timsort.js

/**
 * Default minimum size of a run.
 */
const DEFAULT_MIN_MERGE = 32;

/**
 * Minimum ordered subsequece required to do galloping.
 */
const DEFAULT_MIN_GALLOPING = 7;

/**
 * Default tmp storage length. Can increase depending on the size of the
 * smallest run to merge.
 */
const DEFAULT_TMP_STORAGE_LENGTH = 256;

/**
 * Pre-computed powers of 10 for efficient lexicographic comparison of
 * small integers.
 */
const POWERS_OF_TEN = [1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9]

/**
 * Estimate the logarithm base 10 of a small integer.
 *
 * @param {number} x - The integer to estimate the logarithm of.
 * @return {number} - The estimated logarithm of the integer.
 */
function log10(x) {
  if (x < 1e5) {
    if (x < 1e2) {
      return x < 1e1 ? 0 : 1;
    }

    if (x < 1e4) {
      return x < 1e3 ? 2 : 3;
    }

    return 4;
  }

  if (x < 1e7) {
    return x < 1e6 ? 5 : 6;
  }

  if (x < 1e9) {
    return x < 1e8 ? 7 : 8;
  }

  return 9;
}

/**
 * Default alphabetical comparison of items.
 *
 * @param {string|object|number} a - First element to compare.
 * @param {string|object|number} b - Second element to compare.
 * @return {number} - A positive number if a.toString() > b.toString(), a
 * negative number if .toString() < b.toString(), 0 otherwise.
 */
function alphabeticalCompare(a, b) {
  if (a === b) {
    return 0;
  }

  if (~~a === a && ~~b === b) {
    if (a === 0 || b === 0) {
      return a < b ? -1 : 1;
    }

    if (a < 0 || b < 0) {
      if (b >= 0) {
        return -1;
      }

      if (a >= 0) {
        return 1;
      }

      a = -a;
      b = -b;
    }

    const al = log10(a);
    const bl = log10(b);

    let t = 0;

    if (al < bl) {
      a *= POWERS_OF_TEN[bl - al - 1];
      b /= 10;
      t = -1;
    } else if (al > bl) {
      b *= POWERS_OF_TEN[al - bl - 1];
      a /= 10;
      t = 1;
    }

    if (a === b) {
      return t;
    }

    return a < b ? -1 : 1;
  }

  let aStr = String(a);
  let bStr = String(b);

  if (aStr === bStr) {
    return 0;
  }

  return aStr < bStr ? -1 : 1;
}

/**
 * Compute minimum run length for TimSort
 *
 * @param {number} n - The size of the array to sort.
 */
function minRunLength(n) {
  let r = 0;

  while (n >= DEFAULT_MIN_MERGE) {
    r |= (n & 1);
    n >>= 1;
  }

  return n + r;
}

/**
 * Counts the length of a monotonically ascending or strictly monotonically
 * descending sequence (run) starting at array[lo] in the range [lo, hi). If
 * the run is descending it is made ascending.
 *
 * @param {array} array - The array to reverse.
 * @param {number} lo - First element in the range (inclusive).
 * @param {number} hi - Last element in the range.
 * @param {function} compare - Item comparison function.
 * @return {number} - The length of the run.
 */
function makeAscendingRun(array, lo, hi, compare) {
  let runHi = lo + 1;

  if (runHi === hi) {
    return 1;
  }

  // Descending
  if (compare(array[runHi++], array[lo]) < 0) {
    while (runHi < hi && compare(array[runHi], array[runHi - 1]) < 0) {
      runHi++;
    }

    reverseRun(array, lo, runHi);
    // Ascending
  } else {
    while (runHi < hi && compare(array[runHi], array[runHi - 1]) >= 0) {
      runHi++;
    }
  }

  return runHi - lo;
}

/**
 * Reverse an array in the range [lo, hi).
 *
 * @param {array} array - The array to reverse.
 * @param {number} lo - First element in the range (inclusive).
 * @param {number} hi - Last element in the range.
 */
function reverseRun(array, lo, hi) {
  hi--;

  while (lo < hi) {
    let t = array[lo];
    array[lo++] = array[hi];
    array[hi--] = t;
  }
}

/**
 * Perform the binary sort of the array in the range [lo, hi) where start is
 * the first element possibly out of order.
 *
 * @param {array} array - The array to sort.
 * @param {number} lo - First element in the range (inclusive).
 * @param {number} hi - Last element in the range.
 * @param {number} start - First element possibly out of order.
 * @param {function} compare - Item comparison function.
 */
function binaryInsertionSort(array, lo, hi, start, compare) {
  if (start === lo) {
    start++;
  }

  for (; start < hi; start++) {
    let pivot = array[start];

    // Ranges of the array where pivot belongs
    let left = lo;
    let right = start;

    /*
     *   pivot >= array[i] for i in [lo, left)
     *   pivot <  array[i] for i in  in [right, start)
     */
    while (left < right) {
      let mid = (left + right) >>> 1;

      if (compare(pivot, array[mid]) < 0) {
        right = mid;
      } else {
        left = mid + 1;
      }
    }

    /*
     * Move elements right to make room for the pivot. If there are elements
     * equal to pivot, left points to the first slot after them: this is also
     * a reason for which TimSort is stable
     */
    let n = start - left;
    // Switch is just an optimization for small arrays
    switch (n) {
      case 3:
        array[left + 3] = array[left + 2];
      /* falls through */
      case 2:
        array[left + 2] = array[left + 1];
      /* falls through */
      case 1:
        array[left + 1] = array[left];
        break;
      default:
        while (n > 0) {
          array[left + n] = array[left + n - 1];
          n--;
        }
    }

    array[left] = pivot;
  }
}

/**
 * Find the position at which to insert a value in a sorted range. If the range
 * contains elements equal to the value the leftmost element index is returned
 * (for stability).
 *
 * @param {number} value - Value to insert.
 * @param {array} array - The array in which to insert value.
 * @param {number} start - First element in the range.
 * @param {number} length - Length of the range.
 * @param {number} hint - The index at which to begin the search.
 * @param {function} compare - Item comparison function.
 * @return {number} - The index where to insert value.
 */
function gallopLeft(value, array, start, length, hint, compare) {
  let lastOffset = 0;
  let maxOffset = 0;
  let offset = 1;

  if (compare(value, array[start + hint]) > 0) {
    maxOffset = length - hint;

    while (offset < maxOffset && compare(value, array[start + hint + offset]) > 0) {
      lastOffset = offset;
      offset = (offset << 1) + 1;

      if (offset <= 0) {
        offset = maxOffset;
      }
    }

    if (offset > maxOffset) {
      offset = maxOffset;
    }

    // Make offsets relative to start
    lastOffset += hint;
    offset += hint;

    // value <= array[start + hint]
  } else {
    maxOffset = hint + 1;
    while (offset < maxOffset && compare(value, array[start + hint - offset]) <= 0) {
      lastOffset = offset;
      offset = (offset << 1) + 1;

      if (offset <= 0) {
        offset = maxOffset;
      }
    }
    if (offset > maxOffset) {
      offset = maxOffset;
    }

    // Make offsets relative to start
    let tmp = lastOffset;
    lastOffset = hint - offset;
    offset = hint - tmp;
  }

  /*
   * Now array[start+lastOffset] < value <= array[start+offset], so value
   * belongs somewhere in the range (start + lastOffset, start + offset]. Do a
   * binary search, with invariant array[start + lastOffset - 1] < value <=
   * array[start + offset].
   */
  lastOffset++;
  while (lastOffset < offset) {
    let m = lastOffset + ((offset - lastOffset) >>> 1);

    if (compare(value, array[start + m]) > 0) {
      lastOffset = m + 1;

    } else {
      offset = m;
    }
  }
  return offset;
}

/**
 * Find the position at which to insert a value in a sorted range. If the range
 * contains elements equal to the value the rightmost element index is returned
 * (for stability).
 *
 * @param {number} value - Value to insert.
 * @param {array} array - The array in which to insert value.
 * @param {number} start - First element in the range.
 * @param {number} length - Length of the range.
 * @param {number} hint - The index at which to begin the search.
 * @param {function} compare - Item comparison function.
 * @return {number} - The index where to insert value.
 */
function gallopRight(value, array, start, length, hint, compare) {
  let lastOffset = 0;
  let maxOffset = 0;
  let offset = 1;

  if (compare(value, array[start + hint]) < 0) {
    maxOffset = hint + 1;

    while (offset < maxOffset && compare(value, array[start + hint - offset]) < 0) {
      lastOffset = offset;
      offset = (offset << 1) + 1;

      if (offset <= 0) {
        offset = maxOffset;
      }
    }

    if (offset > maxOffset) {
      offset = maxOffset;
    }

    // Make offsets relative to start
    let tmp = lastOffset;
    lastOffset = hint - offset;
    offset = hint - tmp;

    // value >= array[start + hint]
  } else {
    maxOffset = length - hint;

    while (offset < maxOffset && compare(value, array[start + hint + offset]) >= 0) {
      lastOffset = offset;
      offset = (offset << 1) + 1;

      if (offset <= 0) {
        offset = maxOffset;
      }
    }

    if (offset > maxOffset) {
      offset = maxOffset;
    }

    // Make offsets relative to start
    lastOffset += hint;
    offset += hint;
  }

  /*
   * Now array[start+lastOffset] < value <= array[start+offset], so value
   * belongs somewhere in the range (start + lastOffset, start + offset]. Do a
   * binary search, with invariant array[start + lastOffset - 1] < value <=
   * array[start + offset].
   */
  lastOffset++;

  while (lastOffset < offset) {
    let m = lastOffset + ((offset - lastOffset) >>> 1);

    if (compare(value, array[start + m]) < 0) {
      offset = m;

    } else {
      lastOffset = m + 1;
    }
  }

  return offset;
}

class TimSort {
  array = null;
  compare = null;
  minGallop = DEFAULT_MIN_GALLOPING;
  length = 0;
  tmpStorageLength = DEFAULT_TMP_STORAGE_LENGTH;
  stackLength = 0;
  runStart = null;
  runLength = null;
  stackSize = 0;

  constructor(array, compare) {
    this.array = array;
    this.compare = compare;

    this.length = array.length;

    if (this.length < 2 * DEFAULT_TMP_STORAGE_LENGTH) {
      this.tmpStorageLength = this.length >>> 1;
    }

    this.tmp = new Array(this.tmpStorageLength);

    this.stackLength =
      (this.length < 120 ? 5 :
        this.length < 1542 ? 10 :
          this.length < 119151 ? 19 : 40);

    this.runStart = new Array(this.stackLength);
    this.runLength = new Array(this.stackLength);
  }

  /**
   * Push a new run on TimSort's stack.
   *
   * @param {number} runStart - Start index of the run in the original array.
   * @param {number} runLength - Length of the run;
   */
  pushRun(runStart, runLength) {
    this.runStart[this.stackSize] = runStart;
    this.runLength[this.stackSize] = runLength;
    this.stackSize += 1;
  }

  /**
   * Merge runs on TimSort's stack so that the following holds for all i:
   * 1) runLength[i - 3] > runLength[i - 2] + runLength[i - 1]
   * 2) runLength[i - 2] > runLength[i - 1]
   */
  mergeRuns() {
    while (this.stackSize > 1) {
      let n = this.stackSize - 2;

      if ((n >= 1 &&
        this.runLength[n - 1] <= this.runLength[n] + this.runLength[n + 1]) ||
        (n >= 2 &&
        this.runLength[n - 2] <= this.runLength[n] + this.runLength[n - 1])) {

        if (this.runLength[n - 1] < this.runLength[n + 1]) {
          n--;
        }

      } else if (this.runLength[n] > this.runLength[n + 1]) {
        break;
      }
      this.mergeAt(n);
    }
  }

  /**
   * Merge all runs on TimSort's stack until only one remains.
   */
  forceMergeRuns() {
    while (this.stackSize > 1) {
      let n = this.stackSize - 2;

      if (n > 0 && this.runLength[n - 1] < this.runLength[n + 1]) {
        n--;
      }

      this.mergeAt(n);
    }
  }

  /**
   * Merge the runs on the stack at positions i and i+1. Must be always be called
   * with i=stackSize-2 or i=stackSize-3 (that is, we merge on top of the stack).
   *
   * @param {number} i - Index of the run to merge in TimSort's stack.
   */
  mergeAt(i) {
    let compare = this.compare;
    let array = this.array;

    let start1 = this.runStart[i];
    let length1 = this.runLength[i];
    let start2 = this.runStart[i + 1];
    let length2 = this.runLength[i + 1];

    this.runLength[i] = length1 + length2;

    if (i === this.stackSize - 3) {
      this.runStart[i + 1] = this.runStart[i + 2];
      this.runLength[i + 1] = this.runLength[i + 2];
    }

    this.stackSize--;

    /*
     * Find where the first element in the second run goes in run1. Previous
     * elements in run1 are already in place
     */
    let k = gallopRight(array[start2], array, start1, length1, 0, compare);
    start1 += k;
    length1 -= k;

    if (length1 === 0) {
      return;
    }

    /*
     * Find where the last element in the first run goes in run2. Next elements
     * in run2 are already in place
     */
    length2 = gallopLeft(array[start1 + length1 - 1], array, start2, length2, length2 - 1, compare);

    if (length2 === 0) {
      return;
    }

    /*
     * Merge remaining runs. A tmp array with length = min(length1, length2) is
     * used
     */
    if (length1 <= length2) {
      this.mergeLow(start1, length1, start2, length2);

    } else {
      this.mergeHigh(start1, length1, start2, length2);
    }
  }

  /**
   * Merge two adjacent runs in a stable way. The runs must be such that the
   * first element of run1 is bigger than the first element in run2 and the
   * last element of run1 is greater than all the elements in run2.
   * The method should be called when run1.length <= run2.length as it uses
   * TimSort temporary array to store run1. Use mergeHigh if run1.length >
   * run2.length.
   *
   * @param {number} start1 - First element in run1.
   * @param {number} length1 - Length of run1.
   * @param {number} start2 - First element in run2.
   * @param {number} length2 - Length of run2.
   */
  mergeLow(start1, length1, start2, length2) {

    let compare = this.compare;
    let array = this.array;
    let tmp = this.tmp;
    let i = 0;

    for (i = 0; i < length1; i++) {
      tmp[i] = array[start1 + i];
    }

    let cursor1 = 0;
    let cursor2 = start2;
    let dest = start1;

    array[dest++] = array[cursor2++];

    if (--length2 === 0) {
      for (i = 0; i < length1; i++) {
        array[dest + i] = tmp[cursor1 + i];
      }
      return;
    }

    if (length1 === 1) {
      for (i = 0; i < length2; i++) {
        array[dest + i] = array[cursor2 + i];
      }
      array[dest + length2] = tmp[cursor1];
      return;
    }

    let minGallop = this.minGallop;

    while (true) {
      let count1 = 0;
      let count2 = 0;
      let exit = false;

      do {
        if (compare(array[cursor2], tmp[cursor1]) < 0) {
          array[dest++] = array[cursor2++];
          count2++;
          count1 = 0;

          if (--length2 === 0) {
            exit = true;
            break;
          }

        } else {
          array[dest++] = tmp[cursor1++];
          count1++;
          count2 = 0;
          if (--length1 === 1) {
            exit = true;
            break;
          }
        }
      } while ((count1 | count2) < minGallop);

      if (exit) {
        break;
      }

      do {
        count1 = gallopRight(array[cursor2], tmp, cursor1, length1, 0, compare);

        if (count1 !== 0) {
          for (i = 0; i < count1; i++) {
            array[dest + i] = tmp[cursor1 + i];
          }

          dest += count1;
          cursor1 += count1;
          length1 -= count1;
          if (length1 <= 1) {
            exit = true;
            break;
          }
        }

        array[dest++] = array[cursor2++];

        if (--length2 === 0) {
          exit = true;
          break;
        }

        count2 = gallopLeft(tmp[cursor1], array, cursor2, length2, 0, compare);

        if (count2 !== 0) {
          for (i = 0; i < count2; i++) {
            array[dest + i] = array[cursor2 + i];
          }

          dest += count2;
          cursor2 += count2;
          length2 -= count2;

          if (length2 === 0) {
            exit = true;
            break;
          }
        }
        array[dest++] = tmp[cursor1++];

        if (--length1 === 1) {
          exit = true;
          break;
        }

        minGallop--;

      } while (count1 >= DEFAULT_MIN_GALLOPING || count2 >= DEFAULT_MIN_GALLOPING);

      if (exit) {
        break;
      }

      if (minGallop < 0) {
        minGallop = 0;
      }

      minGallop += 2;
    }

    this.minGallop = minGallop;

    if (minGallop < 1) {
      this.minGallop = 1;
    }

    if (length1 === 1) {
      for (i = 0; i < length2; i++) {
        array[dest + i] = array[cursor2 + i];
      }
      array[dest + length2] = tmp[cursor1];

    } else if (length1 === 0) {
      throw new Error('mergeLow preconditions were not respected');

    } else {
      for (i = 0; i < length1; i++) {
        array[dest + i] = tmp[cursor1 + i];
      }
    }
  }

  /**
   * Merge two adjacent runs in a stable way. The runs must be such that the
   * first element of run1 is bigger than the first element in run2 and the
   * last element of run1 is greater than all the elements in run2.
   * The method should be called when run1.length > run2.length as it uses
   * TimSort temporary array to store run2. Use mergeLow if run1.length <=
   * run2.length.
   *
   * @param {number} start1 - First element in run1.
   * @param {number} length1 - Length of run1.
   * @param {number} start2 - First element in run2.
   * @param {number} length2 - Length of run2.
   */
  mergeHigh(start1, length1, start2, length2) {
    let compare = this.compare;
    let array = this.array;
    let tmp = this.tmp;
    let i = 0;

    for (i = 0; i < length2; i++) {
      tmp[i] = array[start2 + i];
    }

    let cursor1 = start1 + length1 - 1;
    let cursor2 = length2 - 1;
    let dest = start2 + length2 - 1;
    let customCursor = 0;
    let customDest = 0;

    array[dest--] = array[cursor1--];

    if (--length1 === 0) {
      customCursor = dest - (length2 - 1);

      for (i = 0; i < length2; i++) {
        array[customCursor + i] = tmp[i];
      }

      return;
    }

    if (length2 === 1) {
      dest -= length1;
      cursor1 -= length1;
      customDest = dest + 1;
      customCursor = cursor1 + 1;

      for (i = length1 - 1; i >= 0; i--) {
        array[customDest + i] = array[customCursor + i];
      }

      array[dest] = tmp[cursor2];
      return;
    }

    let minGallop = this.minGallop;

    while (true) {
      let count1 = 0;
      let count2 = 0;
      let exit = false;

      do {
        if (compare(tmp[cursor2], array[cursor1]) < 0) {
          array[dest--] = array[cursor1--];
          count1++;
          count2 = 0;
          if (--length1 === 0) {
            exit = true;
            break;
          }

        } else {
          array[dest--] = tmp[cursor2--];
          count2++;
          count1 = 0;
          if (--length2 === 1) {
            exit = true;
            break;
          }
        }

      } while ((count1 | count2) < minGallop);

      if (exit) {
        break;
      }

      do {
        count1 = length1 - gallopRight(tmp[cursor2], array, start1, length1, length1 - 1, compare);

        if (count1 !== 0) {
          dest -= count1;
          cursor1 -= count1;
          length1 -= count1;
          customDest = dest + 1;
          customCursor = cursor1 + 1;

          for (i = count1 - 1; i >= 0; i--) {
            array[customDest + i] = array[customCursor + i];
          }

          if (length1 === 0) {
            exit = true;
            break;
          }
        }

        array[dest--] = tmp[cursor2--];

        if (--length2 === 1) {
          exit = true;
          break;
        }

        count2 = length2 - gallopLeft(array[cursor1], tmp, 0, length2, length2 - 1, compare);

        if (count2 !== 0) {
          dest -= count2;
          cursor2 -= count2;
          length2 -= count2;
          customDest = dest + 1;
          customCursor = cursor2 + 1;

          for (i = 0; i < count2; i++) {
            array[customDest + i] = tmp[customCursor + i];
          }

          if (length2 <= 1) {
            exit = true;
            break;
          }
        }

        array[dest--] = array[cursor1--];

        if (--length1 === 0) {
          exit = true;
          break;
        }

        minGallop--;

      } while (count1 >= DEFAULT_MIN_GALLOPING || count2 >= DEFAULT_MIN_GALLOPING);

      if (exit) {
        break;
      }

      if (minGallop < 0) {
        minGallop = 0;
      }

      minGallop += 2;
    }

    this.minGallop = minGallop;

    if (minGallop < 1) {
      this.minGallop = 1;
    }

    if (length2 === 1) {
      dest -= length1;
      cursor1 -= length1;
      customDest = dest + 1;
      customCursor = cursor1 + 1;

      for (i = length1 - 1; i >= 0; i--) {
        array[customDest + i] = array[customCursor + i];
      }

      array[dest] = tmp[cursor2];

    } else if (length2 === 0) {
      throw new Error('mergeHigh preconditions were not respected');

    } else {
      customCursor = dest - (length2 - 1);
      for (i = 0; i < length2; i++) {
        array[customCursor + i] = tmp[i];
      }
    }
  }
}

/**
 * Sort an array in the range [lo, hi) using TimSort.
 *
 * @param {array} array - The array to sort.
 * @param {function=} compare - Item comparison function. Default is
 *     alphabetical
 * @param {number} lo - First element in the range (inclusive).
 * @param {number} hi - Last element in the range.
 *     comparator.
 */
export function sort(array, compare, lo, hi) {
  if (!Array.isArray(array)) {
    throw new TypeError('Can only sort arrays');
  }

  /*
   * Handle the case where a comparison function is not provided. We do
   * lexicographic sorting
   */
  if (!compare) {
    compare = alphabeticalCompare;

  } else if (typeof compare !== 'function') {
    hi = lo;
    lo = compare;
    compare = alphabeticalCompare;
  }

  if (!lo) {
    lo = 0;
  }
  if (!hi) {
    hi = array.length;
  }

  let remaining = hi - lo;

  // The array is already sorted
  if (remaining < 2) {
    return;
  }

  let runLength = 0;
  // On small arrays binary sort can be used directly
  if (remaining < DEFAULT_MIN_MERGE) {
    runLength = makeAscendingRun(array, lo, hi, compare);
    binaryInsertionSort(array, lo, hi, lo + runLength, compare);
    return;
  }

  let ts = new TimSort(array, compare);

  let minRun = minRunLength(remaining);

  do {
    runLength = makeAscendingRun(array, lo, hi, compare);
    if (runLength < minRun) {
      let force = remaining;
      if (force > minRun) {
        force = minRun;
      }

      binaryInsertionSort(array, lo, lo + force, lo + runLength, compare);
      runLength = force;
    }
    // Push new run and merge if necessary
    ts.pushRun(lo, runLength);
    ts.mergeRuns();

    // Go find next run
    remaining -= runLength;
    lo += runLength;

  } while (remaining !== 0);

  // Force merging of remaining runs
  ts.forceMergeRuns();
}