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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 for inewpivot. // 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}}) } `