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

 // 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)
 	}
 }

 // Quicksort, loosely following Bentley and McIlroy,
 // "Engineering a Sort Function" SP&E November 1993.

 // medianOfThree_func moves the median of the three values data[m0], data[m1], data[m2] into data[m1].
 func medianOfThree_func(data lessSwap, m1, m0, m2 int) {
 	// sort 3 elements
 	if data.Less(m1, m0) {
 		data.Swap(m1, m0)
 	}
 	// data[m0] <= data[m1]
 	if data.Less(m2, m1) {
 		data.Swap(m2, m1)
 		// data[m0] <= data[m2] && data[m1] < data[m2]
 		if data.Less(m1, m0) {
 			data.Swap(m1, m0)
 		}
 	}
 	// now data[m0] <= data[m1] <= data[m2]
 }

 func swapRange_func(data lessSwap, a, b, n int) {
 	for i := 0; i < n; i++ {
 		data.Swap(a+i, b+i)
 	}
 }

 func doPivot_func(data lessSwap, 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
 		medianOfThree_func(data, lo, lo+s, lo+2*s)
 		medianOfThree_func(data, m, m-s, m+s)
 		medianOfThree_func(data, hi-1, hi-1-s, hi-1-2*s)
 	}
 	medianOfThree_func(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.Less(a, pivot); a++ {
 	}
 	b := a
 	for {
 		for ; b < c && !data.Less(pivot, b); b++ { // data[b] <= pivot
 		}
 		for ; b < c && data.Less(pivot, c-1); c-- { // data[c-1] > pivot
 		}
 		if b >= c {
 			break
 		}
 		// data[b] > pivot; data[c-1] <= pivot
 		data.Swap(b, c-1)
 		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.Less(pivot, hi-1) { // data[hi-1] = pivot
 			data.Swap(c, hi-1)
 			c++
 			dups++
 		}
 		if !data.Less(b-1, 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.Less(m, pivot) { // data[m] = pivot
 			data.Swap(m, b-1)
 			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.Less(b-1, pivot); b-- { // data[b] == pivot
 			}
 			for ; a < b && data.Less(a, pivot); a++ { // data[a] < pivot
 			}
 			if a >= b {
 				break
 			}
 			// data[a] == pivot; data[b-1] < pivot
 			data.Swap(a, b-1)
 			a++
 			b--
 		}
 	}
 	// Swap pivot into middle
 	data.Swap(pivot, b-1)
 	return b - 1, c
 }

 func quickSort_func(data lessSwap, a, b, maxDepth int) {
 	for b-a > 12 { // Use ShellSort for slices <= 12 elements
 		if maxDepth == 0 {
 			heapSort_func(data, a, b)
 			return
 		}
 		maxDepth--
 		mlo, mhi := doPivot_func(data, a, b)
 		// Avoiding recursion on the larger subproblem guarantees
 		// a stack depth of at most lg(b-a).
 		if mlo-a < b-mhi {
 			quickSort_func(data, a, mlo, maxDepth)
 			a = mhi // i.e., quickSort_func(data, mhi, b)
 		} else {
 			quickSort_func(data, mhi, b, maxDepth)
 			b = mlo // i.e., quickSort_func(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.Less(i, i-6) {
 				data.Swap(i, i-6)
 			}
 		}
 		insertionSort_func(data, a, b)
 	}
 }

 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)
 }
	// 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)
	}
	}

	// Quicksort, loosely following Bentley and McIlroy,
	// "Engineering a Sort Function" SP&E November 1993.

	// medianOfThree_func moves the median of the three values data[m0], data[m1], data[m2] into data[m1].
	func medianOfThree_func(data lessSwap, m1, m0, m2 int) {
	// sort 3 elements
	if data.Less(m1, m0) {
	data.Swap(m1, m0)
	}
	// data[m0] <= data[m1]
	if data.Less(m2, m1) {
	data.Swap(m2, m1)
	// data[m0] <= data[m2] && data[m1] < data[m2]
	if data.Less(m1, m0) {
	data.Swap(m1, m0)
	}
	}
	// now data[m0] <= data[m1] <= data[m2]
	}

	func swapRange_func(data lessSwap, a, b, n int) {
	for i := 0; i < n; i++ {
	data.Swap(a+i, b+i)
	}
	}

	func doPivot_func(data lessSwap, 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
	medianOfThree_func(data, lo, lo+s, lo+2*s)
	medianOfThree_func(data, m, m-s, m+s)
	medianOfThree_func(data, hi-1, hi-1-s, hi-1-2*s)
	}
	medianOfThree_func(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.Less(a, pivot); a++ {
	}
	b := a
	for {
	for ; b < c && !data.Less(pivot, b); b++ { // data[b] <= pivot
	}
	for ; b < c && data.Less(pivot, c-1); c-- { // data[c-1] > pivot
	}
	if b >= c {
	break
	}
	// data[b] > pivot; data[c-1] <= pivot
	data.Swap(b, c-1)
	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.Less(pivot, hi-1) { // data[hi-1] = pivot
	data.Swap(c, hi-1)
	c++
	dups++
	}
	if !data.Less(b-1, 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.Less(m, pivot) { // data[m] = pivot
	data.Swap(m, b-1)
	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.Less(b-1, pivot); b-- { // data[b] == pivot
	}
	for ; a < b && data.Less(a, pivot); a++ { // data[a] < pivot
	}
	if a >= b {
	break
	}
	// data[a] == pivot; data[b-1] < pivot
	data.Swap(a, b-1)
	a++
	b--
	}
	}
	// Swap pivot into middle
	data.Swap(pivot, b-1)
	return b - 1, c
	}

	func quickSort_func(data lessSwap, a, b, maxDepth int) {
	for b-a > 12 { // Use ShellSort for slices <= 12 elements
	if maxDepth == 0 {
	heapSort_func(data, a, b)
	return
	}
	maxDepth--
	mlo, mhi := doPivot_func(data, a, b)
	// Avoiding recursion on the larger subproblem guarantees
	// a stack depth of at most lg(b-a).
	if mlo-a < b-mhi {
	quickSort_func(data, a, mlo, maxDepth)
	a = mhi // i.e., quickSort_func(data, mhi, b)
	} else {
	quickSort_func(data, mhi, b, maxDepth)
	b = mlo // i.e., quickSort_func(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.Less(i, i-6) {
	data.Swap(i, i-6)
	}
	}
	insertionSort_func(data, a, b)
	}
	}

	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)
	}