1231 lines
39 KiB
Nim
1231 lines
39 KiB
Nim
# Nimbus - Types, data structures and shared utilities used in network sync
|
|
#
|
|
# Copyright (c) 2018-2022 Status Research & Development GmbH
|
|
# Licensed under either of
|
|
# * Apache License, version 2.0, ([LICENSE-APACHE](LICENSE-APACHE) or
|
|
# http://www.apache.org/licenses/LICENSE-2.0)
|
|
# * MIT license ([LICENSE-MIT](LICENSE-MIT) or
|
|
# http://opensource.org/licenses/MIT)
|
|
# at your option. This file may not be copied, modified, or
|
|
# distributed except according to those terms.
|
|
|
|
## Efficient set of non-adjacent disjunct intervals
|
|
## ================================================
|
|
##
|
|
## This molule efficiently manages a set `Q` of non-adjacent intervals `I`
|
|
## over a scalar type `S`. The elements of the intervals are not required to
|
|
## be scalar, yet they need to fulfil some ordering properties and must map
|
|
## into `S` by the `-` operator.
|
|
##
|
|
## Application examples
|
|
## --------------------
|
|
## * Intervals `I` are sub-ranges of `distinct uint`, scalar `S` is `uint64`
|
|
## * Intervals `I` are sub-ranges of `distinct UInt256`, scalar `S` is `Uint256`
|
|
## * Intervals `I` art sub-ranges of `uint`, scalar `S` is `uint`
|
|
##
|
|
## Mathematical heuristic reasoning
|
|
## --------------------------------
|
|
## Let `S` be a scalar structure isomorphic to a sub-ring of `Z`, the ring of
|
|
## integers. Typical representants would be `uint`, `uint64`, `UInt256` when
|
|
## seen as residue classes. `S` need not be bounded. We require `0` and `1` in
|
|
## `S`.
|
|
##
|
|
## Define `P` as a finite set of elements with the following properties:
|
|
##
|
|
## * There is an order relation defined on `P` (ie. `<`, `=` exists and is
|
|
## transitive.)
|
|
##
|
|
## * Define an interval `I` to be a set of elements of `P` with:
|
|
## + If `a`,`b` are in `I`, `w` in `P` with `a<=w<=b`, then `b` is in `I`.
|
|
## + We write `[a,b]` for the interval `I` with `a=min(I)` and `b=max(I)`.
|
|
## + We have `P=[min(P),max(P)]` (note that `P` is ordered.)
|
|
##
|
|
## * There is a binary *minus* operation `-:PxP -> S` with the following
|
|
## properties:
|
|
## + If `a`, `b` are in `P` and `a<=b`, then`b-a=card([a,b])-1`. So
|
|
## `a-a=0` for all `a`.
|
|
## + For any `a<max(P)`, there is a unique element `b=min{w|a<w}` with
|
|
## `b-a=1`. We write `a+1` instead of `b`.
|
|
## + Ditto for `a-1` when `min(P)<a`
|
|
##
|
|
## * The elements of `P` are called points.
|
|
##
|
|
## Efficiency of managing `Q`
|
|
## --------------------------
|
|
## The set `Q` of non-adjacent intervals is constructed as follows:
|
|
## * For `I`, `J` intervals over `P`, define the envelope `I~J` as
|
|
## `[min(I+J),max(I+J)]` derived by interpolating elements beween `I`
|
|
## and `J`. Clearly, `card(I+J)<=card(I~J)` holds (where `+` denotes the
|
|
## union of sets.)
|
|
## * For different `I`, `J` in `Q`, we require `card(I+J)<card(I~J)`. This
|
|
## is the defining property for non-adjacent intervals.
|
|
##
|
|
## The set of intervals `Q` is implemented based on an `O(log n)` complexity
|
|
## `SortedSet` database (where `n` is the size of the database.)
|
|
##
|
|
## An operation on `Q` involving an interval `I` is of complexity
|
|
## `O(log n)+O(card I)` where `card I` is the number of elements in `I`.
|
|
## The worst case complexity applies if every other element of `I` is present
|
|
## as a single element interval in `Q`. So when merging, or reducing the
|
|
## set `Q` by the interval `I`, every other element of `I` that is
|
|
## in the set `Q` will be touched. This number of operations is at most
|
|
## `1 + (card I) / 2`.
|
|
##
|
|
## Data type requirements
|
|
## ----------------------
|
|
## The following operations must be made available when implementing `P`:
|
|
##
|
|
## * Order relation stuff for points of `P`: `==`, `<`, `cmp`, etc.
|
|
## * Maximum and minimum points `high(P)` and `low(P)` must be defined
|
|
## * Difference of points: `-:PxP -> S`, ie. `b-a` is of scalar type `S`.
|
|
## * Right addition of scalar: `+:PxS -> P`, ie. `a+n` is a point `b` and
|
|
## `b-a` is `n`.
|
|
## * The function `$()` must be defined (used for debugging, only)
|
|
##
|
|
## Additional requirements for the scalar type `S`:
|
|
##
|
|
## * `S.default` must be the `0` element (of the additive group)
|
|
## * `S.default+1` must be the `1` element (of the implied multiplicative
|
|
## group)
|
|
## * The scalar space `S` must contain all the numbers `0 .. high(P)-low(P)`
|
|
##
|
|
## User interface considerations
|
|
## -----------------------------
|
|
## The data set descriptor is implemented as an object reference. For deep
|
|
## copy and deep comparison, the functions `dup()` and `==` are provided.
|
|
##
|
|
## For any function, the argument points of `P` are assumed be in the
|
|
## range `low(P) .. high(P)`. This is not checked explicitely. Using points
|
|
## outside this range might have unintended side effects (applicable only
|
|
## if `P` is a proper sub-range of a larger data range.)
|
|
##
|
|
## The data set represents compact intervals `[a,b]` over a point space `P`
|
|
## where the length of the largest possible interval is `card(P)` which might
|
|
## exceed the highest available scalar `high(S)` from the *NIM* implementation
|
|
## of `S`. In order to handle the scalar equivalent of `card(P)`, this package
|
|
## always returns the scalar *zero* (from the scalar space `S`) for `card(S)`.
|
|
## This makes mathematically sense when `P` is seen as a residue class
|
|
## isomorpic to a subclass of `S`.
|
|
##
|
|
|
|
import
|
|
"."/[results, sorted_set]
|
|
|
|
when (NimMajor, NimMinor) < (1, 4):
|
|
{.push raises: [Defect, CatchableError].}
|
|
else:
|
|
{.push raises: [].}
|
|
|
|
export
|
|
`isRed=`,
|
|
`linkLeft=`,
|
|
`linkRight=`,
|
|
results
|
|
|
|
const
|
|
NoisyDebuggingOk = false
|
|
|
|
type
|
|
IntervalSetError* = enum
|
|
## Used for debugging only, see `verify()`
|
|
isNoError = 0
|
|
isErrorBogusInterval ## Illegal interval end points or zero size
|
|
isErrorOverlapping ## Overlapping intervals in database
|
|
isErrorAdjacent ## Adjacent intervals, should be joined
|
|
isErrorTotalMismatch ## Total accumulator register is wrong
|
|
isErrorTotalLastHigh ## Total accumulator mismatch counting `high(P)`
|
|
|
|
Interval*[P,S] = object
|
|
## Compact interval `[least,last]`
|
|
least, last: P
|
|
|
|
IntervalRc*[P,S] = ##\
|
|
## Handy shortcut, used for interval operation results
|
|
Result[Interval[P,S],void]
|
|
|
|
IntervalSetRef*[P,S] = ref object
|
|
## Set of non-adjacent intervals
|
|
ptsCount: S
|
|
## data size covered
|
|
|
|
leftPos: SortedSet[P,BlockRef[S]]
|
|
## list of segments, half-open intervals
|
|
|
|
lastHigh: bool
|
|
## `true` iff `high(P)` is in the interval set
|
|
|
|
# -----
|
|
|
|
Desc[P,S] = ##\
|
|
## Internal shortcut, interval set
|
|
IntervalSetRef[P,S]
|
|
|
|
Segm[P,S] = object
|
|
## Half open interval `[start,start+size)`
|
|
start: P ## Start point
|
|
size: S ## Length of interval
|
|
|
|
BlockRef[S] = ref object
|
|
## Internal, interval set database record reference
|
|
size: S
|
|
|
|
DataRef[P,S] = ##\
|
|
## Internal, shortcut: The `value` part of a successful `SortedSet`
|
|
## operation, a reference to the stored data record.
|
|
SortedSetItemRef[P,BlockRef[S]]
|
|
|
|
Rc[P,S] = ##\
|
|
## Internal shortcut
|
|
Result[DataRef[P,S],void]
|
|
|
|
# ------------------------------------------------------------------------------
|
|
# Private debugging
|
|
# ------------------------------------------------------------------------------
|
|
|
|
when NoisyDebuggingOk:
|
|
import std/[sequtils, strutils]
|
|
|
|
# Forward declarations
|
|
proc verify*[P,S](
|
|
ds: IntervalSetRef[P,S]): Result[void,(RbInfo,IntervalSetError)]
|
|
|
|
proc sayImpl(noisy = false; pfx = "***"; args: varargs[string, `$`]) =
|
|
if noisy:
|
|
if args.len == 0:
|
|
echo "*** ", pfx
|
|
elif 0 < pfx.len and pfx[^1] != ' ':
|
|
echo pfx, " ", args.toSeq.join
|
|
else:
|
|
echo pfx, args.toSeq.join
|
|
|
|
proc pp[P,S](n: S): string =
|
|
let
|
|
lowS = S.default
|
|
highS = S.default + (high(P) - low(P))
|
|
if highS <= n:
|
|
return "high(S)"
|
|
if (highS - 1) <= n:
|
|
return "high(S)-1"
|
|
if (highS - 1 - 1) == n:
|
|
return "high(S)-2"
|
|
if n <= lowS:
|
|
return "low(S)"
|
|
if n <= (lowS + 1):
|
|
return "low(S)+1"
|
|
if n <= (lowS + 1 + 1):
|
|
return "low(S)+2"
|
|
$n
|
|
|
|
proc pp[P,S](pt: P): string =
|
|
template one: untyped = (S.default + 1)
|
|
if high(P) <= pt:
|
|
return "high(P)"
|
|
if (high(P) - one) <= pt:
|
|
return "high(P)-1"
|
|
if (high(P) - one - one) == pt:
|
|
return "high(P)-2"
|
|
if pt <= low(P):
|
|
return "low(P)"
|
|
if pt <= (low(P) + one):
|
|
return "low(P)+1"
|
|
if pt <= (low(P) + one + one):
|
|
return "low(P)+2"
|
|
$pt
|
|
|
|
proc pp[P,S](ds: Desc[P,S]): string =
|
|
if ds.isNil:
|
|
"nil"
|
|
else:
|
|
cast[pointer](ds).repr.strip
|
|
|
|
proc pp[P,S](seg: Segm[P,S]): string =
|
|
template one: untyped = (S.default + 1)
|
|
"[" & pp[P,S](seg.start) & "," & pp[P,S](seg.start + seg.size) & ")"
|
|
|
|
proc pp[P,S](iv: Interval[P,S]): string =
|
|
template one: untyped = (S.default + 1)
|
|
"[" & pp[P,S](iv.least) & "," & pp[P,S](iv.last) & "]"
|
|
|
|
proc pp[P,S](kvp: DataRef[P,S]): string =
|
|
Segm[P,S](start: kvp.key, size: kvp.data.size).pp
|
|
|
|
proc pp[P,S](p: var SortedSet[P,BlockRef[S]]): string =
|
|
template one: untyped = (S.default + 1)
|
|
result = "{"
|
|
var rc = p.ge(low(P))
|
|
while rc.isOk:
|
|
let (key,blk) = (rc.value.key,rc.value.data)
|
|
if 1 < result.len:
|
|
result &= ","
|
|
result &= "[" & pp[P,S](key) & "," & pp[P,S](key + blk.size) & ")"
|
|
rc = p.gt(key)
|
|
result &= "}"
|
|
|
|
var noisy* = false
|
|
else:
|
|
var noisy = false
|
|
|
|
template say(noisy = false; pfx = "***"; v: varargs[untyped]): untyped =
|
|
when NoisyDebuggingOk:
|
|
sayImpl(noisy,pfx, v)
|
|
discard
|
|
|
|
# ------------------------------------------------------------------------------
|
|
# Private helpers
|
|
# ------------------------------------------------------------------------------
|
|
|
|
template maxSegmSize(): untyped =
|
|
(high(P) - low(P))
|
|
|
|
template scalarZero(): untyped =
|
|
## the value `0` from the scalar data type
|
|
(S.default)
|
|
|
|
template scalarOne(): untyped =
|
|
## the value `1` from the scalar data type
|
|
(S.default + 1)
|
|
|
|
proc blk[P,S](kvp: DataRef[P,S]): BlockRef[S] =
|
|
kvp.data
|
|
|
|
proc left[P,S](kvp: DataRef[P,S]): P =
|
|
kvp.key
|
|
|
|
proc right[P,S](kvp: DataRef[P,S]): P =
|
|
kvp.key + kvp.blk.size
|
|
|
|
proc len[P,S](kvp: DataRef[P,S]): S =
|
|
kvp.data.size
|
|
|
|
# -----
|
|
|
|
proc new[P,S](T: type Segm[P,S]; left, right: P): T =
|
|
## Constructor using `[left,right)` points representation
|
|
T(start: left, size: right - left)
|
|
|
|
proc brew[P,S](T: type Segm[P,S]; left, right: P): Result[T,void] =
|
|
## Constructor providing `[left, max(left,right)-left)` (if any.)
|
|
if high(P) <= left:
|
|
return err()
|
|
let length =
|
|
if right <= left:
|
|
scalarOne
|
|
elif right < high(P):
|
|
(right - left) + scalarOne
|
|
else:
|
|
(high(P) - left)
|
|
ok(T(start: left, size: length))
|
|
|
|
proc left[P,S](iv: Segm[P,S]): P =
|
|
iv.start
|
|
|
|
proc right[P,S](iv: Segm[P,S]): P =
|
|
iv.start + iv.size
|
|
|
|
proc len[P,S](iv: Segm[P,S]): S =
|
|
iv.size
|
|
|
|
# ------
|
|
|
|
proc incPt[P,S](a: var P; n: S) =
|
|
## Might not be generally available for point `P` and scalar `S`
|
|
a = a + n
|
|
|
|
proc maxPt[P](a, b: P): P =
|
|
## Instead of max() which might not be generally available
|
|
if a < b: b else: a
|
|
|
|
proc minPt[P](a, b: P): P =
|
|
## Instead of min() which might not be generally available
|
|
if a < b: a else: b
|
|
|
|
# ------
|
|
|
|
proc new[P,S](T: type Interval[P,S]; kvp: DataRef[P,S]): T =
|
|
T(least: kvp.left, last: kvp.right - scalarOne)
|
|
|
|
# ------------------------------------------------------------------------------
|
|
# Private helpers
|
|
# ------------------------------------------------------------------------------
|
|
|
|
proc overlapOrLeftJoin[P,S](ds: Desc[P,S]; l, r: P): Rc[P,S] =
|
|
## Find and return
|
|
## * either the rightmost interval `[a,b)` which overlaps `r`
|
|
## * or `[a,b)` with `b==l`
|
|
doAssert l <= r
|
|
let rc = ds.leftPos.le(r) # search for `max(a) <= r`
|
|
if rc.isOk:
|
|
# note that `b` is the first point outside right of `[a,b)`
|
|
let b = rc.value.right
|
|
if l <= b:
|
|
return ok(rc.value)
|
|
err()
|
|
|
|
proc overlapOrLeftJoin[P,S](ds: Desc[P,S]; iv: Segm[P,S]): Rc[P,S] =
|
|
ds.overlapOrLeftJoin(iv.left, iv.right)
|
|
|
|
|
|
proc overlap[P,S](ds: Desc[P,S]; l, r: P): Rc[P,S] =
|
|
## Find and return the rightmost `[l,r)` overlapping interval `[a,b)`.
|
|
doAssert l < r
|
|
let rc = ds.leftPos.lt(r) # search for `max(a) < r`
|
|
if rc.isOk:
|
|
# note that `b` is the first point outside right of `[a,b)`
|
|
let b = rc.value.right
|
|
if l < b:
|
|
return ok(rc.value)
|
|
err()
|
|
|
|
proc overlap[P,S](ds: Desc[P,S]; iv: Segm[P,S]): Rc[P,S] =
|
|
ds.overlap(iv.left, iv.right)
|
|
|
|
# ------------------------------------------------------------------------------
|
|
# Private transfer function helpers
|
|
# ------------------------------------------------------------------------------
|
|
|
|
proc findInlet[P,S](ds: Desc[P,S]; iv: Segm[P,S]): Segm[P,S] =
|
|
## Find largest sub-segment of `iv` fully contained in another segment
|
|
## of the argument database.
|
|
##
|
|
## If the `src` argument is `nil`, the argument interval `iv` is returned.
|
|
## If there is no overlapping segment, the empty interval
|
|
##`[iv.start,iv.start)` is returned.
|
|
|
|
# Handling edge cases
|
|
if ds.isNil:
|
|
return iv
|
|
|
|
let rc = ds.overlap(iv)
|
|
if rc.isErr:
|
|
return Segm[P,S].new(iv.left, iv.left)
|
|
|
|
let p = rc.value
|
|
Segm[P,S].new(maxPt(p.left,iv.left), minPt(p.right,iv.right))
|
|
|
|
|
|
proc merge[P,S](ds: Desc[P,S]; iv: Segm[P,S]): Segm[P,S] =
|
|
## Merges argument interval into into database and returns
|
|
## the segment really added (if any)
|
|
|
|
if ds.isNil:
|
|
return iv
|
|
|
|
let p = block:
|
|
let rc = ds.overlapOrLeftJoin(iv)
|
|
if rc.isErr:
|
|
let rx = ds.leftPos.insert(iv.left)
|
|
rx.value.data = BlockRef[S](size: iv.len)
|
|
ds.ptsCount += iv.len
|
|
return iv
|
|
rc.value # `rc.value.data` is a reference to the database record
|
|
|
|
doAssert p.blk.size <= ds.ptsCount
|
|
|
|
if p.right < iv.right:
|
|
#
|
|
# iv: ...----------------)
|
|
# p: ...-----)
|
|
#
|
|
let extend = iv.right - p.right
|
|
p.blk.size += extend # update database
|
|
ds.ptsCount += extend # update database
|
|
#
|
|
# iv: ...----------------)
|
|
# p: ...----------------)
|
|
# result: [---------)
|
|
#
|
|
return Segm[P,S].new(p.right - extend, iv.right)
|
|
|
|
# now: iv.right <= p.right and p.left <= iv.left:
|
|
if p.left <= iv.left:
|
|
#
|
|
# iv: [--------)
|
|
# p: [-------------------)
|
|
# result: o
|
|
#
|
|
return Segm[P,S].new(iv.left, iv.left) # empty interval
|
|
|
|
# now: iv.right <= p.right and iv.left < p.left
|
|
if p.left < iv.right:
|
|
#
|
|
# iv: [-----------------)
|
|
# p: [--------------)
|
|
# result: [------)
|
|
#
|
|
result = Segm[P,S].new(iv.left, p.left)
|
|
else:
|
|
# iv: [------)
|
|
# p: [--------------)
|
|
# result: [------)
|
|
#
|
|
result = iv
|
|
|
|
# No need for interval `p` anymore.
|
|
doAssert p.left == result.right
|
|
ds.ptsCount -= p.len
|
|
discard ds.leftPos.delete(p.left)
|
|
|
|
# Check whether there is an `iv` left overlapping interval `q` that can be
|
|
# merged.
|
|
#
|
|
# Note that the deleted `p` was not fully contained in `iv`. So any overlap
|
|
# must be a predecessor. Also, the right end point of the `iv` interval is
|
|
# not part of any predecessor because it was adjacent to, or overlapping with
|
|
# the deleted interval `p`.
|
|
let rc = ds.overlapOrLeftJoin(iv.left, iv.right - scalarOne)
|
|
if rc.isOk and iv.left <= rc.value.right:
|
|
let q = rc.value
|
|
#
|
|
# iv: [------...
|
|
# p: [------) // deleted
|
|
# q: [----)
|
|
# result: [------)
|
|
#
|
|
result = Segm[P,S].new(q.right, result.right)
|
|
#
|
|
# iv: [------...
|
|
# p: [------) // deleted
|
|
# q: [----)
|
|
# result: [---)
|
|
#
|
|
# extend `q` to join `result` and `p`, now
|
|
let exLen = result.len + p.len
|
|
q.blk.size += exLen
|
|
ds.ptsCount += exLen
|
|
#
|
|
# iv: [------...
|
|
# p: [------) // deleted
|
|
# q: [-----------------)
|
|
# result: [----)
|
|
#
|
|
else:
|
|
# So `iv` is fully isolated, i.e. there is no join or overlap. And `iv`
|
|
# joins or overlaps the deleted `p` but does not exceed its right end.
|
|
#
|
|
# iv: [-----------)
|
|
# p: [------) // deleted
|
|
# result: [----)
|
|
#
|
|
let s = BlockRef[S](size: p.right - iv.left)
|
|
ds.leftPos.insert(iv.left).value.data = s
|
|
ds.ptsCount += s.size
|
|
#
|
|
# iv: [------)
|
|
# p: [------) // deleted
|
|
# result: [----)
|
|
# s: [--------------)
|
|
|
|
|
|
proc deleteInlet[P,S](ds: Desc[P,S]; iv: Segm[P,S]) =
|
|
## Delete fully contained interval
|
|
if not ds.isNil and 0 < iv.len:
|
|
|
|
let
|
|
p = ds.overlap(iv).value # `p.blk` is a reference into database
|
|
right = p.right # fix the right end for later trailer handling
|
|
|
|
# [iv) fully contained in [p)
|
|
doAssert p.left <= iv.left and iv.right <= p.right
|
|
|
|
if p.left == iv.left:
|
|
#
|
|
# iv: [--------------)
|
|
# p: [---------------... // deleting
|
|
#
|
|
discard ds.leftPos.delete(p.left)
|
|
ds.ptsCount -= p.len
|
|
else:
|
|
# iv: [-------)
|
|
# p: [----------------...
|
|
#
|
|
let chop = p.right - iv.left # positive as iv.left<iv.right<=p.right
|
|
p.blk.size -= chop # update database
|
|
ds.ptsCount -= chop # update database
|
|
#
|
|
# iv: [-------)
|
|
# p.blk: [-----) ...)
|
|
# ^
|
|
# |
|
|
# right
|
|
|
|
# Correct: re-add trailer
|
|
if iv.right < right:
|
|
#
|
|
# iv: ...-------)
|
|
# p: [---------------) // may have been deleted in `==` clause
|
|
# s: [-------) // adding to database
|
|
#
|
|
let s = BlockRef[S](size: right - iv.right)
|
|
ds.leftPos.insert(iv.right).value.data = s
|
|
ds.ptsCount += s.size
|
|
|
|
# ------------------------------------------------------------------------------
|
|
# Private transfer() function implementation for merge/reduce
|
|
# ------------------------------------------------------------------------------
|
|
|
|
proc transferImpl[P,S](src, trg: Desc[P,S]; iv: Segm[P,S]): S =
|
|
## From the `src` argument database, delete the data segment/interval
|
|
## `[start,start+length)` and merge it into the `trg` argument database.
|
|
## Not both arguments `src` and `trg` must be `nil`.
|
|
doAssert not (src.isNil and trg.isNil)
|
|
|
|
var pfx = iv
|
|
|
|
while 0 < pfx.len:
|
|
# Find sub-interval of `[pfx)` fully contained in a `src` database interval
|
|
var fromIv = src.findInlet(pfx)
|
|
|
|
# Chop right end from [pfx) -> [pfx) + [fromIv)
|
|
pfx = Segm[P,S].new(pfx.left, fromIv.left)
|
|
|
|
# Move the `fromIv` interval from `src` to `trg` database
|
|
while 0 < fromIv.len:
|
|
# Merge sub-interval `[fromIv)` into `trg` database
|
|
let toIv = trg.merge(fromIv)
|
|
|
|
# Chop right end from [fromIv) -> [fromIv) + [toIv)
|
|
fromIv = Segm[P,S].new(fromIv.left, toIv.left)
|
|
|
|
# Delete merged sub-interval from `src` database (if any)
|
|
src.deleteInlet(toIv)
|
|
|
|
result += toIv.len
|
|
|
|
# ------------------------------------------------------------------------------
|
|
# Private covered() function implementation
|
|
# ------------------------------------------------------------------------------
|
|
|
|
proc coveredImpl[P,S](ds: IntervalSetRef[P,S]; start: P; length: S): S =
|
|
## Calulate the accumulated size of the interval `[start,start+length)`
|
|
## covered by intervals in the set `ds`. The result cannot exceed the
|
|
## argument `length` (of course.)
|
|
var iv = Segm[P,S](start: start, size: length)
|
|
|
|
while 0 < iv.len:
|
|
let rc = ds.overlap(iv)
|
|
if rc.isErr:
|
|
break
|
|
|
|
let p = rc.value
|
|
|
|
# Now `p` is the right most interval overlapping `iv`
|
|
if p.left <= iv.left:
|
|
if p.right <= iv.right:
|
|
#
|
|
# iv: [----------------)
|
|
# p: [-------------)
|
|
# overlap: <------->
|
|
#
|
|
result.incPt p.right - iv.left
|
|
else:
|
|
# iv: [--------)
|
|
# p: [--------------------)
|
|
# overlap: <------->
|
|
#
|
|
result.incPt iv.len
|
|
break
|
|
else:
|
|
if iv.right < p.right:
|
|
#
|
|
# iv: [--------------)
|
|
# p: [--------------)
|
|
# overlap: <-------->
|
|
#
|
|
result.incPt iv.right - p.left
|
|
else:
|
|
# iv: [----------------------)
|
|
# p: [----------)
|
|
# overlap: <--------->
|
|
#
|
|
result.incPt p.len
|
|
|
|
iv.size = p.left - iv.left
|
|
# iv: [---)
|
|
# p: [----------)
|
|
|
|
# ------------------------------------------------------------------------------
|
|
# Public constructor, clone, etc.
|
|
# ------------------------------------------------------------------------------
|
|
|
|
proc init*[P,S](T: type IntervalSetRef[P,S]): T =
|
|
## Interval set constructor.
|
|
new result
|
|
result.leftPos.init()
|
|
|
|
proc clone*[P,S](ds: IntervalSetRef[P,S]): IntervalSetRef[P,S] =
|
|
## Return a copy of the interval list. Beware, this might be slow as it
|
|
## needs to copy every interval record.
|
|
result = Desc[P,S].init()
|
|
result.ptsCount = ds.ptsCount
|
|
result.lastHigh = ds.lastHigh
|
|
|
|
var # using fast traversal
|
|
walk = SortedSetWalkRef[P,BlockRef[S]].init(ds.leftPos)
|
|
rc = walk.first
|
|
while rc.isOk:
|
|
result.leftPos.insert(rc.value.key)
|
|
.value.data = BlockRef[S](size: rc.value.data.size)
|
|
rc = walk.next
|
|
# optional clean up, see comments on the destroy() directive
|
|
walk.destroy
|
|
|
|
proc `==`*[P,S](a, b: IntervalSetRef[P,S]): bool =
|
|
## Compare interval sets for equality. Beware, this can be slow. Every
|
|
## interval record has to be checked.
|
|
if a.ptsCount == b.ptsCount and
|
|
a.leftPos.len == b.leftPos.len and
|
|
a.lastHigh == b.lastHigh:
|
|
result = true
|
|
if 0 < a.ptsCount and addr(a.leftPos) != addr(b.leftPos):
|
|
var # using fast traversal
|
|
aWalk = SortedSetWalkRef[P,BlockRef[S]].init(a.leftPos)
|
|
aRc = aWalk.first()
|
|
while aRc.isOk:
|
|
let bRc = b.leftPos.eq(aRc.value.key)
|
|
if bRc.isErr or aRc.value.data.size != bRc.value.data.size:
|
|
result = false
|
|
break
|
|
aRc = aWalk.next()
|
|
# optional clean up, see comments on the destroy() directive
|
|
aWalk.destroy()
|
|
|
|
proc clear*[P,S](ds: IntervalSetRef[P,S]) =
|
|
## Clear the interval set.
|
|
ds.ptsCount = scalarZero
|
|
ds.lastHigh = false
|
|
ds.leftPos.clear()
|
|
|
|
proc new*[P,S](T: type Interval[P,S]; minPt, maxPt: P): T =
|
|
## Create interval `[minPt,max(minPt,maxPt)]`
|
|
Interval[P,S](least: minPt, last: max(minPt, maxPt))
|
|
|
|
# ------------------------------------------------------------------------------
|
|
# Public interval operations add, remove, erc.
|
|
# ------------------------------------------------------------------------------
|
|
|
|
proc merge*[P,S](ds: IntervalSetRef[P,S]; minPt, maxPt: P): S =
|
|
## For the argument interval `I` implied as `[minPt,max(minPt,maxPt)]`,
|
|
## merge `I` with the intervals of the argument set `ds`. The function
|
|
## returns the accumulated number of points that were added to some
|
|
## interval (i.e. which were not contained in any interval of `ds`.)
|
|
##
|
|
## If the argument interval `I` is `[low(P),high(P)]` and is fully merged,
|
|
## the scalar *zero* is returned instead of `high(P)-low(P)+1` (which might
|
|
## not exisit in `S`.).
|
|
let rc = Segm[P,S].brew(minPt, maxPt)
|
|
if rc.isOk:
|
|
result = transferImpl[P,S](src=nil, trg=ds, iv=rc.value)
|
|
|
|
if not ds.lastHigh and high(P) <= max(minPt,maxPt):
|
|
ds.lastHigh = true
|
|
if result < maxSegmSize:
|
|
result += scalarOne
|
|
else:
|
|
result = scalarZero
|
|
|
|
proc merge*[P,S](ds: IntervalSetRef[P,S]; iv: Interval[P,S]): S =
|
|
## Variant of `merge()`
|
|
ds.merge(iv.least, iv.last)
|
|
|
|
|
|
proc reduce*[P,S](ds: IntervalSetRef[P,S]; minPt, maxPt: P): S =
|
|
## For the argument interval `I` implied as `[minPt,max(minPt,maxPt)]`,
|
|
## remove the points from `I` from intervals of the argument set `ds`.
|
|
## The function returns the accumulated number of elements removed (i.e.
|
|
## which were previously contained in some interval of `ds`.)
|
|
##
|
|
## If the argument interval `I` is `[low(P),high(P)]` and is fully removed,
|
|
## the scalar *zero* is returned instead of `high(P)-low(P)+1` (which might
|
|
## not exisit in `S`.).
|
|
let rc = Segm[P,S].brew(minPt, maxPt)
|
|
if rc.isOk:
|
|
result = transferImpl[P,S](src=ds, trg=nil, iv=rc.value)
|
|
|
|
if ds.lastHigh and high(P) <= max(minPt,maxPt):
|
|
ds.lastHigh = false
|
|
if result < maxSegmSize:
|
|
result += scalarOne
|
|
else:
|
|
result = scalarZero
|
|
|
|
proc reduce*[P,S](ds: IntervalSetRef[P,S]; iv: Interval[P,S]): S =
|
|
## Variant of `reduce()`
|
|
ds.reduce(iv.least, iv.last)
|
|
|
|
|
|
proc covered*[P,S](ds: IntervalSetRef[P,S]; minPt, maxPt: P): S =
|
|
## For the argument interval `I` implied as `[minPt,max(minPt,maxPt)]`,
|
|
## calulate the accumulated points `I` contained in some interval in the
|
|
## set `ds`. The return value is the same as that for `reduce()` (only
|
|
## that `ds` is left unchanged, here.)
|
|
let rc = Segm[P,S].brew(minPt, maxPt)
|
|
if rc.isOk:
|
|
result = ds.coveredImpl(rc.value.left, rc.value.size)
|
|
|
|
if ds.lastHigh and high(P) <= max(minPt,maxPt):
|
|
if result < maxSegmSize:
|
|
result += scalarOne
|
|
else:
|
|
result = scalarZero
|
|
|
|
proc covered*[P,S](ds: IntervalSetRef[P,S]; iv: Interval[P,S]): S =
|
|
## Variant of `covered()`
|
|
ds.covered(iv.least, iv.last)
|
|
|
|
|
|
proc ge*[P,S](ds: IntervalSetRef[P,S]; minPt: P): IntervalRc[P,S] =
|
|
## Find smallest interval in the set `ds` with start point (i.e. minimal
|
|
## value in the interval as a set) greater or equal the argument `minPt`.
|
|
let rc = ds.leftPos.ge(minPt)
|
|
if rc.isOk:
|
|
# Check for fringe case intervals [a,b] + [high(P),high(P)]
|
|
if high(P) <= rc.value.right and ds.lastHigh:
|
|
return ok(Interval[P,S].new(rc.value.left, high(P)))
|
|
return ok(Interval[P,S].new(rc.value))
|
|
if ds.lastHigh:
|
|
const preHigh = high(P) - scalarOne
|
|
if ds.covered(preHigh,preHigh) == scalarZero:
|
|
return ok(Interval[P,S].new(high(P),high(P)))
|
|
err()
|
|
|
|
proc ge*[P,S](ds: IntervalSetRef[P,S]): IntervalRc[P,S] =
|
|
## Find the interval with the least elements of type `P` (if any.)
|
|
ds.ge(low(P))
|
|
|
|
proc le*[P,S](ds: IntervalSetRef[P,S]; maxPt: P): IntervalRc[P,S] =
|
|
## Find largest interval in the set `ds` with end point (i.e. maximal
|
|
## value in the interval as a set) smaller or equal to the argument `maxPt`.
|
|
let rc = ds.leftPos.le(maxPt)
|
|
if rc.isOk:
|
|
# only the left end of segment [left,right) is guaranteed to be <= maxPt
|
|
if rc.value.right - scalarOne <= maxPt:
|
|
if ds.lastHigh:
|
|
if high(P) <= maxPt:
|
|
# Check for fringe case intervals [a,b] gap [high(P),high(P)] <= maxPt
|
|
if rc.value.right < high(P):
|
|
return ok(Interval[P,S].new(high(P),high(P)))
|
|
# Check for fringe case intervals [a,b] + [high(P),high(P)] <= maxPt
|
|
if high(P) <= rc.value.right:
|
|
return ok(Interval[P,S].new(rc.value.left,high(P)))
|
|
# So maxPt < high(P)
|
|
if high(P) <= rc.value.right:
|
|
# Now `maxPt` is fully within the inner part of `[left,high(P)]`
|
|
return err()
|
|
return ok(Interval[P,S].new(rc.value))
|
|
# find the next smaller one
|
|
let xc = ds.leftPos.lt(rc.value.key)
|
|
if xc.isOk:
|
|
return ok(Interval[P,S].new(xc.value))
|
|
# lone interval
|
|
if high(P) <= maxPt and ds.lastHigh:
|
|
return ok(Interval[P,S].new(high(P),high(P)))
|
|
err()
|
|
|
|
proc le*[P,S](ds: IntervalSetRef[P,S]): IntervalRc[P,S] =
|
|
## Find the interval with the largest elements of type `P` (if any.)
|
|
ds.le(high(P))
|
|
|
|
|
|
proc envelope*[P,S](ds: IntervalSetRef[P,S]; pt: P): IntervalRc[P,S] =
|
|
## Find the interval that contains the argument point `pt` (if any)
|
|
let rc = ds.leftPos.le(pt)
|
|
if rc.isOk:
|
|
if ds.lastHigh and high(P) <= rc.value.right:
|
|
# This interval ranges `[left,high(P)]`, so `pt` is certainly contained
|
|
return ok(Interval[P,S].new(rc.value.left,high(P)))
|
|
if pt < rc.value.right:
|
|
return ok(Interval[P,S].new(rc.value))
|
|
# Otherwise: interval `[left,right)` ends before `pt`
|
|
if ds.lastHigh and high(P) <= pt:
|
|
return ok(Interval[P,S].new(high(P),high(P)))
|
|
err()
|
|
|
|
|
|
proc delete*[P,S](ds: IntervalSetRef[P,S]; minPt: P): IntervalRc[P,S] =
|
|
## Find the interval `[minPt,maxPt]` for some point `maxPt` in the interval
|
|
## set `ds` and remove it from `ds`. The function returns the deleted
|
|
## interval (if any.)
|
|
block:
|
|
let rc = ds.leftPos.delete(minPt)
|
|
if rc.isOk:
|
|
ds.ptsCount -= rc.value.len
|
|
# Check for fringe case intervals [a,b]+[high(P),high(P)]
|
|
if high(P) <= rc.value.right and ds.lastHigh:
|
|
ds.lastHigh = false
|
|
return ok(Interval[P,S].new(rc.value.left,high(P)))
|
|
return ok(Interval[P,S].new(rc.value))
|
|
if high(P) <= minPt and ds.lastHigh:
|
|
# delete isolated point
|
|
let rc = ds.leftPos.lt(minPt)
|
|
if rc.isErr or rc.value.right < high(P):
|
|
ds.lastHigh = false
|
|
return ok(Interval[P,S].new(high(P),high(P)))
|
|
err()
|
|
|
|
|
|
iterator increasing*[P,S](
|
|
ds: IntervalSetRef[P,S];
|
|
minPt = low(P)
|
|
): Interval[P,S] =
|
|
## Iterate in increasing order through intervals with points greater or
|
|
## equal than the argument point `minPt`.
|
|
##
|
|
## :Note:
|
|
## When running in a loop it is *ok* to delete the current interval and
|
|
## any interval already visited. Intervals not visited yet must not be
|
|
## deleted as the loop would become unpredictable.
|
|
var rc = ds.leftPos.ge(minPt)
|
|
if rc.isErr:
|
|
if ds.lastHigh:
|
|
yield Interval[P,S].new(high(P),high(P))
|
|
else:
|
|
while rc.isOk:
|
|
let key = rc.value.key
|
|
if high(P) <= rc.value.right and ds.lastHigh:
|
|
yield Interval[P,S].new(rc.value.left,high(P))
|
|
else:
|
|
yield Interval[P,S].new(rc.value)
|
|
rc = ds.leftPos.gt(key)
|
|
|
|
iterator decreasing*[P,S](
|
|
ds: IntervalSetRef[P,S];
|
|
maxPt = high(P)
|
|
): Interval[P,S] =
|
|
## Iterate in decreasing order through intervals with points less or equal
|
|
## than the argument point `maxPt`.
|
|
##
|
|
## See the note at the `increasing()` function comment about deleting items.
|
|
var rc = ds.leftPos.le(maxPt)
|
|
if rc.isErr:
|
|
if ds.lastHigh:
|
|
yield Interval[P,S].new(high(P),high(P))
|
|
else:
|
|
let key = rc.value.key
|
|
# last entry: check for additional point
|
|
if high(P) <= rc.value.right and ds.lastHigh:
|
|
yield Interval[P,S].new(rc.value.left,high(P))
|
|
else:
|
|
yield Interval[P,S].new(rc.value)
|
|
# find the next smaller one
|
|
rc = ds.leftPos.lt(key)
|
|
|
|
while rc.isOk:
|
|
let key = rc.value.key
|
|
yield Interval[P,S].new(rc.value)
|
|
rc = ds.leftPos.lt(key)
|
|
|
|
# ------------------------------------------------------------------------------
|
|
# Public interval operators
|
|
# ------------------------------------------------------------------------------
|
|
|
|
proc `==`*[P,S](iv, jv: Interval[P,S]): bool =
|
|
## Compare intervals for equality
|
|
iv.least == jv.least and iv.last == jv.last
|
|
|
|
proc `==`*[P,S](iv: IntervalRc[P,S]; jv: Interval[P,S]): bool =
|
|
## Variant of `==`
|
|
if iv.isOk:
|
|
return iv.value == jv
|
|
|
|
proc `==`*[P,S](iv: Interval[P,S]; jv: IntervalRc[P,S]): bool =
|
|
## Variant of `==`
|
|
if jv.isOk:
|
|
return iv == jv.value
|
|
|
|
proc `==`*[P,S](iv, jv: IntervalRc[P,S]): bool =
|
|
## Variant of `==`
|
|
if iv.isOk:
|
|
if jv.isOk:
|
|
return iv.value == jv.value
|
|
# false
|
|
else:
|
|
return jv.isErr
|
|
# false
|
|
|
|
# ------
|
|
|
|
proc `*`*[P,S](iv, jv: Interval[P,S]): IntervalRc[P,S] =
|
|
## Intersect itervals `iv` and `jv` if this operation results in a
|
|
## non-emty interval. Note that the `*` operation is associative, i.e.
|
|
## ::
|
|
## iv * jv * kv == (iv * jv) * kv == iv * (jv * kv)
|
|
##
|
|
if jv.least <= iv.last and iv.least <= jv.last:
|
|
# intervals overlap
|
|
return ok(Interval[P,S].new(
|
|
maxPt(jv.least,iv.least), minPt(jv.last,iv.last)))
|
|
err()
|
|
|
|
proc `*`*[P,S](iv: IntervalRc[P,S]; jv: Interval[P,S]): IntervalRc[P,S] =
|
|
## Variant of `*`
|
|
if iv.isOk:
|
|
return iv.value * jv
|
|
err()
|
|
|
|
proc `*`*[P,S](iv: Interval[P,S]; jv: IntervalRc[P,S]): IntervalRc[P,S] =
|
|
## Variant of `*`
|
|
if jv.isOk:
|
|
return iv * jv.value
|
|
err()
|
|
|
|
proc `*`*[P,S](iv, jv: IntervalRc[P,S]): IntervalRc[P,S] =
|
|
## Variant of `*`
|
|
if iv.isOk and jv.isOk:
|
|
return iv.value * jv.value
|
|
err()
|
|
|
|
# ------
|
|
|
|
proc `+`*[P,S](iv, jv: Interval[P,S]): IntervalRc[P,S] =
|
|
## Merge intervals `iv` and `jv` if this operation results in an interval.
|
|
## Note that the `+` operation is *not* associative, i.e.
|
|
## ::
|
|
## iv + jv + kv == (iv + jv) + kv is not necessarly iv + (jv + kv)
|
|
##
|
|
if iv.least <= jv.least:
|
|
if jv.least - scalarOne <= iv.last:
|
|
#
|
|
# iv: [--------]
|
|
# jv: [...[-----...
|
|
#
|
|
return ok(Interval[P,S].new(iv.least, maxPt(iv.last,jv.last)))
|
|
|
|
else: # jv.least < iv.least
|
|
if iv.least - scalarOne <= jv.last:
|
|
#
|
|
# iv: [...[-----...
|
|
# jv: [--------]
|
|
#
|
|
return ok(Interval[P,S].new(jv.least, maxPt(iv.last,jv.last)))
|
|
|
|
err()
|
|
|
|
proc `+`*[P,S](iv: IntervalRc[P,S]; jv: Interval[P,S]): IntervalRc[P,S] =
|
|
## Variant of `+`
|
|
if iv.isOk:
|
|
return iv.value + jv
|
|
err()
|
|
|
|
proc `+`*[P,S](iv: Interval[P,S]; jv: IntervalRc[P,S]): IntervalRc[P,S] =
|
|
## Variant of `+`
|
|
if jv.isOk:
|
|
return iv + jv.value
|
|
err()
|
|
|
|
proc `+`*[P,S](iv, jv: IntervalRc[P,S]): IntervalRc[P,S] =
|
|
## Variant of `+`
|
|
if iv.isOk and jv.isOk:
|
|
return iv.value + jv.value
|
|
err()
|
|
|
|
# ------
|
|
|
|
proc `-`*[P,S](iv, jv: Interval[P,S]): IntervalRc[P,S] =
|
|
## Return the interval `iv` reduced by elements of `jv` if this operation
|
|
## results in a non-empty interval.
|
|
## Note that the `-` operation is *not* associative, i.e.
|
|
## ::
|
|
## iv - jv - kv == (iv - jv) - kv is not necessarly iv - (jv - kv)
|
|
##
|
|
if iv.least <= jv.least:
|
|
if jv.least <= iv.last and iv.last <= jv.last:
|
|
#
|
|
# iv: [--------------]
|
|
# jv: [------------]
|
|
#
|
|
if iv.least < jv.least:
|
|
return ok(Interval[P,S].new(iv.least, jv.least - scalarOne))
|
|
# otherwise empty set => error
|
|
|
|
elif iv.last < jv.least:
|
|
#
|
|
# iv: [--------]
|
|
# jv: [------------]
|
|
#
|
|
return ok(iv)
|
|
|
|
else: # so jv.least <= iv.last and jv.last < iv.last
|
|
#
|
|
# iv: [--------------]
|
|
# jv: [------]
|
|
#
|
|
discard # error
|
|
|
|
else: # jv.least < iv.least
|
|
if iv.least <= jv.last and jv.last <= iv.last:
|
|
#
|
|
# iv: [------------]
|
|
# jv: [--------------]
|
|
#
|
|
if jv.last < iv.last:
|
|
return ok(Interval[P,S].new(jv.last + scalarOne, iv.last))
|
|
# otherwise empty set => error
|
|
|
|
elif jv.last < iv.least:
|
|
#
|
|
# iv: [------------]
|
|
# jv: [--------]
|
|
#
|
|
return ok(iv)
|
|
|
|
else: # so iv.least <= jv.last and iv.last < jv.last
|
|
#
|
|
# iv: [------]
|
|
# jv: [--------------]
|
|
#
|
|
discard # error
|
|
|
|
err()
|
|
|
|
proc `-`*[P,S](iv: IntervalRc[P,S]; jv: Interval[P,S]): IntervalRc[P,S] =
|
|
## Variant of `-`
|
|
if iv.isOk:
|
|
return iv.value - jv
|
|
err()
|
|
|
|
proc `-`*[P,S](iv: Interval[P,S]; jv: IntervalRc[P,S]): IntervalRc[P,S] =
|
|
## Variant of `-`
|
|
if jv.isOk:
|
|
return iv - jv.value
|
|
err()
|
|
|
|
proc `-`*[P,S](iv, jv: IntervalRc[P,S]): IntervalRc[P,S] =
|
|
## Variant of `-`
|
|
if iv.isOk and jv.isOk:
|
|
return iv.value - jv.valu
|
|
err()
|
|
|
|
# ------------------------------------------------------------------------------
|
|
# Public getters
|
|
# ------------------------------------------------------------------------------
|
|
|
|
proc len*[P,S](iv: Interval[P,S]): S =
|
|
## Cardinality (ie. length) of argument interval `iv`. If the argument
|
|
## interval `iv` is `[low(P),high(P)]`, the return value will be the scalar
|
|
## *zero* (there are no empty intervals in this implementation.)
|
|
if low(P) == iv.least and high(P) == iv.last:
|
|
scalarZero
|
|
else:
|
|
(iv.last - iv.least) + scalarOne
|
|
|
|
proc minPt*[P,S](iv: Interval[P,S]): P =
|
|
## Left end, smallest point of `P` contained in the interval
|
|
iv.least
|
|
|
|
proc maxPt*[P,S](iv: Interval[P,S]): P =
|
|
## Right end, largest point of `P` contained in the interval
|
|
iv.last
|
|
|
|
proc total*[P,S](ds: IntervalSetRef[P,S]): S =
|
|
## Accumulated size covered by intervals in the interval set `ds`.
|
|
##
|
|
## In the special case when there is only the single interval
|
|
## `[low(P),high(P)]` in the interval set, the return value will be the
|
|
## scalar *zero* (there are no empty intervals in this implementation.)
|
|
if not ds.lastHigh:
|
|
ds.ptsCount
|
|
elif maxSegmSize <= ds.ptsCount:
|
|
scalarZero
|
|
else:
|
|
ds.ptsCount + scalarOne
|
|
|
|
proc chunks*[P,S](ds: IntervalSetRef[P,S]): int =
|
|
## Number of disjunkt intervals (aka chunks) in the interval set `ds`.
|
|
result = ds.leftPos.len
|
|
if ds.lastHigh:
|
|
# check for isolated interval [high(P),high(P)]
|
|
if result == 0 or ds.leftPos.le(high(P)).value.right < high(P):
|
|
result.inc
|
|
|
|
# ------------------------------------------------------------------------------
|
|
# Public debugging functions
|
|
# ------------------------------------------------------------------------------
|
|
|
|
proc `$`*[P,S](p: DataRef[P,S]): string =
|
|
## Needed by `ds.verify()` for printing error messages
|
|
"[" & $p.left & "," & $p.right & ")"
|
|
|
|
proc verify*[P,S](
|
|
ds: IntervalSetRef[P,S]
|
|
): Result[void,(RbInfo,IntervalSetError)] =
|
|
## Verifyn interval set data structure
|
|
try:
|
|
let rc = ds.leftPos.verify
|
|
if rc.isErr:
|
|
return err((rc.error[1],isNoError))
|
|
except CatchableError as e:
|
|
raiseAssert $e.name & ": " & e.msg
|
|
|
|
block:
|
|
var
|
|
count = scalarZero
|
|
maxPt: P
|
|
first = true
|
|
for iv in ds.increasing:
|
|
noisy.say "***", "verify(fwd)", " maxPt=", maxPt, " iv=", iv.pp
|
|
if not(low(P) <= iv.least and iv.least <= iv.last and iv.last <= high(P)):
|
|
noisy.say "***", "verify(fwd)", " error=", isErrorBogusInterval
|
|
return err((rbOk,isErrorBogusInterval))
|
|
if first:
|
|
first = false
|
|
elif iv.least <= maxPt:
|
|
noisy.say "***", "verify(fwd)", " error=", isErrorOverlapping
|
|
return err((rbOk,isErrorOverlapping))
|
|
elif iv.least <= maxPt + scalarOne:
|
|
noisy.say "***", "verify(fwd)", " error=", isErrorAdjacent
|
|
return err((rbOk,isErrorAdjacent))
|
|
maxPt = iv.last
|
|
if iv.least == low(P) and iv.last == high(P):
|
|
if ds.lastHigh and 0 < count or not ds.lastHigh and count == 0:
|
|
return err((rbOk,isErrorTotalLastHigh))
|
|
count += high(P) - low(P)
|
|
elif iv.last == high(P) and ds.lastHigh:
|
|
count += (iv.len - 1)
|
|
else:
|
|
count += iv.len
|
|
|
|
if count != ds.ptsCount:
|
|
noisy.say "***", "verify(fwd)",
|
|
" error=", isErrorTotalMismatch,
|
|
" count=", pp[P,S](ds.ptsCount),
|
|
" expected=", pp[P,S](count)
|
|
return err((rbOk,isErrorTotalMismatch))
|
|
|
|
block:
|
|
var
|
|
count = scalarZero
|
|
minPt: P
|
|
last = true
|
|
for iv in ds.decreasing:
|
|
#noisy.say "***", "verify(rev)", " minPt=", minPt, " iv=", iv.pp
|
|
if not(low(P) <= iv.least and iv.least <= iv.last and iv.last <= high(P)):
|
|
return err((rbOk,isErrorBogusInterval))
|
|
if last:
|
|
last = false
|
|
elif minPt <= iv.least:
|
|
return err((rbOk,isErrorOverlapping))
|
|
elif minPt + scalarOne <= iv.least:
|
|
return err((rbOk,isErrorAdjacent))
|
|
minPt = iv.least
|
|
if iv.least == low(P) and iv.last == high(P):
|
|
if ds.lastHigh and 0 < count or not ds.lastHigh and count == 0:
|
|
return err((rbOk,isErrorTotalLastHigh))
|
|
count += high(P) - low(P)
|
|
elif iv.last == high(P) and ds.lastHigh:
|
|
count += (iv.len - 1)
|
|
else:
|
|
count += iv.len
|
|
|
|
if count != ds.ptsCount:
|
|
noisy.say "***", "verify(rev)",
|
|
" error=", isErrorTotalMismatch,
|
|
" count=", pp[P,S](ds.ptsCount),
|
|
" expected=", pp[P,S](count)
|
|
return err((rbOk,isErrorTotalMismatch))
|
|
|
|
ok()
|
|
|
|
# ------------------------------------------------------------------------------
|
|
# End
|
|
# ------------------------------------------------------------------------------
|