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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(); }