(function (global, factory) { typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() : typeof define === 'function' && define.amd ? define(factory) : (global = typeof globalThis !== 'undefined' ? globalThis : global || self, global.Decimal = factory()); })(this, (function () { 'use strict'; function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } } 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; } _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. */ }, { 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. 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 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 this.first.prev = node; this.first = node; } 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. */ }, { key: "set", value: function set(key, value) { // Ensure that this.maxSize >= 1. if (this.maxSize < 1) { return; } 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); 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. // You can fix it with the power of math... or just make a lookup table. // Faster AND simpler var powersOf10 = []; for (var i = NUMBER_EXP_MIN + 1; i <= NUMBER_EXP_MAX; i++) { powersOf10.push(Number("1e" + i)); } var indexOf0InPowersOf10 = 323; 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); }; var FC = function FC(sign, layer, mag) { return Decimal.fromComponents(sign, layer, mag); }; var FC_NN = function FC_NN(sign, layer, mag) { return Decimal.fromComponents_noNormalize(sign, layer, mag); }; // eslint-disable-next-line @typescript-eslint/no-unused-vars 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 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; ++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; }; 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 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) { return z; } if (z === 1) { return OMEGA; } if (z < 10) { w = 0; } 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)) { return wn; } else { w = wn; } } 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; } /** * The Decimal's value is simply mantissa * 10^exponent. */ var Decimal = /*#__PURE__*/function () { function Decimal(value) { _classCallCheck(this, Decimal); this.sign = 0; this.mag = 0; this.layer = 0; if (value instanceof Decimal) { this.fromDecimal(value); } else if (typeof value === "number") { this.fromNumber(value); } else if (typeof value === "string") { this.fromString(value); } } _createClass(Decimal, [{ key: "m", get: function get() { if (this.sign === 0) { return 0; } 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) { man = 5; } 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 { //mantissa stops being relevant past 1e9e15 / ee15.954 return this.sign; } }, set: function set(value) { if (this.layer <= 2) { this.fromMantissaExponent(value, this.e); } else { //don't even pretend mantissa is meaningful this.sign = Math.sign(value); if (this.sign === 0) { this.layer = 0; this.exponent = 0; } } } }, { key: "e", get: function get() { if (this.sign === 0) { return 0; } else if (this.layer === 0) { return Math.floor(Math.log10(this.mag)); } 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; } }, set: function set(value) { this.fromMantissaExponent(this.m, value); } }, { key: "s", get: function get() { return this.sign; }, set: function set(value) { if (value === 0) { this.sign = 0; this.layer = 0; this.mag = 0; } else { this.sign = value; } } // Object.defineProperty(Decimal.prototype, "mantissa", { }, { key: "mantissa", get: function get() { return this.m; }, set: function set(value) { this.m = value; } }, { key: "exponent", get: function get() { return this.e; }, set: function set(value) { this.e = value; } }, { 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; } }, { 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; } }, { key: "fromString", value: function fromString(value) { var originalValue = value; var cached = Decimal.fromStringCache.get(originalValue); if (cached !== undefined) { return this.fromDecimal(cached); } { 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; } } 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; } } //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; } } 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; } } //Handle x^y format. var powparts = value.split("^"); if (powparts.length === 2) { var _base3 = parseFloat(powparts[0]); var _exponent = parseFloat(powparts[1]); if (isFinite(_base3) && isFinite(_exponent)) { var _result2 = Decimal.pow(_base3, _exponent); 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; } } //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; } } 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; } } } 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; } 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; } //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; } } this.normalize(); if (Decimal.fromStringCache.maxSize >= 1) { Decimal.fromStringCache.set(originalValue, Decimal.fromDecimal(this)); } return this; } }, { key: "fromValue", value: function fromValue(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; } }, { key: "toNumber", value: function toNumber() { 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); } //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.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; }));