diff --git a/js/technical/break_eternity.js b/js/technical/break_eternity.js index a162439..e15caff 100644 --- a/js/technical/break_eternity.js +++ b/js/technical/break_eternity.js @@ -1,62 +1,201 @@ (function (global, factory) { typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() : typeof define === 'function' && define.amd ? define(factory) : - (global = global || self, global.Decimal = factory()); -}(this, function () { 'use strict'; + (global = typeof globalThis !== 'undefined' ? globalThis : global || self, global.Decimal = factory()); +})(this, (function () { 'use strict'; - var padEnd = function (string, maxLength, fillString) { + function _classCallCheck(instance, Constructor) { + if (!(instance instanceof Constructor)) { + throw new TypeError("Cannot call a class as a function"); + } + } - if (string === null || maxLength === null) { - return string; + function _defineProperties(target, props) { + for (var i = 0; i < props.length; i++) { + var descriptor = props[i]; + descriptor.enumerable = descriptor.enumerable || false; + descriptor.configurable = true; + if ("value" in descriptor) descriptor.writable = true; + Object.defineProperty(target, descriptor.key, descriptor); + } + } + + function _createClass(Constructor, protoProps, staticProps) { + if (protoProps) _defineProperties(Constructor.prototype, protoProps); + if (staticProps) _defineProperties(Constructor, staticProps); + Object.defineProperty(Constructor, "prototype", { + writable: false + }); + return Constructor; + } + + /** + * A LRU cache intended for caching pure functions. + */ + var LRUCache = /*#__PURE__*/function () { + /** + * @param maxSize The maximum size for this cache. We recommend setting this + * to be one less than a power of 2, as most hashtables - including V8's + * Object hashtable (https://crsrc.org/c/v8/src/objects/ordered-hash-table.cc) + * - uses powers of two for hashtable sizes. It can't exactly be a power of + * two, as a .set() call could temporarily set the size of the map to be + * maxSize + 1. + */ + function LRUCache(maxSize) { + _classCallCheck(this, LRUCache); + + this.map = new Map(); // Invariant: Exactly one of the below is true before and after calling a + // LRUCache method: + // - first and last are both undefined, and map.size() is 0. + // - first and last are the same object, and map.size() is 1. + // - first and last are different objects, and map.size() is greater than 1. + + this.first = undefined; + this.last = undefined; + this.maxSize = maxSize; } - var result = String(string); - var targetLen = typeof maxLength === 'number' - ? maxLength - : parseInt(maxLength, 10); + _createClass(LRUCache, [{ + key: "size", + get: function get() { + return this.map.size; + } + /** + * Gets the specified key from the cache, or undefined if it is not in the + * cache. + * @param key The key to get. + * @returns The cached value, or undefined if key is not in the cache. + */ - if (isNaN(targetLen) || !isFinite(targetLen)) { - return result; - } + }, { + key: "get", + value: function get(key) { + var node = this.map.get(key); + + if (node === undefined) { + return undefined; + } // It is guaranteed that there is at least one item in the cache. + // Therefore, first and last are guaranteed to be a ListNode... + // but if there is only one item, they might be the same. + // Update the order of the list to make this node the first node in the + // list. + // This isn't needed if this node is already the first node in the list. - var length = result.length; - if (length >= targetLen) { - return result; - } + if (node !== this.first) { + // As this node is DIFFERENT from the first node, it is guaranteed that + // there are at least two items in the cache. + // However, this node could possibly be the last item. + if (node === this.last) { + // This node IS the last node. + this.last = node.prev; // From the invariants, there must be at least two items in the cache, + // so node - which is the original "last node" - must have a defined + // previous node. Therefore, this.last - set above - must be defined + // here. + // eslint-disable-next-line @typescript-eslint/no-non-null-assertion + this.last.next = undefined; + } else { + // This node is somewhere in the middle of the list, so there must be at + // least THREE items in the list, and this node's prev and next must be + // defined here. + // eslint-disable-next-line @typescript-eslint/no-non-null-assertion + node.prev.next = node.next; // eslint-disable-next-line @typescript-eslint/no-non-null-assertion - var filled = fillString === null ? '' : String(fillString); - if (filled === '') { - filled = ' '; - } + node.next.prev = node.prev; + } + node.next = this.first; // From the invariants, there must be at least two items in the cache, so + // this.first must be a valid ListNode. + // eslint-disable-next-line @typescript-eslint/no-non-null-assertion - var fillLen = targetLen - length; + this.first.prev = node; + this.first = node; + } - while (filled.length < fillLen) { - filled += filled; - } + return node.value; + } + /** + * Sets an entry in the cache. + * + * @param key The key of the entry. + * @param value The value of the entry. + * @throws Error, if the map already contains the key. + */ - var truncated = filled.length > fillLen ? filled.substr(0, fillLen) : filled; + }, { + key: "set", + value: function set(key, value) { + // Ensure that this.maxSize >= 1. + if (this.maxSize < 1) { + return; + } - return result + truncated; - }; + if (this.map.has(key)) { + throw new Error("Cannot update existing keys in the cache"); + } + + var node = new ListNode(key, value); // Move node to the front of the list. + + if (this.first === undefined) { + // If the first is undefined, the last is undefined too. + // Therefore, this cache has no items in it. + this.first = node; + this.last = node; + } else { + // This cache has at least one item in it. + node.next = this.first; + this.first.prev = node; + this.first = node; + } + + this.map.set(key, node); + + while (this.map.size > this.maxSize) { + // We are guaranteed that this.maxSize >= 1, + // so this.map.size is guaranteed to be >= 2, + // so this.first and this.last must be different valid ListNodes, + // and this.last.prev must also be a valid ListNode (possibly this.first). + // eslint-disable-next-line @typescript-eslint/no-non-null-assertion + var last = this.last; + this.map["delete"](last.key); + this.last = last.prev; // eslint-disable-next-line @typescript-eslint/no-non-null-assertion + + this.last.next = undefined; + } + } + }]); + + return LRUCache; + }(); + /** + * A node in a doubly linked list. + */ + + var ListNode = /*#__PURE__*/_createClass(function ListNode(key, value) { + _classCallCheck(this, ListNode); + + this.next = undefined; + this.prev = undefined; + this.key = key; + this.value = value; + }); var MAX_SIGNIFICANT_DIGITS = 17; //Maximum number of digits of precision to assume in Number var EXP_LIMIT = 9e15; //If we're ABOVE this value, increase a layer. (9e15 is close to the largest integer that can fit in a Number.) - - var LAYER_DOWN = Math.log10(9e15); //If we're BELOW this value, drop down a layer. About 15.954. - - var FIRST_NEG_LAYER = 1/9e15; //At layer 0, smaller non-zero numbers than this become layer 1 numbers with negative mag. After that the pattern continues as normal. + + var LAYER_DOWN = Math.log10(9e15); + var FIRST_NEG_LAYER = 1 / 9e15; //At layer 0, smaller non-zero numbers than this become layer 1 numbers with negative mag. After that the pattern continues as normal. var NUMBER_EXP_MAX = 308; //The largest exponent that can appear in a Number, though not all mantissas are valid here. var NUMBER_EXP_MIN = -324; //The smallest exponent that can appear in a Number, though not all mantissas are valid here. - + var MAX_ES_IN_A_ROW = 5; //For default toString behaviour, when to swap from eee... to (e^n) syntax. + var DEFAULT_FROM_STRING_CACHE_SIZE = (1 << 10) - 1; // The default size of the LRU cache used to cache Decimal.fromString. + var powerOf10 = function () { // We need this lookup table because Math.pow(10, exponent) // when exponent's absolute value is large is slightly inaccurate. @@ -72,7 +211,35 @@ return function (power) { return powersOf10[power + indexOf0InPowersOf10]; }; - }(); + }(); //tetration/slog to real height stuff + //background info and tables of values for critical functions taken here: https://github.com/Patashu/break_eternity.js/issues/22 + + + var critical_headers = [2, Math.E, 3, 4, 5, 6, 7, 8, 9, 10]; + var critical_tetr_values = [[// Base 2 (using http://myweb.astate.edu/wpaulsen/tetcalc/tetcalc.html ) + 1, 1.0891180521811202527, 1.1789767925673958433, 1.2701455431742086633, 1.3632090180450091941, 1.4587818160364217007, 1.5575237916251418333, 1.6601571006859253673, 1.7674858188369780435, 1.8804192098842727359, 2], [// Base E (using http://myweb.astate.edu/wpaulsen/tetcalc/tetcalc.html ) + 1, 1.1121114330934078681, 1.2310389249316089299, 1.3583836963111376089, 1.4960519303993531879, 1.6463542337511945810, 1.8121385357018724464, 1.9969713246183068478, 2.2053895545527544330, 2.4432574483385252544, Math.E //1.0 + ], [// Base 3 + 1, 1.1187738849693603, 1.2464963939368214, 1.38527004705667, 1.5376664685821402, 1.7068895236551784, 1.897001227148399, 2.1132403089001035, 2.362480153784171, 2.6539010333870774, 3], [// Base 4 + 1, 1.1367350847096405, 1.2889510672956703, 1.4606478703324786, 1.6570295196661111, 1.8850062585672889, 2.1539465047453485, 2.476829779693097, 2.872061932789197, 3.3664204535587183, 4], [// Base 5 + 1, 1.1494592900767588, 1.319708228183931, 1.5166291280087583, 1.748171114438024, 2.0253263297298045, 2.3636668498288547, 2.7858359149579424, 3.3257226212448145, 4.035730287722532, 5], [// Base 6 + 1, 1.159225940787673, 1.343712473580932, 1.5611293155111927, 1.8221199554561318, 2.14183924486326, 2.542468319282638, 3.0574682501653316, 3.7390572020926873, 4.6719550537360774, 6], [// Base 7 + 1, 1.1670905356972596, 1.3632807444991446, 1.5979222279405536, 1.8842640123816674, 2.2416069644878687, 2.69893426559423, 3.3012632110403577, 4.121250340630164, 5.281493033448316, 7], [// Base 8 + 1, 1.1736630594087796, 1.379783782386201, 1.6292821855668218, 1.9378971836180754, 2.3289975651071977, 2.8384347394720835, 3.5232708454565906, 4.478242031114584, 5.868592169644505, 8], [// Base 9 + 1, 1.1793017514670474, 1.394054150657457, 1.65664127441059, 1.985170999970283, 2.4069682290577457, 2.9647310119960752, 3.7278665320924946, 4.814462547283592, 6.436522247411611, 9], [// Base 10 (using http://myweb.astate.edu/wpaulsen/tetcalc/tetcalc.html ) + 1, 1.1840100246247336579, 1.4061375836156954169, 1.6802272208863963918, 2.026757028388618927, 2.4770056063449647580, 3.0805252717554819987, 3.9191964192627283911, 5.1351528408331864230, 6.9899611795347148455, 10]]; + var critical_slog_values = [[// Base 2 + -1, -0.9194161097107025, -0.8335625019330468, -0.7425599821143978, -0.6466611521029437, -0.5462617907227869, -0.4419033816638769, -0.3342645487554494, -0.224140440909962, -0.11241087890006762, 0], [// Base E + -1, -0.90603157029014, -0.80786507256596, -0.7064666939634, -0.60294836853664, -0.49849837513117, -0.39430303318768, -0.29147201034755, -0.19097820800866, -0.09361896280296, 0 //1.0 + ], [// Base 3 + -1, -0.9021579584316141, -0.8005762598234203, -0.6964780623319391, -0.5911906810998454, -0.486050182576545, -0.3823089430815083, -0.28106046722897615, -0.1831906535795894, -0.08935809204418144, 0], [// Base 4 + -1, -0.8917227442365535, -0.781258746326964, -0.6705130326902455, -0.5612813129406509, -0.4551067709033134, -0.35319256652135966, -0.2563741554088552, -0.1651412821106526, -0.0796919581982668, 0], [// Base 5 + -1, -0.8843387974366064, -0.7678744063886243, -0.6529563724510552, -0.5415870994657841, -0.4352842206588936, -0.33504449124791424, -0.24138853420685147, -0.15445285440944467, -0.07409659641336663, 0], [// Base 6 + -1, -0.8786709358426346, -0.7577735191184886, -0.6399546189952064, -0.527284921869926, -0.4211627631006314, -0.3223479611761232, -0.23107655627789858, -0.1472057700818259, -0.07035171210706326, 0], [// Base 7 + -1, -0.8740862815291583, -0.7497032990976209, -0.6297119746181752, -0.5161838335958787, -0.41036238255751956, -0.31277212146489963, -0.2233976621705518, -0.1418697367979619, -0.06762117662323441, 0], [// Base 8 + -1, -0.8702632331800649, -0.7430366914122081, -0.6213373075161548, -0.5072025698095242, -0.40171437727184167, -0.30517930701410456, -0.21736343968190863, -0.137710238299109, -0.06550774483471955, 0], [// Base 9 + -1, -0.8670016295947213, -0.7373984232432306, -0.6143173985094293, -0.49973884395492807, -0.394584953527678, -0.2989649949848695, -0.21245647317021688, -0.13434688362382652, -0.0638072667348083, 0], [// Base 10 + -1, -0.8641642839543857, -0.732534623168535, -0.6083127477059322, -0.4934049257184696, -0.3885773075899922, -0.29376029055315767, -0.2083678561173622, -0.13155653399373268, -0.062401588652553186, 0]]; var D = function D(value) { return Decimal.fromValue_noAlloc(value); @@ -84,122 +251,156 @@ var FC_NN = function FC_NN(sign, layer, mag) { return Decimal.fromComponents_noNormalize(sign, layer, mag); - }; - - var ME = function ME(mantissa, exponent) { - return Decimal.fromMantissaExponent(mantissa, exponent); - }; + }; // eslint-disable-next-line @typescript-eslint/no-unused-vars - var ME_NN = function ME_NN(mantissa, exponent) { - return Decimal.fromMantissaExponent_noNormalize(mantissa, exponent); - }; - var decimalPlaces = function decimalPlaces(value, places) { var len = places + 1; var numDigits = Math.ceil(Math.log10(Math.abs(value))); var rounded = Math.round(value * Math.pow(10, len - numDigits)) * Math.pow(10, numDigits - len); return parseFloat(rounded.toFixed(Math.max(len - numDigits, 0))); }; - - var f_maglog10 = function(n) { - return Math.sign(n)*Math.log10(Math.abs(n)); - } - - //from HyperCalc source code - var f_gamma = function(n) { - if (!isFinite(n)) { return n; } - if (n < -50) - { - if (n === Math.trunc(n)) { return Number.NEGATIVE_INFINITY; } + + var f_maglog10 = function f_maglog10(n) { + return Math.sign(n) * Math.log10(Math.abs(n)); + }; //from HyperCalc source code + + + var f_gamma = function f_gamma(n) { + if (!isFinite(n)) { + return n; + } + + if (n < -50) { + if (n === Math.trunc(n)) { + return Number.NEGATIVE_INFINITY; + } + return 0; } - + var scal1 = 1; - while (n < 10) - { - scal1 = scal1*n; + + while (n < 10) { + scal1 = scal1 * n; ++n; } - + n -= 1; var l = 0.9189385332046727; //0.5*Math.log(2*Math.PI) - l = l + (n+0.5)*Math.log(n); - l = l - n; - var n2 = n*n; - var np = n; - l = l+1/(12*np); - np = np*n2; - l = l+1/(360*np); - np = np*n2; - l = l+1/(1260*np); - np = np*n2; - l = l+1/(1680*np); - np = np*n2; - l = l+1/(1188*np); - np = np*n2; - l = l+691/(360360*np); - np = np*n2; - l = l+7/(1092*np); - np = np*n2; - l = l+3617/(122400*np); - return Math.exp(l)/scal1; + l = l + (n + 0.5) * Math.log(n); + l = l - n; + var n2 = n * n; + var np = n; + l = l + 1 / (12 * np); + np = np * n2; + l = l + 1 / (360 * np); + np = np * n2; + l = l + 1 / (1260 * np); + np = np * n2; + l = l + 1 / (1680 * np); + np = np * n2; + l = l + 1 / (1188 * np); + np = np * n2; + l = l + 691 / (360360 * np); + np = np * n2; + l = l + 7 / (1092 * np); + np = np * n2; + l = l + 3617 / (122400 * np); + return Math.exp(l) / scal1; }; - - var twopi = 6.2831853071795864769252842; // 2*pi - var EXPN1 = 0.36787944117144232159553; // exp(-1) - var OMEGA = 0.56714329040978387299997; // W(1, 0) + + var OMEGA = 0.56714329040978387299997; // W(1, 0) //from https://math.stackexchange.com/a/465183 // The evaluation can become inaccurate very close to the branch point - var f_lambertw = function(z, tol = 1e-10) { + + var f_lambertw = function f_lambertw(z) { + var tol = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 1e-10; var w; var wn; - if (!Number.isFinite(z)) { return z; } - if (z === 0) - { + if (!Number.isFinite(z)) { return z; } - if (z === 1) - { + + if (z === 0) { + return z; + } + + if (z === 1) { return OMEGA; } - if (z < 10) - { + if (z < 10) { w = 0; - } - else - { - w = Math.log(z)-Math.log(Math.log(z)); + } else { + w = Math.log(z) - Math.log(Math.log(z)); } - for (var i = 0; i < 100; ++i) - { - wn = (z * Math.exp(-w) + w * w)/(w + 1); - if (Math.abs(wn - w) < tol*Math.abs(wn)) - { + for (var i = 0; i < 100; ++i) { + wn = (z * Math.exp(-w) + w * w) / (w + 1); + + if (Math.abs(wn - w) < tol * Math.abs(wn)) { return wn; - } - else - { + } else { w = wn; } } - throw Error("Iteration failed to converge: " + z); - //return Number.NaN; + throw Error("Iteration failed to converge: ".concat(z.toString())); //return Number.NaN; + }; //from https://github.com/scipy/scipy/blob/8dba340293fe20e62e173bdf2c10ae208286692f/scipy/special/lambertw.pxd + // The evaluation can become inaccurate very close to the branch point + // at ``-1/e``. In some corner cases, `lambertw` might currently + // fail to converge, or can end up on the wrong branch. + + + function d_lambertw(z) { + var tol = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 1e-10; + var w; + var ew, wewz, wn; + + if (!Number.isFinite(z.mag)) { + return z; + } + + if (z.eq(Decimal.dZero)) { + return z; + } + + if (z.eq(Decimal.dOne)) { + //Split out this case because the asymptotic series blows up + return Decimal.fromNumber(OMEGA); + } //Get an initial guess for Halley's method + + + w = Decimal.ln(z); //Halley's method; see 5.9 in [1] + + for (var i = 0; i < 100; ++i) { + ew = w.neg().exp(); + wewz = w.sub(z.mul(ew)); + wn = w.sub(wewz.div(w.add(1).sub(w.add(2).mul(wewz).div(Decimal.mul(2, w).add(2))))); + + if (Decimal.abs(wn.sub(w)).lt(Decimal.abs(wn).mul(tol))) { + return wn; + } else { + w = wn; + } + } + + throw Error("Iteration failed to converge: ".concat(z.toString())); //return Decimal.dNaN; } - - var Decimal = - /** @class */ - function () { - + /** + * The Decimal's value is simply mantissa * 10^exponent. + */ + + + var Decimal = /*#__PURE__*/function () { function Decimal(value) { - - this.sign = Number.NaN; - this.layer = Number.NaN; - this.mag = Number.NaN; + _classCallCheck(this, Decimal); + + this.sign = 0; + this.mag = 0; + this.layer = 0; if (value instanceof Decimal) { this.fromDecimal(value); @@ -207,90 +408,67 @@ this.fromNumber(value); } else if (typeof value === "string") { this.fromString(value); - } else { - this.sign = 0; - this.layer = 0; - this.mag = 0; } } - Object.defineProperty(Decimal.prototype, "m", { + _createClass(Decimal, [{ + key: "m", get: function get() { - if (this.sign === 0) - { + if (this.sign === 0) { return 0; - } - else if (this.layer === 0) - { - var exp = Math.floor(Math.log10(this.mag)); - //handle special case 5e-324 + } else if (this.layer === 0) { + var exp = Math.floor(Math.log10(this.mag)); //handle special case 5e-324 + var man; - if (this.mag === 5e-324) - { + + if (this.mag === 5e-324) { man = 5; - } - else - { + } else { man = this.mag / powerOf10(exp); } - return this.sign*man; - } - else if (this.layer === 1) - { - var residue = this.mag-Math.floor(this.mag); - return this.sign*Math.pow(10, residue); - } - else - { + + return this.sign * man; + } else if (this.layer === 1) { + var residue = this.mag - Math.floor(this.mag); + return this.sign * Math.pow(10, residue); + } else { //mantissa stops being relevant past 1e9e15 / ee15.954 return this.sign; } }, set: function set(value) { - if (this.layer <= 2) - { + if (this.layer <= 2) { this.fromMantissaExponent(value, this.e); - } - else - { + } else { //don't even pretend mantissa is meaningful this.sign = Math.sign(value); - if (this.sign === 0) { this.layer === 0; this.exponent === 0; } + + if (this.sign === 0) { + this.layer = 0; + this.exponent = 0; + } } - }, - enumerable: true, - configurable: true - }); - Object.defineProperty(Decimal.prototype, "e", { + } + }, { + key: "e", get: function get() { - if (this.sign === 0) - { + if (this.sign === 0) { return 0; - } - else if (this.layer === 0) - { + } else if (this.layer === 0) { return Math.floor(Math.log10(this.mag)); - } - else if (this.layer === 1) - { + } else if (this.layer === 1) { return Math.floor(this.mag); - } - else if (this.layer === 2) - { - return Math.floor(Math.sign(this.mag)*Math.pow(10, Math.abs(this.mag))); - } - else - { - return this.mag*Number.POSITIVE_INFINITY; + } else if (this.layer === 2) { + return Math.floor(Math.sign(this.mag) * Math.pow(10, Math.abs(this.mag))); + } else { + return this.mag * Number.POSITIVE_INFINITY; } }, set: function set(value) { this.fromMantissaExponent(this.m, value); - }, - enumerable: true, - configurable: true - }); - Object.defineProperty(Decimal.prototype, "s", { + } + }, { + key: "s", get: function get() { return this.sign; }, @@ -299,2444 +477,2790 @@ this.sign = 0; this.layer = 0; this.mag = 0; - } - else - { + } else { this.sign = value; } - }, - enumerable: true, - configurable: true - }); - - Object.defineProperty(Decimal.prototype, "mantissa", { + } // Object.defineProperty(Decimal.prototype, "mantissa", { + + }, { + key: "mantissa", get: function get() { return this.m; }, set: function set(value) { this.m = value; - }, - enumerable: true, - configurable: true - }); - - Object.defineProperty(Decimal.prototype, "exponent", { + } + }, { + key: "exponent", get: function get() { return this.e; }, set: function set(value) { this.e = value; - }, - enumerable: true, - configurable: true - }); - - Decimal.fromComponents = function (sign, layer, mag) { - return new Decimal().fromComponents(sign, layer, mag); - }; - - Decimal.fromComponents_noNormalize = function (sign, layer, mag) { - return new Decimal().fromComponents_noNormalize(sign, layer, mag); - }; - - Decimal.fromMantissaExponent = function (mantissa, exponent) { - return new Decimal().fromMantissaExponent(mantissa, exponent); - }; - - Decimal.fromMantissaExponent_noNormalize = function (mantissa, exponent) { - return new Decimal().fromMantissaExponent_noNormalize(mantissa, exponent); - }; - - Decimal.fromDecimal = function (value) { - return new Decimal().fromDecimal(value); - }; - - Decimal.fromNumber = function (value) { - return new Decimal().fromNumber(value); - }; - - Decimal.fromString = function (value) { - return new Decimal().fromString(value); - }; - - Decimal.fromValue = function (value) { - return new Decimal().fromValue(value); - }; - - Decimal.fromValue_noAlloc = function (value) { - return value instanceof Decimal ? value : new Decimal(value); - }; - - Decimal.abs = function (value) { - return D(value).abs(); - }; - - Decimal.neg = function (value) { - return D(value).neg(); - }; - - Decimal.negate = function (value) { - return D(value).neg(); - }; - - Decimal.negated = function (value) { - return D(value).neg(); - }; - - Decimal.sign = function (value) { - return D(value).sign(); - }; - - Decimal.sgn = function (value) { - return D(value).sign(); - }; - - Decimal.round = function (value) { - return D(value).round(); - }; - - Decimal.floor = function (value) { - return D(value).floor(); - }; - - Decimal.ceil = function (value) { - return D(value).ceil(); - }; - - Decimal.trunc = function (value) { - return D(value).trunc(); - }; - - Decimal.add = function (value, other) { - return D(value).add(other); - }; - - Decimal.plus = function (value, other) { - return D(value).add(other); - }; - - Decimal.sub = function (value, other) { - return D(value).sub(other); - }; - - Decimal.subtract = function (value, other) { - return D(value).sub(other); - }; - - Decimal.minus = function (value, other) { - return D(value).sub(other); - }; - - Decimal.mul = function (value, other) { - return D(value).mul(other); - }; - - Decimal.multiply = function (value, other) { - return D(value).mul(other); - }; - - Decimal.times = function (value, other) { - return D(value).mul(other); - }; - - Decimal.div = function (value, other) { - return D(value).div(other); - }; - - Decimal.divide = function (value, other) { - return D(value).div(other); - }; - - Decimal.recip = function (value) { - return D(value).recip(); - }; - - Decimal.reciprocal = function (value) { - return D(value).recip(); - }; - - Decimal.reciprocate = function (value) { - return D(value).reciprocate(); - }; - - Decimal.cmp = function (value, other) { - return D(value).cmp(other); - }; - - Decimal.cmpabs = function (value, other) { - return D(value).cmpabs(other); - }; - - Decimal.compare = function (value, other) { - return D(value).cmp(other); - }; - - Decimal.eq = function (value, other) { - return D(value).eq(other); - }; - - Decimal.equals = function (value, other) { - return D(value).eq(other); - }; - - Decimal.neq = function (value, other) { - return D(value).neq(other); - }; - - Decimal.notEquals = function (value, other) { - return D(value).notEquals(other); - }; - - Decimal.lt = function (value, other) { - return D(value).lt(other); - }; - - Decimal.lte = function (value, other) { - return D(value).lte(other); - }; - - Decimal.gt = function (value, other) { - return D(value).gt(other); - }; - - Decimal.gte = function (value, other) { - return D(value).gte(other); - }; - - Decimal.max = function (value, other) { - return D(value).max(other); - }; - - Decimal.min = function (value, other) { - return D(value).min(other); - }; - - Decimal.minabs = function (value, other) { - return D(value).minabs(other); - }; - - Decimal.maxabs = function (value, other) { - return D(value).maxabs(other); - }; - - Decimal.clamp = function(value, min, max) { - return D(value).clamp(min, max); - } - - Decimal.clampMin = function(value, min) { - return D(value).clampMin(min); - } - - Decimal.clampMax = function(value, max) { - return D(value).clampMax(max); - } - - Decimal.cmp_tolerance = function (value, other, tolerance) { - return D(value).cmp_tolerance(other, tolerance); - }; - - Decimal.compare_tolerance = function (value, other, tolerance) { - return D(value).cmp_tolerance(other, tolerance); - }; - - Decimal.eq_tolerance = function (value, other, tolerance) { - return D(value).eq_tolerance(other, tolerance); - }; - - Decimal.equals_tolerance = function (value, other, tolerance) { - return D(value).eq_tolerance(other, tolerance); - }; - - Decimal.neq_tolerance = function (value, other, tolerance) { - return D(value).neq_tolerance(other, tolerance); - }; - - Decimal.notEquals_tolerance = function (value, other, tolerance) { - return D(value).notEquals_tolerance(other, tolerance); - }; - - Decimal.lt_tolerance = function (value, other, tolerance) { - return D(value).lt_tolerance(other, tolerance); - }; - - Decimal.lte_tolerance = function (value, other, tolerance) { - return D(value).lte_tolerance(other, tolerance); - }; - - Decimal.gt_tolerance = function (value, other, tolerance) { - return D(value).gt_tolerance(other, tolerance); - }; - - Decimal.gte_tolerance = function (value, other, tolerance) { - return D(value).gte_tolerance(other, tolerance); - }; - - Decimal.pLog10 = function (value) { - return D(value).pLog10(); - }; - - Decimal.absLog10 = function (value) { - return D(value).absLog10(); - }; - - Decimal.log10 = function (value) { - return D(value).log10(); - }; - - Decimal.log = function (value, base) { - return D(value).log(base); - }; - - Decimal.log2 = function (value) { - return D(value).log2(); - }; - - Decimal.ln = function (value) { - return D(value).ln(); - }; - - Decimal.logarithm = function (value, base) { - return D(value).logarithm(base); - }; - - Decimal.pow = function (value, other) { - return D(value).pow(other); - }; - - Decimal.pow10 = function (value) { - return D(value).pow10(); - }; - - Decimal.root = function (value, other) { - return D(value).root(other); - }; - - Decimal.factorial = function (value, other) { - return D(value).factorial(); - }; - - Decimal.gamma = function (value, other) { - return D(value).gamma(); - }; - - Decimal.lngamma = function (value, other) { - return D(value).lngamma(); - }; - - Decimal.exp = function (value) { - return D(value).exp(); - }; - - Decimal.sqr = function (value) { - return D(value).sqr(); - }; - - Decimal.sqrt = function (value) { - return D(value).sqrt(); - }; - - Decimal.cube = function (value) { - return D(value).cube(); - }; - - Decimal.cbrt = function (value) { - return D(value).cbrt(); - }; - - Decimal.tetrate = function (value, height = 2, payload = FC_NN(1, 0, 1)) { - return D(value).tetrate(height, payload); - } - - Decimal.iteratedexp = function (value, height = 2, payload = FC_NN(1, 0, 1)) { - return D(value).iteratedexp(height, payload); - } - - Decimal.iteratedlog = function (value, base = 10, times = 1) { - return D(value).iteratedlog(base, times); - } - - Decimal.layeradd10 = function (value, diff) { - return D(value).layeradd10(diff); - } - - Decimal.layeradd = function (value, diff, base = 10) { - return D(value).layeradd(diff, base); - } - - Decimal.slog = function (value, base = 10) { - return D(value).slog(base); - } - - Decimal.lambertw = function(value) { - return D(value).lambertw(); - } - - Decimal.ssqrt = function(value) { - return D(value).ssqrt(); - } - - Decimal.pentate = function (value, height = 2, payload = FC_NN(1, 0, 1)) { - return D(value).pentate(height, payload); - } - - /** - * If you're willing to spend 'resourcesAvailable' and want to buy something - * with exponentially increasing cost each purchase (start at priceStart, - * multiply by priceRatio, already own currentOwned), how much of it can you buy? - * Adapted from Trimps source code. - */ - - - Decimal.affordGeometricSeries = function (resourcesAvailable, priceStart, priceRatio, currentOwned) { - return this.affordGeometricSeries_core(D(resourcesAvailable), D(priceStart), D(priceRatio), currentOwned); - }; - /** - * How much resource would it cost to buy (numItems) items if you already have currentOwned, - * the initial price is priceStart and it multiplies by priceRatio each purchase? - */ - - - Decimal.sumGeometricSeries = function (numItems, priceStart, priceRatio, currentOwned) { - return this.sumGeometricSeries_core(numItems, D(priceStart), D(priceRatio), currentOwned); - }; - /** - * If you're willing to spend 'resourcesAvailable' and want to buy something with additively - * increasing cost each purchase (start at priceStart, add by priceAdd, already own currentOwned), - * how much of it can you buy? - */ - - - Decimal.affordArithmeticSeries = function (resourcesAvailable, priceStart, priceAdd, currentOwned) { - return this.affordArithmeticSeries_core(D(resourcesAvailable), D(priceStart), D(priceAdd), D(currentOwned)); - }; - /** - * How much resource would it cost to buy (numItems) items if you already have currentOwned, - * the initial price is priceStart and it adds priceAdd each purchase? - * Adapted from http://www.mathwords.com/a/arithmetic_series.htm - */ - - - Decimal.sumArithmeticSeries = function (numItems, priceStart, priceAdd, currentOwned) { - return this.sumArithmeticSeries_core(D(numItems), D(priceStart), D(priceAdd), D(currentOwned)); - }; - /** - * When comparing two purchases that cost (resource) and increase your resource/sec by (deltaRpS), - * the lowest efficiency score is the better one to purchase. - * From Frozen Cookies: - * http://cookieclicker.wikia.com/wiki/Frozen_Cookies_(JavaScript_Add-on)#Efficiency.3F_What.27s_that.3F - */ - - - Decimal.efficiencyOfPurchase = function (cost, currentRpS, deltaRpS) { - return this.efficiencyOfPurchase_core(D(cost), D(currentRpS), D(deltaRpS)); - }; - - Decimal.randomDecimalForTesting = function (maxLayers) { - // NOTE: This doesn't follow any kind of sane random distribution, so use this for testing purposes only. - //5% of the time, return 0 - if (Math.random() * 20 < 1) { - return FC_NN(0, 0, 0); } - - var randomsign = Math.random() > 0.5 ? 1 : -1; - - //5% of the time, return 1 or -1 - if (Math.random() * 20 < 1) { - return FC_NN(randomsign, 0, 1); + }, { + key: "normalize", + value: function normalize() { + /* + PSEUDOCODE: + Whenever we are partially 0 (sign is 0 or mag and layer is 0), make it fully 0. + Whenever we are at or hit layer 0, extract sign from negative mag. + If layer === 0 and mag < FIRST_NEG_LAYER (1/9e15), shift to 'first negative layer' (add layer, log10 mag). + While abs(mag) > EXP_LIMIT (9e15), layer += 1, mag = maglog10(mag). + While abs(mag) < LAYER_DOWN (15.954) and layer > 0, layer -= 1, mag = pow(10, mag). + When we're done, all of the following should be true OR one of the numbers is not IsFinite OR layer is not IsInteger (error state): + Any 0 is totally zero (0, 0, 0). + Anything layer 0 has mag 0 OR mag > 1/9e15 and < 9e15. + Anything layer 1 or higher has abs(mag) >= 15.954 and < 9e15. + We will assume in calculations that all Decimals are either erroneous or satisfy these criteria. (Otherwise: Garbage in, garbage out.) + */ + if (this.sign === 0 || this.mag === 0 && this.layer === 0) { + this.sign = 0; + this.mag = 0; + this.layer = 0; + return this; + } + + if (this.layer === 0 && this.mag < 0) { + //extract sign from negative mag at layer 0 + this.mag = -this.mag; + this.sign = -this.sign; + } //Handle shifting from layer 0 to negative layers. + + + if (this.layer === 0 && this.mag < FIRST_NEG_LAYER) { + this.layer += 1; + this.mag = Math.log10(this.mag); + return this; + } + + var absmag = Math.abs(this.mag); + var signmag = Math.sign(this.mag); + + if (absmag >= EXP_LIMIT) { + this.layer += 1; + this.mag = signmag * Math.log10(absmag); + return this; + } else { + while (absmag < LAYER_DOWN && this.layer > 0) { + this.layer -= 1; + + if (this.layer === 0) { + this.mag = Math.pow(10, this.mag); + } else { + this.mag = signmag * Math.pow(10, absmag); + absmag = Math.abs(this.mag); + signmag = Math.sign(this.mag); + } + } + + if (this.layer === 0) { + if (this.mag < 0) { + //extract sign from negative mag at layer 0 + this.mag = -this.mag; + this.sign = -this.sign; + } else if (this.mag === 0) { + //excessive rounding can give us all zeroes + this.sign = 0; + } + } + } + + return this; } - - //pick a random layer - var layer = Math.floor(Math.random()*(maxLayers+1)); - - var randomexp = layer === 0 ? Math.random()*616-308 : Math.random()*16; - //10% of the time, make it a simple power of 10 - if (Math.random() > 0.9) { randomexp = Math.trunc(randomexp); } - var randommag = Math.pow(10, randomexp); - //10% of the time, trunc mag - if (Math.random() > 0.9) { randommag = Math.trunc(randommag); } - return FC(randomsign, layer, randommag); - }; - - Decimal.affordGeometricSeries_core = function (resourcesAvailable, priceStart, priceRatio, currentOwned) { - var actualStart = priceStart.mul(priceRatio.pow(currentOwned)); - return Decimal.floor(resourcesAvailable.div(actualStart).mul(priceRatio.sub(1)).add(1).log10().div(priceRatio.log10())); - }; - - Decimal.sumGeometricSeries_core = function (numItems, priceStart, priceRatio, currentOwned) { - return priceStart.mul(priceRatio.pow(currentOwned)).mul(Decimal.sub(1, priceRatio.pow(numItems))).div(Decimal.sub(1, priceRatio)); - }; - - Decimal.affordArithmeticSeries_core = function (resourcesAvailable, priceStart, priceAdd, currentOwned) { - // n = (-(a-d/2) + sqrt((a-d/2)^2+2dS))/d - // where a is actualStart, d is priceAdd and S is resourcesAvailable - // then floor it and you're done! - var actualStart = priceStart.add(currentOwned.mul(priceAdd)); - var b = actualStart.sub(priceAdd.div(2)); - var b2 = b.pow(2); - return b.neg().add(b2.add(priceAdd.mul(resourcesAvailable).mul(2)).sqrt()).div(priceAdd).floor(); - }; - - Decimal.sumArithmeticSeries_core = function (numItems, priceStart, priceAdd, currentOwned) { - var actualStart = priceStart.add(currentOwned.mul(priceAdd)); // (n/2)*(2*a+(n-1)*d) - - return numItems.div(2).mul(actualStart.mul(2).plus(numItems.sub(1).mul(priceAdd))); - }; - - Decimal.efficiencyOfPurchase_core = function (cost, currentRpS, deltaRpS) { - return cost.div(currentRpS).add(cost.div(deltaRpS)); - }; - - Decimal.prototype.normalize = function () { - /* - PSEUDOCODE: - Whenever we are partially 0 (sign is 0 or mag and layer is 0), make it fully 0. - Whenever we are at or hit layer 0, extract sign from negative mag. - If layer === 0 and mag < FIRST_NEG_LAYER (1/9e15), shift to 'first negative layer' (add layer, log10 mag). - While abs(mag) > EXP_LIMIT (9e15), layer += 1, mag = maglog10(mag). - While abs(mag) < LAYER_DOWN (15.954) and layer > 0, layer -= 1, mag = pow(10, mag). - - When we're done, all of the following should be true OR one of the numbers is not IsFinite OR layer is not IsInteger (error state): - Any 0 is totally zero (0, 0, 0). - Anything layer 0 has mag 0 OR mag > 1/9e15 and < 9e15. - Anything layer 1 or higher has abs(mag) >= 15.954 and < 9e15. - We will assume in calculations that all Decimals are either erroneous or satisfy these criteria. (Otherwise: Garbage in, garbage out.) - */ - if (this.sign === 0 || (this.mag === 0 && this.layer === 0)) - { - this.sign = 0; - this.mag = 0; + }, { + key: "fromComponents", + value: function fromComponents(sign, layer, mag) { + this.sign = sign; + this.layer = layer; + this.mag = mag; + this.normalize(); + return this; + } + }, { + key: "fromComponents_noNormalize", + value: function fromComponents_noNormalize(sign, layer, mag) { + this.sign = sign; + this.layer = layer; + this.mag = mag; + return this; + } + }, { + key: "fromMantissaExponent", + value: function fromMantissaExponent(mantissa, exponent) { + this.layer = 1; + this.sign = Math.sign(mantissa); + mantissa = Math.abs(mantissa); + this.mag = exponent + Math.log10(mantissa); + this.normalize(); + return this; + } + }, { + key: "fromMantissaExponent_noNormalize", + value: function fromMantissaExponent_noNormalize(mantissa, exponent) { + //The idea of 'normalizing' a break_infinity.js style Decimal doesn't really apply. So just do the same thing. + this.fromMantissaExponent(mantissa, exponent); + return this; + } + }, { + key: "fromDecimal", + value: function fromDecimal(value) { + this.sign = value.sign; + this.layer = value.layer; + this.mag = value.mag; + return this; + } + }, { + key: "fromNumber", + value: function fromNumber(value) { + this.mag = Math.abs(value); + this.sign = Math.sign(value); this.layer = 0; + this.normalize(); return this; } - - if (this.layer === 0 && this.mag < 0) - { - //extract sign from negative mag at layer 0 - this.mag = -this.mag; - this.sign = -this.sign; - } - - //Handle shifting from layer 0 to negative layers. - if (this.layer === 0 && this.mag < FIRST_NEG_LAYER) - { - this.layer += 1; - this.mag = Math.log10(this.mag); - return this; - } - - var absmag = Math.abs(this.mag); - var signmag = Math.sign(this.mag); - - if (absmag >= EXP_LIMIT) - { - this.layer += 1; - this.mag = signmag*Math.log10(absmag); - return this; - } - else - { - while (absmag < LAYER_DOWN && this.layer > 0) + }, { + key: "fromString", + value: function fromString(value) { + var originalValue = value; + var cached = Decimal.fromStringCache.get(originalValue); + + if (cached !== undefined) { + return this.fromDecimal(cached); + } + { - this.layer -= 1; - if (this.layer === 0) - { - this.mag = Math.pow(10, this.mag); + value = value.replace(",", ""); + } //Handle x^^^y format. + + + var pentationparts = value.split("^^^"); + + if (pentationparts.length === 2) { + var _base = parseFloat(pentationparts[0]); + + var _height = parseFloat(pentationparts[1]); + + var heightparts = pentationparts[1].split(";"); + var payload = 1; + + if (heightparts.length === 2) { + payload = parseFloat(heightparts[1]); + + if (!isFinite(payload)) { + payload = 1; + } } - else - { - this.mag = signmag*Math.pow(10, absmag); - absmag = Math.abs(this.mag); - signmag = Math.sign(this.mag); + + if (isFinite(_base) && isFinite(_height)) { + var result = Decimal.pentate(_base, _height, payload); + this.sign = result.sign; + this.layer = result.layer; + this.mag = result.mag; + + if (Decimal.fromStringCache.maxSize >= 1) { + Decimal.fromStringCache.set(originalValue, Decimal.fromDecimal(this)); + } + + return this; } - } - if (this.layer === 0) - { - if (this.mag < 0) - { - //extract sign from negative mag at layer 0 - this.mag = -this.mag; - this.sign = -this.sign; + } //Handle x^^y format. + + + var tetrationparts = value.split("^^"); + + if (tetrationparts.length === 2) { + var _base2 = parseFloat(tetrationparts[0]); + + var _height2 = parseFloat(tetrationparts[1]); + + var _heightparts = tetrationparts[1].split(";"); + + var _payload = 1; + + if (_heightparts.length === 2) { + _payload = parseFloat(_heightparts[1]); + + if (!isFinite(_payload)) { + _payload = 1; + } } - else if (this.mag === 0) - { - //excessive rounding can give us all zeroes - this.sign = 0; + + if (isFinite(_base2) && isFinite(_height2)) { + var _result = Decimal.tetrate(_base2, _height2, _payload); + + this.sign = _result.sign; + this.layer = _result.layer; + this.mag = _result.mag; + + if (Decimal.fromStringCache.maxSize >= 1) { + Decimal.fromStringCache.set(originalValue, Decimal.fromDecimal(this)); + } + + return this; } - } - } - - return this; - }; - - Decimal.prototype.fromComponents = function (sign, layer, mag) { - this.sign = sign; - this.layer = layer; - this.mag = mag; - - this.normalize(); - return this; - }; - - Decimal.prototype.fromComponents_noNormalize = function (sign, layer, mag) { - this.sign = sign; - this.layer = layer; - this.mag = mag; - return this; - }; - - Decimal.prototype.fromMantissaExponent = function (mantissa, exponent) { - this.layer = 1; - this.sign = Math.sign(mantissa); - mantissa = Math.abs(mantissa); - this.mag = exponent + Math.log10(mantissa); - - this.normalize(); - return this; - }; + } //Handle x^y format. - Decimal.prototype.fromMantissaExponent_noNormalize = function (mantissa, exponent) { - //The idea of 'normalizing' a break_infinity.js style Decimal doesn't really apply. So just do the same thing. - this.fromMantissaExponent(mantissa, exponent); - return this; - }; + var powparts = value.split("^"); - Decimal.prototype.fromDecimal = function (value) { - this.sign = value.sign; - this.layer = value.layer; - this.mag = value.mag; - return this; - }; + if (powparts.length === 2) { + var _base3 = parseFloat(powparts[0]); - Decimal.prototype.fromNumber = function (value) { - this.mag = Math.abs(value); - this.sign = Math.sign(value); - this.layer = 0; - this.normalize(); - return this; - }; + var _exponent = parseFloat(powparts[1]); - var IGNORE_COMMAS = true; - var COMMAS_ARE_DECIMAL_POINTS = false; - - Decimal.prototype.fromString = function (value) { - if (IGNORE_COMMAS) { value = value.replace(",", ""); } - else if (COMMAS_ARE_DECIMAL_POINTS) { value = value.replace(",", "."); } - - //Handle x^^^y format. - var pentationparts = value.split("^^^"); - if (pentationparts.length === 2) - { - var base = parseFloat(pentationparts[0]); - var height = parseFloat(pentationparts[1]); - var payload = 1; - var heightparts = pentationparts[1].split(";"); - if (heightparts.length === 2) - { - var payload = parseFloat(heightparts[1]); - if (!isFinite(payload)) { payload = 1; } - } - if (isFinite(base) && isFinite(height)) - { - var result = Decimal.pentate(base, height, payload); - this.sign = result.sign; - this.layer = result.layer; - this.mag = result.mag; - return this; - } - } - - //Handle x^^y format. - var tetrationparts = value.split("^^"); - if (tetrationparts.length === 2) - { - var base = parseFloat(tetrationparts[0]); - var height = parseFloat(tetrationparts[1]); - var heightparts = tetrationparts[1].split(";"); - if (heightparts.length === 2) - { - var payload = parseFloat(heightparts[1]); - if (!isFinite(payload)) { payload = 1; } - } - if (isFinite(base) && isFinite(height)) - { - var result = Decimal.tetrate(base, height, payload); - this.sign = result.sign; - this.layer = result.layer; - this.mag = result.mag; - return this; - } - } - - //Handle x^y format. - var powparts = value.split("^"); - if (powparts.length === 2) - { - var base = parseFloat(powparts[0]); - var exponent = parseFloat(powparts[1]); - if (isFinite(base) && isFinite(exponent)) - { - var result = Decimal.pow(base, exponent); - this.sign = result.sign; - this.layer = result.layer; - this.mag = result.mag; - return this; - } - } - - //Handle various cases involving it being a Big Number. - value = value.trim().toLowerCase(); - - //handle X PT Y format. - var ptparts = value.split("pt"); - if (ptparts.length === 2) - { - base = 10; - height = parseFloat(ptparts[0]); - ptparts[1] = ptparts[1].replace("(", ""); - ptparts[1] = ptparts[1].replace(")", ""); - var payload = parseFloat(ptparts[1]); - if (!isFinite(payload)) { payload = 1; } - if (isFinite(base) && isFinite(height)) - { - var result = Decimal.tetrate(base, height, payload); - this.sign = result.sign; - this.layer = result.layer; - this.mag = result.mag; - return this; - } - } - - //handle XpY format (it's the same thing just with p). - var ptparts = value.split("p"); - if (ptparts.length === 2) - { - base = 10; - height = parseFloat(ptparts[0]); - ptparts[1] = ptparts[1].replace("(", ""); - ptparts[1] = ptparts[1].replace(")", ""); - var payload = parseFloat(ptparts[1]); - if (!isFinite(payload)) { payload = 1; } - if (isFinite(base) && isFinite(height)) - { - var result = Decimal.tetrate(base, height, payload); - this.sign = result.sign; - this.layer = result.layer; - this.mag = result.mag; - return this; - } - } + if (isFinite(_base3) && isFinite(_exponent)) { + var _result2 = Decimal.pow(_base3, _exponent); - var parts = value.split("e"); - var ecount = parts.length-1; - - //Handle numbers that are exactly floats (0 or 1 es). - if (ecount === 0) - { - var numberAttempt = parseFloat(value); - if (isFinite(numberAttempt)) - { - return this.fromNumber(numberAttempt); - } - } - else if (ecount === 1) - { - //Very small numbers ("2e-3000" and so on) may look like valid floats but round to 0. - var numberAttempt = parseFloat(value); - if (isFinite(numberAttempt) && numberAttempt !== 0) - { - return this.fromNumber(numberAttempt); - } - } - - //Handle new (e^N)X format. - var newparts = value.split("e^"); - if (newparts.length === 2) - { - this.sign = 1; - if (newparts[0].charAt(0) == "-") - { - this.sign = -1; - } - var layerstring = ""; - for (var i = 0; i < newparts[1].length; ++i) - { - var chrcode = newparts[1].charCodeAt(i); - if ((chrcode >= 43 && chrcode <= 57) || chrcode === 101) //is "0" to "9" or "+" or "-" or "." or "e" (or "," or "/") - { - layerstring += newparts[1].charAt(i); + this.sign = _result2.sign; + this.layer = _result2.layer; + this.mag = _result2.mag; + + if (Decimal.fromStringCache.maxSize >= 1) { + Decimal.fromStringCache.set(originalValue, Decimal.fromDecimal(this)); + } + + return this; } - else //we found the end of the layer count - { - this.layer = parseFloat(layerstring); - this.mag = parseFloat(newparts[1].substr(i+1)); - this.normalize(); + } //Handle various cases involving it being a Big Number. + + + value = value.trim().toLowerCase(); //handle X PT Y format. + + var base; + var height; + var ptparts = value.split("pt"); + + if (ptparts.length === 2) { + base = 10; + height = parseFloat(ptparts[0]); + ptparts[1] = ptparts[1].replace("(", ""); + ptparts[1] = ptparts[1].replace(")", ""); + + var _payload2 = parseFloat(ptparts[1]); + + if (!isFinite(_payload2)) { + _payload2 = 1; + } + + if (isFinite(base) && isFinite(height)) { + var _result3 = Decimal.tetrate(base, height, _payload2); + + this.sign = _result3.sign; + this.layer = _result3.layer; + this.mag = _result3.mag; + + if (Decimal.fromStringCache.maxSize >= 1) { + Decimal.fromStringCache.set(originalValue, Decimal.fromDecimal(this)); + } + + return this; + } + } //handle XpY format (it's the same thing just with p). + + + ptparts = value.split("p"); + + if (ptparts.length === 2) { + base = 10; + height = parseFloat(ptparts[0]); + ptparts[1] = ptparts[1].replace("(", ""); + ptparts[1] = ptparts[1].replace(")", ""); + + var _payload3 = parseFloat(ptparts[1]); + + if (!isFinite(_payload3)) { + _payload3 = 1; + } + + if (isFinite(base) && isFinite(height)) { + var _result4 = Decimal.tetrate(base, height, _payload3); + + this.sign = _result4.sign; + this.layer = _result4.layer; + this.mag = _result4.mag; + + if (Decimal.fromStringCache.maxSize >= 1) { + Decimal.fromStringCache.set(originalValue, Decimal.fromDecimal(this)); + } + return this; } } - } - - if (ecount < 1) { this.sign = 0; this.layer = 0; this.mag = 0; return this; } - var mantissa = parseFloat(parts[0]); - if (mantissa === 0) { this.sign = 0; this.layer = 0; this.mag = 0; return this; } - var exponent = parseFloat(parts[parts.length-1]); - //handle numbers like AeBeC and AeeeeBeC - if (ecount >= 2) - { - var me = parseFloat(parts[parts.length-2]); - if (isFinite(me)) - { - exponent *= Math.sign(me); - exponent += f_maglog10(me); + + var parts = value.split("e"); + var ecount = parts.length - 1; //Handle numbers that are exactly floats (0 or 1 es). + + if (ecount === 0) { + var numberAttempt = parseFloat(value); + + if (isFinite(numberAttempt)) { + this.fromNumber(numberAttempt); + + if (Decimal.fromStringCache.size >= 1) { + Decimal.fromStringCache.set(originalValue, Decimal.fromDecimal(this)); + } + + return this; + } + } else if (ecount === 1) { + //Very small numbers ("2e-3000" and so on) may look like valid floats but round to 0. + var _numberAttempt = parseFloat(value); + + if (isFinite(_numberAttempt) && _numberAttempt !== 0) { + this.fromNumber(_numberAttempt); + + if (Decimal.fromStringCache.maxSize >= 1) { + Decimal.fromStringCache.set(originalValue, Decimal.fromDecimal(this)); + } + + return this; + } + } //Handle new (e^N)X format. + + + var newparts = value.split("e^"); + + if (newparts.length === 2) { + this.sign = 1; + + if (newparts[0].charAt(0) == "-") { + this.sign = -1; + } + + var layerstring = ""; + + for (var i = 0; i < newparts[1].length; ++i) { + var chrcode = newparts[1].charCodeAt(i); + + if (chrcode >= 43 && chrcode <= 57 || chrcode === 101) { + //is "0" to "9" or "+" or "-" or "." or "e" (or "," or "/") + layerstring += newparts[1].charAt(i); + } //we found the end of the layer count + else { + this.layer = parseFloat(layerstring); + this.mag = parseFloat(newparts[1].substr(i + 1)); + this.normalize(); + + if (Decimal.fromStringCache.maxSize >= 1) { + Decimal.fromStringCache.set(originalValue, Decimal.fromDecimal(this)); + } + + return this; + } + } } - } - - //Handle numbers written like eee... (N es) X - if (!isFinite(mantissa)) - { - this.sign = (parts[0] === "-") ? -1 : 1; - this.layer = ecount; - this.mag = exponent; - } - //Handle numbers written like XeY - else if (ecount === 1) - { - this.sign = Math.sign(mantissa); - this.layer = 1; - //Example: 2e10 is equal to 10^log10(2e10) which is equal to 10^(10+log10(2)) - this.mag = exponent + Math.log10(Math.abs(mantissa)); - } - //Handle numbers written like Xeee... (N es) Y - else - { - this.sign = Math.sign(mantissa); - this.layer = ecount; - if (ecount === 2) - { - var result = Decimal.mul(FC(1, 2, exponent), D(mantissa)); - this.sign = result.sign; - this.layer = result.layer; - this.mag = result.mag; + + if (ecount < 1) { + this.sign = 0; + this.layer = 0; + this.mag = 0; + + if (Decimal.fromStringCache.maxSize >= 1) { + Decimal.fromStringCache.set(originalValue, Decimal.fromDecimal(this)); + } + return this; } - else - { - //at eee and above, mantissa is too small to be recognizable! + + var mantissa = parseFloat(parts[0]); + + if (mantissa === 0) { + this.sign = 0; + this.layer = 0; + this.mag = 0; + + if (Decimal.fromStringCache.maxSize >= 1) { + Decimal.fromStringCache.set(originalValue, Decimal.fromDecimal(this)); + } + + return this; + } + + var exponent = parseFloat(parts[parts.length - 1]); //handle numbers like AeBeC and AeeeeBeC + + if (ecount >= 2) { + var me = parseFloat(parts[parts.length - 2]); + + if (isFinite(me)) { + exponent *= Math.sign(me); + exponent += f_maglog10(me); + } + } //Handle numbers written like eee... (N es) X + + + if (!isFinite(mantissa)) { + this.sign = parts[0] === "-" ? -1 : 1; + this.layer = ecount; this.mag = exponent; - } - } - - this.normalize(); - return this; - }; - - Decimal.prototype.fromValue = function (value) { - if (value instanceof Decimal) { - return this.fromDecimal(value); - } - - if (typeof value === "number") { - return this.fromNumber(value); - } - - if (typeof value === "string") { - return this.fromString(value); - } - - this.sign = 0; - this.layer = 0; - this.mag = 0; - return this; - }; - - Decimal.prototype.toNumber = function () { - if (!Number.isFinite(this.layer)) { return Number.NaN; } - if (this.layer === 0) - { - return this.sign*this.mag; - } - else if (this.layer === 1) - { - return this.sign*Math.pow(10, this.mag); - } - else //overflow for any normalized Decimal - { - return this.mag > 0 ? (this.sign > 0 ? Number.POSITIVE_INFINITY : Number.NEGATIVE_INFINITY) : 0; - } - }; - - Decimal.prototype.mantissaWithDecimalPlaces = function (places) { - // https://stackoverflow.com/a/37425022 - if (isNaN(this.m)) { - return Number.NaN; - } - - if (this.m === 0) { - return 0; - } - - return decimalPlaces(this.m, places); - }; - - Decimal.prototype.magnitudeWithDecimalPlaces = function (places) { - // https://stackoverflow.com/a/37425022 - if (isNaN(this.mag)) { - return Number.NaN; - } - - if (this.mag === 0) { - return 0; - } - - return decimalPlaces(this.mag, places); - }; - - Decimal.prototype.toString = function () { - if (this.layer === 0) - { - if ((this.mag < 1e21 && this.mag > 1e-7) || this.mag === 0) - { - return (this.sign*this.mag).toString(); - } - return this.m + "e" + this.e; - } - else if (this.layer === 1) - { - return this.m + "e" + this.e; - } - else - { - //layer 2+ - if (this.layer <= MAX_ES_IN_A_ROW) - { - return (this.sign === -1 ? "-" : "") + "e".repeat(this.layer) + this.mag; - } - else - { - return (this.sign === -1 ? "-" : "") + "(e^" + this.layer + ")" + this.mag; - } - } - }; - - Decimal.prototype.toExponential = function (places) { - if (this.layer === 0) - { - return (this.sign*this.mag).toExponential(places); - } - return this.toStringWithDecimalPlaces(places); - }; - - Decimal.prototype.toFixed = function (places) { - if (this.layer === 0) - { - return (this.sign*this.mag).toFixed(places); - } - return this.toStringWithDecimalPlaces(places); - }; - - Decimal.prototype.toPrecision = function (places) { - if (this.e <= -7) { - return this.toExponential(places - 1); - } - - if (places > this.e) { - return this.toFixed(places - this.exponent - 1); - } - - return this.toExponential(places - 1); - }; - - Decimal.prototype.valueOf = function () { - return this.toString(); - }; - - Decimal.prototype.toJSON = function () { - return this.toString(); - }; - - Decimal.prototype.toStringWithDecimalPlaces = function (places) { - if (this.layer === 0) - { - if ((this.mag < 1e21 && this.mag > 1e-7) || this.mag === 0) - { - return (this.sign*this.mag).toFixed(places); - } - return decimalPlaces(this.m, places) + "e" + decimalPlaces(this.e, places); - } - else if (this.layer === 1) - { - return decimalPlaces(this.m, places) + "e" + decimalPlaces(this.e, places); - } - else - { - //layer 2+ - if (this.layer <= MAX_ES_IN_A_ROW) - { - return (this.sign === -1 ? "-" : "") + "e".repeat(this.layer) + decimalPlaces(this.mag, places); - } - else - { - return (this.sign === -1 ? "-" : "") + "(e^" + this.layer + ")" + decimalPlaces(this.mag, places); - } - } - }; - - Decimal.prototype.abs = function () { - return FC_NN(this.sign === 0 ? 0 : 1, this.layer, this.mag); - }; - - Decimal.prototype.neg = function () { - return FC_NN(-this.sign, this.layer, this.mag); - }; - - Decimal.prototype.negate = function () { - return this.neg(); - }; - - Decimal.prototype.negated = function () { - return this.neg(); - }; - - Decimal.prototype.sign = function () { - return this.sign; - }; - - Decimal.prototype.sgn = function () { - return this.sign; - }; - - Decimal.prototype.round = function () { - if (this.mag < 0) - { - return Decimal.dZero; - } - if (this.layer === 0) - { - return FC(this.sign, 0, Math.round(this.mag)); - } - return this; - }; - - Decimal.prototype.floor = function () { - if (this.mag < 0) - { - return Decimal.dZero; - } - if (this.layer === 0) - { - return FC(this.sign, 0, Math.floor(this.mag)); - } - return this; - }; - - Decimal.prototype.ceil = function () { - if (this.mag < 0) - { - return Decimal.dZero; - } - if (this.layer === 0) - { - return FC(this.sign, 0, Math.ceil(this.mag)); - } - return this; - }; - - Decimal.prototype.trunc = function () { - if (this.mag < 0) - { - return Decimal.dZero; - } - if (this.layer === 0) - { - return FC(this.sign, 0, Math.trunc(this.mag)); - } - return this; - }; - - Decimal.prototype.add = function (value) { - var decimal = D(value); - - //inf/nan check - if (!Number.isFinite(this.layer)) { return this; } - if (!Number.isFinite(decimal.layer)) { return decimal; } - - //Special case - if one of the numbers is 0, return the other number. - if (this.sign === 0) { return decimal; } - if (decimal.sign === 0) { return this; } - - //Special case - Adding a number to its negation produces 0, no matter how large. - if (this.sign === -(decimal.sign) && this.layer === decimal.layer && this.mag === decimal.mag) { return FC_NN(0, 0, 0); } - - var a; - var b; - - //Special case: If one of the numbers is layer 2 or higher, just take the bigger number. - if ((this.layer >= 2 || decimal.layer >= 2)) { return this.maxabs(decimal); } - - if (Decimal.cmpabs(this, decimal) > 0) - { - a = this; - b = decimal; - } - else - { - a = decimal; - b = this; - } - - if (a.layer === 0 && b.layer === 0) { return D(a.sign*a.mag + b.sign*b.mag); } - - var layera = a.layer*Math.sign(a.mag); - var layerb = b.layer*Math.sign(b.mag); - - //If one of the numbers is 2+ layers higher than the other, just take the bigger number. - if (layera - layerb >= 2) { return a; } - - if (layera === 0 && layerb === -1) - { - if (Math.abs(b.mag-Math.log10(a.mag)) > MAX_SIGNIFICANT_DIGITS) - { - return a; - } - else - { - var magdiff = Math.pow(10, Math.log10(a.mag)-b.mag); - var mantissa = (b.sign)+(a.sign*magdiff); - return FC(Math.sign(mantissa), 1, b.mag+Math.log10(Math.abs(mantissa))); - } - } - - if (layera === 1 && layerb === 0) - { - if (Math.abs(a.mag-Math.log10(b.mag)) > MAX_SIGNIFICANT_DIGITS) - { - return a; - } - else - { - var magdiff = Math.pow(10, a.mag-Math.log10(b.mag)); - var mantissa = (b.sign)+(a.sign*magdiff); - return FC(Math.sign(mantissa), 1, Math.log10(b.mag)+Math.log10(Math.abs(mantissa))); - } - } - - if (Math.abs(a.mag-b.mag) > MAX_SIGNIFICANT_DIGITS) - { - return a; - } - else - { - var magdiff = Math.pow(10, a.mag-b.mag); - var mantissa = (b.sign)+(a.sign*magdiff); - return FC(Math.sign(mantissa), 1, b.mag+Math.log10(Math.abs(mantissa))); - } - - throw Error("Bad arguments to add: " + this + ", " + value); - }; - - Decimal.prototype.plus = function (value) { - return this.add(value); - }; - - Decimal.prototype.sub = function (value) { - return this.add(D(value).neg()); - }; - - Decimal.prototype.subtract = function (value) { - return this.sub(value); - }; - - Decimal.prototype.minus = function (value) { - return this.sub(value); - }; - - Decimal.prototype.mul = function (value) { - var decimal = D(value); - - //inf/nan check - if (!Number.isFinite(this.layer)) { return this; } - if (!Number.isFinite(decimal.layer)) { return decimal; } - - //Special case - if one of the numbers is 0, return 0. - if (this.sign === 0 || decimal.sign === 0) { return FC_NN(0, 0, 0); } - - //Special case - Multiplying a number by its own reciprocal yields +/- 1, no matter how large. - if (this.layer === decimal.layer && this.mag === -decimal.mag) { return FC_NN(this.sign*decimal.sign, 0, 1); } - - var a; - var b; - - //Which number is bigger in terms of its multiplicative distance from 1? - if ((this.layer > decimal.layer) || (this.layer == decimal.layer && Math.abs(this.mag) > Math.abs(decimal.mag))) - { - a = this; - b = decimal; - } - else - { - a = decimal; - b = this; - } - - if (a.layer === 0 && b.layer === 0) { return D(a.sign*b.sign*a.mag*b.mag); } - - //Special case: If one of the numbers is layer 3 or higher or one of the numbers is 2+ layers bigger than the other, just take the bigger number. - if (a.layer >= 3 || (a.layer - b.layer >= 2)) { return FC(a.sign*b.sign, a.layer, a.mag); } - - if (a.layer === 1 && b.layer === 0) - { - return FC(a.sign*b.sign, 1, a.mag+Math.log10(b.mag)); - } - - if (a.layer === 1 && b.layer === 1) - { - return FC(a.sign*b.sign, 1, a.mag+b.mag); - } - - if (a.layer === 2 && b.layer === 1) - { - var newmag = FC(Math.sign(a.mag), a.layer-1, Math.abs(a.mag)).add(FC(Math.sign(b.mag), b.layer-1, Math.abs(b.mag))); - return FC(a.sign*b.sign, newmag.layer+1, newmag.sign*newmag.mag); - } - - if (a.layer === 2 && b.layer === 2) - { - var newmag = FC(Math.sign(a.mag), a.layer-1, Math.abs(a.mag)).add(FC(Math.sign(b.mag), b.layer-1, Math.abs(b.mag))); - return FC(a.sign*b.sign, newmag.layer+1, newmag.sign*newmag.mag); - } - - throw Error("Bad arguments to mul: " + this + ", " + value); - }; - - Decimal.prototype.multiply = function (value) { - return this.mul(value); - }; - - Decimal.prototype.times = function (value) { - return this.mul(value); - }; - - Decimal.prototype.div = function (value) { - var decimal = D(value); - return this.mul(decimal.recip()); - }; - - Decimal.prototype.divide = function (value) { - return this.div(value); - }; - - Decimal.prototype.divideBy = function (value) { - return this.div(value); - }; - - Decimal.prototype.dividedBy = function (value) { - return this.div(value); - }; - - Decimal.prototype.recip = function () { - if (this.mag === 0) - { - return Decimal.dNaN; - } - else if (this.layer === 0) - { - return FC(this.sign, 0, 1/this.mag); - } - else - { - return FC(this.sign, this.layer, -this.mag); - } - }; - - Decimal.prototype.reciprocal = function () { - return this.recip(); - }; - - Decimal.prototype.reciprocate = function () { - return this.recip(); - }; - - /** - * -1 for less than value, 0 for equals value, 1 for greater than value - */ - Decimal.prototype.cmp = function (value) { - var decimal = D(value); - if (this.sign > decimal.sign) { return 1; } - if (this.sign < decimal.sign) { return -1; } - return this.sign*this.cmpabs(value); - }; - - Decimal.prototype.cmpabs = function (value) { - var decimal = D(value); - var layera = this.mag > 0 ? this.layer : -this.layer; - var layerb = decimal.mag > 0 ? decimal.layer : -decimal.layer; - if (layera > layerb) { return 1; } - if (layera < layerb) { return -1; } - if (this.mag > decimal.mag) { return 1; } - if (this.mag < decimal.mag) { return -1; } - return 0; - }; - - Decimal.prototype.compare = function (value) { - return this.cmp(value); - }; - - Decimal.prototype.eq = function (value) { - var decimal = D(value); - return this.sign === decimal.sign && this.layer === decimal.layer && this.mag === decimal.mag; - }; - - Decimal.prototype.equals = function (value) { - return this.eq(value); - }; - - Decimal.prototype.neq = function (value) { - return !this.eq(value); - }; - - Decimal.prototype.notEquals = function (value) { - return this.neq(value); - }; - - Decimal.prototype.lt = function (value) { - var decimal = D(value); - return this.cmp(value) === -1; - }; - - Decimal.prototype.lte = function (value) { - return !this.gt(value); - }; - - Decimal.prototype.gt = function (value) { - var decimal = D(value); - return this.cmp(value) === 1; - }; - - Decimal.prototype.gte = function (value) { - return !this.lt(value); - }; - - Decimal.prototype.max = function (value) { - var decimal = D(value); - return this.lt(decimal) ? decimal : this; - }; - - Decimal.prototype.min = function (value) { - var decimal = D(value); - return this.gt(decimal) ? decimal : this; - }; - - Decimal.prototype.maxabs = function (value) { - var decimal = D(value); - return this.cmpabs(decimal) < 0 ? decimal : this; - }; - - Decimal.prototype.minabs = function (value) { - var decimal = D(value); - return this.cmpabs(decimal) > 0 ? decimal : this; - }; - - Decimal.prototype.clamp = function(min, max) { - return this.max(min).min(max); - } - - Decimal.prototype.clampMin = function(min) { - return this.max(min); - } - - Decimal.prototype.clampMax = function(max) { - return this.min(max); - } - - Decimal.prototype.cmp_tolerance = function (value, tolerance) { - var decimal = D(value); - return this.eq_tolerance(decimal, tolerance) ? 0 : this.cmp(decimal); - }; - - Decimal.prototype.compare_tolerance = function (value, tolerance) { - return this.cmp_tolerance(value, tolerance); - }; - - /** - * Tolerance is a relative tolerance, multiplied by the greater of the magnitudes of the two arguments. - * For example, if you put in 1e-9, then any number closer to the - * larger number than (larger number)*1e-9 will be considered equal. - */ - Decimal.prototype.eq_tolerance = function (value, tolerance) { - var decimal = D(value); // https://stackoverflow.com/a/33024979 - if (tolerance == null) { tolerance = 1e-7; } - //Numbers that are too far away are never close. - if (this.sign !== decimal.sign) { return false; } - if (Math.abs(this.layer - decimal.layer) > 1) { return false; } - // return abs(a-b) <= tolerance * max(abs(a), abs(b)) - var magA = this.mag; - var magB = decimal.mag; - if (this.layer > decimal.layer) { magB = f_maglog10(magB); } - if (this.layer < decimal.layer) { magA = f_maglog10(magA); } - return Math.abs(magA-magB) <= tolerance*Math.max(Math.abs(magA), Math.abs(magB)); - }; - - Decimal.prototype.equals_tolerance = function (value, tolerance) { - return this.eq_tolerance(value, tolerance); - }; - - Decimal.prototype.neq_tolerance = function (value, tolerance) { - return !this.eq_tolerance(value, tolerance); - }; - - Decimal.prototype.notEquals_tolerance = function (value, tolerance) { - return this.neq_tolerance(value, tolerance); - }; - - Decimal.prototype.lt_tolerance = function (value, tolerance) { - var decimal = D(value); - return !this.eq_tolerance(decimal, tolerance) && this.lt(decimal); - }; - - Decimal.prototype.lte_tolerance = function (value, tolerance) { - var decimal = D(value); - return this.eq_tolerance(decimal, tolerance) || this.lt(decimal); - }; - - Decimal.prototype.gt_tolerance = function (value, tolerance) { - var decimal = D(value); - return !this.eq_tolerance(decimal, tolerance) && this.gt(decimal); - }; - - Decimal.prototype.gte_tolerance = function (value, tolerance) { - var decimal = D(value); - return this.eq_tolerance(decimal, tolerance) || this.gt(decimal); - }; - - Decimal.prototype.pLog10 = function() { - if (this.lt(Decimal.dZero)) { return Decimal.dZero; } - return this.log10(); - } - - Decimal.prototype.absLog10 = function () { - if (this.sign === 0) - { - return Decimal.dNaN; - } - else if (this.layer > 0) - { - return FC(Math.sign(this.mag), this.layer-1, Math.abs(this.mag)); - } - else - { - return FC(1, 0, Math.log10(this.mag)); - } - }; - - Decimal.prototype.log10 = function () { - if (this.sign <= 0) - { - return Decimal.dNaN; - } - else if (this.layer > 0) - { - return FC(Math.sign(this.mag), this.layer-1, Math.abs(this.mag)); - } - else - { - return FC(this.sign, 0, Math.log10(this.mag)); - } - }; - - Decimal.prototype.log = function (base) { - base = D(base); - if (this.sign <= 0) - { - return Decimal.dNaN; - } - if (base.sign <= 0) - { - return Decimal.dNaN; - } - if (base.sign === 1 && base.layer === 0 && base.mag === 1) - { - return Decimal.dNaN; - } - else if (this.layer === 0 && base.layer === 0) - { - return FC(this.sign, 0, Math.log(this.mag)/Math.log(base.mag)); - } - - return Decimal.div(this.log10(), base.log10()); - }; - - Decimal.prototype.log2 = function () { - if (this.sign <= 0) - { - return Decimal.dNaN; - } - else if (this.layer === 0) - { - return FC(this.sign, 0, Math.log2(this.mag)); - } - else if (this.layer === 1) - { - return FC(Math.sign(this.mag), 0, Math.abs(this.mag)*3.321928094887362); //log2(10) - } - else if (this.layer === 2) - { - return FC(Math.sign(this.mag), 1, Math.abs(this.mag)+0.5213902276543247); //-log10(log10(2)) - } - else - { - return FC(Math.sign(this.mag), this.layer-1, Math.abs(this.mag)); - } - }; - - Decimal.prototype.ln = function () { - if (this.sign <= 0) - { - return Decimal.dNaN; - } - else if (this.layer === 0) - { - return FC(this.sign, 0, Math.log(this.mag)); - } - else if (this.layer === 1) - { - return FC(Math.sign(this.mag), 0, Math.abs(this.mag)*2.302585092994046); //ln(10) - } - else if (this.layer === 2) - { - return FC(Math.sign(this.mag), 1, Math.abs(this.mag)+0.36221568869946325); //log10(log10(e)) - } - else - { - return FC(Math.sign(this.mag), this.layer-1, Math.abs(this.mag)); - } - }; - - Decimal.prototype.logarithm = function (base) { - return this.log(base); - }; - - Decimal.prototype.pow = function (value) { - var decimal = D(value); - var a = this; - var b = decimal; - - //special case: if a is 0, then return 0 (UNLESS b is 0, then return 1) - if (a.sign === 0) { return b.eq(0) ? FC_NN(1, 0, 1) : a; } - //special case: if a is 1, then return 1 - if (a.sign === 1 && a.layer === 0 && a.mag === 1) { return a; } - //special case: if b is 0, then return 1 - if (b.sign === 0) { return FC_NN(1, 0, 1); } - //special case: if b is 1, then return a - if (b.sign === 1 && b.layer === 0 && b.mag === 1) { return a; } - - var result = (a.absLog10().mul(b)).pow10(); - - if (this.sign === -1 && Math.abs(b.toNumber() % 2) === 1) { - return result.neg(); - } - - return result; - }; - - Decimal.prototype.pow10 = function() { - /* - There are four cases we need to consider: - 1) positive sign, positive mag (e15, ee15): +1 layer (e.g. 10^15 becomes e15, 10^e15 becomes ee15) - 2) negative sign, positive mag (-e15, -ee15): +1 layer but sign and mag sign are flipped (e.g. 10^-15 becomes e-15, 10^-e15 becomes ee-15) - 3) positive sign, negative mag (e-15, ee-15): layer 0 case would have been handled in the Math.pow check, so just return 1 - 4) negative sign, negative mag (-e-15, -ee-15): layer 0 case would have been handled in the Math.pow check, so just return 1 - */ - - if (!Number.isFinite(this.layer) || !Number.isFinite(this.mag)) { return Decimal.dNaN; } - - var a = this; - - //handle layer 0 case - if no precision is lost just use Math.pow, else promote one layer - if (a.layer === 0) - { - var newmag = Math.pow(10, a.sign*a.mag); - if (Number.isFinite(newmag) && Math.abs(newmag) > 0.1) { return FC(1, 0, newmag); } - else - { - if (a.sign === 0) { return Decimal.dOne; } - else { a = FC_NN(a.sign, a.layer+1, Math.log10(a.mag)); } - } - } - - //handle all 4 layer 1+ cases individually - if (a.sign > 0 && a.mag > 0) - { - return FC(a.sign, a.layer+1, a.mag); - } - if (a.sign < 0 && a.mag > 0) - { - return FC(-a.sign, a.layer+1, -a.mag); - } - //both the negative mag cases are identical: one +/- rounding error - return Decimal.dOne; - } - - Decimal.prototype.pow_base = function (value) { - return D(value).pow(this); - }; - - Decimal.prototype.root = function (value) { - var decimal = D(value); - return this.pow(decimal.recip()); - } - - Decimal.prototype.factorial = function () { - if (this.mag < 0) - { - return this.toNumber().add(1).gamma(); - } - else if (this.layer === 0) - { - return this.add(1).gamma(); - } - else if (this.layer === 1) - { - return Decimal.exp(Decimal.mul(this, Decimal.ln(this).sub(1))); - } - else - { - return Decimal.exp(this); - } - }; - - //from HyperCalc source code - Decimal.prototype.gamma = function () { - if (this.mag < 0) - { - return this.recip(); - } - else if (this.layer === 0) - { - if (this.lt(FC_NN(1, 0, 24))) - { - return D(f_gamma(this.sign*this.mag)); - } - - var t = this.mag - 1; - var l = 0.9189385332046727; //0.5*Math.log(2*Math.PI) - l = (l+((t+0.5)*Math.log(t))); - l = l-t; - var n2 = t*t; - var np = t; - var lm = 12*np; - var adj = 1/lm; - var l2 = l+adj; - if (l2 === l) - { - return Decimal.exp(l); - } - - l = l2; - np = np*n2; - lm = 360*np; - adj = 1/lm; - l2 = l-adj; - if (l2 === l) - { - return Decimal.exp(l); - } - - l = l2; - np = np*n2; - lm = 1260*np; - var lt = 1/lm; - l = l+lt; - np = np*n2; - lm = 1680*np; - lt = 1/lm; - l = l-lt; - return Decimal.exp(l); - } - else if (this.layer === 1) - { - return Decimal.exp(Decimal.mul(this, Decimal.ln(this).sub(1))); - } - else - { - return Decimal.exp(this); - } - }; - - Decimal.prototype.lngamma = function () { - return this.gamma().ln(); - } - - Decimal.prototype.exp = function () { - if (this.mag < 0) { return Decimal.dOne; } - if (this.layer === 0 && this.mag <= 709.7) { return D(Math.exp(this.sign*this.mag)); } - else if (this.layer === 0) { return FC(1, 1, this.sign*Math.log10(Math.E)*this.mag); } - else if (this.layer === 1) { return FC(1, 2, this.sign*(Math.log10(0.4342944819032518)+this.mag)); } - else { return FC(1, this.layer+1, this.sign*this.mag); } - }; - - Decimal.prototype.sqr = function () { - return this.pow(2); - }; - - Decimal.prototype.sqrt = function () { - if (this.layer === 0) { return D(Math.sqrt(this.sign*this.mag)); } - else if (this.layer === 1) { return FC(1, 2, Math.log10(this.mag)-0.3010299956639812); } - else - { - var result = Decimal.div(FC_NN(this.sign, this.layer-1, this.mag), FC_NN(1, 0, 2)); - result.layer += 1; - result.normalize(); - return result; - } - }; - - Decimal.prototype.cube = function () { - return this.pow(3); - }; - - Decimal.prototype.cbrt = function () { - return this.pow(1/3); - }; - - //Tetration/tetrate: The result of exponentiating 'this' to 'this' 'height' times in a row. https://en.wikipedia.org/wiki/Tetration - //If payload != 1, then this is 'iterated exponentiation', the result of exping (payload) to base (this) (height) times. https://andydude.github.io/tetration/archives/tetration2/ident.html - //Works with negative and positive real heights. - Decimal.prototype.tetrate = function(height = 2, payload = FC_NN(1, 0, 1)) { - if (height === Number.POSITIVE_INFINITY) - { - //Formula for infinite height power tower. - var negln = Decimal.ln(this).neg(); - return negln.lambertw().div(negln); - } - - if (height < 0) - { - return Decimal.iteratedlog(payload, this, -height); - } - - payload = D(payload); - var oldheight = height; - height = Math.trunc(height); - var fracheight = oldheight-height; - - if (fracheight !== 0) - { - if (payload.eq(Decimal.dOne)) - { - ++height; - payload = new Decimal(fracheight); - } - else - { - if (this.eq(10)) - { - payload = payload.layeradd10(fracheight); - } - else - { - payload = payload.layeradd(fracheight, this); + } //Handle numbers written like XeY + else if (ecount === 1) { + this.sign = Math.sign(mantissa); + this.layer = 1; //Example: 2e10 is equal to 10^log10(2e10) which is equal to 10^(10+log10(2)) + + this.mag = exponent + Math.log10(Math.abs(mantissa)); + } //Handle numbers written like Xeee... (N es) Y + else { + this.sign = Math.sign(mantissa); + this.layer = ecount; + + if (ecount === 2) { + var _result5 = Decimal.mul(FC(1, 2, exponent), D(mantissa)); + + this.sign = _result5.sign; + this.layer = _result5.layer; + this.mag = _result5.mag; + + if (Decimal.fromStringCache.maxSize >= 1) { + Decimal.fromStringCache.set(originalValue, Decimal.fromDecimal(this)); + } + + return this; + } else { + //at eee and above, mantissa is too small to be recognizable! + this.mag = exponent; } } - } - - for (var i = 0; i < height; ++i) - { - payload = this.pow(payload); - //bail if we're NaN - if (!isFinite(payload.layer) || !isFinite(payload.mag)) { return payload; } - //shortcut - if (payload.layer - this.layer > 3) { return FC_NN(payload.sign, payload.layer + (height - i - 1), payload.mag); } - //give up after 100 iterations if nothing is happening - if (i > 100) { return payload; } - } - return payload; - } - - //iteratedexp/iterated exponentiation: - all cases handled in tetrate, so just call it - Decimal.prototype.iteratedexp = function(height = 2, payload = FC_NN(1, 0, 1)) { - return this.tetrate(height, payload); - } - - //iterated log/repeated log: The result of applying log(base) 'times' times in a row. Approximately equal to subtracting (times) from the number's slog representation. Equivalent to tetrating to a negative height. - //Works with negative and positive real heights. - Decimal.prototype.iteratedlog = function(base = 10, times = 1) { - if (times < 0) - { - return Decimal.tetrate(base, -times, this); - } - - base = D(base); - var result = D(this); - var fulltimes = times; - times = Math.trunc(times); - var fraction = fulltimes - times; - if (result.layer - base.layer > 3) - { - var layerloss = Math.min(times, (result.layer - base.layer - 3)); - times -= layerloss; - result.layer -= layerloss; - } - - for (var i = 0; i < times; ++i) - { - result = result.log(base); - //bail if we're NaN - if (!isFinite(result.layer) || !isFinite(result.mag)) { return result; } - //give up after 100 iterations if nothing is happening - if (i > 100) { return result; } - } - - //handle fractional part - if (fraction > 0 && fraction < 1) - { - if (base.eq(10)) - { - result = result.layeradd10(-fraction); + + this.normalize(); + + if (Decimal.fromStringCache.maxSize >= 1) { + Decimal.fromStringCache.set(originalValue, Decimal.fromDecimal(this)); } - else - { - result = result.layeradd(-fraction, base); - } - } - - return result; - } - - //Super-logarithm, one of tetration's inverses, tells you what size power tower you'd have to tetrate base to to get number. By definition, will never be higher than 1.8e308 in break_eternity.js, since a power tower 1.8e308 numbers tall is the largest representable number. - // https://en.wikipedia.org/wiki/Super-logarithm - Decimal.prototype.slog = function(base = 10) { - if (this.mag < 0) { return Decimal.dNegOne; } - - base = D(base); - - var result = 0; - var copy = D(this); - if (copy.layer - base.layer > 3) - { - var layerloss = (copy.layer - base.layer - 3); - result += layerloss; - copy.layer -= layerloss; - } - - for (var i = 0; i < 100; ++i) - { - if (copy.lt(Decimal.dZero)) - { - copy = Decimal.pow(base, copy); - result -= 1; - } - else if (copy.lte(Decimal.dOne)) - { - return D(result + copy.toNumber() - 1); //<-- THIS IS THE CRITICAL FUNCTION - //^ Also have to change tetrate payload handling and layeradd10 if this is changed! - } - else - { - result += 1; - copy = Decimal.log(copy, base); - } - } - return D(result); - } - - //Approximations taken from the excellent paper https://web.archive.org/web/20090201164836/http://tetration.itgo.com/paper.html ! - //Not using for now unless I can figure out how to use it in all the related functions. - /*var slog_criticalfunction_1 = function(x, z) { - z = z.toNumber(); - return -1 + z; - } - - var slog_criticalfunction_2 = function(x, z) { - z = z.toNumber(); - var lnx = x.ln(); - if (lnx.layer === 0) - { - lnx = lnx.toNumber(); - return -1 + z*2*lnx/(1+lnx) - z*z*(1-lnx)/(1+lnx); - } - else - { - var term1 = lnx.mul(z*2).div(lnx.add(1)); - var term2 = Decimal.sub(1, lnx).mul(z*z).div(lnx.add(1)); - Decimal.dNegOne.add(Decimal.sub(term1, term2)); - } - } - - var slog_criticalfunction_3 = function(x, z) { - z = z.toNumber(); - var lnx = x.ln(); - var lnx2 = lnx.sqr(); - var lnx3 = lnx.cube(); - if (lnx.layer === 0 && lnx2.layer === 0 && lnx3.layer === 0) - { - lnx = lnx.toNumber(); - lnx2 = lnx2.toNumber(); - lnx3 = lnx3.toNumber(); - - var term1 = 6*z*(lnx+lnx3); - var term2 = 3*z*z*(3*lnx2-2*lnx3); - var term3 = 2*z*z*z*(1-lnx-2*lnx2+lnx3); - var top = term1+term2+term3; - var bottom = 2+4*lnx+5*lnx2+2*lnx3; - - return -1 + top/bottom; - } - else - { - var term1 = (lnx.add(lnx3)).mul(6*z); - var term2 = (lnx2.mul(3).sub(lnx3.mul(2))).mul(3*z*z); - var term3 = (Decimal.dOne.sub(lnx).sub(lnx2.mul(2)).add(lnx3)).mul(2*z*z*z); - var top = term1.add(term2).add(term3); - var bottom = new Decimal(2).add(lnx.mul(4)).add(lnx2.mul(5)).add(lnx3.mul(2)); - - return Decimal.dNegOne.add(top.div(bottom)); - } - }*/ - - //Function for adding/removing layers from a Decimal, even fractional layers (e.g. its slog10 representation). - //Everything continues to use the linear approximation ATM. - Decimal.prototype.layeradd10 = function(diff) { - diff = Decimal.fromValue_noAlloc(diff).toNumber(); - var result = D(this); - if (diff >= 1) - { - var layeradd = Math.trunc(diff); - diff -= layeradd; - result.layer += layeradd; - } - if (diff <= -1) - { - var layeradd = Math.trunc(diff); - diff -= layeradd; - result.layer += layeradd; - if (result.layer < 0) - { - for (var i = 0; i < 100; ++i) - { - result.layer++; - result.mag = Math.log10(result.mag); - if (!isFinite(result.mag)) { return result; } - if (result.layer >= 0) { break; } - } - } - } - - //layeradd10: like adding 'diff' to the number's slog(base) representation. Very similar to tetrate base 10 and iterated log base 10. Also equivalent to adding a fractional amount to the number's layer in its break_eternity.js representation. - if (diff > 0) - { - var subtractlayerslater = 0; - //Ironically, this edge case would be unnecessary if we had 'negative layers'. - while (Number.isFinite(result.mag) && result.mag < 10) - { - result.mag = Math.pow(10, result.mag); - ++subtractlayerslater; - } - - //A^(10^B) === C, solve for B - //B === log10(logA(C)) - - if (result.mag > 1e10) - { - result.mag = Math.log10(result.mag); - result.layer++; - } - - //Note that every integer slog10 value, the formula changes, so if we're near such a number, we have to spend exactly enough layerdiff to hit it, and then use the new formula. - var diffToNextSlog = Math.log10(Math.log(1e10)/Math.log(result.mag), 10); - if (diffToNextSlog < diff) - { - result.mag = Math.log10(1e10); - result.layer++; - diff -= diffToNextSlog; - } - - result.mag = Math.pow(result.mag, Math.pow(10, diff)); - - while (subtractlayerslater > 0) - { - result.mag = Math.log10(result.mag); - --subtractlayerslater; - } - } - else if (diff < 0) - { - var subtractlayerslater = 0; - - while (Number.isFinite(result.mag) && result.mag < 10) - { - result.mag = Math.pow(10, result.mag); - ++subtractlayerslater; - } - - if (result.mag > 1e10) - { - result.mag = Math.log10(result.mag); - result.layer++; - } - - var diffToNextSlog = Math.log10(1/Math.log10(result.mag)); - if (diffToNextSlog > diff) - { - result.mag = 1e10; - result.layer--; - diff -= diffToNextSlog; - } - - result.mag = Math.pow(result.mag, Math.pow(10, diff)); - - while (subtractlayerslater > 0) - { - result.mag = Math.log10(result.mag); - --subtractlayerslater; - } - } - - while (result.layer < 0) - { - result.layer++; - result.mag = Math.log10(result.mag); - } - result.normalize(); - return result; - } - - //layeradd: like adding 'diff' to the number's slog(base) representation. Very similar to tetrate base 'base' and iterated log base 'base'. - Decimal.prototype.layeradd = function(diff, base) { - var slogthis = this.slog(base).toNumber(); - var slogdest = slogthis+diff; - if (slogdest >= 0) - { - return Decimal.tetrate(base, slogdest); - } - else if (!Number.isFinite(slogdest)) - { - return Decimal.dNaN; - } - else if (slogdest >= -1) - { - return Decimal.log(Decimal.tetrate(base, slogdest+1), base); - } - else - { - Decimal.log(Decimal.log(Decimal.tetrate(base, slogdest+2), base), base); - } - } - - //The Lambert W function, also called the omega function or product logarithm, is the solution W(x) === x*e^x. - // https://en.wikipedia.org/wiki/Lambert_W_function - //Some special values, for testing: https://en.wikipedia.org/wiki/Lambert_W_function#Special_values - Decimal.prototype.lambertw = function() { - if (this.lt(-0.3678794411710499)) - { - throw Error("lambertw is unimplemented for results less than -1, sorry!"); - } - else if (this.mag < 0) - { - return D(f_lambertw(this.toNumber())); - } - else if (this.layer === 0) - { - return D(f_lambertw(this.sign*this.mag)); - } - else if (this.layer === 1) - { - return d_lambertw(this); - } - else if (this.layer === 2) - { - return d_lambertw(this); - } - if (this.layer >= 3) - { - return FC_NN(this.sign, this.layer-1, this.mag); - } - } - - //from https://github.com/scipy/scipy/blob/8dba340293fe20e62e173bdf2c10ae208286692f/scipy/special/lambertw.pxd - // The evaluation can become inaccurate very close to the branch point - // at ``-1/e``. In some corner cases, `lambertw` might currently - // fail to converge, or can end up on the wrong branch. - var d_lambertw = function(z, tol = 1e-10) { - var w; - var ew, wew, wewz, wn; - - if (!Number.isFinite(z.mag)) { return z; } - if (z === 0) - { - return z; - } - if (z === 1) - { - //Split out this case because the asymptotic series blows up - return OMEGA; - } - - var absz = Decimal.abs(z); - //Get an initial guess for Halley's method - w = Decimal.ln(z); - - //Halley's method; see 5.9 in [1] - - for (var i = 0; i < 100; ++i) - { - ew = Decimal.exp(-w); - wewz = w.sub(z.mul(ew)); - wn = w.sub(wewz.div(w.add(1).sub((w.add(2)).mul(wewz).div((Decimal.mul(2, w).add(2)))))); - if (Decimal.abs(wn.sub(w)).lt(Decimal.abs(wn).mul(tol))) - { - return wn; - } - else - { - w = wn; - } - } - - throw Error("Iteration failed to converge: " + z); - //return Decimal.dNaN; - } - - //The super square-root function - what number, tetrated to height 2, equals this? - //Other sroots are possible to calculate probably through guess and check methods, this one is easy though. - // https://en.wikipedia.org/wiki/Tetration#Super-root - Decimal.prototype.ssqrt = function() { - if (this.sign == 1 && this.layer >= 3) - { - return FC_NN(this.sign, this.layer-1, this.mag) - } - var lnx = this.ln(); - return lnx.div(lnx.lambertw()); - } -/* -Unit tests for tetrate/iteratedexp/iteratedlog/layeradd10/layeradd/slog: - -for (var i = 0; i < 1000; ++i) -{ - var first = Math.random()*100; - var both = Math.random()*100; - var expected = first+both+1; - var result = new Decimal(10).layeradd10(first).layeradd10(both).slog(); - if (Number.isFinite(result.mag) && !Decimal.eq_tolerance(expected, result)) - { - console.log(first + ", " + both); - } -} - -for (var i = 0; i < 1000; ++i) -{ - var first = Math.random()*100; - var both = Math.random()*100; - first += both; - var expected = first-both+1; - var result = new Decimal(10).layeradd10(first).layeradd10(-both).slog(); - if (Number.isFinite(result.mag) && !Decimal.eq_tolerance(expected, result)) - { - console.log(first + ", " + both); - } -} - -for (var i = 0; i < 1000; ++i) -{ - var first = Math.random()*100; - var both = Math.random()*100; - var base = Math.random()*8+2; - var expected = first+both+1; - var result = new Decimal(base).layeradd(first, base).layeradd(both, base).slog(base); - if (Number.isFinite(result.mag) && !Decimal.eq_tolerance(expected, result)) - { - console.log(first + ", " + both); - } -} - -for (var i = 0; i < 1000; ++i) -{ - var first = Math.random()*100; - var both = Math.random()*100; - var base = Math.random()*8+2; - first += both; - var expected = first-both+1; - var result = new Decimal(base).layeradd(first, base).layeradd(-both, base).slog(base); - if (Number.isFinite(result.mag) && !Decimal.eq_tolerance(expected, result)) - { - console.log(first + ", " + both); - } -} - -for (var i = 0; i < 1000; ++i) -{ - var first = Math.round((Math.random()*30))/10; - var both = Math.round((Math.random()*30))/10; - var tetrateonly = Decimal.tetrate(10, first); - var tetrateandlog = Decimal.tetrate(10, first+both).iteratedlog(10, both); - if (!Decimal.eq_tolerance(tetrateonly, tetrateandlog)) - { - console.log(first + ", " + both); - } -} - -for (var i = 0; i < 1000; ++i) -{ - var first = Math.round((Math.random()*30))/10; - var both = Math.round((Math.random()*30))/10; - var base = Math.random()*8+2; - var tetrateonly = Decimal.tetrate(base, first); - var tetrateandlog = Decimal.tetrate(base, first+both).iteratedlog(base, both); - if (!Decimal.eq_tolerance(tetrateonly, tetrateandlog)) - { - console.log(first + ", " + both); - } -} - -for (var i = 0; i < 1000; ++i) -{ - var first = Math.round((Math.random()*30))/10; - var both = Math.round((Math.random()*30))/10; - var base = Math.random()*8+2; - var tetrateonly = Decimal.tetrate(base, first, base); - var tetrateandlog = Decimal.tetrate(base, first+both, base).iteratedlog(base, both); - if (!Decimal.eq_tolerance(tetrateonly, tetrateandlog)) - { - console.log(first + ", " + both); - } -} - -for (var i = 0; i < 1000; ++i) -{ - var xex = new Decimal(-0.3678794411710499+Math.random()*100); - var x = Decimal.lambertw(xex); - if (!Decimal.eq_tolerance(xex, x.mul(Decimal.exp(x)))) - { - console.log(xex); - } -} - -for (var i = 0; i < 1000; ++i) -{ - var xex = new Decimal(-0.3678794411710499+Math.exp(Math.random()*100)); - var x = Decimal.lambertw(xex); - if (!Decimal.eq_tolerance(xex, x.mul(Decimal.exp(x)))) - { - console.log(xex); - } -} - -for (var i = 0; i < 1000; ++i) -{ - var a = Decimal.randomDecimalForTesting(Math.random() > 0.5 ? 0 : 1); - var b = Decimal.randomDecimalForTesting(Math.random() > 0.5 ? 0 : 1); - if (Math.random() > 0.5) { a = a.recip(); } - if (Math.random() > 0.5) { b = b.recip(); } - var c = a.add(b).toNumber(); - if (Number.isFinite(c) && !Decimal.eq_tolerance(c, a.toNumber()+b.toNumber())) - { - console.log(a + ", " + b); - } -} - -for (var i = 0; i < 100; ++i) -{ - var a = Decimal.randomDecimalForTesting(Math.round(Math.random()*4)); - var b = Decimal.randomDecimalForTesting(Math.round(Math.random()*4)); - if (Math.random() > 0.5) { a = a.recip(); } - if (Math.random() > 0.5) { b = b.recip(); } - var c = a.mul(b).toNumber(); - if (Number.isFinite(c) && Number.isFinite(a.toNumber()) && Number.isFinite(b.toNumber()) && a.toNumber() != 0 && b.toNumber() != 0 && c != 0 && !Decimal.eq_tolerance(c, a.toNumber()*b.toNumber())) - { - console.log("Test 1: " + a + ", " + b); - } - else if (!Decimal.mul(a.recip(), b.recip()).eq_tolerance(Decimal.mul(a, b).recip())) - { - console.log("Test 3: " + a + ", " + b); - } -} - -for (var i = 0; i < 10; ++i) -{ - var a = Decimal.randomDecimalForTesting(Math.round(Math.random()*4)); - var b = Decimal.randomDecimalForTesting(Math.round(Math.random()*4)); - if (Math.random() > 0.5 && a.sign !== 0) { a = a.recip(); } - if (Math.random() > 0.5 && b.sign !== 0) { b = b.recip(); } - var c = a.pow(b); - var d = a.root(b.recip()); - var e = a.pow(b.recip()); - var f = a.root(b); - - if (!c.eq_tolerance(d) && a.sign !== 0 && b.sign !== 0) - { - console.log("Test 1: " + a + ", " + b); - } - if (!e.eq_tolerance(f) && a.sign !== 0 && b.sign !== 0) - { - console.log("Test 2: " + a + ", " + b); - } -} - -for (var i = 0; i < 10; ++i) -{ - var a = Math.round(Math.random()*18-9); - var b = Math.round(Math.random()*100-50); - var c = Math.round(Math.random()*18-9); - var d = Math.round(Math.random()*100-50); - console.log("Decimal.pow(Decimal.fromMantissaExponent(" + a + ", " + b + "), Decimal.fromMantissaExponent(" + c + ", " + d + ")).toString()"); -} - -*/ - - //Pentation/pentate: The result of tetrating 'height' times in a row. An absurdly strong operator - Decimal.pentate(2, 4.28) and Decimal.pentate(10, 2.37) are already too huge for break_eternity.js! - // https://en.wikipedia.org/wiki/Pentation - Decimal.prototype.pentate = function(height = 2, payload = FC_NN(1, 0, 1)) { - payload = D(payload); - var oldheight = height; - height = Math.trunc(height); - var fracheight = oldheight-height; - - //I have no idea if this is a meaningful approximation for pentation to continuous heights, but it is monotonic and continuous. - if (fracheight !== 0) - { - if (payload.eq(Decimal.dOne)) - { - ++height; - payload = new Decimal(fracheight); - } - else - { - if (this.eq(10)) - { - payload = payload.layeradd10(fracheight); - } - else - { - payload = payload.layeradd(fracheight, this); - } - } - } - - for (var i = 0; i < height; ++i) - { - payload = this.tetrate(payload); - //bail if we're NaN - if (!isFinite(payload.layer) || !isFinite(payload.mag)) { return payload; } - //give up after 10 iterations if nothing is happening - if (i > 10) { return payload; } - } - - return payload; - } - - // trig functions! - Decimal.prototype.sin = function () { - if (this.mag < 0) { return this; } - if (this.layer === 0) { return D(Math.sin(this.sign*this.mag)); } - return FC_NN(0, 0, 0); - }; - - Decimal.prototype.cos = function () { - if (this.mag < 0) { return Decimal.dOne; } - if (this.layer === 0) { return D(Math.cos(this.sign*this.mag)); } - return FC_NN(0, 0, 0); - }; - - Decimal.prototype.tan = function () { - if (this.mag < 0) { return this; } - if (this.layer === 0) { return D(Math.tan(this.sign*this.mag)); } - return FC_NN(0, 0, 0); - }; - - Decimal.prototype.asin = function () { - if (this.mag < 0) { return this; } - if (this.layer === 0) { return D(Math.asin(this.sign*this.mag)); } - return FC_NN(Number.NaN, Number.NaN, Number.NaN); - }; - - Decimal.prototype.acos = function () { - if (this.mag < 0) { return D(Math.acos(this.toNumber())); } - if (this.layer === 0) { return D(Math.acos(this.sign*this.mag)); } - return FC_NN(Number.NaN, Number.NaN, Number.NaN); - }; - - Decimal.prototype.atan = function () { - if (this.mag < 0) { return this; } - if (this.layer === 0) { return D(Math.atan(this.sign*this.mag)); } - return D(Math.atan(this.sign*1.8e308)); - }; - - Decimal.prototype.sinh = function () { - return this.exp().sub(this.negate().exp()).div(2); - }; - - Decimal.prototype.cosh = function () { - return this.exp().add(this.negate().exp()).div(2); - }; - - Decimal.prototype.tanh = function () { - return this.sinh().div(this.cosh()); - }; - - Decimal.prototype.asinh = function () { - return Decimal.ln(this.add(this.sqr().add(1).sqrt())); - }; - - Decimal.prototype.acosh = function () { - return Decimal.ln(this.add(this.sqr().sub(1).sqrt())); - }; - - Decimal.prototype.atanh = function () { - if (this.abs().gte(1)) { - return FC_NN(Number.NaN, Number.NaN, Number.NaN); - } - - return Decimal.ln(this.add(1).div(D(1).sub(this))).div(2); - }; - - /** - * Joke function from Realm Grinder - */ - Decimal.prototype.ascensionPenalty = function (ascensions) { - if (ascensions === 0) { return this; } + }, { + key: "fromValue", + value: function fromValue(value) { + if (value instanceof Decimal) { + return this.fromDecimal(value); + } - return this.root(Decimal.pow(10, ascensions)); - }; - - /** - * Joke function from Cookie Clicker. It's 'egg' - */ - Decimal.prototype.egg = function () { - return this.add(9); - }; - - Decimal.prototype.lessThanOrEqualTo = function (other) { - return this.cmp(other) < 1; - }; + if (typeof value === "number") { + return this.fromNumber(value); + } - Decimal.prototype.lessThan = function (other) { - return this.cmp(other) < 0; - }; + if (typeof value === "string") { + return this.fromString(value); + } - Decimal.prototype.greaterThanOrEqualTo = function (other) { - return this.cmp(other) > -1; - }; + this.sign = 0; + this.layer = 0; + this.mag = 0; + return this; + } + }, { + key: "toNumber", + value: function toNumber() { + if (!Number.isFinite(this.layer)) { + return Number.NaN; + } - Decimal.prototype.greaterThan = function (other) { - return this.cmp(other) > 0; - }; + if (this.layer === 0) { + return this.sign * this.mag; + } else if (this.layer === 1) { + return this.sign * Math.pow(10, this.mag); + } //overflow for any normalized Decimal + else { + return this.mag > 0 ? this.sign > 0 ? Number.POSITIVE_INFINITY : Number.NEGATIVE_INFINITY : 0; + } + } + }, { + key: "mantissaWithDecimalPlaces", + value: function mantissaWithDecimalPlaces(places) { + // https://stackoverflow.com/a/37425022 + if (isNaN(this.m)) { + return Number.NaN; + } + + if (this.m === 0) { + return 0; + } + + return decimalPlaces(this.m, places); + } + }, { + key: "magnitudeWithDecimalPlaces", + value: function magnitudeWithDecimalPlaces(places) { + // https://stackoverflow.com/a/37425022 + if (isNaN(this.mag)) { + return Number.NaN; + } + + if (this.mag === 0) { + return 0; + } + + return decimalPlaces(this.mag, places); + } + }, { + key: "toString", + value: function toString() { + if (isNaN(this.layer) || isNaN(this.sign) || isNaN(this.mag)) { + return "NaN"; + } + + if (this.mag === Number.POSITIVE_INFINITY || this.layer === Number.POSITIVE_INFINITY) { + return this.sign === 1 ? "Infinity" : "-Infinity"; + } + + if (this.layer === 0) { + if (this.mag < 1e21 && this.mag > 1e-7 || this.mag === 0) { + return (this.sign * this.mag).toString(); + } + + return this.m + "e" + this.e; + } else if (this.layer === 1) { + return this.m + "e" + this.e; + } else { + //layer 2+ + if (this.layer <= MAX_ES_IN_A_ROW) { + return (this.sign === -1 ? "-" : "") + "e".repeat(this.layer) + this.mag; + } else { + return (this.sign === -1 ? "-" : "") + "(e^" + this.layer + ")" + this.mag; + } + } + } + }, { + key: "toExponential", + value: function toExponential(places) { + if (this.layer === 0) { + return (this.sign * this.mag).toExponential(places); + } + + return this.toStringWithDecimalPlaces(places); + } + }, { + key: "toFixed", + value: function toFixed(places) { + if (this.layer === 0) { + return (this.sign * this.mag).toFixed(places); + } + + return this.toStringWithDecimalPlaces(places); + } + }, { + key: "toPrecision", + value: function toPrecision(places) { + if (this.e <= -7) { + return this.toExponential(places - 1); + } + + if (places > this.e) { + return this.toFixed(places - this.exponent - 1); + } + + return this.toExponential(places - 1); + } + }, { + key: "valueOf", + value: function valueOf() { + return this.toString(); + } + }, { + key: "toJSON", + value: function toJSON() { + return this.toString(); + } + }, { + key: "toStringWithDecimalPlaces", + value: function toStringWithDecimalPlaces(places) { + if (this.layer === 0) { + if (this.mag < 1e21 && this.mag > 1e-7 || this.mag === 0) { + return (this.sign * this.mag).toFixed(places); + } + + return decimalPlaces(this.m, places) + "e" + decimalPlaces(this.e, places); + } else if (this.layer === 1) { + return decimalPlaces(this.m, places) + "e" + decimalPlaces(this.e, places); + } else { + //layer 2+ + if (this.layer <= MAX_ES_IN_A_ROW) { + return (this.sign === -1 ? "-" : "") + "e".repeat(this.layer) + decimalPlaces(this.mag, places); + } else { + return (this.sign === -1 ? "-" : "") + "(e^" + this.layer + ")" + decimalPlaces(this.mag, places); + } + } + } + }, { + key: "abs", + value: function abs() { + return FC_NN(this.sign === 0 ? 0 : 1, this.layer, this.mag); + } + }, { + key: "neg", + value: function neg() { + return FC_NN(-this.sign, this.layer, this.mag); + } + }, { + key: "negate", + value: function negate() { + return this.neg(); + } + }, { + key: "negated", + value: function negated() { + return this.neg(); + } // public sign () { + // return this.sign; + // } + + }, { + key: "sgn", + value: function sgn() { + return this.sign; + } + }, { + key: "round", + value: function round() { + if (this.mag < 0) { + return Decimal.dZero; + } + + if (this.layer === 0) { + return FC(this.sign, 0, Math.round(this.mag)); + } + + return this; + } + }, { + key: "floor", + value: function floor() { + if (this.mag < 0) { + return Decimal.dZero; + } + + if (this.layer === 0) { + return FC(this.sign, 0, Math.floor(this.mag)); + } + + return this; + } + }, { + key: "ceil", + value: function ceil() { + if (this.mag < 0) { + return Decimal.dZero; + } + + if (this.layer === 0) { + return FC(this.sign, 0, Math.ceil(this.mag)); + } + + return this; + } + }, { + key: "trunc", + value: function trunc() { + if (this.mag < 0) { + return Decimal.dZero; + } + + if (this.layer === 0) { + return FC(this.sign, 0, Math.trunc(this.mag)); + } + + return this; + } + }, { + key: "add", + value: function add(value) { + var decimal = D(value); //inf/nan check + + if (!Number.isFinite(this.layer)) { + return this; + } + + if (!Number.isFinite(decimal.layer)) { + return decimal; + } //Special case - if one of the numbers is 0, return the other number. + + + if (this.sign === 0) { + return decimal; + } + + if (decimal.sign === 0) { + return this; + } //Special case - Adding a number to its negation produces 0, no matter how large. + + + if (this.sign === -decimal.sign && this.layer === decimal.layer && this.mag === decimal.mag) { + return FC_NN(0, 0, 0); + } + + var a; + var b; //Special case: If one of the numbers is layer 2 or higher, just take the bigger number. + + if (this.layer >= 2 || decimal.layer >= 2) { + return this.maxabs(decimal); + } + + if (Decimal.cmpabs(this, decimal) > 0) { + a = this; + b = decimal; + } else { + a = decimal; + b = this; + } + + if (a.layer === 0 && b.layer === 0) { + return Decimal.fromNumber(a.sign * a.mag + b.sign * b.mag); + } + + var layera = a.layer * Math.sign(a.mag); + var layerb = b.layer * Math.sign(b.mag); //If one of the numbers is 2+ layers higher than the other, just take the bigger number. + + if (layera - layerb >= 2) { + return a; + } + + if (layera === 0 && layerb === -1) { + if (Math.abs(b.mag - Math.log10(a.mag)) > MAX_SIGNIFICANT_DIGITS) { + return a; + } else { + var magdiff = Math.pow(10, Math.log10(a.mag) - b.mag); + var mantissa = b.sign + a.sign * magdiff; + return FC(Math.sign(mantissa), 1, b.mag + Math.log10(Math.abs(mantissa))); + } + } + + if (layera === 1 && layerb === 0) { + if (Math.abs(a.mag - Math.log10(b.mag)) > MAX_SIGNIFICANT_DIGITS) { + return a; + } else { + var _magdiff = Math.pow(10, a.mag - Math.log10(b.mag)); + + var _mantissa = b.sign + a.sign * _magdiff; + + return FC(Math.sign(_mantissa), 1, Math.log10(b.mag) + Math.log10(Math.abs(_mantissa))); + } + } + + if (Math.abs(a.mag - b.mag) > MAX_SIGNIFICANT_DIGITS) { + return a; + } else { + var _magdiff2 = Math.pow(10, a.mag - b.mag); + + var _mantissa2 = b.sign + a.sign * _magdiff2; + + return FC(Math.sign(_mantissa2), 1, b.mag + Math.log10(Math.abs(_mantissa2))); + } + } + }, { + key: "plus", + value: function plus(value) { + return this.add(value); + } + }, { + key: "sub", + value: function sub(value) { + return this.add(D(value).neg()); + } + }, { + key: "subtract", + value: function subtract(value) { + return this.sub(value); + } + }, { + key: "minus", + value: function minus(value) { + return this.sub(value); + } + }, { + key: "mul", + value: function mul(value) { + var decimal = D(value); //inf/nan check + + if (!Number.isFinite(this.layer)) { + return this; + } + + if (!Number.isFinite(decimal.layer)) { + return decimal; + } //Special case - if one of the numbers is 0, return 0. + + + if (this.sign === 0 || decimal.sign === 0) { + return FC_NN(0, 0, 0); + } //Special case - Multiplying a number by its own reciprocal yields +/- 1, no matter how large. + + + if (this.layer === decimal.layer && this.mag === -decimal.mag) { + return FC_NN(this.sign * decimal.sign, 0, 1); + } + + var a; + var b; //Which number is bigger in terms of its multiplicative distance from 1? + + if (this.layer > decimal.layer || this.layer == decimal.layer && Math.abs(this.mag) > Math.abs(decimal.mag)) { + a = this; + b = decimal; + } else { + a = decimal; + b = this; + } + + if (a.layer === 0 && b.layer === 0) { + return Decimal.fromNumber(a.sign * b.sign * a.mag * b.mag); + } //Special case: If one of the numbers is layer 3 or higher or one of the numbers is 2+ layers bigger than the other, just take the bigger number. + + + if (a.layer >= 3 || a.layer - b.layer >= 2) { + return FC(a.sign * b.sign, a.layer, a.mag); + } + + if (a.layer === 1 && b.layer === 0) { + return FC(a.sign * b.sign, 1, a.mag + Math.log10(b.mag)); + } + + if (a.layer === 1 && b.layer === 1) { + return FC(a.sign * b.sign, 1, a.mag + b.mag); + } + + if (a.layer === 2 && b.layer === 1) { + var newmag = FC(Math.sign(a.mag), a.layer - 1, Math.abs(a.mag)).add(FC(Math.sign(b.mag), b.layer - 1, Math.abs(b.mag))); + return FC(a.sign * b.sign, newmag.layer + 1, newmag.sign * newmag.mag); + } + + if (a.layer === 2 && b.layer === 2) { + var _newmag = FC(Math.sign(a.mag), a.layer - 1, Math.abs(a.mag)).add(FC(Math.sign(b.mag), b.layer - 1, Math.abs(b.mag))); + + return FC(a.sign * b.sign, _newmag.layer + 1, _newmag.sign * _newmag.mag); + } + + throw Error("Bad arguments to mul: " + this + ", " + value); + } + }, { + key: "multiply", + value: function multiply(value) { + return this.mul(value); + } + }, { + key: "times", + value: function times(value) { + return this.mul(value); + } + }, { + key: "div", + value: function div(value) { + var decimal = D(value); + return this.mul(decimal.recip()); + } + }, { + key: "divide", + value: function divide(value) { + return this.div(value); + } + }, { + key: "divideBy", + value: function divideBy(value) { + return this.div(value); + } + }, { + key: "dividedBy", + value: function dividedBy(value) { + return this.div(value); + } + }, { + key: "recip", + value: function recip() { + if (this.mag === 0) { + return Decimal.dNaN; + } else if (this.layer === 0) { + return FC(this.sign, 0, 1 / this.mag); + } else { + return FC(this.sign, this.layer, -this.mag); + } + } + }, { + key: "reciprocal", + value: function reciprocal() { + return this.recip(); + } + }, { + key: "reciprocate", + value: function reciprocate() { + return this.recip(); + } + /** + * -1 for less than value, 0 for equals value, 1 for greater than value + */ + + }, { + key: "cmp", + value: function cmp(value) { + var decimal = D(value); + + if (this.sign > decimal.sign) { + return 1; + } + + if (this.sign < decimal.sign) { + return -1; + } + + return this.sign * this.cmpabs(value); + } + }, { + key: "cmpabs", + value: function cmpabs(value) { + var decimal = D(value); + var layera = this.mag > 0 ? this.layer : -this.layer; + var layerb = decimal.mag > 0 ? decimal.layer : -decimal.layer; + + if (layera > layerb) { + return 1; + } + + if (layera < layerb) { + return -1; + } + + if (this.mag > decimal.mag) { + return 1; + } + + if (this.mag < decimal.mag) { + return -1; + } + + return 0; + } + }, { + key: "compare", + value: function compare(value) { + return this.cmp(value); + } + }, { + key: "isNan", + value: function isNan() { + return isNaN(this.sign) || isNaN(this.layer) || isNaN(this.mag); + } + }, { + key: "isFinite", + value: function (_isFinite2) { + function isFinite() { + return _isFinite2.apply(this, arguments); + } + + isFinite.toString = function () { + return _isFinite2.toString(); + }; + + return isFinite; + }(function () { + return isFinite(this.sign) && isFinite(this.layer) && isFinite(this.mag); + }) + }, { + key: "eq", + value: function eq(value) { + var decimal = D(value); + return this.sign === decimal.sign && this.layer === decimal.layer && this.mag === decimal.mag; + } + }, { + key: "equals", + value: function equals(value) { + return this.eq(value); + } + }, { + key: "neq", + value: function neq(value) { + return !this.eq(value); + } + }, { + key: "notEquals", + value: function notEquals(value) { + return this.neq(value); + } + }, { + key: "lt", + value: function lt(value) { + return this.cmp(value) === -1; + } + }, { + key: "lte", + value: function lte(value) { + return !this.gt(value); + } + }, { + key: "gt", + value: function gt(value) { + return this.cmp(value) === 1; + } + }, { + key: "gte", + value: function gte(value) { + return !this.lt(value); + } + }, { + key: "max", + value: function max(value) { + var decimal = D(value); + return this.lt(decimal) ? decimal : this; + } + }, { + key: "min", + value: function min(value) { + var decimal = D(value); + return this.gt(decimal) ? decimal : this; + } + }, { + key: "maxabs", + value: function maxabs(value) { + var decimal = D(value); + return this.cmpabs(decimal) < 0 ? decimal : this; + } + }, { + key: "minabs", + value: function minabs(value) { + var decimal = D(value); + return this.cmpabs(decimal) > 0 ? decimal : this; + } + }, { + key: "clamp", + value: function clamp(min, max) { + return this.max(min).min(max); + } + }, { + key: "clampMin", + value: function clampMin(min) { + return this.max(min); + } + }, { + key: "clampMax", + value: function clampMax(max) { + return this.min(max); + } + }, { + key: "cmp_tolerance", + value: function cmp_tolerance(value, tolerance) { + var decimal = D(value); + return this.eq_tolerance(decimal, tolerance) ? 0 : this.cmp(decimal); + } + }, { + key: "compare_tolerance", + value: function compare_tolerance(value, tolerance) { + return this.cmp_tolerance(value, tolerance); + } + /** + * Tolerance is a relative tolerance, multiplied by the greater of the magnitudes of the two arguments. + * For example, if you put in 1e-9, then any number closer to the + * larger number than (larger number)*1e-9 will be considered equal. + */ + + }, { + key: "eq_tolerance", + value: function eq_tolerance(value, tolerance) { + var decimal = D(value); // https://stackoverflow.com/a/33024979 + + if (tolerance == null) { + tolerance = 1e-7; + } //Numbers that are too far away are never close. + + + if (this.sign !== decimal.sign) { + return false; + } + + if (Math.abs(this.layer - decimal.layer) > 1) { + return false; + } // return abs(a-b) <= tolerance * max(abs(a), abs(b)) + + + var magA = this.mag; + var magB = decimal.mag; + + if (this.layer > decimal.layer) { + magB = f_maglog10(magB); + } + + if (this.layer < decimal.layer) { + magA = f_maglog10(magA); + } + + return Math.abs(magA - magB) <= tolerance * Math.max(Math.abs(magA), Math.abs(magB)); + } + }, { + key: "equals_tolerance", + value: function equals_tolerance(value, tolerance) { + return this.eq_tolerance(value, tolerance); + } + }, { + key: "neq_tolerance", + value: function neq_tolerance(value, tolerance) { + return !this.eq_tolerance(value, tolerance); + } + }, { + key: "notEquals_tolerance", + value: function notEquals_tolerance(value, tolerance) { + return this.neq_tolerance(value, tolerance); + } + }, { + key: "lt_tolerance", + value: function lt_tolerance(value, tolerance) { + var decimal = D(value); + return !this.eq_tolerance(decimal, tolerance) && this.lt(decimal); + } + }, { + key: "lte_tolerance", + value: function lte_tolerance(value, tolerance) { + var decimal = D(value); + return this.eq_tolerance(decimal, tolerance) || this.lt(decimal); + } + }, { + key: "gt_tolerance", + value: function gt_tolerance(value, tolerance) { + var decimal = D(value); + return !this.eq_tolerance(decimal, tolerance) && this.gt(decimal); + } + }, { + key: "gte_tolerance", + value: function gte_tolerance(value, tolerance) { + var decimal = D(value); + return this.eq_tolerance(decimal, tolerance) || this.gt(decimal); + } + }, { + key: "pLog10", + value: function pLog10() { + if (this.lt(Decimal.dZero)) { + return Decimal.dZero; + } + + return this.log10(); + } + }, { + key: "absLog10", + value: function absLog10() { + if (this.sign === 0) { + return Decimal.dNaN; + } else if (this.layer > 0) { + return FC(Math.sign(this.mag), this.layer - 1, Math.abs(this.mag)); + } else { + return FC(1, 0, Math.log10(this.mag)); + } + } + }, { + key: "log10", + value: function log10() { + if (this.sign <= 0) { + return Decimal.dNaN; + } else if (this.layer > 0) { + return FC(Math.sign(this.mag), this.layer - 1, Math.abs(this.mag)); + } else { + return FC(this.sign, 0, Math.log10(this.mag)); + } + } + }, { + key: "log", + value: function log(base) { + base = D(base); + + if (this.sign <= 0) { + return Decimal.dNaN; + } + + if (base.sign <= 0) { + return Decimal.dNaN; + } + + if (base.sign === 1 && base.layer === 0 && base.mag === 1) { + return Decimal.dNaN; + } else if (this.layer === 0 && base.layer === 0) { + return FC(this.sign, 0, Math.log(this.mag) / Math.log(base.mag)); + } + + return Decimal.div(this.log10(), base.log10()); + } + }, { + key: "log2", + value: function log2() { + if (this.sign <= 0) { + return Decimal.dNaN; + } else if (this.layer === 0) { + return FC(this.sign, 0, Math.log2(this.mag)); + } else if (this.layer === 1) { + return FC(Math.sign(this.mag), 0, Math.abs(this.mag) * 3.321928094887362); //log2(10) + } else if (this.layer === 2) { + return FC(Math.sign(this.mag), 1, Math.abs(this.mag) + 0.5213902276543247); //-log10(log10(2)) + } else { + return FC(Math.sign(this.mag), this.layer - 1, Math.abs(this.mag)); + } + } + }, { + key: "ln", + value: function ln() { + if (this.sign <= 0) { + return Decimal.dNaN; + } else if (this.layer === 0) { + return FC(this.sign, 0, Math.log(this.mag)); + } else if (this.layer === 1) { + return FC(Math.sign(this.mag), 0, Math.abs(this.mag) * 2.302585092994046); //ln(10) + } else if (this.layer === 2) { + return FC(Math.sign(this.mag), 1, Math.abs(this.mag) + 0.36221568869946325); //log10(log10(e)) + } else { + return FC(Math.sign(this.mag), this.layer - 1, Math.abs(this.mag)); + } + } + }, { + key: "logarithm", + value: function logarithm(base) { + return this.log(base); + } + }, { + key: "pow", + value: function pow(value) { + var decimal = D(value); + var a = this; + var b = decimal; //special case: if a is 0, then return 0 (UNLESS b is 0, then return 1) + + if (a.sign === 0) { + return b.eq(0) ? FC_NN(1, 0, 1) : a; + } //special case: if a is 1, then return 1 + + + if (a.sign === 1 && a.layer === 0 && a.mag === 1) { + return a; + } //special case: if b is 0, then return 1 + + + if (b.sign === 0) { + return FC_NN(1, 0, 1); + } //special case: if b is 1, then return a + + + if (b.sign === 1 && b.layer === 0 && b.mag === 1) { + return a; + } + + var result = a.absLog10().mul(b).pow10(); + + if (this.sign === -1) { + if (Math.abs(b.toNumber() % 2) % 2 === 1) { + return result.neg(); + } else if (Math.abs(b.toNumber() % 2) % 2 === 0) { + return result; + } + + return Decimal.dNaN; + } + + return result; + } + }, { + key: "pow10", + value: function pow10() { + /* + There are four cases we need to consider: + 1) positive sign, positive mag (e15, ee15): +1 layer (e.g. 10^15 becomes e15, 10^e15 becomes ee15) + 2) negative sign, positive mag (-e15, -ee15): +1 layer but sign and mag sign are flipped (e.g. 10^-15 becomes e-15, 10^-e15 becomes ee-15) + 3) positive sign, negative mag (e-15, ee-15): layer 0 case would have been handled in the Math.pow check, so just return 1 + 4) negative sign, negative mag (-e-15, -ee-15): layer 0 case would have been handled in the Math.pow check, so just return 1 + */ + if (!Number.isFinite(this.layer) || !Number.isFinite(this.mag)) { + return Decimal.dNaN; + } + + var a = this; //handle layer 0 case - if no precision is lost just use Math.pow, else promote one layer + + if (a.layer === 0) { + var newmag = Math.pow(10, a.sign * a.mag); + + if (Number.isFinite(newmag) && Math.abs(newmag) >= 0.1) { + return FC(1, 0, newmag); + } else { + if (a.sign === 0) { + return Decimal.dOne; + } else { + a = FC_NN(a.sign, a.layer + 1, Math.log10(a.mag)); + } + } + } //handle all 4 layer 1+ cases individually + + + if (a.sign > 0 && a.mag >= 0) { + return FC(a.sign, a.layer + 1, a.mag); + } + + if (a.sign < 0 && a.mag >= 0) { + return FC(-a.sign, a.layer + 1, -a.mag); + } //both the negative mag cases are identical: one +/- rounding error + + + return Decimal.dOne; + } + }, { + key: "pow_base", + value: function pow_base(value) { + return D(value).pow(this); + } + }, { + key: "root", + value: function root(value) { + var decimal = D(value); + return this.pow(decimal.recip()); + } + }, { + key: "factorial", + value: function factorial() { + if (this.mag < 0) { + return this.add(1).gamma(); + } else if (this.layer === 0) { + return this.add(1).gamma(); + } else if (this.layer === 1) { + return Decimal.exp(Decimal.mul(this, Decimal.ln(this).sub(1))); + } else { + return Decimal.exp(this); + } + } //from HyperCalc source code + + }, { + key: "gamma", + value: function gamma() { + if (this.mag < 0) { + return this.recip(); + } else if (this.layer === 0) { + if (this.lt(FC_NN(1, 0, 24))) { + return Decimal.fromNumber(f_gamma(this.sign * this.mag)); + } + + var t = this.mag - 1; + var l = 0.9189385332046727; //0.5*Math.log(2*Math.PI) + + l = l + (t + 0.5) * Math.log(t); + l = l - t; + var n2 = t * t; + var np = t; + var lm = 12 * np; + var adj = 1 / lm; + var l2 = l + adj; + + if (l2 === l) { + return Decimal.exp(l); + } + + l = l2; + np = np * n2; + lm = 360 * np; + adj = 1 / lm; + l2 = l - adj; + + if (l2 === l) { + return Decimal.exp(l); + } + + l = l2; + np = np * n2; + lm = 1260 * np; + var lt = 1 / lm; + l = l + lt; + np = np * n2; + lm = 1680 * np; + lt = 1 / lm; + l = l - lt; + return Decimal.exp(l); + } else if (this.layer === 1) { + return Decimal.exp(Decimal.mul(this, Decimal.ln(this).sub(1))); + } else { + return Decimal.exp(this); + } + } + }, { + key: "lngamma", + value: function lngamma() { + return this.gamma().ln(); + } + }, { + key: "exp", + value: function exp() { + if (this.mag < 0) { + return Decimal.dOne; + } + + if (this.layer === 0 && this.mag <= 709.7) { + return Decimal.fromNumber(Math.exp(this.sign * this.mag)); + } else if (this.layer === 0) { + return FC(1, 1, this.sign * Math.log10(Math.E) * this.mag); + } else if (this.layer === 1) { + return FC(1, 2, this.sign * (Math.log10(0.4342944819032518) + this.mag)); + } else { + return FC(1, this.layer + 1, this.sign * this.mag); + } + } + }, { + key: "sqr", + value: function sqr() { + return this.pow(2); + } + }, { + key: "sqrt", + value: function sqrt() { + if (this.layer === 0) { + return Decimal.fromNumber(Math.sqrt(this.sign * this.mag)); + } else if (this.layer === 1) { + return FC(1, 2, Math.log10(this.mag) - 0.3010299956639812); + } else { + var result = Decimal.div(FC_NN(this.sign, this.layer - 1, this.mag), FC_NN(1, 0, 2)); + result.layer += 1; + result.normalize(); + return result; + } + } + }, { + key: "cube", + value: function cube() { + return this.pow(3); + } + }, { + key: "cbrt", + value: function cbrt() { + return this.pow(1 / 3); + } //Tetration/tetrate: The result of exponentiating 'this' to 'this' 'height' times in a row. https://en.wikipedia.org/wiki/Tetration + //If payload != 1, then this is 'iterated exponentiation', the result of exping (payload) to base (this) (height) times. https://andydude.github.io/tetration/archives/tetration2/ident.html + //Works with negative and positive real heights. + + }, { + key: "tetrate", + value: function tetrate() { + var height = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 2; + var payload = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : FC_NN(1, 0, 1); + + //x^^1 == x + if (height === 1) { + return Decimal.pow(this, payload); + } //x^^0 == 1 + + + if (height === 0) { + return new Decimal(payload); + } //1^^x == 1 + + + if (this.eq(Decimal.dOne)) { + return Decimal.dOne; + } //-1^^x == -1 + + + if (this.eq(-1)) { + return Decimal.pow(this, payload); + } + + if (height === Number.POSITIVE_INFINITY) { + var this_num = this.toNumber(); //within the convergence range? + + if (this_num <= 1.44466786100976613366 && this_num >= 0.06598803584531253708) { + //hotfix for the very edge of the number range not being handled properly + if (this_num > 1.444667861009099) { + return Decimal.fromNumber(Math.E); + } //Formula for infinite height power tower. + + + var negln = Decimal.ln(this).neg(); + return negln.lambertw().div(negln); + } else if (this_num > 1.44466786100976613366) { + //explodes to infinity + // TODO: replace this with Decimal.dInf + return Decimal.fromNumber(Number.POSITIVE_INFINITY); + } else { + //0.06598803584531253708 > this_num >= 0: never converges + //this_num < 0: quickly becomes a complex number + return Decimal.dNaN; + } + } //0^^x oscillates if we define 0^0 == 1 (which in javascript land we do), since then 0^^1 is 0, 0^^2 is 1, 0^^3 is 0, etc. payload is ignored + //using the linear approximation for height (TODO: don't know a better way to calculate it ATM, but it wouldn't surprise me if it's just NaN) + + + if (this.eq(Decimal.dZero)) { + var result = Math.abs((height + 1) % 2); + + if (result > 1) { + result = 2 - result; + } + + return Decimal.fromNumber(result); + } + + if (height < 0) { + return Decimal.iteratedlog(payload, this, -height); + } + + payload = D(payload); + var oldheight = height; + height = Math.trunc(height); + var fracheight = oldheight - height; + + if (this.gt(Decimal.dZero) && this.lte(1.44466786100976613366)) { + //similar to 0^^n, flip-flops between two values, converging slowly (or if it's below 0.06598803584531253708, never. so once again, the fractional part at the end will be a linear approximation (TODO: again pending knowledge of how to approximate better, although tbh I think it should in reality just be NaN) + height = Math.min(10000, height); + + for (var i = 0; i < height; ++i) { + var old_payload = payload; + payload = this.pow(payload); //stop early if we converge + + if (old_payload.eq(payload)) { + return payload; + } + } + + if (fracheight != 0) { + var next_payload = this.pow(payload); + return payload.mul(1 - fracheight).add(next_payload.mul(fracheight)); + } + + return payload; + } //TODO: base < 0, but it's hard for me to reason about (probably all non-integer heights are NaN automatically?) + + + if (fracheight !== 0) { + if (payload.eq(Decimal.dOne)) { + //TODO: for bases above 10, revert to old linear approximation until I can think of something better + if (this.gt(10)) { + payload = this.pow(fracheight); + } else { + payload = Decimal.fromNumber(Decimal.tetrate_critical(this.toNumber(), fracheight)); //TODO: until the critical section grid can handle numbers below 2, scale them to the base + //TODO: maybe once the critical section grid has very large bases, this math can be appropriate for them too? I'll think about it + + if (this.lt(2)) { + payload = payload.sub(1).mul(this.minus(1)).plus(1); + } + } + } else { + if (this.eq(10)) { + payload = payload.layeradd10(fracheight); + } else { + payload = payload.layeradd(fracheight, this); + } + } + } + + for (var _i = 0; _i < height; ++_i) { + payload = this.pow(payload); //bail if we're NaN + + if (!isFinite(payload.layer) || !isFinite(payload.mag)) { + return payload.normalize(); + } //shortcut + + + if (payload.layer - this.layer > 3) { + return FC_NN(payload.sign, payload.layer + (height - _i - 1), payload.mag); + } //give up after 10000 iterations if nothing is happening + + + if (_i > 10000) { + return payload; + } + } + + return payload; + } //iteratedexp/iterated exponentiation: - all cases handled in tetrate, so just call it + + }, { + key: "iteratedexp", + value: function iteratedexp() { + var height = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 2; + var payload = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : FC_NN(1, 0, 1); + return this.tetrate(height, payload); + } //iterated log/repeated log: The result of applying log(base) 'times' times in a row. Approximately equal to subtracting (times) from the number's slog representation. Equivalent to tetrating to a negative height. + //Works with negative and positive real heights. + + }, { + key: "iteratedlog", + value: function iteratedlog() { + var base = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 10; + var times = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 1; + + if (times < 0) { + return Decimal.tetrate(base, -times, this); + } + + base = D(base); + var result = Decimal.fromDecimal(this); + var fulltimes = times; + times = Math.trunc(times); + var fraction = fulltimes - times; + + if (result.layer - base.layer > 3) { + var layerloss = Math.min(times, result.layer - base.layer - 3); + times -= layerloss; + result.layer -= layerloss; + } + + for (var i = 0; i < times; ++i) { + result = result.log(base); //bail if we're NaN + + if (!isFinite(result.layer) || !isFinite(result.mag)) { + return result.normalize(); + } //give up after 10000 iterations if nothing is happening + + + if (i > 10000) { + return result; + } + } //handle fractional part + + + if (fraction > 0 && fraction < 1) { + if (base.eq(10)) { + result = result.layeradd10(-fraction); + } else { + result = result.layeradd(-fraction, base); + } + } + + return result; + } //Super-logarithm, one of tetration's inverses, tells you what size power tower you'd have to tetrate base to to get number. By definition, will never be higher than 1.8e308 in break_eternity.js, since a power tower 1.8e308 numbers tall is the largest representable number. + // https://en.wikipedia.org/wiki/Super-logarithm + // NEW: Accept a number of iterations, and use binary search to, after making an initial guess, hone in on the true value, assuming tetration as the ground truth. + + }, { + key: "slog", + value: function slog() { + var base = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 10; + var iterations = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 100; + var step_size = 0.001; + var has_changed_directions_once = false; + var previously_rose = false; + var result = this.slog_internal(base).toNumber(); + + for (var i = 1; i < iterations; ++i) { + var new_decimal = new Decimal(base).tetrate(result); + var currently_rose = new_decimal.gt(this); + + if (i > 1) { + if (previously_rose != currently_rose) { + has_changed_directions_once = true; + } + } + + previously_rose = currently_rose; + + if (has_changed_directions_once) { + step_size /= 2; + } else { + step_size *= 2; + } + + step_size = Math.abs(step_size) * (currently_rose ? -1 : 1); + result += step_size; + + if (step_size === 0) { + break; + } + } + + return Decimal.fromNumber(result); + } + }, { + key: "slog_internal", + value: function slog_internal() { + var base = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 10; + base = D(base); //special cases: + //slog base 0 or lower is NaN + + if (base.lte(Decimal.dZero)) { + return Decimal.dNaN; + } //slog base 1 is NaN + + + if (base.eq(Decimal.dOne)) { + return Decimal.dNaN; + } //need to handle these small, wobbling bases specially + + + if (base.lt(Decimal.dOne)) { + if (this.eq(Decimal.dOne)) { + return Decimal.dZero; + } + + if (this.eq(Decimal.dZero)) { + return Decimal.dNegOne; + } //0 < this < 1: ambiguous (happens multiple times) + //this < 0: impossible (as far as I can tell) + //this > 1: partially complex (http://myweb.astate.edu/wpaulsen/tetcalc/tetcalc.html base 0.25 for proof) + + + return Decimal.dNaN; + } //slog_n(0) is -1 + + + if (this.mag < 0 || this.eq(Decimal.dZero)) { + return Decimal.dNegOne; + } + + var result = 0; + var copy = Decimal.fromDecimal(this); + + if (copy.layer - base.layer > 3) { + var layerloss = copy.layer - base.layer - 3; + result += layerloss; + copy.layer -= layerloss; + } + + for (var i = 0; i < 100; ++i) { + if (copy.lt(Decimal.dZero)) { + copy = Decimal.pow(base, copy); + result -= 1; + } else if (copy.lte(Decimal.dOne)) { + return Decimal.fromNumber(result + Decimal.slog_critical(base.toNumber(), copy.toNumber())); + } else { + result += 1; + copy = Decimal.log(copy, base); + } + } + + return Decimal.fromNumber(result); + } //background info and tables of values for critical functions taken here: https://github.com/Patashu/break_eternity.js/issues/22 + + }, { + key: "layeradd10", + value: //Function for adding/removing layers from a Decimal, even fractional layers (e.g. its slog10 representation). + //Moved this over to use the same critical section as tetrate/slog. + function layeradd10(diff) { + diff = Decimal.fromValue_noAlloc(diff).toNumber(); + var result = Decimal.fromDecimal(this); + + if (diff >= 1) { + //bug fix: if result is very smol (mag < 0, layer > 0) turn it into 0 first + if (result.mag < 0 && result.layer > 0) { + result.sign = 0; + result.mag = 0; + result.layer = 0; + } else if (result.sign === -1 && result.layer == 0) { + //bug fix - for stuff like -3.layeradd10(1) we need to move the sign to the mag + result.sign = 1; + result.mag = -result.mag; + } + + var layeradd = Math.trunc(diff); + diff -= layeradd; + result.layer += layeradd; + } + + if (diff <= -1) { + var _layeradd = Math.trunc(diff); + + diff -= _layeradd; + result.layer += _layeradd; + + if (result.layer < 0) { + for (var i = 0; i < 100; ++i) { + result.layer++; + result.mag = Math.log10(result.mag); + + if (!isFinite(result.mag)) { + //another bugfix: if we hit -Infinity mag, then we should return negative infinity, not 0. 0.layeradd10(-1) h its this + if (result.sign === 0) { + result.sign = 1; + } //also this, for 0.layeradd10(-2) + + + if (result.layer < 0) { + result.layer = 0; + } + + return result.normalize(); + } + + if (result.layer >= 0) { + break; + } + } + } + } + + while (result.layer < 0) { + result.layer++; + result.mag = Math.log10(result.mag); + } //bugfix: before we normalize: if we started with 0, we now need to manually fix a layer ourselves! + + + if (result.sign === 0) { + result.sign = 1; + + if (result.mag === 0 && result.layer >= 1) { + result.layer -= 1; + result.mag = 1; + } + } + + result.normalize(); //layeradd10: like adding 'diff' to the number's slog(base) representation. Very similar to tetrate base 10 and iterated log base 10. Also equivalent to adding a fractional amount to the number's layer in its break_eternity.js representation. + + if (diff !== 0) { + return result.layeradd(diff, 10); //safe, only calls positive height 1 payload tetration, slog and log + } + + return result; + } //layeradd: like adding 'diff' to the number's slog(base) representation. Very similar to tetrate base 'base' and iterated log base 'base'. + + }, { + key: "layeradd", + value: function layeradd(diff, base) { + var slogthis = this.slog(base).toNumber(); + var slogdest = slogthis + diff; + + if (slogdest >= 0) { + return Decimal.tetrate(base, slogdest); + } else if (!Number.isFinite(slogdest)) { + return Decimal.dNaN; + } else if (slogdest >= -1) { + return Decimal.log(Decimal.tetrate(base, slogdest + 1), base); + } else { + return Decimal.log(Decimal.log(Decimal.tetrate(base, slogdest + 2), base), base); + } + } //The Lambert W function, also called the omega function or product logarithm, is the solution W(x) === x*e^x. + // https://en.wikipedia.org/wiki/Lambert_W_function + //Some special values, for testing: https://en.wikipedia.org/wiki/Lambert_W_function#Special_values + + }, { + key: "lambertw", + value: function lambertw() { + if (this.lt(-0.3678794411710499)) { + throw Error("lambertw is unimplemented for results less than -1, sorry!"); + } else if (this.mag < 0) { + return Decimal.fromNumber(f_lambertw(this.toNumber())); + } else if (this.layer === 0) { + return Decimal.fromNumber(f_lambertw(this.sign * this.mag)); + } else if (this.layer === 1) { + return d_lambertw(this); + } else if (this.layer === 2) { + return d_lambertw(this); + } + + if (this.layer >= 3) { + return FC_NN(this.sign, this.layer - 1, this.mag); + } + + throw "Unhandled behavior in lambertw()"; + } //The super square-root function - what number, tetrated to height 2, equals this? + //Other sroots are possible to calculate probably through guess and check methods, this one is easy though. + // https://en.wikipedia.org/wiki/Tetration#Super-root + + }, { + key: "ssqrt", + value: function ssqrt() { + if (this.sign == 1 && this.layer >= 3) { + return FC_NN(this.sign, this.layer - 1, this.mag); + } + + var lnx = this.ln(); + return lnx.div(lnx.lambertw()); + } //Pentation/pentate: The result of tetrating 'height' times in a row. An absurdly strong operator - Decimal.pentate(2, 4.28) and Decimal.pentate(10, 2.37) are already too huge for break_eternity.js! + // https://en.wikipedia.org/wiki/Pentation + + }, { + key: "pentate", + value: function pentate() { + var height = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 2; + var payload = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : FC_NN(1, 0, 1); + payload = D(payload); + var oldheight = height; + height = Math.trunc(height); + var fracheight = oldheight - height; //I have no idea if this is a meaningful approximation for pentation to continuous heights, but it is monotonic and continuous. + + if (fracheight !== 0) { + if (payload.eq(Decimal.dOne)) { + ++height; + payload = Decimal.fromNumber(fracheight); + } else { + if (this.eq(10)) { + payload = payload.layeradd10(fracheight); + } else { + payload = payload.layeradd(fracheight, this); + } + } + } + + for (var i = 0; i < height; ++i) { + payload = this.tetrate(payload.toNumber()); //bail if we're NaN + + if (!isFinite(payload.layer) || !isFinite(payload.mag)) { + return payload.normalize(); + } //give up after 10 iterations if nothing is happening + + + if (i > 10) { + return payload; + } + } + + return payload; + } // trig functions! + + }, { + key: "sin", + value: function sin() { + if (this.mag < 0) { + return this; + } + + if (this.layer === 0) { + return Decimal.fromNumber(Math.sin(this.sign * this.mag)); + } + + return FC_NN(0, 0, 0); + } + }, { + key: "cos", + value: function cos() { + if (this.mag < 0) { + return Decimal.dOne; + } + + if (this.layer === 0) { + return Decimal.fromNumber(Math.cos(this.sign * this.mag)); + } + + return FC_NN(0, 0, 0); + } + }, { + key: "tan", + value: function tan() { + if (this.mag < 0) { + return this; + } + + if (this.layer === 0) { + return Decimal.fromNumber(Math.tan(this.sign * this.mag)); + } + + return FC_NN(0, 0, 0); + } + }, { + key: "asin", + value: function asin() { + if (this.mag < 0) { + return this; + } + + if (this.layer === 0) { + return Decimal.fromNumber(Math.asin(this.sign * this.mag)); + } + + return FC_NN(Number.NaN, Number.NaN, Number.NaN); + } + }, { + key: "acos", + value: function acos() { + if (this.mag < 0) { + return Decimal.fromNumber(Math.acos(this.toNumber())); + } + + if (this.layer === 0) { + return Decimal.fromNumber(Math.acos(this.sign * this.mag)); + } + + return FC_NN(Number.NaN, Number.NaN, Number.NaN); + } + }, { + key: "atan", + value: function atan() { + if (this.mag < 0) { + return this; + } + + if (this.layer === 0) { + return Decimal.fromNumber(Math.atan(this.sign * this.mag)); + } + + return Decimal.fromNumber(Math.atan(this.sign * 1.8e308)); + } + }, { + key: "sinh", + value: function sinh() { + return this.exp().sub(this.negate().exp()).div(2); + } + }, { + key: "cosh", + value: function cosh() { + return this.exp().add(this.negate().exp()).div(2); + } + }, { + key: "tanh", + value: function tanh() { + return this.sinh().div(this.cosh()); + } + }, { + key: "asinh", + value: function asinh() { + return Decimal.ln(this.add(this.sqr().add(1).sqrt())); + } + }, { + key: "acosh", + value: function acosh() { + return Decimal.ln(this.add(this.sqr().sub(1).sqrt())); + } + }, { + key: "atanh", + value: function atanh() { + if (this.abs().gte(1)) { + return FC_NN(Number.NaN, Number.NaN, Number.NaN); + } + + return Decimal.ln(this.add(1).div(Decimal.fromNumber(1).sub(this))).div(2); + } + /** + * Joke function from Realm Grinder + */ + + }, { + key: "ascensionPenalty", + value: function ascensionPenalty(ascensions) { + if (ascensions === 0) { + return this; + } + + return this.root(Decimal.pow(10, ascensions)); + } + /** + * Joke function from Cookie Clicker. It's 'egg' + */ + + }, { + key: "egg", + value: function egg() { + return this.add(9); + } + }, { + key: "lessThanOrEqualTo", + value: function lessThanOrEqualTo(other) { + return this.cmp(other) < 1; + } + }, { + key: "lessThan", + value: function lessThan(other) { + return this.cmp(other) < 0; + } + }, { + key: "greaterThanOrEqualTo", + value: function greaterThanOrEqualTo(other) { + return this.cmp(other) > -1; + } + }, { + key: "greaterThan", + value: function greaterThan(other) { + return this.cmp(other) > 0; + } + }], [{ + key: "fromComponents", + value: function fromComponents(sign, layer, mag) { + return new Decimal().fromComponents(sign, layer, mag); + } + }, { + key: "fromComponents_noNormalize", + value: function fromComponents_noNormalize(sign, layer, mag) { + return new Decimal().fromComponents_noNormalize(sign, layer, mag); + } + }, { + key: "fromMantissaExponent", + value: function fromMantissaExponent(mantissa, exponent) { + return new Decimal().fromMantissaExponent(mantissa, exponent); + } + }, { + key: "fromMantissaExponent_noNormalize", + value: function fromMantissaExponent_noNormalize(mantissa, exponent) { + return new Decimal().fromMantissaExponent_noNormalize(mantissa, exponent); + } + }, { + key: "fromDecimal", + value: function fromDecimal(value) { + return new Decimal().fromDecimal(value); + } + }, { + key: "fromNumber", + value: function fromNumber(value) { + return new Decimal().fromNumber(value); + } + }, { + key: "fromString", + value: function fromString(value) { + return new Decimal().fromString(value); + } + }, { + key: "fromValue", + value: function fromValue(value) { + return new Decimal().fromValue(value); + } + /** + * Converts a DecimalSource to a Decimal, without constructing a new Decimal + * if the provided value is already a Decimal. + * + * As the return value could be the provided value itself, this function + * returns a read-only Decimal to prevent accidental mutations of the value. + * Use `new Decimal(value)` to explicitly create a writeable copy if mutation + * is required. + */ + + }, { + key: "fromValue_noAlloc", + value: function fromValue_noAlloc(value) { + if (value instanceof Decimal) { + return value; + } else if (typeof value === "string") { + var cached = Decimal.fromStringCache.get(value); + + if (cached !== undefined) { + return cached; + } + + return Decimal.fromString(value); + } else if (typeof value === "number") { + return Decimal.fromNumber(value); + } else { + // This should never happen... but some users like Prestige Tree Rewritten + // pass undefined values in as DecimalSources, so we should handle this + // case to not break them. + return Decimal.dZero; + } + } + }, { + key: "abs", + value: function abs(value) { + return D(value).abs(); + } + }, { + key: "neg", + value: function neg(value) { + return D(value).neg(); + } + }, { + key: "negate", + value: function negate(value) { + return D(value).neg(); + } + }, { + key: "negated", + value: function negated(value) { + return D(value).neg(); + } + }, { + key: "sign", + value: function sign(value) { + return D(value).sign; + } + }, { + key: "sgn", + value: function sgn(value) { + return D(value).sign; + } + }, { + key: "round", + value: function round(value) { + return D(value).round(); + } + }, { + key: "floor", + value: function floor(value) { + return D(value).floor(); + } + }, { + key: "ceil", + value: function ceil(value) { + return D(value).ceil(); + } + }, { + key: "trunc", + value: function trunc(value) { + return D(value).trunc(); + } + }, { + key: "add", + value: function add(value, other) { + return D(value).add(other); + } + }, { + key: "plus", + value: function plus(value, other) { + return D(value).add(other); + } + }, { + key: "sub", + value: function sub(value, other) { + return D(value).sub(other); + } + }, { + key: "subtract", + value: function subtract(value, other) { + return D(value).sub(other); + } + }, { + key: "minus", + value: function minus(value, other) { + return D(value).sub(other); + } + }, { + key: "mul", + value: function mul(value, other) { + return D(value).mul(other); + } + }, { + key: "multiply", + value: function multiply(value, other) { + return D(value).mul(other); + } + }, { + key: "times", + value: function times(value, other) { + return D(value).mul(other); + } + }, { + key: "div", + value: function div(value, other) { + return D(value).div(other); + } + }, { + key: "divide", + value: function divide(value, other) { + return D(value).div(other); + } + }, { + key: "recip", + value: function recip(value) { + return D(value).recip(); + } + }, { + key: "reciprocal", + value: function reciprocal(value) { + return D(value).recip(); + } + }, { + key: "reciprocate", + value: function reciprocate(value) { + return D(value).reciprocate(); + } + }, { + key: "cmp", + value: function cmp(value, other) { + return D(value).cmp(other); + } + }, { + key: "cmpabs", + value: function cmpabs(value, other) { + return D(value).cmpabs(other); + } + }, { + key: "compare", + value: function compare(value, other) { + return D(value).cmp(other); + } + }, { + key: "isNaN", + value: function (_isNaN) { + function isNaN(_x) { + return _isNaN.apply(this, arguments); + } + + isNaN.toString = function () { + return _isNaN.toString(); + }; + + return isNaN; + }(function (value) { + value = D(value); + return isNaN(value.sign) || isNaN(value.layer) || isNaN(value.mag); + }) + }, { + key: "isFinite", + value: function (_isFinite) { + function isFinite(_x2) { + return _isFinite.apply(this, arguments); + } + + isFinite.toString = function () { + return _isFinite.toString(); + }; + + return isFinite; + }(function (value) { + value = D(value); + return isFinite(value.sign) && isFinite(value.layer) && isFinite(value.mag); + }) + }, { + key: "eq", + value: function eq(value, other) { + return D(value).eq(other); + } + }, { + key: "equals", + value: function equals(value, other) { + return D(value).eq(other); + } + }, { + key: "neq", + value: function neq(value, other) { + return D(value).neq(other); + } + }, { + key: "notEquals", + value: function notEquals(value, other) { + return D(value).notEquals(other); + } + }, { + key: "lt", + value: function lt(value, other) { + return D(value).lt(other); + } + }, { + key: "lte", + value: function lte(value, other) { + return D(value).lte(other); + } + }, { + key: "gt", + value: function gt(value, other) { + return D(value).gt(other); + } + }, { + key: "gte", + value: function gte(value, other) { + return D(value).gte(other); + } + }, { + key: "max", + value: function max(value, other) { + return D(value).max(other); + } + }, { + key: "min", + value: function min(value, other) { + return D(value).min(other); + } + }, { + key: "minabs", + value: function minabs(value, other) { + return D(value).minabs(other); + } + }, { + key: "maxabs", + value: function maxabs(value, other) { + return D(value).maxabs(other); + } + }, { + key: "clamp", + value: function clamp(value, min, max) { + return D(value).clamp(min, max); + } + }, { + key: "clampMin", + value: function clampMin(value, min) { + return D(value).clampMin(min); + } + }, { + key: "clampMax", + value: function clampMax(value, max) { + return D(value).clampMax(max); + } + }, { + key: "cmp_tolerance", + value: function cmp_tolerance(value, other, tolerance) { + return D(value).cmp_tolerance(other, tolerance); + } + }, { + key: "compare_tolerance", + value: function compare_tolerance(value, other, tolerance) { + return D(value).cmp_tolerance(other, tolerance); + } + }, { + key: "eq_tolerance", + value: function eq_tolerance(value, other, tolerance) { + return D(value).eq_tolerance(other, tolerance); + } + }, { + key: "equals_tolerance", + value: function equals_tolerance(value, other, tolerance) { + return D(value).eq_tolerance(other, tolerance); + } + }, { + key: "neq_tolerance", + value: function neq_tolerance(value, other, tolerance) { + return D(value).neq_tolerance(other, tolerance); + } + }, { + key: "notEquals_tolerance", + value: function notEquals_tolerance(value, other, tolerance) { + return D(value).notEquals_tolerance(other, tolerance); + } + }, { + key: "lt_tolerance", + value: function lt_tolerance(value, other, tolerance) { + return D(value).lt_tolerance(other, tolerance); + } + }, { + key: "lte_tolerance", + value: function lte_tolerance(value, other, tolerance) { + return D(value).lte_tolerance(other, tolerance); + } + }, { + key: "gt_tolerance", + value: function gt_tolerance(value, other, tolerance) { + return D(value).gt_tolerance(other, tolerance); + } + }, { + key: "gte_tolerance", + value: function gte_tolerance(value, other, tolerance) { + return D(value).gte_tolerance(other, tolerance); + } + }, { + key: "pLog10", + value: function pLog10(value) { + return D(value).pLog10(); + } + }, { + key: "absLog10", + value: function absLog10(value) { + return D(value).absLog10(); + } + }, { + key: "log10", + value: function log10(value) { + return D(value).log10(); + } + }, { + key: "log", + value: function log(value, base) { + return D(value).log(base); + } + }, { + key: "log2", + value: function log2(value) { + return D(value).log2(); + } + }, { + key: "ln", + value: function ln(value) { + return D(value).ln(); + } + }, { + key: "logarithm", + value: function logarithm(value, base) { + return D(value).logarithm(base); + } + }, { + key: "pow", + value: function pow(value, other) { + return D(value).pow(other); + } + }, { + key: "pow10", + value: function pow10(value) { + return D(value).pow10(); + } + }, { + key: "root", + value: function root(value, other) { + return D(value).root(other); + } + }, { + key: "factorial", + value: function factorial(value, _other) { + return D(value).factorial(); + } + }, { + key: "gamma", + value: function gamma(value, _other) { + return D(value).gamma(); + } + }, { + key: "lngamma", + value: function lngamma(value, _other) { + return D(value).lngamma(); + } + }, { + key: "exp", + value: function exp(value) { + return D(value).exp(); + } + }, { + key: "sqr", + value: function sqr(value) { + return D(value).sqr(); + } + }, { + key: "sqrt", + value: function sqrt(value) { + return D(value).sqrt(); + } + }, { + key: "cube", + value: function cube(value) { + return D(value).cube(); + } + }, { + key: "cbrt", + value: function cbrt(value) { + return D(value).cbrt(); + } + }, { + key: "tetrate", + value: function tetrate(value) { + var height = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 2; + var payload = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : FC_NN(1, 0, 1); + return D(value).tetrate(height, payload); + } + }, { + key: "iteratedexp", + value: function iteratedexp(value) { + var height = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 2; + var payload = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : FC_NN(1, 0, 1); + return D(value).iteratedexp(height, payload); + } + }, { + key: "iteratedlog", + value: function iteratedlog(value) { + var base = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 10; + var times = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : 1; + return D(value).iteratedlog(base, times); + } + }, { + key: "layeradd10", + value: function layeradd10(value, diff) { + return D(value).layeradd10(diff); + } + }, { + key: "layeradd", + value: function layeradd(value, diff) { + var base = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : 10; + return D(value).layeradd(diff, base); + } + }, { + key: "slog", + value: function slog(value) { + var base = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 10; + return D(value).slog(base); + } + }, { + key: "lambertw", + value: function lambertw(value) { + return D(value).lambertw(); + } + }, { + key: "ssqrt", + value: function ssqrt(value) { + return D(value).ssqrt(); + } + }, { + key: "pentate", + value: function pentate(value) { + var height = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 2; + var payload = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : FC_NN(1, 0, 1); + return D(value).pentate(height, payload); + } + /** + * If you're willing to spend 'resourcesAvailable' and want to buy something + * with exponentially increasing cost each purchase (start at priceStart, + * multiply by priceRatio, already own currentOwned), how much of it can you buy? + * Adapted from Trimps source code. + */ + + }, { + key: "affordGeometricSeries", + value: function affordGeometricSeries(resourcesAvailable, priceStart, priceRatio, currentOwned) { + return this.affordGeometricSeries_core(D(resourcesAvailable), D(priceStart), D(priceRatio), currentOwned); + } + /** + * How much resource would it cost to buy (numItems) items if you already have currentOwned, + * the initial price is priceStart and it multiplies by priceRatio each purchase? + */ + + }, { + key: "sumGeometricSeries", + value: function sumGeometricSeries(numItems, priceStart, priceRatio, currentOwned) { + return this.sumGeometricSeries_core(numItems, D(priceStart), D(priceRatio), currentOwned); + } + /** + * If you're willing to spend 'resourcesAvailable' and want to buy something with additively + * increasing cost each purchase (start at priceStart, add by priceAdd, already own currentOwned), + * how much of it can you buy? + */ + + }, { + key: "affordArithmeticSeries", + value: function affordArithmeticSeries(resourcesAvailable, priceStart, priceAdd, currentOwned) { + return this.affordArithmeticSeries_core(D(resourcesAvailable), D(priceStart), D(priceAdd), D(currentOwned)); + } + /** + * How much resource would it cost to buy (numItems) items if you already have currentOwned, + * the initial price is priceStart and it adds priceAdd each purchase? + * Adapted from http://www.mathwords.com/a/arithmetic_series.htm + */ + + }, { + key: "sumArithmeticSeries", + value: function sumArithmeticSeries(numItems, priceStart, priceAdd, currentOwned) { + return this.sumArithmeticSeries_core(D(numItems), D(priceStart), D(priceAdd), D(currentOwned)); + } + /** + * When comparing two purchases that cost (resource) and increase your resource/sec by (deltaRpS), + * the lowest efficiency score is the better one to purchase. + * From Frozen Cookies: + * http://cookieclicker.wikia.com/wiki/Frozen_Cookies_(JavaScript_Add-on)#Efficiency.3F_What.27s_that.3F + */ + + }, { + key: "efficiencyOfPurchase", + value: function efficiencyOfPurchase(cost, currentRpS, deltaRpS) { + return this.efficiencyOfPurchase_core(D(cost), D(currentRpS), D(deltaRpS)); + } + }, { + key: "randomDecimalForTesting", + value: function randomDecimalForTesting(maxLayers) { + // NOTE: This doesn't follow any kind of sane random distribution, so use this for testing purposes only. + //5% of the time, return 0 + if (Math.random() * 20 < 1) { + return FC_NN(0, 0, 0); + } + + var randomsign = Math.random() > 0.5 ? 1 : -1; //5% of the time, return 1 or -1 + + if (Math.random() * 20 < 1) { + return FC_NN(randomsign, 0, 1); + } //pick a random layer + + + var layer = Math.floor(Math.random() * (maxLayers + 1)); + var randomexp = layer === 0 ? Math.random() * 616 - 308 : Math.random() * 16; //10% of the time, make it a simple power of 10 + + if (Math.random() > 0.9) { + randomexp = Math.trunc(randomexp); + } + + var randommag = Math.pow(10, randomexp); //10% of the time, trunc mag + + if (Math.random() > 0.9) { + randommag = Math.trunc(randommag); + } + + return FC(randomsign, layer, randommag); + } + }, { + key: "affordGeometricSeries_core", + value: function affordGeometricSeries_core(resourcesAvailable, priceStart, priceRatio, currentOwned) { + var actualStart = priceStart.mul(priceRatio.pow(currentOwned)); + return Decimal.floor(resourcesAvailable.div(actualStart).mul(priceRatio.sub(1)).add(1).log10().div(priceRatio.log10())); + } + }, { + key: "sumGeometricSeries_core", + value: function sumGeometricSeries_core(numItems, priceStart, priceRatio, currentOwned) { + return priceStart.mul(priceRatio.pow(currentOwned)).mul(Decimal.sub(1, priceRatio.pow(numItems))).div(Decimal.sub(1, priceRatio)); + } + }, { + key: "affordArithmeticSeries_core", + value: function affordArithmeticSeries_core(resourcesAvailable, priceStart, priceAdd, currentOwned) { + // n = (-(a-d/2) + sqrt((a-d/2)^2+2dS))/d + // where a is actualStart, d is priceAdd and S is resourcesAvailable + // then floor it and you're done! + var actualStart = priceStart.add(currentOwned.mul(priceAdd)); + var b = actualStart.sub(priceAdd.div(2)); + var b2 = b.pow(2); + return b.neg().add(b2.add(priceAdd.mul(resourcesAvailable).mul(2)).sqrt()).div(priceAdd).floor(); + } + }, { + key: "sumArithmeticSeries_core", + value: function sumArithmeticSeries_core(numItems, priceStart, priceAdd, currentOwned) { + var actualStart = priceStart.add(currentOwned.mul(priceAdd)); // (n/2)*(2*a+(n-1)*d) + + return numItems.div(2).mul(actualStart.mul(2).plus(numItems.sub(1).mul(priceAdd))); + } + }, { + key: "efficiencyOfPurchase_core", + value: function efficiencyOfPurchase_core(cost, currentRpS, deltaRpS) { + return cost.div(currentRpS).add(cost.div(deltaRpS)); + } + }, { + key: "slog_critical", + value: function slog_critical(base, height) { + //TODO: for bases above 10, revert to old linear approximation until I can think of something better + if (base > 10) { + return height - 1; + } + + return Decimal.critical_section(base, height, critical_slog_values); + } + }, { + key: "tetrate_critical", + value: function tetrate_critical(base, height) { + return Decimal.critical_section(base, height, critical_tetr_values); + } + }, { + key: "critical_section", + value: function critical_section(base, height, grid) { + //this part is simple at least, since it's just 0.1 to 0.9 + height *= 10; + + if (height < 0) { + height = 0; + } + + if (height > 10) { + height = 10; + } //have to do this complicated song and dance since one of the critical_headers is Math.E, and in the future I'd like 1.5 as well + + + if (base < 2) { + base = 2; + } + + if (base > 10) { + base = 10; + } + + var lower = 0; + var upper = 0; //basically, if we're between bases, we interpolate each bases' relevant values together + //then we interpolate based on what the fractional height is. + //accuracy could be improved by doing a non-linear interpolation (maybe), by adding more bases and heights (definitely) but this is AFAIK the best you can get without running some pari.gp or mathematica program to calculate exact values + //however, do note http://myweb.astate.edu/wpaulsen/tetcalc/tetcalc.html can do it for arbitrary heights but not for arbitrary bases (2, e, 10 present) + + for (var i = 0; i < critical_headers.length; ++i) { + if (critical_headers[i] == base) { + // exact match + lower = grid[i][Math.floor(height)]; + upper = grid[i][Math.ceil(height)]; + break; + } else if (critical_headers[i] < base && critical_headers[i + 1] > base) { + // interpolate between this and the next + var basefrac = (base - critical_headers[i]) / (critical_headers[i + 1] - critical_headers[i]); + lower = grid[i][Math.floor(height)] * (1 - basefrac) + grid[i + 1][Math.floor(height)] * basefrac; + upper = grid[i][Math.ceil(height)] * (1 - basefrac) + grid[i + 1][Math.ceil(height)] * basefrac; + break; + } + } + + var frac = height - Math.floor(height); //improvement - you get more accuracy (especially around 0.9-1.0) by doing log, then frac, then powing the result + //(we could pre-log the lookup table, but then fractional bases would get Weird) + //also, use old linear for slog (values 0 or less in critical section). maybe something else is better but haven't thought about what yet + + if (lower <= 0 || upper <= 0) { + return lower * (1 - frac) + upper * frac; + } else { + return Math.pow(base, Math.log(lower) / Math.log(base) * (1 - frac) + Math.log(upper) / Math.log(base) * frac); + } + } + }]); return Decimal; }(); - - Decimal.dZero = FC_NN(0, 0, 0); - Decimal.dOne = FC_NN(1, 0, 1); - Decimal.dNegOne = FC_NN(-1, 0, 1); - Decimal.dTwo = FC_NN(1, 0, 2); - Decimal.dTen = FC_NN(1, 0, 10); - Decimal.dNaN = FC_NN(Number.NaN, Number.NaN, Number.NaN); - Decimal.dInf = FC_NN(1, Number.POSITIVE_INFINITY, Number.POSITIVE_INFINITY); - Decimal.dNegInf = FC_NN(-1, Number.NEGATIVE_INFINITY, Number.NEGATIVE_INFINITY); + Decimal.dZero = FC_NN(0, 0, 0); + Decimal.dOne = FC_NN(1, 0, 1); + Decimal.dNegOne = FC_NN(-1, 0, 1); + Decimal.dTwo = FC_NN(1, 0, 2); + Decimal.dTen = FC_NN(1, 0, 10); + Decimal.dNaN = FC_NN(Number.NaN, Number.NaN, Number.NaN); + Decimal.dInf = FC_NN(1, Number.POSITIVE_INFINITY, Number.POSITIVE_INFINITY); + Decimal.dNegInf = FC_NN(-1, Number.NEGATIVE_INFINITY, Number.NEGATIVE_INFINITY); Decimal.dNumberMax = FC(1, 0, Number.MAX_VALUE); Decimal.dNumberMin = FC(1, 0, Number.MIN_VALUE); - + Decimal.fromStringCache = new LRUCache(DEFAULT_FROM_STRING_CACHE_SIZE); // return Decimal; + // Optimise Decimal aliases. + // We can't do this optimisation before Decimal is assigned. + + D = Decimal.fromValue_noAlloc; + FC = Decimal.fromComponents; + FC_NN = Decimal.fromComponents_noNormalize; // eslint-disable-next-line @typescript-eslint/no-unused-vars + + Decimal.fromMantissaExponent; // eslint-disable-next-line @typescript-eslint/no-unused-vars + + Decimal.fromMantissaExponent_noNormalize; + return Decimal; }));