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runcontainer.go
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runcontainer.go
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package roaring
//
// Copyright (c) 2016 by the roaring authors.
// Licensed under the Apache License, Version 2.0.
//
// We derive a few lines of code from the sort.Search
// function in the golang standard library. That function
// is Copyright 2009 The Go Authors, and licensed
// under the following BSD-style license.
/*
Copyright (c) 2009 The Go Authors. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following disclaimer
in the documentation and/or other materials provided with the
distribution.
* Neither the name of Google Inc. nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
import (
"fmt"
"sort"
"unsafe"
)
//go:generate msgp -unexported
// runContainer16 does run-length encoding of sets of
// uint16 integers.
type runContainer16 struct {
iv []interval16
card int64
// avoid allocation during search
myOpts searchOptions `msg:"-"`
}
// interval16 is the internal to runContainer16
// structure that maintains the individual [start, last]
// closed intervals.
type interval16 struct {
start uint16
length uint16 // length minus 1
}
func newInterval16Range(start, last uint16) interval16 {
if last < start {
panic(fmt.Sprintf("last (%d) cannot be smaller than start (%d)", last, start))
}
return interval16{
start,
last - start,
}
}
// runlen returns the count of integers in the interval.
func (iv interval16) runlen() int64 {
return int64(iv.length) + 1
}
func (iv interval16) last() uint16 {
return iv.start + iv.length
}
// String produces a human viewable string of the contents.
func (iv interval16) String() string {
return fmt.Sprintf("[%d, %d]", iv.start, iv.length)
}
func ivalString16(iv []interval16) string {
var s string
var j int
var p interval16
for j, p = range iv {
s += fmt.Sprintf("%v:[%d, %d], ", j, p.start, p.last())
}
return s
}
// String produces a human viewable string of the contents.
func (rc *runContainer16) String() string {
if len(rc.iv) == 0 {
return "runContainer16{}"
}
is := ivalString16(rc.iv)
return `runContainer16{` + is + `}`
}
// uint16Slice is a sort.Sort convenience method
type uint16Slice []uint16
// Len returns the length of p.
func (p uint16Slice) Len() int { return len(p) }
// Less returns p[i] < p[j]
func (p uint16Slice) Less(i, j int) bool { return p[i] < p[j] }
// Swap swaps elements i and j.
func (p uint16Slice) Swap(i, j int) { p[i], p[j] = p[j], p[i] }
//msgp:ignore addHelper
// addHelper helps build a runContainer16.
type addHelper16 struct {
runstart uint16
runlen uint16
actuallyAdded uint16
m []interval16
rc *runContainer16
}
func (ah *addHelper16) storeIval(runstart, runlen uint16) {
mi := interval16{start: runstart, length: runlen}
ah.m = append(ah.m, mi)
}
func (ah *addHelper16) add(cur, prev uint16, i int) {
if cur == prev+1 {
ah.runlen++
ah.actuallyAdded++
} else {
if cur < prev {
panic(fmt.Sprintf("newRunContainer16FromVals sees "+
"unsorted vals; vals[%v]=cur=%v < prev=%v. Sort your vals"+
" before calling us with alreadySorted == true.", i, cur, prev))
}
if cur == prev {
// ignore duplicates
} else {
ah.actuallyAdded++
ah.storeIval(ah.runstart, ah.runlen)
ah.runstart = cur
ah.runlen = 0
}
}
}
// newRunContainerRange makes a new container made of just the specified closed interval [rangestart,rangelast]
func newRunContainer16Range(rangestart uint16, rangelast uint16) *runContainer16 {
rc := &runContainer16{}
rc.iv = append(rc.iv, newInterval16Range(rangestart, rangelast))
return rc
}
// newRunContainer16FromVals makes a new container from vals.
//
// For efficiency, vals should be sorted in ascending order.
// Ideally vals should not contain duplicates, but we detect and
// ignore them. If vals is already sorted in ascending order, then
// pass alreadySorted = true. Otherwise, for !alreadySorted,
// we will sort vals before creating a runContainer16 of them.
// We sort the original vals, so this will change what the
// caller sees in vals as a side effect.
func newRunContainer16FromVals(alreadySorted bool, vals ...uint16) *runContainer16 {
// keep this in sync with newRunContainer16FromArray below
rc := &runContainer16{}
ah := addHelper16{rc: rc}
if !alreadySorted {
sort.Sort(uint16Slice(vals))
}
n := len(vals)
var cur, prev uint16
switch {
case n == 0:
// nothing more
case n == 1:
ah.m = append(ah.m, newInterval16Range(vals[0], vals[0]))
ah.actuallyAdded++
default:
ah.runstart = vals[0]
ah.actuallyAdded++
for i := 1; i < n; i++ {
prev = vals[i-1]
cur = vals[i]
ah.add(cur, prev, i)
}
ah.storeIval(ah.runstart, ah.runlen)
}
rc.iv = ah.m
rc.card = int64(ah.actuallyAdded)
return rc
}
// newRunContainer16FromBitmapContainer makes a new run container from bc,
// somewhat efficiently. For reference, see the Java
// https://github.com/RoaringBitmap/RoaringBitmap/blob/master/src/main/java/org/roaringbitmap/RunContainer.java#L145-L192
func newRunContainer16FromBitmapContainer(bc *bitmapContainer) *runContainer16 {
rc := &runContainer16{}
nbrRuns := bc.numberOfRuns()
if nbrRuns == 0 {
return rc
}
rc.iv = make([]interval16, nbrRuns)
longCtr := 0 // index of current long in bitmap
curWord := bc.bitmap[0] // its value
runCount := 0
for {
// potentially multiword advance to first 1 bit
for curWord == 0 && longCtr < len(bc.bitmap)-1 {
longCtr++
curWord = bc.bitmap[longCtr]
}
if curWord == 0 {
// wrap up, no more runs
return rc
}
localRunStart := countTrailingZeros(curWord)
runStart := localRunStart + 64*longCtr
// stuff 1s into number's LSBs
curWordWith1s := curWord | (curWord - 1)
// find the next 0, potentially in a later word
runEnd := 0
for curWordWith1s == maxWord && longCtr < len(bc.bitmap)-1 {
longCtr++
curWordWith1s = bc.bitmap[longCtr]
}
if curWordWith1s == maxWord {
// a final unterminated run of 1s
runEnd = wordSizeInBits + longCtr*64
rc.iv[runCount].start = uint16(runStart)
rc.iv[runCount].length = uint16(runEnd) - uint16(runStart) - 1
return rc
}
localRunEnd := countTrailingZeros(^curWordWith1s)
runEnd = localRunEnd + longCtr*64
rc.iv[runCount].start = uint16(runStart)
rc.iv[runCount].length = uint16(runEnd) - 1 - uint16(runStart)
runCount++
// now, zero out everything right of runEnd.
curWord = curWordWith1s & (curWordWith1s + 1)
// We've lathered and rinsed, so repeat...
}
}
//
// newRunContainer16FromArray populates a new
// runContainer16 from the contents of arr.
//
func newRunContainer16FromArray(arr *arrayContainer) *runContainer16 {
// keep this in sync with newRunContainer16FromVals above
rc := &runContainer16{}
ah := addHelper16{rc: rc}
n := arr.getCardinality()
var cur, prev uint16
switch {
case n == 0:
// nothing more
case n == 1:
ah.m = append(ah.m, newInterval16Range(arr.content[0], arr.content[0]))
ah.actuallyAdded++
default:
ah.runstart = arr.content[0]
ah.actuallyAdded++
for i := 1; i < n; i++ {
prev = arr.content[i-1]
cur = arr.content[i]
ah.add(cur, prev, i)
}
ah.storeIval(ah.runstart, ah.runlen)
}
rc.iv = ah.m
rc.card = int64(ah.actuallyAdded)
return rc
}
// set adds the integers in vals to the set. Vals
// must be sorted in increasing order; if not, you should set
// alreadySorted to false, and we will sort them in place for you.
// (Be aware of this side effect -- it will affect the callers
// view of vals).
//
// If you have a small number of additions to an already
// big runContainer16, calling Add() may be faster.
func (rc *runContainer16) set(alreadySorted bool, vals ...uint16) {
rc2 := newRunContainer16FromVals(alreadySorted, vals...)
un := rc.union(rc2)
rc.iv = un.iv
rc.card = 0
}
// canMerge returns true iff the intervals
// a and b either overlap or they are
// contiguous and so can be merged into
// a single interval.
func canMerge16(a, b interval16) bool {
if int64(a.last())+1 < int64(b.start) {
return false
}
return int64(b.last())+1 >= int64(a.start)
}
// haveOverlap differs from canMerge in that
// it tells you if the intersection of a
// and b would contain an element (otherwise
// it would be the empty set, and we return
// false).
func haveOverlap16(a, b interval16) bool {
if int64(a.last())+1 <= int64(b.start) {
return false
}
return int64(b.last())+1 > int64(a.start)
}
// mergeInterval16s joins a and b into a
// new interval, and panics if it cannot.
func mergeInterval16s(a, b interval16) (res interval16) {
if !canMerge16(a, b) {
panic(fmt.Sprintf("cannot merge %#v and %#v", a, b))
}
if b.start < a.start {
res.start = b.start
} else {
res.start = a.start
}
if b.last() > a.last() {
res.length = b.last() - res.start
} else {
res.length = a.last() - res.start
}
return
}
// intersectInterval16s returns the intersection
// of a and b. The isEmpty flag will be true if
// a and b were disjoint.
func intersectInterval16s(a, b interval16) (res interval16, isEmpty bool) {
if !haveOverlap16(a, b) {
isEmpty = true
return
}
if b.start > a.start {
res.start = b.start
} else {
res.start = a.start
}
bEnd := b.last()
aEnd := a.last()
var resEnd uint16
if bEnd < aEnd {
resEnd = bEnd
} else {
resEnd = aEnd
}
res.length = resEnd - res.start
return
}
// union merges two runContainer16s, producing
// a new runContainer16 with the union of rc and b.
func (rc *runContainer16) union(b *runContainer16) *runContainer16 {
// rc is also known as 'a' here, but golint insisted we
// call it rc for consistency with the rest of the methods.
var m []interval16
alim := int64(len(rc.iv))
blim := int64(len(b.iv))
var na int64 // next from a
var nb int64 // next from b
// merged holds the current merge output, which might
// get additional merges before being appended to m.
var merged interval16
var mergedUsed bool // is merged being used at the moment?
var cura interval16 // currently considering this interval16 from a
var curb interval16 // currently considering this interval16 from b
pass := 0
for na < alim && nb < blim {
pass++
cura = rc.iv[na]
curb = b.iv[nb]
if mergedUsed {
mergedUpdated := false
if canMerge16(cura, merged) {
merged = mergeInterval16s(cura, merged)
na = rc.indexOfIntervalAtOrAfter(int64(merged.last())+1, na+1)
mergedUpdated = true
}
if canMerge16(curb, merged) {
merged = mergeInterval16s(curb, merged)
nb = b.indexOfIntervalAtOrAfter(int64(merged.last())+1, nb+1)
mergedUpdated = true
}
if !mergedUpdated {
// we know that merged is disjoint from cura and curb
m = append(m, merged)
mergedUsed = false
}
continue
} else {
// !mergedUsed
if !canMerge16(cura, curb) {
if cura.start < curb.start {
m = append(m, cura)
na++
} else {
m = append(m, curb)
nb++
}
} else {
merged = mergeInterval16s(cura, curb)
mergedUsed = true
na = rc.indexOfIntervalAtOrAfter(int64(merged.last())+1, na+1)
nb = b.indexOfIntervalAtOrAfter(int64(merged.last())+1, nb+1)
}
}
}
var aDone, bDone bool
if na >= alim {
aDone = true
}
if nb >= blim {
bDone = true
}
// finish by merging anything remaining into merged we can:
if mergedUsed {
if !aDone {
aAdds:
for na < alim {
cura = rc.iv[na]
if canMerge16(cura, merged) {
merged = mergeInterval16s(cura, merged)
na = rc.indexOfIntervalAtOrAfter(int64(merged.last())+1, na+1)
} else {
break aAdds
}
}
}
if !bDone {
bAdds:
for nb < blim {
curb = b.iv[nb]
if canMerge16(curb, merged) {
merged = mergeInterval16s(curb, merged)
nb = b.indexOfIntervalAtOrAfter(int64(merged.last())+1, nb+1)
} else {
break bAdds
}
}
}
m = append(m, merged)
}
if na < alim {
m = append(m, rc.iv[na:]...)
}
if nb < blim {
m = append(m, b.iv[nb:]...)
}
res := &runContainer16{iv: m}
return res
}
// unionCardinality returns the cardinality of the merger of two runContainer16s, the union of rc and b.
func (rc *runContainer16) unionCardinality(b *runContainer16) uint64 {
// rc is also known as 'a' here, but golint insisted we
// call it rc for consistency with the rest of the methods.
answer := uint64(0)
alim := int64(len(rc.iv))
blim := int64(len(b.iv))
var na int64 // next from a
var nb int64 // next from b
// merged holds the current merge output, which might
// get additional merges before being appended to m.
var merged interval16
var mergedUsed bool // is merged being used at the moment?
var cura interval16 // currently considering this interval16 from a
var curb interval16 // currently considering this interval16 from b
pass := 0
for na < alim && nb < blim {
pass++
cura = rc.iv[na]
curb = b.iv[nb]
if mergedUsed {
mergedUpdated := false
if canMerge16(cura, merged) {
merged = mergeInterval16s(cura, merged)
na = rc.indexOfIntervalAtOrAfter(int64(merged.last())+1, na+1)
mergedUpdated = true
}
if canMerge16(curb, merged) {
merged = mergeInterval16s(curb, merged)
nb = b.indexOfIntervalAtOrAfter(int64(merged.last())+1, nb+1)
mergedUpdated = true
}
if !mergedUpdated {
// we know that merged is disjoint from cura and curb
//m = append(m, merged)
answer += uint64(merged.last()) - uint64(merged.start) + 1
mergedUsed = false
}
continue
} else {
// !mergedUsed
if !canMerge16(cura, curb) {
if cura.start < curb.start {
answer += uint64(cura.last()) - uint64(cura.start) + 1
//m = append(m, cura)
na++
} else {
answer += uint64(curb.last()) - uint64(curb.start) + 1
//m = append(m, curb)
nb++
}
} else {
merged = mergeInterval16s(cura, curb)
mergedUsed = true
na = rc.indexOfIntervalAtOrAfter(int64(merged.last())+1, na+1)
nb = b.indexOfIntervalAtOrAfter(int64(merged.last())+1, nb+1)
}
}
}
var aDone, bDone bool
if na >= alim {
aDone = true
}
if nb >= blim {
bDone = true
}
// finish by merging anything remaining into merged we can:
if mergedUsed {
if !aDone {
aAdds:
for na < alim {
cura = rc.iv[na]
if canMerge16(cura, merged) {
merged = mergeInterval16s(cura, merged)
na = rc.indexOfIntervalAtOrAfter(int64(merged.last())+1, na+1)
} else {
break aAdds
}
}
}
if !bDone {
bAdds:
for nb < blim {
curb = b.iv[nb]
if canMerge16(curb, merged) {
merged = mergeInterval16s(curb, merged)
nb = b.indexOfIntervalAtOrAfter(int64(merged.last())+1, nb+1)
} else {
break bAdds
}
}
}
//m = append(m, merged)
answer += uint64(merged.last()) - uint64(merged.start) + 1
}
for _, r := range rc.iv[na:] {
answer += uint64(r.last()) - uint64(r.start) + 1
}
for _, r := range b.iv[nb:] {
answer += uint64(r.last()) - uint64(r.start) + 1
}
return answer
}
// indexOfIntervalAtOrAfter is a helper for union.
func (rc *runContainer16) indexOfIntervalAtOrAfter(key int64, startIndex int64) int64 {
rc.myOpts.startIndex = startIndex
rc.myOpts.endxIndex = 0
w, already, _ := rc.search(key, &rc.myOpts)
if already {
return w
}
return w + 1
}
// intersect returns a new runContainer16 holding the
// intersection of rc (also known as 'a') and b.
func (rc *runContainer16) intersect(b *runContainer16) *runContainer16 {
a := rc
numa := int64(len(a.iv))
numb := int64(len(b.iv))
res := &runContainer16{}
if numa == 0 || numb == 0 {
return res
}
if numa == 1 && numb == 1 {
if !haveOverlap16(a.iv[0], b.iv[0]) {
return res
}
}
var output []interval16
var acuri int64
var bcuri int64
astart := int64(a.iv[acuri].start)
bstart := int64(b.iv[bcuri].start)
var intersection interval16
var leftoverstart int64
var isOverlap, isLeftoverA, isLeftoverB bool
var done bool
toploop:
for acuri < numa && bcuri < numb {
isOverlap, isLeftoverA, isLeftoverB, leftoverstart, intersection =
intersectWithLeftover16(astart, int64(a.iv[acuri].last()), bstart, int64(b.iv[bcuri].last()))
if !isOverlap {
switch {
case astart < bstart:
acuri, done = a.findNextIntervalThatIntersectsStartingFrom(acuri+1, bstart)
if done {
break toploop
}
astart = int64(a.iv[acuri].start)
case astart > bstart:
bcuri, done = b.findNextIntervalThatIntersectsStartingFrom(bcuri+1, astart)
if done {
break toploop
}
bstart = int64(b.iv[bcuri].start)
//default:
// panic("impossible that astart == bstart, since !isOverlap")
}
} else {
// isOverlap
output = append(output, intersection)
switch {
case isLeftoverA:
// note that we change astart without advancing acuri,
// since we need to capture any 2ndary intersections with a.iv[acuri]
astart = leftoverstart
bcuri++
if bcuri >= numb {
break toploop
}
bstart = int64(b.iv[bcuri].start)
case isLeftoverB:
// note that we change bstart without advancing bcuri,
// since we need to capture any 2ndary intersections with b.iv[bcuri]
bstart = leftoverstart
acuri++
if acuri >= numa {
break toploop
}
astart = int64(a.iv[acuri].start)
default:
// neither had leftover, both completely consumed
// optionally, assert for sanity:
//if a.iv[acuri].endx != b.iv[bcuri].endx {
// panic("huh? should only be possible that endx agree now!")
//}
// advance to next a interval
acuri++
if acuri >= numa {
break toploop
}
astart = int64(a.iv[acuri].start)
// advance to next b interval
bcuri++
if bcuri >= numb {
break toploop
}
bstart = int64(b.iv[bcuri].start)
}
}
} // end for toploop
if len(output) == 0 {
return res
}
res.iv = output
return res
}
// intersectCardinality returns the cardinality of the
// intersection of rc (also known as 'a') and b.
func (rc *runContainer16) intersectCardinality(b *runContainer16) int64 {
answer := int64(0)
a := rc
numa := int64(len(a.iv))
numb := int64(len(b.iv))
if numa == 0 || numb == 0 {
return 0
}
if numa == 1 && numb == 1 {
if !haveOverlap16(a.iv[0], b.iv[0]) {
return 0
}
}
var acuri int64
var bcuri int64
astart := int64(a.iv[acuri].start)
bstart := int64(b.iv[bcuri].start)
var intersection interval16
var leftoverstart int64
var isOverlap, isLeftoverA, isLeftoverB bool
var done bool
pass := 0
toploop:
for acuri < numa && bcuri < numb {
pass++
isOverlap, isLeftoverA, isLeftoverB, leftoverstart, intersection =
intersectWithLeftover16(astart, int64(a.iv[acuri].last()), bstart, int64(b.iv[bcuri].last()))
if !isOverlap {
switch {
case astart < bstart:
acuri, done = a.findNextIntervalThatIntersectsStartingFrom(acuri+1, bstart)
if done {
break toploop
}
astart = int64(a.iv[acuri].start)
case astart > bstart:
bcuri, done = b.findNextIntervalThatIntersectsStartingFrom(bcuri+1, astart)
if done {
break toploop
}
bstart = int64(b.iv[bcuri].start)
//default:
// panic("impossible that astart == bstart, since !isOverlap")
}
} else {
// isOverlap
answer += int64(intersection.last()) - int64(intersection.start) + 1
switch {
case isLeftoverA:
// note that we change astart without advancing acuri,
// since we need to capture any 2ndary intersections with a.iv[acuri]
astart = leftoverstart
bcuri++
if bcuri >= numb {
break toploop
}
bstart = int64(b.iv[bcuri].start)
case isLeftoverB:
// note that we change bstart without advancing bcuri,
// since we need to capture any 2ndary intersections with b.iv[bcuri]
bstart = leftoverstart
acuri++
if acuri >= numa {
break toploop
}
astart = int64(a.iv[acuri].start)
default:
// neither had leftover, both completely consumed
// optionally, assert for sanity:
//if a.iv[acuri].endx != b.iv[bcuri].endx {
// panic("huh? should only be possible that endx agree now!")
//}
// advance to next a interval
acuri++
if acuri >= numa {
break toploop
}
astart = int64(a.iv[acuri].start)
// advance to next b interval
bcuri++
if bcuri >= numb {
break toploop
}
bstart = int64(b.iv[bcuri].start)
}
}
} // end for toploop
return answer
}
// get returns true iff key is in the container.
func (rc *runContainer16) contains(key uint16) bool {
_, in, _ := rc.search(int64(key), nil)
return in
}
// numIntervals returns the count of intervals in the container.
func (rc *runContainer16) numIntervals() int {
return len(rc.iv)
}
// searchOptions allows us to accelerate search with
// prior knowledge of (mostly lower) bounds. This is used by Union
// and Intersect.
type searchOptions struct {
// start here instead of at 0
startIndex int64
// upper bound instead of len(rc.iv);
// endxIndex == 0 means ignore the bound and use
// endxIndex == n ==len(rc.iv) which is also
// naturally the default for search()
// when opt = nil.
endxIndex int64
}
// search returns alreadyPresent to indicate if the
// key is already in one of our interval16s.
//
// If key is alreadyPresent, then whichInterval16 tells
// you where.
//
// If key is not already present, then whichInterval16 is
// set as follows:
//
// a) whichInterval16 == len(rc.iv)-1 if key is beyond our
// last interval16 in rc.iv;
//
// b) whichInterval16 == -1 if key is before our first
// interval16 in rc.iv;
//
// c) whichInterval16 is set to the minimum index of rc.iv
// which comes strictly before the key;
// so rc.iv[whichInterval16].last < key,
// and if whichInterval16+1 exists, then key < rc.iv[whichInterval16+1].start
// (Note that whichInterval16+1 won't exist when
// whichInterval16 is the last interval.)
//
// runContainer16.search always returns whichInterval16 < len(rc.iv).
//
// If not nil, opts can be used to further restrict
// the search space.
//
func (rc *runContainer16) search(key int64, opts *searchOptions) (whichInterval16 int64, alreadyPresent bool, numCompares int) {
n := int64(len(rc.iv))
if n == 0 {
return -1, false, 0
}
startIndex := int64(0)
endxIndex := n
if opts != nil {
startIndex = opts.startIndex
// let endxIndex == 0 mean no effect
if opts.endxIndex > 0 {
endxIndex = opts.endxIndex
}
}
// sort.Search returns the smallest index i
// in [0, n) at which f(i) is true, assuming that on the range [0, n),
// f(i) == true implies f(i+1) == true.
// If there is no such index, Search returns n.
// For correctness, this began as verbatim snippet from
// sort.Search in the Go standard lib.
// We inline our comparison function for speed, and
// annotate with numCompares
// to observe and test that extra bounds are utilized.
i, j := startIndex, endxIndex
for i < j {
h := i + (j-i)/2 // avoid overflow when computing h as the bisector
// i <= h < j
numCompares++
if !(key < int64(rc.iv[h].start)) {
i = h + 1
} else {
j = h
}
}
below := i
// end std lib snippet.
// The above is a simple in-lining and annotation of:
/* below := sort.Search(n,
func(i int) bool {
return key < rc.iv[i].start
})
*/
whichInterval16 = below - 1
if below == n {
// all falses => key is >= start of all interval16s
// ... so does it belong to the last interval16?
if key < int64(rc.iv[n-1].last())+1 {
// yes, it belongs to the last interval16
alreadyPresent = true
return
}
// no, it is beyond the last interval16.
// leave alreadyPreset = false
return
}
// INVAR: key is below rc.iv[below]
if below == 0 {
// key is before the first first interval16.
// leave alreadyPresent = false
return
}
// INVAR: key is >= rc.iv[below-1].start and
// key is < rc.iv[below].start
// is key in below-1 interval16?
if key >= int64(rc.iv[below-1].start) && key < int64(rc.iv[below-1].last())+1 {
// yes, it is. key is in below-1 interval16.
alreadyPresent = true
return
}
// INVAR: key >= rc.iv[below-1].endx && key < rc.iv[below].start
// leave alreadyPresent = false
return
}
// cardinality returns the count of the integers stored in the
// runContainer16.
func (rc *runContainer16) cardinality() int64 {
if len(rc.iv) == 0 {
rc.card = 0
return 0
}
if rc.card > 0 {
return rc.card // already cached
}
// have to compute it
var n int64
for _, p := range rc.iv {
n += p.runlen()
}
rc.card = n // cache it
return n
}