diff --git a/flate/huffman_code.go b/flate/huffman_code.go index 1810c6898d..863ef8eedc 100644 --- a/flate/huffman_code.go +++ b/flate/huffman_code.go @@ -7,7 +7,6 @@ package flate import ( "math" "math/bits" - "sort" ) const ( @@ -25,8 +24,6 @@ type huffmanEncoder struct { codes []hcode freqcache []literalNode bitCount [17]int32 - lns byLiteral // stored to avoid repeated allocation in generate - lfs byFreq // stored to avoid repeated allocation in generate } type literalNode struct { @@ -270,7 +267,7 @@ func (h *huffmanEncoder) assignEncodingAndSize(bitCount []int32, list []literalN // assigned in literal order (not frequency order). chunk := list[len(list)-int(bits):] - h.lns.sort(chunk) + sortByLiteral(chunk) for _, node := range chunk { h.codes[node.literal] = hcode{code: reverseBits(code, uint8(n)), len: uint16(n)} code++ @@ -315,7 +312,7 @@ func (h *huffmanEncoder) generate(freq []uint16, maxBits int32) { } return } - h.lfs.sort(list) + sortByFreq(list) // Get the number of literals for each bit count bitCount := h.bitCounts(list, maxBits) @@ -323,39 +320,6 @@ func (h *huffmanEncoder) generate(freq []uint16, maxBits int32) { h.assignEncodingAndSize(bitCount, list) } -type byLiteral []literalNode - -func (s *byLiteral) sort(a []literalNode) { - *s = byLiteral(a) - sort.Sort(s) -} - -func (s byLiteral) Len() int { return len(s) } - -func (s byLiteral) Less(i, j int) bool { - return s[i].literal < s[j].literal -} - -func (s byLiteral) Swap(i, j int) { s[i], s[j] = s[j], s[i] } - -type byFreq []literalNode - -func (s *byFreq) sort(a []literalNode) { - *s = byFreq(a) - sort.Sort(s) -} - -func (s byFreq) Len() int { return len(s) } - -func (s byFreq) Less(i, j int) bool { - if s[i].freq == s[j].freq { - return s[i].literal < s[j].literal - } - return s[i].freq < s[j].freq -} - -func (s byFreq) Swap(i, j int) { s[i], s[j] = s[j], s[i] } - // histogramSize accumulates a histogram of b in h. // An estimated size in bits is returned. // Unassigned values are assigned '1' in the histogram. diff --git a/flate/huffman_sortByFreq.go b/flate/huffman_sortByFreq.go new file mode 100644 index 0000000000..2077802990 --- /dev/null +++ b/flate/huffman_sortByFreq.go @@ -0,0 +1,178 @@ +// 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 flate + +// Sort sorts data. +// 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. +func sortByFreq(data []literalNode) { + n := len(data) + quickSortByFreq(data, 0, n, maxDepth(n)) +} + +func quickSortByFreq(data []literalNode, a, b, maxDepth int) { + for b-a > 12 { // Use ShellSort for slices <= 12 elements + if maxDepth == 0 { + heapSort(data, a, b) + return + } + maxDepth-- + mlo, mhi := doPivotByFreq(data, a, b) + // Avoiding recursion on the larger subproblem guarantees + // a stack depth of at most lg(b-a). + if mlo-a < b-mhi { + quickSortByFreq(data, a, mlo, maxDepth) + a = mhi // i.e., quickSortByFreq(data, mhi, b) + } else { + quickSortByFreq(data, mhi, b, maxDepth) + b = mlo // i.e., quickSortByFreq(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].freq == data[i-6].freq && data[i].literal < data[i-6].literal || data[i].freq < data[i-6].freq { + data[i], data[i-6] = data[i-6], data[i] + } + } + insertionSortByFreq(data, a, b) + } +} + +// siftDownByFreq implements the heap property on data[lo, hi). +// first is an offset into the array where the root of the heap lies. +func siftDownByFreq(data []literalNode, lo, hi, first int) { + root := lo + for { + child := 2*root + 1 + if child >= hi { + break + } + if child+1 < hi && (data[first+child].freq == data[first+child+1].freq && data[first+child].literal < data[first+child+1].literal || data[first+child].freq < data[first+child+1].freq) { + child++ + } + if data[first+root].freq == data[first+child].freq && data[first+root].literal > data[first+child].literal || data[first+root].freq > data[first+child].freq { + return + } + data[first+root], data[first+child] = data[first+child], data[first+root] + root = child + } +} +func doPivotByFreq(data []literalNode, 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 + medianOfThreeSortByFreq(data, lo, lo+s, lo+2*s) + medianOfThreeSortByFreq(data, m, m-s, m+s) + medianOfThreeSortByFreq(data, hi-1, hi-1-s, hi-1-2*s) + } + medianOfThreeSortByFreq(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].freq == data[pivot].freq && data[a].literal < data[pivot].literal || data[a].freq < data[pivot].freq); a++ { + } + b := a + for { + for ; b < c && (data[pivot].freq == data[b].freq && data[pivot].literal > data[b].literal || data[pivot].freq > data[b].freq); b++ { // data[b] <= pivot + } + for ; b < c && (data[pivot].freq == data[c-1].freq && data[pivot].literal < data[c-1].literal || data[pivot].freq < data[c-1].freq); 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].freq == data[hi-1].freq && data[pivot].literal > data[hi-1].literal || data[pivot].freq > data[hi-1].freq { // data[hi-1] = pivot + data[c], data[hi-1] = data[hi-1], data[c] + c++ + dups++ + } + if data[b-1].freq == data[pivot].freq && data[b-1].literal > data[pivot].literal || data[b-1].freq > data[pivot].freq { // 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].freq == data[pivot].freq && data[m].literal > data[pivot].literal || data[m].freq > data[pivot].freq { // 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].freq == data[pivot].freq && data[b-1].literal > data[pivot].literal || data[b-1].freq > data[pivot].freq); b-- { // data[b] == pivot + } + for ; a < b && (data[a].freq == data[pivot].freq && data[a].literal < data[pivot].literal || data[a].freq < data[pivot].freq); 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 +} + +// Insertion sort +func insertionSortByFreq(data []literalNode, a, b int) { + for i := a + 1; i < b; i++ { + for j := i; j > a && (data[j].freq == data[j-1].freq && data[j].literal < data[j-1].literal || data[j].freq < data[j-1].freq); j-- { + data[j], data[j-1] = data[j-1], data[j] + } + } +} + +// quickSortByFreq, loosely following Bentley and McIlroy, +// ``Engineering a Sort Function,'' SP&E November 1993. + +// medianOfThreeSortByFreq moves the median of the three values data[m0], data[m1], data[m2] into data[m1]. +func medianOfThreeSortByFreq(data []literalNode, m1, m0, m2 int) { + // sort 3 elements + if data[m1].freq == data[m0].freq && data[m1].literal < data[m0].literal || data[m1].freq < data[m0].freq { + data[m1], data[m0] = data[m0], data[m1] + } + // data[m0] <= data[m1] + if data[m2].freq == data[m1].freq && data[m2].literal < data[m1].literal || data[m2].freq < data[m1].freq { + data[m2], data[m1] = data[m1], data[m2] + // data[m0] <= data[m2] && data[m1] < data[m2] + if data[m1].freq == data[m0].freq && data[m1].literal < data[m0].literal || data[m1].freq < data[m0].freq { + data[m1], data[m0] = data[m0], data[m1] + } + } + // now data[m0] <= data[m1] <= data[m2] +} diff --git a/flate/huffman_sortByLiteral.go b/flate/huffman_sortByLiteral.go new file mode 100644 index 0000000000..93f1aea109 --- /dev/null +++ b/flate/huffman_sortByLiteral.go @@ -0,0 +1,201 @@ +// 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 flate + +// Sort sorts data. +// 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. +func sortByLiteral(data []literalNode) { + n := len(data) + quickSort(data, 0, n, maxDepth(n)) +} + +func quickSort(data []literalNode, a, b, maxDepth int) { + for b-a > 12 { // Use ShellSort for slices <= 12 elements + if maxDepth == 0 { + heapSort(data, a, b) + return + } + maxDepth-- + mlo, mhi := doPivot(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(data, a, mlo, maxDepth) + a = mhi // i.e., quickSort(data, mhi, b) + } else { + quickSort(data, mhi, b, maxDepth) + b = mlo // i.e., quickSort(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].literal < data[i-6].literal { + data[i], data[i-6] = data[i-6], data[i] + } + } + insertionSort(data, a, b) + } +} +func heapSort(data []literalNode, 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[first], data[first+i] = data[first+i], data[first] + siftDown(data, lo, i, first) + } +} + +// 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 []literalNode, lo, hi, first int) { + root := lo + for { + child := 2*root + 1 + if child >= hi { + break + } + if child+1 < hi && data[first+child].literal < data[first+child+1].literal { + child++ + } + if data[first+root].literal > data[first+child].literal { + return + } + data[first+root], data[first+child] = data[first+child], data[first+root] + root = child + } +} +func doPivot(data []literalNode, 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(data, lo, lo+s, lo+2*s) + medianOfThree(data, m, m-s, m+s) + medianOfThree(data, hi-1, hi-1-s, hi-1-2*s) + } + medianOfThree(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].literal < data[pivot].literal; a++ { + } + b := a + for { + for ; b < c && data[pivot].literal > data[b].literal; b++ { // data[b] <= pivot + } + for ; b < c && data[pivot].literal < data[c-1].literal; 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].literal > data[hi-1].literal { // data[hi-1] = pivot + data[c], data[hi-1] = data[hi-1], data[c] + c++ + dups++ + } + if data[b-1].literal > data[pivot].literal { // 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].literal > data[pivot].literal { // 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].literal > data[pivot].literal; b-- { // data[b] == pivot + } + for ; a < b && data[a].literal < data[pivot].literal; 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 +} + +// Insertion sort +func insertionSort(data []literalNode, a, b int) { + for i := a + 1; i < b; i++ { + for j := i; j > a && data[j].literal < data[j-1].literal; j-- { + data[j], data[j-1] = data[j-1], data[j] + } + } +} + +// maxDepth returns a threshold at which quicksort should switch +// to heapsort. It returns 2*ceil(lg(n+1)). +func maxDepth(n int) int { + var depth int + for i := n; i > 0; i >>= 1 { + depth++ + } + return depth * 2 +} + +// medianOfThree moves the median of the three values data[m0], data[m1], data[m2] into data[m1]. +func medianOfThree(data []literalNode, m1, m0, m2 int) { + // sort 3 elements + if data[m1].literal < data[m0].literal { + data[m1], data[m0] = data[m0], data[m1] + } + // data[m0] <= data[m1] + if data[m2].literal < data[m1].literal { + data[m2], data[m1] = data[m1], data[m2] + // data[m0] <= data[m2] && data[m1] < data[m2] + if data[m1].literal < data[m0].literal { + data[m1], data[m0] = data[m0], data[m1] + } + } + // now data[m0] <= data[m1] <= data[m2] +}