1 // Code generated by gen_sort_variants.go; DO NOT EDIT.
2 3 // Copyright 2022 The Go Authors. All rights reserved.
4 // Use of this source code is governed by a BSD-style
5 // license that can be found in the LICENSE file.
6 7 package sort
8 9 // insertionSort sorts data[a:b] using insertion sort.
10 func insertionSort(data Interface, a, b int) {
11 for i := a + 1; i < b; i++ {
12 for j := i; j > a && data.Less(j, j-1); j-- {
13 data.Swap(j, j-1)
14 }
15 }
16 }
17 18 // siftDown implements the heap property on data[lo:hi].
19 // first is an offset into the array where the root of the heap lies.
20 func siftDown(data Interface, lo, hi, first int) {
21 root := lo
22 for {
23 child := 2*root + 1
24 if child >= hi {
25 break
26 }
27 if child+1 < hi && data.Less(first+child, first+child+1) {
28 child++
29 }
30 if !data.Less(first+root, first+child) {
31 return
32 }
33 data.Swap(first+root, first+child)
34 root = child
35 }
36 }
37 38 func heapSort(data Interface, a, b int) {
39 first := a
40 lo := 0
41 hi := b - a
42 43 // Build heap with greatest element at top.
44 for i := (hi - 1) / 2; i >= 0; i-- {
45 siftDown(data, i, hi, first)
46 }
47 48 // Pop elements, largest first, into end of data.
49 for i := hi - 1; i >= 0; i-- {
50 data.Swap(first, first+i)
51 siftDown(data, lo, i, first)
52 }
53 }
54 55 // pdqsort sorts data[a:b].
56 // The algorithm based on pattern-defeating quicksort(pdqsort), but without the optimizations from BlockQuicksort.
57 // pdqsort paper: https://arxiv.org/pdf/2106.05123.pdf
58 // C++ implementation: https://github.com/orlp/pdqsort
59 // Rust implementation: https://docs.rs/pdqsort/latest/pdqsort/
60 // limit is the number of allowed bad (very unbalanced) pivots before falling back to heapsort.
61 func pdqsort(data Interface, a, b, limit int) {
62 const maxInsertion = 12
63 64 var (
65 wasBalanced = true // whether the last partitioning was reasonably balanced
66 wasPartitioned = true // whether the slice was already partitioned
67 )
68 69 for {
70 length := b - a
71 72 if length <= maxInsertion {
73 insertionSort(data, a, b)
74 return
75 }
76 77 // Fall back to heapsort if too many bad choices were made.
78 if limit == 0 {
79 heapSort(data, a, b)
80 return
81 }
82 83 // If the last partitioning was imbalanced, we need to breaking patterns.
84 if !wasBalanced {
85 breakPatterns(data, a, b)
86 limit--
87 }
88 89 pivot, hint := choosePivot(data, a, b)
90 if hint == decreasingHint {
91 reverseRange(data, a, b)
92 // The chosen pivot was pivot-a elements after the start of the array.
93 // After reversing it is pivot-a elements before the end of the array.
94 // The idea came from Rust's implementation.
95 pivot = (b - 1) - (pivot - a)
96 hint = increasingHint
97 }
98 99 // The slice is likely already sorted.
100 if wasBalanced && wasPartitioned && hint == increasingHint {
101 if partialInsertionSort(data, a, b) {
102 return
103 }
104 }
105 106 // Probably the slice contains many duplicate elements, partition the slice into
107 // elements equal to and elements greater than the pivot.
108 if a > 0 && !data.Less(a-1, pivot) {
109 mid := partitionEqual(data, a, b, pivot)
110 a = mid
111 continue
112 }
113 114 mid, alreadyPartitioned := partition(data, a, b, pivot)
115 wasPartitioned = alreadyPartitioned
116 117 leftLen, rightLen := mid-a, b-mid
118 balanceThreshold := length / 8
119 if leftLen < rightLen {
120 wasBalanced = leftLen >= balanceThreshold
121 pdqsort(data, a, mid, limit)
122 a = mid + 1
123 } else {
124 wasBalanced = rightLen >= balanceThreshold
125 pdqsort(data, mid+1, b, limit)
126 b = mid
127 }
128 }
129 }
130 131 // partition does one quicksort partition.
132 // Let p = data[pivot]
133 // Moves elements in data[a:b] around, so that data[i]<p and data[j]>=p for i<newpivot and j>newpivot.
134 // On return, data[newpivot] = p
135 func partition(data Interface, a, b, pivot int) (newpivot int, alreadyPartitioned bool) {
136 data.Swap(a, pivot)
137 i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned
138 139 for i <= j && data.Less(i, a) {
140 i++
141 }
142 for i <= j && !data.Less(j, a) {
143 j--
144 }
145 if i > j {
146 data.Swap(j, a)
147 return j, true
148 }
149 data.Swap(i, j)
150 i++
151 j--
152 153 for {
154 for i <= j && data.Less(i, a) {
155 i++
156 }
157 for i <= j && !data.Less(j, a) {
158 j--
159 }
160 if i > j {
161 break
162 }
163 data.Swap(i, j)
164 i++
165 j--
166 }
167 data.Swap(j, a)
168 return j, false
169 }
170 171 // partitionEqual partitions data[a:b] into elements equal to data[pivot] followed by elements greater than data[pivot].
172 // It assumed that data[a:b] does not contain elements smaller than the data[pivot].
173 func partitionEqual(data Interface, a, b, pivot int) (newpivot int) {
174 data.Swap(a, pivot)
175 i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned
176 177 for {
178 for i <= j && !data.Less(a, i) {
179 i++
180 }
181 for i <= j && data.Less(a, j) {
182 j--
183 }
184 if i > j {
185 break
186 }
187 data.Swap(i, j)
188 i++
189 j--
190 }
191 return i
192 }
193 194 // partialInsertionSort partially sorts a slice, returns true if the slice is sorted at the end.
195 func partialInsertionSort(data Interface, a, b int) bool {
196 const (
197 maxSteps = 5 // maximum number of adjacent out-of-order pairs that will get shifted
198 shortestShifting = 50 // don't shift any elements on short arrays
199 )
200 i := a + 1
201 for j := 0; j < maxSteps; j++ {
202 for i < b && !data.Less(i, i-1) {
203 i++
204 }
205 206 if i == b {
207 return true
208 }
209 210 if b-a < shortestShifting {
211 return false
212 }
213 214 data.Swap(i, i-1)
215 216 // Shift the smaller one to the left.
217 if i-a >= 2 {
218 for j := i - 1; j >= 1; j-- {
219 if !data.Less(j, j-1) {
220 break
221 }
222 data.Swap(j, j-1)
223 }
224 }
225 // Shift the greater one to the right.
226 if b-i >= 2 {
227 for j := i + 1; j < b; j++ {
228 if !data.Less(j, j-1) {
229 break
230 }
231 data.Swap(j, j-1)
232 }
233 }
234 }
235 return false
236 }
237 238 // breakPatterns scatters some elements around in an attempt to break some patterns
239 // that might cause imbalanced partitions in quicksort.
240 func breakPatterns(data Interface, a, b int) {
241 length := b - a
242 if length >= 8 {
243 random := xorshift(length)
244 modulus := nextPowerOfTwo(length)
245 246 for idx := a + (length/4)*2 - 1; idx <= a+(length/4)*2+1; idx++ {
247 other := int(uint(random.Next()) & (modulus - 1))
248 if other >= length {
249 other -= length
250 }
251 data.Swap(idx, a+other)
252 }
253 }
254 }
255 256 // choosePivot chooses a pivot in data[a:b].
257 //
258 // [0,8): chooses a static pivot.
259 // [8,shortestNinther): uses the simple median-of-three method.
260 // [shortestNinther,∞): uses the Tukey ninther method.
261 func choosePivot(data Interface, a, b int) (pivot int, hint sortedHint) {
262 const (
263 shortestNinther = 50
264 maxSwaps = 4 * 3
265 )
266 267 l := b - a
268 269 var (
270 swaps int
271 i = a + l/4*1
272 j = a + l/4*2
273 k = a + l/4*3
274 )
275 276 if l >= 8 {
277 if l >= shortestNinther {
278 // Tukey ninther method, the idea came from Rust's implementation.
279 i = medianAdjacent(data, i, &swaps)
280 j = medianAdjacent(data, j, &swaps)
281 k = medianAdjacent(data, k, &swaps)
282 }
283 // Find the median among i, j, k and stores it into j.
284 j = median(data, i, j, k, &swaps)
285 }
286 287 switch swaps {
288 case 0:
289 return j, increasingHint
290 case maxSwaps:
291 return j, decreasingHint
292 default:
293 return j, unknownHint
294 }
295 }
296 297 // order2 returns x,y where data[x] <= data[y], where x,y=a,b or x,y=b,a.
298 func order2(data Interface, a, b int, swaps *int) (int, int) {
299 if data.Less(b, a) {
300 *swaps++
301 return b, a
302 }
303 return a, b
304 }
305 306 // median returns x where data[x] is the median of data[a],data[b],data[c], where x is a, b, or c.
307 func median(data Interface, a, b, c int, swaps *int) int {
308 a, b = order2(data, a, b, swaps)
309 b, c = order2(data, b, c, swaps)
310 a, b = order2(data, a, b, swaps)
311 return b
312 }
313 314 // medianAdjacent finds the median of data[a - 1], data[a], data[a + 1] and stores the index into a.
315 func medianAdjacent(data Interface, a int, swaps *int) int {
316 return median(data, a-1, a, a+1, swaps)
317 }
318 319 func reverseRange(data Interface, a, b int) {
320 i := a
321 j := b - 1
322 for i < j {
323 data.Swap(i, j)
324 i++
325 j--
326 }
327 }
328 329 func swapRange(data Interface, a, b, n int) {
330 for i := 0; i < n; i++ {
331 data.Swap(a+i, b+i)
332 }
333 }
334 335 func stable(data Interface, n int) {
336 blockSize := 20 // must be > 0
337 a, b := 0, blockSize
338 for b <= n {
339 insertionSort(data, a, b)
340 a = b
341 b += blockSize
342 }
343 insertionSort(data, a, n)
344 345 for blockSize < n {
346 a, b = 0, 2*blockSize
347 for b <= n {
348 symMerge(data, a, a+blockSize, b)
349 a = b
350 b += 2 * blockSize
351 }
352 if m := a + blockSize; m < n {
353 symMerge(data, a, m, n)
354 }
355 blockSize *= 2
356 }
357 }
358 359 // symMerge merges the two sorted subsequences data[a:m] and data[m:b] using
360 // the SymMerge algorithm from Pok-Son Kim and Arne Kutzner, "Stable Minimum
361 // Storage Merging by Symmetric Comparisons", in Susanne Albers and Tomasz
362 // Radzik, editors, Algorithms - ESA 2004, volume 3221 of Lecture Notes in
363 // Computer Science, pages 714-723. Springer, 2004.
364 //
365 // Let M = m-a and N = b-n. Wolog M < N.
366 // The recursion depth is bound by ceil(log(N+M)).
367 // The algorithm needs O(M*log(N/M + 1)) calls to data.Less.
368 // The algorithm needs O((M+N)*log(M)) calls to data.Swap.
369 //
370 // The paper gives O((M+N)*log(M)) as the number of assignments assuming a
371 // rotation algorithm which uses O(M+N+gcd(M+N)) assignments. The argumentation
372 // in the paper carries through for Swap operations, especially as the block
373 // swapping rotate uses only O(M+N) Swaps.
374 //
375 // symMerge assumes non-degenerate arguments: a < m && m < b.
376 // Having the caller check this condition eliminates many leaf recursion calls,
377 // which improves performance.
378 func symMerge(data Interface, a, m, b int) {
379 // Avoid unnecessary recursions of symMerge
380 // by direct insertion of data[a] into data[m:b]
381 // if data[a:m] only contains one element.
382 if m-a == 1 {
383 // Use binary search to find the lowest index i
384 // such that data[i] >= data[a] for m <= i < b.
385 // Exit the search loop with i == b in case no such index exists.
386 i := m
387 j := b
388 for i < j {
389 h := int(uint(i+j) >> 1)
390 if data.Less(h, a) {
391 i = h + 1
392 } else {
393 j = h
394 }
395 }
396 // Swap values until data[a] reaches the position before i.
397 for k := a; k < i-1; k++ {
398 data.Swap(k, k+1)
399 }
400 return
401 }
402 403 // Avoid unnecessary recursions of symMerge
404 // by direct insertion of data[m] into data[a:m]
405 // if data[m:b] only contains one element.
406 if b-m == 1 {
407 // Use binary search to find the lowest index i
408 // such that data[i] > data[m] for a <= i < m.
409 // Exit the search loop with i == m in case no such index exists.
410 i := a
411 j := m
412 for i < j {
413 h := int(uint(i+j) >> 1)
414 if !data.Less(m, h) {
415 i = h + 1
416 } else {
417 j = h
418 }
419 }
420 // Swap values until data[m] reaches the position i.
421 for k := m; k > i; k-- {
422 data.Swap(k, k-1)
423 }
424 return
425 }
426 427 mid := int(uint(a+b) >> 1)
428 n := mid + m
429 var start, r int
430 if m > mid {
431 start = n - b
432 r = mid
433 } else {
434 start = a
435 r = m
436 }
437 p := n - 1
438 439 for start < r {
440 c := int(uint(start+r) >> 1)
441 if !data.Less(p-c, c) {
442 start = c + 1
443 } else {
444 r = c
445 }
446 }
447 448 end := n - start
449 if start < m && m < end {
450 rotate(data, start, m, end)
451 }
452 if a < start && start < mid {
453 symMerge(data, a, start, mid)
454 }
455 if mid < end && end < b {
456 symMerge(data, mid, end, b)
457 }
458 }
459 460 // rotate rotates two consecutive blocks u = data[a:m] and v = data[m:b] in data:
461 // Data of the form 'x u v y' is changed to 'x v u y'.
462 // rotate performs at most b-a many calls to data.Swap,
463 // and it assumes non-degenerate arguments: a < m && m < b.
464 func rotate(data Interface, a, m, b int) {
465 i := m - a
466 j := b - m
467 468 for i != j {
469 if i > j {
470 swapRange(data, m-i, m, j)
471 i -= j
472 } else {
473 swapRange(data, m-i, m+j-i, i)
474 j -= i
475 }
476 }
477 // i == j
478 swapRange(data, m-i, m, i)
479 }
480