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/**
* 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();
}