src/sort/gen_sort_variants.go - go - Git at Google

 // Copyright 2022 The Go Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.

 //go:build ignore

 // This program is run via "go generate" (via a directive in sort.go)
 // to generate implementation variants of the underlying sorting algorithm.
 // When passed the -generic flag it generates generic variants of sorting;
 // otherwise it generates the non-generic variants used by the sort package.

 package main

 import (
 	"bytes"
 	"flag"
 	"fmt"
 	"go/format"
 	"log"
 	"os"
 	"text/template"
 )

 type Variant struct {
 	// Name is the variant name: should be unique among variants.
 	Name string

 	// Path is the file path into which the generator will emit the code for this
 	// variant.
 	Path string

 	// Package is the package this code will be emitted into.
 	Package string

 	// Imports is the imports needed for this package.
 	Imports string

 	// FuncSuffix is appended to all function names in this variant's code. All
 	// suffixes should be unique within a package.
 	FuncSuffix string

 	// DataType is the type of the data parameter of functions in this variant's
 	// code.
 	DataType string

 	// TypeParam is the optional type parameter for the function.
 	TypeParam string

 	// ExtraParam is an extra parameter to pass to the function. Should begin with
 	// ", " to separate from other params.
 	ExtraParam string

 	// ExtraArg is an extra argument to pass to calls between functions; typically
 	// it invokes ExtraParam. Should begin with ", " to separate from other args.
 	ExtraArg string

 	// Funcs is a map of functions used from within the template. The following
 	// functions are expected to exist:
 	//
 	//    Less (name, i, j):
 	//      emits a comparison expression that checks if the value `name` at
 	//      index `i` is smaller than at index `j`.
 	//
 	//    Swap (name, i, j):
 	//      emits a statement that performs a data swap between elements `i` and
 	//      `j` of the value `name`.
 	Funcs template.FuncMap
 }

 var (
 	traditionalVariants = []Variant{
 		Variant{
 			Name:       "interface",
 			Path:       "zsortinterface.go",
 			Package:    "sort",
 			Imports:    "",
 			FuncSuffix: "",
 			TypeParam:  "",
 			ExtraParam: "",
 			ExtraArg:   "",
 			DataType:   "Interface",
 			Funcs: template.FuncMap{
 				"Less": func(name, i, j string) string {
 					return fmt.Sprintf("%s.Less(%s, %s)", name, i, j)
 				},
 				"Swap": func(name, i, j string) string {
 					return fmt.Sprintf("%s.Swap(%s, %s)", name, i, j)
 				},
 			},
 		},
 		Variant{
 			Name:       "func",
 			Path:       "zsortfunc.go",
 			Package:    "sort",
 			Imports:    "",
 			FuncSuffix: "_func",
 			TypeParam:  "",
 			ExtraParam: "",
 			ExtraArg:   "",
 			DataType:   "lessSwap",
 			Funcs: template.FuncMap{
 				"Less": func(name, i, j string) string {
 					return fmt.Sprintf("%s.Less(%s, %s)", name, i, j)
 				},
 				"Swap": func(name, i, j string) string {
 					return fmt.Sprintf("%s.Swap(%s, %s)", name, i, j)
 				},
 			},
 		},
 	}

 	genericVariants = []Variant{
 		Variant{
 			Name:       "generic_ordered",
 			Path:       "zsortordered.go",
 			Package:    "slices",
 			Imports:    "import \"cmp\"\n",
 			FuncSuffix: "Ordered",
 			TypeParam:  "[E cmp.Ordered]",
 			ExtraParam: "",
 			ExtraArg:   "",
 			DataType:   "[]E",
 			Funcs: template.FuncMap{
 				"Less": func(name, i, j string) string {
 					return fmt.Sprintf("cmp.Less(%s[%s], %s[%s])", name, i, name, j)
 				},
 				"Swap": func(name, i, j string) string {
 					return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
 				},
 			},
 		},
 		Variant{
 			Name:       "generic_func",
 			Path:       "zsortanyfunc.go",
 			Package:    "slices",
 			FuncSuffix: "CmpFunc",
 			TypeParam:  "[E any]",
 			ExtraParam: ", cmp func(a, b E) int",
 			ExtraArg:   ", cmp",
 			DataType:   "[]E",
 			Funcs: template.FuncMap{
 				"Less": func(name, i, j string) string {
 					return fmt.Sprintf("(cmp(%s[%s], %s[%s]) < 0)", name, i, name, j)
 				},
 				"Swap": func(name, i, j string) string {
 					return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
 				},
 			},
 		},
 	}

 	expVariants = []Variant{
 		Variant{
 			Name:       "exp_ordered",
 			Path:       "zsortordered.go",
 			Package:    "slices",
 			Imports:    "import \"golang.org/x/exp/constraints\"\n",
 			FuncSuffix: "Ordered",
 			TypeParam:  "[E constraints.Ordered]",
 			ExtraParam: "",
 			ExtraArg:   "",
 			DataType:   "[]E",
 			Funcs: template.FuncMap{
 				"Less": func(name, i, j string) string {
 					return fmt.Sprintf("cmpLess(%s[%s], %s[%s])", name, i, name, j)
 				},
 				"Swap": func(name, i, j string) string {
 					return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
 				},
 			},
 		},
 		Variant{
 			Name:       "exp_func",
 			Path:       "zsortanyfunc.go",
 			Package:    "slices",
 			FuncSuffix: "CmpFunc",
 			TypeParam:  "[E any]",
 			ExtraParam: ", cmp func(a, b E) int",
 			ExtraArg:   ", cmp",
 			DataType:   "[]E",
 			Funcs: template.FuncMap{
 				"Less": func(name, i, j string) string {
 					return fmt.Sprintf("(cmp(%s[%s], %s[%s]) < 0)", name, i, name, j)
 				},
 				"Swap": func(name, i, j string) string {
 					return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
 				},
 			},
 		},
 	}
 )

 func main() {
 	genGeneric := flag.Bool("generic", false, "generate generic versions")
 	genExp := flag.Bool("exp", false, "generate x/exp/slices versions")
 	flag.Parse()

 	var variants []Variant
 	if *genExp {
 		variants = expVariants
 	} else if *genGeneric {
 		variants = genericVariants
 	} else {
 		variants = traditionalVariants
 	}
 	for i := range variants {
 		generate(&variants[i])
 	}
 }

 // generate generates the code for variant `v` into a file named by `v.Path`.
 func generate(v *Variant) {
 	// Parse templateCode anew for each variant because Parse requires Funcs to be
 	// registered, and it helps type-check the funcs.
 	tmpl, err := template.New("gen").Funcs(v.Funcs).Parse(templateCode)
 	if err != nil {
 		log.Fatal("template Parse:", err)
 	}

 	var out bytes.Buffer
 	err = tmpl.Execute(&out, v)
 	if err != nil {
 		log.Fatal("template Execute:", err)
 	}

 	formatted, err := format.Source(out.Bytes())
 	if err != nil {
 		log.Fatal("format:", err)
 	}

 	if err := os.WriteFile(v.Path, formatted, 0644); err != nil {
 		log.Fatal("WriteFile:", err)
 	}
 }

 var templateCode = `// Code generated by gen_sort_variants.go; DO NOT EDIT.

 // Copyright 2022 The Go Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.

 package {{.Package}}

 {{.Imports}}

 // insertionSort{{.FuncSuffix}} sorts data[a:b] using insertion sort.
 func insertionSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
 	for i := a + 1; i < b; i++ {
 		for j := i; j > a && {{Less "data" "j" "j-1"}}; j-- {
 			{{Swap "data" "j" "j-1"}}
 		}
 	}
 }

 // siftDown{{.FuncSuffix}} implements the heap property on data[lo:hi].
 // first is an offset into the array where the root of the heap lies.
 func siftDown{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, lo, hi, first int {{.ExtraParam}}) {
 	root := lo
 	for {
 		child := 2*root + 1
 		if child >= hi {
 			break
 		}
 		if child+1 < hi && {{Less "data" "first+child" "first+child+1"}} {
 			child++
 		}
 		if !{{Less "data" "first+root" "first+child"}} {
 			return
 		}
 		{{Swap "data" "first+root" "first+child"}}
 		root = child
 	}
 }

 func heapSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
 	first := a
 	lo := 0
 	hi := b - a

 	// Build heap with greatest element at top.
 	for i := (hi - 1) / 2; i >= 0; i-- {
 		siftDown{{.FuncSuffix}}(data, i, hi, first {{.ExtraArg}})
 	}

 	// Pop elements, largest first, into end of data.
 	for i := hi - 1; i >= 0; i-- {
 		{{Swap "data" "first" "first+i"}}
 		siftDown{{.FuncSuffix}}(data, lo, i, first {{.ExtraArg}})
 	}
 }

 // pdqsort{{.FuncSuffix}} sorts data[a:b].
 // The algorithm based on pattern-defeating quicksort(pdqsort), but without the optimizations from BlockQuicksort.
 // pdqsort paper: https://arxiv.org/pdf/2106.05123.pdf
 // C++ implementation: https://github.com/orlp/pdqsort
 // Rust implementation: https://docs.rs/pdqsort/latest/pdqsort/
 // limit is the number of allowed bad (very unbalanced) pivots before falling back to heapsort.
 func pdqsort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, limit int {{.ExtraParam}}) {
 	const maxInsertion = 12

 	var (
 		wasBalanced    = true // whether the last partitioning was reasonably balanced
 		wasPartitioned = true // whether the slice was already partitioned
 	)

 	for {
 		length := b - a

 		if length <= maxInsertion {
 			insertionSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
 			return
 		}

 		// Fall back to heapsort if too many bad choices were made.
 		if limit == 0 {
 			heapSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
 			return
 		}

 		// If the last partitioning was imbalanced, we need to breaking patterns.
 		if !wasBalanced {
 			breakPatterns{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
 			limit--
 		}

 		pivot, hint := choosePivot{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
 		if hint == decreasingHint {
 			reverseRange{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
 			// The chosen pivot was pivot-a elements after the start of the array.
 			// After reversing it is pivot-a elements before the end of the array.
 			// The idea came from Rust's implementation.
 			pivot = (b - 1) - (pivot - a)
 			hint = increasingHint
 		}

 		// The slice is likely already sorted.
 		if wasBalanced && wasPartitioned && hint == increasingHint {
 			if partialInsertionSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}}) {
 				return
 			}
 		}

 		// Probably the slice contains many duplicate elements, partition the slice into
 		// elements equal to and elements greater than the pivot.
 		if a > 0 && !{{Less "data" "a-1" "pivot"}} {
 			mid := partitionEqual{{.FuncSuffix}}(data, a, b, pivot {{.ExtraArg}})
 			a = mid
 			continue
 		}

 		mid, alreadyPartitioned := partition{{.FuncSuffix}}(data, a, b, pivot {{.ExtraArg}})
 		wasPartitioned = alreadyPartitioned

 		leftLen, rightLen := mid-a, b-mid
 		balanceThreshold := length / 8
 		if leftLen < rightLen {
 			wasBalanced = leftLen >= balanceThreshold
 			pdqsort{{.FuncSuffix}}(data, a, mid, limit {{.ExtraArg}})
 			a = mid + 1
 		} else {
 			wasBalanced = rightLen >= balanceThreshold
 			pdqsort{{.FuncSuffix}}(data, mid+1, b, limit {{.ExtraArg}})
 			b = mid
 		}
 	}
 }

 // partition{{.FuncSuffix}} does one quicksort partition.
 // Let p = data[pivot]
 // Moves elements in data[a:b] around, so that data[i]<p and data[j]>=p for i<newpivot and j>newpivot.
 // On return, data[newpivot] = p
 func partition{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, pivot int {{.ExtraParam}}) (newpivot int, alreadyPartitioned bool) {
 	{{Swap "data" "a" "pivot"}}
 	i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned

 	for i <= j && {{Less "data" "i" "a"}} {
 		i++
 	}
 	for i <= j && !{{Less "data" "j" "a"}} {
 		j--
 	}
 	if i > j {
 		{{Swap "data" "j" "a"}}
 		return j, true
 	}
 	{{Swap "data" "i" "j"}}
 	i++
 	j--

 	for {
 		for i <= j && {{Less "data" "i" "a"}} {
 			i++
 		}
 		for i <= j && !{{Less "data" "j" "a"}} {
 			j--
 		}
 		if i > j {
 			break
 		}
 		{{Swap "data" "i" "j"}}
 		i++
 		j--
 	}
 	{{Swap "data" "j" "a"}}
 	return j, false
 }

 // partitionEqual{{.FuncSuffix}} partitions data[a:b] into elements equal to data[pivot] followed by elements greater than data[pivot].
 // It assumed that data[a:b] does not contain elements smaller than the data[pivot].
 func partitionEqual{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, pivot int {{.ExtraParam}}) (newpivot int) {
 	{{Swap "data" "a" "pivot"}}
 	i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned

 	for {
 		for i <= j && !{{Less "data" "a" "i"}} {
 			i++
 		}
 		for i <= j && {{Less "data" "a" "j"}} {
 			j--
 		}
 		if i > j {
 			break
 		}
 		{{Swap "data" "i" "j"}}
 		i++
 		j--
 	}
 	return i
 }

 // partialInsertionSort{{.FuncSuffix}} partially sorts a slice, returns true if the slice is sorted at the end.
 func partialInsertionSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) bool {
 	const (
 		maxSteps         = 5  // maximum number of adjacent out-of-order pairs that will get shifted
 		shortestShifting = 50 // don't shift any elements on short arrays
 	)
 	i := a + 1
 	for j := 0; j < maxSteps; j++ {
 		for i < b && !{{Less "data" "i" "i-1"}} {
 			i++
 		}

 		if i == b {
 			return true
 		}

 		if b-a < shortestShifting {
 			return false
 		}

 		{{Swap "data" "i" "i-1"}}

 		// Shift the smaller one to the left.
 		if i-a >= 2 {
 			for j := i - 1; j >= 1; j-- {
 				if !{{Less "data" "j" "j-1"}} {
 					break
 				}
 				{{Swap "data" "j" "j-1"}}
 			}
 		}
 		// Shift the greater one to the right.
 		if b-i >= 2 {
 			for j := i + 1; j < b; j++ {
 				if !{{Less "data" "j" "j-1"}} {
 					break
 				}
 				{{Swap "data" "j" "j-1"}}
 			}
 		}
 	}
 	return false
 }

 // breakPatterns{{.FuncSuffix}} scatters some elements around in an attempt to break some patterns
 // that might cause imbalanced partitions in quicksort.
 func breakPatterns{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
 	length := b - a
 	if length >= 8 {
 		random := xorshift(length)
 		modulus := nextPowerOfTwo(length)

 		for idx := a + (length/4)*2 - 1; idx <= a + (length/4)*2 + 1; idx++ {
 			other := int(uint(random.Next()) & (modulus - 1))
 			if other >= length {
 				other -= length
 			}
 			{{Swap "data" "idx" "a+other"}}
 		}
 	}
 }

 // choosePivot{{.FuncSuffix}} chooses a pivot in data[a:b].
 //
 // [0,8): chooses a static pivot.
 // [8,shortestNinther): uses the simple median-of-three method.
 // [shortestNinther,∞): uses the Tukey ninther method.
 func choosePivot{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) (pivot int, hint sortedHint) {
 	const (
 		shortestNinther = 50
 		maxSwaps        = 4 * 3
 	)

 	l := b - a

 	var (
 		swaps int
 		i     = a + l/4*1
 		j     = a + l/4*2
 		k     = a + l/4*3
 	)

 	if l >= 8 {
 		if l >= shortestNinther {
 			// Tukey ninther method, the idea came from Rust's implementation.
 			i = medianAdjacent{{.FuncSuffix}}(data, i, &swaps {{.ExtraArg}})
 			j = medianAdjacent{{.FuncSuffix}}(data, j, &swaps {{.ExtraArg}})
 			k = medianAdjacent{{.FuncSuffix}}(data, k, &swaps {{.ExtraArg}})
 		}
 		// Find the median among i, j, k and stores it into j.
 		j = median{{.FuncSuffix}}(data, i, j, k, &swaps {{.ExtraArg}})
 	}

 	switch swaps {
 	case 0:
 		return j, increasingHint
 	case maxSwaps:
 		return j, decreasingHint
 	default:
 		return j, unknownHint
 	}
 }

 // order2{{.FuncSuffix}} returns x,y where data[x] <= data[y], where x,y=a,b or x,y=b,a.
 func order2{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int, swaps *int {{.ExtraParam}}) (int, int) {
 	if {{Less "data" "b" "a"}} {
 		*swaps++
 		return b, a
 	}
 	return a, b
 }

 // median{{.FuncSuffix}} returns x where data[x] is the median of data[a],data[b],data[c], where x is a, b, or c.
 func median{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, c int, swaps *int {{.ExtraParam}}) int {
 	a, b = order2{{.FuncSuffix}}(data, a, b, swaps {{.ExtraArg}})
 	b, c = order2{{.FuncSuffix}}(data, b, c, swaps {{.ExtraArg}})
 	a, b = order2{{.FuncSuffix}}(data, a, b, swaps {{.ExtraArg}})
 	return b
 }

 // medianAdjacent{{.FuncSuffix}} finds the median of data[a - 1], data[a], data[a + 1] and stores the index into a.
 func medianAdjacent{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a int, swaps *int {{.ExtraParam}}) int {
 	return median{{.FuncSuffix}}(data, a-1, a, a+1, swaps {{.ExtraArg}})
 }

 func reverseRange{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
 	i := a
 	j := b - 1
 	for i < j {
 		{{Swap "data" "i" "j"}}
 		i++
 		j--
 	}
 }

 func swapRange{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, n int {{.ExtraParam}}) {
 	for i := 0; i < n; i++ {
 		{{Swap "data" "a+i" "b+i"}}
 	}
 }

 func stable{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, n int {{.ExtraParam}}) {
 	blockSize := 20 // must be > 0
 	a, b := 0, blockSize
 	for b <= n {
 		insertionSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
 		a = b
 		b += blockSize
 	}
 	insertionSort{{.FuncSuffix}}(data, a, n {{.ExtraArg}})

 	for blockSize < n {
 		a, b = 0, 2*blockSize
 		for b <= n {
 			symMerge{{.FuncSuffix}}(data, a, a+blockSize, b {{.ExtraArg}})
 			a = b
 			b += 2 * blockSize
 		}
 		if m := a + blockSize; m < n {
 			symMerge{{.FuncSuffix}}(data, a, m, n {{.ExtraArg}})
 		}
 		blockSize *= 2
 	}
 }

 // symMerge{{.FuncSuffix}} merges the two sorted subsequences data[a:m] and data[m:b] using
 // the SymMerge algorithm from Pok-Son Kim and Arne Kutzner, "Stable Minimum
 // Storage Merging by Symmetric Comparisons", in Susanne Albers and Tomasz
 // Radzik, editors, Algorithms - ESA 2004, volume 3221 of Lecture Notes in
 // Computer Science, pages 714-723. Springer, 2004.
 //
 // Let M = m-a and N = b-n. Wolog M < N.
 // The recursion depth is bound by ceil(log(N+M)).
 // The algorithm needs O(M*log(N/M + 1)) calls to data.Less.
 // The algorithm needs O((M+N)*log(M)) calls to data.Swap.
 //
 // The paper gives O((M+N)*log(M)) as the number of assignments assuming a
 // rotation algorithm which uses O(M+N+gcd(M+N)) assignments. The argumentation
 // in the paper carries through for Swap operations, especially as the block
 // swapping rotate uses only O(M+N) Swaps.
 //
 // symMerge assumes non-degenerate arguments: a < m && m < b.
 // Having the caller check this condition eliminates many leaf recursion calls,
 // which improves performance.
 func symMerge{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, m, b int {{.ExtraParam}}) {
 	// Avoid unnecessary recursions of symMerge
 	// by direct insertion of data[a] into data[m:b]
 	// if data[a:m] only contains one element.
 	if m-a == 1 {
 		// Use binary search to find the lowest index i
 		// such that data[i] >= data[a] for m <= i < b.
 		// Exit the search loop with i == b in case no such index exists.
 		i := m
 		j := b
 		for i < j {
 			h := int(uint(i+j) >> 1)
 			if {{Less "data" "h" "a"}} {
 				i = h + 1
 			} else {
 				j = h
 			}
 		}
 		// Swap values until data[a] reaches the position before i.
 		for k := a; k < i-1; k++ {
 			{{Swap "data" "k" "k+1"}}
 		}
 		return
 	}

 	// Avoid unnecessary recursions of symMerge
 	// by direct insertion of data[m] into data[a:m]
 	// if data[m:b] only contains one element.
 	if b-m == 1 {
 		// Use binary search to find the lowest index i
 		// such that data[i] > data[m] for a <= i < m.
 		// Exit the search loop with i == m in case no such index exists.
 		i := a
 		j := m
 		for i < j {
 			h := int(uint(i+j) >> 1)
 			if !{{Less "data" "m" "h"}} {
 				i = h + 1
 			} else {
 				j = h
 			}
 		}
 		// Swap values until data[m] reaches the position i.
 		for k := m; k > i; k-- {
 			{{Swap "data" "k" "k-1"}}
 		}
 		return
 	}

 	mid := int(uint(a+b) >> 1)
 	n := mid + m
 	var start, r int
 	if m > mid {
 		start = n - b
 		r = mid
 	} else {
 		start = a
 		r = m
 	}
 	p := n - 1

 	for start < r {
 		c := int(uint(start+r) >> 1)
 		if !{{Less "data" "p-c" "c"}} {
 			start = c + 1
 		} else {
 			r = c
 		}
 	}

 	end := n - start
 	if start < m && m < end {
 		rotate{{.FuncSuffix}}(data, start, m, end {{.ExtraArg}})
 	}
 	if a < start && start < mid {
 		symMerge{{.FuncSuffix}}(data, a, start, mid {{.ExtraArg}})
 	}
 	if mid < end && end < b {
 		symMerge{{.FuncSuffix}}(data, mid, end, b {{.ExtraArg}})
 	}
 }

 // rotate{{.FuncSuffix}} rotates two consecutive blocks u = data[a:m] and v = data[m:b] in data:
 // Data of the form 'x u v y' is changed to 'x v u y'.
 // rotate performs at most b-a many calls to data.Swap,
 // and it assumes non-degenerate arguments: a < m && m < b.
 func rotate{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, m, b int {{.ExtraParam}}) {
 	i := m - a
 	j := b - m

 	for i != j {
 		if i > j {
 			swapRange{{.FuncSuffix}}(data, m-i, m, j {{.ExtraArg}})
 			i -= j
 		} else {
 			swapRange{{.FuncSuffix}}(data, m-i, m+j-i, i {{.ExtraArg}})
 			j -= i
 		}
 	}
 	// i == j
 	swapRange{{.FuncSuffix}}(data, m-i, m, i {{.ExtraArg}})
 }
 `
	// Copyright 2022 The Go Authors. All rights reserved.
	// Use of this source code is governed by a BSD-style
	// license that can be found in the LICENSE file.

	//go:build ignore

	// This program is run via "go generate" (via a directive in sort.go)
	// to generate implementation variants of the underlying sorting algorithm.
	// When passed the -generic flag it generates generic variants of sorting;
	// otherwise it generates the non-generic variants used by the sort package.

	package main

	import (
	"bytes"
	"flag"
	"fmt"
	"go/format"
	"log"
	"os"
	"text/template"
	)

	type Variant struct {
	// Name is the variant name: should be unique among variants.
	Name string

	// Path is the file path into which the generator will emit the code for this
	// variant.
	Path string

	// Package is the package this code will be emitted into.
	Package string

	// Imports is the imports needed for this package.
	Imports string

	// FuncSuffix is appended to all function names in this variant's code. All
	// suffixes should be unique within a package.
	FuncSuffix string

	// DataType is the type of the data parameter of functions in this variant's
	// code.
	DataType string

	// TypeParam is the optional type parameter for the function.
	TypeParam string

	// ExtraParam is an extra parameter to pass to the function. Should begin with
	// ", " to separate from other params.
	ExtraParam string

	// ExtraArg is an extra argument to pass to calls between functions; typically
	// it invokes ExtraParam. Should begin with ", " to separate from other args.
	ExtraArg string

	// Funcs is a map of functions used from within the template. The following
	// functions are expected to exist:
	//
	// Less (name, i, j):
	// emits a comparison expression that checks if the value `name` at
	// index `i` is smaller than at index `j`.
	//
	// Swap (name, i, j):
	// emits a statement that performs a data swap between elements `i` and
	// `j` of the value `name`.
	Funcs template.FuncMap
	}

	var (
	traditionalVariants = []Variant{
	Variant{
	Name: "interface",
	Path: "zsortinterface.go",
	Package: "sort",
	Imports: "",
	FuncSuffix: "",
	TypeParam: "",
	ExtraParam: "",
	ExtraArg: "",
	DataType: "Interface",
	Funcs: template.FuncMap{
	"Less": func(name, i, j string) string {
	return fmt.Sprintf("%s.Less(%s, %s)", name, i, j)
	},
	"Swap": func(name, i, j string) string {
	return fmt.Sprintf("%s.Swap(%s, %s)", name, i, j)
	},
	},
	},
	Variant{
	Name: "func",
	Path: "zsortfunc.go",
	Package: "sort",
	Imports: "",
	FuncSuffix: "_func",
	TypeParam: "",
	ExtraParam: "",
	ExtraArg: "",
	DataType: "lessSwap",
	Funcs: template.FuncMap{
	"Less": func(name, i, j string) string {
	return fmt.Sprintf("%s.Less(%s, %s)", name, i, j)
	},
	"Swap": func(name, i, j string) string {
	return fmt.Sprintf("%s.Swap(%s, %s)", name, i, j)
	},
	},
	},
	}

	genericVariants = []Variant{
	Variant{
	Name: "generic_ordered",
	Path: "zsortordered.go",
	Package: "slices",
	Imports: "import \"cmp\"\n",
	FuncSuffix: "Ordered",
	TypeParam: "[E cmp.Ordered]",
	ExtraParam: "",
	ExtraArg: "",
	DataType: "[]E",
	Funcs: template.FuncMap{
	"Less": func(name, i, j string) string {
	return fmt.Sprintf("cmp.Less(%s[%s], %s[%s])", name, i, name, j)
	},
	"Swap": func(name, i, j string) string {
	return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
	},
	},
	},
	Variant{
	Name: "generic_func",
	Path: "zsortanyfunc.go",
	Package: "slices",
	FuncSuffix: "CmpFunc",
	TypeParam: "[E any]",
	ExtraParam: ", cmp func(a, b E) int",
	ExtraArg: ", cmp",
	DataType: "[]E",
	Funcs: template.FuncMap{
	"Less": func(name, i, j string) string {
	return fmt.Sprintf("(cmp(%s[%s], %s[%s]) < 0)", name, i, name, j)
	},
	"Swap": func(name, i, j string) string {
	return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
	},
	},
	},
	}

	expVariants = []Variant{
	Variant{
	Name: "exp_ordered",
	Path: "zsortordered.go",
	Package: "slices",
	Imports: "import \"golang.org/x/exp/constraints\"\n",
	FuncSuffix: "Ordered",
	TypeParam: "[E constraints.Ordered]",
	ExtraParam: "",
	ExtraArg: "",
	DataType: "[]E",
	Funcs: template.FuncMap{
	"Less": func(name, i, j string) string {
	return fmt.Sprintf("cmpLess(%s[%s], %s[%s])", name, i, name, j)
	},
	"Swap": func(name, i, j string) string {
	return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
	},
	},
	},
	Variant{
	Name: "exp_func",
	Path: "zsortanyfunc.go",
	Package: "slices",
	FuncSuffix: "CmpFunc",
	TypeParam: "[E any]",
	ExtraParam: ", cmp func(a, b E) int",
	ExtraArg: ", cmp",
	DataType: "[]E",
	Funcs: template.FuncMap{
	"Less": func(name, i, j string) string {
	return fmt.Sprintf("(cmp(%s[%s], %s[%s]) < 0)", name, i, name, j)
	},
	"Swap": func(name, i, j string) string {
	return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
	},
	},
	},
	}
	)

	func main() {
	genGeneric := flag.Bool("generic", false, "generate generic versions")
	genExp := flag.Bool("exp", false, "generate x/exp/slices versions")
	flag.Parse()

	var variants []Variant
	if *genExp {
	variants = expVariants
	} else if *genGeneric {
	variants = genericVariants
	} else {
	variants = traditionalVariants
	}
	for i := range variants {
	generate(&variants[i])
	}
	}

	// generate generates the code for variant `v` into a file named by `v.Path`.
	func generate(v *Variant) {
	// Parse templateCode anew for each variant because Parse requires Funcs to be
	// registered, and it helps type-check the funcs.
	tmpl, err := template.New("gen").Funcs(v.Funcs).Parse(templateCode)
	if err != nil {
	log.Fatal("template Parse:", err)
	}

	var out bytes.Buffer
	err = tmpl.Execute(&out, v)
	if err != nil {
	log.Fatal("template Execute:", err)
	}

	formatted, err := format.Source(out.Bytes())
	if err != nil {
	log.Fatal("format:", err)
	}

	if err := os.WriteFile(v.Path, formatted, 0644); err != nil {
	log.Fatal("WriteFile:", err)
	}
	}

	var templateCode = `// Code generated by gen_sort_variants.go; DO NOT EDIT.

	// Copyright 2022 The Go Authors. All rights reserved.
	// Use of this source code is governed by a BSD-style
	// license that can be found in the LICENSE file.

	package {{.Package}}

	{{.Imports}}

	// insertionSort{{.FuncSuffix}} sorts data[a:b] using insertion sort.
	func insertionSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
	for i := a + 1; i < b; i++ {
	for j := i; j > a && {{Less "data" "j" "j-1"}}; j-- {
	{{Swap "data" "j" "j-1"}}
	}
	}
	}

	// siftDown{{.FuncSuffix}} implements the heap property on data[lo:hi].
	// first is an offset into the array where the root of the heap lies.
	func siftDown{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, lo, hi, first int {{.ExtraParam}}) {
	root := lo
	for {
	child := 2*root + 1
	if child >= hi {
	break
	}
	if child+1 < hi && {{Less "data" "first+child" "first+child+1"}} {
	child++
	}
	if !{{Less "data" "first+root" "first+child"}} {
	return
	}
	{{Swap "data" "first+root" "first+child"}}
	root = child
	}
	}

	func heapSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
	first := a
	lo := 0
	hi := b - a

	// Build heap with greatest element at top.
	for i := (hi - 1) / 2; i >= 0; i-- {
	siftDown{{.FuncSuffix}}(data, i, hi, first {{.ExtraArg}})
	}

	// Pop elements, largest first, into end of data.
	for i := hi - 1; i >= 0; i-- {
	{{Swap "data" "first" "first+i"}}
	siftDown{{.FuncSuffix}}(data, lo, i, first {{.ExtraArg}})
	}
	}

	// pdqsort{{.FuncSuffix}} sorts data[a:b].
	// The algorithm based on pattern-defeating quicksort(pdqsort), but without the optimizations from BlockQuicksort.
	// pdqsort paper: https://arxiv.org/pdf/2106.05123.pdf
	// C++ implementation: https://github.com/orlp/pdqsort
	// Rust implementation: https://docs.rs/pdqsort/latest/pdqsort/
	// limit is the number of allowed bad (very unbalanced) pivots before falling back to heapsort.
	func pdqsort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, limit int {{.ExtraParam}}) {
	const maxInsertion = 12

	var (
	wasBalanced = true // whether the last partitioning was reasonably balanced
	wasPartitioned = true // whether the slice was already partitioned
	)

	for {
	length := b - a

	if length <= maxInsertion {
	insertionSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
	return
	}

	// Fall back to heapsort if too many bad choices were made.
	if limit == 0 {
	heapSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
	return
	}

	// If the last partitioning was imbalanced, we need to breaking patterns.
	if !wasBalanced {
	breakPatterns{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
	limit--
	}

	pivot, hint := choosePivot{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
	if hint == decreasingHint {
	reverseRange{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
	// The chosen pivot was pivot-a elements after the start of the array.
	// After reversing it is pivot-a elements before the end of the array.
	// The idea came from Rust's implementation.
	pivot = (b - 1) - (pivot - a)
	hint = increasingHint
	}

	// The slice is likely already sorted.
	if wasBalanced && wasPartitioned && hint == increasingHint {
	if partialInsertionSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}}) {
	return
	}
	}

	// Probably the slice contains many duplicate elements, partition the slice into
	// elements equal to and elements greater than the pivot.
	if a > 0 && !{{Less "data" "a-1" "pivot"}} {
	mid := partitionEqual{{.FuncSuffix}}(data, a, b, pivot {{.ExtraArg}})
	a = mid
	continue
	}

	mid, alreadyPartitioned := partition{{.FuncSuffix}}(data, a, b, pivot {{.ExtraArg}})
	wasPartitioned = alreadyPartitioned

	leftLen, rightLen := mid-a, b-mid
	balanceThreshold := length / 8
	if leftLen < rightLen {
	wasBalanced = leftLen >= balanceThreshold
	pdqsort{{.FuncSuffix}}(data, a, mid, limit {{.ExtraArg}})
	a = mid + 1
	} else {
	wasBalanced = rightLen >= balanceThreshold
	pdqsort{{.FuncSuffix}}(data, mid+1, b, limit {{.ExtraArg}})
	b = mid
	}
	}
	}

	// partition{{.FuncSuffix}} does one quicksort partition.
	// Let p = data[pivot]
	// Moves elements in data[a:b] around, so that data[i]<p and data[j]>=p for i<newpivot and j>newpivot.
	// On return, data[newpivot] = p
	func partition{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, pivot int {{.ExtraParam}}) (newpivot int, alreadyPartitioned bool) {
	{{Swap "data" "a" "pivot"}}
	i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned

	for i <= j && {{Less "data" "i" "a"}} {
	i++
	}
	for i <= j && !{{Less "data" "j" "a"}} {
	j--
	}
	if i > j {
	{{Swap "data" "j" "a"}}
	return j, true
	}
	{{Swap "data" "i" "j"}}
	i++
	j--

	for {
	for i <= j && {{Less "data" "i" "a"}} {
	i++
	}
	for i <= j && !{{Less "data" "j" "a"}} {
	j--
	}
	if i > j {
	break
	}
	{{Swap "data" "i" "j"}}
	i++
	j--
	}
	{{Swap "data" "j" "a"}}
	return j, false
	}

	// partitionEqual{{.FuncSuffix}} partitions data[a:b] into elements equal to data[pivot] followed by elements greater than data[pivot].
	// It assumed that data[a:b] does not contain elements smaller than the data[pivot].
	func partitionEqual{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, pivot int {{.ExtraParam}}) (newpivot int) {
	{{Swap "data" "a" "pivot"}}
	i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned

	for {
	for i <= j && !{{Less "data" "a" "i"}} {
	i++
	}
	for i <= j && {{Less "data" "a" "j"}} {
	j--
	}
	if i > j {
	break
	}
	{{Swap "data" "i" "j"}}
	i++
	j--
	}
	return i
	}

	// partialInsertionSort{{.FuncSuffix}} partially sorts a slice, returns true if the slice is sorted at the end.
	func partialInsertionSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) bool {
	const (
	maxSteps = 5 // maximum number of adjacent out-of-order pairs that will get shifted
	shortestShifting = 50 // don't shift any elements on short arrays
	)
	i := a + 1
	for j := 0; j < maxSteps; j++ {
	for i < b && !{{Less "data" "i" "i-1"}} {
	i++
	}

	if i == b {
	return true
	}

	if b-a < shortestShifting {
	return false
	}

	{{Swap "data" "i" "i-1"}}

	// Shift the smaller one to the left.
	if i-a >= 2 {
	for j := i - 1; j >= 1; j-- {
	if !{{Less "data" "j" "j-1"}} {
	break
	}
	{{Swap "data" "j" "j-1"}}
	}
	}
	// Shift the greater one to the right.
	if b-i >= 2 {
	for j := i + 1; j < b; j++ {
	if !{{Less "data" "j" "j-1"}} {
	break
	}
	{{Swap "data" "j" "j-1"}}
	}
	}
	}
	return false
	}

	// breakPatterns{{.FuncSuffix}} scatters some elements around in an attempt to break some patterns
	// that might cause imbalanced partitions in quicksort.
	func breakPatterns{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
	length := b - a
	if length >= 8 {
	random := xorshift(length)
	modulus := nextPowerOfTwo(length)

	for idx := a + (length/4)2 - 1; idx <= a + (length/4)2 + 1; idx++ {
	other := int(uint(random.Next()) & (modulus - 1))
	if other >= length {
	other -= length
	}
	{{Swap "data" "idx" "a+other"}}
	}
	}
	}

	// choosePivot{{.FuncSuffix}} chooses a pivot in data[a:b].
	//
	// [0,8): chooses a static pivot.
	// [8,shortestNinther): uses the simple median-of-three method.
	// [shortestNinther,∞): uses the Tukey ninther method.
	func choosePivot{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) (pivot int, hint sortedHint) {
	const (
	shortestNinther = 50
	maxSwaps = 4 * 3
	)

	l := b - a

	var (
	swaps int
	i = a + l/4*1
	j = a + l/4*2
	k = a + l/4*3
	)

	if l >= 8 {
	if l >= shortestNinther {
	// Tukey ninther method, the idea came from Rust's implementation.
	i = medianAdjacent{{.FuncSuffix}}(data, i, &swaps {{.ExtraArg}})
	j = medianAdjacent{{.FuncSuffix}}(data, j, &swaps {{.ExtraArg}})
	k = medianAdjacent{{.FuncSuffix}}(data, k, &swaps {{.ExtraArg}})
	}
	// Find the median among i, j, k and stores it into j.
	j = median{{.FuncSuffix}}(data, i, j, k, &swaps {{.ExtraArg}})
	}

	switch swaps {
	case 0:
	return j, increasingHint
	case maxSwaps:
	return j, decreasingHint
	default:
	return j, unknownHint
	}
	}

	// order2{{.FuncSuffix}} returns x,y where data[x] <= data[y], where x,y=a,b or x,y=b,a.
	func order2{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int, swaps *int {{.ExtraParam}}) (int, int) {
	if {{Less "data" "b" "a"}} {
	*swaps++
	return b, a
	}
	return a, b
	}

	// median{{.FuncSuffix}} returns x where data[x] is the median of data[a],data[b],data[c], where x is a, b, or c.
	func median{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, c int, swaps *int {{.ExtraParam}}) int {
	a, b = order2{{.FuncSuffix}}(data, a, b, swaps {{.ExtraArg}})
	b, c = order2{{.FuncSuffix}}(data, b, c, swaps {{.ExtraArg}})
	a, b = order2{{.FuncSuffix}}(data, a, b, swaps {{.ExtraArg}})
	return b
	}

	// medianAdjacent{{.FuncSuffix}} finds the median of data[a - 1], data[a], data[a + 1] and stores the index into a.
	func medianAdjacent{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a int, swaps *int {{.ExtraParam}}) int {
	return median{{.FuncSuffix}}(data, a-1, a, a+1, swaps {{.ExtraArg}})
	}

	func reverseRange{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
	i := a
	j := b - 1
	for i < j {
	{{Swap "data" "i" "j"}}
	i++
	j--
	}
	}

	func swapRange{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, n int {{.ExtraParam}}) {
	for i := 0; i < n; i++ {
	{{Swap "data" "a+i" "b+i"}}
	}
	}

	func stable{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, n int {{.ExtraParam}}) {
	blockSize := 20 // must be > 0
	a, b := 0, blockSize
	for b <= n {
	insertionSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
	a = b
	b += blockSize
	}
	insertionSort{{.FuncSuffix}}(data, a, n {{.ExtraArg}})

	for blockSize < n {
	a, b = 0, 2*blockSize
	for b <= n {
	symMerge{{.FuncSuffix}}(data, a, a+blockSize, b {{.ExtraArg}})
	a = b
	b += 2 * blockSize
	}
	if m := a + blockSize; m < n {
	symMerge{{.FuncSuffix}}(data, a, m, n {{.ExtraArg}})
	}
	blockSize *= 2
	}
	}

	// symMerge{{.FuncSuffix}} merges the two sorted subsequences data[a:m] and data[m:b] using
	// the SymMerge algorithm from Pok-Son Kim and Arne Kutzner, "Stable Minimum
	// Storage Merging by Symmetric Comparisons", in Susanne Albers and Tomasz
	// Radzik, editors, Algorithms - ESA 2004, volume 3221 of Lecture Notes in
	// Computer Science, pages 714-723. Springer, 2004.
	//
	// Let M = m-a and N = b-n. Wolog M < N.
	// The recursion depth is bound by ceil(log(N+M)).
	// The algorithm needs O(M*log(N/M + 1)) calls to data.Less.
	// The algorithm needs O((M+N)*log(M)) calls to data.Swap.
	//
	// The paper gives O((M+N)*log(M)) as the number of assignments assuming a
	// rotation algorithm which uses O(M+N+gcd(M+N)) assignments. The argumentation
	// in the paper carries through for Swap operations, especially as the block
	// swapping rotate uses only O(M+N) Swaps.
	//
	// symMerge assumes non-degenerate arguments: a < m && m < b.
	// Having the caller check this condition eliminates many leaf recursion calls,
	// which improves performance.
	func symMerge{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, m, b int {{.ExtraParam}}) {
	// Avoid unnecessary recursions of symMerge
	// by direct insertion of data[a] into data[m:b]
	// if data[a:m] only contains one element.
	if m-a == 1 {
	// Use binary search to find the lowest index i
	// such that data[i] >= data[a] for m <= i < b.
	// Exit the search loop with i == b in case no such index exists.
	i := m
	j := b
	for i < j {
	h := int(uint(i+j) >> 1)
	if {{Less "data" "h" "a"}} {
	i = h + 1
	} else {
	j = h
	}
	}
	// Swap values until data[a] reaches the position before i.
	for k := a; k < i-1; k++ {
	{{Swap "data" "k" "k+1"}}
	}
	return
	}

	// Avoid unnecessary recursions of symMerge
	// by direct insertion of data[m] into data[a:m]
	// if data[m:b] only contains one element.
	if b-m == 1 {
	// Use binary search to find the lowest index i
	// such that data[i] > data[m] for a <= i < m.
	// Exit the search loop with i == m in case no such index exists.
	i := a
	j := m
	for i < j {
	h := int(uint(i+j) >> 1)
	if !{{Less "data" "m" "h"}} {
	i = h + 1
	} else {
	j = h
	}
	}
	// Swap values until data[m] reaches the position i.
	for k := m; k > i; k-- {
	{{Swap "data" "k" "k-1"}}
	}
	return
	}

	mid := int(uint(a+b) >> 1)
	n := mid + m
	var start, r int
	if m > mid {
	start = n - b
	r = mid
	} else {
	start = a
	r = m
	}
	p := n - 1

	for start < r {
	c := int(uint(start+r) >> 1)
	if !{{Less "data" "p-c" "c"}} {
	start = c + 1
	} else {
	r = c
	}
	}

	end := n - start
	if start < m && m < end {
	rotate{{.FuncSuffix}}(data, start, m, end {{.ExtraArg}})
	}
	if a < start && start < mid {
	symMerge{{.FuncSuffix}}(data, a, start, mid {{.ExtraArg}})
	}
	if mid < end && end < b {
	symMerge{{.FuncSuffix}}(data, mid, end, b {{.ExtraArg}})
	}
	}

	// rotate{{.FuncSuffix}} rotates two consecutive blocks u = data[a:m] and v = data[m:b] in data:
	// Data of the form 'x u v y' is changed to 'x v u y'.
	// rotate performs at most b-a many calls to data.Swap,
	// and it assumes non-degenerate arguments: a < m && m < b.
	func rotate{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, m, b int {{.ExtraParam}}) {
	i := m - a
	j := b - m

	for i != j {
	if i > j {
	swapRange{{.FuncSuffix}}(data, m-i, m, j {{.ExtraArg}})
	i -= j
	} else {
	swapRange{{.FuncSuffix}}(data, m-i, m+j-i, i {{.ExtraArg}})
	j -= i
	}
	}
	// i == j
	swapRange{{.FuncSuffix}}(data, m-i, m, i {{.ExtraArg}})
	}
	`