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Subject: zlib Technical Details
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<H1 align=3Dcenter><IMG height=3D204 alt=3Dzlib=20
src=3D"http://www.zlib.net/images/zlib3d-b1.png" width=3D369 =
align=3Dmiddle> </H1>
<H2 align=3Dcenter>Technical Details </H2><!--            GRR:  add =
algorithm.doc           --><!--            GRR:  add patent info?        =
    -->
<P>
<HR>

<P>
<H3>Maximum Expansion Factor </H3>
<P><B>zlib</B>'s compression method, an LZ77 variant called deflation, =
emits=20
compressed data as a sequence of blocks. Various block types are =
allowed, one of=20
which is stored blocks=97these are simply composed of the raw input data =
plus a=20
few header bytes. In the worst possible case, where the other block =
types would=20
expand the data, deflation falls back to stored (uncompressed) blocks. =
Thus for=20
the default settings used by deflateInit(), compress(), and compress2(), =
the=20
only expansion is an overhead of five bytes per 16 KB block (about =
0.03%), plus=20
a one-time overhead of six bytes for the entire stream. Even if the last =
or only=20
block is smaller than 16 KB, the overhead is still five bytes. In the =
absolute=20
worst case of a single-byte input stream, the overhead therefore amounts =
to=20
1100% (eleven bytes of overhead, one byte of actual data). For larger =
stream=20
sizes, the overhead approaches the limiting value of 0.03%.=20
<P>deflateInit2() includes arguments for windowBits and memLevel that =
permit=20
settings other than the defaults. These parameters can be used to adjust =
the=20
memory required for the compressor as well as the decompressor for =
special=20
applications, though usually with a reduction in compression. For =
various=20
combinations of the allowed values for those parameters, the expansion =
can be=20
larger than for the default settings. The worst case choice of =
parameters can=20
result in an expansion of at most 13.5%, plus eleven bytes.=20
<P>The deflateBound() and compressBound() functions can be used to =
provide an=20
upper limit on the expansion in order to permit the allocation of an =
output=20
buffer assured to be large enough to hold the entire compressed output.=20
deflateBound() takes into account any deflateInit2() options.=20
<P>
<HR>

<P>
<H3>Maximum Compression Factor </H3>
<P>Empirically, the deflate method is capable of compression factors =
exceeding=20
1000:1. (The test case was a 50MB file filled with zeros; it compressed =
to <!-- new:  67108864 uncompressed, 65132 compressed --><!-- (retest =
with zlibcomp) -->roughly=20
49&nbsp;KB.) Mark loves to calculate stuff like this and reports that =
the=20
theoretical limit for the zlib <I>format</I> (as opposed to its=20
<I>implementation</I> in the currently available sources) is 1032:1. To =
quote=20
him,=20
<P>
<BLOCKQUOTE>The limit comes from the fact that one length/distance pair =
can=20
  represent at most 258 output bytes. A length requires at least one bit =
and a=20
  distance requires at least one bit, so two bits in can give 258 bytes =
out, or=20
  eight bits in give 1032 bytes out. A dynamic block has no length =
restriction,=20
  so you could get arbitrarily close to the limit of 1032:1. =
</BLOCKQUOTE>
<P>He goes on to note that the current implementation limits its dynamic =
blocks=20
to about 8&nbsp;KB (corresponding to 8MB of input data); together with a =
few=20
bits of overhead, this implies an actual compression limit of about =
1030.3:1.=20
Not only that, but the compressed data stream is itself likely to be =
rather=20
compressible (in this special case only), so running it through deflate =
again=20
should produce further gains.=20
<P>By way of comparison, note that a version of run-length encoding =
optimized=20
for this sort of unusual data file -- that is, by using 32-bit integers =
for the=20
lengths rather than the more usual 8-bit bytes or 16-bit words -- could =
encode=20
the test file in five bytes. That would be a compression factor of =
10,000,000:1=20
(or 10.000.000:1 for you Europeans, or <!-- <FONT =
SIZE=3D"-1">10<SUP>7</SUP></FONT>:1 -->10<SUP>7</SUP>:1 for all of you=20
engineers and scientists whose browsers support superscripts). <!-- IMG =
ALIGN=3D"middle" SRC=3D"images/smile.happy.png" ALT=3D":-)" -->
<P>Finally, please note that this level of compression is =
<I>extremely</I> rare=20
and only occurs with really trivial files (e.g., a megabyte of zeros). =
<FONT=20
color=3D#00aa00><B>More typical zlib compression ratios are on the order =
of 2:1 to=20
5:1.</B></FONT>=20
<P>
<HR>

<P>
<H3>Compression Factor Design Quirk </H3><!-- NEW 20010414 -->
<P>A design choice in the <B>zlib</B> implementation (as opposed to the =
zlib and=20
deflate specifications) limits match distances to 2<SUP><FONT=20
size=3D-1>windowBits</FONT></SUP>&nbsp;-&nbsp;262 rather than the =
2<SUP><FONT=20
size=3D-1>windowBits</FONT></SUP> that one might naively expect. This =
limitation=20
mainly affects applications that try to optimize decoder memory usage by =

reducing the window size for small files; in some cases, compression =
might be=20
degraded because an otherwise valid match (according to the spec) near =
the=20
theoretical distance limit won't be found by zlib.=20
<P>One workaround would be to set the window size to the next larger =
power of=20
two for encoding (but no more than the maximum size of 32&nbsp;KB, =
obviously)=20
and then modify the CINFO field in the zlib header after the stream is=20
compressed. <FONT color=3D#cc0000><B>Such an approach is not =
recommended, however,=20
and should be attempted only by experts.</B></FONT>=20
<P>
<HR>

<P>
<H3>Memory Footprint </H3>
<P><B>zlib</B>'s memory footprint can also be specified fairly =
precisely. It is=20
larger for compression than for decompression, and the exact =
requirements depend=20
on how the library was compiled.=20
<P>The memory requirements for compression depend on two parameters,=20
<B>windowBits</B> and <B>memLevel</B>:=20
<P>
<BLOCKQUOTE><TT>deflate memory usage (bytes) =3D=20
  (1&nbsp;&lt;&lt;&nbsp;(windowBits+2)) + =
(1&nbsp;&lt;&lt;&nbsp;(memLevel+9))=20
  </TT></BLOCKQUOTE>
<P>For the default values of 15 and 8, respectively, this is =
256&nbsp;KB. Both=20
windowBits and memLevel can be set to lower values at compile time via =
the=20
MAX_WBITS and MAX_MEM_LEVEL macros, but only at a cost in compression=20
efficiency.=20
<P>The memory requirements for decompression depend only on =
<B>windowBits</B>,=20
but this is, in a sense, a harsher limitation: whereas data streams =
compressed=20
with a smaller window will merely be a bit larger than they would have=20
otherwise, a reduced window size for decompression means that streams =
compressed=20
with larger windows <I>cannot be decompressed at all</I>. Having said =
that:=20
<P>
<BLOCKQUOTE><TT>inflate memory usage (bytes) =3D=20
  (1&nbsp;&lt;&lt;&nbsp;windowBits) + 1440*2*sizeof(int) =
</TT></BLOCKQUOTE>
<P>Typically, therefore, inflate() requires no more than 44&nbsp;KB of =
storage=20
on a 32-bit machine--this includes the 32768-byte sliding window and =
11520 bytes=20
of inflate_huft allocations. There are a few additional (fixed) amounts =
of=20
memory usage not included here, but they are small compared to these =
items.=20
<P>
<HR>

<P>
<H3>Adler-32 versus CRC-32 </H3>
<P>
<BLOCKQUOTE><I>This section uses superscripts, which are not supported =
by some=20
  older browsers.</I> </BLOCKQUOTE>
<P>Both Adler-32 and CRC-32 (<I>cyclic redundancy check</I>) are 32-bit =
checks.=20
But while the CRC can take on any 32-bit value (2<SUP>32</SUP> =
possibilities),=20
Adler-32 is limited to 65521<SUP>2</SUP> possibilities. So the =
probability of a=20
false positive on random errors for CRC-32 is=20
2.3283&nbsp;x&nbsp;10<SUP>-10</SUP>, whereas it is very slightly higher =
for=20
Adler-32 at 2.3294&nbsp;x&nbsp;10<SUP>-10</SUP>.=20
<P>The above assumes that all the values are accessible given the amount =
of=20
data. That is true after only four bytes for the CRC-32, but Adler-32 =
requires,=20
on the average, about 0.5&nbsp;KB of data to get rolling--or 1&nbsp;KB =
if it's=20
ASCII data (text). So if the Adler-32 is used on significantly less than =
about a=20
kilobyte, it will be noticeably weaker than a CRC-32 on the same small =
block.=20
<P>A properly constructed CRC-<I>n</I> has the nice property that less =
than=20
<I>n</I> bits in error is always detectable. This is not always true for =

Adler-32--it can detect all one- or two-byte errors but can miss some =
three-byte=20
errors. However, Adler-32 has been constructed to minimize the ways to =
make=20
small changes in the data that result in the same check value, through =
the use=20
of sums significantly larger than the bytes and by using a prime (65521) =
for the=20
modulus. It is in this area that some analysis is deserved, but it has =
not yet=20
been done.=20
<P>This last potential weakness is not a major concern in the =
application of=20
Adler-32 to <B>zlib</B> (or any other history-based compressor), since =
if there=20
is an error at some point in a stream, it will be massively propagated =
after=20
that. It would be of concern in an application with transmission or =
storage that=20
has a borderline signal-to-noise ratio, for which small numbers of =
random errors=20
are expected. For that sort of application one would certainly want to =
use a CRC=20
or, better yet, Reed-Solomon error-correction coding. But even in this =
case, if=20
the data being transmitted or stored uses some sort of history-dependent =

compression (as in <B>zlib</B>) <I>and was compressible to begin =
with</I>, then=20
an Adler-32 used after decompression would be adequate since the =
decompressor=20
would significantly amplify any small errors in the compressed stream. =
(For=20
incompressible data, most modern compressors operate in a pass-through =
mode, so=20
the original comment about using a CRC or ECC holds.)=20
<P>The main reason for Adler-32 is, of course, speed in software=20
implementations. The authors wanted a check on zlib's decompression, but =
not a=20
significant speed penalty just for the check. So Mark came up with the =
Adler-32=20
as a faster but still effective alternative to the CRC-32.=20
<P>An alternative to Adler-32 is Fletcher-32, which replaces the modulo =
of 65521=20
with 65535. <A =
href=3D"http://www.zlib.net/maxino06_fletcher-adler.pdf">This=20
paper</A> shows that Fletcher-32 is superior for channels with low-rate =
random=20
bit errors. However as noted above, you should be using a CRC-32 or =
Reed-Solomon=20
code on such channels.=20
<P>
<HR>

<P>Click here for an informal explanation of the <A=20
href=3D"http://www.zlib.net/feldspar.html">deflate =
algorithm</A>.<BR>Click here to=20
return to the <A href=3D"http://www.zlib.net/zlib.html">zlib Home =
Page</A>.=20
<P>
<HR>
<I>Last modified 1 May 2006 </I>
<HR>

<TABLE cellPadding=3D0 width=3D"100%" border=3D0>
  <TBODY>
  <TR>
    <TD align=3Dleft><FONT size=3D-1>Web page copyright =A9 1996-2006 <A =

      href=3D"http://pobox.com/~newt/">Greg Roelofs</A> and <A=20
      href=3D"http://gailly.net/">Jean-loup Gailly</A>.<BR>zlib software =
copyright=20
      =A9 1995-2005 <A href=3D"http://gailly.net/">Jean-loup Gailly</A> =
and <A=20
      href=3D"http://www.alumni.caltech.edu/~madler/">Mark Adler</A>. =
</FONT></TD>
    <TD vAlign=3Dtop align=3Dright><FONT size=3D-1><!--  <A =
HREF=3D"http://www.info-zip.org/pub/infozip/zlib/">Primary site</A>=0A=
      hosted by=0A=
      <A =
HREF=3D"http://www.freesoftware.com/"><B>FreeSoftware.com</B></A>.=0A=
--><A=20
      href=3D"http://www.zlib.net/index.html">Primary site</A> hosted by =
<A=20
      href=3D"http://www.teaser.fr/"><B>France =
Teaser</B></A>.<BR><I>zlib.org</I>=20
      domain name donated by <A>
      <SCRIPT type=3Dtext/javascript>mail_to("ag","em.net")</SCRIPT>
      Andrew Green</A>. </FONT></TD></TR></TBODY></TABLE></BODY></HTML>

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