1// Copyright 2022 The Go Authors. All rights reserved.
2// Use of this source code is governed by a BSD-style
3// license that can be found in the LICENSE file.
4
5//go:build ignore
6
7// This program is run via "go generate" (via a directive in sort.go)
8// to generate implementation variants of the underlying sorting algorithm.
9// When passed the -generic flag it generates generic variants of sorting;
10// otherwise it generates the non-generic variants used by the sort package.
11
12package main
13
14import (
15	"bytes"
16	"flag"
17	"fmt"
18	"go/format"
19	"log"
20	"os"
21	"text/template"
22)
23
24type Variant struct {
25	// Name is the variant name: should be unique among variants.
26	Name string
27
28	// Path is the file path into which the generator will emit the code for this
29	// variant.
30	Path string
31
32	// Package is the package this code will be emitted into.
33	Package string
34
35	// Imports is the imports needed for this package.
36	Imports string
37
38	// FuncSuffix is appended to all function names in this variant's code. All
39	// suffixes should be unique within a package.
40	FuncSuffix string
41
42	// DataType is the type of the data parameter of functions in this variant's
43	// code.
44	DataType string
45
46	// TypeParam is the optional type parameter for the function.
47	TypeParam string
48
49	// ExtraParam is an extra parameter to pass to the function. Should begin with
50	// ", " to separate from other params.
51	ExtraParam string
52
53	// ExtraArg is an extra argument to pass to calls between functions; typically
54	// it invokes ExtraParam. Should begin with ", " to separate from other args.
55	ExtraArg string
56
57	// Funcs is a map of functions used from within the template. The following
58	// functions are expected to exist:
59	//
60	//    Less (name, i, j):
61	//      emits a comparison expression that checks if the value `name` at
62	//      index `i` is smaller than at index `j`.
63	//
64	//    Swap (name, i, j):
65	//      emits a statement that performs a data swap between elements `i` and
66	//      `j` of the value `name`.
67	Funcs template.FuncMap
68}
69
70var (
71	traditionalVariants = []Variant{
72		Variant{
73			Name:       "interface",
74			Path:       "zsortinterface.go",
75			Package:    "sort",
76			Imports:    "",
77			FuncSuffix: "",
78			TypeParam:  "",
79			ExtraParam: "",
80			ExtraArg:   "",
81			DataType:   "Interface",
82			Funcs: template.FuncMap{
83				"Less": func(name, i, j string) string {
84					return fmt.Sprintf("%s.Less(%s, %s)", name, i, j)
85				},
86				"Swap": func(name, i, j string) string {
87					return fmt.Sprintf("%s.Swap(%s, %s)", name, i, j)
88				},
89			},
90		},
91		Variant{
92			Name:       "func",
93			Path:       "zsortfunc.go",
94			Package:    "sort",
95			Imports:    "",
96			FuncSuffix: "_func",
97			TypeParam:  "",
98			ExtraParam: "",
99			ExtraArg:   "",
100			DataType:   "lessSwap",
101			Funcs: template.FuncMap{
102				"Less": func(name, i, j string) string {
103					return fmt.Sprintf("%s.Less(%s, %s)", name, i, j)
104				},
105				"Swap": func(name, i, j string) string {
106					return fmt.Sprintf("%s.Swap(%s, %s)", name, i, j)
107				},
108			},
109		},
110	}
111
112	genericVariants = []Variant{
113		Variant{
114			Name:       "generic_ordered",
115			Path:       "zsortordered.go",
116			Package:    "slices",
117			Imports:    "import \"cmp\"\n",
118			FuncSuffix: "Ordered",
119			TypeParam:  "[E cmp.Ordered]",
120			ExtraParam: "",
121			ExtraArg:   "",
122			DataType:   "[]E",
123			Funcs: template.FuncMap{
124				"Less": func(name, i, j string) string {
125					return fmt.Sprintf("cmp.Less(%s[%s], %s[%s])", name, i, name, j)
126				},
127				"Swap": func(name, i, j string) string {
128					return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
129				},
130			},
131		},
132		Variant{
133			Name:       "generic_func",
134			Path:       "zsortanyfunc.go",
135			Package:    "slices",
136			FuncSuffix: "CmpFunc",
137			TypeParam:  "[E any]",
138			ExtraParam: ", cmp func(a, b E) int",
139			ExtraArg:   ", cmp",
140			DataType:   "[]E",
141			Funcs: template.FuncMap{
142				"Less": func(name, i, j string) string {
143					return fmt.Sprintf("(cmp(%s[%s], %s[%s]) < 0)", name, i, name, j)
144				},
145				"Swap": func(name, i, j string) string {
146					return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
147				},
148			},
149		},
150	}
151
152	expVariants = []Variant{
153		Variant{
154			Name:       "exp_ordered",
155			Path:       "zsortordered.go",
156			Package:    "slices",
157			Imports:    "import \"golang.org/x/exp/constraints\"\n",
158			FuncSuffix: "Ordered",
159			TypeParam:  "[E constraints.Ordered]",
160			ExtraParam: "",
161			ExtraArg:   "",
162			DataType:   "[]E",
163			Funcs: template.FuncMap{
164				"Less": func(name, i, j string) string {
165					return fmt.Sprintf("cmpLess(%s[%s], %s[%s])", name, i, name, j)
166				},
167				"Swap": func(name, i, j string) string {
168					return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
169				},
170			},
171		},
172		Variant{
173			Name:       "exp_func",
174			Path:       "zsortanyfunc.go",
175			Package:    "slices",
176			FuncSuffix: "CmpFunc",
177			TypeParam:  "[E any]",
178			ExtraParam: ", cmp func(a, b E) int",
179			ExtraArg:   ", cmp",
180			DataType:   "[]E",
181			Funcs: template.FuncMap{
182				"Less": func(name, i, j string) string {
183					return fmt.Sprintf("(cmp(%s[%s], %s[%s]) < 0)", name, i, name, j)
184				},
185				"Swap": func(name, i, j string) string {
186					return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
187				},
188			},
189		},
190	}
191)
192
193func main() {
194	genGeneric := flag.Bool("generic", false, "generate generic versions")
195	genExp := flag.Bool("exp", false, "generate x/exp/slices versions")
196	flag.Parse()
197
198	var variants []Variant
199	if *genExp {
200		variants = expVariants
201	} else if *genGeneric {
202		variants = genericVariants
203	} else {
204		variants = traditionalVariants
205	}
206	for i := range variants {
207		generate(&variants[i])
208	}
209}
210
211// generate generates the code for variant `v` into a file named by `v.Path`.
212func generate(v *Variant) {
213	// Parse templateCode anew for each variant because Parse requires Funcs to be
214	// registered, and it helps type-check the funcs.
215	tmpl, err := template.New("gen").Funcs(v.Funcs).Parse(templateCode)
216	if err != nil {
217		log.Fatal("template Parse:", err)
218	}
219
220	var out bytes.Buffer
221	err = tmpl.Execute(&out, v)
222	if err != nil {
223		log.Fatal("template Execute:", err)
224	}
225
226	formatted, err := format.Source(out.Bytes())
227	if err != nil {
228		log.Fatal("format:", err)
229	}
230
231	if err := os.WriteFile(v.Path, formatted, 0644); err != nil {
232		log.Fatal("WriteFile:", err)
233	}
234}
235
236var templateCode = `// Code generated by gen_sort_variants.go; DO NOT EDIT.
237
238// Copyright 2022 The Go Authors. All rights reserved.
239// Use of this source code is governed by a BSD-style
240// license that can be found in the LICENSE file.
241
242package {{.Package}}
243
244{{.Imports}}
245
246// insertionSort{{.FuncSuffix}} sorts data[a:b] using insertion sort.
247func insertionSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
248	for i := a + 1; i < b; i++ {
249		for j := i; j > a && {{Less "data" "j" "j-1"}}; j-- {
250			{{Swap "data" "j" "j-1"}}
251		}
252	}
253}
254
255// siftDown{{.FuncSuffix}} implements the heap property on data[lo:hi].
256// first is an offset into the array where the root of the heap lies.
257func siftDown{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, lo, hi, first int {{.ExtraParam}}) {
258	root := lo
259	for {
260		child := 2*root + 1
261		if child >= hi {
262			break
263		}
264		if child+1 < hi && {{Less "data" "first+child" "first+child+1"}} {
265			child++
266		}
267		if !{{Less "data" "first+root" "first+child"}} {
268			return
269		}
270		{{Swap "data" "first+root" "first+child"}}
271		root = child
272	}
273}
274
275func heapSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
276	first := a
277	lo := 0
278	hi := b - a
279
280	// Build heap with greatest element at top.
281	for i := (hi - 1) / 2; i >= 0; i-- {
282		siftDown{{.FuncSuffix}}(data, i, hi, first {{.ExtraArg}})
283	}
284
285	// Pop elements, largest first, into end of data.
286	for i := hi - 1; i >= 0; i-- {
287		{{Swap "data" "first" "first+i"}}
288		siftDown{{.FuncSuffix}}(data, lo, i, first {{.ExtraArg}})
289	}
290}
291
292// pdqsort{{.FuncSuffix}} sorts data[a:b].
293// The algorithm based on pattern-defeating quicksort(pdqsort), but without the optimizations from BlockQuicksort.
294// pdqsort paper: https://arxiv.org/pdf/2106.05123.pdf
295// C++ implementation: https://github.com/orlp/pdqsort
296// Rust implementation: https://docs.rs/pdqsort/latest/pdqsort/
297// limit is the number of allowed bad (very unbalanced) pivots before falling back to heapsort.
298func pdqsort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, limit int {{.ExtraParam}}) {
299	const maxInsertion = 12
300
301	var (
302		wasBalanced    = true // whether the last partitioning was reasonably balanced
303		wasPartitioned = true // whether the slice was already partitioned
304	)
305
306	for {
307		length := b - a
308
309		if length <= maxInsertion {
310			insertionSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
311			return
312		}
313
314		// Fall back to heapsort if too many bad choices were made.
315		if limit == 0 {
316			heapSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
317			return
318		}
319
320		// If the last partitioning was imbalanced, we need to breaking patterns.
321		if !wasBalanced {
322			breakPatterns{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
323			limit--
324		}
325
326		pivot, hint := choosePivot{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
327		if hint == decreasingHint {
328			reverseRange{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
329			// The chosen pivot was pivot-a elements after the start of the array.
330			// After reversing it is pivot-a elements before the end of the array.
331			// The idea came from Rust's implementation.
332			pivot = (b - 1) - (pivot - a)
333			hint = increasingHint
334		}
335
336		// The slice is likely already sorted.
337		if wasBalanced && wasPartitioned && hint == increasingHint {
338			if partialInsertionSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}}) {
339				return
340			}
341		}
342
343		// Probably the slice contains many duplicate elements, partition the slice into
344		// elements equal to and elements greater than the pivot.
345		if a > 0 && !{{Less "data" "a-1" "pivot"}} {
346			mid := partitionEqual{{.FuncSuffix}}(data, a, b, pivot {{.ExtraArg}})
347			a = mid
348			continue
349		}
350
351		mid, alreadyPartitioned := partition{{.FuncSuffix}}(data, a, b, pivot {{.ExtraArg}})
352		wasPartitioned = alreadyPartitioned
353
354		leftLen, rightLen := mid-a, b-mid
355		balanceThreshold := length / 8
356		if leftLen < rightLen {
357			wasBalanced = leftLen >= balanceThreshold
358			pdqsort{{.FuncSuffix}}(data, a, mid, limit {{.ExtraArg}})
359			a = mid + 1
360		} else {
361			wasBalanced = rightLen >= balanceThreshold
362			pdqsort{{.FuncSuffix}}(data, mid+1, b, limit {{.ExtraArg}})
363			b = mid
364		}
365	}
366}
367
368// partition{{.FuncSuffix}} does one quicksort partition.
369// Let p = data[pivot]
370// Moves elements in data[a:b] around, so that data[i]<p and data[j]>=p for i<newpivot and j>newpivot.
371// On return, data[newpivot] = p
372func partition{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, pivot int {{.ExtraParam}}) (newpivot int, alreadyPartitioned bool) {
373	{{Swap "data" "a" "pivot"}}
374	i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned
375
376	for i <= j && {{Less "data" "i" "a"}} {
377		i++
378	}
379	for i <= j && !{{Less "data" "j" "a"}} {
380		j--
381	}
382	if i > j {
383		{{Swap "data" "j" "a"}}
384		return j, true
385	}
386	{{Swap "data" "i" "j"}}
387	i++
388	j--
389
390	for {
391		for i <= j && {{Less "data" "i" "a"}} {
392			i++
393		}
394		for i <= j && !{{Less "data" "j" "a"}} {
395			j--
396		}
397		if i > j {
398			break
399		}
400		{{Swap "data" "i" "j"}}
401		i++
402		j--
403	}
404	{{Swap "data" "j" "a"}}
405	return j, false
406}
407
408// partitionEqual{{.FuncSuffix}} partitions data[a:b] into elements equal to data[pivot] followed by elements greater than data[pivot].
409// It assumed that data[a:b] does not contain elements smaller than the data[pivot].
410func partitionEqual{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, pivot int {{.ExtraParam}}) (newpivot int) {
411	{{Swap "data" "a" "pivot"}}
412	i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned
413
414	for {
415		for i <= j && !{{Less "data" "a" "i"}} {
416			i++
417		}
418		for i <= j && {{Less "data" "a" "j"}} {
419			j--
420		}
421		if i > j {
422			break
423		}
424		{{Swap "data" "i" "j"}}
425		i++
426		j--
427	}
428	return i
429}
430
431// partialInsertionSort{{.FuncSuffix}} partially sorts a slice, returns true if the slice is sorted at the end.
432func partialInsertionSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) bool {
433	const (
434		maxSteps         = 5  // maximum number of adjacent out-of-order pairs that will get shifted
435		shortestShifting = 50 // don't shift any elements on short arrays
436	)
437	i := a + 1
438	for j := 0; j < maxSteps; j++ {
439		for i < b && !{{Less "data" "i" "i-1"}} {
440			i++
441		}
442
443		if i == b {
444			return true
445		}
446
447		if b-a < shortestShifting {
448			return false
449		}
450
451		{{Swap "data" "i" "i-1"}}
452
453		// Shift the smaller one to the left.
454		if i-a >= 2 {
455			for j := i - 1; j >= 1; j-- {
456				if !{{Less "data" "j" "j-1"}} {
457					break
458				}
459				{{Swap "data" "j" "j-1"}}
460			}
461		}
462		// Shift the greater one to the right.
463		if b-i >= 2 {
464			for j := i + 1; j < b; j++ {
465				if !{{Less "data" "j" "j-1"}} {
466					break
467				}
468				{{Swap "data" "j" "j-1"}}
469			}
470		}
471	}
472	return false
473}
474
475// breakPatterns{{.FuncSuffix}} scatters some elements around in an attempt to break some patterns
476// that might cause imbalanced partitions in quicksort.
477func breakPatterns{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
478	length := b - a
479	if length >= 8 {
480		random := xorshift(length)
481		modulus := nextPowerOfTwo(length)
482
483		for idx := a + (length/4)*2 - 1; idx <= a + (length/4)*2 + 1; idx++ {
484			other := int(uint(random.Next()) & (modulus - 1))
485			if other >= length {
486				other -= length
487			}
488			{{Swap "data" "idx" "a+other"}}
489		}
490	}
491}
492
493// choosePivot{{.FuncSuffix}} chooses a pivot in data[a:b].
494//
495// [0,8): chooses a static pivot.
496// [8,shortestNinther): uses the simple median-of-three method.
497// [shortestNinther,∞): uses the Tukey ninther method.
498func choosePivot{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) (pivot int, hint sortedHint) {
499	const (
500		shortestNinther = 50
501		maxSwaps        = 4 * 3
502	)
503
504	l := b - a
505
506	var (
507		swaps int
508		i     = a + l/4*1
509		j     = a + l/4*2
510		k     = a + l/4*3
511	)
512
513	if l >= 8 {
514		if l >= shortestNinther {
515			// Tukey ninther method, the idea came from Rust's implementation.
516			i = medianAdjacent{{.FuncSuffix}}(data, i, &swaps {{.ExtraArg}})
517			j = medianAdjacent{{.FuncSuffix}}(data, j, &swaps {{.ExtraArg}})
518			k = medianAdjacent{{.FuncSuffix}}(data, k, &swaps {{.ExtraArg}})
519		}
520		// Find the median among i, j, k and stores it into j.
521		j = median{{.FuncSuffix}}(data, i, j, k, &swaps {{.ExtraArg}})
522	}
523
524	switch swaps {
525	case 0:
526		return j, increasingHint
527	case maxSwaps:
528		return j, decreasingHint
529	default:
530		return j, unknownHint
531	}
532}
533
534// order2{{.FuncSuffix}} returns x,y where data[x] <= data[y], where x,y=a,b or x,y=b,a.
535func order2{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int, swaps *int {{.ExtraParam}}) (int, int) {
536	if {{Less "data" "b" "a"}} {
537		*swaps++
538		return b, a
539	}
540	return a, b
541}
542
543// median{{.FuncSuffix}} returns x where data[x] is the median of data[a],data[b],data[c], where x is a, b, or c.
544func median{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, c int, swaps *int {{.ExtraParam}}) int {
545	a, b = order2{{.FuncSuffix}}(data, a, b, swaps {{.ExtraArg}})
546	b, c = order2{{.FuncSuffix}}(data, b, c, swaps {{.ExtraArg}})
547	a, b = order2{{.FuncSuffix}}(data, a, b, swaps {{.ExtraArg}})
548	return b
549}
550
551// medianAdjacent{{.FuncSuffix}} finds the median of data[a - 1], data[a], data[a + 1] and stores the index into a.
552func medianAdjacent{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a int, swaps *int {{.ExtraParam}}) int {
553	return median{{.FuncSuffix}}(data, a-1, a, a+1, swaps {{.ExtraArg}})
554}
555
556func reverseRange{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
557	i := a
558	j := b - 1
559	for i < j {
560		{{Swap "data" "i" "j"}}
561		i++
562		j--
563	}
564}
565
566func swapRange{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, n int {{.ExtraParam}}) {
567	for i := 0; i < n; i++ {
568		{{Swap "data" "a+i" "b+i"}}
569	}
570}
571
572func stable{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, n int {{.ExtraParam}}) {
573	blockSize := 20 // must be > 0
574	a, b := 0, blockSize
575	for b <= n {
576		insertionSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
577		a = b
578		b += blockSize
579	}
580	insertionSort{{.FuncSuffix}}(data, a, n {{.ExtraArg}})
581
582	for blockSize < n {
583		a, b = 0, 2*blockSize
584		for b <= n {
585			symMerge{{.FuncSuffix}}(data, a, a+blockSize, b {{.ExtraArg}})
586			a = b
587			b += 2 * blockSize
588		}
589		if m := a + blockSize; m < n {
590			symMerge{{.FuncSuffix}}(data, a, m, n {{.ExtraArg}})
591		}
592		blockSize *= 2
593	}
594}
595
596// symMerge{{.FuncSuffix}} merges the two sorted subsequences data[a:m] and data[m:b] using
597// the SymMerge algorithm from Pok-Son Kim and Arne Kutzner, "Stable Minimum
598// Storage Merging by Symmetric Comparisons", in Susanne Albers and Tomasz
599// Radzik, editors, Algorithms - ESA 2004, volume 3221 of Lecture Notes in
600// Computer Science, pages 714-723. Springer, 2004.
601//
602// Let M = m-a and N = b-n. Wolog M < N.
603// The recursion depth is bound by ceil(log(N+M)).
604// The algorithm needs O(M*log(N/M + 1)) calls to data.Less.
605// The algorithm needs O((M+N)*log(M)) calls to data.Swap.
606//
607// The paper gives O((M+N)*log(M)) as the number of assignments assuming a
608// rotation algorithm which uses O(M+N+gcd(M+N)) assignments. The argumentation
609// in the paper carries through for Swap operations, especially as the block
610// swapping rotate uses only O(M+N) Swaps.
611//
612// symMerge assumes non-degenerate arguments: a < m && m < b.
613// Having the caller check this condition eliminates many leaf recursion calls,
614// which improves performance.
615func symMerge{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, m, b int {{.ExtraParam}}) {
616	// Avoid unnecessary recursions of symMerge
617	// by direct insertion of data[a] into data[m:b]
618	// if data[a:m] only contains one element.
619	if m-a == 1 {
620		// Use binary search to find the lowest index i
621		// such that data[i] >= data[a] for m <= i < b.
622		// Exit the search loop with i == b in case no such index exists.
623		i := m
624		j := b
625		for i < j {
626			h := int(uint(i+j) >> 1)
627			if {{Less "data" "h" "a"}} {
628				i = h + 1
629			} else {
630				j = h
631			}
632		}
633		// Swap values until data[a] reaches the position before i.
634		for k := a; k < i-1; k++ {
635			{{Swap "data" "k" "k+1"}}
636		}
637		return
638	}
639
640	// Avoid unnecessary recursions of symMerge
641	// by direct insertion of data[m] into data[a:m]
642	// if data[m:b] only contains one element.
643	if b-m == 1 {
644		// Use binary search to find the lowest index i
645		// such that data[i] > data[m] for a <= i < m.
646		// Exit the search loop with i == m in case no such index exists.
647		i := a
648		j := m
649		for i < j {
650			h := int(uint(i+j) >> 1)
651			if !{{Less "data" "m" "h"}} {
652				i = h + 1
653			} else {
654				j = h
655			}
656		}
657		// Swap values until data[m] reaches the position i.
658		for k := m; k > i; k-- {
659			{{Swap "data" "k" "k-1"}}
660		}
661		return
662	}
663
664	mid := int(uint(a+b) >> 1)
665	n := mid + m
666	var start, r int
667	if m > mid {
668		start = n - b
669		r = mid
670	} else {
671		start = a
672		r = m
673	}
674	p := n - 1
675
676	for start < r {
677		c := int(uint(start+r) >> 1)
678		if !{{Less "data" "p-c" "c"}} {
679			start = c + 1
680		} else {
681			r = c
682		}
683	}
684
685	end := n - start
686	if start < m && m < end {
687		rotate{{.FuncSuffix}}(data, start, m, end {{.ExtraArg}})
688	}
689	if a < start && start < mid {
690		symMerge{{.FuncSuffix}}(data, a, start, mid {{.ExtraArg}})
691	}
692	if mid < end && end < b {
693		symMerge{{.FuncSuffix}}(data, mid, end, b {{.ExtraArg}})
694	}
695}
696
697// rotate{{.FuncSuffix}} rotates two consecutive blocks u = data[a:m] and v = data[m:b] in data:
698// Data of the form 'x u v y' is changed to 'x v u y'.
699// rotate performs at most b-a many calls to data.Swap,
700// and it assumes non-degenerate arguments: a < m && m < b.
701func rotate{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, m, b int {{.ExtraParam}}) {
702	i := m - a
703	j := b - m
704
705	for i != j {
706		if i > j {
707			swapRange{{.FuncSuffix}}(data, m-i, m, j {{.ExtraArg}})
708			i -= j
709		} else {
710			swapRange{{.FuncSuffix}}(data, m-i, m+j-i, i {{.ExtraArg}})
711			j -= i
712		}
713	}
714	// i == j
715	swapRange{{.FuncSuffix}}(data, m-i, m, i {{.ExtraArg}})
716}
717`
718