| // 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 slices |
| |
| import "golang.org/x/exp/constraints" |
| |
| // insertionSortOrdered sorts data[a:b] using insertion sort. |
| func insertionSortOrdered[Elem constraints.Ordered](data []Elem, a, b int) { |
| for i := a + 1; i < b; i++ { |
| for j := i; j > a && (data[j] < data[j-1]); j-- { |
| data[j], data[j-1] = data[j-1], data[j] |
| } |
| } |
| } |
| |
| // siftDownOrdered implements the heap property on data[lo:hi]. |
| // first is an offset into the array where the root of the heap lies. |
| func siftDownOrdered[Elem constraints.Ordered](data []Elem, lo, hi, first int) { |
| root := lo |
| for { |
| child := 2*root + 1 |
| if child >= hi { |
| break |
| } |
| if child+1 < hi && (data[first+child] < data[first+child+1]) { |
| child++ |
| } |
| if !(data[first+root] < data[first+child]) { |
| return |
| } |
| data[first+root], data[first+child] = data[first+child], data[first+root] |
| root = child |
| } |
| } |
| |
| func heapSortOrdered[Elem constraints.Ordered](data []Elem, 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-- { |
| siftDownOrdered(data, i, hi, first) |
| } |
| |
| // Pop elements, largest first, into end of data. |
| for i := hi - 1; i >= 0; i-- { |
| data[first], data[first+i] = data[first+i], data[first] |
| siftDownOrdered(data, lo, i, first) |
| } |
| } |
| |
| // Quicksort, loosely following Bentley and McIlroy, |
| // "Engineering a Sort Function" SP&E November 1993. |
| |
| // medianOfThreeOrdered moves the median of the three values data[m0], data[m1], data[m2] into data[m1]. |
| func medianOfThreeOrdered[Elem constraints.Ordered](data []Elem, m1, m0, m2 int) { |
| // sort 3 elements |
| if data[m1] < data[m0] { |
| data[m1], data[m0] = data[m0], data[m1] |
| } |
| // data[m0] <= data[m1] |
| if data[m2] < data[m1] { |
| data[m2], data[m1] = data[m1], data[m2] |
| // data[m0] <= data[m2] && data[m1] < data[m2] |
| if data[m1] < data[m0] { |
| data[m1], data[m0] = data[m0], data[m1] |
| } |
| } |
| // now data[m0] <= data[m1] <= data[m2] |
| } |
| |
| func swapRangeOrdered[Elem constraints.Ordered](data []Elem, a, b, n int) { |
| for i := 0; i < n; i++ { |
| data[a+i], data[b+i] = data[b+i], data[a+i] |
| } |
| } |
| |
| func doPivotOrdered[Elem constraints.Ordered](data []Elem, lo, hi int) (midlo, midhi int) { |
| m := int(uint(lo+hi) >> 1) // Written like this to avoid integer overflow. |
| if hi-lo > 40 { |
| // Tukey's "Ninther" median of three medians of three. |
| s := (hi - lo) / 8 |
| medianOfThreeOrdered(data, lo, lo+s, lo+2*s) |
| medianOfThreeOrdered(data, m, m-s, m+s) |
| medianOfThreeOrdered(data, hi-1, hi-1-s, hi-1-2*s) |
| } |
| medianOfThreeOrdered(data, lo, m, hi-1) |
| |
| // Invariants are: |
| // data[lo] = pivot (set up by ChoosePivot) |
| // data[lo < i < a] < pivot |
| // data[a <= i < b] <= pivot |
| // data[b <= i < c] unexamined |
| // data[c <= i < hi-1] > pivot |
| // data[hi-1] >= pivot |
| pivot := lo |
| a, c := lo+1, hi-1 |
| |
| for ; a < c && (data[a] < data[pivot]); a++ { |
| } |
| b := a |
| for { |
| for ; b < c && !(data[pivot] < data[b]); b++ { // data[b] <= pivot |
| } |
| for ; b < c && (data[pivot] < data[c-1]); c-- { // data[c-1] > pivot |
| } |
| if b >= c { |
| break |
| } |
| // data[b] > pivot; data[c-1] <= pivot |
| data[b], data[c-1] = data[c-1], data[b] |
| b++ |
| c-- |
| } |
| // If hi-c<3 then there are duplicates (by property of median of nine). |
| // Let's be a bit more conservative, and set border to 5. |
| protect := hi-c < 5 |
| if !protect && hi-c < (hi-lo)/4 { |
| // Lets test some points for equality to pivot |
| dups := 0 |
| if !(data[pivot] < data[hi-1]) { // data[hi-1] = pivot |
| data[c], data[hi-1] = data[hi-1], data[c] |
| c++ |
| dups++ |
| } |
| if !(data[b-1] < data[pivot]) { // data[b-1] = pivot |
| b-- |
| dups++ |
| } |
| // m-lo = (hi-lo)/2 > 6 |
| // b-lo > (hi-lo)*3/4-1 > 8 |
| // ==> m < b ==> data[m] <= pivot |
| if !(data[m] < data[pivot]) { // data[m] = pivot |
| data[m], data[b-1] = data[b-1], data[m] |
| b-- |
| dups++ |
| } |
| // if at least 2 points are equal to pivot, assume skewed distribution |
| protect = dups > 1 |
| } |
| if protect { |
| // Protect against a lot of duplicates |
| // Add invariant: |
| // data[a <= i < b] unexamined |
| // data[b <= i < c] = pivot |
| for { |
| for ; a < b && !(data[b-1] < data[pivot]); b-- { // data[b] == pivot |
| } |
| for ; a < b && (data[a] < data[pivot]); a++ { // data[a] < pivot |
| } |
| if a >= b { |
| break |
| } |
| // data[a] == pivot; data[b-1] < pivot |
| data[a], data[b-1] = data[b-1], data[a] |
| a++ |
| b-- |
| } |
| } |
| // Swap pivot into middle |
| data[pivot], data[b-1] = data[b-1], data[pivot] |
| return b - 1, c |
| } |
| |
| func quickSortOrdered[Elem constraints.Ordered](data []Elem, a, b, maxDepth int) { |
| for b-a > 12 { // Use ShellSort for slices <= 12 elements |
| if maxDepth == 0 { |
| heapSortOrdered(data, a, b) |
| return |
| } |
| maxDepth-- |
| mlo, mhi := doPivotOrdered(data, a, b) |
| // Avoiding recursion on the larger subproblem guarantees |
| // a stack depth of at most lg(b-a). |
| if mlo-a < b-mhi { |
| quickSortOrdered(data, a, mlo, maxDepth) |
| a = mhi // i.e., quickSortOrdered(data, mhi, b) |
| } else { |
| quickSortOrdered(data, mhi, b, maxDepth) |
| b = mlo // i.e., quickSortOrdered(data, a, mlo) |
| } |
| } |
| if b-a > 1 { |
| // Do ShellSort pass with gap 6 |
| // It could be written in this simplified form cause b-a <= 12 |
| for i := a + 6; i < b; i++ { |
| if data[i] < data[i-6] { |
| data[i], data[i-6] = data[i-6], data[i] |
| } |
| } |
| insertionSortOrdered(data, a, b) |
| } |
| } |
| |
| func stableOrdered[Elem constraints.Ordered](data []Elem, n int) { |
| blockSize := 20 // must be > 0 |
| a, b := 0, blockSize |
| for b <= n { |
| insertionSortOrdered(data, a, b) |
| a = b |
| b += blockSize |
| } |
| insertionSortOrdered(data, a, n) |
| |
| for blockSize < n { |
| a, b = 0, 2*blockSize |
| for b <= n { |
| symMergeOrdered(data, a, a+blockSize, b) |
| a = b |
| b += 2 * blockSize |
| } |
| if m := a + blockSize; m < n { |
| symMergeOrdered(data, a, m, n) |
| } |
| blockSize *= 2 |
| } |
| } |
| |
| // symMergeOrdered 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 symMergeOrdered[Elem constraints.Ordered](data []Elem, 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[h] < data[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[k], data[k+1] = data[k+1], data[k] |
| } |
| 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[m] < data[h]) { |
| i = h + 1 |
| } else { |
| j = h |
| } |
| } |
| // Swap values until data[m] reaches the position i. |
| for k := m; k > i; k-- { |
| data[k], data[k-1] = data[k-1], data[k] |
| } |
| 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[p-c] < data[c]) { |
| start = c + 1 |
| } else { |
| r = c |
| } |
| } |
| |
| end := n - start |
| if start < m && m < end { |
| rotateOrdered(data, start, m, end) |
| } |
| if a < start && start < mid { |
| symMergeOrdered(data, a, start, mid) |
| } |
| if mid < end && end < b { |
| symMergeOrdered(data, mid, end, b) |
| } |
| } |
| |
| // rotateOrdered 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 rotateOrdered[Elem constraints.Ordered](data []Elem, a, m, b int) { |
| i := m - a |
| j := b - m |
| |
| for i != j { |
| if i > j { |
| swapRangeOrdered(data, m-i, m, j) |
| i -= j |
| } else { |
| swapRangeOrdered(data, m-i, m+j-i, i) |
| j -= i |
| } |
| } |
| // i == j |
| swapRangeOrdered(data, m-i, m, i) |
| } |