mirror of https://go.googlesource.com/go
718 lines
20 KiB
Go
718 lines
20 KiB
Go
// Copyright 2022 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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//go:build ignore
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// This program is run via "go generate" (via a directive in sort.go)
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// to generate implementation variants of the underlying sorting algorithm.
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// When passed the -generic flag it generates generic variants of sorting;
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// otherwise it generates the non-generic variants used by the sort package.
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package main
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import (
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"bytes"
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"flag"
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"fmt"
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"go/format"
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"log"
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"os"
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"text/template"
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)
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type Variant struct {
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// Name is the variant name: should be unique among variants.
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Name string
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// Path is the file path into which the generator will emit the code for this
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// variant.
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Path string
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// Package is the package this code will be emitted into.
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Package string
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// Imports is the imports needed for this package.
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Imports string
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// FuncSuffix is appended to all function names in this variant's code. All
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// suffixes should be unique within a package.
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FuncSuffix string
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// DataType is the type of the data parameter of functions in this variant's
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// code.
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DataType string
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// TypeParam is the optional type parameter for the function.
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TypeParam string
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// ExtraParam is an extra parameter to pass to the function. Should begin with
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// ", " to separate from other params.
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ExtraParam string
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// ExtraArg is an extra argument to pass to calls between functions; typically
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// it invokes ExtraParam. Should begin with ", " to separate from other args.
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ExtraArg string
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// Funcs is a map of functions used from within the template. The following
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// functions are expected to exist:
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//
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// Less (name, i, j):
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// emits a comparison expression that checks if the value `name` at
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// index `i` is smaller than at index `j`.
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//
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// Swap (name, i, j):
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// emits a statement that performs a data swap between elements `i` and
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// `j` of the value `name`.
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Funcs template.FuncMap
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}
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var (
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traditionalVariants = []Variant{
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Variant{
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Name: "interface",
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Path: "zsortinterface.go",
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Package: "sort",
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Imports: "",
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FuncSuffix: "",
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TypeParam: "",
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ExtraParam: "",
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ExtraArg: "",
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DataType: "Interface",
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Funcs: template.FuncMap{
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"Less": func(name, i, j string) string {
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return fmt.Sprintf("%s.Less(%s, %s)", name, i, j)
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},
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"Swap": func(name, i, j string) string {
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return fmt.Sprintf("%s.Swap(%s, %s)", name, i, j)
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},
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},
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},
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Variant{
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Name: "func",
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Path: "zsortfunc.go",
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Package: "sort",
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Imports: "",
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FuncSuffix: "_func",
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TypeParam: "",
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ExtraParam: "",
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ExtraArg: "",
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DataType: "lessSwap",
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Funcs: template.FuncMap{
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"Less": func(name, i, j string) string {
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return fmt.Sprintf("%s.Less(%s, %s)", name, i, j)
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},
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"Swap": func(name, i, j string) string {
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return fmt.Sprintf("%s.Swap(%s, %s)", name, i, j)
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},
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},
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},
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}
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genericVariants = []Variant{
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Variant{
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Name: "generic_ordered",
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Path: "zsortordered.go",
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Package: "slices",
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Imports: "import \"cmp\"\n",
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FuncSuffix: "Ordered",
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TypeParam: "[E cmp.Ordered]",
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ExtraParam: "",
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ExtraArg: "",
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DataType: "[]E",
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Funcs: template.FuncMap{
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"Less": func(name, i, j string) string {
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return fmt.Sprintf("cmp.Less(%s[%s], %s[%s])", name, i, name, j)
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},
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"Swap": func(name, i, j string) string {
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return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
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},
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},
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},
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Variant{
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Name: "generic_func",
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Path: "zsortanyfunc.go",
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Package: "slices",
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FuncSuffix: "CmpFunc",
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TypeParam: "[E any]",
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ExtraParam: ", cmp func(a, b E) int",
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ExtraArg: ", cmp",
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DataType: "[]E",
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Funcs: template.FuncMap{
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"Less": func(name, i, j string) string {
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return fmt.Sprintf("(cmp(%s[%s], %s[%s]) < 0)", name, i, name, j)
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},
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"Swap": func(name, i, j string) string {
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return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
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},
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},
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},
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}
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expVariants = []Variant{
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Variant{
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Name: "exp_ordered",
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Path: "zsortordered.go",
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Package: "slices",
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Imports: "import \"golang.org/x/exp/constraints\"\n",
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FuncSuffix: "Ordered",
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TypeParam: "[E constraints.Ordered]",
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ExtraParam: "",
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ExtraArg: "",
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DataType: "[]E",
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Funcs: template.FuncMap{
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"Less": func(name, i, j string) string {
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return fmt.Sprintf("cmpLess(%s[%s], %s[%s])", name, i, name, j)
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},
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"Swap": func(name, i, j string) string {
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return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
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},
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},
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},
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Variant{
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Name: "exp_func",
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Path: "zsortanyfunc.go",
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Package: "slices",
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FuncSuffix: "CmpFunc",
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TypeParam: "[E any]",
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ExtraParam: ", cmp func(a, b E) int",
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ExtraArg: ", cmp",
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DataType: "[]E",
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Funcs: template.FuncMap{
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"Less": func(name, i, j string) string {
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return fmt.Sprintf("(cmp(%s[%s], %s[%s]) < 0)", name, i, name, j)
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},
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"Swap": func(name, i, j string) string {
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return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i)
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},
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},
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},
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}
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)
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func main() {
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genGeneric := flag.Bool("generic", false, "generate generic versions")
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genExp := flag.Bool("exp", false, "generate x/exp/slices versions")
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flag.Parse()
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var variants []Variant
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if *genExp {
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variants = expVariants
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} else if *genGeneric {
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variants = genericVariants
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} else {
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variants = traditionalVariants
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}
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for i := range variants {
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generate(&variants[i])
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}
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}
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// generate generates the code for variant `v` into a file named by `v.Path`.
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func generate(v *Variant) {
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// Parse templateCode anew for each variant because Parse requires Funcs to be
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// registered, and it helps type-check the funcs.
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tmpl, err := template.New("gen").Funcs(v.Funcs).Parse(templateCode)
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if err != nil {
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log.Fatal("template Parse:", err)
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}
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var out bytes.Buffer
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err = tmpl.Execute(&out, v)
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if err != nil {
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log.Fatal("template Execute:", err)
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}
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formatted, err := format.Source(out.Bytes())
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if err != nil {
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log.Fatal("format:", err)
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}
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if err := os.WriteFile(v.Path, formatted, 0644); err != nil {
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log.Fatal("WriteFile:", err)
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}
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}
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var templateCode = `// Code generated by gen_sort_variants.go; DO NOT EDIT.
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// Copyright 2022 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package {{.Package}}
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{{.Imports}}
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// insertionSort{{.FuncSuffix}} sorts data[a:b] using insertion sort.
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func insertionSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
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for i := a + 1; i < b; i++ {
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for j := i; j > a && {{Less "data" "j" "j-1"}}; j-- {
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{{Swap "data" "j" "j-1"}}
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}
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}
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}
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// siftDown{{.FuncSuffix}} implements the heap property on data[lo:hi].
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// first is an offset into the array where the root of the heap lies.
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func siftDown{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, lo, hi, first int {{.ExtraParam}}) {
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root := lo
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for {
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child := 2*root + 1
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if child >= hi {
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break
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}
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if child+1 < hi && {{Less "data" "first+child" "first+child+1"}} {
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child++
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}
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if !{{Less "data" "first+root" "first+child"}} {
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return
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}
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{{Swap "data" "first+root" "first+child"}}
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root = child
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}
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}
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func heapSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
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first := a
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lo := 0
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hi := b - a
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// Build heap with greatest element at top.
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for i := (hi - 1) / 2; i >= 0; i-- {
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siftDown{{.FuncSuffix}}(data, i, hi, first {{.ExtraArg}})
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}
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// Pop elements, largest first, into end of data.
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for i := hi - 1; i >= 0; i-- {
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{{Swap "data" "first" "first+i"}}
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siftDown{{.FuncSuffix}}(data, lo, i, first {{.ExtraArg}})
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}
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}
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// pdqsort{{.FuncSuffix}} sorts data[a:b].
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// The algorithm based on pattern-defeating quicksort(pdqsort), but without the optimizations from BlockQuicksort.
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// pdqsort paper: https://arxiv.org/pdf/2106.05123.pdf
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// C++ implementation: https://github.com/orlp/pdqsort
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// Rust implementation: https://docs.rs/pdqsort/latest/pdqsort/
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// limit is the number of allowed bad (very unbalanced) pivots before falling back to heapsort.
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func pdqsort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, limit int {{.ExtraParam}}) {
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const maxInsertion = 12
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var (
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wasBalanced = true // whether the last partitioning was reasonably balanced
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wasPartitioned = true // whether the slice was already partitioned
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)
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for {
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length := b - a
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if length <= maxInsertion {
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insertionSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
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return
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}
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// Fall back to heapsort if too many bad choices were made.
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if limit == 0 {
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heapSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
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return
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}
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// If the last partitioning was imbalanced, we need to breaking patterns.
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if !wasBalanced {
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breakPatterns{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
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limit--
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}
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pivot, hint := choosePivot{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
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if hint == decreasingHint {
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reverseRange{{.FuncSuffix}}(data, a, b {{.ExtraArg}})
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// The chosen pivot was pivot-a elements after the start of the array.
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// After reversing it is pivot-a elements before the end of the array.
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// The idea came from Rust's implementation.
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pivot = (b - 1) - (pivot - a)
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hint = increasingHint
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}
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// The slice is likely already sorted.
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if wasBalanced && wasPartitioned && hint == increasingHint {
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if partialInsertionSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}}) {
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return
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}
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}
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// Probably the slice contains many duplicate elements, partition the slice into
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// elements equal to and elements greater than the pivot.
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if a > 0 && !{{Less "data" "a-1" "pivot"}} {
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mid := partitionEqual{{.FuncSuffix}}(data, a, b, pivot {{.ExtraArg}})
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a = mid
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continue
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}
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mid, alreadyPartitioned := partition{{.FuncSuffix}}(data, a, b, pivot {{.ExtraArg}})
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wasPartitioned = alreadyPartitioned
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leftLen, rightLen := mid-a, b-mid
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balanceThreshold := length / 8
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if leftLen < rightLen {
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wasBalanced = leftLen >= balanceThreshold
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pdqsort{{.FuncSuffix}}(data, a, mid, limit {{.ExtraArg}})
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a = mid + 1
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} else {
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wasBalanced = rightLen >= balanceThreshold
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pdqsort{{.FuncSuffix}}(data, mid+1, b, limit {{.ExtraArg}})
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b = mid
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}
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}
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}
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// partition{{.FuncSuffix}} does one quicksort partition.
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// Let p = data[pivot]
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// Moves elements in data[a:b] around, so that data[i]<p and data[j]>=p for i<newpivot and j>newpivot.
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// On return, data[newpivot] = p
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func partition{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, pivot int {{.ExtraParam}}) (newpivot int, alreadyPartitioned bool) {
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{{Swap "data" "a" "pivot"}}
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i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned
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for i <= j && {{Less "data" "i" "a"}} {
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i++
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}
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for i <= j && !{{Less "data" "j" "a"}} {
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j--
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}
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if i > j {
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{{Swap "data" "j" "a"}}
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return j, true
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}
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{{Swap "data" "i" "j"}}
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i++
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j--
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for {
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for i <= j && {{Less "data" "i" "a"}} {
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i++
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}
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for i <= j && !{{Less "data" "j" "a"}} {
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j--
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}
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if i > j {
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break
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}
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{{Swap "data" "i" "j"}}
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i++
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j--
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}
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{{Swap "data" "j" "a"}}
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return j, false
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}
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// partitionEqual{{.FuncSuffix}} partitions data[a:b] into elements equal to data[pivot] followed by elements greater than data[pivot].
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// It assumed that data[a:b] does not contain elements smaller than the data[pivot].
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func partitionEqual{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, pivot int {{.ExtraParam}}) (newpivot int) {
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{{Swap "data" "a" "pivot"}}
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i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned
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for {
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for i <= j && !{{Less "data" "a" "i"}} {
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i++
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}
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for i <= j && {{Less "data" "a" "j"}} {
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j--
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}
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if i > j {
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break
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}
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{{Swap "data" "i" "j"}}
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i++
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j--
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}
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return i
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}
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// partialInsertionSort{{.FuncSuffix}} partially sorts a slice, returns true if the slice is sorted at the end.
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func partialInsertionSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) bool {
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const (
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maxSteps = 5 // maximum number of adjacent out-of-order pairs that will get shifted
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shortestShifting = 50 // don't shift any elements on short arrays
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)
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i := a + 1
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for j := 0; j < maxSteps; j++ {
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for i < b && !{{Less "data" "i" "i-1"}} {
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i++
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}
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if i == b {
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return true
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}
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if b-a < shortestShifting {
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return false
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}
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{{Swap "data" "i" "i-1"}}
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// Shift the smaller one to the left.
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if i-a >= 2 {
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for j := i - 1; j >= 1; j-- {
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if !{{Less "data" "j" "j-1"}} {
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break
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}
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{{Swap "data" "j" "j-1"}}
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}
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}
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// Shift the greater one to the right.
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if b-i >= 2 {
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for j := i + 1; j < b; j++ {
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if !{{Less "data" "j" "j-1"}} {
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break
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}
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{{Swap "data" "j" "j-1"}}
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}
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}
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}
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return false
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}
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// breakPatterns{{.FuncSuffix}} scatters some elements around in an attempt to break some patterns
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// that might cause imbalanced partitions in quicksort.
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func breakPatterns{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) {
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length := b - a
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if length >= 8 {
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random := xorshift(length)
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modulus := nextPowerOfTwo(length)
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for idx := a + (length/4)*2 - 1; idx <= a + (length/4)*2 + 1; idx++ {
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other := int(uint(random.Next()) & (modulus - 1))
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if other >= length {
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other -= length
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}
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{{Swap "data" "idx" "a+other"}}
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}
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}
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}
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// choosePivot{{.FuncSuffix}} chooses a pivot in data[a:b].
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//
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// [0,8): chooses a static pivot.
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// [8,shortestNinther): uses the simple median-of-three method.
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// [shortestNinther,∞): uses the Tukey ninther method.
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func choosePivot{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) (pivot int, hint sortedHint) {
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const (
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shortestNinther = 50
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maxSwaps = 4 * 3
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)
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l := b - a
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var (
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swaps int
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i = a + l/4*1
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j = a + l/4*2
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k = a + l/4*3
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)
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if l >= 8 {
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if l >= shortestNinther {
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// Tukey ninther method, the idea came from Rust's implementation.
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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}})
|
|
}
|
|
`
|