@alcorexchange/alcor-swap-sdk/src/utils/tickMath.ts

## Installation ​​ **npm** ``` npm i @alcorexchange/alcor-swap-sdk ``` **yarn** ``` yarn add @alcorexchange/alcor-swap-sdk ``` ## Usage ### Import:

import JSBI from "jsbi";
import invariant from "tiny-invariant";
import { ONE, ZERO, MaxUint256, Q64 } from "../internalConstants";
import { mostSignificantBit } from "./mostSignificantBit";

function mulShift(val: JSBI, mulBy: string): JSBI {
  return JSBI.signedRightShift(
    JSBI.multiply(val, JSBI.BigInt(mulBy)),
    JSBI.BigInt(128)
  );
}

export abstract class TickMath {
  /**
   * The minimum tick that can be used on any pool.
   */
  public static MIN_TICK = -443636;
  /**
   * The maximum tick that can be used on any pool.
   */
  public static MAX_TICK: number = -TickMath.MIN_TICK;

  /**
   * The sqrt ratio corresponding to the minimum tick that could be used on any pool.
   */
  public static MIN_SQRT_RATIO: JSBI = JSBI.BigInt("4295048017");
  /**
   * The sqrt ratio corresponding to the maximum tick that could be used on any pool.
   */
  public static MAX_SQRT_RATIO: JSBI = JSBI.BigInt(
    "79226673515401279992447579062"
  );

  /**
   * Returns the sqrt ratio as a Q64.96 for the given tick. The sqrt ratio is computed as sqrt(1.0001)^tick
   * @param tick the tick for which to compute the sqrt ratio
   */
  public static getSqrtRatioAtTick(tick: number): JSBI {
    invariant(
      tick >= TickMath.MIN_TICK &&
        tick <= TickMath.MAX_TICK &&
        Number.isInteger(tick),
      "TICK"
    );
    const absTick: number = tick < 0 ? tick * -1 : tick;

    let ratio: JSBI =
      (absTick & 0x1) != 0
        ? JSBI.BigInt("0xfffcb933bd6fad37aa2d162d1a594001")
        : JSBI.BigInt("0x100000000000000000000000000000000");
    if ((absTick & 0x2) != 0)
      ratio = mulShift(ratio, "0xfff97272373d413259a46990580e213a");
    if ((absTick & 0x4) != 0)
      ratio = mulShift(ratio, "0xfff2e50f5f656932ef12357cf3c7fdcc");
    if ((absTick & 0x8) != 0)
      ratio = mulShift(ratio, "0xffe5caca7e10e4e61c3624eaa0941cd0");
    if ((absTick & 0x10) != 0)
      ratio = mulShift(ratio, "0xffcb9843d60f6159c9db58835c926644");
    if ((absTick & 0x20) != 0)
      ratio = mulShift(ratio, "0xff973b41fa98c081472e6896dfb254c0");
    if ((absTick & 0x40) != 0)
      ratio = mulShift(ratio, "0xff2ea16466c96a3843ec78b326b52861");
    if ((absTick & 0x80) != 0)
      ratio = mulShift(ratio, "0xfe5dee046a99a2a811c461f1969c3053");
    if ((absTick & 0x100) != 0)
      ratio = mulShift(ratio, "0xfcbe86c7900a88aedcffc83b479aa3a4");
    if ((absTick & 0x200) != 0)
      ratio = mulShift(ratio, "0xf987a7253ac413176f2b074cf7815e54");
    if ((absTick & 0x400) != 0)
      ratio = mulShift(ratio, "0xf3392b0822b70005940c7a398e4b70f3");
    if ((absTick & 0x800) != 0)
      ratio = mulShift(ratio, "0xe7159475a2c29b7443b29c7fa6e889d9");
    if ((absTick & 0x1000) != 0)
      ratio = mulShift(ratio, "0xd097f3bdfd2022b8845ad8f792aa5825");
    if ((absTick & 0x2000) != 0)
      ratio = mulShift(ratio, "0xa9f746462d870fdf8a65dc1f90e061e5");
    if ((absTick & 0x4000) != 0)
      ratio = mulShift(ratio, "0x70d869a156d2a1b890bb3df62baf32f7");
    if ((absTick & 0x8000) != 0)
      ratio = mulShift(ratio, "0x31be135f97d08fd981231505542fcfa6");
    if ((absTick & 0x10000) != 0)
      ratio = mulShift(ratio, "0x9aa508b5b7a84e1c677de54f3e99bc9");
    if ((absTick & 0x20000) != 0)
      ratio = mulShift(ratio, "0x5d6af8dedb81196699c329225ee604");
    if ((absTick & 0x40000) != 0)
      ratio = mulShift(ratio, "0x2216e584f5fa1ea926041bedfe98");
    if ((absTick & 0x80000) != 0)
      ratio = mulShift(ratio, "0x48a170391f7dc42444e8fa2");

    if (tick > 0) ratio = JSBI.divide(MaxUint256, ratio);

    // back to Q64
    return JSBI.greaterThan(JSBI.remainder(ratio, Q64), ZERO)
      ? JSBI.add(JSBI.divide(ratio, Q64), ONE)
      : JSBI.divide(ratio, Q64);
  }

  /**
   * Returns the tick corresponding to a given sqrt ratio, s.t. #getSqrtRatioAtTick(tick) <= sqrtRatioX64
   * and #getSqrtRatioAtTick(tick + 1) > sqrtRatioX64
   * @param sqrtRatioX64 the sqrt ratio as a Q64.96 for which to compute the tick
   */
  public static getTickAtSqrtRatio(sqrtRatioX64: JSBI): number {
    invariant(
      JSBI.greaterThanOrEqual(sqrtRatioX64, TickMath.MIN_SQRT_RATIO) &&
        JSBI.lessThan(sqrtRatioX64, TickMath.MAX_SQRT_RATIO),
      "SQRT_RATIO"
    );

    const sqrtRatioX128 = JSBI.leftShift(sqrtRatioX64, JSBI.BigInt(64));

    const msb = mostSignificantBit(sqrtRatioX128);

    let r: JSBI;
    if (JSBI.greaterThanOrEqual(JSBI.BigInt(msb), JSBI.BigInt(128))) {
      r = JSBI.signedRightShift(sqrtRatioX128, JSBI.BigInt(msb - 127));
    } else {
      r = JSBI.leftShift(sqrtRatioX128, JSBI.BigInt(127 - msb));
    }

    let log_2: JSBI = JSBI.leftShift(
      JSBI.subtract(JSBI.BigInt(msb), JSBI.BigInt(128)),
      JSBI.BigInt(64)
    );

    for (let i = 0; i < 14; i++) {
      r = JSBI.signedRightShift(JSBI.multiply(r, r), JSBI.BigInt(127));
      const f = JSBI.signedRightShift(r, JSBI.BigInt(128));
      log_2 = JSBI.bitwiseOr(log_2, JSBI.leftShift(f, JSBI.BigInt(63 - i)));
      r = JSBI.signedRightShift(r, f);
    }

    const log_sqrt10001 = JSBI.multiply(
      log_2,
      JSBI.BigInt("255738958999603826347141")
    );

    const tickLow = JSBI.toNumber(
      JSBI.signedRightShift(
        JSBI.subtract(
          log_sqrt10001,
          JSBI.BigInt("3402992956809132418596140100660247210")
        ),
        JSBI.BigInt(128)
      )
    );
    const tickHigh = JSBI.toNumber(
      JSBI.signedRightShift(
        JSBI.add(
          log_sqrt10001,
          JSBI.BigInt("291339464771989622907027621153398088495")
        ),
        JSBI.BigInt(128)
      )
    );

    return tickLow === tickHigh
      ? tickLow
      : JSBI.lessThanOrEqual(
          TickMath.getSqrtRatioAtTick(tickHigh),
          sqrtRatioX64
        )
      ? tickHigh
      : tickLow;
  }
}