@stellar/stellar-sdk/lib/esm/base/util/continued_fraction.js

A library for working with the Stellar network, including communication with the Horizon and Soroban RPC servers.

import BigNumber from './bignumber.js';

const MAX_INT = (1 << 31 >>> 0) - 1;
const MAX_INT_BN = new BigNumber(MAX_INT);
function best_r(rawNumber) {
  let number = new BigNumber(rawNumber);
  let a;
  let f;
  const fractions = [
    [new BigNumber(0), new BigNumber(1)],
    [new BigNumber(1), new BigNumber(0)]
  ];
  let i = 2;
  while (true) {
    if (number.gt(MAX_INT)) {
      break;
    }
    a = number.integerValue(BigNumber.ROUND_FLOOR);
    f = number.minus(a);
    const prev1 = fractions[i - 1];
    const prev2 = fractions[i - 2];
    if (!prev1 || !prev2) {
      throw new Error(
        `Continued fraction approximation failed: missing fraction elements at indices ${i - 1} and/or ${i - 2}`
      );
    }
    const h = a.times(prev1[0]).plus(prev2[0]);
    const k = a.times(prev1[1]).plus(prev2[1]);
    if (h.gt(MAX_INT) || k.gt(MAX_INT)) {
      break;
    }
    fractions.push([h, k]);
    if (f.eq(0)) {
      break;
    }
    number = new BigNumber(1).div(f);
    i += 1;
  }
  const lastFraction = fractions[fractions.length - 1];
  if (!lastFraction) {
    throw new Error(
      "Missing last fraction element in continued fraction approximation"
    );
  }
  const [n, d] = lastFraction;
  if (n.isZero() || d.isZero()) {
    const input = new BigNumber(rawNumber);
    if (input.isZero()) {
      throw new Error("Couldn't find approximation");
    }
    const prev1 = fractions[fractions.length - 1];
    const prev2 = fractions[fractions.length - 2];
    if (prev1 && prev2) {
      let aMax = MAX_INT_BN;
      if (prev1[0].gt(0)) {
        aMax = BigNumber.min(
          aMax,
          MAX_INT_BN.minus(prev2[0]).div(prev1[0]).integerValue(BigNumber.ROUND_FLOOR)
        );
      }
      if (prev1[1].gt(0)) {
        aMax = BigNumber.min(
          aMax,
          MAX_INT_BN.minus(prev2[1]).div(prev1[1]).integerValue(BigNumber.ROUND_FLOOR)
        );
      }
      if (aMax.gte(1)) {
        const hn = aMax.times(prev1[0]).plus(prev2[0]);
        const kn = aMax.times(prev1[1]).plus(prev2[1]);
        if (!hn.isZero() && !kn.isZero()) {
          return [hn.toNumber(), kn.toNumber()];
        }
      }
    }
    throw new Error("Couldn't find approximation");
  }
  return [n.toNumber(), d.toNumber()];
}

export { best_r };
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