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authorDaniel Baumann <daniel.baumann@progress-linux.org>2024-04-16 19:25:22 +0000
committerDaniel Baumann <daniel.baumann@progress-linux.org>2024-04-16 19:25:22 +0000
commitf6ad4dcef54c5ce997a4bad5a6d86de229015700 (patch)
tree7cfa4e31ace5c2bd95c72b154d15af494b2bcbef /src/sort
parentInitial commit. (diff)
downloadgolang-1.22-f6ad4dcef54c5ce997a4bad5a6d86de229015700.tar.xz
golang-1.22-f6ad4dcef54c5ce997a4bad5a6d86de229015700.zip
Adding upstream version 1.22.1.upstream/1.22.1
Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>
Diffstat (limited to 'src/sort')
-rw-r--r--src/sort/example_interface_test.go58
-rw-r--r--src/sort/example_keys_test.go96
-rw-r--r--src/sort/example_multi_test.go132
-rw-r--r--src/sort/example_search_test.go74
-rw-r--r--src/sort/example_test.go122
-rw-r--r--src/sort/example_wrapper_test.go77
-rw-r--r--src/sort/export_test.go13
-rw-r--r--src/sort/gen_sort_variants.go717
-rw-r--r--src/sort/search.go150
-rw-r--r--src/sort/search_test.go266
-rw-r--r--src/sort/slice.go61
-rw-r--r--src/sort/sort.go283
-rw-r--r--src/sort/sort_impl_120.go15
-rw-r--r--src/sort/sort_impl_go121.go22
-rw-r--r--src/sort/sort_slices_benchmark_test.go201
-rw-r--r--src/sort/sort_test.go753
-rw-r--r--src/sort/zsortfunc.go479
-rw-r--r--src/sort/zsortinterface.go479
18 files changed, 3998 insertions, 0 deletions
diff --git a/src/sort/example_interface_test.go b/src/sort/example_interface_test.go
new file mode 100644
index 0000000..72d3017
--- /dev/null
+++ b/src/sort/example_interface_test.go
@@ -0,0 +1,58 @@
+// Copyright 2011 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 sort_test
+
+import (
+ "fmt"
+ "sort"
+)
+
+type Person struct {
+ Name string
+ Age int
+}
+
+func (p Person) String() string {
+ return fmt.Sprintf("%s: %d", p.Name, p.Age)
+}
+
+// ByAge implements sort.Interface for []Person based on
+// the Age field.
+type ByAge []Person
+
+func (a ByAge) Len() int { return len(a) }
+func (a ByAge) Swap(i, j int) { a[i], a[j] = a[j], a[i] }
+func (a ByAge) Less(i, j int) bool { return a[i].Age < a[j].Age }
+
+func Example() {
+ people := []Person{
+ {"Bob", 31},
+ {"John", 42},
+ {"Michael", 17},
+ {"Jenny", 26},
+ }
+
+ fmt.Println(people)
+ // There are two ways to sort a slice. First, one can define
+ // a set of methods for the slice type, as with ByAge, and
+ // call sort.Sort. In this first example we use that technique.
+ sort.Sort(ByAge(people))
+ fmt.Println(people)
+
+ // The other way is to use sort.Slice with a custom Less
+ // function, which can be provided as a closure. In this
+ // case no methods are needed. (And if they exist, they
+ // are ignored.) Here we re-sort in reverse order: compare
+ // the closure with ByAge.Less.
+ sort.Slice(people, func(i, j int) bool {
+ return people[i].Age > people[j].Age
+ })
+ fmt.Println(people)
+
+ // Output:
+ // [Bob: 31 John: 42 Michael: 17 Jenny: 26]
+ // [Michael: 17 Jenny: 26 Bob: 31 John: 42]
+ // [John: 42 Bob: 31 Jenny: 26 Michael: 17]
+}
diff --git a/src/sort/example_keys_test.go b/src/sort/example_keys_test.go
new file mode 100644
index 0000000..648f919
--- /dev/null
+++ b/src/sort/example_keys_test.go
@@ -0,0 +1,96 @@
+// Copyright 2013 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 sort_test
+
+import (
+ "fmt"
+ "sort"
+)
+
+// A couple of type definitions to make the units clear.
+type earthMass float64
+type au float64
+
+// A Planet defines the properties of a solar system object.
+type Planet struct {
+ name string
+ mass earthMass
+ distance au
+}
+
+// By is the type of a "less" function that defines the ordering of its Planet arguments.
+type By func(p1, p2 *Planet) bool
+
+// Sort is a method on the function type, By, that sorts the argument slice according to the function.
+func (by By) Sort(planets []Planet) {
+ ps := &planetSorter{
+ planets: planets,
+ by: by, // The Sort method's receiver is the function (closure) that defines the sort order.
+ }
+ sort.Sort(ps)
+}
+
+// planetSorter joins a By function and a slice of Planets to be sorted.
+type planetSorter struct {
+ planets []Planet
+ by func(p1, p2 *Planet) bool // Closure used in the Less method.
+}
+
+// Len is part of sort.Interface.
+func (s *planetSorter) Len() int {
+ return len(s.planets)
+}
+
+// Swap is part of sort.Interface.
+func (s *planetSorter) Swap(i, j int) {
+ s.planets[i], s.planets[j] = s.planets[j], s.planets[i]
+}
+
+// Less is part of sort.Interface. It is implemented by calling the "by" closure in the sorter.
+func (s *planetSorter) Less(i, j int) bool {
+ return s.by(&s.planets[i], &s.planets[j])
+}
+
+var planets = []Planet{
+ {"Mercury", 0.055, 0.4},
+ {"Venus", 0.815, 0.7},
+ {"Earth", 1.0, 1.0},
+ {"Mars", 0.107, 1.5},
+}
+
+// ExampleSortKeys demonstrates a technique for sorting a struct type using programmable sort criteria.
+func Example_sortKeys() {
+ // Closures that order the Planet structure.
+ name := func(p1, p2 *Planet) bool {
+ return p1.name < p2.name
+ }
+ mass := func(p1, p2 *Planet) bool {
+ return p1.mass < p2.mass
+ }
+ distance := func(p1, p2 *Planet) bool {
+ return p1.distance < p2.distance
+ }
+ decreasingDistance := func(p1, p2 *Planet) bool {
+ return distance(p2, p1)
+ }
+
+ // Sort the planets by the various criteria.
+ By(name).Sort(planets)
+ fmt.Println("By name:", planets)
+
+ By(mass).Sort(planets)
+ fmt.Println("By mass:", planets)
+
+ By(distance).Sort(planets)
+ fmt.Println("By distance:", planets)
+
+ By(decreasingDistance).Sort(planets)
+ fmt.Println("By decreasing distance:", planets)
+
+ // Output: By name: [{Earth 1 1} {Mars 0.107 1.5} {Mercury 0.055 0.4} {Venus 0.815 0.7}]
+ // By mass: [{Mercury 0.055 0.4} {Mars 0.107 1.5} {Venus 0.815 0.7} {Earth 1 1}]
+ // By distance: [{Mercury 0.055 0.4} {Venus 0.815 0.7} {Earth 1 1} {Mars 0.107 1.5}]
+ // By decreasing distance: [{Mars 0.107 1.5} {Earth 1 1} {Venus 0.815 0.7} {Mercury 0.055 0.4}]
+}
diff --git a/src/sort/example_multi_test.go b/src/sort/example_multi_test.go
new file mode 100644
index 0000000..93f2d3e
--- /dev/null
+++ b/src/sort/example_multi_test.go
@@ -0,0 +1,132 @@
+// Copyright 2013 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 sort_test
+
+import (
+ "fmt"
+ "sort"
+)
+
+// A Change is a record of source code changes, recording user, language, and delta size.
+type Change struct {
+ user string
+ language string
+ lines int
+}
+
+type lessFunc func(p1, p2 *Change) bool
+
+// multiSorter implements the Sort interface, sorting the changes within.
+type multiSorter struct {
+ changes []Change
+ less []lessFunc
+}
+
+// Sort sorts the argument slice according to the less functions passed to OrderedBy.
+func (ms *multiSorter) Sort(changes []Change) {
+ ms.changes = changes
+ sort.Sort(ms)
+}
+
+// OrderedBy returns a Sorter that sorts using the less functions, in order.
+// Call its Sort method to sort the data.
+func OrderedBy(less ...lessFunc) *multiSorter {
+ return &multiSorter{
+ less: less,
+ }
+}
+
+// Len is part of sort.Interface.
+func (ms *multiSorter) Len() int {
+ return len(ms.changes)
+}
+
+// Swap is part of sort.Interface.
+func (ms *multiSorter) Swap(i, j int) {
+ ms.changes[i], ms.changes[j] = ms.changes[j], ms.changes[i]
+}
+
+// Less is part of sort.Interface. It is implemented by looping along the
+// less functions until it finds a comparison that discriminates between
+// the two items (one is less than the other). Note that it can call the
+// less functions twice per call. We could change the functions to return
+// -1, 0, 1 and reduce the number of calls for greater efficiency: an
+// exercise for the reader.
+func (ms *multiSorter) Less(i, j int) bool {
+ p, q := &ms.changes[i], &ms.changes[j]
+ // Try all but the last comparison.
+ var k int
+ for k = 0; k < len(ms.less)-1; k++ {
+ less := ms.less[k]
+ switch {
+ case less(p, q):
+ // p < q, so we have a decision.
+ return true
+ case less(q, p):
+ // p > q, so we have a decision.
+ return false
+ }
+ // p == q; try the next comparison.
+ }
+ // All comparisons to here said "equal", so just return whatever
+ // the final comparison reports.
+ return ms.less[k](p, q)
+}
+
+var changes = []Change{
+ {"gri", "Go", 100},
+ {"ken", "C", 150},
+ {"glenda", "Go", 200},
+ {"rsc", "Go", 200},
+ {"r", "Go", 100},
+ {"ken", "Go", 200},
+ {"dmr", "C", 100},
+ {"r", "C", 150},
+ {"gri", "Smalltalk", 80},
+}
+
+// ExampleMultiKeys demonstrates a technique for sorting a struct type using different
+// sets of multiple fields in the comparison. We chain together "Less" functions, each of
+// which compares a single field.
+func Example_sortMultiKeys() {
+ // Closures that order the Change structure.
+ user := func(c1, c2 *Change) bool {
+ return c1.user < c2.user
+ }
+ language := func(c1, c2 *Change) bool {
+ return c1.language < c2.language
+ }
+ increasingLines := func(c1, c2 *Change) bool {
+ return c1.lines < c2.lines
+ }
+ decreasingLines := func(c1, c2 *Change) bool {
+ return c1.lines > c2.lines // Note: > orders downwards.
+ }
+
+ // Simple use: Sort by user.
+ OrderedBy(user).Sort(changes)
+ fmt.Println("By user:", changes)
+
+ // More examples.
+ OrderedBy(user, increasingLines).Sort(changes)
+ fmt.Println("By user,<lines:", changes)
+
+ OrderedBy(user, decreasingLines).Sort(changes)
+ fmt.Println("By user,>lines:", changes)
+
+ OrderedBy(language, increasingLines).Sort(changes)
+ fmt.Println("By language,<lines:", changes)
+
+ OrderedBy(language, increasingLines, user).Sort(changes)
+ fmt.Println("By language,<lines,user:", changes)
+
+ // Output:
+ // By user: [{dmr C 100} {glenda Go 200} {gri Go 100} {gri Smalltalk 80} {ken C 150} {ken Go 200} {r Go 100} {r C 150} {rsc Go 200}]
+ // By user,<lines: [{dmr C 100} {glenda Go 200} {gri Smalltalk 80} {gri Go 100} {ken C 150} {ken Go 200} {r Go 100} {r C 150} {rsc Go 200}]
+ // By user,>lines: [{dmr C 100} {glenda Go 200} {gri Go 100} {gri Smalltalk 80} {ken Go 200} {ken C 150} {r C 150} {r Go 100} {rsc Go 200}]
+ // By language,<lines: [{dmr C 100} {ken C 150} {r C 150} {gri Go 100} {r Go 100} {glenda Go 200} {ken Go 200} {rsc Go 200} {gri Smalltalk 80}]
+ // By language,<lines,user: [{dmr C 100} {ken C 150} {r C 150} {gri Go 100} {r Go 100} {glenda Go 200} {ken Go 200} {rsc Go 200} {gri Smalltalk 80}]
+
+}
diff --git a/src/sort/example_search_test.go b/src/sort/example_search_test.go
new file mode 100644
index 0000000..856422a
--- /dev/null
+++ b/src/sort/example_search_test.go
@@ -0,0 +1,74 @@
+// Copyright 2016 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 sort_test
+
+import (
+ "fmt"
+ "sort"
+)
+
+// This example demonstrates searching a list sorted in ascending order.
+func ExampleSearch() {
+ a := []int{1, 3, 6, 10, 15, 21, 28, 36, 45, 55}
+ x := 6
+
+ i := sort.Search(len(a), func(i int) bool { return a[i] >= x })
+ if i < len(a) && a[i] == x {
+ fmt.Printf("found %d at index %d in %v\n", x, i, a)
+ } else {
+ fmt.Printf("%d not found in %v\n", x, a)
+ }
+ // Output:
+ // found 6 at index 2 in [1 3 6 10 15 21 28 36 45 55]
+}
+
+// This example demonstrates searching a list sorted in descending order.
+// The approach is the same as searching a list in ascending order,
+// but with the condition inverted.
+func ExampleSearch_descendingOrder() {
+ a := []int{55, 45, 36, 28, 21, 15, 10, 6, 3, 1}
+ x := 6
+
+ i := sort.Search(len(a), func(i int) bool { return a[i] <= x })
+ if i < len(a) && a[i] == x {
+ fmt.Printf("found %d at index %d in %v\n", x, i, a)
+ } else {
+ fmt.Printf("%d not found in %v\n", x, a)
+ }
+ // Output:
+ // found 6 at index 7 in [55 45 36 28 21 15 10 6 3 1]
+}
+
+// This example demonstrates searching for float64 in a list sorted in ascending order.
+func ExampleSearchFloat64s() {
+ a := []float64{1.0, 2.0, 3.3, 4.6, 6.1, 7.2, 8.0}
+
+ x := 2.0
+ i := sort.SearchFloat64s(a, x)
+ fmt.Printf("found %g at index %d in %v\n", x, i, a)
+
+ x = 0.5
+ i = sort.SearchFloat64s(a, x)
+ fmt.Printf("%g not found, can be inserted at index %d in %v\n", x, i, a)
+ // Output:
+ // found 2 at index 1 in [1 2 3.3 4.6 6.1 7.2 8]
+ // 0.5 not found, can be inserted at index 0 in [1 2 3.3 4.6 6.1 7.2 8]
+}
+
+// This example demonstrates searching for int in a list sorted in ascending order.
+func ExampleSearchInts() {
+ a := []int{1, 2, 3, 4, 6, 7, 8}
+
+ x := 2
+ i := sort.SearchInts(a, x)
+ fmt.Printf("found %d at index %d in %v\n", x, i, a)
+
+ x = 5
+ i = sort.SearchInts(a, x)
+ fmt.Printf("%d not found, can be inserted at index %d in %v\n", x, i, a)
+ // Output:
+ // found 2 at index 1 in [1 2 3 4 6 7 8]
+ // 5 not found, can be inserted at index 4 in [1 2 3 4 6 7 8]
+}
diff --git a/src/sort/example_test.go b/src/sort/example_test.go
new file mode 100644
index 0000000..1f85dbc
--- /dev/null
+++ b/src/sort/example_test.go
@@ -0,0 +1,122 @@
+// Copyright 2011 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 sort_test
+
+import (
+ "fmt"
+ "math"
+ "sort"
+)
+
+func ExampleInts() {
+ s := []int{5, 2, 6, 3, 1, 4} // unsorted
+ sort.Ints(s)
+ fmt.Println(s)
+ // Output: [1 2 3 4 5 6]
+}
+
+func ExampleIntsAreSorted() {
+ s := []int{1, 2, 3, 4, 5, 6} // sorted ascending
+ fmt.Println(sort.IntsAreSorted(s))
+
+ s = []int{6, 5, 4, 3, 2, 1} // sorted descending
+ fmt.Println(sort.IntsAreSorted(s))
+
+ s = []int{3, 2, 4, 1, 5} // unsorted
+ fmt.Println(sort.IntsAreSorted(s))
+
+ // Output: true
+ // false
+ // false
+}
+
+func ExampleFloat64s() {
+ s := []float64{5.2, -1.3, 0.7, -3.8, 2.6} // unsorted
+ sort.Float64s(s)
+ fmt.Println(s)
+
+ s = []float64{math.Inf(1), math.NaN(), math.Inf(-1), 0.0} // unsorted
+ sort.Float64s(s)
+ fmt.Println(s)
+
+ // Output: [-3.8 -1.3 0.7 2.6 5.2]
+ // [NaN -Inf 0 +Inf]
+}
+
+func ExampleFloat64sAreSorted() {
+ s := []float64{0.7, 1.3, 2.6, 3.8, 5.2} // sorted ascending
+ fmt.Println(sort.Float64sAreSorted(s))
+
+ s = []float64{5.2, 3.8, 2.6, 1.3, 0.7} // sorted descending
+ fmt.Println(sort.Float64sAreSorted(s))
+
+ s = []float64{5.2, 1.3, 0.7, 3.8, 2.6} // unsorted
+ fmt.Println(sort.Float64sAreSorted(s))
+
+ // Output: true
+ // false
+ // false
+}
+
+func ExampleReverse() {
+ s := []int{5, 2, 6, 3, 1, 4} // unsorted
+ sort.Sort(sort.Reverse(sort.IntSlice(s)))
+ fmt.Println(s)
+ // Output: [6 5 4 3 2 1]
+}
+
+func ExampleSlice() {
+ people := []struct {
+ Name string
+ Age int
+ }{
+ {"Gopher", 7},
+ {"Alice", 55},
+ {"Vera", 24},
+ {"Bob", 75},
+ }
+ sort.Slice(people, func(i, j int) bool { return people[i].Name < people[j].Name })
+ fmt.Println("By name:", people)
+
+ sort.Slice(people, func(i, j int) bool { return people[i].Age < people[j].Age })
+ fmt.Println("By age:", people)
+ // Output: By name: [{Alice 55} {Bob 75} {Gopher 7} {Vera 24}]
+ // By age: [{Gopher 7} {Vera 24} {Alice 55} {Bob 75}]
+}
+
+func ExampleSliceStable() {
+
+ people := []struct {
+ Name string
+ Age int
+ }{
+ {"Alice", 25},
+ {"Elizabeth", 75},
+ {"Alice", 75},
+ {"Bob", 75},
+ {"Alice", 75},
+ {"Bob", 25},
+ {"Colin", 25},
+ {"Elizabeth", 25},
+ }
+
+ // Sort by name, preserving original order
+ sort.SliceStable(people, func(i, j int) bool { return people[i].Name < people[j].Name })
+ fmt.Println("By name:", people)
+
+ // Sort by age preserving name order
+ sort.SliceStable(people, func(i, j int) bool { return people[i].Age < people[j].Age })
+ fmt.Println("By age,name:", people)
+
+ // Output: By name: [{Alice 25} {Alice 75} {Alice 75} {Bob 75} {Bob 25} {Colin 25} {Elizabeth 75} {Elizabeth 25}]
+ // By age,name: [{Alice 25} {Bob 25} {Colin 25} {Elizabeth 25} {Alice 75} {Alice 75} {Bob 75} {Elizabeth 75}]
+}
+
+func ExampleStrings() {
+ s := []string{"Go", "Bravo", "Gopher", "Alpha", "Grin", "Delta"}
+ sort.Strings(s)
+ fmt.Println(s)
+ // Output: [Alpha Bravo Delta Go Gopher Grin]
+}
diff --git a/src/sort/example_wrapper_test.go b/src/sort/example_wrapper_test.go
new file mode 100644
index 0000000..cf6d74c
--- /dev/null
+++ b/src/sort/example_wrapper_test.go
@@ -0,0 +1,77 @@
+// Copyright 2011 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 sort_test
+
+import (
+ "fmt"
+ "sort"
+)
+
+type Grams int
+
+func (g Grams) String() string { return fmt.Sprintf("%dg", int(g)) }
+
+type Organ struct {
+ Name string
+ Weight Grams
+}
+
+type Organs []*Organ
+
+func (s Organs) Len() int { return len(s) }
+func (s Organs) Swap(i, j int) { s[i], s[j] = s[j], s[i] }
+
+// ByName implements sort.Interface by providing Less and using the Len and
+// Swap methods of the embedded Organs value.
+type ByName struct{ Organs }
+
+func (s ByName) Less(i, j int) bool { return s.Organs[i].Name < s.Organs[j].Name }
+
+// ByWeight implements sort.Interface by providing Less and using the Len and
+// Swap methods of the embedded Organs value.
+type ByWeight struct{ Organs }
+
+func (s ByWeight) Less(i, j int) bool { return s.Organs[i].Weight < s.Organs[j].Weight }
+
+func Example_sortWrapper() {
+ s := []*Organ{
+ {"brain", 1340},
+ {"heart", 290},
+ {"liver", 1494},
+ {"pancreas", 131},
+ {"prostate", 62},
+ {"spleen", 162},
+ }
+
+ sort.Sort(ByWeight{s})
+ fmt.Println("Organs by weight:")
+ printOrgans(s)
+
+ sort.Sort(ByName{s})
+ fmt.Println("Organs by name:")
+ printOrgans(s)
+
+ // Output:
+ // Organs by weight:
+ // prostate (62g)
+ // pancreas (131g)
+ // spleen (162g)
+ // heart (290g)
+ // brain (1340g)
+ // liver (1494g)
+ // Organs by name:
+ // brain (1340g)
+ // heart (290g)
+ // liver (1494g)
+ // pancreas (131g)
+ // prostate (62g)
+ // spleen (162g)
+}
+
+func printOrgans(s []*Organ) {
+ for _, o := range s {
+ fmt.Printf("%-8s (%v)\n", o.Name, o.Weight)
+ }
+}
diff --git a/src/sort/export_test.go b/src/sort/export_test.go
new file mode 100644
index 0000000..2a3c21f
--- /dev/null
+++ b/src/sort/export_test.go
@@ -0,0 +1,13 @@
+// Copyright 2011 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 sort
+
+func Heapsort(data Interface) {
+ heapSort(data, 0, data.Len())
+}
+
+func ReverseRange(data Interface, a, b int) {
+ reverseRange(data, a, b)
+}
diff --git a/src/sort/gen_sort_variants.go b/src/sort/gen_sort_variants.go
new file mode 100644
index 0000000..95fca70
--- /dev/null
+++ b/src/sort/gen_sort_variants.go
@@ -0,0 +1,717 @@
+// 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}})
+}
+`
diff --git a/src/sort/search.go b/src/sort/search.go
new file mode 100644
index 0000000..ccf76db
--- /dev/null
+++ b/src/sort/search.go
@@ -0,0 +1,150 @@
+// Copyright 2010 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.
+
+// This file implements binary search.
+
+package sort
+
+// Search uses binary search to find and return the smallest index i
+// in [0, n) at which f(i) is true, assuming that on the range [0, n),
+// f(i) == true implies f(i+1) == true. That is, Search requires that
+// f is false for some (possibly empty) prefix of the input range [0, n)
+// and then true for the (possibly empty) remainder; Search returns
+// the first true index. If there is no such index, Search returns n.
+// (Note that the "not found" return value is not -1 as in, for instance,
+// strings.Index.)
+// Search calls f(i) only for i in the range [0, n).
+//
+// A common use of Search is to find the index i for a value x in
+// a sorted, indexable data structure such as an array or slice.
+// In this case, the argument f, typically a closure, captures the value
+// to be searched for, and how the data structure is indexed and
+// ordered.
+//
+// For instance, given a slice data sorted in ascending order,
+// the call Search(len(data), func(i int) bool { return data[i] >= 23 })
+// returns the smallest index i such that data[i] >= 23. If the caller
+// wants to find whether 23 is in the slice, it must test data[i] == 23
+// separately.
+//
+// Searching data sorted in descending order would use the <=
+// operator instead of the >= operator.
+//
+// To complete the example above, the following code tries to find the value
+// x in an integer slice data sorted in ascending order:
+//
+// x := 23
+// i := sort.Search(len(data), func(i int) bool { return data[i] >= x })
+// if i < len(data) && data[i] == x {
+// // x is present at data[i]
+// } else {
+// // x is not present in data,
+// // but i is the index where it would be inserted.
+// }
+//
+// As a more whimsical example, this program guesses your number:
+//
+// func GuessingGame() {
+// var s string
+// fmt.Printf("Pick an integer from 0 to 100.\n")
+// answer := sort.Search(100, func(i int) bool {
+// fmt.Printf("Is your number <= %d? ", i)
+// fmt.Scanf("%s", &s)
+// return s != "" && s[0] == 'y'
+// })
+// fmt.Printf("Your number is %d.\n", answer)
+// }
+func Search(n int, f func(int) bool) int {
+ // Define f(-1) == false and f(n) == true.
+ // Invariant: f(i-1) == false, f(j) == true.
+ i, j := 0, n
+ for i < j {
+ h := int(uint(i+j) >> 1) // avoid overflow when computing h
+ // i ≤ h < j
+ if !f(h) {
+ i = h + 1 // preserves f(i-1) == false
+ } else {
+ j = h // preserves f(j) == true
+ }
+ }
+ // i == j, f(i-1) == false, and f(j) (= f(i)) == true => answer is i.
+ return i
+}
+
+// Find uses binary search to find and return the smallest index i in [0, n)
+// at which cmp(i) <= 0. If there is no such index i, Find returns i = n.
+// The found result is true if i < n and cmp(i) == 0.
+// Find calls cmp(i) only for i in the range [0, n).
+//
+// To permit binary search, Find requires that cmp(i) > 0 for a leading
+// prefix of the range, cmp(i) == 0 in the middle, and cmp(i) < 0 for
+// the final suffix of the range. (Each subrange could be empty.)
+// The usual way to establish this condition is to interpret cmp(i)
+// as a comparison of a desired target value t against entry i in an
+// underlying indexed data structure x, returning <0, 0, and >0
+// when t < x[i], t == x[i], and t > x[i], respectively.
+//
+// For example, to look for a particular string in a sorted, random-access
+// list of strings:
+//
+// i, found := sort.Find(x.Len(), func(i int) int {
+// return strings.Compare(target, x.At(i))
+// })
+// if found {
+// fmt.Printf("found %s at entry %d\n", target, i)
+// } else {
+// fmt.Printf("%s not found, would insert at %d", target, i)
+// }
+func Find(n int, cmp func(int) int) (i int, found bool) {
+ // The invariants here are similar to the ones in Search.
+ // Define cmp(-1) > 0 and cmp(n) <= 0
+ // Invariant: cmp(i-1) > 0, cmp(j) <= 0
+ i, j := 0, n
+ for i < j {
+ h := int(uint(i+j) >> 1) // avoid overflow when computing h
+ // i ≤ h < j
+ if cmp(h) > 0 {
+ i = h + 1 // preserves cmp(i-1) > 0
+ } else {
+ j = h // preserves cmp(j) <= 0
+ }
+ }
+ // i == j, cmp(i-1) > 0 and cmp(j) <= 0
+ return i, i < n && cmp(i) == 0
+}
+
+// Convenience wrappers for common cases.
+
+// SearchInts searches for x in a sorted slice of ints and returns the index
+// as specified by [Search]. The return value is the index to insert x if x is
+// not present (it could be len(a)).
+// The slice must be sorted in ascending order.
+func SearchInts(a []int, x int) int {
+ return Search(len(a), func(i int) bool { return a[i] >= x })
+}
+
+// SearchFloat64s searches for x in a sorted slice of float64s and returns the index
+// as specified by [Search]. The return value is the index to insert x if x is not
+// present (it could be len(a)).
+// The slice must be sorted in ascending order.
+func SearchFloat64s(a []float64, x float64) int {
+ return Search(len(a), func(i int) bool { return a[i] >= x })
+}
+
+// SearchStrings searches for x in a sorted slice of strings and returns the index
+// as specified by Search. The return value is the index to insert x if x is not
+// present (it could be len(a)).
+// The slice must be sorted in ascending order.
+func SearchStrings(a []string, x string) int {
+ return Search(len(a), func(i int) bool { return a[i] >= x })
+}
+
+// Search returns the result of applying [SearchInts] to the receiver and x.
+func (p IntSlice) Search(x int) int { return SearchInts(p, x) }
+
+// Search returns the result of applying [SearchFloat64s] to the receiver and x.
+func (p Float64Slice) Search(x float64) int { return SearchFloat64s(p, x) }
+
+// Search returns the result of applying [SearchStrings] to the receiver and x.
+func (p StringSlice) Search(x string) int { return SearchStrings(p, x) }
diff --git a/src/sort/search_test.go b/src/sort/search_test.go
new file mode 100644
index 0000000..49813ea
--- /dev/null
+++ b/src/sort/search_test.go
@@ -0,0 +1,266 @@
+// Copyright 2010 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 sort_test
+
+import (
+ "runtime"
+ . "sort"
+ stringspkg "strings"
+ "testing"
+)
+
+func f(a []int, x int) func(int) bool {
+ return func(i int) bool {
+ return a[i] >= x
+ }
+}
+
+var data = []int{0: -10, 1: -5, 2: 0, 3: 1, 4: 2, 5: 3, 6: 5, 7: 7, 8: 11, 9: 100, 10: 100, 11: 100, 12: 1000, 13: 10000}
+
+var tests = []struct {
+ name string
+ n int
+ f func(int) bool
+ i int
+}{
+ {"empty", 0, nil, 0},
+ {"1 1", 1, func(i int) bool { return i >= 1 }, 1},
+ {"1 true", 1, func(i int) bool { return true }, 0},
+ {"1 false", 1, func(i int) bool { return false }, 1},
+ {"1e9 991", 1e9, func(i int) bool { return i >= 991 }, 991},
+ {"1e9 true", 1e9, func(i int) bool { return true }, 0},
+ {"1e9 false", 1e9, func(i int) bool { return false }, 1e9},
+ {"data -20", len(data), f(data, -20), 0},
+ {"data -10", len(data), f(data, -10), 0},
+ {"data -9", len(data), f(data, -9), 1},
+ {"data -6", len(data), f(data, -6), 1},
+ {"data -5", len(data), f(data, -5), 1},
+ {"data 3", len(data), f(data, 3), 5},
+ {"data 11", len(data), f(data, 11), 8},
+ {"data 99", len(data), f(data, 99), 9},
+ {"data 100", len(data), f(data, 100), 9},
+ {"data 101", len(data), f(data, 101), 12},
+ {"data 10000", len(data), f(data, 10000), 13},
+ {"data 10001", len(data), f(data, 10001), 14},
+ {"descending a", 7, func(i int) bool { return []int{99, 99, 59, 42, 7, 0, -1, -1}[i] <= 7 }, 4},
+ {"descending 7", 1e9, func(i int) bool { return 1e9-i <= 7 }, 1e9 - 7},
+ {"overflow", 2e9, func(i int) bool { return false }, 2e9},
+}
+
+func TestSearch(t *testing.T) {
+ for _, e := range tests {
+ i := Search(e.n, e.f)
+ if i != e.i {
+ t.Errorf("%s: expected index %d; got %d", e.name, e.i, i)
+ }
+ }
+}
+
+func TestFind(t *testing.T) {
+ str1 := []string{"foo"}
+ str2 := []string{"ab", "ca"}
+ str3 := []string{"mo", "qo", "vo"}
+ str4 := []string{"ab", "ad", "ca", "xy"}
+
+ // slice with repeating elements
+ strRepeats := []string{"ba", "ca", "da", "da", "da", "ka", "ma", "ma", "ta"}
+
+ // slice with all element equal
+ strSame := []string{"xx", "xx", "xx"}
+
+ tests := []struct {
+ data []string
+ target string
+ wantPos int
+ wantFound bool
+ }{
+ {[]string{}, "foo", 0, false},
+ {[]string{}, "", 0, false},
+
+ {str1, "foo", 0, true},
+ {str1, "bar", 0, false},
+ {str1, "zx", 1, false},
+
+ {str2, "aa", 0, false},
+ {str2, "ab", 0, true},
+ {str2, "ad", 1, false},
+ {str2, "ca", 1, true},
+ {str2, "ra", 2, false},
+
+ {str3, "bb", 0, false},
+ {str3, "mo", 0, true},
+ {str3, "nb", 1, false},
+ {str3, "qo", 1, true},
+ {str3, "tr", 2, false},
+ {str3, "vo", 2, true},
+ {str3, "xr", 3, false},
+
+ {str4, "aa", 0, false},
+ {str4, "ab", 0, true},
+ {str4, "ac", 1, false},
+ {str4, "ad", 1, true},
+ {str4, "ax", 2, false},
+ {str4, "ca", 2, true},
+ {str4, "cc", 3, false},
+ {str4, "dd", 3, false},
+ {str4, "xy", 3, true},
+ {str4, "zz", 4, false},
+
+ {strRepeats, "da", 2, true},
+ {strRepeats, "db", 5, false},
+ {strRepeats, "ma", 6, true},
+ {strRepeats, "mb", 8, false},
+
+ {strSame, "xx", 0, true},
+ {strSame, "ab", 0, false},
+ {strSame, "zz", 3, false},
+ }
+
+ for _, tt := range tests {
+ t.Run(tt.target, func(t *testing.T) {
+ cmp := func(i int) int {
+ return stringspkg.Compare(tt.target, tt.data[i])
+ }
+
+ pos, found := Find(len(tt.data), cmp)
+ if pos != tt.wantPos || found != tt.wantFound {
+ t.Errorf("Find got (%v, %v), want (%v, %v)", pos, found, tt.wantPos, tt.wantFound)
+ }
+ })
+ }
+}
+
+// log2 computes the binary logarithm of x, rounded up to the next integer.
+// (log2(0) == 0, log2(1) == 0, log2(2) == 1, log2(3) == 2, etc.)
+func log2(x int) int {
+ n := 0
+ for p := 1; p < x; p += p {
+ // p == 2**n
+ n++
+ }
+ // p/2 < x <= p == 2**n
+ return n
+}
+
+func TestSearchEfficiency(t *testing.T) {
+ n := 100
+ step := 1
+ for exp := 2; exp < 10; exp++ {
+ // n == 10**exp
+ // step == 10**(exp-2)
+ max := log2(n)
+ for x := 0; x < n; x += step {
+ count := 0
+ i := Search(n, func(i int) bool { count++; return i >= x })
+ if i != x {
+ t.Errorf("n = %d: expected index %d; got %d", n, x, i)
+ }
+ if count > max {
+ t.Errorf("n = %d, x = %d: expected <= %d calls; got %d", n, x, max, count)
+ }
+ }
+ n *= 10
+ step *= 10
+ }
+}
+
+// Smoke tests for convenience wrappers - not comprehensive.
+
+var fdata = []float64{0: -3.14, 1: 0, 2: 1, 3: 2, 4: 1000.7}
+var sdata = []string{0: "f", 1: "foo", 2: "foobar", 3: "x"}
+
+var wrappertests = []struct {
+ name string
+ result int
+ i int
+}{
+ {"SearchInts", SearchInts(data, 11), 8},
+ {"SearchFloat64s", SearchFloat64s(fdata, 2.1), 4},
+ {"SearchStrings", SearchStrings(sdata, ""), 0},
+ {"IntSlice.Search", IntSlice(data).Search(0), 2},
+ {"Float64Slice.Search", Float64Slice(fdata).Search(2.0), 3},
+ {"StringSlice.Search", StringSlice(sdata).Search("x"), 3},
+}
+
+func TestSearchWrappers(t *testing.T) {
+ for _, e := range wrappertests {
+ if e.result != e.i {
+ t.Errorf("%s: expected index %d; got %d", e.name, e.i, e.result)
+ }
+ }
+}
+
+func runSearchWrappers() {
+ SearchInts(data, 11)
+ SearchFloat64s(fdata, 2.1)
+ SearchStrings(sdata, "")
+ IntSlice(data).Search(0)
+ Float64Slice(fdata).Search(2.0)
+ StringSlice(sdata).Search("x")
+}
+
+func TestSearchWrappersDontAlloc(t *testing.T) {
+ if testing.Short() {
+ t.Skip("skipping malloc count in short mode")
+ }
+ if runtime.GOMAXPROCS(0) > 1 {
+ t.Skip("skipping; GOMAXPROCS>1")
+ }
+ allocs := testing.AllocsPerRun(100, runSearchWrappers)
+ if allocs != 0 {
+ t.Errorf("expected no allocs for runSearchWrappers, got %v", allocs)
+ }
+}
+
+func BenchmarkSearchWrappers(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ runSearchWrappers()
+ }
+}
+
+// Abstract exhaustive test: all sizes up to 100,
+// all possible return values. If there are any small
+// corner cases, this test exercises them.
+func TestSearchExhaustive(t *testing.T) {
+ for size := 0; size <= 100; size++ {
+ for targ := 0; targ <= size; targ++ {
+ i := Search(size, func(i int) bool { return i >= targ })
+ if i != targ {
+ t.Errorf("Search(%d, %d) = %d", size, targ, i)
+ }
+ }
+ }
+}
+
+// Abstract exhaustive test for Find.
+func TestFindExhaustive(t *testing.T) {
+ // Test Find for different sequence sizes and search targets.
+ // For each size, we have a (unmaterialized) sequence of integers:
+ // 2,4...size*2
+ // And we're looking for every possible integer between 1 and size*2 + 1.
+ for size := 0; size <= 100; size++ {
+ for x := 1; x <= size*2+1; x++ {
+ var wantFound bool
+ var wantPos int
+
+ cmp := func(i int) int {
+ // Encodes the unmaterialized sequence with elem[i] == (i+1)*2
+ return x - (i+1)*2
+ }
+ pos, found := Find(size, cmp)
+
+ if x%2 == 0 {
+ wantPos = x/2 - 1
+ wantFound = true
+ } else {
+ wantPos = x / 2
+ wantFound = false
+ }
+ if found != wantFound || pos != wantPos {
+ t.Errorf("Find(%d, %d): got (%v, %v), want (%v, %v)", size, x, pos, found, wantPos, wantFound)
+ }
+ }
+ }
+}
diff --git a/src/sort/slice.go b/src/sort/slice.go
new file mode 100644
index 0000000..bc9dd84
--- /dev/null
+++ b/src/sort/slice.go
@@ -0,0 +1,61 @@
+// Copyright 2017 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 sort
+
+import (
+ "internal/reflectlite"
+ "math/bits"
+)
+
+// Slice sorts the slice x given the provided less function.
+// It panics if x is not a slice.
+//
+// The sort is not guaranteed to be stable: equal elements
+// may be reversed from their original order.
+// For a stable sort, use [SliceStable].
+//
+// The less function must satisfy the same requirements as
+// the Interface type's Less method.
+//
+// Note: in many situations, the newer [slices.SortFunc] function is more
+// ergonomic and runs faster.
+func Slice(x any, less func(i, j int) bool) {
+ rv := reflectlite.ValueOf(x)
+ swap := reflectlite.Swapper(x)
+ length := rv.Len()
+ limit := bits.Len(uint(length))
+ pdqsort_func(lessSwap{less, swap}, 0, length, limit)
+}
+
+// SliceStable sorts the slice x using the provided less
+// function, keeping equal elements in their original order.
+// It panics if x is not a slice.
+//
+// The less function must satisfy the same requirements as
+// the Interface type's Less method.
+//
+// Note: in many situations, the newer [slices.SortStableFunc] function is more
+// ergonomic and runs faster.
+func SliceStable(x any, less func(i, j int) bool) {
+ rv := reflectlite.ValueOf(x)
+ swap := reflectlite.Swapper(x)
+ stable_func(lessSwap{less, swap}, rv.Len())
+}
+
+// SliceIsSorted reports whether the slice x is sorted according to the provided less function.
+// It panics if x is not a slice.
+//
+// Note: in many situations, the newer [slices.IsSortedFunc] function is more
+// ergonomic and runs faster.
+func SliceIsSorted(x any, less func(i, j int) bool) bool {
+ rv := reflectlite.ValueOf(x)
+ n := rv.Len()
+ for i := n - 1; i > 0; i-- {
+ if less(i, i-1) {
+ return false
+ }
+ }
+ return true
+}
diff --git a/src/sort/sort.go b/src/sort/sort.go
new file mode 100644
index 0000000..6db161f
--- /dev/null
+++ b/src/sort/sort.go
@@ -0,0 +1,283 @@
+// Copyright 2009 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:generate go run gen_sort_variants.go
+
+// Package sort provides primitives for sorting slices and user-defined collections.
+package sort
+
+import "math/bits"
+
+// An implementation of Interface can be sorted by the routines in this package.
+// The methods refer to elements of the underlying collection by integer index.
+type Interface interface {
+ // Len is the number of elements in the collection.
+ Len() int
+
+ // Less reports whether the element with index i
+ // must sort before the element with index j.
+ //
+ // If both Less(i, j) and Less(j, i) are false,
+ // then the elements at index i and j are considered equal.
+ // Sort may place equal elements in any order in the final result,
+ // while Stable preserves the original input order of equal elements.
+ //
+ // Less must describe a transitive ordering:
+ // - if both Less(i, j) and Less(j, k) are true, then Less(i, k) must be true as well.
+ // - if both Less(i, j) and Less(j, k) are false, then Less(i, k) must be false as well.
+ //
+ // Note that floating-point comparison (the < operator on float32 or float64 values)
+ // is not a transitive ordering when not-a-number (NaN) values are involved.
+ // See Float64Slice.Less for a correct implementation for floating-point values.
+ Less(i, j int) bool
+
+ // Swap swaps the elements with indexes i and j.
+ Swap(i, j int)
+}
+
+// Sort sorts data in ascending order as determined by the Less method.
+// It makes one call to data.Len to determine n and O(n*log(n)) calls to
+// data.Less and data.Swap. The sort is not guaranteed to be stable.
+//
+// Note: in many situations, the newer [slices.SortFunc] function is more
+// ergonomic and runs faster.
+func Sort(data Interface) {
+ n := data.Len()
+ if n <= 1 {
+ return
+ }
+ limit := bits.Len(uint(n))
+ pdqsort(data, 0, n, limit)
+}
+
+type sortedHint int // hint for pdqsort when choosing the pivot
+
+const (
+ unknownHint sortedHint = iota
+ increasingHint
+ decreasingHint
+)
+
+// xorshift paper: https://www.jstatsoft.org/article/view/v008i14/xorshift.pdf
+type xorshift uint64
+
+func (r *xorshift) Next() uint64 {
+ *r ^= *r << 13
+ *r ^= *r >> 17
+ *r ^= *r << 5
+ return uint64(*r)
+}
+
+func nextPowerOfTwo(length int) uint {
+ shift := uint(bits.Len(uint(length)))
+ return uint(1 << shift)
+}
+
+// lessSwap is a pair of Less and Swap function for use with the
+// auto-generated func-optimized variant of sort.go in
+// zfuncversion.go.
+type lessSwap struct {
+ Less func(i, j int) bool
+ Swap func(i, j int)
+}
+
+type reverse struct {
+ // This embedded Interface permits Reverse to use the methods of
+ // another Interface implementation.
+ Interface
+}
+
+// Less returns the opposite of the embedded implementation's Less method.
+func (r reverse) Less(i, j int) bool {
+ return r.Interface.Less(j, i)
+}
+
+// Reverse returns the reverse order for data.
+func Reverse(data Interface) Interface {
+ return &reverse{data}
+}
+
+// IsSorted reports whether data is sorted.
+//
+// Note: in many situations, the newer [slices.IsSortedFunc] function is more
+// ergonomic and runs faster.
+func IsSorted(data Interface) bool {
+ n := data.Len()
+ for i := n - 1; i > 0; i-- {
+ if data.Less(i, i-1) {
+ return false
+ }
+ }
+ return true
+}
+
+// Convenience types for common cases
+
+// IntSlice attaches the methods of Interface to []int, sorting in increasing order.
+type IntSlice []int
+
+func (x IntSlice) Len() int { return len(x) }
+func (x IntSlice) Less(i, j int) bool { return x[i] < x[j] }
+func (x IntSlice) Swap(i, j int) { x[i], x[j] = x[j], x[i] }
+
+// Sort is a convenience method: x.Sort() calls Sort(x).
+func (x IntSlice) Sort() { Sort(x) }
+
+// Float64Slice implements Interface for a []float64, sorting in increasing order,
+// with not-a-number (NaN) values ordered before other values.
+type Float64Slice []float64
+
+func (x Float64Slice) Len() int { return len(x) }
+
+// Less reports whether x[i] should be ordered before x[j], as required by the sort Interface.
+// Note that floating-point comparison by itself is not a transitive relation: it does not
+// report a consistent ordering for not-a-number (NaN) values.
+// This implementation of Less places NaN values before any others, by using:
+//
+// x[i] < x[j] || (math.IsNaN(x[i]) && !math.IsNaN(x[j]))
+func (x Float64Slice) Less(i, j int) bool { return x[i] < x[j] || (isNaN(x[i]) && !isNaN(x[j])) }
+func (x Float64Slice) Swap(i, j int) { x[i], x[j] = x[j], x[i] }
+
+// isNaN is a copy of math.IsNaN to avoid a dependency on the math package.
+func isNaN(f float64) bool {
+ return f != f
+}
+
+// Sort is a convenience method: x.Sort() calls Sort(x).
+func (x Float64Slice) Sort() { Sort(x) }
+
+// StringSlice attaches the methods of Interface to []string, sorting in increasing order.
+type StringSlice []string
+
+func (x StringSlice) Len() int { return len(x) }
+func (x StringSlice) Less(i, j int) bool { return x[i] < x[j] }
+func (x StringSlice) Swap(i, j int) { x[i], x[j] = x[j], x[i] }
+
+// Sort is a convenience method: x.Sort() calls Sort(x).
+func (x StringSlice) Sort() { Sort(x) }
+
+// Convenience wrappers for common cases
+
+// Ints sorts a slice of ints in increasing order.
+//
+// Note: as of Go 1.22, this function simply calls [slices.Sort].
+func Ints(x []int) { intsImpl(x) }
+
+// Float64s sorts a slice of float64s in increasing order.
+// Not-a-number (NaN) values are ordered before other values.
+//
+// Note: as of Go 1.22, this function simply calls [slices.Sort].
+func Float64s(x []float64) { float64sImpl(x) }
+
+// Strings sorts a slice of strings in increasing order.
+//
+// Note: as of Go 1.22, this function simply calls [slices.Sort].
+func Strings(x []string) { stringsImpl(x) }
+
+// IntsAreSorted reports whether the slice x is sorted in increasing order.
+//
+// Note: as of Go 1.22, this function simply calls [slices.IsSorted].
+func IntsAreSorted(x []int) bool { return intsAreSortedImpl(x) }
+
+// Float64sAreSorted reports whether the slice x is sorted in increasing order,
+// with not-a-number (NaN) values before any other values.
+//
+// Note: as of Go 1.22, this function simply calls [slices.IsSorted].
+func Float64sAreSorted(x []float64) bool { return float64sAreSortedImpl(x) }
+
+// StringsAreSorted reports whether the slice x is sorted in increasing order.
+//
+// Note: as of Go 1.22, this function simply calls [slices.IsSorted].
+func StringsAreSorted(x []string) bool { return stringsAreSortedImpl(x) }
+
+// Notes on stable sorting:
+// The used algorithms are simple and provable correct on all input and use
+// only logarithmic additional stack space. They perform well if compared
+// experimentally to other stable in-place sorting algorithms.
+//
+// Remarks on other algorithms evaluated:
+// - GCC's 4.6.3 stable_sort with merge_without_buffer from libstdc++:
+// Not faster.
+// - GCC's __rotate for block rotations: Not faster.
+// - "Practical in-place mergesort" from Jyrki Katajainen, Tomi A. Pasanen
+// and Jukka Teuhola; Nordic Journal of Computing 3,1 (1996), 27-40:
+// The given algorithms are in-place, number of Swap and Assignments
+// grow as n log n but the algorithm is not stable.
+// - "Fast Stable In-Place Sorting with O(n) Data Moves" J.I. Munro and
+// V. Raman in Algorithmica (1996) 16, 115-160:
+// This algorithm either needs additional 2n bits or works only if there
+// are enough different elements available to encode some permutations
+// which have to be undone later (so not stable on any input).
+// - All the optimal in-place sorting/merging algorithms I found are either
+// unstable or rely on enough different elements in each step to encode the
+// performed block rearrangements. See also "In-Place Merging Algorithms",
+// Denham Coates-Evely, Department of Computer Science, Kings College,
+// January 2004 and the references in there.
+// - Often "optimal" algorithms are optimal in the number of assignments
+// but Interface has only Swap as operation.
+
+// Stable sorts data in ascending order as determined by the Less method,
+// while keeping the original order of equal elements.
+//
+// It makes one call to data.Len to determine n, O(n*log(n)) calls to
+// data.Less and O(n*log(n)*log(n)) calls to data.Swap.
+//
+// Note: in many situations, the newer slices.SortStableFunc function is more
+// ergonomic and runs faster.
+func Stable(data Interface) {
+ stable(data, data.Len())
+}
+
+/*
+Complexity of Stable Sorting
+
+
+Complexity of block swapping rotation
+
+Each Swap puts one new element into its correct, final position.
+Elements which reach their final position are no longer moved.
+Thus block swapping rotation needs |u|+|v| calls to Swaps.
+This is best possible as each element might need a move.
+
+Pay attention when comparing to other optimal algorithms which
+typically count the number of assignments instead of swaps:
+E.g. the optimal algorithm of Dudzinski and Dydek for in-place
+rotations uses O(u + v + gcd(u,v)) assignments which is
+better than our O(3 * (u+v)) as gcd(u,v) <= u.
+
+
+Stable sorting by SymMerge and BlockSwap rotations
+
+SymMerg complexity for same size input M = N:
+Calls to Less: O(M*log(N/M+1)) = O(N*log(2)) = O(N)
+Calls to Swap: O((M+N)*log(M)) = O(2*N*log(N)) = O(N*log(N))
+
+(The following argument does not fuzz over a missing -1 or
+other stuff which does not impact the final result).
+
+Let n = data.Len(). Assume n = 2^k.
+
+Plain merge sort performs log(n) = k iterations.
+On iteration i the algorithm merges 2^(k-i) blocks, each of size 2^i.
+
+Thus iteration i of merge sort performs:
+Calls to Less O(2^(k-i) * 2^i) = O(2^k) = O(2^log(n)) = O(n)
+Calls to Swap O(2^(k-i) * 2^i * log(2^i)) = O(2^k * i) = O(n*i)
+
+In total k = log(n) iterations are performed; so in total:
+Calls to Less O(log(n) * n)
+Calls to Swap O(n + 2*n + 3*n + ... + (k-1)*n + k*n)
+ = O((k/2) * k * n) = O(n * k^2) = O(n * log^2(n))
+
+
+Above results should generalize to arbitrary n = 2^k + p
+and should not be influenced by the initial insertion sort phase:
+Insertion sort is O(n^2) on Swap and Less, thus O(bs^2) per block of
+size bs at n/bs blocks: O(bs*n) Swaps and Less during insertion sort.
+Merge sort iterations start at i = log(bs). With t = log(bs) constant:
+Calls to Less O((log(n)-t) * n + bs*n) = O(log(n)*n + (bs-t)*n)
+ = O(n * log(n))
+Calls to Swap O(n * log^2(n) - (t^2+t)/2*n) = O(n * log^2(n))
+
+*/
diff --git a/src/sort/sort_impl_120.go b/src/sort/sort_impl_120.go
new file mode 100644
index 0000000..5980da6
--- /dev/null
+++ b/src/sort/sort_impl_120.go
@@ -0,0 +1,15 @@
+// Copyright 2023 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 !go1.21
+
+package sort
+
+func intsImpl(x []int) { Sort(IntSlice(x)) }
+func float64sImpl(x []float64) { Sort(Float64Slice(x)) }
+func stringsImpl(x []string) { Sort(StringSlice(x)) }
+
+func intsAreSortedImpl(x []int) bool { return IsSorted(IntSlice(x)) }
+func float64sAreSortedImpl(x []float64) bool { return IsSorted(Float64Slice(x)) }
+func stringsAreSortedImpl(x []string) bool { return IsSorted(StringSlice(x)) }
diff --git a/src/sort/sort_impl_go121.go b/src/sort/sort_impl_go121.go
new file mode 100644
index 0000000..0a6a6a6
--- /dev/null
+++ b/src/sort/sort_impl_go121.go
@@ -0,0 +1,22 @@
+// Copyright 2023 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 go1.21
+
+// Starting with Go 1.21, we can leverage the new generic functions from the
+// slices package to implement some `sort` functions faster. However, until
+// the bootstrap compiler uses Go 1.21 or later, we keep a fallback version
+// in sort_impl_120.go that retains the old implementation.
+
+package sort
+
+import "slices"
+
+func intsImpl(x []int) { slices.Sort(x) }
+func float64sImpl(x []float64) { slices.Sort(x) }
+func stringsImpl(x []string) { slices.Sort(x) }
+
+func intsAreSortedImpl(x []int) bool { return slices.IsSorted(x) }
+func float64sAreSortedImpl(x []float64) bool { return slices.IsSorted(x) }
+func stringsAreSortedImpl(x []string) bool { return slices.IsSorted(x) }
diff --git a/src/sort/sort_slices_benchmark_test.go b/src/sort/sort_slices_benchmark_test.go
new file mode 100644
index 0000000..37f3b1b
--- /dev/null
+++ b/src/sort/sort_slices_benchmark_test.go
@@ -0,0 +1,201 @@
+// Copyright 2023 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 sort_test
+
+import (
+ "math/rand"
+ "slices"
+ . "sort"
+ "strconv"
+ stringspkg "strings"
+ "testing"
+)
+
+// Benchmarks comparing sorting from the slices package with functions from
+// the sort package (avoiding functions that are just forwarding to the slices
+// package).
+
+func makeRandomInts(n int) []int {
+ rand.Seed(42)
+ ints := make([]int, n)
+ for i := 0; i < n; i++ {
+ ints[i] = rand.Intn(n)
+ }
+ return ints
+}
+
+func makeSortedInts(n int) []int {
+ ints := make([]int, n)
+ for i := 0; i < n; i++ {
+ ints[i] = i
+ }
+ return ints
+}
+
+func makeReversedInts(n int) []int {
+ ints := make([]int, n)
+ for i := 0; i < n; i++ {
+ ints[i] = n - i
+ }
+ return ints
+}
+
+func makeSortedStrings(n int) []string {
+ x := make([]string, n)
+ for i := 0; i < n; i++ {
+ x[i] = strconv.Itoa(i)
+ }
+ Strings(x)
+ return x
+}
+
+const N = 100_000
+
+func BenchmarkSortInts(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ b.StopTimer()
+ ints := makeRandomInts(N)
+ b.StartTimer()
+ Sort(IntSlice(ints))
+ }
+}
+
+func BenchmarkSlicesSortInts(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ b.StopTimer()
+ ints := makeRandomInts(N)
+ b.StartTimer()
+ slices.Sort(ints)
+ }
+}
+
+func BenchmarkSortIsSorted(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ b.StopTimer()
+ ints := makeSortedInts(N)
+ b.StartTimer()
+ IsSorted(IntSlice(ints))
+ }
+}
+
+func BenchmarkSlicesIsSorted(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ b.StopTimer()
+ ints := makeSortedInts(N)
+ b.StartTimer()
+ slices.IsSorted(ints)
+ }
+}
+
+// makeRandomStrings generates n random strings with alphabetic runes of
+// varying lengths.
+func makeRandomStrings(n int) []string {
+ rand.Seed(42)
+ var letters = []rune("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ")
+ ss := make([]string, n)
+ for i := 0; i < n; i++ {
+ var sb stringspkg.Builder
+ slen := 2 + rand.Intn(50)
+ for j := 0; j < slen; j++ {
+ sb.WriteRune(letters[rand.Intn(len(letters))])
+ }
+ ss[i] = sb.String()
+ }
+ return ss
+}
+
+func BenchmarkSortStrings(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ b.StopTimer()
+ ss := makeRandomStrings(N)
+ b.StartTimer()
+ Sort(StringSlice(ss))
+ }
+}
+
+func BenchmarkSlicesSortStrings(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ b.StopTimer()
+ ss := makeRandomStrings(N)
+ b.StartTimer()
+ slices.Sort(ss)
+ }
+}
+
+func BenchmarkSortStrings_Sorted(b *testing.B) {
+ ss := makeSortedStrings(N)
+ b.ResetTimer()
+
+ for i := 0; i < b.N; i++ {
+ Sort(StringSlice(ss))
+ }
+}
+
+func BenchmarkSlicesSortStrings_Sorted(b *testing.B) {
+ ss := makeSortedStrings(N)
+ b.ResetTimer()
+
+ for i := 0; i < b.N; i++ {
+ slices.Sort(ss)
+ }
+}
+
+// These benchmarks compare sorting a slice of structs with sort.Sort vs.
+// slices.SortFunc.
+type myStruct struct {
+ a, b, c, d string
+ n int
+}
+
+type myStructs []*myStruct
+
+func (s myStructs) Len() int { return len(s) }
+func (s myStructs) Less(i, j int) bool { return s[i].n < s[j].n }
+func (s myStructs) Swap(i, j int) { s[i], s[j] = s[j], s[i] }
+
+func makeRandomStructs(n int) myStructs {
+ rand.Seed(42)
+ structs := make([]*myStruct, n)
+ for i := 0; i < n; i++ {
+ structs[i] = &myStruct{n: rand.Intn(n)}
+ }
+ return structs
+}
+
+func TestStructSorts(t *testing.T) {
+ ss := makeRandomStructs(200)
+ ss2 := make([]*myStruct, len(ss))
+ for i := range ss {
+ ss2[i] = &myStruct{n: ss[i].n}
+ }
+
+ Sort(ss)
+ slices.SortFunc(ss2, func(a, b *myStruct) int { return a.n - b.n })
+
+ for i := range ss {
+ if *ss[i] != *ss2[i] {
+ t.Fatalf("ints2 mismatch at %d; %v != %v", i, *ss[i], *ss2[i])
+ }
+ }
+}
+
+func BenchmarkSortStructs(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ b.StopTimer()
+ ss := makeRandomStructs(N)
+ b.StartTimer()
+ Sort(ss)
+ }
+}
+
+func BenchmarkSortFuncStructs(b *testing.B) {
+ cmpFunc := func(a, b *myStruct) int { return a.n - b.n }
+ for i := 0; i < b.N; i++ {
+ b.StopTimer()
+ ss := makeRandomStructs(N)
+ b.StartTimer()
+ slices.SortFunc(ss, cmpFunc)
+ }
+}
diff --git a/src/sort/sort_test.go b/src/sort/sort_test.go
new file mode 100644
index 0000000..ccb8987
--- /dev/null
+++ b/src/sort/sort_test.go
@@ -0,0 +1,753 @@
+// Copyright 2009 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 sort_test
+
+import (
+ "cmp"
+ "fmt"
+ "internal/testenv"
+ "math"
+ "math/rand"
+ "slices"
+ . "sort"
+ "strconv"
+ stringspkg "strings"
+ "testing"
+)
+
+var ints = [...]int{74, 59, 238, -784, 9845, 959, 905, 0, 0, 42, 7586, -5467984, 7586}
+var float64s = [...]float64{74.3, 59.0, math.Inf(1), 238.2, -784.0, 2.3, math.NaN(), math.NaN(), math.Inf(-1), 9845.768, -959.7485, 905, 7.8, 7.8}
+var strings = [...]string{"", "Hello", "foo", "bar", "foo", "f00", "%*&^*&^&", "***"}
+
+func TestSortIntSlice(t *testing.T) {
+ data := ints
+ a := IntSlice(data[0:])
+ Sort(a)
+ if !IsSorted(a) {
+ t.Errorf("sorted %v", ints)
+ t.Errorf(" got %v", data)
+ }
+}
+
+func TestSortFloat64Slice(t *testing.T) {
+ data := float64s
+ a := Float64Slice(data[0:])
+ Sort(a)
+ if !IsSorted(a) {
+ t.Errorf("sorted %v", float64s)
+ t.Errorf(" got %v", data)
+ }
+}
+
+// Compare Sort with slices.Sort sorting a float64 slice containing NaNs.
+func TestSortFloat64sCompareSlicesSort(t *testing.T) {
+ slice1 := slices.Clone(float64s[:])
+ slice2 := slices.Clone(float64s[:])
+
+ Sort(Float64Slice(slice1))
+ slices.Sort(slice2)
+
+ // Compare for equality using cmp.Compare, which considers NaNs equal.
+ if !slices.EqualFunc(slice1, slice1, func(a, b float64) bool { return cmp.Compare(a, b) == 0 }) {
+ t.Errorf("mismatch between Sort and slices.Sort: got %v, want %v", slice1, slice2)
+ }
+}
+
+func TestSortStringSlice(t *testing.T) {
+ data := strings
+ a := StringSlice(data[0:])
+ Sort(a)
+ if !IsSorted(a) {
+ t.Errorf("sorted %v", strings)
+ t.Errorf(" got %v", data)
+ }
+}
+
+func TestInts(t *testing.T) {
+ data := ints
+ Ints(data[0:])
+ if !IntsAreSorted(data[0:]) {
+ t.Errorf("sorted %v", ints)
+ t.Errorf(" got %v", data)
+ }
+}
+
+func TestFloat64s(t *testing.T) {
+ data := float64s
+ Float64s(data[0:])
+ if !Float64sAreSorted(data[0:]) {
+ t.Errorf("sorted %v", float64s)
+ t.Errorf(" got %v", data)
+ }
+}
+
+func TestStrings(t *testing.T) {
+ data := strings
+ Strings(data[0:])
+ if !StringsAreSorted(data[0:]) {
+ t.Errorf("sorted %v", strings)
+ t.Errorf(" got %v", data)
+ }
+}
+
+func TestSlice(t *testing.T) {
+ data := strings
+ Slice(data[:], func(i, j int) bool {
+ return data[i] < data[j]
+ })
+ if !SliceIsSorted(data[:], func(i, j int) bool { return data[i] < data[j] }) {
+ t.Errorf("sorted %v", strings)
+ t.Errorf(" got %v", data)
+ }
+}
+
+func TestSortLarge_Random(t *testing.T) {
+ n := 1000000
+ if testing.Short() {
+ n /= 100
+ }
+ data := make([]int, n)
+ for i := 0; i < len(data); i++ {
+ data[i] = rand.Intn(100)
+ }
+ if IntsAreSorted(data) {
+ t.Fatalf("terrible rand.rand")
+ }
+ Ints(data)
+ if !IntsAreSorted(data) {
+ t.Errorf("sort didn't sort - 1M ints")
+ }
+}
+
+func TestReverseSortIntSlice(t *testing.T) {
+ data := ints
+ data1 := ints
+ a := IntSlice(data[0:])
+ Sort(a)
+ r := IntSlice(data1[0:])
+ Sort(Reverse(r))
+ for i := 0; i < len(data); i++ {
+ if a[i] != r[len(data)-1-i] {
+ t.Errorf("reverse sort didn't sort")
+ }
+ if i > len(data)/2 {
+ break
+ }
+ }
+}
+
+func TestBreakPatterns(t *testing.T) {
+ // Special slice used to trigger breakPatterns.
+ data := make([]int, 30)
+ for i := range data {
+ data[i] = 10
+ }
+ data[(len(data)/4)*1] = 0
+ data[(len(data)/4)*2] = 1
+ data[(len(data)/4)*3] = 2
+ Sort(IntSlice(data))
+}
+
+func TestReverseRange(t *testing.T) {
+ data := []int{1, 2, 3, 4, 5, 6, 7}
+ ReverseRange(IntSlice(data), 0, len(data))
+ for i := len(data) - 1; i > 0; i-- {
+ if data[i] > data[i-1] {
+ t.Fatalf("reverseRange didn't work")
+ }
+ }
+
+ data1 := []int{1, 2, 3, 4, 5, 6, 7}
+ data2 := []int{1, 2, 5, 4, 3, 6, 7}
+ ReverseRange(IntSlice(data1), 2, 5)
+ for i, v := range data1 {
+ if v != data2[i] {
+ t.Fatalf("reverseRange didn't work")
+ }
+ }
+}
+
+type nonDeterministicTestingData struct {
+ r *rand.Rand
+}
+
+func (t *nonDeterministicTestingData) Len() int {
+ return 500
+}
+func (t *nonDeterministicTestingData) Less(i, j int) bool {
+ if i < 0 || j < 0 || i >= t.Len() || j >= t.Len() {
+ panic("nondeterministic comparison out of bounds")
+ }
+ return t.r.Float32() < 0.5
+}
+func (t *nonDeterministicTestingData) Swap(i, j int) {
+ if i < 0 || j < 0 || i >= t.Len() || j >= t.Len() {
+ panic("nondeterministic comparison out of bounds")
+ }
+}
+
+func TestNonDeterministicComparison(t *testing.T) {
+ // Ensure that sort.Sort does not panic when Less returns inconsistent results.
+ // See https://golang.org/issue/14377.
+ defer func() {
+ if r := recover(); r != nil {
+ t.Error(r)
+ }
+ }()
+
+ td := &nonDeterministicTestingData{
+ r: rand.New(rand.NewSource(0)),
+ }
+
+ for i := 0; i < 10; i++ {
+ Sort(td)
+ }
+}
+
+func BenchmarkSortString1K(b *testing.B) {
+ b.StopTimer()
+ unsorted := make([]string, 1<<10)
+ for i := range unsorted {
+ unsorted[i] = strconv.Itoa(i ^ 0x2cc)
+ }
+ data := make([]string, len(unsorted))
+
+ for i := 0; i < b.N; i++ {
+ copy(data, unsorted)
+ b.StartTimer()
+ Strings(data)
+ b.StopTimer()
+ }
+}
+
+func BenchmarkSortString1K_Slice(b *testing.B) {
+ b.StopTimer()
+ unsorted := make([]string, 1<<10)
+ for i := range unsorted {
+ unsorted[i] = strconv.Itoa(i ^ 0x2cc)
+ }
+ data := make([]string, len(unsorted))
+
+ for i := 0; i < b.N; i++ {
+ copy(data, unsorted)
+ b.StartTimer()
+ Slice(data, func(i, j int) bool { return data[i] < data[j] })
+ b.StopTimer()
+ }
+}
+
+func BenchmarkStableString1K(b *testing.B) {
+ b.StopTimer()
+ unsorted := make([]string, 1<<10)
+ for i := range unsorted {
+ unsorted[i] = strconv.Itoa(i ^ 0x2cc)
+ }
+ data := make([]string, len(unsorted))
+
+ for i := 0; i < b.N; i++ {
+ copy(data, unsorted)
+ b.StartTimer()
+ Stable(StringSlice(data))
+ b.StopTimer()
+ }
+}
+
+func BenchmarkSortInt1K(b *testing.B) {
+ b.StopTimer()
+ for i := 0; i < b.N; i++ {
+ data := make([]int, 1<<10)
+ for i := 0; i < len(data); i++ {
+ data[i] = i ^ 0x2cc
+ }
+ b.StartTimer()
+ Ints(data)
+ b.StopTimer()
+ }
+}
+
+func BenchmarkSortInt1K_Sorted(b *testing.B) {
+ b.StopTimer()
+ for i := 0; i < b.N; i++ {
+ data := make([]int, 1<<10)
+ for i := 0; i < len(data); i++ {
+ data[i] = i
+ }
+ b.StartTimer()
+ Ints(data)
+ b.StopTimer()
+ }
+}
+
+func BenchmarkSortInt1K_Reversed(b *testing.B) {
+ b.StopTimer()
+ for i := 0; i < b.N; i++ {
+ data := make([]int, 1<<10)
+ for i := 0; i < len(data); i++ {
+ data[i] = len(data) - i
+ }
+ b.StartTimer()
+ Ints(data)
+ b.StopTimer()
+ }
+}
+
+func BenchmarkSortInt1K_Mod8(b *testing.B) {
+ b.StopTimer()
+ for i := 0; i < b.N; i++ {
+ data := make([]int, 1<<10)
+ for i := 0; i < len(data); i++ {
+ data[i] = i % 8
+ }
+ b.StartTimer()
+ Ints(data)
+ b.StopTimer()
+ }
+}
+
+func BenchmarkStableInt1K(b *testing.B) {
+ b.StopTimer()
+ unsorted := make([]int, 1<<10)
+ for i := range unsorted {
+ unsorted[i] = i ^ 0x2cc
+ }
+ data := make([]int, len(unsorted))
+ for i := 0; i < b.N; i++ {
+ copy(data, unsorted)
+ b.StartTimer()
+ Stable(IntSlice(data))
+ b.StopTimer()
+ }
+}
+
+func BenchmarkStableInt1K_Slice(b *testing.B) {
+ b.StopTimer()
+ unsorted := make([]int, 1<<10)
+ for i := range unsorted {
+ unsorted[i] = i ^ 0x2cc
+ }
+ data := make([]int, len(unsorted))
+ for i := 0; i < b.N; i++ {
+ copy(data, unsorted)
+ b.StartTimer()
+ SliceStable(data, func(i, j int) bool { return data[i] < data[j] })
+ b.StopTimer()
+ }
+}
+
+func BenchmarkSortInt64K(b *testing.B) {
+ b.StopTimer()
+ for i := 0; i < b.N; i++ {
+ data := make([]int, 1<<16)
+ for i := 0; i < len(data); i++ {
+ data[i] = i ^ 0xcccc
+ }
+ b.StartTimer()
+ Ints(data)
+ b.StopTimer()
+ }
+}
+
+func BenchmarkSortInt64K_Slice(b *testing.B) {
+ b.StopTimer()
+ for i := 0; i < b.N; i++ {
+ data := make([]int, 1<<16)
+ for i := 0; i < len(data); i++ {
+ data[i] = i ^ 0xcccc
+ }
+ b.StartTimer()
+ Slice(data, func(i, j int) bool { return data[i] < data[j] })
+ b.StopTimer()
+ }
+}
+
+func BenchmarkStableInt64K(b *testing.B) {
+ b.StopTimer()
+ for i := 0; i < b.N; i++ {
+ data := make([]int, 1<<16)
+ for i := 0; i < len(data); i++ {
+ data[i] = i ^ 0xcccc
+ }
+ b.StartTimer()
+ Stable(IntSlice(data))
+ b.StopTimer()
+ }
+}
+
+const (
+ _Sawtooth = iota
+ _Rand
+ _Stagger
+ _Plateau
+ _Shuffle
+ _NDist
+)
+
+const (
+ _Copy = iota
+ _Reverse
+ _ReverseFirstHalf
+ _ReverseSecondHalf
+ _Sorted
+ _Dither
+ _NMode
+)
+
+type testingData struct {
+ desc string
+ t *testing.T
+ data []int
+ maxswap int // number of swaps allowed
+ ncmp, nswap int
+}
+
+func (d *testingData) Len() int { return len(d.data) }
+func (d *testingData) Less(i, j int) bool {
+ d.ncmp++
+ return d.data[i] < d.data[j]
+}
+func (d *testingData) Swap(i, j int) {
+ if d.nswap >= d.maxswap {
+ d.t.Fatalf("%s: used %d swaps sorting slice of %d", d.desc, d.nswap, len(d.data))
+ }
+ d.nswap++
+ d.data[i], d.data[j] = d.data[j], d.data[i]
+}
+
+func lg(n int) int {
+ i := 0
+ for 1<<uint(i) < n {
+ i++
+ }
+ return i
+}
+
+func testBentleyMcIlroy(t *testing.T, sort func(Interface), maxswap func(int) int) {
+ sizes := []int{100, 1023, 1024, 1025}
+ if testing.Short() {
+ sizes = []int{100, 127, 128, 129}
+ }
+ dists := []string{"sawtooth", "rand", "stagger", "plateau", "shuffle"}
+ modes := []string{"copy", "reverse", "reverse1", "reverse2", "sort", "dither"}
+ var tmp1, tmp2 [1025]int
+ for _, n := range sizes {
+ for m := 1; m < 2*n; m *= 2 {
+ for dist := 0; dist < _NDist; dist++ {
+ j := 0
+ k := 1
+ data := tmp1[0:n]
+ for i := 0; i < n; i++ {
+ switch dist {
+ case _Sawtooth:
+ data[i] = i % m
+ case _Rand:
+ data[i] = rand.Intn(m)
+ case _Stagger:
+ data[i] = (i*m + i) % n
+ case _Plateau:
+ data[i] = min(i, m)
+ case _Shuffle:
+ if rand.Intn(m) != 0 {
+ j += 2
+ data[i] = j
+ } else {
+ k += 2
+ data[i] = k
+ }
+ }
+ }
+
+ mdata := tmp2[0:n]
+ for mode := 0; mode < _NMode; mode++ {
+ switch mode {
+ case _Copy:
+ for i := 0; i < n; i++ {
+ mdata[i] = data[i]
+ }
+ case _Reverse:
+ for i := 0; i < n; i++ {
+ mdata[i] = data[n-i-1]
+ }
+ case _ReverseFirstHalf:
+ for i := 0; i < n/2; i++ {
+ mdata[i] = data[n/2-i-1]
+ }
+ for i := n / 2; i < n; i++ {
+ mdata[i] = data[i]
+ }
+ case _ReverseSecondHalf:
+ for i := 0; i < n/2; i++ {
+ mdata[i] = data[i]
+ }
+ for i := n / 2; i < n; i++ {
+ mdata[i] = data[n-(i-n/2)-1]
+ }
+ case _Sorted:
+ for i := 0; i < n; i++ {
+ mdata[i] = data[i]
+ }
+ // Ints is known to be correct
+ // because mode Sort runs after mode _Copy.
+ Ints(mdata)
+ case _Dither:
+ for i := 0; i < n; i++ {
+ mdata[i] = data[i] + i%5
+ }
+ }
+
+ desc := fmt.Sprintf("n=%d m=%d dist=%s mode=%s", n, m, dists[dist], modes[mode])
+ d := &testingData{desc: desc, t: t, data: mdata[0:n], maxswap: maxswap(n)}
+ sort(d)
+ // Uncomment if you are trying to improve the number of compares/swaps.
+ //t.Logf("%s: ncmp=%d, nswp=%d", desc, d.ncmp, d.nswap)
+
+ // If we were testing C qsort, we'd have to make a copy
+ // of the slice and sort it ourselves and then compare
+ // x against it, to ensure that qsort was only permuting
+ // the data, not (for example) overwriting it with zeros.
+ //
+ // In go, we don't have to be so paranoid: since the only
+ // mutating method Sort can call is TestingData.swap,
+ // it suffices here just to check that the final slice is sorted.
+ if !IntsAreSorted(mdata) {
+ t.Fatalf("%s: ints not sorted\n\t%v", desc, mdata)
+ }
+ }
+ }
+ }
+ }
+}
+
+func TestSortBM(t *testing.T) {
+ testBentleyMcIlroy(t, Sort, func(n int) int { return n * lg(n) * 12 / 10 })
+}
+
+func TestHeapsortBM(t *testing.T) {
+ testBentleyMcIlroy(t, Heapsort, func(n int) int { return n * lg(n) * 12 / 10 })
+}
+
+func TestStableBM(t *testing.T) {
+ testBentleyMcIlroy(t, Stable, func(n int) int { return n * lg(n) * lg(n) / 3 })
+}
+
+// This is based on the "antiquicksort" implementation by M. Douglas McIlroy.
+// See https://www.cs.dartmouth.edu/~doug/mdmspe.pdf for more info.
+type adversaryTestingData struct {
+ t *testing.T
+ data []int // item values, initialized to special gas value and changed by Less
+ maxcmp int // number of comparisons allowed
+ ncmp int // number of comparisons (calls to Less)
+ nsolid int // number of elements that have been set to non-gas values
+ candidate int // guess at current pivot
+ gas int // special value for unset elements, higher than everything else
+}
+
+func (d *adversaryTestingData) Len() int { return len(d.data) }
+
+func (d *adversaryTestingData) Less(i, j int) bool {
+ if d.ncmp >= d.maxcmp {
+ d.t.Fatalf("used %d comparisons sorting adversary data with size %d", d.ncmp, len(d.data))
+ }
+ d.ncmp++
+
+ if d.data[i] == d.gas && d.data[j] == d.gas {
+ if i == d.candidate {
+ // freeze i
+ d.data[i] = d.nsolid
+ d.nsolid++
+ } else {
+ // freeze j
+ d.data[j] = d.nsolid
+ d.nsolid++
+ }
+ }
+
+ if d.data[i] == d.gas {
+ d.candidate = i
+ } else if d.data[j] == d.gas {
+ d.candidate = j
+ }
+
+ return d.data[i] < d.data[j]
+}
+
+func (d *adversaryTestingData) Swap(i, j int) {
+ d.data[i], d.data[j] = d.data[j], d.data[i]
+}
+
+func newAdversaryTestingData(t *testing.T, size int, maxcmp int) *adversaryTestingData {
+ gas := size - 1
+ data := make([]int, size)
+ for i := 0; i < size; i++ {
+ data[i] = gas
+ }
+ return &adversaryTestingData{t: t, data: data, maxcmp: maxcmp, gas: gas}
+}
+
+func TestAdversary(t *testing.T) {
+ const size = 10000 // large enough to distinguish between O(n^2) and O(n*log(n))
+ maxcmp := size * lg(size) * 4 // the factor 4 was found by trial and error
+ d := newAdversaryTestingData(t, size, maxcmp)
+ Sort(d) // This should degenerate to heapsort.
+ // Check data is fully populated and sorted.
+ for i, v := range d.data {
+ if v != i {
+ t.Fatalf("adversary data not fully sorted")
+ }
+ }
+}
+
+func TestStableInts(t *testing.T) {
+ data := ints
+ Stable(IntSlice(data[0:]))
+ if !IntsAreSorted(data[0:]) {
+ t.Errorf("nsorted %v\n got %v", ints, data)
+ }
+}
+
+type intPairs []struct {
+ a, b int
+}
+
+// IntPairs compare on a only.
+func (d intPairs) Len() int { return len(d) }
+func (d intPairs) Less(i, j int) bool { return d[i].a < d[j].a }
+func (d intPairs) Swap(i, j int) { d[i], d[j] = d[j], d[i] }
+
+// Record initial order in B.
+func (d intPairs) initB() {
+ for i := range d {
+ d[i].b = i
+ }
+}
+
+// InOrder checks if a-equal elements were not reordered.
+func (d intPairs) inOrder() bool {
+ lastA, lastB := -1, 0
+ for i := 0; i < len(d); i++ {
+ if lastA != d[i].a {
+ lastA = d[i].a
+ lastB = d[i].b
+ continue
+ }
+ if d[i].b <= lastB {
+ return false
+ }
+ lastB = d[i].b
+ }
+ return true
+}
+
+func TestStability(t *testing.T) {
+ n, m := 100000, 1000
+ if testing.Short() {
+ n, m = 1000, 100
+ }
+ data := make(intPairs, n)
+
+ // random distribution
+ for i := 0; i < len(data); i++ {
+ data[i].a = rand.Intn(m)
+ }
+ if IsSorted(data) {
+ t.Fatalf("terrible rand.rand")
+ }
+ data.initB()
+ Stable(data)
+ if !IsSorted(data) {
+ t.Errorf("Stable didn't sort %d ints", n)
+ }
+ if !data.inOrder() {
+ t.Errorf("Stable wasn't stable on %d ints", n)
+ }
+
+ // already sorted
+ data.initB()
+ Stable(data)
+ if !IsSorted(data) {
+ t.Errorf("Stable shuffled sorted %d ints (order)", n)
+ }
+ if !data.inOrder() {
+ t.Errorf("Stable shuffled sorted %d ints (stability)", n)
+ }
+
+ // sorted reversed
+ for i := 0; i < len(data); i++ {
+ data[i].a = len(data) - i
+ }
+ data.initB()
+ Stable(data)
+ if !IsSorted(data) {
+ t.Errorf("Stable didn't sort %d ints", n)
+ }
+ if !data.inOrder() {
+ t.Errorf("Stable wasn't stable on %d ints", n)
+ }
+}
+
+var countOpsSizes = []int{1e2, 3e2, 1e3, 3e3, 1e4, 3e4, 1e5, 3e5, 1e6}
+
+func countOps(t *testing.T, algo func(Interface), name string) {
+ sizes := countOpsSizes
+ if testing.Short() {
+ sizes = sizes[:5]
+ }
+ if !testing.Verbose() {
+ t.Skip("Counting skipped as non-verbose mode.")
+ }
+ for _, n := range sizes {
+ td := testingData{
+ desc: name,
+ t: t,
+ data: make([]int, n),
+ maxswap: 1<<31 - 1,
+ }
+ for i := 0; i < n; i++ {
+ td.data[i] = rand.Intn(n / 5)
+ }
+ algo(&td)
+ t.Logf("%s %8d elements: %11d Swap, %10d Less", name, n, td.nswap, td.ncmp)
+ }
+}
+
+func TestCountStableOps(t *testing.T) { countOps(t, Stable, "Stable") }
+func TestCountSortOps(t *testing.T) { countOps(t, Sort, "Sort ") }
+
+func bench(b *testing.B, size int, algo func(Interface), name string) {
+ if stringspkg.HasSuffix(testenv.Builder(), "-race") && size > 1e4 {
+ b.Skip("skipping slow benchmark on race builder")
+ }
+ b.StopTimer()
+ data := make(intPairs, size)
+ x := ^uint32(0)
+ for i := 0; i < b.N; i++ {
+ for n := size - 3; n <= size+3; n++ {
+ for i := 0; i < len(data); i++ {
+ x += x
+ x ^= 1
+ if int32(x) < 0 {
+ x ^= 0x88888eef
+ }
+ data[i].a = int(x % uint32(n/5))
+ }
+ data.initB()
+ b.StartTimer()
+ algo(data)
+ b.StopTimer()
+ if !IsSorted(data) {
+ b.Errorf("%s did not sort %d ints", name, n)
+ }
+ if name == "Stable" && !data.inOrder() {
+ b.Errorf("%s unstable on %d ints", name, n)
+ }
+ }
+ }
+}
+
+func BenchmarkSort1e2(b *testing.B) { bench(b, 1e2, Sort, "Sort") }
+func BenchmarkStable1e2(b *testing.B) { bench(b, 1e2, Stable, "Stable") }
+func BenchmarkSort1e4(b *testing.B) { bench(b, 1e4, Sort, "Sort") }
+func BenchmarkStable1e4(b *testing.B) { bench(b, 1e4, Stable, "Stable") }
+func BenchmarkSort1e6(b *testing.B) { bench(b, 1e6, Sort, "Sort") }
+func BenchmarkStable1e6(b *testing.B) { bench(b, 1e6, Stable, "Stable") }
diff --git a/src/sort/zsortfunc.go b/src/sort/zsortfunc.go
new file mode 100644
index 0000000..49b6169
--- /dev/null
+++ b/src/sort/zsortfunc.go
@@ -0,0 +1,479 @@
+// 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 sort
+
+// insertionSort_func sorts data[a:b] using insertion sort.
+func insertionSort_func(data lessSwap, a, b int) {
+ for i := a + 1; i < b; i++ {
+ for j := i; j > a && data.Less(j, j-1); j-- {
+ data.Swap(j, j-1)
+ }
+ }
+}
+
+// siftDown_func implements the heap property on data[lo:hi].
+// first is an offset into the array where the root of the heap lies.
+func siftDown_func(data lessSwap, lo, hi, first int) {
+ root := lo
+ for {
+ child := 2*root + 1
+ if child >= hi {
+ break
+ }
+ if child+1 < hi && data.Less(first+child, first+child+1) {
+ child++
+ }
+ if !data.Less(first+root, first+child) {
+ return
+ }
+ data.Swap(first+root, first+child)
+ root = child
+ }
+}
+
+func heapSort_func(data lessSwap, a, b int) {
+ first := a
+ lo := 0
+ hi := b - a
+
+ // Build heap with greatest element at top.
+ for i := (hi - 1) / 2; i >= 0; i-- {
+ siftDown_func(data, i, hi, first)
+ }
+
+ // Pop elements, largest first, into end of data.
+ for i := hi - 1; i >= 0; i-- {
+ data.Swap(first, first+i)
+ siftDown_func(data, lo, i, first)
+ }
+}
+
+// pdqsort_func 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_func(data lessSwap, a, b, limit int) {
+ 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_func(data, a, b)
+ return
+ }
+
+ // Fall back to heapsort if too many bad choices were made.
+ if limit == 0 {
+ heapSort_func(data, a, b)
+ return
+ }
+
+ // If the last partitioning was imbalanced, we need to breaking patterns.
+ if !wasBalanced {
+ breakPatterns_func(data, a, b)
+ limit--
+ }
+
+ pivot, hint := choosePivot_func(data, a, b)
+ if hint == decreasingHint {
+ reverseRange_func(data, a, b)
+ // 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_func(data, a, b) {
+ return
+ }
+ }
+
+ // Probably the slice contains many duplicate elements, partition the slice into
+ // elements equal to and elements greater than the pivot.
+ if a > 0 && !data.Less(a-1, pivot) {
+ mid := partitionEqual_func(data, a, b, pivot)
+ a = mid
+ continue
+ }
+
+ mid, alreadyPartitioned := partition_func(data, a, b, pivot)
+ wasPartitioned = alreadyPartitioned
+
+ leftLen, rightLen := mid-a, b-mid
+ balanceThreshold := length / 8
+ if leftLen < rightLen {
+ wasBalanced = leftLen >= balanceThreshold
+ pdqsort_func(data, a, mid, limit)
+ a = mid + 1
+ } else {
+ wasBalanced = rightLen >= balanceThreshold
+ pdqsort_func(data, mid+1, b, limit)
+ b = mid
+ }
+ }
+}
+
+// partition_func 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_func(data lessSwap, a, b, pivot int) (newpivot int, alreadyPartitioned bool) {
+ data.Swap(a, pivot)
+ i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned
+
+ for i <= j && data.Less(i, a) {
+ i++
+ }
+ for i <= j && !data.Less(j, a) {
+ j--
+ }
+ if i > j {
+ data.Swap(j, a)
+ return j, true
+ }
+ data.Swap(i, j)
+ i++
+ j--
+
+ for {
+ for i <= j && data.Less(i, a) {
+ i++
+ }
+ for i <= j && !data.Less(j, a) {
+ j--
+ }
+ if i > j {
+ break
+ }
+ data.Swap(i, j)
+ i++
+ j--
+ }
+ data.Swap(j, a)
+ return j, false
+}
+
+// partitionEqual_func 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_func(data lessSwap, a, b, pivot int) (newpivot int) {
+ data.Swap(a, pivot)
+ i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned
+
+ for {
+ for i <= j && !data.Less(a, i) {
+ i++
+ }
+ for i <= j && data.Less(a, j) {
+ j--
+ }
+ if i > j {
+ break
+ }
+ data.Swap(i, j)
+ i++
+ j--
+ }
+ return i
+}
+
+// partialInsertionSort_func partially sorts a slice, returns true if the slice is sorted at the end.
+func partialInsertionSort_func(data lessSwap, a, b int) 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 && !data.Less(i, i-1) {
+ i++
+ }
+
+ if i == b {
+ return true
+ }
+
+ if b-a < shortestShifting {
+ return false
+ }
+
+ data.Swap(i, i-1)
+
+ // Shift the smaller one to the left.
+ if i-a >= 2 {
+ for j := i - 1; j >= 1; j-- {
+ if !data.Less(j, j-1) {
+ break
+ }
+ data.Swap(j, j-1)
+ }
+ }
+ // Shift the greater one to the right.
+ if b-i >= 2 {
+ for j := i + 1; j < b; j++ {
+ if !data.Less(j, j-1) {
+ break
+ }
+ data.Swap(j, j-1)
+ }
+ }
+ }
+ return false
+}
+
+// breakPatterns_func scatters some elements around in an attempt to break some patterns
+// that might cause imbalanced partitions in quicksort.
+func breakPatterns_func(data lessSwap, a, b int) {
+ 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
+ }
+ data.Swap(idx, a+other)
+ }
+ }
+}
+
+// choosePivot_func 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_func(data lessSwap, a, b int) (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_func(data, i, &swaps)
+ j = medianAdjacent_func(data, j, &swaps)
+ k = medianAdjacent_func(data, k, &swaps)
+ }
+ // Find the median among i, j, k and stores it into j.
+ j = median_func(data, i, j, k, &swaps)
+ }
+
+ switch swaps {
+ case 0:
+ return j, increasingHint
+ case maxSwaps:
+ return j, decreasingHint
+ default:
+ return j, unknownHint
+ }
+}
+
+// order2_func returns x,y where data[x] <= data[y], where x,y=a,b or x,y=b,a.
+func order2_func(data lessSwap, a, b int, swaps *int) (int, int) {
+ if data.Less(b, a) {
+ *swaps++
+ return b, a
+ }
+ return a, b
+}
+
+// median_func returns x where data[x] is the median of data[a],data[b],data[c], where x is a, b, or c.
+func median_func(data lessSwap, a, b, c int, swaps *int) int {
+ a, b = order2_func(data, a, b, swaps)
+ b, c = order2_func(data, b, c, swaps)
+ a, b = order2_func(data, a, b, swaps)
+ return b
+}
+
+// medianAdjacent_func finds the median of data[a - 1], data[a], data[a + 1] and stores the index into a.
+func medianAdjacent_func(data lessSwap, a int, swaps *int) int {
+ return median_func(data, a-1, a, a+1, swaps)
+}
+
+func reverseRange_func(data lessSwap, a, b int) {
+ i := a
+ j := b - 1
+ for i < j {
+ data.Swap(i, j)
+ i++
+ j--
+ }
+}
+
+func swapRange_func(data lessSwap, a, b, n int) {
+ for i := 0; i < n; i++ {
+ data.Swap(a+i, b+i)
+ }
+}
+
+func stable_func(data lessSwap, n int) {
+ blockSize := 20 // must be > 0
+ a, b := 0, blockSize
+ for b <= n {
+ insertionSort_func(data, a, b)
+ a = b
+ b += blockSize
+ }
+ insertionSort_func(data, a, n)
+
+ for blockSize < n {
+ a, b = 0, 2*blockSize
+ for b <= n {
+ symMerge_func(data, a, a+blockSize, b)
+ a = b
+ b += 2 * blockSize
+ }
+ if m := a + blockSize; m < n {
+ symMerge_func(data, a, m, n)
+ }
+ blockSize *= 2
+ }
+}
+
+// symMerge_func 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_func(data lessSwap, a, m, b int) {
+ // 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 data.Less(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++ {
+ data.Swap(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 !data.Less(m, h) {
+ i = h + 1
+ } else {
+ j = h
+ }
+ }
+ // Swap values until data[m] reaches the position i.
+ for k := m; k > i; k-- {
+ data.Swap(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 !data.Less(p-c, c) {
+ start = c + 1
+ } else {
+ r = c
+ }
+ }
+
+ end := n - start
+ if start < m && m < end {
+ rotate_func(data, start, m, end)
+ }
+ if a < start && start < mid {
+ symMerge_func(data, a, start, mid)
+ }
+ if mid < end && end < b {
+ symMerge_func(data, mid, end, b)
+ }
+}
+
+// rotate_func 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_func(data lessSwap, a, m, b int) {
+ i := m - a
+ j := b - m
+
+ for i != j {
+ if i > j {
+ swapRange_func(data, m-i, m, j)
+ i -= j
+ } else {
+ swapRange_func(data, m-i, m+j-i, i)
+ j -= i
+ }
+ }
+ // i == j
+ swapRange_func(data, m-i, m, i)
+}
diff --git a/src/sort/zsortinterface.go b/src/sort/zsortinterface.go
new file mode 100644
index 0000000..51fa503
--- /dev/null
+++ b/src/sort/zsortinterface.go
@@ -0,0 +1,479 @@
+// 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 sort
+
+// insertionSort sorts data[a:b] using insertion sort.
+func insertionSort(data Interface, a, b int) {
+ for i := a + 1; i < b; i++ {
+ for j := i; j > a && data.Less(j, j-1); j-- {
+ data.Swap(j, j-1)
+ }
+ }
+}
+
+// siftDown implements the heap property on data[lo:hi].
+// first is an offset into the array where the root of the heap lies.
+func siftDown(data Interface, lo, hi, first int) {
+ root := lo
+ for {
+ child := 2*root + 1
+ if child >= hi {
+ break
+ }
+ if child+1 < hi && data.Less(first+child, first+child+1) {
+ child++
+ }
+ if !data.Less(first+root, first+child) {
+ return
+ }
+ data.Swap(first+root, first+child)
+ root = child
+ }
+}
+
+func heapSort(data Interface, a, b int) {
+ first := a
+ lo := 0
+ hi := b - a
+
+ // Build heap with greatest element at top.
+ for i := (hi - 1) / 2; i >= 0; i-- {
+ siftDown(data, i, hi, first)
+ }
+
+ // Pop elements, largest first, into end of data.
+ for i := hi - 1; i >= 0; i-- {
+ data.Swap(first, first+i)
+ siftDown(data, lo, i, first)
+ }
+}
+
+// pdqsort 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(data Interface, a, b, limit int) {
+ 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(data, a, b)
+ return
+ }
+
+ // Fall back to heapsort if too many bad choices were made.
+ if limit == 0 {
+ heapSort(data, a, b)
+ return
+ }
+
+ // If the last partitioning was imbalanced, we need to breaking patterns.
+ if !wasBalanced {
+ breakPatterns(data, a, b)
+ limit--
+ }
+
+ pivot, hint := choosePivot(data, a, b)
+ if hint == decreasingHint {
+ reverseRange(data, a, b)
+ // 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(data, a, b) {
+ return
+ }
+ }
+
+ // Probably the slice contains many duplicate elements, partition the slice into
+ // elements equal to and elements greater than the pivot.
+ if a > 0 && !data.Less(a-1, pivot) {
+ mid := partitionEqual(data, a, b, pivot)
+ a = mid
+ continue
+ }
+
+ mid, alreadyPartitioned := partition(data, a, b, pivot)
+ wasPartitioned = alreadyPartitioned
+
+ leftLen, rightLen := mid-a, b-mid
+ balanceThreshold := length / 8
+ if leftLen < rightLen {
+ wasBalanced = leftLen >= balanceThreshold
+ pdqsort(data, a, mid, limit)
+ a = mid + 1
+ } else {
+ wasBalanced = rightLen >= balanceThreshold
+ pdqsort(data, mid+1, b, limit)
+ b = mid
+ }
+ }
+}
+
+// partition 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(data Interface, a, b, pivot int) (newpivot int, alreadyPartitioned bool) {
+ data.Swap(a, pivot)
+ i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned
+
+ for i <= j && data.Less(i, a) {
+ i++
+ }
+ for i <= j && !data.Less(j, a) {
+ j--
+ }
+ if i > j {
+ data.Swap(j, a)
+ return j, true
+ }
+ data.Swap(i, j)
+ i++
+ j--
+
+ for {
+ for i <= j && data.Less(i, a) {
+ i++
+ }
+ for i <= j && !data.Less(j, a) {
+ j--
+ }
+ if i > j {
+ break
+ }
+ data.Swap(i, j)
+ i++
+ j--
+ }
+ data.Swap(j, a)
+ return j, false
+}
+
+// partitionEqual 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(data Interface, a, b, pivot int) (newpivot int) {
+ data.Swap(a, pivot)
+ i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned
+
+ for {
+ for i <= j && !data.Less(a, i) {
+ i++
+ }
+ for i <= j && data.Less(a, j) {
+ j--
+ }
+ if i > j {
+ break
+ }
+ data.Swap(i, j)
+ i++
+ j--
+ }
+ return i
+}
+
+// partialInsertionSort partially sorts a slice, returns true if the slice is sorted at the end.
+func partialInsertionSort(data Interface, a, b int) 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 && !data.Less(i, i-1) {
+ i++
+ }
+
+ if i == b {
+ return true
+ }
+
+ if b-a < shortestShifting {
+ return false
+ }
+
+ data.Swap(i, i-1)
+
+ // Shift the smaller one to the left.
+ if i-a >= 2 {
+ for j := i - 1; j >= 1; j-- {
+ if !data.Less(j, j-1) {
+ break
+ }
+ data.Swap(j, j-1)
+ }
+ }
+ // Shift the greater one to the right.
+ if b-i >= 2 {
+ for j := i + 1; j < b; j++ {
+ if !data.Less(j, j-1) {
+ break
+ }
+ data.Swap(j, j-1)
+ }
+ }
+ }
+ return false
+}
+
+// breakPatterns scatters some elements around in an attempt to break some patterns
+// that might cause imbalanced partitions in quicksort.
+func breakPatterns(data Interface, a, b int) {
+ 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
+ }
+ data.Swap(idx, a+other)
+ }
+ }
+}
+
+// choosePivot 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(data Interface, a, b int) (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(data, i, &swaps)
+ j = medianAdjacent(data, j, &swaps)
+ k = medianAdjacent(data, k, &swaps)
+ }
+ // Find the median among i, j, k and stores it into j.
+ j = median(data, i, j, k, &swaps)
+ }
+
+ switch swaps {
+ case 0:
+ return j, increasingHint
+ case maxSwaps:
+ return j, decreasingHint
+ default:
+ return j, unknownHint
+ }
+}
+
+// order2 returns x,y where data[x] <= data[y], where x,y=a,b or x,y=b,a.
+func order2(data Interface, a, b int, swaps *int) (int, int) {
+ if data.Less(b, a) {
+ *swaps++
+ return b, a
+ }
+ return a, b
+}
+
+// median returns x where data[x] is the median of data[a],data[b],data[c], where x is a, b, or c.
+func median(data Interface, a, b, c int, swaps *int) int {
+ a, b = order2(data, a, b, swaps)
+ b, c = order2(data, b, c, swaps)
+ a, b = order2(data, a, b, swaps)
+ return b
+}
+
+// medianAdjacent finds the median of data[a - 1], data[a], data[a + 1] and stores the index into a.
+func medianAdjacent(data Interface, a int, swaps *int) int {
+ return median(data, a-1, a, a+1, swaps)
+}
+
+func reverseRange(data Interface, a, b int) {
+ i := a
+ j := b - 1
+ for i < j {
+ data.Swap(i, j)
+ i++
+ j--
+ }
+}
+
+func swapRange(data Interface, a, b, n int) {
+ for i := 0; i < n; i++ {
+ data.Swap(a+i, b+i)
+ }
+}
+
+func stable(data Interface, n int) {
+ blockSize := 20 // must be > 0
+ a, b := 0, blockSize
+ for b <= n {
+ insertionSort(data, a, b)
+ a = b
+ b += blockSize
+ }
+ insertionSort(data, a, n)
+
+ for blockSize < n {
+ a, b = 0, 2*blockSize
+ for b <= n {
+ symMerge(data, a, a+blockSize, b)
+ a = b
+ b += 2 * blockSize
+ }
+ if m := a + blockSize; m < n {
+ symMerge(data, a, m, n)
+ }
+ blockSize *= 2
+ }
+}
+
+// symMerge 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(data Interface, a, m, b int) {
+ // 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 data.Less(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++ {
+ data.Swap(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 !data.Less(m, h) {
+ i = h + 1
+ } else {
+ j = h
+ }
+ }
+ // Swap values until data[m] reaches the position i.
+ for k := m; k > i; k-- {
+ data.Swap(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 !data.Less(p-c, c) {
+ start = c + 1
+ } else {
+ r = c
+ }
+ }
+
+ end := n - start
+ if start < m && m < end {
+ rotate(data, start, m, end)
+ }
+ if a < start && start < mid {
+ symMerge(data, a, start, mid)
+ }
+ if mid < end && end < b {
+ symMerge(data, mid, end, b)
+ }
+}
+
+// rotate 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(data Interface, a, m, b int) {
+ i := m - a
+ j := b - m
+
+ for i != j {
+ if i > j {
+ swapRange(data, m-i, m, j)
+ i -= j
+ } else {
+ swapRange(data, m-i, m+j-i, i)
+ j -= i
+ }
+ }
+ // i == j
+ swapRange(data, m-i, m, i)
+}