@raydium-io/raydium-sdk-v2/lib/raydium/clmm/utils/tickarrayBitmap.mjs.map

An SDK for building applications on top of Raydium.

{"version":3,"sources":["../../../../src/raydium/clmm/utils/constants.ts","../../../../src/raydium/clmm/utils/tick.ts","../../../../node_modules/decimal.js/decimal.mjs","../../../../src/raydium/clmm/utils/math.ts","../../../../src/common/transfer.ts","../../../../src/common/accountInfo.ts","../../../../src/common/logger.ts","../../../../src/common/bignumber.ts","../../../../src/module/amount.ts","../../../../src/module/formatter.ts","../../../../src/module/fraction.ts","../../../../src/common/constant.ts","../../../../src/raydium/token/constant.ts","../../../../src/module/token.ts","../../../../src/common/pubKey.ts","../../../../src/module/currency.ts","../../../../src/module/percent.ts","../../../../src/module/price.ts","../../../../src/common/lodash.ts","../../../../src/common/pda.ts","../../../../src/common/txTool/txUtils.ts","../../../../src/common/programId.ts","../../../../src/common/txTool/lookupTable.ts","../../../../src/common/txTool/txTool.ts","../../../../src/common/utility.ts","../../../../src/common/fee.ts","../../../../src/raydium/clmm/utils/util.ts","../../../../src/raydium/clmm/utils/pda.ts","../../../../src/raydium/clmm/utils/pool.ts","../../../../src/marshmallow/index.ts","../../../../src/marshmallow/buffer-layout.ts","../../../../src/raydium/clmm/layout.ts","../../../../src/raydium/clmm/utils/position.ts","../../../../src/raydium/clmm/utils/tickQuery.ts","../../../../src/raydium/clmm/utils/tickarrayBitmap.ts"],"sourcesContent":["import BN from \"bn.js\";\n\nexport const ZERO = new BN(0);\nexport const ONE = new BN(1);\nexport const NEGATIVE_ONE = new BN(-1);\n\nexport const Q64 = new BN(1).shln(64);\nexport const Q128 = new BN(1).shln(128);\n\nexport const MaxU64 = Q64.sub(ONE);\n\nexport const U64Resolution = 64;\n\nexport const MaxUint128 = Q128.subn(1);\n\nexport const MIN_TICK = -443636;\nexport const MAX_TICK = -MIN_TICK;\n\nexport const MIN_SQRT_PRICE_X64: BN = new BN(\"4295048016\");\nexport const MAX_SQRT_PRICE_X64: BN = new BN(\"79226673521066979257578248091\");\n\nexport const MIN_SQRT_PRICE_X64_ADD_ONE: BN = new BN(\"4295048017\");\nexport const MAX_SQRT_PRICE_X64_SUB_ONE: BN = new BN(\"79226673521066979257578248090\");\n\n// export const MIN_TICK_ARRAY_START_INDEX = -307200;\n// export const MAX_TICK_ARRAY_START_INDEX = 306600;\n\nexport const BIT_PRECISION = 16;\nexport const LOG_B_2_X32 = \"59543866431248\";\nexport const LOG_B_P_ERR_MARGIN_LOWER_X64 = \"184467440737095516\";\nexport const LOG_B_P_ERR_MARGIN_UPPER_X64 = \"15793534762490258745\";\n\nexport const FEE_RATE_DENOMINATOR = new BN(10).pow(new BN(6));\n\nexport enum Fee {\n  rate_500 = 500, //  500 / 10e6 = 0.0005\n  rate_3000 = 3000, // 3000/ 10e6 = 0.003\n  rate_10000 = 10000, // 10000 /10e6 = 0.01\n}\nexport const TICK_SPACINGS: { [amount in Fee]: number } = {\n  [Fee.rate_500]: 10,\n  [Fee.rate_3000]: 60,\n  [Fee.rate_10000]: 200,\n};\n\nexport const mockCreatePoolInfo = {\n  version: 6,\n  liquidity: ZERO,\n  tickCurrent: 0,\n  feeGrowthGlobalX64A: ZERO,\n  feeGrowthGlobalX64B: ZERO,\n  protocolFeesTokenA: ZERO,\n  protocolFeesTokenB: ZERO,\n  swapInAmountTokenA: ZERO,\n  swapOutAmountTokenB: ZERO,\n  swapInAmountTokenB: ZERO,\n  swapOutAmountTokenA: ZERO,\n  tickArrayBitmap: [],\n\n  rewardInfos: [],\n\n  day: {\n    volume: 0,\n    volumeFee: 0,\n    feeA: 0,\n    feeB: 0,\n    feeApr: 0,\n    rewardApr: { A: 0, B: 0, C: 0 },\n    apr: 0,\n    priceMax: 0,\n    priceMin: 0,\n  },\n  week: {\n    volume: 0,\n    volumeFee: 0,\n    feeA: 0,\n    feeB: 0,\n    feeApr: 0,\n    rewardApr: { A: 0, B: 0, C: 0 },\n    apr: 0,\n    priceMax: 0,\n    priceMin: 0,\n  },\n  month: {\n    volume: 0,\n    volumeFee: 0,\n    feeA: 0,\n    feeB: 0,\n    feeApr: 0,\n    rewardApr: { A: 0, B: 0, C: 0 },\n    apr: 0,\n    priceMax: 0,\n    priceMin: 0,\n  },\n  tvl: 0,\n};\n\nexport const mockV3CreatePoolInfo = {\n  tvl: 0,\n  volumeQuote: 0,\n  mintAmountA: 0,\n  mintAmountB: 0,\n  rewardDefaultInfos: [],\n  farmUpcomingCount: 0,\n  farmOngoingCount: 0,\n  farmFinishedCount: 0,\n\n  day: {\n    volume: 0,\n    volumeQuote: 0,\n    volumeFee: 0,\n    apr: 0,\n    feeApr: 0,\n    priceMin: 0,\n    priceMax: 0,\n    rewardApr: [0],\n  },\n  week: {\n    volume: 0,\n    volumeQuote: 0,\n    volumeFee: 0,\n    apr: 0,\n    feeApr: 0,\n    priceMin: 0,\n    priceMax: 0,\n    rewardApr: [0],\n  },\n  month: {\n    volume: 0,\n    volumeQuote: 0,\n    volumeFee: 0,\n    apr: 0,\n    feeApr: 0,\n    priceMin: 0,\n    priceMax: 0,\n    rewardApr: [0],\n  },\n  pooltype: [],\n};\n\nexport const U64_IGNORE_RANGE = new BN(\"18446744073700000000\");\n","import { PublicKey } from \"@solana/web3.js\";\nimport BN from \"bn.js\";\nimport Decimal from \"decimal.js\";\n\nimport { ApiV3PoolInfoConcentratedItem } from \"../../../api/type\";\nimport { ClmmPoolInfo } from \"../type\";\nimport { MAX_TICK, MIN_TICK } from \"./constants\";\nimport { SqrtPriceMath, TickMath } from \"./math\";\nimport { getPdaTickArrayAddress } from \"./pda\";\nimport { TickQuery } from \"./tickQuery\";\nimport { TickArrayBitmapExtensionLayout } from \"../layout\";\n\nexport const TICK_ARRAY_SIZE = 60;\nexport const TICK_ARRAY_BITMAP_SIZE = 512;\n\nexport interface ReturnTypeGetTickPrice {\n  tick: number;\n  price: Decimal;\n  tickSqrtPriceX64: BN;\n}\n\nexport interface ReturnTypeGetPriceAndTick {\n  tick: number;\n  price: Decimal;\n}\n\nexport type Tick = {\n  tick: number;\n  liquidityNet: BN;\n  liquidityGross: BN;\n  feeGrowthOutsideX64A: BN;\n  feeGrowthOutsideX64B: BN;\n  rewardGrowthsOutsideX64: BN[];\n};\n\nexport type TickArray = {\n  address: PublicKey;\n  poolId: PublicKey;\n  startTickIndex: number;\n  ticks: Tick[];\n  initializedTickCount: number;\n};\n\nexport type TickState = {\n  tick: number;\n  liquidityNet: BN;\n  liquidityGross: BN;\n  feeGrowthOutsideX64A: BN;\n  feeGrowthOutsideX64B: BN;\n  tickCumulativeOutside: BN;\n  secondsPerLiquidityOutsideX64: BN;\n  secondsOutside: number;\n  rewardGrowthsOutside: BN[];\n};\n\nexport type TickArrayState = {\n  ammPool: PublicKey;\n  startTickIndex: number;\n  ticks: TickState[];\n  initializedTickCount: number;\n};\n\nexport class TickUtils {\n  public static getTickArrayAddressByTick(\n    programId: PublicKey,\n    poolId: PublicKey,\n    tickIndex: number,\n    tickSpacing: number,\n  ): PublicKey {\n    const startIndex = TickUtils.getTickArrayStartIndexByTick(tickIndex, tickSpacing);\n    const { publicKey: tickArrayAddress } = getPdaTickArrayAddress(programId, poolId, startIndex);\n    return tickArrayAddress;\n  }\n\n  public static getTickOffsetInArray(tickIndex: number, tickSpacing: number): number {\n    if (tickIndex % tickSpacing != 0) {\n      throw new Error(\"tickIndex % tickSpacing not equal 0\");\n    }\n    const startTickIndex = TickUtils.getTickArrayStartIndexByTick(tickIndex, tickSpacing);\n    const offsetInArray = Math.floor((tickIndex - startTickIndex) / tickSpacing);\n    if (offsetInArray < 0 || offsetInArray >= TICK_ARRAY_SIZE) {\n      throw new Error(\"tick offset in array overflow\");\n    }\n    return offsetInArray;\n  }\n\n  public static getTickArrayBitIndex(tickIndex: number, tickSpacing: number): number {\n    const ticksInArray = TickQuery.tickCount(tickSpacing);\n\n    let startIndex: number = tickIndex / ticksInArray;\n    if (tickIndex < 0 && tickIndex % ticksInArray != 0) {\n      startIndex = Math.ceil(startIndex) - 1;\n    } else {\n      startIndex = Math.floor(startIndex);\n    }\n    return startIndex;\n  }\n\n  public static getTickArrayStartIndexByTick(tickIndex: number, tickSpacing: number): number {\n    return this.getTickArrayBitIndex(tickIndex, tickSpacing) * TickQuery.tickCount(tickSpacing);\n  }\n\n  public static getTickArrayOffsetInBitmapByTick(tick: number, tickSpacing: number): number {\n    const multiplier = tickSpacing * TICK_ARRAY_SIZE;\n    const compressed = Math.floor(tick / multiplier) + 512;\n    return Math.abs(compressed);\n  }\n\n  public static checkTickArrayIsInitialized(\n    bitmap: BN,\n    tick: number,\n    tickSpacing: number,\n  ): {\n    isInitialized: boolean;\n    startIndex: number;\n  } {\n    const multiplier = tickSpacing * TICK_ARRAY_SIZE;\n    const compressed = Math.floor(tick / multiplier) + 512;\n    const bitPos = Math.abs(compressed);\n    return {\n      isInitialized: bitmap.testn(bitPos),\n      startIndex: (bitPos - 512) * multiplier,\n    };\n  }\n\n  public static getNextTickArrayStartIndex(\n    lastTickArrayStartIndex: number,\n    tickSpacing: number,\n    zeroForOne: boolean,\n  ): number {\n    return zeroForOne\n      ? lastTickArrayStartIndex - tickSpacing * TICK_ARRAY_SIZE\n      : lastTickArrayStartIndex + tickSpacing * TICK_ARRAY_SIZE;\n  }\n\n  public static mergeTickArrayBitmap(bns: BN[]): BN {\n    let b = new BN(0);\n    for (let i = 0; i < bns.length; i++) {\n      b = b.add(bns[i].shln(64 * i));\n    }\n    return b;\n  }\n\n  public static getInitializedTickArrayInRange(\n    tickArrayBitmap: BN[],\n    exTickArrayBitmap: ReturnType<typeof TickArrayBitmapExtensionLayout.decode>,\n    tickSpacing: number,\n    tickArrayStartIndex: number,\n    expectedCount: number,\n  ): number[] {\n    const tickArrayOffset = Math.floor(tickArrayStartIndex / (tickSpacing * TICK_ARRAY_SIZE));\n    return [\n      // find right of currenct offset\n      ...TickUtils.searchLowBitFromStart(\n        tickArrayBitmap,\n        exTickArrayBitmap,\n        tickArrayOffset - 1,\n        expectedCount,\n        tickSpacing,\n      ),\n\n      // find left of current offset\n      ...TickUtils.searchHightBitFromStart(\n        tickArrayBitmap,\n        exTickArrayBitmap,\n        tickArrayOffset,\n        expectedCount,\n        tickSpacing,\n      ),\n    ];\n  }\n\n  public static getAllInitializedTickArrayStartIndex(\n    tickArrayBitmap: BN[],\n    exTickArrayBitmap: ReturnType<typeof TickArrayBitmapExtensionLayout.decode>,\n    tickSpacing: number,\n  ): number[] {\n    // find from offset 0 to 1024\n    return TickUtils.searchHightBitFromStart(\n      tickArrayBitmap,\n      exTickArrayBitmap,\n      -7680,\n      TICK_ARRAY_BITMAP_SIZE,\n      tickSpacing,\n    );\n  }\n\n  public static getAllInitializedTickArrayInfo(\n    programId: PublicKey,\n    poolId: PublicKey,\n    tickArrayBitmap: BN[],\n    exTickArrayBitmap: ReturnType<typeof TickArrayBitmapExtensionLayout.decode>,\n    tickSpacing: number,\n  ): {\n    tickArrayStartIndex: number;\n    tickArrayAddress: PublicKey;\n  }[] {\n    const result: {\n      tickArrayStartIndex: number;\n      tickArrayAddress: PublicKey;\n    }[] = [];\n    const allInitializedTickArrayIndex: number[] = TickUtils.getAllInitializedTickArrayStartIndex(\n      tickArrayBitmap,\n      exTickArrayBitmap,\n      tickSpacing,\n    );\n    for (const startIndex of allInitializedTickArrayIndex) {\n      const { publicKey: address } = getPdaTickArrayAddress(programId, poolId, startIndex);\n      result.push({\n        tickArrayStartIndex: startIndex,\n        tickArrayAddress: address,\n      });\n    }\n    return result;\n  }\n\n  public static getAllInitializedTickInTickArray(tickArray: TickArrayState): TickState[] {\n    return tickArray.ticks.filter((i) => i.liquidityGross.gtn(0));\n  }\n\n  public static searchLowBitFromStart(\n    tickArrayBitmap: BN[],\n    exTickArrayBitmap: ReturnType<typeof TickArrayBitmapExtensionLayout.decode>,\n    currentTickArrayBitStartIndex: number,\n    expectedCount: number,\n    tickSpacing: number,\n  ): number[] {\n    const tickArrayBitmaps = [\n      ...[...exTickArrayBitmap.negativeTickArrayBitmap].reverse(),\n      tickArrayBitmap.slice(0, 8),\n      tickArrayBitmap.slice(8, 16),\n      ...exTickArrayBitmap.positiveTickArrayBitmap,\n    ].map((i) => TickUtils.mergeTickArrayBitmap(i));\n    const result: number[] = [];\n    while (currentTickArrayBitStartIndex >= -7680) {\n      const arrayIndex = Math.floor((currentTickArrayBitStartIndex + 7680) / 512);\n      const searchIndex = (currentTickArrayBitStartIndex + 7680) % 512;\n\n      if (tickArrayBitmaps[arrayIndex].testn(searchIndex)) result.push(currentTickArrayBitStartIndex);\n\n      currentTickArrayBitStartIndex--;\n      if (result.length === expectedCount) break;\n    }\n\n    const tickCount = TickQuery.tickCount(tickSpacing);\n    return result.map((i) => i * tickCount);\n  }\n\n  public static searchHightBitFromStart(\n    tickArrayBitmap: BN[],\n    exTickArrayBitmap: ReturnType<typeof TickArrayBitmapExtensionLayout.decode>,\n    currentTickArrayBitStartIndex: number,\n    expectedCount: number,\n    tickSpacing: number,\n  ): number[] {\n    const tickArrayBitmaps = [\n      ...[...exTickArrayBitmap.negativeTickArrayBitmap].reverse(),\n      tickArrayBitmap.slice(0, 8),\n      tickArrayBitmap.slice(8, 16),\n      ...exTickArrayBitmap.positiveTickArrayBitmap,\n    ].map((i) => TickUtils.mergeTickArrayBitmap(i));\n    const result: number[] = [];\n    while (currentTickArrayBitStartIndex < 7680) {\n      const arrayIndex = Math.floor((currentTickArrayBitStartIndex + 7680) / 512);\n      const searchIndex = (currentTickArrayBitStartIndex + 7680) % 512;\n\n      if (tickArrayBitmaps[arrayIndex].testn(searchIndex)) result.push(currentTickArrayBitStartIndex);\n\n      currentTickArrayBitStartIndex++;\n      if (result.length === expectedCount) break;\n    }\n\n    const tickCount = TickQuery.tickCount(tickSpacing);\n    return result.map((i) => i * tickCount);\n  }\n\n  public static checkIsOutOfBoundary(tick: number): boolean {\n    return tick < MIN_TICK || tick > MAX_TICK;\n  }\n\n  public static nextInitTick(\n    tickArrayCurrent: TickArray,\n    currentTickIndex: number,\n    tickSpacing: number,\n    zeroForOne: boolean,\n    t: boolean,\n  ): Tick | null {\n    const currentTickArrayStartIndex = TickQuery.getArrayStartIndex(currentTickIndex, tickSpacing);\n    if (currentTickArrayStartIndex != tickArrayCurrent.startTickIndex) {\n      return null;\n    }\n    let offsetInArray = Math.floor((currentTickIndex - tickArrayCurrent.startTickIndex) / tickSpacing);\n\n    if (zeroForOne) {\n      while (offsetInArray >= 0) {\n        if (tickArrayCurrent.ticks[offsetInArray].liquidityGross.gtn(0)) {\n          return tickArrayCurrent.ticks[offsetInArray];\n        }\n        offsetInArray = offsetInArray - 1;\n      }\n    } else {\n      if (!t) offsetInArray = offsetInArray + 1;\n      while (offsetInArray < TICK_ARRAY_SIZE) {\n        if (tickArrayCurrent.ticks[offsetInArray].liquidityGross.gtn(0)) {\n          return tickArrayCurrent.ticks[offsetInArray];\n        }\n        offsetInArray = offsetInArray + 1;\n      }\n    }\n    return null;\n  }\n\n  public static firstInitializedTick(tickArrayCurrent: TickArray, zeroForOne: boolean): Tick {\n    if (zeroForOne) {\n      let i = TICK_ARRAY_SIZE - 1;\n      while (i >= 0) {\n        if (tickArrayCurrent.ticks[i].liquidityGross.gtn(0)) {\n          return tickArrayCurrent.ticks[i];\n        }\n        i = i - 1;\n      }\n    } else {\n      let i = 0;\n      while (i < TICK_ARRAY_SIZE) {\n        if (tickArrayCurrent.ticks[i].liquidityGross.gtn(0)) {\n          return tickArrayCurrent.ticks[i];\n        }\n        i = i + 1;\n      }\n    }\n\n    throw Error(`firstInitializedTick check error: ${tickArrayCurrent} - ${zeroForOne}`);\n  }\n\n  public static _getTickPriceLegacy({\n    poolInfo,\n    tick,\n    baseIn,\n  }: {\n    poolInfo: ClmmPoolInfo;\n    tick: number;\n    baseIn: boolean;\n  }): ReturnTypeGetTickPrice {\n    const tickSqrtPriceX64 = SqrtPriceMath.getSqrtPriceX64FromTick(tick);\n    const tickPrice = SqrtPriceMath.sqrtPriceX64ToPrice(\n      tickSqrtPriceX64,\n      poolInfo.mintA.decimals,\n      poolInfo.mintB.decimals,\n    );\n\n    return baseIn\n      ? { tick, price: tickPrice, tickSqrtPriceX64 }\n      : { tick, price: new Decimal(1).div(tickPrice), tickSqrtPriceX64 };\n  }\n\n  public static _getPriceAndTickLegacy({\n    poolInfo,\n    price,\n    baseIn,\n  }: {\n    poolInfo: ClmmPoolInfo;\n    price: Decimal;\n    baseIn: boolean;\n  }): ReturnTypeGetPriceAndTick {\n    const _price = baseIn ? price : new Decimal(1).div(price);\n\n    const tick = TickMath.getTickWithPriceAndTickspacing(\n      _price,\n      poolInfo.ammConfig.tickSpacing,\n      poolInfo.mintA.decimals,\n      poolInfo.mintB.decimals,\n    );\n    const tickSqrtPriceX64 = SqrtPriceMath.getSqrtPriceX64FromTick(tick);\n    const tickPrice = SqrtPriceMath.sqrtPriceX64ToPrice(\n      tickSqrtPriceX64,\n      poolInfo.mintA.decimals,\n      poolInfo.mintB.decimals,\n    );\n\n    return baseIn ? { tick, price: tickPrice } : { tick, price: new Decimal(1).div(tickPrice) };\n  }\n\n  public static getTickPrice({\n    poolInfo,\n    tick,\n    baseIn,\n  }: {\n    poolInfo: ApiV3PoolInfoConcentratedItem;\n    tick: number;\n    baseIn: boolean;\n  }): ReturnTypeGetTickPrice {\n    const tickSqrtPriceX64 = SqrtPriceMath.getSqrtPriceX64FromTick(tick);\n    const tickPrice = SqrtPriceMath.sqrtPriceX64ToPrice(\n      tickSqrtPriceX64,\n      poolInfo.mintA.decimals,\n      poolInfo.mintB.decimals,\n    );\n\n    return baseIn\n      ? { tick, price: tickPrice, tickSqrtPriceX64 }\n      : { tick, price: new Decimal(1).div(tickPrice), tickSqrtPriceX64 };\n  }\n\n  public static getPriceAndTick({\n    poolInfo,\n    price,\n    baseIn,\n  }: {\n    poolInfo: ApiV3PoolInfoConcentratedItem;\n    price: Decimal;\n    baseIn: boolean;\n  }): ReturnTypeGetPriceAndTick {\n    const _price = baseIn ? price : new Decimal(1).div(price);\n\n    const tick = TickMath.getTickWithPriceAndTickspacing(\n      _price,\n      poolInfo.config.tickSpacing,\n      poolInfo.mintA.decimals,\n      poolInfo.mintB.decimals,\n    );\n    const tickSqrtPriceX64 = SqrtPriceMath.getSqrtPriceX64FromTick(tick);\n    const tickPrice = SqrtPriceMath.sqrtPriceX64ToPrice(\n      tickSqrtPriceX64,\n      poolInfo.mintA.decimals,\n      poolInfo.mintB.decimals,\n    );\n\n    return baseIn ? { tick, price: tickPrice } : { tick, price: new Decimal(1).div(tickPrice) };\n  }\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 thi