]?(e=n.precision,t=n.rounding,n.precision=e+Math.max(r.e,r.sd())+Re,n.rounding=1,r=c(n,O(n,r)),n.precision=e,n.rounding=t,f(2==ge||3==ge?r.neg():r,e,t,!0)):new n(1):new n(NaN)},Le.cubeRoot=Le.cbrt=function(){var e,t,r,n,i,o,s,u,c,l,p=this,h=p.constructor;if(!p.isFinite()||p.isZero())return new h(p);for(Me=!1,o=p.s*Math.pow(p.s*p,1/3),o&&Math.abs(o)!=1/0?n=new h(o.toString()):(r=a(p.d),e=p.e,(o=(e-r.length+1)%3)&&(r+=1==o||-2==o?"0":"00"),o=Math.pow(r,1/3),e=Te((e+1)/3)-(e%3==(0>e?-1:2)),o==1/0?r="5e"+e:(r=o.toExponential(),r=r.slice(0,r.indexOf("e")+1)+e),n=new h(r),n.s=p.s),s=(e=h.precision)+3;;)if(u=n,c=u.times(u).times(u),l=c.plus(p),n=je(l.plus(p).times(u),l.plus(c),s+2,1),a(u.d).slice(0,s)===(r=a(n.d)).slice(0,s)){if(r=r.slice(s-3,s+1),"9999"!=r&&(i||"4999"!=r)){(!+r||!+r.slice(1)&&"5"==r.charAt(0))&&(f(n,e+1,1),t=!n.times(n).times(n).eq(p));break}if(!i&&(f(u,e+1,0),u.times(u).times(u).eq(p))){n=u;break}s+=4,i=1}return Me=!0,f(n,e,h.rounding,t)},Le.decimalPlaces=Le.dp=function(){var e,t=this.d,r=NaN;if(t){if(e=t.length-1,r=(e-Te(this.e/Re))*Re,e=t[e])for(;e%10==0;e/=10)r--;0>r&&(r=0)}return r},Le.dividedBy=Le.div=function(e){return je(this,new this.constructor(e))},Le.dividedToIntegerBy=Le.divToInt=function(e){var t=this,r=t.constructor;return f(je(t,new r(e),0,1,1),r.precision,r.rounding)},Le.equals=Le.eq=function(e){return 0===this.cmp(e)},Le.floor=function(){return f(new this.constructor(this),this.e+1,3)},Le.greaterThan=Le.gt=function(e){return this.cmp(e)>0},Le.greaterThanOrEqualTo=Le.gte=function(e){var t=this.cmp(e);return 1==t||0===t},Le.hyperbolicCosine=Le.cosh=function(){var e,t,r,n,i,a=this,o=a.constructor,s=new o(1);if(!a.isFinite())return new o(a.s?1/0:NaN);if(a.isZero())return s;r=o.precision,n=o.rounding,o.precision=r+Math.max(a.e,a.sd())+4,o.rounding=1,i=a.d.length,32>i?(e=Math.ceil(i/3),t=Math.pow(4,-e).toString()):(e=16,t="2.3283064365386962890625e-10"),a=_(o,1,a.times(t),new o(1),!0);for(var u,c=e,l=new o(8);c--;)u=a.times(a),a=s.minus(u.times(l.minus(u.times(l))));return f(a,o.precision=r,o.rounding=n,!0)},Le.hyperbolicSine=Le.sinh=function(){var e,t,r,n,i=this,a=i.constructor;if(!i.isFinite()||i.isZero())return new a(i);if(t=a.precision,r=a.rounding,a.precision=t+Math.max(i.e,i.sd())+4,a.rounding=1,n=i.d.length,3>n)i=_(a,2,i,i,!0);else{e=1.4*Math.sqrt(n),e=e>16?16:0|e,i=i.times(Math.pow(5,-e)),i=_(a,2,i,i,!0);for(var o,s=new a(5),u=new a(16),c=new a(20);e--;)o=i.times(i),i=i.times(s.plus(o.times(u.times(o).plus(c))))}return a.precision=t,a.rounding=r,f(i,t,r,!0)},Le.hyperbolicTangent=Le.tanh=function(){var e,t,r=this,n=r.constructor;return r.isFinite()?r.isZero()?new n(r):(e=n.precision,t=n.rounding,n.precision=e+7,n.rounding=1,je(r.sinh(),r.cosh(),n.precision=e,n.rounding=t)):new n(r.s)},Le.inverseCosine=Le.acos=function(){var e,t=this,r=t.constructor,n=t.abs().cmp(1),i=r.precision,a=r.rounding;return-1!==n?0===n?t.isNeg()?m(r,i,a):new r(0):new r(NaN):t.isZero()?m(r,i+4,a).times(.5):(r.precision=i+6,r.rounding=1,t=t.asin(),e=m(r,i+4,a).times(.5),r.precision=i,r.rounding=a,e.minus(t))},Le.inverseHyperbolicCosine=Le.acosh=function(){var e,t,r=this,n=r.constructor;return r.lte(1)?new n(r.eq(1)?0:NaN):r.isFinite()?(e=n.precision,t=n.rounding,n.precision=e+Math.max(Math.abs(r.e),r.sd())+4,n.rounding=1,Me=!1,r=r.times(r).minus(1).sqrt().plus(r),Me=!0,n.precision=e,n.rounding=t,r.ln()):new n(r)},Le.inverseHyperbolicSine=Le.asinh=function(){var e,t,r=this,n=r.constructor;return!r.isFinite()||r.isZero()?new n(r):(e=n.precision,t=n.rounding,n.precision=e+2*Math.max(Math.abs(r.e),r.sd())+6,n.rounding=1,Me=!1,r=r.times(r).plus(1).sqrt().plus(r),Me=!0,n.precision=e,n.rounding=t,r.ln())},Le.inverseHyperbolicTangent=Le.atanh=function(){var e,t,r,n,i=this,a=i.constructor;return i.isFinite()?i.e>=0?new a(i.abs().eq(1)?i.s/0:i.isZero()?i:NaN):(e=a.precision,t=a.rounding,n=i.sd(),Math.max(n,e)<2*-i.e-1?f(new a(i),e,t,!0):(a.precision=r=n-i.e,i=je(i.plus(1),new a(1).minus(i),r+e,1),a.precision=e+4,a.rounding=1,i=i.ln(),a.precision=e,a.rounding=t,i.times(.5))):new a(NaN)},Le.inverseSine=Le.asin=function(){var e,t,r,n,i=this,a=i.constructor;return i.isZero()?new a(i):(t=i.abs().cmp(1),r=a.precision,n=a.rounding,-1!==t?0===t?(e=m(a,r+4,n).times(.5),e.s=i.s,e):new a(NaN):(a.precision=r+6,a.rounding=1,i=i.div(new a(1).minus(i.times(i)).sqrt().plus(1)).atan(),a.precision=r,a.rounding=n,i.times(2)))},Le.inverseTangent=Le.atan=function(){var e,t,r,n,i,a,o,s,u,c=this,l=c.constructor,p=l.precision,h=l.rounding;if(c.isFinite()){if(c.isZero())return new l(c);if(c.abs().eq(1)&&qe>=p+4)return o=m(l,p+4,h).times(.25),o.s=c.s,o}else{if(!c.s)return new l(NaN);if(qe>=p+4)return o=m(l,p+4,h).times(.5),o.s=c.s,o}for(l.precision=s=p+10,l.rounding=1,r=Math.min(28,s/Re+2|0),e=r;e;--e)c=c.div(c.times(c).plus(1).sqrt().plus(1));for(Me=!1,t=Math.ceil(s/Re),n=1,u=c.times(c),o=new l(c),i=c;-1!==e;)if(i=i.times(u),a=o.minus(i.div(n+=2)),i=i.times(u),o=a.plus(i.div(n+=2)),void 0!==o.d[t])for(e=t;o.d[e]===a.d[e]&&e--;);return r&&(o=o.times(2<<r-1)),Me=!0,f(o,l.precision=p,l.rounding=h,!0)},Le.isFini