From: Brian Warner <warner@lothar.com>
Date: Wed, 4 Aug 2010 07:26:00 +0000 (-0700)
Subject: Add a byte-spans utility class, like perl's Set::IntSpan for .newsrc files.
X-Git-Tag: allmydata-tahoe-1.8.0b2~23
X-Git-Url: https://git.rkrishnan.org/components/provisioning?a=commitdiff_plain;h=cbcb728e7ea0031d25738297f906a7f247fa2f75;p=tahoe-lafs%2Ftahoe-lafs.git

Add a byte-spans utility class, like perl's Set::IntSpan for .newsrc files.
Also a data-spans class, which records a byte (instead of a bit) for each
index.
---

diff --git a/src/allmydata/test/test_util.py b/src/allmydata/test/test_util.py
index 6ba9ff66..48d4711d 100644
--- a/src/allmydata/test/test_util.py
+++ b/src/allmydata/test/test_util.py
@@ -7,12 +7,14 @@ from twisted.trial import unittest
 from twisted.internet import defer, reactor
 from twisted.python.failure import Failure
 from twisted.python import log
+from hashlib import md5
 
 from allmydata.util import base32, idlib, humanreadable, mathutil, hashutil
 from allmydata.util import assertutil, fileutil, deferredutil, abbreviate
 from allmydata.util import limiter, time_format, pollmixin, cachedir
 from allmydata.util import statistics, dictutil, pipeline
 from allmydata.util import log as tahoe_log
+from allmydata.util.spans import Spans, overlap, DataSpans
 
 class Base32(unittest.TestCase):
     def test_b2a_matches_Pythons(self):
@@ -1568,3 +1570,566 @@ class Log(unittest.TestCase):
         tahoe_log.err(format="intentional sample error",
                       failure=f, level=tahoe_log.OPERATIONAL, umid="wO9UoQ")
         self.flushLoggedErrors(SampleError)
+
+
+class SimpleSpans:
+    # this is a simple+inefficient form of util.spans.Spans . We compare the
+    # behavior of this reference model against the real (efficient) form.
+
+    def __init__(self, _span_or_start=None, length=None):
+        self._have = set()
+        if length is not None:
+            for i in range(_span_or_start, _span_or_start+length):
+                self._have.add(i)
+        elif _span_or_start:
+            for (start,length) in _span_or_start:
+                self.add(start, length)
+
+    def add(self, start, length):
+        for i in range(start, start+length):
+            self._have.add(i)
+        return self
+
+    def remove(self, start, length):
+        for i in range(start, start+length):
+            self._have.discard(i)
+        return self
+
+    def each(self):
+        return sorted(self._have)
+
+    def __iter__(self):
+        items = sorted(self._have)
+        prevstart = None
+        prevend = None
+        for i in items:
+            if prevstart is None:
+                prevstart = prevend = i
+                continue
+            if i == prevend+1:
+                prevend = i
+                continue
+            yield (prevstart, prevend-prevstart+1)
+            prevstart = prevend = i
+        if prevstart is not None:
+            yield (prevstart, prevend-prevstart+1)
+
+    def __len__(self):
+        # this also gets us bool(s)
+        return len(self._have)
+
+    def __add__(self, other):
+        s = self.__class__(self)
+        for (start, length) in other:
+            s.add(start, length)
+        return s
+
+    def __sub__(self, other):
+        s = self.__class__(self)
+        for (start, length) in other:
+            s.remove(start, length)
+        return s
+
+    def __iadd__(self, other):
+        for (start, length) in other:
+            self.add(start, length)
+        return self
+
+    def __isub__(self, other):
+        for (start, length) in other:
+            self.remove(start, length)
+        return self
+
+    def __and__(self, other):
+        s = self.__class__()
+        for i in other.each():
+            if i in self._have:
+                s.add(i, 1)
+        return s
+
+    def __contains__(self, (start,length)):
+        for i in range(start, start+length):
+            if i not in self._have:
+                return False
+        return True
+
+class ByteSpans(unittest.TestCase):
+    def test_basic(self):
+        s = Spans()
+        self.failUnlessEqual(list(s), [])
+        self.failIf(s)
+        self.failIf((0,1) in s)
+        self.failUnlessEqual(len(s), 0)
+
+        s1 = Spans(3, 4) # 3,4,5,6
+        self._check1(s1)
+
+        s2 = Spans(s1)
+        self._check1(s2)
+
+        s2.add(10,2) # 10,11
+        self._check1(s1)
+        self.failUnless((10,1) in s2)
+        self.failIf((10,1) in s1)
+        self.failUnlessEqual(list(s2.each()), [3,4,5,6,10,11])
+        self.failUnlessEqual(len(s2), 6)
+
+        s2.add(15,2).add(20,2)
+        self.failUnlessEqual(list(s2.each()), [3,4,5,6,10,11,15,16,20,21])
+        self.failUnlessEqual(len(s2), 10)
+
+        s2.remove(4,3).remove(15,1)
+        self.failUnlessEqual(list(s2.each()), [3,10,11,16,20,21])
+        self.failUnlessEqual(len(s2), 6)
+
+        s1 = SimpleSpans(3, 4) # 3 4 5 6
+        s2 = SimpleSpans(5, 4) # 5 6 7 8
+        i = s1 & s2
+        self.failUnlessEqual(list(i.each()), [5, 6])
+
+    def _check1(self, s):
+        self.failUnlessEqual(list(s), [(3,4)])
+        self.failUnless(s)
+        self.failUnlessEqual(len(s), 4)
+        self.failIf((0,1) in s)
+        self.failUnless((3,4) in s)
+        self.failUnless((3,1) in s)
+        self.failUnless((5,2) in s)
+        self.failUnless((6,1) in s)
+        self.failIf((6,2) in s)
+        self.failIf((7,1) in s)
+        self.failUnlessEqual(list(s.each()), [3,4,5,6])
+
+    def test_math(self):
+        s1 = Spans(0, 10) # 0,1,2,3,4,5,6,7,8,9
+        s2 = Spans(5, 3) # 5,6,7
+        s3 = Spans(8, 4) # 8,9,10,11
+
+        s = s1 - s2
+        self.failUnlessEqual(list(s.each()), [0,1,2,3,4,8,9])
+        s = s1 - s3
+        self.failUnlessEqual(list(s.each()), [0,1,2,3,4,5,6,7])
+        s = s2 - s3
+        self.failUnlessEqual(list(s.each()), [5,6,7])
+        s = s1 & s2
+        self.failUnlessEqual(list(s.each()), [5,6,7])
+        s = s2 & s1
+        self.failUnlessEqual(list(s.each()), [5,6,7])
+        s = s1 & s3
+        self.failUnlessEqual(list(s.each()), [8,9])
+        s = s3 & s1
+        self.failUnlessEqual(list(s.each()), [8,9])
+        s = s2 & s3
+        self.failUnlessEqual(list(s.each()), [])
+        s = s3 & s2
+        self.failUnlessEqual(list(s.each()), [])
+        s = Spans() & s3
+        self.failUnlessEqual(list(s.each()), [])
+        s = s3 & Spans()
+        self.failUnlessEqual(list(s.each()), [])
+
+        s = s1 + s2
+        self.failUnlessEqual(list(s.each()), [0,1,2,3,4,5,6,7,8,9])
+        s = s1 + s3
+        self.failUnlessEqual(list(s.each()), [0,1,2,3,4,5,6,7,8,9,10,11])
+        s = s2 + s3
+        self.failUnlessEqual(list(s.each()), [5,6,7,8,9,10,11])
+
+        s = Spans(s1)
+        s -= s2
+        self.failUnlessEqual(list(s.each()), [0,1,2,3,4,8,9])
+        s = Spans(s1)
+        s -= s3
+        self.failUnlessEqual(list(s.each()), [0,1,2,3,4,5,6,7])
+        s = Spans(s2)
+        s -= s3
+        self.failUnlessEqual(list(s.each()), [5,6,7])
+
+        s = Spans(s1)
+        s += s2
+        self.failUnlessEqual(list(s.each()), [0,1,2,3,4,5,6,7,8,9])
+        s = Spans(s1)
+        s += s3
+        self.failUnlessEqual(list(s.each()), [0,1,2,3,4,5,6,7,8,9,10,11])
+        s = Spans(s2)
+        s += s3
+        self.failUnlessEqual(list(s.each()), [5,6,7,8,9,10,11])
+
+    def test_random(self):
+        # attempt to increase coverage of corner cases by comparing behavior
+        # of a simple-but-slow model implementation against the
+        # complex-but-fast actual implementation, in a large number of random
+        # operations
+        S1 = SimpleSpans
+        S2 = Spans
+        s1 = S1(); s2 = S2()
+        seed = ""
+        def _create(subseed):
+            ns1 = S1(); ns2 = S2()
+            for i in range(10):
+                what = md5(subseed+str(i)).hexdigest()
+                start = int(what[2:4], 16)
+                length = max(1,int(what[5:6], 16))
+                ns1.add(start, length); ns2.add(start, length)
+            return ns1, ns2
+
+        #print
+        for i in range(1000):
+            what = md5(seed+str(i)).hexdigest()
+            op = what[0]
+            subop = what[1]
+            start = int(what[2:4], 16)
+            length = max(1,int(what[5:6], 16))
+            #print what
+            if op in "0":
+                if subop in "01234":
+                    s1 = S1(); s2 = S2()
+                elif subop in "5678":
+                    s1 = S1(start, length); s2 = S2(start, length)
+                else:
+                    s1 = S1(s1); s2 = S2(s2)
+                #print "s2 = %s" % s2.dump()
+            elif op in "123":
+                #print "s2.add(%d,%d)" % (start, length)
+                s1.add(start, length); s2.add(start, length)
+            elif op in "456":
+                #print "s2.remove(%d,%d)" % (start, length)
+                s1.remove(start, length); s2.remove(start, length)
+            elif op in "78":
+                ns1, ns2 = _create(what[7:11])
+                #print "s2 + %s" % ns2.dump()
+                s1 = s1 + ns1; s2 = s2 + ns2
+            elif op in "9a":
+                ns1, ns2 = _create(what[7:11])
+                #print "%s - %s" % (s2.dump(), ns2.dump())
+                s1 = s1 - ns1; s2 = s2 - ns2
+            elif op in "bc":
+                ns1, ns2 = _create(what[7:11])
+                #print "s2 += %s" % ns2.dump()
+                s1 += ns1; s2 += ns2
+            elif op in "de":
+                ns1, ns2 = _create(what[7:11])
+                #print "%s -= %s" % (s2.dump(), ns2.dump())
+                s1 -= ns1; s2 -= ns2
+            else:
+                ns1, ns2 = _create(what[7:11])
+                #print "%s &= %s" % (s2.dump(), ns2.dump())
+                s1 = s1 & ns1; s2 = s2 & ns2
+            #print "s2 now %s" % s2.dump()
+            self.failUnlessEqual(list(s1.each()), list(s2.each()))
+            self.failUnlessEqual(len(s1), len(s2))
+            self.failUnlessEqual(bool(s1), bool(s2))
+            self.failUnlessEqual(list(s1), list(s2))
+            for j in range(10):
+                what = md5(what[12:14]+str(j)).hexdigest()
+                start = int(what[2:4], 16)
+                length = max(1, int(what[5:6], 16))
+                span = (start, length)
+                self.failUnlessEqual(bool(span in s1), bool(span in s2))
+
+
+    # s()
+    # s(start,length)
+    # s(s0)
+    # s.add(start,length) : returns s
+    # s.remove(start,length)
+    # s.each() -> list of byte offsets, mostly for testing
+    # list(s) -> list of (start,length) tuples, one per span
+    # (start,length) in s -> True if (start..start+length-1) are all members
+    #  NOT equivalent to x in list(s)
+    # len(s) -> number of bytes, for testing, bool(), and accounting/limiting
+    # bool(s)  (__len__)
+    # s = s1+s2, s1-s2, +=s1, -=s1
+
+    def test_overlap(self):
+        for a in range(20):
+            for b in range(10):
+                for c in range(20):
+                    for d in range(10):
+                        self._test_overlap(a,b,c,d)
+
+    def _test_overlap(self, a, b, c, d):
+        s1 = set(range(a,a+b))
+        s2 = set(range(c,c+d))
+        #print "---"
+        #self._show_overlap(s1, "1")
+        #self._show_overlap(s2, "2")
+        o = overlap(a,b,c,d)
+        expected = s1.intersection(s2)
+        if not expected:
+            self.failUnlessEqual(o, None)
+        else:
+            start,length = o
+            so = set(range(start,start+length))
+            #self._show(so, "o")
+            self.failUnlessEqual(so, expected)
+
+    def _show_overlap(self, s, c):
+        import sys
+        out = sys.stdout
+        if s:
+            for i in range(max(s)):
+                if i in s:
+                    out.write(c)
+                else:
+                    out.write(" ")
+        out.write("\n")
+
+def extend(s, start, length, fill):
+    if len(s) >= start+length:
+        return s
+    assert len(fill) == 1
+    return s + fill*(start+length-len(s))
+
+def replace(s, start, data):
+    assert len(s) >= start+len(data)
+    return s[:start] + data + s[start+len(data):]
+
+class SimpleDataSpans:
+    def __init__(self, other=None):
+        self.missing = "" # "1" where missing, "0" where found
+        self.data = ""
+        if other:
+            for (start, data) in other.get_chunks():
+                self.add(start, data)
+
+    def __len__(self):
+        return len(self.missing.translate(None, "1"))
+    def _dump(self):
+        return [i for (i,c) in enumerate(self.missing) if c == "0"]
+    def _have(self, start, length):
+        m = self.missing[start:start+length]
+        if not m or len(m)<length or int(m):
+            return False
+        return True
+    def get_chunks(self):
+        for i in self._dump():
+            yield (i, self.data[i])
+    def get_spans(self):
+        return SimpleSpans([(start,len(data))
+                            for (start,data) in self.get_chunks()])
+    def get(self, start, length):
+        if self._have(start, length):
+            return self.data[start:start+length]
+        return None
+    def pop(self, start, length):
+        data = self.get(start, length)
+        if data:
+            self.remove(start, length)
+        return data
+    def remove(self, start, length):
+        self.missing = replace(extend(self.missing, start, length, "1"),
+                               start, "1"*length)
+    def add(self, start, data):
+        self.missing = replace(extend(self.missing, start, len(data), "1"),
+                               start, "0"*len(data))
+        self.data = replace(extend(self.data, start, len(data), " "),
+                            start, data)
+
+
+class StringSpans(unittest.TestCase):
+    def do_basic(self, klass):
+        ds = klass()
+        self.failUnlessEqual(len(ds), 0)
+        self.failUnlessEqual(list(ds._dump()), [])
+        self.failUnlessEqual(sum([len(d) for (s,d) in ds.get_chunks()]), 0)
+        s = ds.get_spans()
+        self.failUnlessEqual(ds.get(0, 4), None)
+        self.failUnlessEqual(ds.pop(0, 4), None)
+        ds.remove(0, 4)
+
+        ds.add(2, "four")
+        self.failUnlessEqual(len(ds), 4)
+        self.failUnlessEqual(list(ds._dump()), [2,3,4,5])
+        self.failUnlessEqual(sum([len(d) for (s,d) in ds.get_chunks()]), 4)
+        s = ds.get_spans()
+        self.failUnless((2,2) in s)
+        self.failUnlessEqual(ds.get(0, 4), None)
+        self.failUnlessEqual(ds.pop(0, 4), None)
+        self.failUnlessEqual(ds.get(4, 4), None)
+
+        ds2 = klass(ds)
+        self.failUnlessEqual(len(ds2), 4)
+        self.failUnlessEqual(list(ds2._dump()), [2,3,4,5])
+        self.failUnlessEqual(sum([len(d) for (s,d) in ds2.get_chunks()]), 4)
+        self.failUnlessEqual(ds2.get(0, 4), None)
+        self.failUnlessEqual(ds2.pop(0, 4), None)
+        self.failUnlessEqual(ds2.pop(2, 3), "fou")
+        self.failUnlessEqual(sum([len(d) for (s,d) in ds2.get_chunks()]), 1)
+        self.failUnlessEqual(ds2.get(2, 3), None)
+        self.failUnlessEqual(ds2.get(5, 1), "r")
+        self.failUnlessEqual(ds.get(2, 3), "fou")
+        self.failUnlessEqual(sum([len(d) for (s,d) in ds.get_chunks()]), 4)
+
+        ds.add(0, "23")
+        self.failUnlessEqual(len(ds), 6)
+        self.failUnlessEqual(list(ds._dump()), [0,1,2,3,4,5])
+        self.failUnlessEqual(sum([len(d) for (s,d) in ds.get_chunks()]), 6)
+        self.failUnlessEqual(ds.get(0, 4), "23fo")
+        self.failUnlessEqual(ds.pop(0, 4), "23fo")
+        self.failUnlessEqual(sum([len(d) for (s,d) in ds.get_chunks()]), 2)
+        self.failUnlessEqual(ds.get(0, 4), None)
+        self.failUnlessEqual(ds.pop(0, 4), None)
+
+        ds = klass()
+        ds.add(2, "four")
+        ds.add(3, "ea")
+        self.failUnlessEqual(ds.get(2, 4), "fear")
+
+    def do_scan(self, klass):
+        # do a test with gaps and spans of size 1 and 2
+        #  left=(1,11) * right=(1,11) * gapsize=(1,2)
+        # 111, 112, 121, 122, 211, 212, 221, 222
+        #    211
+        #      121
+        #         112
+        #            212
+        #               222
+        #                   221
+        #                      111
+        #                        122
+        #  11 1  1 11 11  11  1 1  111
+        # 0123456789012345678901234567
+        # abcdefghijklmnopqrstuvwxyz-=
+        pieces = [(1, "bc"),
+                  (4, "e"),
+                  (7, "h"),
+                  (9, "jk"),
+                  (12, "mn"),
+                  (16, "qr"),
+                  (20, "u"),
+                  (22, "w"),
+                  (25, "z-="),
+                  ]
+        p_elements = set([1,2,4,7,9,10,12,13,16,17,20,22,25,26,27])
+        S = "abcdefghijklmnopqrstuvwxyz-="
+        # TODO: when adding data, add capital letters, to make sure we aren't
+        # just leaving the old data in place
+        l = len(S)
+        def base():
+            ds = klass()
+            for start, data in pieces:
+                ds.add(start, data)
+            return ds
+        def dump(s):
+            p = set(s._dump())
+            # wow, this is the first time I've ever wanted ?: in python
+            # note: this requires python2.5
+            d = "".join([(S[i] if i in p else " ") for i in range(l)])
+            assert len(d) == l
+            return d
+        DEBUG = False
+        for start in range(0, l):
+            for end in range(start+1, l):
+                # add [start-end) to the baseline
+                which = "%d-%d" % (start, end-1)
+                p_added = set(range(start, end))
+                b = base()
+                if DEBUG:
+                    print
+                    print dump(b), which
+                    add = klass(); add.add(start, S[start:end])
+                    print dump(add)
+                b.add(start, S[start:end])
+                if DEBUG:
+                    print dump(b)
+                # check that the new span is there
+                d = b.get(start, end-start)
+                self.failUnlessEqual(d, S[start:end], which)
+                # check that all the original pieces are still there
+                for t_start, t_data in pieces:
+                    t_len = len(t_data)
+                    self.failUnlessEqual(b.get(t_start, t_len),
+                                         S[t_start:t_start+t_len],
+                                         "%s %d+%d" % (which, t_start, t_len))
+                # check that a lot of subspans are mostly correct
+                for t_start in range(l):
+                    for t_len in range(1,4):
+                        d = b.get(t_start, t_len)
+                        if d is not None:
+                            which2 = "%s+(%d-%d)" % (which, t_start,
+                                                     t_start+t_len-1)
+                            self.failUnlessEqual(d, S[t_start:t_start+t_len],
+                                                 which2)
+                        # check that removing a subspan gives the right value
+                        b2 = klass(b)
+                        b2.remove(t_start, t_len)
+                        removed = set(range(t_start, t_start+t_len))
+                        for i in range(l):
+                            exp = (((i in p_elements) or (i in p_added))
+                                   and (i not in removed))
+                            which2 = "%s-(%d-%d)" % (which, t_start,
+                                                     t_start+t_len-1)
+                            self.failUnlessEqual(bool(b2.get(i, 1)), exp,
+                                                 which2+" %d" % i)
+
+    def test_test(self):
+        self.do_basic(SimpleDataSpans)
+        self.do_scan(SimpleDataSpans)
+
+    def test_basic(self):
+        self.do_basic(DataSpans)
+        self.do_scan(DataSpans)
+
+    def test_random(self):
+        # attempt to increase coverage of corner cases by comparing behavior
+        # of a simple-but-slow model implementation against the
+        # complex-but-fast actual implementation, in a large number of random
+        # operations
+        S1 = SimpleDataSpans
+        S2 = DataSpans
+        s1 = S1(); s2 = S2()
+        seed = ""
+        def _randstr(length, seed):
+            created = 0
+            pieces = []
+            while created < length:
+                piece = md5(seed + str(created)).hexdigest()
+                pieces.append(piece)
+                created += len(piece)
+            return "".join(pieces)[:length]
+        def _create(subseed):
+            ns1 = S1(); ns2 = S2()
+            for i in range(10):
+                what = md5(subseed+str(i)).hexdigest()
+                start = int(what[2:4], 16)
+                length = max(1,int(what[5:6], 16))
+                ns1.add(start, _randstr(length, what[7:9]));
+                ns2.add(start, _randstr(length, what[7:9]))
+            return ns1, ns2
+
+        #print
+        for i in range(1000):
+            what = md5(seed+str(i)).hexdigest()
+            op = what[0]
+            subop = what[1]
+            start = int(what[2:4], 16)
+            length = max(1,int(what[5:6], 16))
+            #print what
+            if op in "0":
+                if subop in "0123456":
+                    s1 = S1(); s2 = S2()
+                else:
+                    s1, s2 = _create(what[7:11])
+                #print "s2 = %s" % list(s2._dump())
+            elif op in "123456":
+                #print "s2.add(%d,%d)" % (start, length)
+                s1.add(start, _randstr(length, what[7:9]));
+                s2.add(start, _randstr(length, what[7:9]))
+            elif op in "789abc":
+                #print "s2.remove(%d,%d)" % (start, length)
+                s1.remove(start, length); s2.remove(start, length)
+            else:
+                #print "s2.pop(%d,%d)" % (start, length)
+                d1 = s1.pop(start, length); d2 = s2.pop(start, length)
+                self.failUnlessEqual(d1, d2)
+            #print "s1 now %s" % list(s1._dump())
+            #print "s2 now %s" % list(s2._dump())
+            self.failUnlessEqual(len(s1), len(s2))
+            self.failUnlessEqual(list(s1._dump()), list(s2._dump()))
+            for j in range(100):
+                what = md5(what[12:14]+str(j)).hexdigest()
+                start = int(what[2:4], 16)
+                length = max(1, int(what[5:6], 16))
+                d1 = s1.get(start, length); d2 = s2.get(start, length)
+                self.failUnlessEqual(d1, d2, "%d+%d" % (start, length))
diff --git a/src/allmydata/util/spans.py b/src/allmydata/util/spans.py
new file mode 100755
index 00000000..2a199f07
--- /dev/null
+++ b/src/allmydata/util/spans.py
@@ -0,0 +1,431 @@
+
+class Spans:
+    """I represent a compressed list of booleans, one per index (an integer).
+    Typically, each index represents an offset into a large string, pointing
+    to a specific byte of a share. In this context, True means that byte has
+    been received, or has been requested.
+
+    Another way to look at this is maintaining a set of integers, optimized
+    for operations on spans like 'add range to set' and 'is range in set?'.
+
+    This is a python equivalent of perl's Set::IntSpan module, frequently
+    used to represent .newsrc contents.
+
+    Rather than storing an actual (large) list or dictionary, I represent my
+    internal state as a sorted list of spans, each with a start and a length.
+    My API is presented in terms of start+length pairs. I provide set
+    arithmetic operators, to efficiently answer questions like 'I want bytes
+    XYZ, I already requested bytes ABC, and I've already received bytes DEF:
+    what bytes should I request now?'.
+
+    The new downloader will use it to keep track of which bytes we've requested
+    or received already.
+    """
+
+    def __init__(self, _span_or_start=None, length=None):
+        self._spans = list()
+        if length is not None:
+            self._spans.append( (_span_or_start, length) )
+        elif _span_or_start:
+            for (start,length) in _span_or_start:
+                self.add(start, length)
+        self._check()
+
+    def _check(self):
+        assert sorted(self._spans) == self._spans
+        prev_end = None
+        try:
+            for (start,length) in self._spans:
+                if prev_end is not None:
+                    assert start > prev_end
+                prev_end = start+length
+        except AssertionError:
+            print "BAD:", self.dump()
+            raise
+
+    def add(self, start, length):
+        assert start >= 0
+        assert length > 0
+        #print " ADD [%d+%d -%d) to %s" % (start, length, start+length, self.dump())
+        first_overlap = last_overlap = None
+        for i,(s_start,s_length) in enumerate(self._spans):
+            #print "  (%d+%d)-> overlap=%s adjacent=%s" % (s_start,s_length, overlap(s_start, s_length, start, length), adjacent(s_start, s_length, start, length))
+            if (overlap(s_start, s_length, start, length)
+                or adjacent(s_start, s_length, start, length)):
+                last_overlap = i
+                if first_overlap is None:
+                    first_overlap = i
+                continue
+            # no overlap
+            if first_overlap is not None:
+                break
+        #print "  first_overlap", first_overlap, last_overlap
+        if first_overlap is None:
+            # no overlap, so just insert the span and sort by starting
+            # position.
+            self._spans.insert(0, (start,length))
+            self._spans.sort()
+        else:
+            # everything from [first_overlap] to [last_overlap] overlapped
+            first_start,first_length = self._spans[first_overlap]
+            last_start,last_length = self._spans[last_overlap]
+            newspan_start = min(start, first_start)
+            newspan_end = max(start+length, last_start+last_length)
+            newspan_length = newspan_end - newspan_start
+            newspan = (newspan_start, newspan_length)
+            self._spans[first_overlap:last_overlap+1] = [newspan]
+        #print "  ADD done: %s" % self.dump()
+        self._check()
+
+        return self
+
+    def remove(self, start, length):
+        assert start >= 0
+        assert length > 0
+        #print " REMOVE [%d+%d -%d) from %s" % (start, length, start+length, self.dump())
+        first_complete_overlap = last_complete_overlap = None
+        for i,(s_start,s_length) in enumerate(self._spans):
+            s_end = s_start + s_length
+            o = overlap(s_start, s_length, start, length)
+            if o:
+                o_start, o_length = o
+                o_end = o_start+o_length
+                if o_start == s_start and o_end == s_end:
+                    # delete this span altogether
+                    if first_complete_overlap is None:
+                        first_complete_overlap = i
+                    last_complete_overlap = i
+                elif o_start == s_start:
+                    # we only overlap the left side, so trim the start
+                    #    1111
+                    #  rrrr
+                    #    oo
+                    # ->   11
+                    new_start = o_end
+                    new_end = s_end
+                    assert new_start > s_start
+                    new_length = new_end - new_start
+                    self._spans[i] = (new_start, new_length)
+                elif o_end == s_end:
+                    # we only overlap the right side
+                    #    1111
+                    #      rrrr
+                    #      oo
+                    # -> 11
+                    new_start = s_start
+                    new_end = o_start
+                    assert new_end < s_end
+                    new_length = new_end - new_start
+                    self._spans[i] = (new_start, new_length)
+                else:
+                    # we overlap the middle, so create a new span. No need to
+                    # examine any other spans.
+                    #    111111
+                    #      rr
+                    #    LL  RR
+                    left_start = s_start
+                    left_end = o_start
+                    left_length = left_end - left_start
+                    right_start = o_end
+                    right_end = s_end
+                    right_length = right_end - right_start
+                    self._spans[i] = (left_start, left_length)
+                    self._spans.append( (right_start, right_length) )
+                    self._spans.sort()
+                    break
+        if first_complete_overlap is not None:
+            del self._spans[first_complete_overlap:last_complete_overlap+1]
+        #print "  REMOVE done: %s" % self.dump()
+        self._check()
+        return self
+
+    def dump(self):
+        return "len=%d: %s" % (len(self),
+                               ",".join(["[%d-%d]" % (start,start+l-1)
+                                         for (start,l) in self._spans]) )
+
+    def each(self):
+        for start, length in self._spans:
+            for i in range(start, start+length):
+                yield i
+
+    def __iter__(self):
+        for s in self._spans:
+            yield s
+
+    def __len__(self):
+        # this also gets us bool(s)
+        return sum([length for start,length in self._spans])
+
+    def __add__(self, other):
+        s = self.__class__(self)
+        for (start, length) in other:
+            s.add(start, length)
+        return s
+
+    def __sub__(self, other):
+        s = self.__class__(self)
+        for (start, length) in other:
+            s.remove(start, length)
+        return s
+
+    def __iadd__(self, other):
+        for (start, length) in other:
+            self.add(start, length)
+        return self
+
+    def __isub__(self, other):
+        for (start, length) in other:
+            self.remove(start, length)
+        return self
+
+    def __and__(self, other):
+        if not self._spans:
+            return self.__class__()
+        bounds = self.__class__(self._spans[0][0],
+                                self._spans[-1][0]+self._spans[-1][1])
+        not_other = bounds - other
+        return self - not_other
+
+    def __contains__(self, (start,length)):
+        for span_start,span_length in self._spans:
+            o = overlap(start, length, span_start, span_length)
+            if o:
+                o_start,o_length = o
+                if o_start == start and o_length == length:
+                    return True
+        return False
+
+def overlap(start0, length0, start1, length1):
+    # return start2,length2 of the overlapping region, or None
+    #  00      00   000   0000  00  00 000  00   00  00      00
+    #     11    11   11    11   111 11 11  1111 111 11    11
+    left = max(start0, start1)
+    right = min(start0+length0, start1+length1)
+    # if there is overlap, 'left' will be its start, and right-1 will
+    # be the end'
+    if left < right:
+        return (left, right-left)
+    return None
+
+def adjacent(start0, length0, start1, length1):
+    if (start0 < start1) and start0+length0 == start1:
+        return True
+    elif (start1 < start0) and start1+length1 == start0:
+        return True
+    return False
+
+class DataSpans:
+    """I represent portions of a large string. Equivalently, I can be said to
+    maintain a large array of characters (with gaps of empty elements). I can
+    be used to manage access to a remote share, where some pieces have been
+    retrieved, some have been requested, and others have not been read.
+    """
+
+    def __init__(self, other=None):
+        self.spans = [] # (start, data) tuples, non-overlapping, merged
+        if other:
+            for (start, data) in other.get_chunks():
+                self.add(start, data)
+
+    def __len__(self):
+        # return number of bytes we're holding
+        return sum([len(data) for (start,data) in self.spans])
+
+    def _dump(self):
+        # return iterator of sorted list of offsets, one per byte
+        for (start,data) in self.spans:
+            for i in range(start, start+len(data)):
+                yield i
+
+    def dump(self):
+        return "len=%d: %s" % (len(self),
+                               ",".join(["[%d-%d]" % (start,start+len(data)-1)
+                                         for (start,data) in self.spans]) )
+
+    def get_chunks(self):
+        return list(self.spans)
+
+    def get_spans(self):
+        """Return a Spans object with a bit set for each byte I hold"""
+        return Spans([(start, len(data)) for (start,data) in self.spans])
+
+    def assert_invariants(self):
+        if not self.spans:
+            return
+        prev_start = self.spans[0][0]
+        prev_end = prev_start + len(self.spans[0][1])
+        for start, data in self.spans[1:]:
+            if not start > prev_end:
+                # adjacent or overlapping: bad
+                print "ASSERTION FAILED", self.spans
+                raise AssertionError
+
+    def get(self, start, length):
+        # returns a string of LENGTH, or None
+        #print "get", start, length, self.spans
+        end = start+length
+        for (s_start,s_data) in self.spans:
+            s_end = s_start+len(s_data)
+            #print " ",s_start,s_end
+            if s_start <= start < s_end:
+                # we want some data from this span. Because we maintain
+                # strictly merged and non-overlapping spans, everything we
+                # want must be in this span.
+                offset = start - s_start
+                if offset + length > len(s_data):
+                    #print " None, span falls short"
+                    return None # span falls short
+                #print " some", s_data[offset:offset+length]
+                return s_data[offset:offset+length]
+            if s_start >= end:
+                # we've gone too far: no further spans will overlap
+                #print " None, gone too far"
+                return None
+        #print " None, ran out of spans"
+        return None
+
+    def add(self, start, data):
+        # first: walk through existing spans, find overlap, modify-in-place
+        #  create list of new spans
+        #  add new spans
+        #  sort
+        #  merge adjacent spans
+        #print "add", start, data, self.spans
+        end = start + len(data)
+        i = 0
+        while len(data):
+            #print " loop", start, data, i, len(self.spans), self.spans
+            if i >= len(self.spans):
+                #print " append and done"
+                # append a last span
+                self.spans.append( (start, data) )
+                break
+            (s_start,s_data) = self.spans[i]
+            # five basic cases:
+            #  a: OLD  b:OLDD  c1:OLD  c2:OLD   d1:OLDD  d2:OLD  e: OLLDD
+            #    NEW     NEW      NEW     NEWW      NEW      NEW     NEW
+            #
+            # we handle A by inserting a new segment (with "N") and looping,
+            # turning it into B or C. We handle B by replacing a prefix and
+            # terminating. We handle C (both c1 and c2) by replacing the
+            # segment (and, for c2, looping, turning it into A). We handle D
+            # by replacing a suffix (and, for d2, looping, turning it into
+            # A). We handle E by replacing the middle and terminating.
+            if start < s_start:
+                # case A: insert a new span, then loop with the remainder
+                #print " insert new psan"
+                s_len = s_start-start
+                self.spans.insert(i, (start, data[:s_len]))
+                i += 1
+                start = s_start
+                data = data[s_len:]
+                continue
+            s_len = len(s_data)
+            s_end = s_start+s_len
+            if s_start <= start < s_end:
+                #print " modify this span", s_start, start, s_end
+                # we want to modify some data in this span: a prefix, a
+                # suffix, or the whole thing
+                if s_start == start:
+                    if s_end <= end:
+                        #print " replace whole segment"
+                        # case C: replace this segment
+                        self.spans[i] = (s_start, data[:s_len])
+                        i += 1
+                        start += s_len
+                        data = data[s_len:]
+                        # C2 is where len(data)>0
+                        continue
+                    # case B: modify the prefix, retain the suffix
+                    #print " modify prefix"
+                    self.spans[i] = (s_start, data + s_data[len(data):])
+                    break
+                if start > s_start and end < s_end:
+                    # case E: modify the middle
+                    #print " modify middle"
+                    prefix_len = start - s_start # we retain this much
+                    suffix_len = s_end - end # and retain this much
+                    newdata = s_data[:prefix_len] + data + s_data[-suffix_len:]
+                    self.spans[i] = (s_start, newdata)
+                    break
+                # case D: retain the prefix, modify the suffix
+                #print " modify suffix"
+                prefix_len = start - s_start # we retain this much
+                suffix_len = s_len - prefix_len # we replace this much
+                #print "  ", s_data, prefix_len, suffix_len, s_len, data
+                self.spans[i] = (s_start,
+                                 s_data[:prefix_len] + data[:suffix_len])
+                i += 1
+                start += suffix_len
+                data = data[suffix_len:]
+                #print "  now", start, data
+                # D2 is where len(data)>0
+                continue
+            # else we're not there yet
+            #print " still looking"
+            i += 1
+            continue
+        # now merge adjacent spans
+        #print " merging", self.spans
+        newspans = []
+        for (s_start,s_data) in self.spans:
+            if newspans and adjacent(newspans[-1][0], len(newspans[-1][1]),
+                                     s_start, len(s_data)):
+                newspans[-1] = (newspans[-1][0], newspans[-1][1] + s_data)
+            else:
+                newspans.append( (s_start, s_data) )
+        self.spans = newspans
+        self.assert_invariants()
+        #print " done", self.spans
+
+    def remove(self, start, length):
+        i = 0
+        end = start + length
+        #print "remove", start, length, self.spans
+        while i < len(self.spans):
+            (s_start,s_data) = self.spans[i]
+            if s_start >= end:
+                # this segment is entirely right of the removed region, and
+                # all further segments are even further right. We're done.
+                break
+            s_len = len(s_data)
+            s_end = s_start + s_len
+            o = overlap(start, length, s_start, s_len)
+            if not o:
+                i += 1
+                continue
+            o_start, o_len = o
+            o_end = o_start + o_len
+            if o_len == s_len:
+                # remove the whole segment
+                del self.spans[i]
+                continue
+            if o_start == s_start:
+                # remove a prefix, leaving the suffix from o_end to s_end
+                prefix_len = o_end - o_start
+                self.spans[i] = (o_end, s_data[prefix_len:])
+                i += 1
+                continue
+            elif o_end == s_end:
+                # remove a suffix, leaving the prefix from s_start to o_start
+                prefix_len = o_start - s_start
+                self.spans[i] = (s_start, s_data[:prefix_len])
+                i += 1
+                continue
+            # remove the middle, creating a new segment
+            # left is s_start:o_start, right is o_end:s_end
+            left_len = o_start - s_start
+            left = s_data[:left_len]
+            right_len = s_end - o_end
+            right = s_data[-right_len:]
+            self.spans[i] = (s_start, left)
+            self.spans.insert(i+1, (o_end, right))
+            break
+        #print " done", self.spans
+
+    def pop(self, start, length):
+        data = self.get(start, length)
+        if data:
+            self.remove(start, length)
+        return data