Skip to content

G
go
Commit 6ca324f2 authored by Russ Cox's avatar Russ Cox
Browse files
Options

index/suffixarray: index 3-10X faster in half the memory 

This CL changes the index/suffixarray construction algorithm from QSufSort to SAIS.

For an N-byte input, QSufSort runs in O(N log N) time and requires
an N-int temporary work space in addition to the N-int output.

In contrast, SAIS runs in O(N) time and, for essentially all real inputs,
is able to use the N-int output buffer as its temporary work space.
(In pathological cases, SAIS must allocate a temporary work space of
at most N/2 ints. There exist more complex variants that guarantee
to avoid the work space in all cases, but they hardly seem worth the cost
given how rare these pathological cases are.)

The SAIS code therefore uses 50% of the memory across the board.
It also runs 3-10X faster on real input text.

This CL also adds more extensive algorithmic tests, including an
exhaustive test over small inputs to catch corner case problems.

name                                   old speed      new speed        delta
New/text=opticks/size=100K/bits=32-12  6.15MB/s ± 1%   26.79MB/s ± 1%   +335.89%  (p=0.008 n=5+5)
New/text=opticks/size=100K/bits=64-12  5.90MB/s ± 2%   27.29MB/s ± 2%   +362.23%  (p=0.008 n=5+5)
New/text=opticks/size=500K/bits=32-12  4.99MB/s ± 3%   25.37MB/s ± 2%   +408.01%  (p=0.008 n=5+5)
New/text=opticks/size=500K/bits=64-12  4.88MB/s ± 1%   25.66MB/s ± 4%   +425.52%  (p=0.008 n=5+5)
New/text=go/size=100K/bits=32-12       5.81MB/s ± 1%   26.49MB/s ± 2%   +355.85%  (p=0.008 n=5+5)
New/text=go/size=100K/bits=64-12       5.76MB/s ± 2%   26.65MB/s ± 3%   +362.60%  (p=0.008 n=5+5)
New/text=go/size=500K/bits=32-12       4.91MB/s ± 1%   25.12MB/s ± 2%   +411.86%  (p=0.008 n=5+5)
New/text=go/size=500K/bits=64-12       4.83MB/s ± 2%   25.79MB/s ± 2%   +434.44%  (p=0.008 n=5+5)
New/text=go/size=1M/bits=32-12         4.62MB/s ± 2%   24.87MB/s ± 2%   +438.78%  (p=0.008 n=5+5)
New/text=go/size=1M/bits=64-12         4.39MB/s ± 2%   24.61MB/s ± 2%   +460.68%  (p=0.008 n=5+5)
New/text=go/size=5M/bits=32-12         2.85MB/s ± 2%   24.78MB/s ± 7%   +768.33%  (p=0.008 n=5+5)
New/text=go/size=5M/bits=64-12         2.28MB/s ± 1%   18.70MB/s ± 7%   +719.63%  (p=0.008 n=5+5)
New/text=go/size=10M/bits=32-12        2.08MB/s ± 1%   21.04MB/s ± 6%   +909.60%  (p=0.008 n=5+5)
New/text=go/size=10M/bits=64-12        1.83MB/s ± 1%   16.64MB/s ± 2%   +809.18%  (p=0.008 n=5+5)
New/text=go/size=50M/bits=32-12        1.51MB/s ± 0%   10.58MB/s ± 1%   +602.52%  (p=0.008 n=5+5)
New/text=go/size=50M/bits=64-12        1.34MB/s ± 4%    9.00MB/s ± 1%   +569.35%  (p=0.008 n=5+5)
New/text=zero/size=100K/bits=32-12     4.17MB/s ± 0%  157.56MB/s ± 1%  +3678.42%  (p=0.016 n=4+5)
New/text=zero/size=100K/bits=64-12     4.19MB/s ± 2%  162.72MB/s ± 2%  +3783.63%  (p=0.008 n=5+5)
New/text=zero/size=500K/bits=32-12     3.72MB/s ± 5%  159.17MB/s ± 1%  +4176.57%  (p=0.008 n=5+5)
New/text=zero/size=500K/bits=64-12     3.77MB/s ± 3%  164.95MB/s ± 4%  +4277.60%  (p=0.008 n=5+5)
New/text=zero/size=1M/bits=32-12       3.46MB/s ± 3%  158.42MB/s ± 1%  +4476.08%  (p=0.008 n=5+5)
New/text=zero/size=1M/bits=64-12       3.41MB/s ± 4%  163.70MB/s ± 2%  +4700.65%  (p=0.008 n=5+5)
New/text=zero/size=5M/bits=32-12       3.12MB/s ± 2%  151.92MB/s ± 4%  +4775.48%  (p=0.008 n=5+5)
New/text=zero/size=5M/bits=64-12       3.09MB/s ± 2%  166.19MB/s ± 2%  +5274.84%  (p=0.008 n=5+5)
New/text=zero/size=10M/bits=32-12      2.97MB/s ± 1%  157.75MB/s ± 1%  +5211.38%  (p=0.008 n=5+5)
New/text=zero/size=10M/bits=64-12      2.92MB/s ± 1%  162.75MB/s ± 2%  +5473.77%  (p=0.008 n=5+5)
New/text=zero/size=50M/bits=32-12      2.67MB/s ± 1%  144.43MB/s ± 5%  +5305.39%  (p=0.008 n=5+5)
New/text=zero/size=50M/bits=64-12      2.61MB/s ± 1%  125.19MB/s ± 2%  +4700.33%  (p=0.016 n=5+4)
New/text=rand/size=100K/bits=32-12     8.69MB/s ± 6%   27.60MB/s ± 1%   +217.73%  (p=0.008 n=5+5)
New/text=rand/size=100K/bits=64-12     8.92MB/s ± 1%   26.37MB/s ± 4%   +195.50%  (p=0.008 n=5+5)
New/text=rand/size=500K/bits=32-12     7.11MB/s ± 2%   25.23MB/s ± 2%   +254.78%  (p=0.008 n=5+5)
New/text=rand/size=500K/bits=64-12     7.08MB/s ± 1%   25.45MB/s ± 2%   +259.56%  (p=0.008 n=5+5)
New/text=rand/size=1M/bits=32-12       6.45MB/s ± 2%   24.47MB/s ± 3%   +279.11%  (p=0.008 n=5+5)
New/text=rand/size=1M/bits=64-12       6.09MB/s ± 4%   23.00MB/s ± 4%   +277.85%  (p=0.008 n=5+5)
New/text=rand/size=5M/bits=32-12       3.68MB/s ± 3%   10.34MB/s ± 5%   +181.08%  (p=0.008 n=5+5)
New/text=rand/size=5M/bits=64-12       3.25MB/s ± 1%    6.23MB/s ± 1%    +91.93%  (p=0.008 n=5+5)
New/text=rand/size=10M/bits=32-12      3.03MB/s ± 1%    5.61MB/s ± 2%    +85.28%  (p=0.008 n=5+5)
New/text=rand/size=10M/bits=64-12      2.80MB/s ± 1%    4.29MB/s ± 2%    +53.40%  (p=0.008 n=5+5)
New/text=rand/size=50M/bits=32-12      2.11MB/s ± 0%    2.45MB/s ± 1%    +16.23%  (p=0.029 n=4+4)
New/text=rand/size=50M/bits=64-12      2.04MB/s ± 1%    2.24MB/s ± 1%    +10.03%  (p=0.016 n=5+4)
SaveRestore/bits=32-12                  327MB/s ± 5%     319MB/s ± 2%       ~     (p=0.310 n=5+5)
SaveRestore/bits=64-12                  306MB/s ± 3%     306MB/s ± 2%       ~     (p=0.841 n=5+5)

name                                   old alloc/op   new alloc/op     delta
New/text=opticks/size=100K/bits=32-12     811kB ± 0%       401kB ± 0%    -50.51%  (p=0.008 n=5+5)
New/text=opticks/size=100K/bits=64-12    1.62MB ± 0%      0.80MB ± 0%    -50.51%  (p=0.008 n=5+5)
New/text=opticks/size=500K/bits=32-12    4.04MB ± 0%      2.01MB ± 0%    -50.37%  (p=0.008 n=5+5)
New/text=opticks/size=500K/bits=64-12    8.07MB ± 0%      4.01MB ± 0%    -50.36%  (p=0.016 n=4+5)
New/text=go/size=100K/bits=32-12          811kB ± 0%       401kB ± 0%       ~     (p=0.079 n=4+5)
New/text=go/size=100K/bits=64-12         1.62MB ± 0%      0.80MB ± 0%    -50.50%  (p=0.008 n=5+5)
New/text=go/size=500K/bits=32-12         4.04MB ± 0%      2.01MB ± 0%       ~     (p=0.079 n=4+5)
New/text=go/size=500K/bits=64-12         8.07MB ± 0%      4.01MB ± 0%    -50.36%  (p=0.000 n=4+5)
New/text=go/size=1M/bits=32-12           8.07MB ± 0%      4.01MB ± 0%    -50.36%  (p=0.008 n=5+5)
New/text=go/size=1M/bits=64-12           16.1MB ± 0%       8.0MB ± 0%    -50.36%  (p=0.008 n=5+5)
New/text=go/size=5M/bits=32-12           40.2MB ± 0%      20.0MB ± 0%    -50.18%  (p=0.008 n=5+5)
New/text=go/size=5M/bits=64-12           80.3MB ± 0%      40.0MB ± 0%    -50.18%  (p=0.008 n=5+5)
New/text=go/size=10M/bits=32-12          80.2MB ± 0%      40.0MB ± 0%    -50.09%  (p=0.000 n=5+4)
New/text=go/size=10M/bits=64-12           160MB ± 0%        80MB ± 0%    -50.09%  (p=0.000 n=5+4)
New/text=go/size=50M/bits=32-12           402MB ± 0%       200MB ± 0%    -50.29%  (p=0.000 n=5+4)
New/text=go/size=50M/bits=64-12           805MB ± 0%       400MB ± 0%    -50.29%  (p=0.000 n=5+4)
New/text=zero/size=100K/bits=32-12       1.46MB ± 0%      0.40MB ± 0%    -72.46%  (p=0.008 n=5+5)
New/text=zero/size=100K/bits=64-12       3.02MB ± 0%      0.80MB ± 0%    -73.45%  (p=0.008 n=5+5)
New/text=zero/size=500K/bits=32-12       8.66MB ± 0%      2.01MB ± 0%       ~     (p=0.079 n=4+5)
New/text=zero/size=500K/bits=64-12       19.7MB ± 0%       4.0MB ± 0%    -79.63%  (p=0.008 n=5+5)
New/text=zero/size=1M/bits=32-12         19.7MB ± 0%       4.0MB ± 0%       ~     (p=0.079 n=4+5)
New/text=zero/size=1M/bits=64-12         39.0MB ± 0%       8.0MB ± 0%    -79.48%  (p=0.000 n=5+4)
New/text=zero/size=5M/bits=32-12         85.2MB ± 0%      20.0MB ± 0%    -76.52%  (p=0.008 n=5+5)
New/text=zero/size=5M/bits=64-12          169MB ± 0%        40MB ± 0%    -76.27%  (p=0.008 n=5+5)
New/text=zero/size=10M/bits=32-12         169MB ± 0%        40MB ± 0%    -76.26%  (p=0.000 n=5+4)
New/text=zero/size=10M/bits=64-12         333MB ± 0%        80MB ± 0%    -75.99%  (p=0.008 n=5+5)
New/text=zero/size=50M/bits=32-12         739MB ± 0%       200MB ± 0%    -72.93%  (p=0.000 n=4+5)
New/text=zero/size=50M/bits=64-12        1.63GB ± 0%      0.40GB ± 0%    -75.42%  (p=0.008 n=5+5)
New/text=rand/size=100K/bits=32-12        807kB ± 0%       401kB ± 0%    -50.25%  (p=0.008 n=5+5)
New/text=rand/size=100K/bits=64-12       1.61MB ± 0%      0.80MB ± 0%    -50.25%  (p=0.008 n=5+5)
New/text=rand/size=500K/bits=32-12       4.04MB ± 0%      2.01MB ± 0%       ~     (p=0.079 n=4+5)
New/text=rand/size=500K/bits=64-12       8.07MB ± 0%      4.01MB ± 0%       ~     (p=0.079 n=4+5)
New/text=rand/size=1M/bits=32-12         8.07MB ± 0%      4.01MB ± 0%    -50.36%  (p=0.000 n=5+4)
New/text=rand/size=1M/bits=64-12         16.1MB ± 0%       8.0MB ± 0%    -50.36%  (p=0.008 n=5+5)
New/text=rand/size=5M/bits=32-12         40.3MB ± 0%      20.0MB ± 0%    -50.35%  (p=0.029 n=4+4)
New/text=rand/size=5M/bits=64-12         80.7MB ± 0%      40.0MB ± 0%       ~     (p=0.079 n=4+5)
New/text=rand/size=10M/bits=32-12        80.7MB ± 0%      40.0MB ± 0%    -50.41%  (p=0.008 n=5+5)
New/text=rand/size=10M/bits=64-12         161MB ± 0%        80MB ± 0%    -50.44%  (p=0.029 n=4+4)
New/text=rand/size=50M/bits=32-12         403MB ± 0%       200MB ± 0%    -50.36%  (p=0.000 n=5+4)
New/text=rand/size=50M/bits=64-12         806MB ± 0%       400MB ± 0%       ~     (p=0.079 n=4+5)
SaveRestore/bits=32-12                   5.28MB ± 0%      5.28MB ± 0%       ~     (p=1.000 n=5+5)
SaveRestore/bits=64-12                   9.47MB ± 0%      9.47MB ± 0%       ~     (p=0.286 n=5+5)

https://perf.golang.org/search?q=upload:20190426.1

Fixes #15480.

Change-Id: I0790f6edf67f5a9c02b4462632b4942e0c37988b
Reviewed-on: https://go-review.googlesource.com/c/go/+/174100
Run-TryBot: Russ Cox <rsc@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: default avatarEric Roshan-Eisner <edre@google.com>
Reviewed-by: default avatarBrad Fitzpatrick <bradfitz@golang.org>
parent 7a43f8a5
Show whitespace changes
Inline Side-by-side
Showing with 2889 additions and 377 deletions
src/index/suffixarray/gen.go 0 → 100644
View file @ 6ca324f2
// Copyright 2019 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.
// +build ignore
// Gen generates sais2.go by duplicating functions in sais.go
// using different input types.
// See the comment at the top of sais.go for details.
package main
import (
"bytes"
"io/ioutil"
"log"
"strings"
)
func main() {
log.SetPrefix("gen: ")
log.SetFlags(0)
data, err := ioutil.ReadFile("sais.go")
if err != nil {
log.Fatal(err)
}
x := bytes.Index(data, []byte("\n\n"))
if x < 0 {
log.Fatal("cannot find blank line after copyright comment")
}
var buf bytes.Buffer
buf.Write(data[:x])
buf.WriteString("\n\n// Code generated by go generate; DO NOT EDIT.\n\npackage suffixarray\n")
for {
x := bytes.Index(data, []byte("\nfunc "))
if x < 0 {
break
}
data = data[x:]
p := bytes.IndexByte(data, '(')
if p < 0 {
p = len(data)
}
name := string(data[len("\nfunc "):p])
x = bytes.Index(data, []byte("\n}\n"))
if x < 0 {
log.Fatalf("cannot find end of func %s", name)
}
fn := string(data[:x+len("\n}\n")])
data = data[x+len("\n}"):]
if strings.HasSuffix(name, "_32") {
buf.WriteString(fix32.Replace(fn))
}
if strings.HasSuffix(name, "_8_32") {
// x_8_32 -> x_8_64 done above
fn = fix8_32.Replace(stripByteOnly(fn))
buf.WriteString(fn)
buf.WriteString(fix32.Replace(fn))
}
}
if err := ioutil.WriteFile("sais2.go", buf.Bytes(), 0666); err != nil {
log.Fatal(err)
}
}
var fix32 = strings.NewReplacer(
"32", "64",
"int32", "int64",
)
var fix8_32 = strings.NewReplacer(
"_8_32", "_32",
"byte", "int32",
)
func stripByteOnly(s string) string {
lines := strings.SplitAfter(s, "\n")
w := 0
for _, line := range lines {
if !strings.Contains(line, "256") && !strings.Contains(line, "byte-only") {
lines[w] = line
w++
}
}
return strings.Join(lines[:w], "")
}
src/index/suffixarray/gen64.go deleted 100644 → 0
View file @ 7a43f8a5
// Copyright 2019 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.
// +build ignore
// Gen64 generates qsufsort64.go from qsufsort.go by s/32/64/g.
package main
import (
"bytes"
"io/ioutil"
"log"
)
func main() {
log.SetPrefix("gen64: ")
log.SetFlags(0)
data, err := ioutil.ReadFile("qsufsort.go")
if err != nil {
log.Fatal(err)
}
data = bytes.Replace(data, []byte("\n\n"), []byte("\n\n// Code generated by gen64.go; DO NOT EDIT.\n//go:generate go run gen64.go\n\n"), 1)
data = bytes.Replace(data, []byte("32"), []byte("64"), -1)
if err := ioutil.WriteFile("qsufsort64.go", data, 0666); err != nil {
log.Fatal(err)
}
}
src/index/suffixarray/qsufsort.go deleted 100644 → 0
View file @ 7a43f8a5
// 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 unambiguously 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 qsufsort32(data []byte) []int32 {
// initial sorting by first byte of suffix
sa := sortedByFirstByte32(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 := initGroups32(sa, data)
// the index starts 1-ordered
sufSortable := &suffixSortable32{sa: sa, inv: inv, h: 1}
for sa[0] > -int32(len(sa)) { // until all suffixes are one big sorted group
// The suffixes are h-ordered, make them 2*h-ordered
pi := int32(0) // pi is first position of first group
sl := int32(0) // sl is negated length of sorted groups
for pi < int32(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]] = int32(i)
}
return sa
}
func sortedByFirstByte32(data []byte) []int32 {
// total byte counts
var count [256]int
for _, b := range data {
count[b]++
}
// make count[b] equal index of first occurrence 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([]int32, len(data))
for i, b := range data {
sa[count[b]] = int32(i)
count[b]++
}
return sa
}
func initGroups32(sa []int32, data []byte) []int32 {
// label contiguous same-letter groups with the same group number
inv := make([]int32, len(data))
prevGroup := int32(len(sa)) - 1
groupByte := data[sa[prevGroup]]
for i := int32(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 := int32(-1)
for i := range sa {
if sa[i] >= 0 {
if data[sa[i]] == lastByte && s == -1 {
s = int32(i)
}
if sa[i] == int32(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 suffixSortable32 struct {
sa []int32
inv []int32
h int32
buf []int32 // common scratch space
}
func (x *suffixSortable32) Len() int { return len(x.sa) }
func (x *suffixSortable32) Less(i, j int) bool { return x.inv[x.sa[i]+x.h] < x.inv[x.sa[j]+x.h] }
func (x *suffixSortable32) Swap(i, j int) { x.sa[i], x.sa[j] = x.sa[j], x.sa[i] }
func (x *suffixSortable32) updateGroups(offset int32) {
bounds := x.buf[0:0]
group := x.inv[x.sa[0]+x.h]
for i := 1; i < len(x.sa); i++ {
if g := x.inv[x.sa[i]+x.h]; g > group {
bounds = append(bounds, int32(i))
group = g
}
}
bounds = append(bounds, int32(len(x.sa)))
x.buf = bounds
// update the group numberings after all new groups are determined
prev := int32(0)
for _, b := range bounds {
for i := prev; i < b; i++ {
x.inv[x.sa[i]] = offset + b - 1
}
if b-prev == 1 {
x.sa[prev] = -1
}
prev = b
}
}
src/index/suffixarray/qsufsort64.go deleted 100644 → 0
View file @ 7a43f8a5
// 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.
// Code generated by gen64.go; DO NOT EDIT.
//go:generate go run gen64.go
// 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 unambiguously 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 qsufsort64(data []byte) []int64 {
// initial sorting by first byte of suffix
sa := sortedByFirstByte64(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 := initGroups64(sa, data)
// the index starts 1-ordered
sufSortable := &suffixSortable64{sa: sa, inv: inv, h: 1}
for sa[0] > -int64(len(sa)) { // until all suffixes are one big sorted group
// The suffixes are h-ordered, make them 2*h-ordered
pi := int64(0) // pi is first position of first group
sl := int64(0) // sl is negated length of sorted groups
for pi < int64(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]] = int64(i)
}
return sa
}
func sortedByFirstByte64(data []byte) []int64 {
// total byte counts
var count [256]int
for _, b := range data {
count[b]++
}
// make count[b] equal index of first occurrence 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([]int64, len(data))
for i, b := range data {
sa[count[b]] = int64(i)
count[b]++
}
return sa
}
func initGroups64(sa []int64, data []byte) []int64 {
// label contiguous same-letter groups with the same group number
inv := make([]int64, len(data))
prevGroup := int64(len(sa)) - 1
groupByte := data[sa[prevGroup]]
for i := int64(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 := int64(-1)
for i := range sa {
if sa[i] >= 0 {
if data[sa[i]] == lastByte && s == -1 {
s = int64(i)
}
if sa[i] == int64(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 suffixSortable64 struct {
sa []int64
inv []int64
h int64
buf []int64 // common scratch space
}
func (x *suffixSortable64) Len() int { return len(x.sa) }
func (x *suffixSortable64) Less(i, j int) bool { return x.inv[x.sa[i]+x.h] < x.inv[x.sa[j]+x.h] }
func (x *suffixSortable64) Swap(i, j int) { x.sa[i], x.sa[j] = x.sa[j], x.sa[i] }
func (x *suffixSortable64) updateGroups(offset int64) {
bounds := x.buf[0:0]
group := x.inv[x.sa[0]+x.h]
for i := 1; i < len(x.sa); i++ {
if g := x.inv[x.sa[i]+x.h]; g > group {
bounds = append(bounds, int64(i))
group = g
}
}
bounds = append(bounds, int64(len(x.sa)))
x.buf = bounds
// update the group numberings after all new groups are determined
prev := int64(0)
for _, b := range bounds {
for i := prev; i < b; i++ {
x.inv[x.sa[i]] = offset + b - 1
}
if b-prev == 1 {
x.sa[prev] = -1
}
prev = b
}
}
src/index/suffixarray/sais.go 0 → 100644
View file @ 6ca324f2
// Copyright 2019 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.
// Suffix array construction by induced sorting (SAIS).
// See Ge Nong, Sen Zhang, and Wai Hong Chen,
// "Two Efficient Algorithms for Linear Time Suffix Array Construction",
// especially section 3 (https://ieeexplore.ieee.org/document/5582081).
// See also http://zork.net/~st/jottings/sais.html.
//
// With optimizations inspired by Yuta Mori's sais-lite
// (https://sites.google.com/site/yuta256/sais).
//
// And with other new optimizations.
// Many of these functions are parameterized by the sizes of
// the types they operate on. The generator gen.go makes
// copies of these functions for use with other sizes.
// Specifically:
//
// - A function with a name ending in _8_32 takes []byte and []int32 arguments
// and is duplicated into _32_32, _8_64, and _64_64 forms.
// The _32_32 and _64_64_ suffixes are shortened to plain _32 and _64.
// Any lines in the function body that contain the text "byte-only" or "256"
// are stripped when creating _32_32 and _64_64 forms.
// (Those lines are typically 8-bit-specific optimizations.)
//
// - A function with a name ending only in _32 operates on []int32
// and is duplicated into a _64 form. (Note that it may still take a []byte,
// but there is no need for a version of the function in which the []byte
// is widened to a full integer array.)
// The overall runtime of this code is linear in the input size:
// it runs a sequence of linear passes to reduce the problem to
// a subproblem at most half as big, invokes itself recursively,
// and then runs a sequence of linear passes to turn the answer
// for the subproblem into the answer for the original problem.
// This gives T(N) = O(N) + T(N/2) = O(N) + O(N/2) + O(N/4) + ... = O(N).
//
// The outline of the code, with the forward and backward scans
// through O(N)-sized arrays called out, is:
//
// sais_I_N
// placeLMS_I_B
// bucketMax_I_B
// freq_I_B
// <scan +text> (1)
// <scan +freq> (2)
// <scan -text, random bucket> (3)
// induceSubL_I_B
// bucketMin_I_B
// freq_I_B
// <scan +text, often optimized away> (4)
// <scan +freq> (5)
// <scan +sa, random text, random bucket> (6)
// induceSubS_I_B
// bucketMax_I_B
// freq_I_B
// <scan +text, often optimized away> (7)
// <scan +freq> (8)
// <scan -sa, random text, random bucket> (9)
// assignID_I_B
// <scan +sa, random text substrings> (10)
// map_B
// <scan -sa> (11)
// recurse_B
// (recursive call to sais_B_B for a subproblem of size at most 1/2 input, often much smaller)
// unmap_I_B
// <scan -text> (12)
// <scan +sa> (13)
// expand_I_B
// bucketMax_I_B
// freq_I_B
// <scan +text, often optimized away> (14)
// <scan +freq> (15)
// <scan -sa, random text, random bucket> (16)
// induceL_I_B
// bucketMin_I_B
// freq_I_B
// <scan +text, often optimized away> (17)
// <scan +freq> (18)
// <scan +sa, random text, random bucket> (19)
// induceS_I_B
// bucketMax_I_B
// freq_I_B
// <scan +text, often optimized away> (20)
// <scan +freq> (21)
// <scan -sa, random text, random bucket> (22)
//
// Here, _B indicates the suffix array size (_32 or _64) and _I the input size (_8 or _B).
//
// The outline shows there are in general 22 scans through
// O(N)-sized arrays for a given level of the recursion.
// In the top level, operating on 8-bit input text,
// the six freq scans are fixed size (256) instead of potentially
// input-sized. Also, the frequency is counted once and cached
// whenever there is room to do so (there is nearly always room in general,
// and always room at the top level), which eliminates all but
// the first freq_I_B text scans (that is, 5 of the 6).
// So the top level of the recursion only does 22 - 6 - 5 = 11
// input-sized scans and a typical level does 16 scans.
//
// The linear scans do not cost anywhere near as much as
// the random accesses to the text made during a few of
// the scans (specifically #6, #9, #16, #19, #22 marked above).
// In real texts, there is not much but some locality to
// the accesses, due to the repetitive structure of the text
// (the same reason Burrows-Wheeler compression is so effective).
// For random inputs, there is no locality, which makes those
// accesses even more expensive, especially once the text
// no longer fits in cache.
// For example, running on 50 MB of Go source code, induceSubL_8_32
// (which runs only once, at the top level of the recursion)
// takes 0.44s, while on 50 MB of random input, it takes 2.55s.
// Nearly all the relative slowdown is explained by the text access:
//
// c0, c1 := text[k-1], text[k]
//
// That line runs for 0.23s on the Go text and 2.02s on random text.
//go:generate go run gen.go
package suffixarray
// text_32 returns the suffix array for the input text.
// It requires that len(text) fit in an int32
// and that the caller zero sa.
func text_32(text []byte, sa []int32) {
if int(int32(len(text))) != len(text) || len(text) != len(sa) {
panic("suffixarray: misuse of text_32")
}
sais_8_32(text, 256, sa, make([]int32, 2*256))
}
// sais_8_32 computes the suffix array of text.
// The text must contain only values in [0, textMax).
// The suffix array is stored in sa, which the caller
// must ensure is already zeroed.
// The caller must also provide temporary space tmp
// with len(tmp) ≥ textMax. If len(tmp) ≥ 2*textMax
// then the algorithm runs a little faster.
// If sais_8_32 modifies tmp, it sets tmp[0] = -1 on return.
func sais_8_32(text []byte, textMax int, sa, tmp []int32) {
if len(sa) != len(text) || len(tmp) < int(textMax) {
panic("suffixarray: misuse of sais_8_32")
}
// Trivial base cases. Sorting 0 or 1 things is easy.
if len(text) == 0 {
return
}
if len(text) == 1 {
sa[0] = 0
return
}
// Establish slices indexed by text character
// holding character frequency and bucket-sort offsets.
// If there's only enough tmp for one slice,
// we make it the bucket offsets and recompute
// the character frequency each time we need it.
var freq, bucket []int32
if len(tmp) >= 2*textMax {
freq, bucket = tmp[:textMax], tmp[textMax:2*textMax]
freq[0] = -1 // mark as uninitialized
} else {
freq, bucket = nil, tmp[:textMax]
}
// The SAIS algorithm.
// Each of these calls makes one scan through sa.
// See the individual functions for documentation
// about each's role in the algorithm.
numLMS := placeLMS_8_32(text, sa, freq, bucket)
if numLMS <= 1 {
// 0 or 1 items are already sorted. Do nothing.
} else {
induceSubL_8_32(text, sa, freq, bucket)
induceSubS_8_32(text, sa, freq, bucket)
length_8_32(text, sa, numLMS)
maxID := assignID_8_32(text, sa, numLMS)
if maxID < numLMS {
map_32(sa, numLMS)
recurse_32(sa, tmp, numLMS, maxID)
unmap_8_32(text, sa, numLMS)
} else {
// If maxID == numLMS, then each LMS-substring
// is unique, so the relative ordering of two LMS-suffixes
// is determined by just the leading LMS-substring.
// That is, the LMS-suffix sort order matches the
// (simpler) LMS-substring sort order.
// Copy the original LMS-substring order into the
// suffix array destination.
copy(sa, sa[len(sa)-numLMS:])
}
expand_8_32(text, freq, bucket, sa, numLMS)
}
induceL_8_32(text, sa, freq, bucket)
induceS_8_32(text, sa, freq, bucket)
// Mark for caller that we overwrote tmp.
tmp[0] = -1
}
// freq_8_32 returns the character frequencies
// for text, as a slice indexed by character value.
// If freq is nil, freq_8_32 uses and returns bucket.
// If freq is non-nil, freq_8_32 assumes that freq[0] >= 0
// means the frequencies are already computed.
// If the frequency data is overwritten or uninitialized,
// the caller must set freq[0] = -1 to force recomputation
// the next time it is needed.
func freq_8_32(text []byte, freq, bucket []int32) []int32 {
if freq != nil && freq[0] >= 0 {
return freq // already computed
}
if freq == nil {
freq = bucket
}
freq = freq[:256] // eliminate bounds check for freq[c] below
for i := range freq {
freq[i] = 0
}
for _, c := range text {
freq[c]++
}
return freq
}
// bucketMin_8_32 stores into bucket[c] the minimum index
// in the bucket for character c in a bucket-sort of text.
func bucketMin_8_32(text []byte, freq, bucket []int32) {
freq = freq_8_32(text, freq, bucket)
freq = freq[:256] // establish len(freq) = 256, so 0 ≤ i < 256 below
bucket = bucket[:256] // eliminate bounds check for bucket[i] below
total := int32(0)
for i, n := range freq {
bucket[i] = total
total += n
}
}
// bucketMax_8_32 stores into bucket[c] the maximum index
// in the bucket for character c in a bucket-sort of text.
// The bucket indexes for c are [min, max).
// That is, max is one past the final index in that bucket.
func bucketMax_8_32(text []byte, freq, bucket []int32) {
freq = freq_8_32(text, freq, bucket)
freq = freq[:256] // establish len(freq) = 256, so 0 ≤ i < 256 below
bucket = bucket[:256] // eliminate bounds check for bucket[i] below
total := int32(0)
for i, n := range freq {
total += n
bucket[i] = total
}
}
// The SAIS algorithm proceeds in a sequence of scans through sa.
// Each of the following functions implements one scan,
// and the functions appear here in the order they execute in the algorithm.
// placeLMS_8_32 places into sa the indexes of the
// final characters of the LMS substrings of text,
// sorted into the rightmost ends of their correct buckets
// in the suffix array.
//
// The imaginary sentinel character at the end of the text
// is the final character of the final LMS substring, but there
// is no bucket for the imaginary sentinel character,
// which has a smaller value than any real character.
// The caller must therefore pretend that sa[-1] == len(text).
//
// The text indexes of LMS-substring characters are always ≥ 1
// (the first LMS-substring must be preceded by one or more L-type
// characters that are not part of any LMS-substring),
// so using 0 as a “not present” suffix array entry is safe,
// both in this function and in most later functions
// (until induceL_8_32 below).
func placeLMS_8_32(text []byte, sa, freq, bucket []int32) int {
bucketMax_8_32(text, freq, bucket)
numLMS := 0
lastB := int32(-1)
bucket = bucket[:256] // eliminate bounds check for bucket[c1] below
// The next stanza of code (until the blank line) loop backward
// over text, stopping to execute a code body at each position i
// such that text[i] is an L-character and text[i+1] is an S-character.
// That is, i+1 is the position of the start of an LMS-substring.
// These could be hoisted out into a function with a callback,
// but at a significant speed cost. Instead, we just write these
// seven lines a few times in this source file. The copies below
// refer back to the pattern established by this original as the
// "LMS-substring iterator".
//
// In every scan through the text, c0, c1 are successive characters of text.
// In this backward scan, c0 == text[i] and c1 == text[i+1].
// By scanning backward, we can keep track of whether the current
// position is type-S or type-L according to the usual definition:
//
// - position len(text) is type S with text[len(text)] == -1 (the sentinel)
// - position i is type S if text[i] < text[i+1], or if text[i] == text[i+1] && i+1 is type S.
// - position i is type L if text[i] > text[i+1], or if text[i] == text[i+1] && i+1 is type L.
//
// The backward scan lets us maintain the current type,
// update it when we see c0 != c1, and otherwise leave it alone.
// We want to identify all S positions with a preceding L.
// Position len(text) is one such position by definition, but we have
// nowhere to write it down, so we eliminate it by untruthfully
// setting isTypeS = false at the start of the loop.
c0, c1, isTypeS := byte(0), byte(0), false
for i := len(text) - 1; i >= 0; i-- {
c0, c1 = text[i], c0
if c0 < c1 {
isTypeS = true
} else if c0 > c1 && isTypeS {
isTypeS = false
// Bucket the index i+1 for the start of an LMS-substring.
b := bucket[c1] - 1
bucket[c1] = b
sa[b] = int32(i + 1)
lastB = b
numLMS++
}
}
// We recorded the LMS-substring starts but really want the ends.
// Luckily, with two differences, the start indexes and the end indexes are the same.
// The first difference is that the rightmost LMS-substring's end index is len(text),
// so the caller must pretend that sa[-1] == len(text), as noted above.
// The second difference is that the first leftmost LMS-substring start index
// does not end an earlier LMS-substring, so as an optimization we can omit
// that leftmost LMS-substring start index (the last one we wrote).
//
// Exception: if numLMS <= 1, the caller is not going to bother with
// the recursion at all and will treat the result as containing LMS-substring starts.
// In that case, we don't remove the final entry.
if numLMS > 1 {
sa[lastB] = 0
}
return numLMS
}
// induceSubL_8_32 inserts the L-type text indexes of LMS-substrings
// into sa, assuming that the final characters of the LMS-substrings
// are already inserted into sa, sorted by final character, and at the
// right (not left) end of the corresponding character bucket.
// Each LMS-substring has the form (as a regexp) /S+L+S/:
// one or more S-type, one or more L-type, final S-type.
// induceSubL_8_32 leaves behind only the leftmost L-type text
// index for each LMS-substring. That is, it removes the final S-type
// indexes that are present on entry, and it inserts but then removes
// the interior L-type indexes too.
// (Only the leftmost L-type index is needed by induceSubS_8_32.)
func induceSubL_8_32(text []byte, sa, freq, bucket []int32) {
// Initialize positions for left side of character buckets.
bucketMin_8_32(text, freq, bucket)
bucket = bucket[:256] // eliminate bounds check for bucket[cB] below
// As we scan the array left-to-right, each sa[i] = j > 0 is a correctly
// sorted suffix array entry (for text[j:]) for which we know that j-1 is type L.
// Because j-1 is type L, inserting it into sa now will sort it correctly.
// But we want to distinguish a j-1 with j-2 of type L from type S.
// We can process the former but want to leave the latter for the caller.
// We record the difference by negating j-1 if it is preceded by type S.
// Either way, the insertion (into the text[j-1] bucket) is guaranteed to
// happen at sa[i´] for some i´ > i, that is, in the portion of sa we have
// yet to scan. A single pass therefore sees indexes j, j-1, j-2, j-3,
// and so on, in sorted but not necessarily adjacent order, until it finds
// one preceded by an index of type S, at which point it must stop.
//
// As we scan through the array, we clear the worked entries (sa[i] > 0) to zero,
// and we flip sa[i] < 0 to -sa[i], so that the loop finishes with sa containing
// only the indexes of the leftmost L-type indexes for each LMS-substring.
//
// The suffix array sa therefore serves simultaneously as input, output,
// and a miraculously well-tailored work queue.
// placeLMS_8_32 left out the implicit entry sa[-1] == len(text),
// corresponding to the identified type-L index len(text)-1.
// Process it before the left-to-right scan of sa proper.
// See body in loop for commentary.
k := len(text) - 1
c0, c1 := text[k-1], text[k]
if c0 < c1 {
k = -k
}
// Cache recently used bucket index:
// we're processing suffixes in sorted order
// and accessing buckets indexed by the
// byte before the sorted order, which still
// has very good locality.
// Invariant: b is cached, possibly dirty copy of bucket[cB].
cB := c1
b := bucket[cB]
sa[b] = int32(k)
b++
for i := 0; i < len(sa); i++ {
j := int(sa[i])
if j == 0 {
// Skip empty entry.
continue
}
if j < 0 {
// Leave discovered type-S index for caller.
sa[i] = int32(-j)
continue
}
sa[i] = 0
// Index j was on work queue, meaning k := j-1 is L-type,
// so we can now place k correctly into sa.
// If k-1 is L-type, queue k for processing later in this loop.
// If k-1 is S-type (text[k-1] < text[k]), queue -k to save for the caller.
k := j - 1
c0, c1 := text[k-1], text[k]
if c0 < c1 {
k = -k
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
sa[b] = int32(k)
b++
}
}
// induceSubS_8_32 inserts the S-type text indexes of LMS-substrings
// into sa, assuming that the leftmost L-type text indexes are already
// inserted into sa, sorted by LMS-substring suffix, and at the
// left end of the corresponding character bucket.
// Each LMS-substring has the form (as a regexp) /S+L+S/:
// one or more S-type, one or more L-type, final S-type.
// induceSubS_8_32 leaves behind only the leftmost S-type text
// index for each LMS-substring, in sorted order, at the right end of sa.
// That is, it removes the L-type indexes that are present on entry,
// and it inserts but then removes the interior S-type indexes too,
// leaving the LMS-substring start indexes packed into sa[len(sa)-numLMS:].
// (Only the LMS-substring start indexes are processed by the recursion.)
func induceSubS_8_32(text []byte, sa, freq, bucket []int32) {
// Initialize positions for right side of character buckets.
bucketMax_8_32(text, freq, bucket)
bucket = bucket[:256] // eliminate bounds check for bucket[cB] below
// Analogous to induceSubL_8_32 above,
// as we scan the array right-to-left, each sa[i] = j > 0 is a correctly
// sorted suffix array entry (for text[j:]) for which we know that j-1 is type S.
// Because j-1 is type S, inserting it into sa now will sort it correctly.
// But we want to distinguish a j-1 with j-2 of type S from type L.
// We can process the former but want to leave the latter for the caller.
// We record the difference by negating j-1 if it is preceded by type L.
// Either way, the insertion (into the text[j-1] bucket) is guaranteed to
// happen at sa[i´] for some i´ < i, that is, in the portion of sa we have
// yet to scan. A single pass therefore sees indexes j, j-1, j-2, j-3,
// and so on, in sorted but not necessarily adjacent order, until it finds
// one preceded by an index of type L, at which point it must stop.
// That index (preceded by one of type L) is an LMS-substring start.
//
// As we scan through the array, we clear the worked entries (sa[i] > 0) to zero,
// and we flip sa[i] < 0 to -sa[i] and compact into the top of sa,
// so that the loop finishes with the top of sa containing exactly
// the LMS-substring start indexes, sorted by LMS-substring.
// Cache recently used bucket index:
cB := byte(0)
b := bucket[cB]
top := len(sa)
for i := len(sa) - 1; i >= 0; i-- {
j := int(sa[i])
if j == 0 {
// Skip empty entry.
continue
}
sa[i] = 0
if j < 0 {
// Leave discovered LMS-substring start index for caller.
top--
sa[top] = int32(-j)
continue
}
// Index j was on work queue, meaning k := j-1 is S-type,
// so we can now place k correctly into sa.
// If k-1 is S-type, queue k for processing later in this loop.
// If k-1 is L-type (text[k-1] > text[k]), queue -k to save for the caller.
k := j - 1
c1 := text[k]
c0 := text[k-1]
if c0 > c1 {
k = -k
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
b--
sa[b] = int32(k)
}
}
// length_8_32 computes and records the length of each LMS-substring in text.
// The length of the LMS-substring at index j is stored at sa[j/2],
// avoiding the LMS-substring indexes already stored in the top half of sa.
// (If index j is an LMS-substring start, then index j-1 is type L and cannot be.)
// There are two exceptions, made for optimizations in name_8_32 below.
//
// First, the final LMS-substring is recorded as having length 0, which is otherwise
// impossible, instead of giving it a length that includes the implicit sentinel.
// This ensures the final LMS-substring has length unequal to all others
// and therefore can be detected as different without text comparison
// (it is unequal because it is the only one that ends in the implicit sentinel,
// and the text comparison would be problematic since the implicit sentinel
// is not actually present at text[len(text)]).
//
// Second, to avoid text comparison entirely, if an LMS-substring is very short,
// sa[j/2] records its actual text instead of its length, so that if two such
// substrings have matching “length,” the text need not be read at all.
// The definition of “very short” is that the text bytes must pack into an uint32,
// and the unsigned encoding e must be ≥ len(text), so that it can be
// distinguished from a valid length.
func length_8_32(text []byte, sa []int32, numLMS int) {
end := 0 // index of current LMS-substring end (0 indicates final LMS-substring)
// The encoding of N text bytes into a “length” word
// adds 1 to each byte, packs them into the bottom
// N*8 bits of a word, and then bitwise inverts the result.
// That is, the text sequence A B C (hex 41 42 43)
// encodes as ^uint32(0x42_43_44).
// LMS-substrings can never start or end with 0xFF.
// Adding 1 ensures the encoded byte sequence never
// starts or ends with 0x00, so that present bytes can be
// distinguished from zero-padding in the top bits,
// so the length need not be separately encoded.
// Inverting the bytes increases the chance that a
// 4-byte encoding will still be ≥ len(text).
// In particular, if the first byte is ASCII (<= 0x7E, so +1 <= 0x7F)
// then the high bit of the inversion will be set,
// making it clearly not a valid length (it would be a negative one).
//
// cx holds the pre-inverted encoding (the packed incremented bytes).
cx := uint32(0) // byte-only
// This stanza (until the blank line) is the "LMS-substring iterator",
// described in placeLMS_8_32 above, with one line added to maintain cx.
c0, c1, isTypeS := byte(0), byte(0), false
for i := len(text) - 1; i >= 0; i-- {
c0, c1 = text[i], c0
cx = cx<<8 | uint32(c1+1) // byte-only
if c0 < c1 {
isTypeS = true
} else if c0 > c1 && isTypeS {
isTypeS = false
// Index j = i+1 is the start of an LMS-substring.
// Compute length or encoded text to store in sa[j/2].
j := i + 1
var code int32
if end == 0 {
code = 0
} else {
code = int32(end - j)
if code <= 32/8 && ^cx >= uint32(len(text)) { // byte-only
code = int32(^cx) // byte-only
} // byte-only
}
sa[j>>1] = code
end = j + 1
cx = uint32(c1 + 1) // byte-only
}
}
}
// assignID_8_32 assigns a dense ID numbering to the
// set of LMS-substrings respecting string ordering and equality,
// returning the maximum assigned ID.
// For example given the input "ababab", the LMS-substrings
// are "aba", "aba", and "ab", renumbered as 2 2 1.
// sa[len(sa)-numLMS:] holds the LMS-substring indexes
// sorted in string order, so to assign numbers we can
// consider each in turn, removing adjacent duplicates.
// The new ID for the LMS-substring at index j is written to sa[j/2],
// overwriting the length previously stored there (by length_8_32 above).
func assignID_8_32(text []byte, sa []int32, numLMS int) int {
id := 0
lastLen := int32(-1) // impossible
lastPos := int32(0)
for _, j := range sa[len(sa)-numLMS:] {
// Is the LMS-substring at index j new, or is it the same as the last one we saw?
n := sa[j/2]
if n != lastLen {
goto New
}
if uint32(n) >= uint32(len(text)) {
// “Length” is really encoded full text, and they match.
goto Same
}
{
// Compare actual texts.
n := int(n)
this := text[j:][:n]
last := text[lastPos:][:n]
for i := 0; i < n; i++ {
if this[i] != last[i] {
goto New
}
}
goto Same
}
New:
id++
lastPos = j
lastLen = n
Same:
sa[j/2] = int32(id)
}
return id
}
// map_32 maps the LMS-substrings in text to their new IDs,
// producing the subproblem for the recursion.
// The mapping itself was mostly applied by assignID_8_32:
// sa[i] is either 0, the ID for the LMS-substring at index 2*i,
// or the ID for the LMS-substring at index 2*i+1.
// To produce the subproblem we need only remove the zeros
// and change ID into ID-1 (our IDs start at 1, but text chars start at 0).
//
// map_32 packs the result, which is the input to the recursion,
// into the top of sa, so that the recursion result can be stored
// in the bottom of sa, which sets up for expand_8_32 well.
func map_32(sa []int32, numLMS int) {
w := len(sa)
for i := len(sa) / 2; i >= 0; i-- {
j := sa[i]
if j > 0 {
w--
sa[w] = j - 1
}
}
}
// recurse_32 calls sais_32 recursively to solve the subproblem we've built.
// The subproblem is at the right end of sa, the suffix array result will be
// written at the left end of sa, and the middle of sa is available for use as
// temporary frequency and bucket storage.
func recurse_32(sa, oldTmp []int32, numLMS, maxID int) {
dst, saTmp, text := sa[:numLMS], sa[numLMS:len(sa)-numLMS], sa[len(sa)-numLMS:]
// Set up temporary space for recursive call.
// We must pass sais_32 a tmp buffer wiith at least maxID entries.
//
// The subproblem is guaranteed to have length at most len(sa)/2,
// so that sa can hold both the subproblem and its suffix array.
// Nearly all the time, however, the subproblem has length < len(sa)/3,
// in which case there is a subproblem-sized middle of sa that
// we can reuse for temporary space (saTmp).
// When recurse_32 is called from sais_8_32, oldTmp is length 512
// (from text_32), and saTmp will typically be much larger, so we'll use saTmp.
// When deeper recursions come back to recurse_32, now oldTmp is
// the saTmp from the top-most recursion, it is typically larger than
// the current saTmp (because the current sa gets smaller and smaller
// as the recursion gets deeper), and we keep reusing that top-most
// large saTmp instead of the offered smaller ones.
//
// Why is the subproblem length so often just under len(sa)/3?
// See Nong, Zhang, and Chen, section 3.6 for a plausible explanation.
// In brief, the len(sa)/2 case would correspond to an SLSLSLSLSLSL pattern
// in the input, perfect alternation of larger and smaller input bytes.
// Real text doesn't do that. If each L-type index is randomly followed
// by either an L-type or S-type index, then half the substrings will
// be of the form SLS, but the other half will be longer. Of that half,
// half (a quarter overall) will be SLLS; an eighth will be SLLLS, and so on.
// Not counting the final S in each (which overlaps the first S in the next),
// This works out to an average length 2×½ + 3×¼ + 4×⅛ + ... = 3.
// The space we need is further reduced by the fact that many of the
// short patterns like SLS will often be the same character sequences
// repeated throughout the text, reducing maxID relative to numLMS.
//
// For short inputs, the averages may not run in our favor, but then we
// can often fall back to using the length-512 tmp available in the
// top-most call. (Also a short allocation would not be a big deal.)
//
// For pathological inputs, we fall back to allocating a new tmp of length
// max(maxID, numLMS/2). This level of the recursion needs maxID,
// and all deeper levels of the recursion will need no more than numLMS/2,
// so this one allocation is guaranteed to suffice for the entire stack
// of recursive calls.
tmp := oldTmp
if len(tmp) < len(saTmp) {
tmp = saTmp
}
if len(tmp) < numLMS {
// TestSAIS/forcealloc reaches this code.
n := maxID
if n < numLMS/2 {
n = numLMS / 2
}
tmp = make([]int32, n)
}
// sais_32 requires that the caller arrange to clear dst,
// because in general the caller may know dst is
// freshly-allocated and already cleared. But this one is not.
for i := range dst {
dst[i] = 0
}
sais_32(text, maxID, dst, tmp)
}
// unmap_8_32 unmaps the subproblem back to the original.
// sa[:numLMS] is the LMS-substring numbers, which don't matter much anymore.
// sa[len(sa)-numLMS:] is the sorted list of those LMS-substring numbers.
// The key part is that if the list says K that means the K'th substring.
// We can replace sa[:numLMS] with the indexes of the LMS-substrings.
// Then if the list says K it really means sa[K].
// Having mapped the list back to LMS-substring indexes,
// we can place those into the right buckets.
func unmap_8_32(text []byte, sa []int32, numLMS int) {
unmap := sa[len(sa)-numLMS:]
j := len(unmap)
// "LMS-substring iterator" (see placeLMS_8_32 above).
c0, c1, isTypeS := byte(0), byte(0), false
for i := len(text) - 1; i >= 0; i-- {
c0, c1 = text[i], c0
if c0 < c1 {
isTypeS = true
} else if c0 > c1 && isTypeS {
isTypeS = false
// Populate inverse map.
j--
unmap[j] = int32(i + 1)
}
}
// Apply inverse map to subproblem suffix array.
sa = sa[:numLMS]
for i := 0; i < len(sa); i++ {
sa[i] = unmap[sa[i]]
}
}
// expand_8_32 distributes the compacted, sorted LMS-suffix indexes
// from sa[:numLMS] into the tops of the appropriate buckets in sa,
// preserving the sorted order and making room for the L-type indexes
// to be slotted into the sorted sequence by induceL_8_32.
func expand_8_32(text []byte, freq, bucket, sa []int32, numLMS int) {
bucketMax_8_32(text, freq, bucket)
bucket = bucket[:256] // eliminate bound check for bucket[c] below
// Loop backward through sa, always tracking
// the next index to populate from sa[:numLMS].
// When we get to one, populate it.
// Zero the rest of the slots; they have dead values in them.
x := numLMS - 1
saX := sa[x]
c := text[saX]
b := bucket[c] - 1
bucket[c] = b
for i := len(sa) - 1; i >= 0; i-- {
if i != int(b) {
sa[i] = 0
continue
}
sa[i] = saX
// Load next entry to put down (if any).
if x > 0 {
x--
saX = sa[x] // TODO bounds check
c = text[saX]
b = bucket[c] - 1
bucket[c] = b
}
}
}
// induceL_8_32 inserts L-type text indexes into sa,
// assuming that the leftmost S-type indexes are inserted
// into sa, in sorted order, in the right bucket halves.
// It leaves all the L-type indexes in sa, but the
// leftmost L-type indexes are negated, to mark them
// for processing by induceS_8_32.
func induceL_8_32(text []byte, sa, freq, bucket []int32) {
// Initialize positions for left side of character buckets.
bucketMin_8_32(text, freq, bucket)
bucket = bucket[:256] // eliminate bounds check for bucket[cB] below
// This scan is similar to the one in induceSubL_8_32 above.
// That one arranges to clear all but the leftmost L-type indexes.
// This scan leaves all the L-type indexes and the original S-type
// indexes, but it negates the positive leftmost L-type indexes
// (the ones that induceS_8_32 needs to process).
// expand_8_32 left out the implicit entry sa[-1] == len(text),
// corresponding to the identified type-L index len(text)-1.
// Process it before the left-to-right scan of sa proper.
// See body in loop for commentary.
k := len(text) - 1
c0, c1 := text[k-1], text[k]
if c0 < c1 {
k = -k
}
// Cache recently used bucket index.
cB := c1
b := bucket[cB]
sa[b] = int32(k)
b++
for i := 0; i < len(sa); i++ {
j := int(sa[i])
if j <= 0 {
// Skip empty or negated entry (including negated zero).
continue
}
// Index j was on work queue, meaning k := j-1 is L-type,
// so we can now place k correctly into sa.
// If k-1 is L-type, queue k for processing later in this loop.
// If k-1 is S-type (text[k-1] < text[k]), queue -k to save for the caller.
// If k is zero, k-1 doesn't exist, so we only need to leave it
// for the caller. The caller can't tell the difference between
// an empty slot and a non-empty zero, but there's no need
// to distinguish them anyway: the final suffix array will end up
// with one zero somewhere, and that will be a real zero.
k := j - 1
c1 := text[k]
if k > 0 {
if c0 := text[k-1]; c0 < c1 {
k = -k
}
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
sa[b] = int32(k)
b++
}
}
func induceS_8_32(text []byte, sa, freq, bucket []int32) {
// Initialize positions for right side of character buckets.
bucketMax_8_32(text, freq, bucket)
bucket = bucket[:256] // eliminate bounds check for bucket[cB] below
cB := byte(0)
b := bucket[cB]
for i := len(sa) - 1; i >= 0; i-- {
j := int(sa[i])
if j >= 0 {
// Skip non-flagged entry.
// (This loop can't see an empty entry; 0 means the real zero index.)
continue
}
// Negative j is a work queue entry; rewrite to positive j for final suffix array.
j = -j
sa[i] = int32(j)
// Index j was on work queue (encoded as -j but now decoded),
// meaning k := j-1 is L-type,
// so we can now place k correctly into sa.
// If k-1 is S-type, queue -k for processing later in this loop.
// If k-1 is L-type (text[k-1] > text[k]), queue k to save for the caller.
// If k is zero, k-1 doesn't exist, so we only need to leave it
// for the caller.
k := j - 1
c1 := text[k]
if k > 0 {
if c0 := text[k-1]; c0 <= c1 {
k = -k
}
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
b--
sa[b] = int32(k)
}
}
src/index/suffixarray/sais2.go 0 → 100644
View file @ 6ca324f2
// Copyright 2019 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.
// Code generated by go generate; DO NOT EDIT.
package suffixarray
func text_64(text []byte, sa []int64) {
if int(int64(len(text))) != len(text) || len(text) != len(sa) {
panic("suffixarray: misuse of text_64")
}
sais_8_64(text, 256, sa, make([]int64, 2*256))
}
func sais_8_64(text []byte, textMax int, sa, tmp []int64) {
if len(sa) != len(text) || len(tmp) < int(textMax) {
panic("suffixarray: misuse of sais_8_64")
}
// Trivial base cases. Sorting 0 or 1 things is easy.
if len(text) == 0 {
return
}
if len(text) == 1 {
sa[0] = 0
return
}
// Establish slices indexed by text character
// holding character frequency and bucket-sort offsets.
// If there's only enough tmp for one slice,
// we make it the bucket offsets and recompute
// the character frequency each time we need it.
var freq, bucket []int64
if len(tmp) >= 2*textMax {
freq, bucket = tmp[:textMax], tmp[textMax:2*textMax]
freq[0] = -1 // mark as uninitialized
} else {
freq, bucket = nil, tmp[:textMax]
}
// The SAIS algorithm.
// Each of these calls makes one scan through sa.
// See the individual functions for documentation
// about each's role in the algorithm.
numLMS := placeLMS_8_64(text, sa, freq, bucket)
if numLMS <= 1 {
// 0 or 1 items are already sorted. Do nothing.
} else {
induceSubL_8_64(text, sa, freq, bucket)
induceSubS_8_64(text, sa, freq, bucket)
length_8_64(text, sa, numLMS)
maxID := assignID_8_64(text, sa, numLMS)
if maxID < numLMS {
map_64(sa, numLMS)
recurse_64(sa, tmp, numLMS, maxID)
unmap_8_64(text, sa, numLMS)
} else {
// If maxID == numLMS, then each LMS-substring
// is unique, so the relative ordering of two LMS-suffixes
// is determined by just the leading LMS-substring.
// That is, the LMS-suffix sort order matches the
// (simpler) LMS-substring sort order.
// Copy the original LMS-substring order into the
// suffix array destination.
copy(sa, sa[len(sa)-numLMS:])
}
expand_8_64(text, freq, bucket, sa, numLMS)
}
induceL_8_64(text, sa, freq, bucket)
induceS_8_64(text, sa, freq, bucket)
// Mark for caller that we overwrote tmp.
tmp[0] = -1
}
func sais_32(text []int32, textMax int, sa, tmp []int32) {
if len(sa) != len(text) || len(tmp) < int(textMax) {
panic("suffixarray: misuse of sais_32")
}
// Trivial base cases. Sorting 0 or 1 things is easy.
if len(text) == 0 {
return
}
if len(text) == 1 {
sa[0] = 0
return
}
// Establish slices indexed by text character
// holding character frequency and bucket-sort offsets.
// If there's only enough tmp for one slice,
// we make it the bucket offsets and recompute
// the character frequency each time we need it.
var freq, bucket []int32
if len(tmp) >= 2*textMax {
freq, bucket = tmp[:textMax], tmp[textMax:2*textMax]
freq[0] = -1 // mark as uninitialized
} else {
freq, bucket = nil, tmp[:textMax]
}
// The SAIS algorithm.
// Each of these calls makes one scan through sa.
// See the individual functions for documentation
// about each's role in the algorithm.
numLMS := placeLMS_32(text, sa, freq, bucket)
if numLMS <= 1 {
// 0 or 1 items are already sorted. Do nothing.
} else {
induceSubL_32(text, sa, freq, bucket)
induceSubS_32(text, sa, freq, bucket)
length_32(text, sa, numLMS)
maxID := assignID_32(text, sa, numLMS)
if maxID < numLMS {
map_32(sa, numLMS)
recurse_32(sa, tmp, numLMS, maxID)
unmap_32(text, sa, numLMS)
} else {
// If maxID == numLMS, then each LMS-substring
// is unique, so the relative ordering of two LMS-suffixes
// is determined by just the leading LMS-substring.
// That is, the LMS-suffix sort order matches the
// (simpler) LMS-substring sort order.
// Copy the original LMS-substring order into the
// suffix array destination.
copy(sa, sa[len(sa)-numLMS:])
}
expand_32(text, freq, bucket, sa, numLMS)
}
induceL_32(text, sa, freq, bucket)
induceS_32(text, sa, freq, bucket)
// Mark for caller that we overwrote tmp.
tmp[0] = -1
}
func sais_64(text []int64, textMax int, sa, tmp []int64) {
if len(sa) != len(text) || len(tmp) < int(textMax) {
panic("suffixarray: misuse of sais_64")
}
// Trivial base cases. Sorting 0 or 1 things is easy.
if len(text) == 0 {
return
}
if len(text) == 1 {
sa[0] = 0
return
}
// Establish slices indexed by text character
// holding character frequency and bucket-sort offsets.
// If there's only enough tmp for one slice,
// we make it the bucket offsets and recompute
// the character frequency each time we need it.
var freq, bucket []int64
if len(tmp) >= 2*textMax {
freq, bucket = tmp[:textMax], tmp[textMax:2*textMax]
freq[0] = -1 // mark as uninitialized
} else {
freq, bucket = nil, tmp[:textMax]
}
// The SAIS algorithm.
// Each of these calls makes one scan through sa.
// See the individual functions for documentation
// about each's role in the algorithm.
numLMS := placeLMS_64(text, sa, freq, bucket)
if numLMS <= 1 {
// 0 or 1 items are already sorted. Do nothing.
} else {
induceSubL_64(text, sa, freq, bucket)
induceSubS_64(text, sa, freq, bucket)
length_64(text, sa, numLMS)
maxID := assignID_64(text, sa, numLMS)
if maxID < numLMS {
map_64(sa, numLMS)
recurse_64(sa, tmp, numLMS, maxID)
unmap_64(text, sa, numLMS)
} else {
// If maxID == numLMS, then each LMS-substring
// is unique, so the relative ordering of two LMS-suffixes
// is determined by just the leading LMS-substring.
// That is, the LMS-suffix sort order matches the
// (simpler) LMS-substring sort order.
// Copy the original LMS-substring order into the
// suffix array destination.
copy(sa, sa[len(sa)-numLMS:])
}
expand_64(text, freq, bucket, sa, numLMS)
}
induceL_64(text, sa, freq, bucket)
induceS_64(text, sa, freq, bucket)
// Mark for caller that we overwrote tmp.
tmp[0] = -1
}
func freq_8_64(text []byte, freq, bucket []int64) []int64 {
if freq != nil && freq[0] >= 0 {
return freq // already computed
}
if freq == nil {
freq = bucket
}
freq = freq[:256] // eliminate bounds check for freq[c] below
for i := range freq {
freq[i] = 0
}
for _, c := range text {
freq[c]++
}
return freq
}
func freq_32(text []int32, freq, bucket []int32) []int32 {
if freq != nil && freq[0] >= 0 {
return freq // already computed
}
if freq == nil {
freq = bucket
}
for i := range freq {
freq[i] = 0
}
for _, c := range text {
freq[c]++
}
return freq
}
func freq_64(text []int64, freq, bucket []int64) []int64 {
if freq != nil && freq[0] >= 0 {
return freq // already computed
}
if freq == nil {
freq = bucket
}
for i := range freq {
freq[i] = 0
}
for _, c := range text {
freq[c]++
}
return freq
}
func bucketMin_8_64(text []byte, freq, bucket []int64) {
freq = freq_8_64(text, freq, bucket)
freq = freq[:256] // establish len(freq) = 256, so 0 ≤ i < 256 below
bucket = bucket[:256] // eliminate bounds check for bucket[i] below
total := int64(0)
for i, n := range freq {
bucket[i] = total
total += n
}
}
func bucketMin_32(text []int32, freq, bucket []int32) {
freq = freq_32(text, freq, bucket)
total := int32(0)
for i, n := range freq {
bucket[i] = total
total += n
}
}
func bucketMin_64(text []int64, freq, bucket []int64) {
freq = freq_64(text, freq, bucket)
total := int64(0)
for i, n := range freq {
bucket[i] = total
total += n
}
}
func bucketMax_8_64(text []byte, freq, bucket []int64) {
freq = freq_8_64(text, freq, bucket)
freq = freq[:256] // establish len(freq) = 256, so 0 ≤ i < 256 below
bucket = bucket[:256] // eliminate bounds check for bucket[i] below
total := int64(0)
for i, n := range freq {
total += n
bucket[i] = total
}
}
func bucketMax_32(text []int32, freq, bucket []int32) {
freq = freq_32(text, freq, bucket)
total := int32(0)
for i, n := range freq {
total += n
bucket[i] = total
}
}
func bucketMax_64(text []int64, freq, bucket []int64) {
freq = freq_64(text, freq, bucket)
total := int64(0)
for i, n := range freq {
total += n
bucket[i] = total
}
}
func placeLMS_8_64(text []byte, sa, freq, bucket []int64) int {
bucketMax_8_64(text, freq, bucket)
numLMS := 0
lastB := int64(-1)
bucket = bucket[:256] // eliminate bounds check for bucket[c1] below
// The next stanza of code (until the blank line) loop backward
// over text, stopping to execute a code body at each position i
// such that text[i] is an L-character and text[i+1] is an S-character.
// That is, i+1 is the position of the start of an LMS-substring.
// These could be hoisted out into a function with a callback,
// but at a significant speed cost. Instead, we just write these
// seven lines a few times in this source file. The copies below
// refer back to the pattern established by this original as the
// "LMS-substring iterator".
//
// In every scan through the text, c0, c1 are successive characters of text.
// In this backward scan, c0 == text[i] and c1 == text[i+1].
// By scanning backward, we can keep track of whether the current
// position is type-S or type-L according to the usual definition:
//
// - position len(text) is type S with text[len(text)] == -1 (the sentinel)
// - position i is type S if text[i] < text[i+1], or if text[i] == text[i+1] && i+1 is type S.
// - position i is type L if text[i] > text[i+1], or if text[i] == text[i+1] && i+1 is type L.
//
// The backward scan lets us maintain the current type,
// update it when we see c0 != c1, and otherwise leave it alone.
// We want to identify all S positions with a preceding L.
// Position len(text) is one such position by definition, but we have
// nowhere to write it down, so we eliminate it by untruthfully
// setting isTypeS = false at the start of the loop.
c0, c1, isTypeS := byte(0), byte(0), false
for i := len(text) - 1; i >= 0; i-- {
c0, c1 = text[i], c0
if c0 < c1 {
isTypeS = true
} else if c0 > c1 && isTypeS {
isTypeS = false
// Bucket the index i+1 for the start of an LMS-substring.
b := bucket[c1] - 1
bucket[c1] = b
sa[b] = int64(i + 1)
lastB = b
numLMS++
}
}
// We recorded the LMS-substring starts but really want the ends.
// Luckily, with two differences, the start indexes and the end indexes are the same.
// The first difference is that the rightmost LMS-substring's end index is len(text),
// so the caller must pretend that sa[-1] == len(text), as noted above.
// The second difference is that the first leftmost LMS-substring start index
// does not end an earlier LMS-substring, so as an optimization we can omit
// that leftmost LMS-substring start index (the last one we wrote).
//
// Exception: if numLMS <= 1, the caller is not going to bother with
// the recursion at all and will treat the result as containing LMS-substring starts.
// In that case, we don't remove the final entry.
if numLMS > 1 {
sa[lastB] = 0
}
return numLMS
}
func placeLMS_32(text []int32, sa, freq, bucket []int32) int {
bucketMax_32(text, freq, bucket)
numLMS := 0
lastB := int32(-1)
// The next stanza of code (until the blank line) loop backward
// over text, stopping to execute a code body at each position i
// such that text[i] is an L-character and text[i+1] is an S-character.
// That is, i+1 is the position of the start of an LMS-substring.
// These could be hoisted out into a function with a callback,
// but at a significant speed cost. Instead, we just write these
// seven lines a few times in this source file. The copies below
// refer back to the pattern established by this original as the
// "LMS-substring iterator".
//
// In every scan through the text, c0, c1 are successive characters of text.
// In this backward scan, c0 == text[i] and c1 == text[i+1].
// By scanning backward, we can keep track of whether the current
// position is type-S or type-L according to the usual definition:
//
// - position len(text) is type S with text[len(text)] == -1 (the sentinel)
// - position i is type S if text[i] < text[i+1], or if text[i] == text[i+1] && i+1 is type S.
// - position i is type L if text[i] > text[i+1], or if text[i] == text[i+1] && i+1 is type L.
//
// The backward scan lets us maintain the current type,
// update it when we see c0 != c1, and otherwise leave it alone.
// We want to identify all S positions with a preceding L.
// Position len(text) is one such position by definition, but we have
// nowhere to write it down, so we eliminate it by untruthfully
// setting isTypeS = false at the start of the loop.
c0, c1, isTypeS := int32(0), int32(0), false
for i := len(text) - 1; i >= 0; i-- {
c0, c1 = text[i], c0
if c0 < c1 {
isTypeS = true
} else if c0 > c1 && isTypeS {
isTypeS = false
// Bucket the index i+1 for the start of an LMS-substring.
b := bucket[c1] - 1
bucket[c1] = b
sa[b] = int32(i + 1)
lastB = b
numLMS++
}
}
// We recorded the LMS-substring starts but really want the ends.
// Luckily, with two differences, the start indexes and the end indexes are the same.
// The first difference is that the rightmost LMS-substring's end index is len(text),
// so the caller must pretend that sa[-1] == len(text), as noted above.
// The second difference is that the first leftmost LMS-substring start index
// does not end an earlier LMS-substring, so as an optimization we can omit
// that leftmost LMS-substring start index (the last one we wrote).
//
// Exception: if numLMS <= 1, the caller is not going to bother with
// the recursion at all and will treat the result as containing LMS-substring starts.
// In that case, we don't remove the final entry.
if numLMS > 1 {
sa[lastB] = 0
}
return numLMS
}
func placeLMS_64(text []int64, sa, freq, bucket []int64) int {
bucketMax_64(text, freq, bucket)
numLMS := 0
lastB := int64(-1)
// The next stanza of code (until the blank line) loop backward
// over text, stopping to execute a code body at each position i
// such that text[i] is an L-character and text[i+1] is an S-character.
// That is, i+1 is the position of the start of an LMS-substring.
// These could be hoisted out into a function with a callback,
// but at a significant speed cost. Instead, we just write these
// seven lines a few times in this source file. The copies below
// refer back to the pattern established by this original as the
// "LMS-substring iterator".
//
// In every scan through the text, c0, c1 are successive characters of text.
// In this backward scan, c0 == text[i] and c1 == text[i+1].
// By scanning backward, we can keep track of whether the current
// position is type-S or type-L according to the usual definition:
//
// - position len(text) is type S with text[len(text)] == -1 (the sentinel)
// - position i is type S if text[i] < text[i+1], or if text[i] == text[i+1] && i+1 is type S.
// - position i is type L if text[i] > text[i+1], or if text[i] == text[i+1] && i+1 is type L.
//
// The backward scan lets us maintain the current type,
// update it when we see c0 != c1, and otherwise leave it alone.
// We want to identify all S positions with a preceding L.
// Position len(text) is one such position by definition, but we have
// nowhere to write it down, so we eliminate it by untruthfully
// setting isTypeS = false at the start of the loop.
c0, c1, isTypeS := int64(0), int64(0), false
for i := len(text) - 1; i >= 0; i-- {
c0, c1 = text[i], c0
if c0 < c1 {
isTypeS = true
} else if c0 > c1 && isTypeS {
isTypeS = false
// Bucket the index i+1 for the start of an LMS-substring.
b := bucket[c1] - 1
bucket[c1] = b
sa[b] = int64(i + 1)
lastB = b
numLMS++
}
}
// We recorded the LMS-substring starts but really want the ends.
// Luckily, with two differences, the start indexes and the end indexes are the same.
// The first difference is that the rightmost LMS-substring's end index is len(text),
// so the caller must pretend that sa[-1] == len(text), as noted above.
// The second difference is that the first leftmost LMS-substring start index
// does not end an earlier LMS-substring, so as an optimization we can omit
// that leftmost LMS-substring start index (the last one we wrote).
//
// Exception: if numLMS <= 1, the caller is not going to bother with
// the recursion at all and will treat the result as containing LMS-substring starts.
// In that case, we don't remove the final entry.
if numLMS > 1 {
sa[lastB] = 0
}
return numLMS
}
func induceSubL_8_64(text []byte, sa, freq, bucket []int64) {
// Initialize positions for left side of character buckets.
bucketMin_8_64(text, freq, bucket)
bucket = bucket[:256] // eliminate bounds check for bucket[cB] below
// As we scan the array left-to-right, each sa[i] = j > 0 is a correctly
// sorted suffix array entry (for text[j:]) for which we know that j-1 is type L.
// Because j-1 is type L, inserting it into sa now will sort it correctly.
// But we want to distinguish a j-1 with j-2 of type L from type S.
// We can process the former but want to leave the latter for the caller.
// We record the difference by negating j-1 if it is preceded by type S.
// Either way, the insertion (into the text[j-1] bucket) is guaranteed to
// happen at sa[i´] for some i´ > i, that is, in the portion of sa we have
// yet to scan. A single pass therefore sees indexes j, j-1, j-2, j-3,
// and so on, in sorted but not necessarily adjacent order, until it finds
// one preceded by an index of type S, at which point it must stop.
//
// As we scan through the array, we clear the worked entries (sa[i] > 0) to zero,
// and we flip sa[i] < 0 to -sa[i], so that the loop finishes with sa containing
// only the indexes of the leftmost L-type indexes for each LMS-substring.
//
// The suffix array sa therefore serves simultaneously as input, output,
// and a miraculously well-tailored work queue.
// placeLMS_8_64 left out the implicit entry sa[-1] == len(text),
// corresponding to the identified type-L index len(text)-1.
// Process it before the left-to-right scan of sa proper.
// See body in loop for commentary.
k := len(text) - 1
c0, c1 := text[k-1], text[k]
if c0 < c1 {
k = -k
}
// Cache recently used bucket index:
// we're processing suffixes in sorted order
// and accessing buckets indexed by the
// byte before the sorted order, which still
// has very good locality.
// Invariant: b is cached, possibly dirty copy of bucket[cB].
cB := c1
b := bucket[cB]
sa[b] = int64(k)
b++
for i := 0; i < len(sa); i++ {
j := int(sa[i])
if j == 0 {
// Skip empty entry.
continue
}
if j < 0 {
// Leave discovered type-S index for caller.
sa[i] = int64(-j)
continue
}
sa[i] = 0
// Index j was on work queue, meaning k := j-1 is L-type,
// so we can now place k correctly into sa.
// If k-1 is L-type, queue k for processing later in this loop.
// If k-1 is S-type (text[k-1] < text[k]), queue -k to save for the caller.
k := j - 1
c0, c1 := text[k-1], text[k]
if c0 < c1 {
k = -k
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
sa[b] = int64(k)
b++
}
}
func induceSubL_32(text []int32, sa, freq, bucket []int32) {
// Initialize positions for left side of character buckets.
bucketMin_32(text, freq, bucket)
// As we scan the array left-to-right, each sa[i] = j > 0 is a correctly
// sorted suffix array entry (for text[j:]) for which we know that j-1 is type L.
// Because j-1 is type L, inserting it into sa now will sort it correctly.
// But we want to distinguish a j-1 with j-2 of type L from type S.
// We can process the former but want to leave the latter for the caller.
// We record the difference by negating j-1 if it is preceded by type S.
// Either way, the insertion (into the text[j-1] bucket) is guaranteed to
// happen at sa[i´] for some i´ > i, that is, in the portion of sa we have
// yet to scan. A single pass therefore sees indexes j, j-1, j-2, j-3,
// and so on, in sorted but not necessarily adjacent order, until it finds
// one preceded by an index of type S, at which point it must stop.
//
// As we scan through the array, we clear the worked entries (sa[i] > 0) to zero,
// and we flip sa[i] < 0 to -sa[i], so that the loop finishes with sa containing
// only the indexes of the leftmost L-type indexes for each LMS-substring.
//
// The suffix array sa therefore serves simultaneously as input, output,
// and a miraculously well-tailored work queue.
// placeLMS_32 left out the implicit entry sa[-1] == len(text),
// corresponding to the identified type-L index len(text)-1.
// Process it before the left-to-right scan of sa proper.
// See body in loop for commentary.
k := len(text) - 1
c0, c1 := text[k-1], text[k]
if c0 < c1 {
k = -k
}
// Cache recently used bucket index:
// we're processing suffixes in sorted order
// and accessing buckets indexed by the
// int32 before the sorted order, which still
// has very good locality.
// Invariant: b is cached, possibly dirty copy of bucket[cB].
cB := c1
b := bucket[cB]
sa[b] = int32(k)
b++
for i := 0; i < len(sa); i++ {
j := int(sa[i])
if j == 0 {
// Skip empty entry.
continue
}
if j < 0 {
// Leave discovered type-S index for caller.
sa[i] = int32(-j)
continue
}
sa[i] = 0
// Index j was on work queue, meaning k := j-1 is L-type,
// so we can now place k correctly into sa.
// If k-1 is L-type, queue k for processing later in this loop.
// If k-1 is S-type (text[k-1] < text[k]), queue -k to save for the caller.
k := j - 1
c0, c1 := text[k-1], text[k]
if c0 < c1 {
k = -k
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
sa[b] = int32(k)
b++
}
}
func induceSubL_64(text []int64, sa, freq, bucket []int64) {
// Initialize positions for left side of character buckets.
bucketMin_64(text, freq, bucket)
// As we scan the array left-to-right, each sa[i] = j > 0 is a correctly
// sorted suffix array entry (for text[j:]) for which we know that j-1 is type L.
// Because j-1 is type L, inserting it into sa now will sort it correctly.
// But we want to distinguish a j-1 with j-2 of type L from type S.
// We can process the former but want to leave the latter for the caller.
// We record the difference by negating j-1 if it is preceded by type S.
// Either way, the insertion (into the text[j-1] bucket) is guaranteed to
// happen at sa[i´] for some i´ > i, that is, in the portion of sa we have
// yet to scan. A single pass therefore sees indexes j, j-1, j-2, j-3,
// and so on, in sorted but not necessarily adjacent order, until it finds
// one preceded by an index of type S, at which point it must stop.
//
// As we scan through the array, we clear the worked entries (sa[i] > 0) to zero,
// and we flip sa[i] < 0 to -sa[i], so that the loop finishes with sa containing
// only the indexes of the leftmost L-type indexes for each LMS-substring.
//
// The suffix array sa therefore serves simultaneously as input, output,
// and a miraculously well-tailored work queue.
// placeLMS_64 left out the implicit entry sa[-1] == len(text),
// corresponding to the identified type-L index len(text)-1.
// Process it before the left-to-right scan of sa proper.
// See body in loop for commentary.
k := len(text) - 1
c0, c1 := text[k-1], text[k]
if c0 < c1 {
k = -k
}
// Cache recently used bucket index:
// we're processing suffixes in sorted order
// and accessing buckets indexed by the
// int64 before the sorted order, which still
// has very good locality.
// Invariant: b is cached, possibly dirty copy of bucket[cB].
cB := c1
b := bucket[cB]
sa[b] = int64(k)
b++
for i := 0; i < len(sa); i++ {
j := int(sa[i])
if j == 0 {
// Skip empty entry.
continue
}
if j < 0 {
// Leave discovered type-S index for caller.
sa[i] = int64(-j)
continue
}
sa[i] = 0
// Index j was on work queue, meaning k := j-1 is L-type,
// so we can now place k correctly into sa.
// If k-1 is L-type, queue k for processing later in this loop.
// If k-1 is S-type (text[k-1] < text[k]), queue -k to save for the caller.
k := j - 1
c0, c1 := text[k-1], text[k]
if c0 < c1 {
k = -k
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
sa[b] = int64(k)
b++
}
}
func induceSubS_8_64(text []byte, sa, freq, bucket []int64) {
// Initialize positions for right side of character buckets.
bucketMax_8_64(text, freq, bucket)
bucket = bucket[:256] // eliminate bounds check for bucket[cB] below
// Analogous to induceSubL_8_64 above,
// as we scan the array right-to-left, each sa[i] = j > 0 is a correctly
// sorted suffix array entry (for text[j:]) for which we know that j-1 is type S.
// Because j-1 is type S, inserting it into sa now will sort it correctly.
// But we want to distinguish a j-1 with j-2 of type S from type L.
// We can process the former but want to leave the latter for the caller.
// We record the difference by negating j-1 if it is preceded by type L.
// Either way, the insertion (into the text[j-1] bucket) is guaranteed to
// happen at sa[i´] for some i´ < i, that is, in the portion of sa we have
// yet to scan. A single pass therefore sees indexes j, j-1, j-2, j-3,
// and so on, in sorted but not necessarily adjacent order, until it finds
// one preceded by an index of type L, at which point it must stop.
// That index (preceded by one of type L) is an LMS-substring start.
//
// As we scan through the array, we clear the worked entries (sa[i] > 0) to zero,
// and we flip sa[i] < 0 to -sa[i] and compact into the top of sa,
// so that the loop finishes with the top of sa containing exactly
// the LMS-substring start indexes, sorted by LMS-substring.
// Cache recently used bucket index:
cB := byte(0)
b := bucket[cB]
top := len(sa)
for i := len(sa) - 1; i >= 0; i-- {
j := int(sa[i])
if j == 0 {
// Skip empty entry.
continue
}
sa[i] = 0
if j < 0 {
// Leave discovered LMS-substring start index for caller.
top--
sa[top] = int64(-j)
continue
}
// Index j was on work queue, meaning k := j-1 is S-type,
// so we can now place k correctly into sa.
// If k-1 is S-type, queue k for processing later in this loop.
// If k-1 is L-type (text[k-1] > text[k]), queue -k to save for the caller.
k := j - 1
c1 := text[k]
c0 := text[k-1]
if c0 > c1 {
k = -k
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
b--
sa[b] = int64(k)
}
}
func induceSubS_32(text []int32, sa, freq, bucket []int32) {
// Initialize positions for right side of character buckets.
bucketMax_32(text, freq, bucket)
// Analogous to induceSubL_32 above,
// as we scan the array right-to-left, each sa[i] = j > 0 is a correctly
// sorted suffix array entry (for text[j:]) for which we know that j-1 is type S.
// Because j-1 is type S, inserting it into sa now will sort it correctly.
// But we want to distinguish a j-1 with j-2 of type S from type L.
// We can process the former but want to leave the latter for the caller.
// We record the difference by negating j-1 if it is preceded by type L.
// Either way, the insertion (into the text[j-1] bucket) is guaranteed to
// happen at sa[i´] for some i´ < i, that is, in the portion of sa we have
// yet to scan. A single pass therefore sees indexes j, j-1, j-2, j-3,
// and so on, in sorted but not necessarily adjacent order, until it finds
// one preceded by an index of type L, at which point it must stop.
// That index (preceded by one of type L) is an LMS-substring start.
//
// As we scan through the array, we clear the worked entries (sa[i] > 0) to zero,
// and we flip sa[i] < 0 to -sa[i] and compact into the top of sa,
// so that the loop finishes with the top of sa containing exactly
// the LMS-substring start indexes, sorted by LMS-substring.
// Cache recently used bucket index:
cB := int32(0)
b := bucket[cB]
top := len(sa)
for i := len(sa) - 1; i >= 0; i-- {
j := int(sa[i])
if j == 0 {
// Skip empty entry.
continue
}
sa[i] = 0
if j < 0 {
// Leave discovered LMS-substring start index for caller.
top--
sa[top] = int32(-j)
continue
}
// Index j was on work queue, meaning k := j-1 is S-type,
// so we can now place k correctly into sa.
// If k-1 is S-type, queue k for processing later in this loop.
// If k-1 is L-type (text[k-1] > text[k]), queue -k to save for the caller.
k := j - 1
c1 := text[k]
c0 := text[k-1]
if c0 > c1 {
k = -k
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
b--
sa[b] = int32(k)
}
}
func induceSubS_64(text []int64, sa, freq, bucket []int64) {
// Initialize positions for right side of character buckets.
bucketMax_64(text, freq, bucket)
// Analogous to induceSubL_64 above,
// as we scan the array right-to-left, each sa[i] = j > 0 is a correctly
// sorted suffix array entry (for text[j:]) for which we know that j-1 is type S.
// Because j-1 is type S, inserting it into sa now will sort it correctly.
// But we want to distinguish a j-1 with j-2 of type S from type L.
// We can process the former but want to leave the latter for the caller.
// We record the difference by negating j-1 if it is preceded by type L.
// Either way, the insertion (into the text[j-1] bucket) is guaranteed to
// happen at sa[i´] for some i´ < i, that is, in the portion of sa we have
// yet to scan. A single pass therefore sees indexes j, j-1, j-2, j-3,
// and so on, in sorted but not necessarily adjacent order, until it finds
// one preceded by an index of type L, at which point it must stop.
// That index (preceded by one of type L) is an LMS-substring start.
//
// As we scan through the array, we clear the worked entries (sa[i] > 0) to zero,
// and we flip sa[i] < 0 to -sa[i] and compact into the top of sa,
// so that the loop finishes with the top of sa containing exactly
// the LMS-substring start indexes, sorted by LMS-substring.
// Cache recently used bucket index:
cB := int64(0)
b := bucket[cB]
top := len(sa)
for i := len(sa) - 1; i >= 0; i-- {
j := int(sa[i])
if j == 0 {
// Skip empty entry.
continue
}
sa[i] = 0
if j < 0 {
// Leave discovered LMS-substring start index for caller.
top--
sa[top] = int64(-j)
continue
}
// Index j was on work queue, meaning k := j-1 is S-type,
// so we can now place k correctly into sa.
// If k-1 is S-type, queue k for processing later in this loop.
// If k-1 is L-type (text[k-1] > text[k]), queue -k to save for the caller.
k := j - 1
c1 := text[k]
c0 := text[k-1]
if c0 > c1 {
k = -k
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
b--
sa[b] = int64(k)
}
}
func length_8_64(text []byte, sa []int64, numLMS int) {
end := 0 // index of current LMS-substring end (0 indicates final LMS-substring)
// The encoding of N text bytes into a “length” word
// adds 1 to each byte, packs them into the bottom
// N*8 bits of a word, and then bitwise inverts the result.
// That is, the text sequence A B C (hex 41 42 43)
// encodes as ^uint64(0x42_43_44).
// LMS-substrings can never start or end with 0xFF.
// Adding 1 ensures the encoded byte sequence never
// starts or ends with 0x00, so that present bytes can be
// distinguished from zero-padding in the top bits,
// so the length need not be separately encoded.
// Inverting the bytes increases the chance that a
// 4-byte encoding will still be ≥ len(text).
// In particular, if the first byte is ASCII (<= 0x7E, so +1 <= 0x7F)
// then the high bit of the inversion will be set,
// making it clearly not a valid length (it would be a negative one).
//
// cx holds the pre-inverted encoding (the packed incremented bytes).
cx := uint64(0) // byte-only
// This stanza (until the blank line) is the "LMS-substring iterator",
// described in placeLMS_8_64 above, with one line added to maintain cx.
c0, c1, isTypeS := byte(0), byte(0), false
for i := len(text) - 1; i >= 0; i-- {
c0, c1 = text[i], c0
cx = cx<<8 | uint64(c1+1) // byte-only
if c0 < c1 {
isTypeS = true
} else if c0 > c1 && isTypeS {
isTypeS = false
// Index j = i+1 is the start of an LMS-substring.
// Compute length or encoded text to store in sa[j/2].
j := i + 1
var code int64
if end == 0 {
code = 0
} else {
code = int64(end - j)
if code <= 64/8 && ^cx >= uint64(len(text)) { // byte-only
code = int64(^cx) // byte-only
} // byte-only
}
sa[j>>1] = code
end = j + 1
cx = uint64(c1 + 1) // byte-only
}
}
}
func length_32(text []int32, sa []int32, numLMS int) {
end := 0 // index of current LMS-substring end (0 indicates final LMS-substring)
// The encoding of N text int32s into a “length” word
// adds 1 to each int32, packs them into the bottom
// N*8 bits of a word, and then bitwise inverts the result.
// That is, the text sequence A B C (hex 41 42 43)
// encodes as ^uint32(0x42_43_44).
// LMS-substrings can never start or end with 0xFF.
// Adding 1 ensures the encoded int32 sequence never
// starts or ends with 0x00, so that present int32s can be
// distinguished from zero-padding in the top bits,
// so the length need not be separately encoded.
// Inverting the int32s increases the chance that a
// 4-int32 encoding will still be ≥ len(text).
// In particular, if the first int32 is ASCII (<= 0x7E, so +1 <= 0x7F)
// then the high bit of the inversion will be set,
// making it clearly not a valid length (it would be a negative one).
//
// cx holds the pre-inverted encoding (the packed incremented int32s).
// This stanza (until the blank line) is the "LMS-substring iterator",
// described in placeLMS_32 above, with one line added to maintain cx.
c0, c1, isTypeS := int32(0), int32(0), false
for i := len(text) - 1; i >= 0; i-- {
c0, c1 = text[i], c0
if c0 < c1 {
isTypeS = true
} else if c0 > c1 && isTypeS {
isTypeS = false
// Index j = i+1 is the start of an LMS-substring.
// Compute length or encoded text to store in sa[j/2].
j := i + 1
var code int32
if end == 0 {
code = 0
} else {
code = int32(end - j)
}
sa[j>>1] = code
end = j + 1
}
}
}
func length_64(text []int64, sa []int64, numLMS int) {
end := 0 // index of current LMS-substring end (0 indicates final LMS-substring)
// The encoding of N text int64s into a “length” word
// adds 1 to each int64, packs them into the bottom
// N*8 bits of a word, and then bitwise inverts the result.
// That is, the text sequence A B C (hex 41 42 43)
// encodes as ^uint64(0x42_43_44).
// LMS-substrings can never start or end with 0xFF.
// Adding 1 ensures the encoded int64 sequence never
// starts or ends with 0x00, so that present int64s can be
// distinguished from zero-padding in the top bits,
// so the length need not be separately encoded.
// Inverting the int64s increases the chance that a
// 4-int64 encoding will still be ≥ len(text).
// In particular, if the first int64 is ASCII (<= 0x7E, so +1 <= 0x7F)
// then the high bit of the inversion will be set,
// making it clearly not a valid length (it would be a negative one).
//
// cx holds the pre-inverted encoding (the packed incremented int64s).
// This stanza (until the blank line) is the "LMS-substring iterator",
// described in placeLMS_64 above, with one line added to maintain cx.
c0, c1, isTypeS := int64(0), int64(0), false
for i := len(text) - 1; i >= 0; i-- {
c0, c1 = text[i], c0
if c0 < c1 {
isTypeS = true
} else if c0 > c1 && isTypeS {
isTypeS = false
// Index j = i+1 is the start of an LMS-substring.
// Compute length or encoded text to store in sa[j/2].
j := i + 1
var code int64
if end == 0 {
code = 0
} else {
code = int64(end - j)
}
sa[j>>1] = code
end = j + 1
}
}
}
func assignID_8_64(text []byte, sa []int64, numLMS int) int {
id := 0
lastLen := int64(-1) // impossible
lastPos := int64(0)
for _, j := range sa[len(sa)-numLMS:] {
// Is the LMS-substring at index j new, or is it the same as the last one we saw?
n := sa[j/2]
if n != lastLen {
goto New
}
if uint64(n) >= uint64(len(text)) {
// “Length” is really encoded full text, and they match.
goto Same
}
{
// Compare actual texts.
n := int(n)
this := text[j:][:n]
last := text[lastPos:][:n]
for i := 0; i < n; i++ {
if this[i] != last[i] {
goto New
}
}
goto Same
}
New:
id++
lastPos = j
lastLen = n
Same:
sa[j/2] = int64(id)
}
return id
}
func assignID_32(text []int32, sa []int32, numLMS int) int {
id := 0
lastLen := int32(-1) // impossible
lastPos := int32(0)
for _, j := range sa[len(sa)-numLMS:] {
// Is the LMS-substring at index j new, or is it the same as the last one we saw?
n := sa[j/2]
if n != lastLen {
goto New
}
if uint32(n) >= uint32(len(text)) {
// “Length” is really encoded full text, and they match.
goto Same
}
{
// Compare actual texts.
n := int(n)
this := text[j:][:n]
last := text[lastPos:][:n]
for i := 0; i < n; i++ {
if this[i] != last[i] {
goto New
}
}
goto Same
}
New:
id++
lastPos = j
lastLen = n
Same:
sa[j/2] = int32(id)
}
return id
}
func assignID_64(text []int64, sa []int64, numLMS int) int {
id := 0
lastLen := int64(-1) // impossible
lastPos := int64(0)
for _, j := range sa[len(sa)-numLMS:] {
// Is the LMS-substring at index j new, or is it the same as the last one we saw?
n := sa[j/2]
if n != lastLen {
goto New
}
if uint64(n) >= uint64(len(text)) {
// “Length” is really encoded full text, and they match.
goto Same
}
{
// Compare actual texts.
n := int(n)
this := text[j:][:n]
last := text[lastPos:][:n]
for i := 0; i < n; i++ {
if this[i] != last[i] {
goto New
}
}
goto Same
}
New:
id++
lastPos = j
lastLen = n
Same:
sa[j/2] = int64(id)
}
return id
}
func map_64(sa []int64, numLMS int) {
w := len(sa)
for i := len(sa) / 2; i >= 0; i-- {
j := sa[i]
if j > 0 {
w--
sa[w] = j - 1
}
}
}
func recurse_64(sa, oldTmp []int64, numLMS, maxID int) {
dst, saTmp, text := sa[:numLMS], sa[numLMS:len(sa)-numLMS], sa[len(sa)-numLMS:]
// Set up temporary space for recursive call.
// We must pass sais_64 a tmp buffer wiith at least maxID entries.
//
// The subproblem is guaranteed to have length at most len(sa)/2,
// so that sa can hold both the subproblem and its suffix array.
// Nearly all the time, however, the subproblem has length < len(sa)/3,
// in which case there is a subproblem-sized middle of sa that
// we can reuse for temporary space (saTmp).
// When recurse_64 is called from sais_8_64, oldTmp is length 512
// (from text_64), and saTmp will typically be much larger, so we'll use saTmp.
// When deeper recursions come back to recurse_64, now oldTmp is
// the saTmp from the top-most recursion, it is typically larger than
// the current saTmp (because the current sa gets smaller and smaller
// as the recursion gets deeper), and we keep reusing that top-most
// large saTmp instead of the offered smaller ones.
//
// Why is the subproblem length so often just under len(sa)/3?
// See Nong, Zhang, and Chen, section 3.6 for a plausible explanation.
// In brief, the len(sa)/2 case would correspond to an SLSLSLSLSLSL pattern
// in the input, perfect alternation of larger and smaller input bytes.
// Real text doesn't do that. If each L-type index is randomly followed
// by either an L-type or S-type index, then half the substrings will
// be of the form SLS, but the other half will be longer. Of that half,
// half (a quarter overall) will be SLLS; an eighth will be SLLLS, and so on.
// Not counting the final S in each (which overlaps the first S in the next),
// This works out to an average length 2×½ + 3×¼ + 4×⅛ + ... = 3.
// The space we need is further reduced by the fact that many of the
// short patterns like SLS will often be the same character sequences
// repeated throughout the text, reducing maxID relative to numLMS.
//
// For short inputs, the averages may not run in our favor, but then we
// can often fall back to using the length-512 tmp available in the
// top-most call. (Also a short allocation would not be a big deal.)
//
// For pathological inputs, we fall back to allocating a new tmp of length
// max(maxID, numLMS/2). This level of the recursion needs maxID,
// and all deeper levels of the recursion will need no more than numLMS/2,
// so this one allocation is guaranteed to suffice for the entire stack
// of recursive calls.
tmp := oldTmp
if len(tmp) < len(saTmp) {
tmp = saTmp
}
if len(tmp) < numLMS {
// TestSAIS/forcealloc reaches this code.
n := maxID
if n < numLMS/2 {
n = numLMS / 2
}
tmp = make([]int64, n)
}
// sais_64 requires that the caller arrange to clear dst,
// because in general the caller may know dst is
// freshly-allocated and already cleared. But this one is not.
for i := range dst {
dst[i] = 0
}
sais_64(text, maxID, dst, tmp)
}
func unmap_8_64(text []byte, sa []int64, numLMS int) {
unmap := sa[len(sa)-numLMS:]
j := len(unmap)
// "LMS-substring iterator" (see placeLMS_8_64 above).
c0, c1, isTypeS := byte(0), byte(0), false
for i := len(text) - 1; i >= 0; i-- {
c0, c1 = text[i], c0
if c0 < c1 {
isTypeS = true
} else if c0 > c1 && isTypeS {
isTypeS = false
// Populate inverse map.
j--
unmap[j] = int64(i + 1)
}
}
// Apply inverse map to subproblem suffix array.
sa = sa[:numLMS]
for i := 0; i < len(sa); i++ {
sa[i] = unmap[sa[i]]
}
}
func unmap_32(text []int32, sa []int32, numLMS int) {
unmap := sa[len(sa)-numLMS:]
j := len(unmap)
// "LMS-substring iterator" (see placeLMS_32 above).
c0, c1, isTypeS := int32(0), int32(0), false
for i := len(text) - 1; i >= 0; i-- {
c0, c1 = text[i], c0
if c0 < c1 {
isTypeS = true
} else if c0 > c1 && isTypeS {
isTypeS = false
// Populate inverse map.
j--
unmap[j] = int32(i + 1)
}
}
// Apply inverse map to subproblem suffix array.
sa = sa[:numLMS]
for i := 0; i < len(sa); i++ {
sa[i] = unmap[sa[i]]
}
}
func unmap_64(text []int64, sa []int64, numLMS int) {
unmap := sa[len(sa)-numLMS:]
j := len(unmap)
// "LMS-substring iterator" (see placeLMS_64 above).
c0, c1, isTypeS := int64(0), int64(0), false
for i := len(text) - 1; i >= 0; i-- {
c0, c1 = text[i], c0
if c0 < c1 {
isTypeS = true
} else if c0 > c1 && isTypeS {
isTypeS = false
// Populate inverse map.
j--
unmap[j] = int64(i + 1)
}
}
// Apply inverse map to subproblem suffix array.
sa = sa[:numLMS]
for i := 0; i < len(sa); i++ {
sa[i] = unmap[sa[i]]
}
}
func expand_8_64(text []byte, freq, bucket, sa []int64, numLMS int) {
bucketMax_8_64(text, freq, bucket)
bucket = bucket[:256] // eliminate bound check for bucket[c] below
// Loop backward through sa, always tracking
// the next index to populate from sa[:numLMS].
// When we get to one, populate it.
// Zero the rest of the slots; they have dead values in them.
x := numLMS - 1
saX := sa[x]
c := text[saX]
b := bucket[c] - 1
bucket[c] = b
for i := len(sa) - 1; i >= 0; i-- {
if i != int(b) {
sa[i] = 0
continue
}
sa[i] = saX
// Load next entry to put down (if any).
if x > 0 {
x--
saX = sa[x] // TODO bounds check
c = text[saX]
b = bucket[c] - 1
bucket[c] = b
}
}
}
func expand_32(text []int32, freq, bucket, sa []int32, numLMS int) {
bucketMax_32(text, freq, bucket)
// Loop backward through sa, always tracking
// the next index to populate from sa[:numLMS].
// When we get to one, populate it.
// Zero the rest of the slots; they have dead values in them.
x := numLMS - 1
saX := sa[x]
c := text[saX]
b := bucket[c] - 1
bucket[c] = b
for i := len(sa) - 1; i >= 0; i-- {
if i != int(b) {
sa[i] = 0
continue
}
sa[i] = saX
// Load next entry to put down (if any).
if x > 0 {
x--
saX = sa[x] // TODO bounds check
c = text[saX]
b = bucket[c] - 1
bucket[c] = b
}
}
}
func expand_64(text []int64, freq, bucket, sa []int64, numLMS int) {
bucketMax_64(text, freq, bucket)
// Loop backward through sa, always tracking
// the next index to populate from sa[:numLMS].
// When we get to one, populate it.
// Zero the rest of the slots; they have dead values in them.
x := numLMS - 1
saX := sa[x]
c := text[saX]
b := bucket[c] - 1
bucket[c] = b
for i := len(sa) - 1; i >= 0; i-- {
if i != int(b) {
sa[i] = 0
continue
}
sa[i] = saX
// Load next entry to put down (if any).
if x > 0 {
x--
saX = sa[x] // TODO bounds check
c = text[saX]
b = bucket[c] - 1
bucket[c] = b
}
}
}
func induceL_8_64(text []byte, sa, freq, bucket []int64) {
// Initialize positions for left side of character buckets.
bucketMin_8_64(text, freq, bucket)
bucket = bucket[:256] // eliminate bounds check for bucket[cB] below
// This scan is similar to the one in induceSubL_8_64 above.
// That one arranges to clear all but the leftmost L-type indexes.
// This scan leaves all the L-type indexes and the original S-type
// indexes, but it negates the positive leftmost L-type indexes
// (the ones that induceS_8_64 needs to process).
// expand_8_64 left out the implicit entry sa[-1] == len(text),
// corresponding to the identified type-L index len(text)-1.
// Process it before the left-to-right scan of sa proper.
// See body in loop for commentary.
k := len(text) - 1
c0, c1 := text[k-1], text[k]
if c0 < c1 {
k = -k
}
// Cache recently used bucket index.
cB := c1
b := bucket[cB]
sa[b] = int64(k)
b++
for i := 0; i < len(sa); i++ {
j := int(sa[i])
if j <= 0 {
// Skip empty or negated entry (including negated zero).
continue
}
// Index j was on work queue, meaning k := j-1 is L-type,
// so we can now place k correctly into sa.
// If k-1 is L-type, queue k for processing later in this loop.
// If k-1 is S-type (text[k-1] < text[k]), queue -k to save for the caller.
// If k is zero, k-1 doesn't exist, so we only need to leave it
// for the caller. The caller can't tell the difference between
// an empty slot and a non-empty zero, but there's no need
// to distinguish them anyway: the final suffix array will end up
// with one zero somewhere, and that will be a real zero.
k := j - 1
c1 := text[k]
if k > 0 {
if c0 := text[k-1]; c0 < c1 {
k = -k
}
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
sa[b] = int64(k)
b++
}
}
func induceL_32(text []int32, sa, freq, bucket []int32) {
// Initialize positions for left side of character buckets.
bucketMin_32(text, freq, bucket)
// This scan is similar to the one in induceSubL_32 above.
// That one arranges to clear all but the leftmost L-type indexes.
// This scan leaves all the L-type indexes and the original S-type
// indexes, but it negates the positive leftmost L-type indexes
// (the ones that induceS_32 needs to process).
// expand_32 left out the implicit entry sa[-1] == len(text),
// corresponding to the identified type-L index len(text)-1.
// Process it before the left-to-right scan of sa proper.
// See body in loop for commentary.
k := len(text) - 1
c0, c1 := text[k-1], text[k]
if c0 < c1 {
k = -k
}
// Cache recently used bucket index.
cB := c1
b := bucket[cB]
sa[b] = int32(k)
b++
for i := 0; i < len(sa); i++ {
j := int(sa[i])
if j <= 0 {
// Skip empty or negated entry (including negated zero).
continue
}
// Index j was on work queue, meaning k := j-1 is L-type,
// so we can now place k correctly into sa.
// If k-1 is L-type, queue k for processing later in this loop.
// If k-1 is S-type (text[k-1] < text[k]), queue -k to save for the caller.
// If k is zero, k-1 doesn't exist, so we only need to leave it
// for the caller. The caller can't tell the difference between
// an empty slot and a non-empty zero, but there's no need
// to distinguish them anyway: the final suffix array will end up
// with one zero somewhere, and that will be a real zero.
k := j - 1
c1 := text[k]
if k > 0 {
if c0 := text[k-1]; c0 < c1 {
k = -k
}
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
sa[b] = int32(k)
b++
}
}
func induceL_64(text []int64, sa, freq, bucket []int64) {
// Initialize positions for left side of character buckets.
bucketMin_64(text, freq, bucket)
// This scan is similar to the one in induceSubL_64 above.
// That one arranges to clear all but the leftmost L-type indexes.
// This scan leaves all the L-type indexes and the original S-type
// indexes, but it negates the positive leftmost L-type indexes
// (the ones that induceS_64 needs to process).
// expand_64 left out the implicit entry sa[-1] == len(text),
// corresponding to the identified type-L index len(text)-1.
// Process it before the left-to-right scan of sa proper.
// See body in loop for commentary.
k := len(text) - 1
c0, c1 := text[k-1], text[k]
if c0 < c1 {
k = -k
}
// Cache recently used bucket index.
cB := c1
b := bucket[cB]
sa[b] = int64(k)
b++
for i := 0; i < len(sa); i++ {
j := int(sa[i])
if j <= 0 {
// Skip empty or negated entry (including negated zero).
continue
}
// Index j was on work queue, meaning k := j-1 is L-type,
// so we can now place k correctly into sa.
// If k-1 is L-type, queue k for processing later in this loop.
// If k-1 is S-type (text[k-1] < text[k]), queue -k to save for the caller.
// If k is zero, k-1 doesn't exist, so we only need to leave it
// for the caller. The caller can't tell the difference between
// an empty slot and a non-empty zero, but there's no need
// to distinguish them anyway: the final suffix array will end up
// with one zero somewhere, and that will be a real zero.
k := j - 1
c1 := text[k]
if k > 0 {
if c0 := text[k-1]; c0 < c1 {
k = -k
}
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
sa[b] = int64(k)
b++
}
}
func induceS_8_64(text []byte, sa, freq, bucket []int64) {
// Initialize positions for right side of character buckets.
bucketMax_8_64(text, freq, bucket)
bucket = bucket[:256] // eliminate bounds check for bucket[cB] below
cB := byte(0)
b := bucket[cB]
for i := len(sa) - 1; i >= 0; i-- {
j := int(sa[i])
if j >= 0 {
// Skip non-flagged entry.
// (This loop can't see an empty entry; 0 means the real zero index.)
continue
}
// Negative j is a work queue entry; rewrite to positive j for final suffix array.
j = -j
sa[i] = int64(j)
// Index j was on work queue (encoded as -j but now decoded),
// meaning k := j-1 is L-type,
// so we can now place k correctly into sa.
// If k-1 is S-type, queue -k for processing later in this loop.
// If k-1 is L-type (text[k-1] > text[k]), queue k to save for the caller.
// If k is zero, k-1 doesn't exist, so we only need to leave it
// for the caller.
k := j - 1
c1 := text[k]
if k > 0 {
if c0 := text[k-1]; c0 <= c1 {
k = -k
}
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
b--
sa[b] = int64(k)
}
}
func induceS_32(text []int32, sa, freq, bucket []int32) {
// Initialize positions for right side of character buckets.
bucketMax_32(text, freq, bucket)
cB := int32(0)
b := bucket[cB]
for i := len(sa) - 1; i >= 0; i-- {
j := int(sa[i])
if j >= 0 {
// Skip non-flagged entry.
// (This loop can't see an empty entry; 0 means the real zero index.)
continue
}
// Negative j is a work queue entry; rewrite to positive j for final suffix array.
j = -j
sa[i] = int32(j)
// Index j was on work queue (encoded as -j but now decoded),
// meaning k := j-1 is L-type,
// so we can now place k correctly into sa.
// If k-1 is S-type, queue -k for processing later in this loop.
// If k-1 is L-type (text[k-1] > text[k]), queue k to save for the caller.
// If k is zero, k-1 doesn't exist, so we only need to leave it
// for the caller.
k := j - 1
c1 := text[k]
if k > 0 {
if c0 := text[k-1]; c0 <= c1 {
k = -k
}
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
b--
sa[b] = int32(k)
}
}
func induceS_64(text []int64, sa, freq, bucket []int64) {
// Initialize positions for right side of character buckets.
bucketMax_64(text, freq, bucket)
cB := int64(0)
b := bucket[cB]
for i := len(sa) - 1; i >= 0; i-- {
j := int(sa[i])
if j >= 0 {
// Skip non-flagged entry.
// (This loop can't see an empty entry; 0 means the real zero index.)
continue
}
// Negative j is a work queue entry; rewrite to positive j for final suffix array.
j = -j
sa[i] = int64(j)
// Index j was on work queue (encoded as -j but now decoded),
// meaning k := j-1 is L-type,
// so we can now place k correctly into sa.
// If k-1 is S-type, queue -k for processing later in this loop.
// If k-1 is L-type (text[k-1] > text[k]), queue k to save for the caller.
// If k is zero, k-1 doesn't exist, so we only need to leave it
// for the caller.
k := j - 1
c1 := text[k]
if k > 0 {
if c0 := text[k-1]; c0 <= c1 {
k = -k
}
}
if cB != c1 {
bucket[cB] = b
cB = c1
b = bucket[cB]
}
b--
sa[b] = int64(k)
}
}
src/index/suffixarray/suffixarray.go
View file @ 6ca324f2
...@@ -72,13 +72,15 @@ func (a *ints) slice(i, j int) ints { ...@@ -72,13 +72,15 @@ func (a *ints) slice(i, j int) ints {
} }
// New creates a new Index for data. // New creates a new Index for data.
// Index creation time is O(N*log(N)) for N = len(data). // Index creation time is O(N) for N = len(data).
func New(data []byte) *Index { func New(data []byte) *Index {
ix := &Index{data: data} ix := &Index{data: data}
if len(data) <= maxData32 { if len(data) <= maxData32 {
ix.sa.int32 = qsufsort32(data) ix.sa.int32 = make([]int32, len(data))
text_32(data, ix.sa.int32)
} else { } else {
ix.sa.int64 = qsufsort64(data) ix.sa.int64 = make([]int64, len(data))
text_64(data, ix.sa.int64)
} }
return ix return ix
} }
......
src/index/suffixarray/suffixarray_test.go
View file @ 6ca324f2
...@@ -314,6 +314,158 @@ func TestIndex64(t *testing.T) { ...@@ -314,6 +314,158 @@ func TestIndex64(t *testing.T) {
testIndex(t) testIndex(t)
} }
func TestNew32(t *testing.T) {
test(t, func(x []byte) []int {
sa := make([]int32, len(x))
text_32(x, sa)
out := make([]int, len(sa))
for i, v := range sa {
out[i] = int(v)
}
return out
})
}
func TestNew64(t *testing.T) {
test(t, func(x []byte) []int {
sa := make([]int64, len(x))
text_64(x, sa)
out := make([]int, len(sa))
for i, v := range sa {
out[i] = int(v)
}
return out
})
}
// test tests an arbitrary suffix array construction function.
// Generates many inputs, builds and checks suffix arrays.
func test(t *testing.T, build func([]byte) []int) {
t.Run("ababab...", func(t *testing.T) {
// Very repetitive input has numLMS = len(x)/2-1
// at top level, the largest it can be.
// But maxID is only two (aba and ab$).
size := 100000
if testing.Short() {
size = 10000
}
x := make([]byte, size)
for i := range x {
x[i] = "ab"[i%2]
}
testSA(t, x, build)
})
t.Run("forcealloc", func(t *testing.T) {
// Construct a pathological input that forces
// recurse_32 to allocate a new temporary buffer.
// The input must have more than N/3 LMS-substrings,
// which we arrange by repeating an SLSLSLSLSLSL pattern
// like ababab... above, but then we must also arrange
// for a large number of distinct LMS-substrings.
// We use this pattern:
// 1 255 1 254 1 253 1 ... 1 2 1 255 2 254 2 253 2 252 2 ...
// This gives approximately 2¹⁵ distinct LMS-substrings.
// We need to repeat at least one substring, though,
// or else the recursion can be bypassed entirely.
x := make([]byte, 100000, 100001)
lo := byte(1)
hi := byte(255)
for i := range x {
if i%2 == 0 {
x[i] = lo
} else {
x[i] = hi
hi--
if hi <= lo {
lo++
if lo == 0 {
lo = 1
}
hi = 255
}
}
}
x[:cap(x)][len(x)] = 0 // for sais.New
testSA(t, x, build)
})
t.Run("exhaustive2", func(t *testing.T) {
// All inputs over {0,1} up to length 21.
// Runs in about 10 seconds on my laptop.
x := make([]byte, 30)
numFail := 0
for n := 0; n <= 21; n++ {
if n > 12 && testing.Short() {
break
}
x[n] = 0 // for sais.New
testRec(t, x[:n], 0, 2, &numFail, build)
}
})
t.Run("exhaustive3", func(t *testing.T) {
// All inputs over {0,1,2} up to length 14.
// Runs in about 10 seconds on my laptop.
x := make([]byte, 30)
numFail := 0
for n := 0; n <= 14; n++ {
if n > 8 && testing.Short() {
break
}
x[n] = 0 // for sais.New
testRec(t, x[:n], 0, 3, &numFail, build)
}
})
}
// testRec fills x[i:] with all possible combinations of values in [1,max]
// and then calls testSA(t, x, build) for each one.
func testRec(t *testing.T, x []byte, i, max int, numFail *int, build func([]byte) []int) {
if i < len(x) {
for x[i] = 1; x[i] <= byte(max); x[i]++ {
testRec(t, x, i+1, max, numFail, build)
}
return
}
if !testSA(t, x, build) {
*numFail++
if *numFail >= 10 {
t.Errorf("stopping after %d failures", *numFail)
t.FailNow()
}
}
}
// testSA tests the suffix array build function on the input x.
// It constructs the suffix array and then checks that it is correct.
func testSA(t *testing.T, x []byte, build func([]byte) []int) bool {
defer func() {
if e := recover(); e != nil {
t.Logf("build %v", x)
panic(e)
}
}()
sa := build(x)
if len(sa) != len(x) {
t.Errorf("build %v: len(sa) = %d, want %d", x, len(sa), len(x))
return false
}
for i := 0; i+1 < len(sa); i++ {
if sa[i] < 0 || sa[i] >= len(x) || sa[i+1] < 0 || sa[i+1] >= len(x) {
t.Errorf("build %s: sa out of range: %v\n", x, sa)
return false
}
if bytes.Compare(x[sa[i]:], x[sa[i+1]:]) >= 0 {
t.Errorf("build %v -> %v\nsa[%d:] = %d,%d out of order", x, sa, i, sa[i], sa[i+1])
return false
}
}
return true
}
var ( var (
benchdata = make([]byte, 1e6) benchdata = make([]byte, 1e6)
benchrand = make([]byte, 1e6) benchrand = make([]byte, 1e6)
......
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment
GitLab Nexedi Edition | About GitLab | About Nexedi | 沪ICP备2021021310号-2 | 沪ICP备2021021310号-7