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#
#
# Nimrod's Runtime Library
# (c) Copyright 2012 Andreas Rumpf
#
# See the file "copying.txt", included in this
# distribution, for details about the copyright.
#
## The ``intsets`` module implements an efficient int set implemented as a
## sparse bit set.
## **Note**: Since Nimrod currently does not allow the assignment operator to
## be overloaded, ``=`` for int sets performs some rather meaningless shallow
## copy; use ``assign`` to get a deep copy.
import
os, hashes, math
type
TBitScalar = int
const
InitIntSetSize = 8 # must be a power of two!
TrunkShift = 9
BitsPerTrunk = 1 shl TrunkShift # needs to be a power of 2 and
# divisible by 64
TrunkMask = BitsPerTrunk - 1
IntsPerTrunk = BitsPerTrunk div (sizeof(TBitScalar) * 8)
IntShift = 5 + ord(sizeof(TBitScalar) == 8) # 5 or 6, depending on int width
IntMask = 1 shl IntShift - 1
type
PTrunk = ref TTrunk
TTrunk {.final.} = object
next: PTrunk # all nodes are connected with this pointer
key: int # start address at bit 0
bits: array[0..IntsPerTrunk - 1, TBitScalar] # a bit vector
TTrunkSeq = seq[PTrunk]
TIntSet* {.final.} = object ## an efficient set of 'int' implemented as a
## sparse bit set
counter, max: int
head: PTrunk
data: TTrunkSeq
proc mustRehash(length, counter: int): bool {.inline.} =
assert(length > counter)
result = (length * 2 < counter * 3) or (length - counter < 4)
proc nextTry(h, maxHash: THash): THash {.inline.} =
result = ((5 * h) + 1) and maxHash
proc intSetGet(t: TIntSet, key: int): PTrunk =
var h = key and t.max
while t.data[h] != nil:
if t.data[h].key == key:
return t.data[h]
h = nextTry(h, t.max)
result = nil
proc intSetRawInsert(t: TIntSet, data: var TTrunkSeq, desc: PTrunk) =
var h = desc.key and t.max
while data[h] != nil:
assert(data[h] != desc)
h = nextTry(h, t.max)
assert(data[h] == nil)
data[h] = desc
proc intSetEnlarge(t: var TIntSet) =
var n: TTrunkSeq
var oldMax = t.max
t.max = ((t.max + 1) * 2) - 1
newSeq(n, t.max + 1)
for i in countup(0, oldMax):
if t.data[i] != nil: intSetRawInsert(t, n, t.data[i])
swap(t.data, n)
proc intSetPut(t: var TIntSet, key: int): PTrunk =
var h = key and t.max
while t.data[h] != nil:
if t.data[h].key == key:
return t.data[h]
h = nextTry(h, t.max)
if mustRehash(t.max + 1, t.counter): intSetEnlarge(t)
inc(t.counter)
h = key and t.max
while t.data[h] != nil: h = nextTry(h, t.max)
assert(t.data[h] == nil)
new(result)
result.next = t.head
result.key = key
t.head = result
t.data[h] = result
proc contains*(s: TIntSet, key: int): bool =
## returns true iff `key` is in `s`.
var t = intSetGet(s, `shr`(key, TrunkShift))
if t != nil:
var u = key and TrunkMask
result = (t.bits[`shr`(u, IntShift)] and `shl`(1, u and IntMask)) != 0
else:
result = false
proc incl*(s: var TIntSet, key: int) =
## includes an element `key` in `s`.
var t = intSetPut(s, `shr`(key, TrunkShift))
var u = key and TrunkMask
t.bits[`shr`(u, IntShift)] = t.bits[`shr`(u, IntShift)] or
`shl`(1, u and IntMask)
proc excl*(s: var TIntSet, key: int) =
## excludes `key` from the set `s`.
var t = intSetGet(s, `shr`(key, TrunkShift))
if t != nil:
var u = key and TrunkMask
t.bits[`shr`(u, IntShift)] = t.bits[`shr`(u, IntShift)] and
not `shl`(1, u and IntMask)
proc containsOrIncl*(s: var TIntSet, key: int): bool =
## returns true if `s` contains `key`, otherwise `key` is included in `s`
## and false is returned.
var t = intSetGet(s, `shr`(key, TrunkShift))
if t != nil:
var u = key and TrunkMask
result = (t.bits[`shr`(u, IntShift)] and `shl`(1, u and IntMask)) != 0
if not result:
t.bits[`shr`(u, IntShift)] = t.bits[`shr`(u, IntShift)] or
`shl`(1, u and IntMask)
else:
incl(s, key)
result = false
proc initIntSet*: TIntSet =
## creates a new int set that is empty.
newSeq(result.data, InitIntSetSize)
result.max = InitIntSetSize-1
result.counter = 0
result.head = nil
proc assign*(dest: var TIntSet, src: TIntSet) =
## copies `src` to `dest`. `dest` does not need to be initialized by
## `initIntSet`.
dest.counter = src.counter
dest.max = src.max
newSeq(dest.data, src.data.len)
var it = src.head
while it != nil:
var h = it.key and dest.max
while dest.data[h] != nil: h = nextTry(h, dest.max)
assert(dest.data[h] == nil)
var n: PTrunk
new(n)
n.next = dest.head
n.key = it.key
n.bits = it.bits
dest.head = n
dest.data[h] = n
it = it.next
iterator items*(s: TIntSet): int {.inline.} =
## iterates over any included element of `s`.
var r = s.head
while r != nil:
var i = 0
while i <= high(r.bits):
var w = r.bits[i]
# taking a copy of r.bits[i] here is correct, because
# modifying operations are not allowed during traversation
var j = 0
while w != 0: # test all remaining bits for zero
if (w and 1) != 0: # the bit is set!
yield (r.key shl TrunkShift) or (i shl IntShift +% j)
inc(j)
w = w shr 1
inc(i)
r = r.next
template dollarImpl(): stmt =
result = "{"
for key in items(s):
if result.len > 1: result.add(", ")
result.add($key)
result.add("}")
proc `$`*(s: TIntSet): string =
## The `$` operator for int sets.
dollarImpl()
proc empty*(s: TIntSet): bool {.inline.} =
## returns true if `s` is empty. This is safe to call even before
## the set has been initialized with `initIntSet`.
result = s.counter == 0
when isMainModule:
var x = initIntSet()
x.incl(1)
x.incl(2)
x.incl(7)
x.incl(1056)
for e in items(x): echo e
var y: TIntSet
assign(y, x)
for e in items(y): echo e
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