suffixarray: faster creation algorithm

This implements the algorithm qsufsort using the sort package
as a sorting primitive. Its worst-case performance is O(N*log(N)), and it
uses only an additional slice of N ints of memory during creation.

Benchmarks (seconds):
           old    new
10k nulls          149    0.044
1M English corpus  32.0   3.6

R=gri, gri1
CC=golang-dev
https://golang.org/cl/3752044

src/pkg/index/suffixarray/Makefile

@@ -6,6 +6,7 @@ include ../../../Make.inc
 
 TARG=index/suffixarray
 GOFILES=\
+	qsufsort.go\
 	suffixarray.go\
 
 include ../../../Make.pkg

src/pkg/index/suffixarray/qsufsort.go

@@ -0,0 +1,164 @@
+// 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.
+
+// This algorithm is based on "Faster Suffix Sorting"
+//   by N. Jesper Larsson and Kunihiko Sadakane
+// paper: http://www.larsson.dogma.net/ssrev-tr.pdf
+// code:  http://www.larsson.dogma.net/qsufsort.c
+
+// This algorithm computes the suffix array sa by computing its inverse.
+// Consecutive groups of suffixes in sa are labeled as sorted groups or
+// unsorted groups. For a given pass of the sorter, all suffixes are ordered
+// up to their first h characters, and sa is h-ordered. Suffixes in their
+// final positions and unambiguouly sorted in h-order are in a sorted group.
+// Consecutive groups of suffixes with identical first h characters are an
+// unsorted group. In each pass of the algorithm, unsorted groups are sorted
+// according to the group number of their following suffix.
+
+// In the implementation, if sa[i] is negative, it indicates that i is
+// the first element of a sorted group of length -sa[i], and can be skipped.
+// An unsorted group sa[i:k] is given the group number of the index of its
+// last element, k-1. The group numbers are stored in the inverse slice (inv),
+// and when all groups are sorted, this slice is the inverse suffix array.
+
+package suffixarray
+
+import "sort"
+
+func qsufsort(data []byte) []int {
+	// initial sorting by first byte of suffix
+	sa := sortedByFirstByte(data)
+	if len(sa) < 2 {
+		return sa
+	}
+	// initialize the group lookup table
+	// this becomes the inverse of the suffix array when all groups are sorted
+	inv := initGroups(sa, data)
+
+	// the index starts 1-ordered
+	sufSortable := &suffixSortable{sa, inv, 1}
+
+	for sa[0] > -len(sa) { // until all suffixes are one big sorted group
+		// The suffixes are h-ordered, make them 2*h-ordered
+		pi := 0 // pi is first position of first group
+		sl := 0 // sl is negated length of sorted groups
+		for pi < len(sa) {
+			if s := sa[pi]; s < 0 { // if pi starts sorted group
+				pi -= s // skip over sorted group
+				sl += s // add negated length to sl
+			} else { // if pi starts unsorted group
+				if sl != 0 {
+					sa[pi+sl] = sl // combine sorted groups before pi
+					sl = 0
+				}
+				pk := inv[s] + 1 // pk-1 is last position of unsorted group
+				sufSortable.sa = sa[pi:pk]
+				sort.Sort(sufSortable)
+				sufSortable.updateGroups(pi)
+				pi = pk // next group
+			}
+		}
+		if sl != 0 { // if the array ends with a sorted group
+			sa[pi+sl] = sl // combine sorted groups at end of sa
+		}
+
+		sufSortable.h *= 2 // double sorted depth
+	}
+
+	for i := range sa { // reconstruct suffix array from inverse
+		sa[inv[i]] = i
+	}
+	return sa
+}
+
+
+func sortedByFirstByte(data []byte) []int {
+	// total byte counts
+	var count [256]int
+	for _, b := range data {
+		count[b]++
+	}
+	// make count[b] equal index of first occurence of b in sorted array
+	sum := 0
+	for b := range count {
+		count[b], sum = sum, count[b]+sum
+	}
+	// iterate through bytes, placing index into the correct spot in sa
+	sa := make([]int, len(data))
+	for i, b := range data {
+		sa[count[b]] = i
+		count[b]++
+	}
+	return sa
+}
+
+
+func initGroups(sa []int, data []byte) []int {
+	// label contiguous same-letter groups with the same group number
+	inv := make([]int, len(data))
+	prevGroup := len(sa) - 1
+	groupByte := data[sa[prevGroup]]
+	for i := len(sa) - 1; i >= 0; i-- {
+		if b := data[sa[i]]; b < groupByte {
+			if prevGroup == i+1 {
+				sa[i+1] = -1
+			}
+			groupByte = b
+			prevGroup = i
+		}
+		inv[sa[i]] = prevGroup
+		if prevGroup == 0 {
+			sa[0] = -1
+		}
+	}
+	// Separate out the final suffix to the start of its group.
+	// This is necessary to ensure the suffix "a" is before "aba"
+	// when using a potentially unstable sort.
+	lastByte := data[len(data)-1]
+	s := -1
+	for i := range sa {
+		if sa[i] >= 0 {
+			if data[sa[i]] == lastByte && s == -1 {
+				s = i
+			}
+			if sa[i] == len(sa)-1 {
+				sa[i], sa[s] = sa[s], sa[i]
+				inv[sa[s]] = s
+				sa[s] = -1 // mark it as an isolated sorted group
+				break
+			}
+		}
+	}
+	return inv
+}
+
+
+type suffixSortable struct {
+	sa  []int
+	inv []int
+	h   int
+}
+
+func (x *suffixSortable) Len() int           { return len(x.sa) }
+func (x *suffixSortable) Less(i, j int) bool { return x.inv[x.sa[i]+x.h] < x.inv[x.sa[j]+x.h] }
+func (x *suffixSortable) Swap(i, j int)      { x.sa[i], x.sa[j] = x.sa[j], x.sa[i] }
+
+
+func (x *suffixSortable) updateGroups(offset int) {
+	prev := len(x.sa) - 1
+	group := x.inv[x.sa[prev]+x.h]
+	for i := prev; i >= 0; i-- {
+		if g := x.inv[x.sa[i]+x.h]; g < group {
+			if prev == i+1 { // previous group had size 1 and is thus sorted
+				x.sa[i+1] = -1
+			}
+			group = g
+			prev = i
+		}
+		x.inv[x.sa[i]] = prev + offset
+		if prev == 0 { // first group has size 1 and is thus sorted
+			x.sa[0] = -1
+		}
+	}
+}

src/pkg/index/suffixarray/suffixarray.go

@@ -22,11 +22,6 @@ import (
 	"sort"
 )
 
-// BUG(gri): For larger data (10MB) which contains very long (say 100000)
-// contiguous sequences of identical bytes, index creation time will be extremely slow.
-
-// TODO(gri): Use a more sophisticated algorithm to create the suffix array.
-
 
 // Index implements a suffix array for fast substring search.
 type Index struct {
@@ -36,16 +31,9 @@ type Index struct {
 
 
 // New creates a new Index for data.
-// Index creation time is approximately O(N*log(N)) for N = len(data).
-//
+// Index creation time is O(N*log(N)) for N = len(data).
 func New(data []byte) *Index {
-	sa := make([]int, len(data))
-	for i := range sa {
-		sa[i] = i
-	}
-	x := &Index{data, sa}
-	sort.Sort((*index)(x))
-	return x
+	return &Index{data, qsufsort(data)}
 }
 
 
@@ -192,12 +180,3 @@ func (x *Index) FindAllIndex(r *regexp.Regexp, n int) (result [][]int) {
 	}
 	return
 }
-
-
-// index is used to hide the sort.Interface
-type index Index
-
-func (x *index) Len() int           { return len(x.sa) }
-func (x *index) Less(i, j int) bool { return bytes.Compare(x.at(i), x.at(j)) < 0 }
-func (x *index) Swap(i, j int)      { x.sa[i], x.sa[j] = x.sa[j], x.sa[i] }
-func (a *index) at(i int) []byte    { return a.data[a.sa[i]:] }

src/pkg/index/suffixarray/suffixarray_test.go

@@ -5,6 +5,7 @@
 package suffixarray
 
 import (
+	"bytes"
 	"container/vector"
 	"regexp"
 	"sort"
@@ -204,9 +205,26 @@ func testLookups(t *testing.T, tc *testCase, x *Index, n int) {
 }
 
 
+// index is used to hide the sort.Interface
+type index Index
+
+func (x *index) Len() int           { return len(x.sa) }
+func (x *index) Less(i, j int) bool { return bytes.Compare(x.at(i), x.at(j)) < 0 }
+func (x *index) Swap(i, j int)      { x.sa[i], x.sa[j] = x.sa[j], x.sa[i] }
+func (a *index) at(i int) []byte    { return a.data[a.sa[i]:] }
+
+
+func testConstruction(t *testing.T, tc *testCase, x *Index) {
+	if !sort.IsSorted((*index)(x)) {
+		t.Errorf("testConstruction failed %s", tc.name)
+	}
+}
+
+
 func TestIndex(t *testing.T) {
 	for _, tc := range testCases {
 		x := New([]byte(tc.source))
+		testConstruction(t, &tc, x)
 		testLookups(t, &tc, x, 0)
 		testLookups(t, &tc, x, 1)
 		testLookups(t, &tc, x, 10)