123456789101112131415161718192021222324252627282930313233343536373839404142434445464748
/** * Our default sum is the [Kahan-Babuska algorithm](https://pdfs.semanticscholar.org/1760/7d467cda1d0277ad272deb2113533131dc09.pdf). * This method is an improvement over the classical * [Kahan summation algorithm](https://en.wikipedia.org/wiki/Kahan_summation_algorithm). * It aims at computing the sum of a list of numbers while correcting for * floating-point errors. Traditionally, sums are calculated as many * successive additions, each one with its own floating-point roundoff. These * losses in precision add up as the number of numbers increases. This alternative * algorithm is more accurate than the simple way of calculating sums by simple * addition. * * This runs on `O(n)`, linear time in respect to the array. * * @param {number[]} x input * @return {number} sum of all input numbers * @example * sum([1, 2, 3]); // => 6 */export function sum(x: number[]): number {  if (x.length === 0) {    return 0;  }
  let sum = x[0];
  // Keeping track of the floating-point error correction  let correction = 0;
  let transition;
  for (let i = 1; i < x.length; i++) {    transition = sum + x[i];
    // Here we need to update the correction in a different fashion    // if the new absolute value is greater than the absolute sum    if (Math.abs(sum) >= Math.abs(x[i])) {      correction += sum - transition + x[i];    } else {      correction += x[i] - transition + sum;    }
    sum = transition;  }
  // Returning the corrected sum  return sum + correction;}