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// Copyright 2015 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package bidi
import (
// This file contains a port of the reference implementation of the
// Bidi Parentheses Algorithm:
// The implementation in this file covers definitions BD14-BD16 and rule N0
// of UAX#9.
// Some preprocessing is done for each rune before data is passed to this
// algorithm:
// - opening and closing brackets are identified
// - a bracket pair type, like '(' and ')' is assigned a unique identifier that
// is identical for the opening and closing bracket. It is left to do these
// mappings.
// - The BPA algorithm requires that bracket characters that are canonical
// equivalents of each other be able to be substituted for each other.
// It is the responsibility of the caller to do this canonicalization.
// In implementing BD16, this implementation departs slightly from the "logical"
// algorithm defined in UAX#9. In particular, the stack referenced there
// supports operations that go beyond a "basic" stack. An equivalent
// implementation based on a linked list is used here.
// Bidi_Paired_Bracket_Type
// BD14. An opening paired bracket is a character whose
// Bidi_Paired_Bracket_Type property value is Open.
// BD15. A closing paired bracket is a character whose
// Bidi_Paired_Bracket_Type property value is Close.
type bracketType byte
const (
bpNone bracketType = iota
// bracketPair holds a pair of index values for opening and closing bracket
// location of a bracket pair.
type bracketPair struct {
opener int
closer int
func (b *bracketPair) String() string {
return fmt.Sprintf("(%v, %v)", b.opener, b.closer)
// bracketPairs is a slice of bracketPairs with a sort.Interface implementation.
type bracketPairs []bracketPair
func (b bracketPairs) Len() int { return len(b) }
func (b bracketPairs) Swap(i, j int) { b[i], b[j] = b[j], b[i] }
func (b bracketPairs) Less(i, j int) bool { return b[i].opener < b[j].opener }
// resolvePairedBrackets runs the paired bracket part of the UBA algorithm.
// For each rune, it takes the indexes into the original string, the class the
// bracket type (in pairTypes) and the bracket identifier (pairValues). It also
// takes the direction type for the start-of-sentence and the embedding level.
// The identifiers for bracket types are the rune of the canonicalized opening
// bracket for brackets (open or close) or 0 for runes that are not brackets.
func resolvePairedBrackets(s *isolatingRunSequence) {
p := bracketPairer{
sos: s.sos,
openers: list.New(),
codesIsolatedRun: s.types,
indexes: s.indexes,
dirEmbed := L
if s.level&1 != 0 {
dirEmbed = R
p.locateBrackets(s.p.pairTypes, s.p.pairValues)
p.resolveBrackets(dirEmbed, s.p.initialTypes)
type bracketPairer struct {
sos Class // direction corresponding to start of sequence
// The following is a restatement of BD 16 using non-algorithmic language.
// A bracket pair is a pair of characters consisting of an opening
// paired bracket and a closing paired bracket such that the
// Bidi_Paired_Bracket property value of the former equals the latter,
// subject to the following constraints.
// - both characters of a pair occur in the same isolating run sequence
// - the closing character of a pair follows the opening character
// - any bracket character can belong at most to one pair, the earliest possible one
// - any bracket character not part of a pair is treated like an ordinary character
// - pairs may nest properly, but their spans may not overlap otherwise
// Bracket characters with canonical decompositions are supposed to be
// treated as if they had been normalized, to allow normalized and non-
// normalized text to give the same result. In this implementation that step
// is pushed out to the caller. The caller has to ensure that the pairValue
// slices contain the rune of the opening bracket after normalization for
// any opening or closing bracket.
openers *list.List // list of positions for opening brackets
// bracket pair positions sorted by location of opening bracket
pairPositions bracketPairs
codesIsolatedRun []Class // directional bidi codes for an isolated run
indexes []int // array of index values into the original string
// matchOpener reports whether characters at given positions form a matching
// bracket pair.
func (p *bracketPairer) matchOpener(pairValues []rune, opener, closer int) bool {
return pairValues[p.indexes[opener]] == pairValues[p.indexes[closer]]
const maxPairingDepth = 63
// locateBrackets locates matching bracket pairs according to BD16.
// This implementation uses a linked list instead of a stack, because, while
// elements are added at the front (like a push) they are not generally removed
// in atomic 'pop' operations, reducing the benefit of the stack archetype.
func (p *bracketPairer) locateBrackets(pairTypes []bracketType, pairValues []rune) {
// traverse the run
// do that explicitly (not in a for-each) so we can record position
for i, index := range p.indexes {
// look at the bracket type for each character
if pairTypes[index] == bpNone || p.codesIsolatedRun[i] != ON {
// continue scanning
switch pairTypes[index] {
case bpOpen:
// check if maximum pairing depth reached
if p.openers.Len() == maxPairingDepth {
// remember opener location, most recent first
case bpClose:
// see if there is a match
count := 0
for elem := p.openers.Front(); elem != nil; elem = elem.Next() {
opener := elem.Value.(int)
if p.matchOpener(pairValues, opener, i) {
// if the opener matches, add nested pair to the ordered list
p.pairPositions = append(p.pairPositions, bracketPair{opener, i})
// remove up to and including matched opener
for ; count > 0; count-- {
// if we get here, the closing bracket matched no openers
// and gets ignored
// Bracket pairs within an isolating run sequence are processed as units so
// that both the opening and the closing paired bracket in a pair resolve to
// the same direction.
// N0. Process bracket pairs in an isolating run sequence sequentially in
// the logical order of the text positions of the opening paired brackets
// using the logic given below. Within this scope, bidirectional types EN
// and AN are treated as R.
// Identify the bracket pairs in the current isolating run sequence
// according to BD16. For each bracket-pair element in the list of pairs of
// text positions:
// a Inspect the bidirectional types of the characters enclosed within the
// bracket pair.
// b If any strong type (either L or R) matching the embedding direction is
// found, set the type for both brackets in the pair to match the embedding
// direction.
// o [ e ] o -> o e e e o
// o [ o e ] -> o e o e e
// o [ NI e ] -> o e NI e e
// c Otherwise, if a strong type (opposite the embedding direction) is
// found, test for adjacent strong types as follows: 1 First, check
// backwards before the opening paired bracket until the first strong type
// (L, R, or sos) is found. If that first preceding strong type is opposite
// the embedding direction, then set the type for both brackets in the pair
// to that type. 2 Otherwise, set the type for both brackets in the pair to
// the embedding direction.
// o [ o ] e -> o o o o e
// o [ o NI ] o -> o o o NI o o
// e [ o ] o -> e e o e o
// e [ o ] e -> e e o e e
// e ( o [ o ] NI ) e -> e e o o o o NI e e
// d Otherwise, do not set the type for the current bracket pair. Note that
// if the enclosed text contains no strong types the paired brackets will
// both resolve to the same level when resolved individually using rules N1
// and N2.
// e ( NI ) o -> e ( NI ) o
// getStrongTypeN0 maps character's directional code to strong type as required
// by rule N0.
// TODO: have separate type for "strong" directionality.
func (p *bracketPairer) getStrongTypeN0(index int) Class {
switch p.codesIsolatedRun[index] {
// in the scope of N0, number types are treated as R
case EN, AN, AL, R:
return R
case L:
return L
return ON
// classifyPairContent reports the strong types contained inside a Bracket Pair,
// assuming the given embedding direction.
// It returns ON if no strong type is found. If a single strong type is found,
// it returns this this type. Otherwise it returns the embedding direction.
// TODO: use separate type for "strong" directionality.
func (p *bracketPairer) classifyPairContent(loc bracketPair, dirEmbed Class) Class {
dirOpposite := ON
for i := loc.opener + 1; i < loc.closer; i++ {
dir := p.getStrongTypeN0(i)
if dir == ON {
if dir == dirEmbed {
return dir // type matching embedding direction found
dirOpposite = dir
// return ON if no strong type found, or class opposite to dirEmbed
return dirOpposite
// classBeforePair determines which strong types are present before a Bracket
// Pair. Return R or L if strong type found, otherwise ON.
func (p *bracketPairer) classBeforePair(loc bracketPair) Class {
for i := loc.opener - 1; i >= 0; i-- {
if dir := p.getStrongTypeN0(i); dir != ON {
return dir
// no strong types found, return sos
return p.sos
// assignBracketType implements rule N0 for a single bracket pair.
func (p *bracketPairer) assignBracketType(loc bracketPair, dirEmbed Class, initialTypes []Class) {
// rule "N0, a", inspect contents of pair
dirPair := p.classifyPairContent(loc, dirEmbed)
// dirPair is now L, R, or N (no strong type found)
// the following logical tests are performed out of order compared to
// the statement of the rules but yield the same results
if dirPair == ON {
return // case "d" - nothing to do
if dirPair != dirEmbed {
// case "c": strong type found, opposite - check before (c.1)
dirPair = p.classBeforePair(loc)
if dirPair == dirEmbed || dirPair == ON {
// no strong opposite type found before - use embedding (c.2)
dirPair = dirEmbed
// else: case "b", strong type found matching embedding,
// no explicit action needed, as dirPair is already set to embedding
// direction
// set the bracket types to the type found
p.setBracketsToType(loc, dirPair, initialTypes)
func (p *bracketPairer) setBracketsToType(loc bracketPair, dirPair Class, initialTypes []Class) {
p.codesIsolatedRun[loc.opener] = dirPair
p.codesIsolatedRun[loc.closer] = dirPair
for i := loc.opener + 1; i < loc.closer; i++ {
index := p.indexes[i]
if initialTypes[index] != NSM {
p.codesIsolatedRun[i] = dirPair
for i := loc.closer + 1; i < len(p.indexes); i++ {
index := p.indexes[i]
if initialTypes[index] != NSM {
p.codesIsolatedRun[i] = dirPair
// resolveBrackets implements rule N0 for a list of pairs.
func (p *bracketPairer) resolveBrackets(dirEmbed Class, initialTypes []Class) {
for _, loc := range p.pairPositions {
p.assignBracketType(loc, dirEmbed, initialTypes)