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BigNumber from 'bignumber.js';\n\nimport { BigIntMath, toBigInt } from '../utils/BigIntUtils';\nimport { HyperbolaPayoutCurve } from './HyperbolaPayoutCurve';\nimport { PolynomialPayoutCurve } from './PolynomialPayoutCurve';\n\nexport function zipWithIndex<T>(arr: T[]): [T, number][] {\n  return arr.map((a, i) => [a, i]);\n}\n\nexport function dropUntil<T>(data: T[], check: (_: T) => boolean): T[] {\n  for (let i = 0; i < data.length; i++) {\n    if (check(data[i])) {\n      return data.slice(i);\n    }\n  }\n  return [];\n}\n\nexport function decompose(\n  num: bigint,\n  base: number,\n  numDigits: number,\n): number[] {\n  let currentNumber = num;\n  const digits = [];\n  while (numDigits > 0) {\n    digits.push(Number(currentNumber % BigInt(base)));\n    currentNumber = currentNumber / BigInt(base);\n    numDigits--;\n  }\n  return digits.reverse();\n}\n\nexport function separatePrefix(\n  start: bigint,\n  end: bigint,\n  base: number,\n  numDigits: number,\n): {\n  prefixDigits: number[];\n  startDigits: number[];\n  endDigits: number[];\n} {\n  const startDigits = decompose(start, base, numDigits);\n  const endDigits = decompose(end, base, numDigits);\n\n  const prefixDigits: number[] = [];\n  for (let i = 0; i < startDigits.length; i++) {\n    if (startDigits[i] === endDigits[i]) {\n      prefixDigits.push(startDigits[i]);\n    } else break;\n  }\n\n  return {\n    prefixDigits,\n    startDigits: startDigits.splice(prefixDigits.length),\n    endDigits: endDigits.splice(prefixDigits.length),\n  };\n}\n\nexport function frontGroupings(digits: number[], base: number): number[][] {\n  const digitsReversed = Array.from(digits).reverse();\n  const nonZeroDigits = dropUntil(\n    zipWithIndex(digitsReversed),\n    (a) => a[0] !== 0,\n  );\n\n  if (nonZeroDigits.length === 0) {\n    return [[0]];\n  }\n  const fromFront = nonZeroDigits\n    .filter((_, i) => i !== nonZeroDigits.length - 1)\n    .flatMap(([d, i]) => {\n      const fixedDigits = Array.from(digits);\n      fixedDigits.length = fixedDigits.length - (i + 1);\n\n      const result: number[][] = [];\n      for (let n = d + 1; n < base; n++) {\n        result.push([...Array.from(fixedDigits), n]);\n      }\n      return result;\n    });\n\n  return [nonZeroDigits.map((a) => a[0]).reverse(), ...fromFront];\n}\n\nexport function backGroupings(digits: number[], base: number): number[][] {\n  const digitsReversed = Array.from(digits).reverse();\n  const nonMaxDigits = dropUntil(\n    zipWithIndex(digitsReversed),\n    (a) => a[0] !== base - 1,\n  );\n\n  if (nonMaxDigits.length === 0) {\n    return [[base - 1]];\n  }\n\n  const fromBack = nonMaxDigits\n    .filter((_, i) => i !== nonMaxDigits.length - 1)\n    .flatMap(([d, i]) => {\n      const fixedDigits = Array.from(digits);\n      fixedDigits.length = fixedDigits.length - (i + 1);\n\n      const result: number[][] = [];\n      for (let n = d - 1; n >= 0; n--) {\n        result.push([...Array.from(fixedDigits), n]);\n      }\n\n      return result;\n    });\n\n  return [...fromBack.reverse(), nonMaxDigits.map((a) => a[0]).reverse()];\n}\n\nexport function middleGroupings(\n  firstDigitStart: number,\n  firstDigitEnd: number,\n): number[][] {\n  const result = [];\n  while (++firstDigitStart < firstDigitEnd) {\n    result.push([firstDigitStart]);\n  }\n  return result;\n}\n\nexport function groupByIgnoringDigits(\n  start: bigint,\n  end: bigint,\n  base: number,\n  numDigits: number,\n): number[][] {\n  const { prefixDigits, startDigits, endDigits } = separatePrefix(\n    start,\n    end,\n    base,\n    numDigits,\n  );\n\n  if (\n    start === end ||\n    (startDigits.every((n) => n === 0) &&\n      endDigits.every((n) => n === base - 1) &&\n      prefixDigits.length !== 0)\n  ) {\n    return [prefixDigits];\n  } else if (prefixDigits.length === numDigits - 1) {\n    const result = [];\n    for (\n      let i = startDigits[startDigits.length - 1];\n      i <= endDigits[endDigits.length - 1];\n      i++\n    ) {\n      result.push([...prefixDigits, i]);\n    }\n\n    return result;\n  } else {\n    const front = frontGroupings(startDigits, base);\n    const middle = middleGroupings(startDigits[0], endDigits[0]);\n    const back = backGroupings(endDigits, base);\n\n    const groupings = [...front, ...middle, ...back];\n\n    return groupings.map((g) => [...prefixDigits, ...g]);\n  }\n}\n\nexport interface RoundingInterval {\n  beginInterval: bigint;\n  roundingMod: bigint;\n}\n\nexport type CETPayout = {\n  indexFrom: bigint;\n  indexTo: bigint;\n  payout: bigint;\n};\n\n/**\n * Performs optimized evaluation and rounding for strictly monotonic hyperbolas on intervals (from, to)\n * e.g. hyperbolas with the form b = c = 0\n *\n * The next start of a payout range is determined by finding the outcome at the next mid-rounding payout.\n * Uses an inverse function of the hyperbola to find the outcome.\n *\n * Optimizes rounding from O(to - from) to O(totalCollateral / rounding)\n *\n *\n * Evaluates and rounds a payout_function equivalent to:\n *\n *   payout_function_v0\n *    num_pieces: 1\n *    endpoint_0: from\n *    endpoint_payout_0: fromPayout\n *    extra_precision_0: 0\n *    payout_curve_piece: HyperbolaPayoutCurve\n *    endpoint_1: to\n *    endpoint_payout_1: toPayout\n */\nexport function splitIntoRanges(\n  from: bigint,\n  to: bigint,\n  fromPayout: bigint, // endpoint_payout\n  toPayout: bigint, // endpoint_payout\n  totalCollateral: bigint,\n  curve: HyperbolaPayoutCurve | PolynomialPayoutCurve,\n  roundingIntervals: RoundingInterval[],\n): CETPayout[] {\n  if (to - from <= 0) {\n    throw new Error('`to` must be strictly greater than `from`');\n  }\n\n  const reversedIntervals = [...roundingIntervals].reverse();\n\n  const getRoundingForOutcome = (outcome: bigint): [bigint, number] => {\n    const roundingIndex = reversedIntervals.findIndex(\n      (interval) => interval.beginInterval <= outcome,\n    );\n\n    return [\n      roundingIndex !== -1\n        ? reversedIntervals[roundingIndex].roundingMod\n        : BigInt(1),\n      roundingIndex,\n    ];\n  };\n\n  const clamp = (val: bigint) =>\n    BigIntMath.clamp(BigInt(0), val, totalCollateral);\n\n  const totalCollateralBN = new BigNumber(totalCollateral.toString());\n  const clampBN = (val: BigNumber) =>\n    BigNumber.max(0, BigNumber.min(val, totalCollateralBN));\n\n  const result: CETPayout[] = [];\n\n  // outcome = endpoint_0\n  result.push({\n    payout: fromPayout,\n    indexFrom: from,\n    indexTo: from,\n  });\n\n  // In the case of a constant payout curve (fromPayout === toPayout), we can skip the range evaluation\n  if (fromPayout === toPayout) {\n    result.push({\n      payout: toPayout,\n      indexFrom: from,\n      indexTo: to,\n    });\n    // outcome = endpoint_1\n    result.push({\n      payout: toPayout,\n      indexFrom: to,\n      indexTo: to,\n    });\n    // merge neighbouring ranges with same payout\n    return mergePayouts(result);\n  }\n\n  let currentOutcome = from + BigInt(1);\n\n  // iterate over entire range of outcomes from [from, to]\n  while (currentOutcome < to) {\n    const [rounding, roundingIndex] = getRoundingForOutcome(currentOutcome);\n\n    // either the next rounding interval, or the end of the range\n    const nextFirstRoundingOutcome =\n      reversedIntervals[roundingIndex - 1]?.beginInterval || to;\n\n    // temporary variable to hold the current payout\n    let currentPayout = new BigNumber(\n      roundPayout(\n        clampBN(curve.getPayout(currentOutcome)),\n        rounding,\n      ).toString(),\n    );\n\n    let currentMidRoundedOutcome = currentOutcome;\n\n    const isAscending = curve\n      .getPayout(nextFirstRoundingOutcome)\n      .gt(currentPayout);\n\n    while (currentMidRoundedOutcome < nextFirstRoundingOutcome) {\n      const nextRoundedPayout = currentPayout\n        .integerValue()\n        .plus(isAscending ? Number(rounding) : -Number(rounding));\n\n      const nextRoundedPayoutBigInt = toBigInt(nextRoundedPayout);\n\n      const nextMidRoundedPayout = currentPayout.plus(\n        isAscending ? Number(rounding) / 2 : -Number(rounding) / 2,\n      );\n\n      let nextMidRoundedOutcome = curve.getOutcomeForPayout(\n        nextMidRoundedPayout,\n      );\n\n      if (\n        (!isAscending &&\n          curve.getPayout(nextMidRoundedOutcome).lt(nextMidRoundedPayout)) ||\n        (isAscending &&\n          curve.getPayout(nextMidRoundedOutcome).gte(nextMidRoundedPayout))\n      ) {\n        nextMidRoundedOutcome = nextMidRoundedOutcome - BigInt(1);\n      }\n\n      const nextOutcome = curve.getOutcomeForPayout(nextRoundedPayout);\n\n      if (nextMidRoundedOutcome >= nextFirstRoundingOutcome) {\n        result.push({\n          payout: clamp(toBigInt(currentPayout)),\n          indexFrom: currentMidRoundedOutcome,\n          indexTo: nextFirstRoundingOutcome - BigInt(1),\n        });\n\n        currentOutcome = nextFirstRoundingOutcome;\n        break;\n      }\n\n      if (\n        nextRoundedPayoutBigInt > totalCollateral ||\n        nextRoundedPayoutBigInt < 0 ||\n        nextOutcome >= to ||\n        nextOutcome < 0 // undefined on curve\n      ) {\n        if (nextMidRoundedOutcome < from || nextMidRoundedOutcome > to) {\n          result.push({\n            payout: clamp(toBigInt(currentPayout)),\n            indexFrom: currentMidRoundedOutcome,\n            indexTo: to,\n          });\n        } else {\n          result.push(\n            {\n              payout: clamp(toBigInt(currentPayout)),\n              indexFrom: currentMidRoundedOutcome,\n              indexTo: nextMidRoundedOutcome,\n            },\n            {\n              payout: clamp(nextRoundedPayoutBigInt),\n              indexFrom: nextMidRoundedOutcome + BigInt(1),\n              indexTo: to - BigInt(1),\n            },\n          );\n        }\n\n        currentOutcome = to;\n        break;\n      }\n\n      result.push({\n        payout: clamp(toBigInt(currentPayout)),\n        indexFrom: currentMidRoundedOutcome,\n        indexTo: nextMidRoundedOutcome,\n      });\n\n      currentOutcome = nextOutcome + BigInt(1);\n      currentPayout = nextRoundedPayout;\n\n      currentMidRoundedOutcome = nextMidRoundedOutcome + BigInt(1);\n    }\n  }\n\n  // outcome = endpoint_1\n  result.push({\n    payout: toPayout,\n    indexFrom: to,\n    indexTo: to,\n  });\n\n  // merge neighbouring ranges with same payout\n  return mergePayouts(result);\n}\n\nexport const mergePayouts = (payouts: CETPayout[]): CETPayout[] => {\n  return payouts.reduce((acc: CETPayout[], range) => {\n    const prev = acc[acc.length - 1];\n    if (prev) {\n      if (\n        (prev.indexTo === range.indexFrom ||\n          prev.indexTo + BigInt(1) === range.indexFrom) &&\n        prev.payout === range.payout\n      ) {\n        prev.indexTo = range.indexTo;\n        return acc;\n      }\n    }\n\n    return [...acc, range];\n  }, []);\n};\n\nexport function roundPayout(payout: BigNumber, rounding: bigint): bigint {\n  const roundingBN = new BigNumber(rounding.toString());\n  const mod = payout.gte(0)\n    ? 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