@powrldgr/raydium-sdk-v2/lib/raydium/liquidity/utils.mjs.map

An SDK for building applications on top of Raydium.

{"version":3,"sources":["../../../src/raydium/liquidity/utils.ts","../../../node_modules/decimal.js/decimal.mjs","../../../src/common/txTool/txUtils.ts","../../../src/common/logger.ts","../../../src/raydium/token/utils.ts","../../../src/module/amount.ts","../../../src/common/bignumber.ts","../../../src/raydium/token/constant.ts","../../../src/module/token.ts","../../../src/common/pubKey.ts","../../../src/module/currency.ts","../../../src/module/fraction.ts","../../../src/common/constant.ts","../../../src/module/formatter.ts","../../../src/module/percent.ts","../../../src/module/price.ts","../../../src/common/utility.ts","../../../src/common/accountInfo.ts","../../../src/common/pda.ts","../../../src/common/programId.ts","../../../src/common/transfer.ts","../../../src/common/txTool/lookupTable.ts","../../../src/common/txTool/txTool.ts","../../../src/common/fee.ts","../../../src/raydium/liquidity/instruction.ts","../../../src/marshmallow/index.ts","../../../src/marshmallow/buffer-layout.ts","../../../src/raydium/liquidity/layout.ts","../../../src/raydium/liquidity/serum.ts","../../../src/raydium/liquidity/constant.ts","../../../src/raydium/liquidity/stable.ts","../../../src/raydium/account/layout.ts","../../../src/raydium/account/util.ts","../../../src/raydium/account/instruction.ts","../../../src/raydium/token/layout.ts"],"sourcesContent":["import { Connection, PublicKey } from \"@solana/web3.js\";\nimport BN from \"bn.js\";\nimport Decimal from \"decimal.js\";\nimport { AmmV4Keys, AmmV5Keys } from \"../../api/type\";\nimport { TOKEN_PROGRAM_ID } from \"@solana/spl-token\";\nimport {\n  findProgramAddress,\n  parseSimulateLogToJson,\n  parseSimulateValue,\n  simulateMultipleInstruction,\n} from \"@/common/txTool/txUtils\";\nimport { toApiV3Token } from \"../../raydium/token/utils\";\nimport { makeSimulatePoolInfoInstruction } from \"./instruction\";\nimport { getSerumAssociatedAuthority } from \"./serum\";\nimport { StableLayout } from \"./stable\";\nimport { AmmRpcData, ComputeAmountOutParam, LiquidityPoolKeys } from \"./type\";\nimport { liquidityStateV4Layout } from \"./layout\";\nimport { splAccountLayout } from \"../account\";\nimport { SPL_MINT_LAYOUT } from \"../token\";\n\ntype AssociatedName =\n  | \"amm_associated_seed\"\n  | \"lp_mint_associated_seed\"\n  | \"coin_vault_associated_seed\"\n  | \"pc_vault_associated_seed\"\n  | \"lp_mint_associated_seed\"\n  | \"temp_lp_token_associated_seed\"\n  | \"open_order_associated_seed\"\n  | \"target_associated_seed\"\n  | \"withdraw_associated_seed\";\n\ninterface GetAssociatedParam {\n  name: AssociatedName;\n  programId: PublicKey;\n  marketId: PublicKey;\n}\n\nexport function getAssociatedConfigId({ programId }: { programId: PublicKey }): PublicKey {\n  const { publicKey } = findProgramAddress([Buffer.from(\"amm_config_account_seed\", \"utf-8\")], programId);\n  return publicKey;\n}\n\nexport function getLiquidityAssociatedId({ name, programId, marketId }: GetAssociatedParam): PublicKey {\n  const { publicKey } = findProgramAddress(\n    [programId.toBuffer(), marketId.toBuffer(), Buffer.from(name, \"utf-8\")],\n    programId,\n  );\n  return publicKey;\n}\n\nexport function getAssociatedOpenOrders({ programId, marketId }: { programId: PublicKey; marketId: PublicKey }) {\n  const { publicKey } = findProgramAddress(\n    [programId.toBuffer(), marketId.toBuffer(), Buffer.from(\"open_order_associated_seed\", \"utf-8\")],\n    programId,\n  );\n  return publicKey;\n}\n\nexport function getLiquidityAssociatedAuthority({ programId }: { programId: PublicKey }): {\n  publicKey: PublicKey;\n  nonce: number;\n} {\n  return findProgramAddress([Buffer.from([97, 109, 109, 32, 97, 117, 116, 104, 111, 114, 105, 116, 121])], programId);\n}\n\nexport function getAssociatedPoolKeys({\n  version,\n  marketVersion,\n  marketId,\n  baseMint,\n  quoteMint,\n  baseDecimals,\n  quoteDecimals,\n  programId,\n  marketProgramId,\n}: {\n  version: 4 | 5;\n  marketVersion: 3;\n  marketId: PublicKey;\n  baseMint: PublicKey;\n  quoteMint: PublicKey;\n  baseDecimals: number;\n  quoteDecimals: number;\n  programId: PublicKey;\n  marketProgramId: PublicKey;\n}): LiquidityPoolKeys {\n  const id = getLiquidityAssociatedId({ name: \"amm_associated_seed\", programId, marketId });\n  const lpMint = getLiquidityAssociatedId({ name: \"lp_mint_associated_seed\", programId, marketId });\n  const { publicKey: authority, nonce } = getLiquidityAssociatedAuthority({ programId });\n  const baseVault = getLiquidityAssociatedId({ name: \"coin_vault_associated_seed\", programId, marketId });\n  const quoteVault = getLiquidityAssociatedId({ name: \"pc_vault_associated_seed\", programId, marketId });\n  const lpVault = getLiquidityAssociatedId({ name: \"temp_lp_token_associated_seed\", programId, marketId });\n  const openOrders = getAssociatedOpenOrders({ programId, marketId });\n  const targetOrders = getLiquidityAssociatedId({ name: \"target_associated_seed\", programId, marketId });\n  const withdrawQueue = getLiquidityAssociatedId({ name: \"withdraw_associated_seed\", programId, marketId });\n\n  const { publicKey: marketAuthority } = getSerumAssociatedAuthority({\n    programId: marketProgramId,\n    marketId,\n  });\n\n  return {\n    // base\n    id,\n    baseMint,\n    quoteMint,\n    lpMint,\n    baseDecimals,\n    quoteDecimals,\n    lpDecimals: baseDecimals,\n    // version\n    version,\n    programId,\n    // keys\n    authority,\n    nonce,\n    baseVault,\n    quoteVault,\n    lpVault,\n    openOrders,\n    targetOrders,\n    withdrawQueue,\n    // market version\n    marketVersion,\n    marketProgramId,\n    // market keys\n    marketId,\n    marketAuthority,\n    lookupTableAccount: PublicKey.default,\n    configId: getAssociatedConfigId({ programId }),\n  };\n}\n\nlet stableLayout: StableLayout | undefined;\n\nexport async function fetchMultipleInfo({\n  connection,\n  poolKeysList,\n  // eslint-disable-next-line @typescript-eslint/no-unused-vars\n  config,\n  modelDataPubKey,\n}: {\n  connection: Connection;\n  poolKeysList: (AmmV4Keys | AmmV5Keys)[];\n  config: any;\n  modelDataPubKey?: PublicKey;\n}): Promise<\n  {\n    status: BN;\n    baseDecimals: number;\n    quoteDecimals: number;\n    lpDecimals: number;\n    baseReserve: BN;\n    quoteReserve: BN;\n    lpSupply: BN;\n    startTime: BN;\n  }[]\n> {\n  // eslint-disable-next-line @typescript-eslint/ban-ts-comment\n  // @ts-ignore\n  const loadStable = poolKeysList.find((i) => i.modelDataAccount);\n  if (loadStable) {\n    if (!stableLayout) {\n      stableLayout = new StableLayout({ connection, modelDataPubKey });\n      await stableLayout.initStableModelLayout();\n    }\n  }\n  return await Promise.all(\n    poolKeysList.map(async (itemPoolKey) => {\n      // eslint-disable-next-line @typescript-eslint/ban-ts-comment\n      // @ts-ignore\n      if (itemPoolKey.modelDataAccount) {\n        const instructions = makeSimulatePoolInfoInstruction({ poolKeys: itemPoolKey });\n        const logs = await simulateMultipleInstruction(connection, [instructions.instruction], \"GetPoolData\");\n        const poolsInfo = logs.map((log) => {\n          const json = parseSimulateLogToJson(log, \"GetPoolData\");\n          const status = new BN(parseSimulateValue(json, \"status\"));\n          const baseDecimals = Number(parseSimulateValue(json, \"coin_decimals\"));\n          const quoteDecimals = Number(parseSimulateValue(json, \"pc_decimals\"));\n          const lpDecimals = Number(parseSimulateValue(json, \"lp_decimals\"));\n          const baseReserve = new BN(parseSimulateValue(json, \"pool_coin_amount\"));\n          const quoteReserve = new BN(parseSimulateValue(json, \"pool_pc_amount\"));\n          const lpSupply = new BN(parseSimulateValue(json, \"pool_lp_supply\"));\n          // TODO fix it when split stable\n          let startTime = \"0\";\n          try {\n            startTime = parseSimulateValue(json, \"pool_open_time\");\n          } catch (error) {\n            //\n          }\n          return {\n            status,\n            baseDecimals,\n            quoteDecimals,\n            lpDecimals,\n            baseReserve,\n            quoteReserve,\n            lpSupply,\n            startTime: new BN(startTime),\n          };\n        })[0];\n        return poolsInfo;\n      } else {\n        const [poolAcc, vaultAccA, vaultAccB, mintAccLp] = await connection.getMultipleAccountsInfo([\n          new PublicKey(itemPoolKey.id),\n          new PublicKey(itemPoolKey.vault.A),\n          new PublicKey(itemPoolKey.vault.B),\n          new PublicKey(itemPoolKey.mintLp.address),\n        ]);\n        if (poolAcc === null) throw Error(\"fetch pool error\");\n        if (vaultAccA === null) throw Error(\"fetch vaultAccA error\");\n        if (vaultAccB === null) throw Error(\"fetch vaultAccB error\");\n        if (mintAccLp === null) throw Error(\"fetch mintAccLp error\");\n        const poolInfo = liquidityStateV4Layout.decode(poolAcc.data);\n        const vaultInfoA = splAccountLayout.decode(vaultAccA.data);\n        const vaultInfoB = splAccountLayout.decode(vaultAccB.data);\n        const lpInfo = SPL_MINT_LAYOUT.decode(mintAccLp.data);\n        return {\n          status: poolInfo.status,\n          baseDecimals: poolInfo.baseDecimal.toNumber(),\n          quoteDecimals: poolInfo.quoteDecimal.toNumber(),\n          lpDecimals: lpInfo.decimals,\n          baseReserve: vaultInfoA.amount.sub(poolInfo.baseNeedTakePnl),\n          quoteReserve: vaultInfoB.amount.sub(poolInfo.quoteNeedTakePnl),\n          lpSupply: poolInfo.lpReserve,\n          startTime: poolInfo.poolOpenTime,\n        };\n      }\n    }),\n  );\n}\n\nconst mockRewardData = {\n  volume: 0,\n  volumeQuote: 0,\n  volumeFee: 0,\n  apr: 0,\n  feeApr: 0,\n  priceMin: 0,\n  priceMax: 0,\n  rewardApr: [],\n};\n\nexport const toAmmComputePoolInfo = (\n  poolData: Record<string, AmmRpcData>,\n): Record<string, ComputeAmountOutParam[\"poolInfo\"]> => {\n  const data: Record<string, ComputeAmountOutParam[\"poolInfo\"]> = {};\n  const tokenProgramStr = TOKEN_PROGRAM_ID.toBase58();\n\n  Object.keys(poolData).map((poolId) => {\n    const poolInfo = poolData[poolId];\n    const [mintA, mintB] = [poolInfo.baseMint.toBase58(), poolInfo.quoteMint.toBase58()];\n    data[poolId] = {\n      id: poolId,\n      version: 4,\n      status: poolInfo.status.toNumber(),\n      programId: poolInfo.programId.toBase58(), // needed\n      mintA: toApiV3Token({\n        address: mintA, // needed\n        programId: tokenProgramStr,\n        decimals: poolInfo.baseDecimal.toNumber(),\n      }),\n      mintB: toApiV3Token({\n        address: mintB, // needed\n        programId: tokenProgramStr,\n        decimals: poolInfo.quoteDecimal.toNumber(),\n      }),\n      rewardDefaultInfos: [],\n      rewardDefaultPoolInfos: \"Ecosystem\",\n      price: poolInfo.poolPrice.toNumber(),\n      mintAmountA: new Decimal(poolInfo.mintAAmount.toString()).div(10 ** poolInfo.baseDecimal.toNumber()).toNumber(),\n      mintAmountB: new Decimal(poolInfo.mintBAmount.toString()).div(10 ** poolInfo.quoteDecimal.toNumber()).toNumber(),\n      baseReserve: poolInfo.baseReserve, // needed\n      quoteReserve: poolInfo.quoteReserve, // needed\n      feeRate: new Decimal(poolInfo.tradeFeeNumerator.toString())\n        .div(poolInfo.tradeFeeDenominator.toString())\n        .toNumber(),\n      openTime: poolInfo.poolOpenTime.toString(),\n      tvl: 0,\n      day: mockRewardData,\n      week: mockRewardData,\n      month: mockRewardData,\n      pooltype: [],\n      farmUpcomingCount: 0,\n      farmOngoingCount: 0,\n      farmFinishedCount: 0,\n      type: \"Standard\",\n      marketId: poolInfo.marketId.toBase58(),\n      configId: getAssociatedConfigId({ programId: poolInfo.programId }).toBase58(),\n      lpPrice: 0,\n      lpAmount: new Decimal(poolInfo.lpReserve.toString())\n        .div(10 ** Math.min(poolInfo.baseDecimal.toNumber(), poolInfo.quoteDecimal.toNumber()))\n        .toNumber(),\n      lpMint: toApiV3Token({\n        address: poolInfo.lpMint.toBase58(),\n        programId: tokenProgramStr,\n        decimals: Math.min(poolInfo.baseDecimal.toNumber(), poolInfo.quoteDecimal.toNumber()),\n      }),\n      burnPercent: 0,\n    };\n  });\n  return data;\n};\n","/*\r\n *  decimal.js v10.3.1\r\n *  An arbitrary-precision Decimal type for JavaScript.\r\n *  https://github.com/MikeMcl/decimal.js\r\n *  Copyright (c) 2021 Michael Mclaughlin <M8ch88l@gmail.com>\r\n *  MIT Licence\r\n */\r\n\r\n\r\n// -----------------------------------  EDITABLE DEFAULTS  ------------------------------------ //\r\n\r\n\r\n  // The maximum exponent magnitude.\r\n  // The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`.\r\nvar EXP_LIMIT = 9e15,                      // 0 to 9e15\r\n\r\n  // The limit on the value of `precision`, and on the value of the first argument to\r\n  // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`.\r\n  MAX_DIGITS = 1e9,                        // 0 to 1e9\r\n\r\n  // Base conversion alphabet.\r\n  NUMERALS = '0123456789abcdef',\r\n\r\n  // The natural logarithm of 10 (1025 digits).\r\n  LN10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058',\r\n\r\n  // Pi (1025 digits).\r\n  PI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789',\r\n\r\n\r\n  // The initial configuration properties of the Decimal constructor.\r\n  DEFAULTS = {\r\n\r\n    // These values must be integers within the stated ranges (inclusive).\r\n    // Most of these values can be changed at run-time using the `Decimal.config` method.\r\n\r\n    // The maximum number of significant digits of the result of a calculation or base conversion.\r\n    // E.g. `Decimal.config({ precision: 20 });`\r\n    precision: 20,                         // 1 to MAX_DIGITS\r\n\r\n    // The rounding mode used when rounding to `precision`.\r\n    //\r\n    // ROUND_UP         0 Away from zero.\r\n    // ROUND_DOWN       1 Towards zero.\r\n    // ROUND_CEIL       2 Towards +Infinity.\r\n    // ROUND_FLOOR      3 Towards -Infinity.\r\n    // ROUND_HALF_UP    4 Towards nearest neighbour. If equidistant, up.\r\n    // ROUND_HALF_DOWN  5 Towards nearest neighbour. If equidistant, down.\r\n    // ROUND_HALF_EVEN  6 Towards nearest neighbour. If equidistant, towards even neighbour.\r\n    // ROUND_HALF_CEIL  7 Towards nearest neighbour. If equidistant, towards +Infinity.\r\n    // ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.\r\n    //\r\n    // E.g.\r\n    // `Decimal.rounding = 4;`\r\n    // `Decimal.rounding = Decimal.ROUND_HALF_UP;`\r\n    rounding: 4,                           // 0 to 8\r\n\r\n    // The modulo mode used when calculating the modulus: a mod n.\r\n    // The quotient (q = a / n) is calculated according to the corresponding rounding mode.\r\n    // The remainder (r) is calculated as: r = a - n * q.\r\n    //\r\n    // UP         0 The remainder is positive if the dividend is negative, else is negative.\r\n    // DOWN       1 The remainder has the same sign as the dividend (JavaScript %).\r\n    // FLOOR      3 The remainder has the same sign as the divisor (Python %).\r\n    // HALF_EVEN  6 The IEEE 754 remainder function.\r\n    // EUCLID     9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive.\r\n    //\r\n    // Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian\r\n    // division (9) are commonly used for the modulus operation. The other rounding modes can also\r\n    // be used, but they may not give useful results.\r\n    modulo: 1,                             // 0 to 9\r\n\r\n    // The exponent value at and beneath which `toString` returns exponential notation.\r\n    // JavaScript numbers: -7\r\n    toExpNeg: -7,                          // 0 to -EXP_LIMIT\r\n\r\n    // The exponent value at and above which `toString` returns exponential notation.\r\n    // JavaScript numbers: 21\r\n    toExpPos:  21,                         // 0 to EXP_LIMIT\r\n\r\n    // The minimum exponent value, beneath which underflow to zero occurs.\r\n    // JavaScript numbers: -324  (5e-324)\r\n    minE: -EXP_LIMIT,                      // -1 to -EXP_LIMIT\r\n\r\n    // The maximum exponent value, above which overflow to Infinity occurs.\r\n    // JavaScript numbers: 308  (1.7976931348623157e+308)\r\n    maxE: EXP_LIMIT,                       // 1 to EXP_LIMIT\r\n\r\n    // Whether to use cryptographically-secure random number generation, if available.\r\n    crypto: false                          // true/false\r\n  },\r\n\r\n\r\n// ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- //\r\n\r\n\r\n  inexact, quadrant,\r\n  external = true,\r\n\r\n  decimalError = '[DecimalError] ',\r\n  invalidArgument = decimalError + 'Invalid argument: ',\r\n  precisionLimitExceeded = decimalError + 'Precision limit exceeded',\r\n  cryptoUnavailable = decimalError + 'crypto unavailable',\r\n  tag = '[object Decimal]',\r\n\r\n  mathfloor = Math.floor,\r\n  mathpow = Math.pow,\r\n\r\n  isBinary = /^0b([01]+(\\.[01]*)?|\\.[01]+)(p[+-]?\\d+)?$/i,\r\n  isHex = /^0x([0-9a-f]+(\\.[0-9a-f]*)?|\\.[0-9a-f]+)(p[+-]?\\d+)?$/i,\r\n  isOctal = /^0o([0-7]+(\\.[0-7]*)?|\\.[0-7]+)(p[+-]?\\d+)?$/i,\r\n  isDecimal = /^(\\d+(\\.\\d*)?|\\.\\d+)(e[+-]?\\d+)?$/i,\r\n\r\n  BASE = 1e7,\r\n  LOG_BASE = 7,\r\n  MAX_SAFE_INTEGER = 9007199254740991,\r\n\r\n  LN10_PRECISION = LN10.length - 1,\r\n  PI_PRECISION = PI.length - 1,\r\n\r\n  // Decimal.prototype object\r\n  P = { toStringTag: tag };\r\n\r\n\r\n// Decimal prototype methods\r\n\r\n\r\n/*\r\n *  absoluteValue             abs\r\n *  ceil\r\n *  clampedTo                 clamp\r\n *  comparedTo                cmp\r\n *  cosine                    cos\r\n *  cubeRoot                  cbrt\r\n *  decimalPlaces             dp\r\n *  dividedBy                 div\r\n *  dividedToIntegerBy        divToInt\r\n *  equals                    eq\r\n *  floor\r\n *  greaterThan               gt\r\n *  greaterThanOrEqualTo      gte\r\n *  hyperbolicCosine          cosh\r\n *  hyperbolicSine            sinh\r\n *  hyperbolicTangent         tanh\r\n *  inverseCosine             acos\r\n *  inverseHyperbolicCosine   acosh\r\n *  inverseHyperbolicSine     asinh\r\n *  inverseHyperbolicTangent  atanh\r\n *  inverseSine               asin\r\n *  inverseTangent            atan\r\n *  isFinite\r\n *  isInteger                 isInt\r\n *  isNaN\r\n *  isNegative                isNeg\r\n *  isPositive                isPos\r\n *  isZero\r\n *  lessThan                  lt\r\n *  lessThanOrEqualTo         lte\r\n *  logarithm                 log\r\n *  [maximum]                 [max]\r\n *  [minimum]                 [min]\r\n *  minus                     sub\r\n *  modulo                    mod\r\n *  naturalExponential        exp\r\n *  naturalLogarithm          ln\r\n *  negated                   neg\r\n *  plus                      add\r\n *  precision                 sd\r\n *  round\r\n *  sine                      sin\r\n *  squareRoot                sqrt\r\n *  tangent                   tan\r\n *  times                     mul\r\n *  toBinary\r\n *  toDecimalPlaces           toDP\r\n *  toExponential\r\n *  toFixed\r\n *  toFraction\r\n *  toHexadecimal             toHex\r\n *  toNearest\r\n *  toNumber\r\n *  toOctal\r\n *  toPower                   pow\r\n *  toPrecision\r\n *  toSignificantDigits       toSD\r\n *  toString\r\n *  truncated                 trunc\r\n *  valueOf                   toJSON\r\n */\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the absolute value of this Decimal.\r\n *\r\n */\r\nP.absoluteValue = P.abs = function () {\r\n  var x = new this.constructor(this);\r\n  if (x.s < 0) x.s = 1;\r\n  return finalise(x);\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the\r\n * direction of positive Infinity.\r\n *\r\n */\r\nP.ceil = function () {\r\n  return finalise(new this.constructor(this), this.e + 1, 2);\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the value of this Decimal clamped to the range\r\n * delineated by `min` and `max`.\r\n *\r\n * min {number|string|Decimal}\r\n * max {number|string|Decimal}\r\n *\r\n */\r\nP.clampedTo = P.clamp = function (min, max) {\r\n  var k,\r\n    x = this,\r\n    Ctor = x.constructor;\r\n  min = new Ctor(min);\r\n  max = new Ctor(max);\r\n  if (!min.s || !max.s) return new Ctor(NaN);\r\n  if (min.gt(max)) throw Error(invalidArgument + max);\r\n  k = x.cmp(min);\r\n  return k < 0 ? min : x.cmp(max) > 0 ? max : new Ctor(x);\r\n};\r\n\r\n\r\n/*\r\n * Return\r\n *   1    if the value of this Decimal is greater than the value of `y`,\r\n *  -1    if the value of this Decimal is less than the value of `y`,\r\n *   0    if they have the same value,\r\n *   NaN  if the value of either Decimal is NaN.\r\n *\r\n */\r\nP.comparedTo = P.cmp = function (y) {\r\n  var i, j, xdL, ydL,\r\n    x = this,\r\n    xd = x.d,\r\n    yd = (y = new x.constructor(y)).d,\r\n    xs = x.s,\r\n    ys = y.s;\r\n\r\n  // Either NaN or ±Infinity?\r\n  if (!xd || !yd) {\r\n    return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1;\r\n  }\r\n\r\n  // Either zero?\r\n  if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0;\r\n\r\n  // Signs differ?\r\n  if (xs !== ys) return xs;\r\n\r\n  // Compare exponents.\r\n  if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1;\r\n\r\n  xdL = xd.length;\r\n  ydL = yd.length;\r\n\r\n  // Compare digit by digit.\r\n  for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) {\r\n    if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1;\r\n  }\r\n\r\n  // Compare lengths.\r\n  return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1;\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the cosine of the value in radians of this Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-1, 1]\r\n *\r\n * cos(0)         = 1\r\n * cos(-0)        = 1\r\n * cos(Infinity)  = NaN\r\n * cos(-Infinity) = NaN\r\n * cos(NaN)       = NaN\r\n *\r\n */\r\nP.cosine = P.cos = function () {\r\n  var pr, rm,\r\n    x = this,\r\n    Ctor = x.constructor;\r\n\r\n  if (!x.d) return new Ctor(NaN);\r\n\r\n  // cos(0) = cos(-0) = 1\r\n  if (!x.d[0]) return new Ctor(1);\r\n\r\n  pr = Ctor.precision;\r\n  rm = Ctor.rounding;\r\n  Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;\r\n  Ctor.rounding = 1;\r\n\r\n  x = cosine(Ctor, toLessThanHalfPi(Ctor, x));\r\n\r\n  Ctor.precision = pr;\r\n  Ctor.rounding = rm;\r\n\r\n  return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true);\r\n};\r\n\r\n\r\n/*\r\n *\r\n * Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to\r\n * `precision` significant digits using rounding mode `rounding`.\r\n *\r\n *  cbrt(0)  =  0\r\n *  cbrt(-0) = -0\r\n *  cbrt(1)  =  1\r\n *  cbrt(-1) = -1\r\n *  cbrt(N)  =  N\r\n *  cbrt(-I) = -I\r\n *  cbrt(I)  =  I\r\n *\r\n * Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3))\r\n *\r\n */\r\nP.cubeRoot = P.cbrt = function () {\r\n  var e, m, n, r, rep, s, sd, t, t3, t3plusx,\r\n    x = this,\r\n    Ctor = x.constructor;\r\n\r\n  if (!x.isFinite() || x.isZero()) return new Ctor(x);\r\n  external = false;\r\n\r\n  // Initial estimate.\r\n  s = x.s * mathpow(x.s * x, 1 / 3);\r\n\r\n   // Math.cbrt underflow/overflow?\r\n   // Pass x to Math.pow as integer, then adjust the exponent of the result.\r\n  if (!s || Math.abs(s) == 1 / 0) {\r\n    n = digitsToString(x.d);\r\n    e = x.e;\r\n\r\n    // Adjust n exponent so it is a multiple of 3 away from x exponent.\r\n    if (s = (e - n.length + 1) % 3) n += (s == 1 || s == -2 ? '0' : '00');\r\n    s = mathpow(n, 1 / 3);\r\n\r\n    // Rarely, e may be one less than the result exponent value.\r\n    e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2));\r\n\r\n    if (s == 1 / 0) {\r\n      n = '5e' + e;\r\n    } else {\r\n      n = s.toExponential();\r\n      n = n.slice(0, n.indexOf('e') + 1) + e;\r\n    }\r\n\r\n    r = new Ctor(n);\r\n    r.s = x.s;\r\n  } else {\r\n    r = new Ctor(s.toString());\r\n  }\r\n\r\n  sd = (e = Ctor.precision) + 3;\r\n\r\n  // Halley's method.\r\n  // TODO? Compare Newton's method.\r\n  for (;;) {\r\n    t = r;\r\n    t3 = t.times(t).times(t);\r\n    t3plusx = t3.plus(x);\r\n    r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1);\r\n\r\n    // TODO? Replace with for-loop and checkRoundingDigits.\r\n    if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {\r\n      n = n.slice(sd - 3, sd + 1);\r\n\r\n      // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999\r\n      // , i.e. approaching a rounding boundary, continue the iteration.\r\n      if (n == '9999' || !rep && n == '4999') {\r\n\r\n        // On the first iteration only, check to see if rounding up gives the exact result as the\r\n        // nines may infinitely repeat.\r\n        if (!rep) {\r\n          finalise(t, e + 1, 0);\r\n\r\n          if (t.times(t).times(t).eq(x)) {\r\n            r = t;\r\n            break;\r\n          }\r\n        }\r\n\r\n        sd += 4;\r\n        rep = 1;\r\n      } else {\r\n\r\n        // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.\r\n        // If not, then there are further digits and m will be truthy.\r\n        if (!+n || !+n.slice(1) && n.charAt(0) == '5') {\r\n\r\n          // Truncate to the first rounding digit.\r\n          finalise(r, e + 1, 1);\r\n          m = !r.times(r).times(r).eq(x);\r\n        }\r\n\r\n        break;\r\n      }\r\n    }\r\n  }\r\n\r\n  external = true;\r\n\r\n  return finalise(r, e, Ctor.rounding, m);\r\n};\r\n\r\n\r\n/*\r\n * Return the number of decimal places of the value of this Decimal.\r\n *\r\n */\r\nP.decimalPlaces = P.dp = function () {\r\n  var w,\r\n    d = this.d,\r\n    n = NaN;\r\n\r\n  if (d) {\r\n    w = d.length - 1;\r\n    n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE;\r\n\r\n    // Subtract the number of trailing zeros of the last word.\r\n    w = d[w];\r\n    if (w) for (; w % 10 == 0; w /= 10) n--;\r\n    if (n < 0) n = 0;\r\n  }\r\n\r\n  return n;\r\n};\r\n\r\n\r\n/*\r\n *  n / 0 = I\r\n *  n / N = N\r\n *  n / I = 0\r\n *  0 / n = 0\r\n *  0 / 0 = N\r\n *  0 / N = N\r\n *  0 / I = 0\r\n *  N / n = N\r\n *  N / 0 = N\r\n *  N / N = N\r\n *  N / I = N\r\n *  I / n = I\r\n *  I / 0 = I\r\n *  I / N = N\r\n *  I / I = N\r\n *\r\n * Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to\r\n * `precision` significant digits using rounding mode `rounding`.\r\n *\r\n */\r\nP.dividedBy = P.div = function (y) {\r\n  return divide(this, new this.constructor(y));\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the integer part of dividing the value of this Decimal\r\n * by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`.\r\n *\r\n */\r\nP.dividedToIntegerBy = P.divToInt = function (y) {\r\n  var x = this,\r\n    Ctor = x.constructor;\r\n  return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding);\r\n};\r\n\r\n\r\n/*\r\n * Return true if the value of this Decimal is equal to the value of `y`, otherwise return false.\r\n *\r\n */\r\nP.equals = P.eq = function (y) {\r\n  return this.cmp(y) === 0;\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the\r\n * direction of negative Infinity.\r\n *\r\n */\r\nP.floor = function () {\r\n  return finalise(new this.constructor(this), this.e + 1, 3);\r\n};\r\n\r\n\r\n/*\r\n * Return true if the value of this Decimal is greater than the value of `y`, otherwise return\r\n * false.\r\n *\r\n */\r\nP.greaterThan = P.gt = function (y) {\r\n  return this.cmp(y) > 0;\r\n};\r\n\r\n\r\n/*\r\n * Return true if the value of this Decimal is greater than or equal to the value of `y`,\r\n * otherwise return false.\r\n *\r\n */\r\nP.greaterThanOrEqualTo = P.gte = function (y) {\r\n  var k = this.cmp(y);\r\n  return k == 1 || k === 0;\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this\r\n * Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [1, Infinity]\r\n *\r\n * cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ...\r\n *\r\n * cosh(0)         = 1\r\n * cosh(-0)        = 1\r\n * cosh(Infinity)  = Infinity\r\n * cosh(-Infinity) = Infinity\r\n * cosh(NaN)       = NaN\r\n *\r\n *  x        time taken (ms)   result\r\n * 1000      9                 9.8503555700852349694e+433\r\n * 10000     25                4.4034091128314607936e+4342\r\n * 100000    171               1.4033316802130615897e+43429\r\n * 1000000   3817              1.5166076984010437725e+434294\r\n * 10000000  abandoned after 2 minute wait\r\n *\r\n * TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x))\r\n *\r\n */\r\nP.hyperbolicCosine = P.cosh = function () {\r\n  var k, n, pr, rm, len,\r\n    x = this,\r\n    Ctor = x.constructor,\r\n    one = new Ctor(1);\r\n\r\n  if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN);\r\n  if (x.isZero()) return one;\r\n\r\n  pr = Ctor.precision;\r\n  rm = Ctor.rounding;\r\n  Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;\r\n  Ctor.rounding = 1;\r\n  len = x.d.length;\r\n\r\n  // Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1\r\n  // i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4))\r\n\r\n  // Estimate the optimum number of times to use the argument reduction.\r\n  // TODO? Estimation reused from cosine() and may not be optimal here.\r\n  if (len < 32) {\r\n    k = Math.ceil(len / 3);\r\n    n = (1 / tinyPow(4, k)).toString();\r\n  } else {\r\n    k = 16;\r\n    n = '2.3283064365386962890625e-10';\r\n  }\r\n\r\n  x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true);\r\n\r\n  // Reverse argument reduction\r\n  var cosh2_x,\r\n    i = k,\r\n    d8 = new Ctor(8);\r\n  for (; i--;) {\r\n    cosh2_x = x.times(x);\r\n    x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8))));\r\n  }\r\n\r\n  return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true);\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the hyperbolic sine of the value in radians of this\r\n * Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-Infinity, Infinity]\r\n *\r\n * sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ...\r\n *\r\n * sinh(0)         = 0\r\n * sinh(-0)        = -0\r\n * sinh(Infinity)  = Infinity\r\n * sinh(-Infinity) = -Infinity\r\n * sinh(NaN)       = NaN\r\n *\r\n * x        time taken (ms)\r\n * 10       2 ms\r\n * 100      5 ms\r\n * 1000     14 ms\r\n * 10000    82 ms\r\n * 100000   886 ms            1.4033316802130615897e+43429\r\n * 200000   2613 ms\r\n * 300000   5407 ms\r\n * 400000   8824 ms\r\n * 500000   13026 ms          8.7080643612718084129e+217146\r\n * 1000000  48543 ms\r\n *\r\n * TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x))\r\n *\r\n */\r\nP.hyperbolicSine = P.sinh = function () {\r\n  var k, pr, rm, len,\r\n    x = this,\r\n    Ctor = x.constructor;\r\n\r\n  if (!x.isFinite() || x.isZero()) return new Ctor(x);\r\n\r\n  pr = Ctor.precision;\r\n  rm = Ctor.rounding;\r\n  Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;\r\n  Ctor.rounding = 1;\r\n  len = x.d.length;\r\n\r\n  if (len < 3) {\r\n    x = taylorSeries(Ctor, 2, x, x, true);\r\n  } else {\r\n\r\n    // Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x))\r\n    // i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3))\r\n    // 3 multiplications and 1 addition\r\n\r\n    // Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x)))\r\n    // i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5)))\r\n    // 4 multiplications and 2 additions\r\n\r\n    // Estimate the optimum number of times to use the argument reduction.\r\n    k = 1.4 * Math.sqrt(len);\r\n    k = k > 16 ? 16 : k | 0;\r\n\r\n    x = x.times(1 / tinyPow(5, k));\r\n    x = taylorSeries(Ctor, 2, x, x, true);\r\n\r\n    // Reverse argument reduction\r\n    var sinh2_x,\r\n      d5 = new Ctor(5),\r\n      d16 = new Ctor(16),\r\n      d20 = new Ctor(20);\r\n    for (; k--;) {\r\n      sinh2_x = x.times(x);\r\n      x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20))));\r\n    }\r\n  }\r\n\r\n  Ctor.precision = pr;\r\n  Ctor.rounding = rm;\r\n\r\n  return finalise(x, pr, rm, true);\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this\r\n * Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-1, 1]\r\n *\r\n * tanh(x) = sinh(x) / cosh(x)\r\n *\r\n * tanh(0)         = 0\r\n * tanh(-0)        = -0\r\n * tanh(Infinity)  = 1\r\n * tanh(-Infinity) = -1\r\n * tanh(NaN)       = NaN\r\n *\r\n */\r\nP.hyperbolicTangent = P.tanh = function () {\r\n  var pr, rm,\r\n    x = this,\r\n    Ctor = x.constructor;\r\n\r\n  if (!x.isFinite()) return new Ctor(x.s);\r\n  if (x.isZero()) return new Ctor(x);\r\n\r\n  pr = Ctor.precision;\r\n  rm = Ctor.rounding;\r\n  Ctor.precision = pr + 7;\r\n  Ctor.rounding = 1;\r\n\r\n  return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm);\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of\r\n * this Decimal.\r\n *\r\n * Domain: [-1, 1]\r\n * Range: [0, pi]\r\n *\r\n * acos(x) = pi/2 - asin(x)\r\n *\r\n * acos(0)       = pi/2\r\n * acos(-0)      = pi/2\r\n * acos(1)       = 0\r\n * acos(-1)      = pi\r\n * acos(1/2)     = pi/3\r\n * acos(-1/2)    = 2*pi/3\r\n * acos(|x| > 1) = NaN\r\n * acos(NaN)     = NaN\r\n *\r\n */\r\nP.inverseCosine = P.acos = function () {\r\n  var halfPi,\r\n    x = this,\r\n    Ctor = x.constructor,\r\n    k = x.abs().cmp(1),\r\n    pr = Ctor.precision,\r\n    rm = Ctor.rounding;\r\n\r\n  if (k !== -1) {\r\n    return k === 0\r\n      // |x| is 1\r\n      ? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0)\r\n      // |x| > 1 or x is NaN\r\n      : new Ctor(NaN);\r\n  }\r\n\r\n  if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5);\r\n\r\n  // TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3\r\n\r\n  Ctor.precision = pr + 6;\r\n  Ctor.rounding = 1;\r\n\r\n  x = x.asin();\r\n  halfPi = getPi(Ctor, pr + 4, rm).times(0.5);\r\n\r\n  Ctor.precision = pr;\r\n  Ctor.rounding = rm;\r\n\r\n  return halfPi.minus(x);\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the\r\n * value of this Decimal.\r\n *\r\n * Domain: [1, Infinity]\r\n * Range: [0, Infinity]\r\n *\r\n * acosh(x) = ln(x + sqrt(x^2 - 1))\r\n *\r\n * acosh(x < 1)     = NaN\r\n * acosh(NaN)       = NaN\r\n * acosh(Infinity)  = Infinity\r\n * acosh(-Infinity) = NaN\r\n * acosh(0)         = NaN\r\n * acosh(-0)        = NaN\r\n * acosh(1)         = 0\r\n * acosh(-1)        = NaN\r\n *\r\n */\r\nP.inverseHyperbolicCosine = P.acosh = function () {\r\n  var pr, rm,\r\n    x = this,\r\n    Ctor = x.constructor;\r\n\r\n  if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN);\r\n  if (!x.isFinite()) return new Ctor(x);\r\n\r\n  pr = Ctor.precision;\r\n  rm = Ctor.rounding;\r\n  Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4;\r\n  Ctor.rounding = 1;\r\n  external = false;\r\n\r\n  x = x.times(x).minus(1).sqrt().plus(x);\r\n\r\n  external = true;\r\n  Ctor.precision = pr;\r\n  Ctor.rounding = rm;\r\n\r\n  return x.ln();\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value\r\n * of this Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-Infinity, Infinity]\r\n *\r\n * asinh(x) = ln(x + sqrt(x^2 + 1))\r\n *\r\n * asinh(NaN)       = NaN\r\n * asinh(Infinity)  = Infinity\r\n * asinh(-Infinity) = -Infinity\r\n * asinh(0)         = 0\r\n * asinh(-0)        = -0\r\n *\r\n */\r\nP.inverseHyperbolicSine = P.asinh = function () {\r\n  var pr, rm,\r\n    x = this,\r\n    Ctor = x.constructor;\r\n\r\n  if (!x.isFinite() || x.isZero()) return new Ctor(x);\r\n\r\n  pr = Ctor.precision;\r\n  rm = Ctor.rounding;\r\n  Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6;\r\n  Ctor.rounding = 1;\r\n  external = false;\r\n\r\n  x = x.times(x).plus(1).sqrt().plus(x);\r\n\r\n  external = true;\r\n  Ctor.precision = pr;\r\n  Ctor.rounding = rm;\r\n\r\n  return x.ln();\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the\r\n * value of this Decimal.\r\n *\r\n * Domain: [-1, 1]\r\n * Range: [-Infinity, Infinity]\r\n *\r\n * atanh(x) = 0.5 * ln((1 + x) / (1 - x))\r\n *\r\n * atanh(|x| > 1)   = NaN\r\n * atanh(NaN)       = NaN\r\n * atanh(Infinity)  = NaN\r\n * atanh(-Infinity) = NaN\r\n * atanh(0)         = 0\r\n * atanh(-0)        = -0\r\n * atanh(1)         = Infinity\r\n * atanh(-1)        = -Infinity\r\n *\r\n */\r\nP.inverseHyperbolicTangent = P.atanh = function () {\r\n  var pr, rm, wpr, xsd,\r\n    x = this,\r\n    Ctor = x.constructor;\r\n\r\n  if (!x.isFinite()) return new Ctor(NaN);\r\n  if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN);\r\n\r\n  pr = Ctor.precision;\r\n  rm = Ctor.rounding;\r\n  xsd = x.sd();\r\n\r\n  if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true);\r\n\r\n  Ctor.precision = wpr = xsd - x.e;\r\n\r\n  x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1);\r\n\r\n  Ctor.precision = pr + 4;\r\n  Ctor.rounding = 1;\r\n\r\n  x = x.ln();\r\n\r\n  Ctor.precision = pr;\r\n  Ctor.rounding = rm;\r\n\r\n  return x.times(0.5);\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this\r\n * Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-pi/2, pi/2]\r\n *\r\n * asin(x) = 2*atan(x/(1 + sqrt(1 - x^2)))\r\n *\r\n * asin(0)       = 0\r\n * asin(-0)      = -0\r\n * asin(1/2)     = pi/6\r\n * asin(-1/2)    = -pi/6\r\n * asin(1)       = pi/2\r\n * asin(-1)      = -pi/2\r\n * asin(|x| > 1) = NaN\r\n * asin(NaN)     = NaN\r\n *\r\n * TODO? Compare performance of Taylor series.\r\n *\r\n */\r\nP.inverseSine = P.asin = function () {\r\n  var halfPi, k,\r\n    pr, rm,\r\n    x = this,\r\n    Ctor = x.constructor;\r\n\r\n  if (x.isZero()) return new Ctor(x);\r\n\r\n  k = x.abs().cmp(1);\r\n  pr = Ctor.precision;\r\n  rm = Ctor.rounding;\r\n\r\n  if (k !== -1) {\r\n\r\n    // |x| is 1\r\n    if (k === 0) {\r\n      halfPi = getPi(Ctor, pr + 4, rm).times(0.5);\r\n      halfPi.s = x.s;\r\n      return halfPi;\r\n    }\r\n\r\n    // |x| > 1 or x is NaN\r\n    return new Ctor(NaN);\r\n  }\r\n\r\n  // TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6\r\n\r\n  Ctor.precision = pr + 6;\r\n  Ctor.rounding = 1;\r\n\r\n  x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan();\r\n\r\n  Ctor.precision = pr;\r\n  Ctor.rounding = rm;\r\n\r\n  return x.times(2);\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value\r\n * of this Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-pi/2, pi/2]\r\n *\r\n * atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...\r\n *\r\n * atan(0)         = 0\r\n * atan(-0)        = -0\r\n * atan(1)         = pi/4\r\n * atan(-1)        = -pi/4\r\n * atan(Infinity)  = pi/2\r\n * atan(-Infinity) = -pi/2\r\n * atan(NaN)       = NaN\r\n *\r\n */\r\nP.inverseTangent = P.atan = function () {\r\n  var i, j, k, n, px, t, r, wpr, x2,\r\n    x = this,\r\n    Ctor = x.constructor,\r\n    pr = Ctor.precision,\r\n    rm = Ctor.rounding;\r\n\r\n  if (!x.isFinite()) {\r\n    if (!x.s) return new Ctor(NaN);\r\n    if (pr + 4 <= PI_PRECISION) {\r\n      r = getPi(Ctor, pr + 4, rm).times(0.5);\r\n      r.s = x.s;\r\n      return r;\r\n    }\r\n  } else if (x.isZero()) {\r\n    return new Ctor(x);\r\n  } else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) {\r\n    r = getPi(Ctor, pr + 4, rm).times(0.25);\r\n    r.s = x.s;\r\n    return r;\r\n  }\r\n\r\n  Ctor.precision = wpr = pr + 10;\r\n  Ctor.rounding = 1;\r\n\r\n  // TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x);\r\n\r\n  // Argument reduction\r\n  // Ensure |x| < 0.42\r\n  // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2)))\r\n\r\n  k = Math.min(28, wpr / LOG_BASE + 2 | 0);\r\n\r\n  for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1));\r\n\r\n  external = false;\r\n\r\n  j = Math.ceil(wpr / LOG_BASE);\r\n  n = 1;\r\n  x2 = x.times(x);\r\n  r = new Ctor(x);\r\n  px = x;\r\n\r\n  // atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...\r\n  for (; i !== -1;) {\r\n    px = px.times(x2);\r\n    t = r.minus(px.div(n += 2));\r\n\r\n    px = px.times(x2);\r\n    r = t.plus(px.div(n += 2));\r\n\r\n    if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;);\r\n  }\r\n\r\n  if (k) r = r.times(2 << (k - 1));\r\n\r\n  external = true;\r\n\r\n  return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true);\r\n};\r\n\r\n\r\n/*\r\n * Return true if the value of this Decimal is a finite number, otherwise return false.\r\n *\r\n */\r\nP.isFinite = function () {\r\n  return !!this.d;\r\n};\r\n\r\n\r\n/*\r\n * Return true if the value of this Decimal is an integer, otherwise return false.\r\n *\r\n */\r\nP.isInteger = P.isInt = function () {\r\n  return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2;\r\n};\r\n\r\n\r\n/*\r\n * Return true if the value of this Decimal is NaN, otherwise return false.\r\n *\r\n */\r\nP.isNaN = function () {\r\n  return !this.s;\r\n};\r\n\r\n\r\n/*\r\n * Return true if the value of this Decimal is negative, otherwise return false.\r\n *\r\n */\r\nP.isNegative = P.isNeg = function () {\r\n  return this.s < 0;\r\n};\r\n\r\n\r\n/*\r\n * Return true if the value of this Decimal is positive, otherwise return false.\r\n *\r\n */\r\nP.isPositive = P.isPos = function () {\r\n  return this.s > 0;\r\n};\r\n\r\n\r\n/*\r\n * Return true if the value of this Decimal is 0 or -0, otherwise return false.\r\n *\r\n */\r\nP.isZero = function () {\r\n  return !!this.d && this.d[0] === 0;\r\n};\r\n\r\n\r\n/*\r\n * Return true if the value of this Decimal is less than `y`, otherwise return false.\r\n *\r\n */\r\nP.lessThan = P.lt = function (y) {\r\n  return this.cmp(y) < 0;\r\n};\r\n\r\n\r\n/*\r\n * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false.\r\n *\r\n */\r\nP.lessThanOrEqualTo = P.lte = function (y) {\r\n  return this.cmp(y) < 1;\r\n};\r\n\r\n\r\n/*\r\n * Return the logarithm of the value of this Decimal to the specified base, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * If no base is specified, return log[10](arg).\r\n *\r\n * log[base](arg) = ln(arg) / ln(base)\r\n *\r\n * The result will always be correctly rounded if the base of the log is 10, and 'almost always'\r\n * otherwise:\r\n *\r\n * Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen\r\n * rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error\r\n * between the result and the correctly rounded result will be one ulp (unit in the last place).\r\n *\r\n * log[-b](a)       = NaN\r\n * log[0](a)        = NaN\r\n * log[1](a)        = NaN\r\n * log[NaN](a)      = NaN\r\n * log[Infinity](a) = NaN\r\n * log[b](0)        = -Infinity\r\n * log[b](-0)       = -Infinity\r\n * log[b](-a)       = NaN\r\n * log[b](1)        = 0\r\n * log[b](Infinity) = Infinity\r\n * log[b](NaN)      = NaN\r\n *\r\n * [base] {number|string|Decimal} The base of the logarithm.\r\n *\r\n */\r\nP.logarithm = P.log = function (base) {\r\n  var isBase10, d, denominator, k, inf, num, sd, r,\r\n    arg = this,\r\n    Ctor = arg.constructor,\r\n    pr = Ctor.precision,\r\n    rm = Ctor.rounding,\r\n    guard = 5;\r\n\r\n  // Default base is 10.\r\n  if (base == null) {\r\n    base = new Ctor(10);\r\n    isBase10 = true;\r\n  } else {\r\n    base = new Ctor(base);\r\n    d = base.d;\r\n\r\n    // Return NaN if base is negative, or non-finite, or is 0 or 1.\r\n    if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN);\r\n\r\n    isBase10 = base.eq(10);\r\n  }\r\n\r\n  d = arg.d;\r\n\r\n  // Is arg negative, non-finite, 0 or 1?\r\n  if (arg.s < 0 || !d || !d[0] || arg.eq(1)) {\r\n    return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0);\r\n  }\r\n\r\n  // The result will have a non-terminating decimal expansion if base is 10 and arg is not an\r\n  // integer power of 10.\r\n  if (isBase10) {\r\n    if (d.length > 1) {\r\n      inf = true;\r\n    } else {\r\n      for (k = d[0]; k % 10 === 0;) k /= 10;\r\n      inf = k !== 1;\r\n    }\r\n  }\r\n\r\n  external = false;\r\n  sd = pr + guard;\r\n  num = naturalLogarithm(arg, sd);\r\n  denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);\r\n\r\n  // The result will have 5 rounding digits.\r\n  r = divide(num, denominator, sd, 1);\r\n\r\n  // If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000,\r\n  // calculate 10 further digits.\r\n  //\r\n  // If the result is known to have an infinite decimal expansion, repeat this until it is clear\r\n  // that the result is above or below the boundary. Otherwise, if after calculating the 10\r\n  // further digits, the last 14 are nines, round up and assume the result is exact.\r\n  // Also assume the result is exact if the last 14 are zero.\r\n  //\r\n  // Example of a result that will be incorrectly rounded:\r\n  // log[1048576](4503599627370502) = 2.60000000000000009610279511444746...\r\n  // The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it\r\n  // will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so\r\n  // the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal\r\n  // place is still 2.6.\r\n  if (checkRoundingDigits(r.d, k = pr, rm)) {\r\n\r\n    do {\r\n      sd += 10;\r\n      num = naturalLogarithm(arg, sd);\r\n      denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);\r\n      r = divide(num, denominator, sd, 1);\r\n\r\n      if (!inf) {\r\n\r\n        // Check for 14 nines from the 2nd rounding digit, as the first may be 4.\r\n        if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) {\r\n          r = finalise(r, pr + 1, 0);\r\n        }\r\n\r\n        break;\r\n      }\r\n    } while (checkRoundingDigits(r.d, k += 10, rm));\r\n  }\r\n\r\n  external = true;\r\n\r\n  return finalise(r, pr, rm);\r\n};\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal.\r\n *\r\n * arguments {number|string|Decimal}\r\n *\r\nP.max = function () {\r\n  Array.prototype.push.call(arguments, this);\r\n  return maxOrMin(this.constructor, arguments, 'lt');\r\n};\r\n */\r\n\r\n\r\n/*\r\n * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal.\r\n *\r\n * arguments {number|string|Decimal}\r\n *\r\nP.min = function () {\r\n  Array.prototype.push.call(arguments, this);\r\n  return maxOrMin(this.constructor, arguments, 'gt');\r\n};\r\n */\r\n\r\n\r\n/*\r\n *  n - 0 = n\r\n *  n - N = N\r\n *  n - I = -I\r\n *  0 - n = -n\r\n *  0 - 0 = 0\r\n *  0 - N = N\r\n *  0 - I = -I\r\n *  N - n = N\r\n *  N - 0 = N\r\n *  N - N = N\r\n *  N - I = N\r\n *  I - n = I\r\n *  I - 0 = I\r\n *  I - N = N\r\n *  I - I = N\r\n *\r\n * Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n */\r\nP.minus = P.sub = function (y) {\r\n  var d, e, i, j, k, len, pr, rm, xd, xe, xLTy, yd,\r\n    x = this,\r\n    Ctor = x.constructor;\r\n\r\n  y = new Ctor(y);\r\n\r\n  // If either is not finite...\r\n  if (!x.d || !y.d) {\r\n\r\n