Consider an example
1 0 0 2 1 hcodes_jzlib_ i.5
+-----+-------+-------+-+---+
|1 1 1|1 1 0 0|1 1 0 1|0|1 0|
+-----+-------+-------+-+---+
#&> 1 0 0 2 1 hcodes_jzlib_ i.5
3 4 4 1 2
(0~:1 0 0 2 1)* #&> 1 0 0 2 1 hcodes_jzlib_ i.5
3 0 0 1 2
classic huffman did not expect a 0 frequency and if there were
it assigns the longest bit length to them. I think this is
reasonable because it must have a non-zero bit length to encode
an entity. For zlib, it seems that there is a third rule:
For the bit length vector, bit lengths for zero frequency symbols
are zero.
From discussion here, I think using hcodes directly
or indirectly for zlib is a wrong direction.
Пт, 12 сен 2014, Raul Miller написал(а):
> That's what I thought at first, also.
>
> But, let's look at the example at
> http://www.jsoftware.com/pipermail/programming/2014-September/039299.html
>
> and the bit widths given at
> http://www.jsoftware.com/pipermail/programming/2014-September/039327.html
>
> Here's how it looks to me:
>
> bits -:#@>F hcodes A
> 0
>
> Now.. is this a problem?
>
> I think it is. Consider:
>
> #0 -.~#@>F hcodes A
> 286
> #0 -.~bits
> 260
>
> Incidentally, I found a bug in my code, while trying to understand and
> express this concept.
>
> Fixed version here:
>
> bl_count=:3 :0 NB. y is result of freqs
> 0,}.<:#/.~(,~ [: i. 1 + >./)y
> )
>
> start_vals=: +:@+/\.&.|.@}:@,~&0
>
> find_codes=:3 :0 NB. y is result of freqs
> b=. bl_count y
> v=. start_vals b
> n=. /:~ ~.y-.0
> o=. ;({./.~ /:~ (</. i.@#)) y-.0
> c=. ;<"1&.>n (([#2:) #: ])&.> (*b)#v+&.>i.&.>b
> c /: o
> )
>
> An alternate version of the result from find_codes would be given by:
>
> def_code=:3 :0
> b=. bl_count y
> v=. start_vals b
> n=. /:~ ~.y-.0
> o=. ;({./.~ /:~ (</. i.@#)) y-.0
> c=. ;n,.&.>(*b)#v+&.>i.&.>b
> (,. i.@#)c /: o
> )
>
> Thanks,
>
> --
> Raul
>
>
> On Thu, Sep 11, 2014 at 8:33 PM, Joe Bogner <[email protected]> wrote:
> > The bit widths are calculated from the huffman tree
> >
> > See
> >
> > http://stackoverflow.com/questions/759707/efficient-way-of-storing-huffman-tree
> >
> > http://www.siggraph.org/education/materials/HyperGraph/video/mpeg/mpegfaq/huffman_tutorial.html
> >
> > The timing is interesting considering we were talking about trees the other
> > day:
> > http://jsoftware.2058.n7.nabble.com/Ragged-Array-Shapes-are-Trees-td63207.html
> >
> > I was thinking to myself then how I hadn't used trees more than a few times
> > in 18 years of programming.
> >
> > I am not sure how to apply your code to the problem. I also am not
> > completely sure what problem we are solving. If it is creating a
> > standalone J deflate implementation or PNG compression it may be a tall
> > order. I would be curious why not just interface to a C library like what
> > is done in the image3 addon:
> > http://www.jsoftware.com/jwiki/Addons/media/image3
> > On Sep 11, 2014 6:27 PM, "Raul Miller" <[email protected]> wrote:
> >
> >> Here's the code I came up with, with Bill's help:
> >>
> >> bl_count=:3 :0 NB. y is result of freqs
> >> 0,}.<:#/.~(,~ [: i. 1 + >./)y
> >> )
> >>
> >> start_vals=: +:@+/\.&.|.@}:@,~&0
> >>
> >> find_codes=:3 :0 NB. y is result of freqs
> >> b=. bl_count y
> >> v=. start_vals b
> >> n=. /:~ ~.y-.0
> >> o=. ;({./.~ /:~ (</. i.@#)) y
> >> c=. ;<"1&.>n (([#2:) #: ])&.> (*b)#v+&.>i.&.>b
> >> c /: o
> >> )
> >>
> >> An alternate version of the result from find_codes would be given by:
> >>
> >> def_code=:3 :0
> >> b=. bl_count y
> >> v=. start_vals b
> >> n=. /:~ ~.y-.0
> >> o=. ;({./.~ /:~ (</. i.@#)) y
> >> c=. ;n,.&.>(*b)#v+&.>i.&.>b
> >> (,. i.@#)c /: o
> >> )
> >>
> >> The argument to find_codes or def_code is the bit widths for each symbol.
> >>
> >> I have not been able to figure out, from rfc 1951, how the bit widths
> >> are calculated.
> >>
> >> Thanks,
> >>
> >> --
> >> Raul
> >>
> >>
> >>
> >> On Thu, Sep 11, 2014 at 4:47 PM, Joe Bogner <[email protected]> wrote:
> >> > bill, I'd be interested in a solution but I don't think I can
> >> > contribute any more on this. I played with
> >> > https://code.google.com/p/miniz/ and became even more convinced of the
> >> > complexity. It seems as though the compressor can decide whether to
> >> > include the dictionary code table or not -- likely based on the size
> >> > of the table.
> >> >
> >> >
> >> > http://tools.ietf.org/html/rfc1950
> >> >
> >> > A preset dictionary is specially useful to compress short input
> >> > sequences. The compressor can take advantage of the dictionary
> >> > context to encode the input in a more compact manner.
> >> >
> >> >
> >> > More links for anyone who is following and cares to go down the rabbit
> >> hole too:
> >> >
> >> > http://en.wikipedia.org/wiki/Canonical_Huffman_code
> >> >
> >> >
> >> http://stackoverflow.com/questions/759707/efficient-way-of-storing-huffman-tree
> >> >
> >> >
> >> >
> >> > On Thu, Sep 11, 2014 at 1:28 PM, bill lam <[email protected]> wrote:
> >> >> This codes seemed invalid.
> >> >>
> >> >> 1 is a prefix of 11 which is a prefix of 111. Suppose there
> >> >> is a bit pattern of 1 1 , it is ambiguous to mean
> >> >> [68,'1'] [68,'1']
> >> >> or [65,'11']
> >> >>
> >> >> The huffman code in rfc is canonical meaning there is exactly one
> >> >> possible huffman codes for a given bit length vector. This is
> >> >> important because the huffman code table itself will not be
> >> >> stored inside the deflate stream. The decoder only gets the bit
> >> >> length vector, if encoder and decoder use different huffman code
> >> >> for the same bit length vectors, it will not work.
> >> >>
> >> >> Чт, 11 сен 2014, Joe Bogner написал(а):
> >> >>> Ignore the pako.js example output... It was just outputting the binary
> >> >>> representation of A-Z, not the huffman code
> >> >>>
> >> >>> This is what I meant to send
> >> >>>
> >> >>> For ABCD:
> >> >>>
> >> >>> [65,'11'],
> >> >>> [66,'0'],
> >> >>> [67,'10'],
> >> >>> [68,'1'],
> >> >>> [256,'111']
> >> >>>
> >> >>> It still doesn't seem to be sorting correctly lexographically, but I'm
> >> >>> not really in my comfort zone of understanding:
> >> >>>
> >> >>> The RFC has this instead:
> >> >>>
> >> >>> Symbol Code
> >> >>> ------ ----
> >> >>> A 10
> >> >>> B 0
> >> >>> C 110
> >> >>> D 111
> >> >>>
> >> >>> I don't really know if it has to match the RFC or if each
> >> >>> implementation is able to do its own thing as long since it includes
> >> >>> the distance/reverse lookup table (whatever it's called).
> >> >>>
> >> >>> FYI
> >> >>>
> >> >>>
> >> >>> This is where I inserted my code:
> >> >>>
> >> >>> /*
> >> ===========================================================================
> >> >>> * Generate the codes for a given tree and bit counts (which need not
> >> be
> >> >>> * optimal).
> >> >>> * IN assertion: the array bl_count contains the bit length statistics
> >> for
> >> >>> * the given tree and the field len is set for all tree elements.
> >> >>> * OUT assertion: the field code is set for all tree elements of non
> >> >>> * zero code length.
> >> >>> */
> >> >>> function gen_codes(tree, max_code, bl_count)
> >> >>> // ct_data *tree; /* the tree to decorate */
> >> >>> // int max_code; /* largest code with non zero
> >> frequency */
> >> >>> // ushf *bl_count; /* number of codes at each bit length
> >> */
> >> >>> {
> >> >>> var next_code = new Array(MAX_BITS+1); /* next code value for each
> >> >>> bit length */
> >> >>> var code = 0; /* running code value */
> >> >>> var bits; /* bit index */
> >> >>> var n; /* code index */
> >> >>>
> >> >>> /* The distribution counts are first used to generate the code values
> >> >>> * without bit reversal.
> >> >>> */
> >> >>> for (bits = 1; bits <= MAX_BITS; bits++) {
> >> >>> next_code[bits] = code = (code + bl_count[bits-1]) << 1;
> >> >>> }
> >> >>> /* Check that the bit counts in bl_count are consistent. The last
> >> code
> >> >>> * must be all ones.
> >> >>> */
> >> >>> //Assert (code + bl_count[MAX_BITS]-1 == (1<<MAX_BITS)-1,
> >> >>> // "inconsistent bit counts");
> >> >>> //Tracev((stderr,"\ngen_codes: max_code %d ", max_code));
> >> >>>
> >> >>> for (n = 0; n <= max_code; n++) {
> >> >>> var len = tree[n*2 + 1]/*.Len*/;
> >> >>> if (len === 0) { continue; }
> >> >>> /* Now reverse the bits */
> >> >>> tree[n*2]/*.Code*/ = bi_reverse(next_code[len]++, len);
> >> >>>
> >> >>> if (tree!=static_ltree) {
> >> >>> var v = tree[n*2];
> >> >>> console.log('[' + n + ",'" + v.toString(2) + "'],");
> >> >>> }
> >> >>> //Tracecv(tree != static_ltree, (stderr,"\nn %3d %c l %2d c %4x
> >> (%x) ",
> >> >>> // n, (isgraph(n) ? n : ' '), len, tree[n].Code,
> >> next_code[len]-1));
> >> >>> }
> >> >>>
> >> >>> }
> >> >>>
> >> >>> On Thu, Sep 11, 2014 at 11:55 AM, Joe Bogner <[email protected]>
> >> wrote:
> >> >>> > I think the prefix coding looks OK, but the 2 rules does not:
> >> >>> >
> >> >>> > I modified the code[1] to allow passing in a string and outputting
> >> the codes
> >> >>> >
> >> >>> > C:\temp>deflate ABCDEFGHIJKLMONPQRSTUVWXYZ
> >> >>> > code 65 : 0 00000000000000000000000000000000
> >> >>> > code 66 : 6 00000000000000000000000000000110
> >> >>> > code 67 : 8 00000000000000000000000000001000
> >> >>> > code 68 : 4 00000000000000000000000000000100
> >> >>> > code 69 : 22 00000000000000000000000000010110
> >> >>> > code 70 : 14 00000000000000000000000000001110
> >> >>> > code 71 : 30 00000000000000000000000000011110
> >> >>> > code 72 : 1 00000000000000000000000000000001
> >> >>> > code 73 : 17 00000000000000000000000000010001
> >> >>> > code 74 : 12 00000000000000000000000000001100
> >> >>> > code 75 : 9 00000000000000000000000000001001
> >> >>> > code 76 : 25 00000000000000000000000000011001
> >> >>> > code 77 : 5 00000000000000000000000000000101
> >> >>> > code 78 : 21 00000000000000000000000000010101
> >> >>> > code 79 : 13 00000000000000000000000000001101
> >> >>> > code 80 : 29 00000000000000000000000000011101
> >> >>> > code 81 : 3 00000000000000000000000000000011
> >> >>> > code 82 : 19 00000000000000000000000000010011
> >> >>> > code 83 : 11 00000000000000000000000000001011
> >> >>> > code 84 : 27 00000000000000000000000000011011
> >> >>> > code 85 : 7 00000000000000000000000000000111
> >> >>> > code 86 : 23 00000000000000000000000000010111
> >> >>> > code 87 : 15 00000000000000000000000000001111
> >> >>> > code 88 : 31 00000000000000000000000000011111
> >> >>> > code 89 : 2 00000000000000000000000000000010
> >> >>> > code 90 : 10 00000000000000000000000000001010
> >> >>> >
> >> >>> >
> >> >>> > I think it violates the consecutive rule... Each letter has the same
> >> >>> > frequency. ABCD have the same bit length. The order is off:
> >> >>> >
> >> >>> > If I sort it lexographically using javascript:
> >> >>> >
> >> >>> > JSON.stringify([['a','00000000000000000000000000000000'],
> >> >>> > ['b','00000000000000000000000000000110'],
> >> >>> > ['c','00000000000000000000000000001000'],
> >> >>> > ['d','00000000000000000000000000000100']].sort(function(x,y) { return
> >> >>> > x[1] - y[1] }))
> >> >>> >
> >> >>> >
> >> "[["a","00000000000000000000000000000000"],["d","00000000000000000000000000000100"],["b","00000000000000000000000000000110"],["c","00000000000000000000000000001000"]]"
> >> >>> >
> >> >>> > As you can see, the order comes out a,d,b,c
> >> >>> >
> >> >>> > I played around with a javascript implementation, pako[2]. It seems
> >> to
> >> >>> > work correctly:
> >> >>> >
> >> >>> > As you can see, it sorts lexographically
> >> >>> >
> >> >>> > JSON.stringify([[65,'1000001'],
> >> >>> > [66,'1000010'],
> >> >>> > [67,'1000011'],
> >> >>> > [68,'1000100'],
> >> >>> > [69,'1000101'],
> >> >>> > [70,'1000110'],
> >> >>> > [71,'1000111'],
> >> >>> > [72,'1001000'],
> >> >>> > [73,'1001001'],
> >> >>> > [74,'1001010'],
> >> >>> > [75,'1001011'],
> >> >>> > [76,'1001100'],
> >> >>> > [77,'1001101'],
> >> >>> > [78,'1001110'],
> >> >>> > [79,'1001111'],
> >> >>> > [80,'1010000'],
> >> >>> > [81,'1010001'],
> >> >>> > [82,'1010010'],
> >> >>> > [83,'1010011'],
> >> >>> > [84,'1010100'],
> >> >>> > [85,'1010101'],
> >> >>> > [86,'1010110'],
> >> >>> > [87,'1010111'],
> >> >>> > [88,'1011000'],
> >> >>> > [89,'1011001'],
> >> >>> > [90,'1011010']].sort(function(x,y) { return x[1] - y[1] }))
> >> >>> >
> >> >>> >
> >> "[[65,"1000001"],[66,"1000010"],[67,"1000011"],[68,"1000100"],[69,"1000101"],[70,"1000110"],[71,"1000111"],[72,"1001000"],[73,"1001001"],[74,"1001010"],[75,"1001011"],[76,"1001100"],[77,"1001101"],[78,"1001110"],[79,"1001111"],[80,"1010000"],[81,"1010001"],[82,"1010010"],[83,"1010011"],[84,"1010100"],[85,"1010101"],[86,"1010110"],[87,"1010111"],[88,"1011000"],[89,"1011001"],[90,"1011010"]]"
> >> >>> >
> >> >>> > All the values are sorted correctly.
> >> >>> >
> >> >>> > Here it is with the same ABCD example:
> >> >>> >
> >> >>> > var pako = require('pako');
> >> >>> > var binaryString = pako.deflate('ABCD', { to: 'string' });
> >> >>> > console.log(binaryString);
> >> >>> > var restored = pako.inflate(binaryString, { to: 'string' });
> >> >>> > console.log(restored);
> >> >>> >
> >> >>> > It successfully deflates and inflates itself
> >> >>> >
> >> >>> > x?♣A☺☺ ? mcÿ7♣A♫☻?☺♂
> >> >>> > ABCD
> >> >>> >
> >> >>> >
> >> >>> > Hope this helps...
> >> >>> >
> >> >>> > [1] -
> >> https://gist.github.com/joebo/a3c2932f0e5a7a0c3f07#file-deflate-c-L2613
> >> >>> > [2] - https://rawgit.com/nodeca/pako/master/dist/pako.js
> >> >>> >
> >> >>> > On Thu, Sep 11, 2014 at 11:33 AM, bill lam <[email protected]>
> >> wrote:
> >> >>> >> This is strange since every author must had decode its own encoded
> >> >>> >> data as a smoke test.
> >> >>> >>
> >> >>> >> Did you test if huffman code or bit lengths it produced was
> >> >>> >> correct or not, ie it is a prefix coding and it satisfy the 2
> >> >>> >> rules in rfc.
> >> >>> >>
> >> >>> >> Чт, 11 сен 2014, Joe Bogner написал(а):
> >> >>> >>> unfortunately the dynamic coding in the putty fork doesn't seem to
> >> work:
> >> >>> >>>
> >> >>> >>> deflate -c deflate.c > out
> >> >>> >>> deflate -d out
> >> >>> >>>
> >> >>> >>> decoding error: incorrect data checksum
> >> >>> >>>
> >> >>> >>>
> >> >>> >>> it works fine with static tables
> >> >>> >>>
> >> >>> >>> C:\temp>echo ABCD > ABCD
> >> >>> >>>
> >> >>> >>> C:\temp>deflate -c ABCD > out
> >> >>> >>>
> >> >>> >>> C:\temp>deflate -d out
> >> >>> >>> ABCD
> >> >>> >>>
> >> >>> >>> I added some debugging code to determine that deflating deflate.c
> >> >>> >>> would be a dynamic table... Assuming it's broke, I probably
> >> wouldn't
> >> >>> >>> use it as a reference implementation after all
> >> >>> >>>
> >> >>> >>> On Thu, Sep 11, 2014 at 3:45 AM, bill lam <[email protected]>
> >> wrote:
> >> >>> >>> > the frequencies (guessing from bit lengths) should be something
> >> like 2 3 1 1
> >> >>> >>> > (2 3 1 1) hcodes 'ABCD'
> >> >>> >>> >
> >> >>> >>> > the hard part is the inverse problem: how to get the huffman
> >> code with
> >> >>> >>> > prior knowing the bits for each symbol. Your pointer to the
> >> putty
> >> >>> >>> > fork looks like helpful. The comment is in lines 861 to 914,
> >> the code
> >> >>> >>> > itself in line 915 to 964. Do you know how to express it in J?
> >> >>> >>> > Thanks.
> >> >>> >>> >
> >> >>> >>> > On Thu, Sep 11, 2014 at 2:57 PM, Joe Bogner <[email protected]>
> >> wrote:
> >> >>> >>> >> Here a few other links ... after reading through the RFC. Not
> >> sure if
> >> >>> >>> >> they help, but just sharing from my own research into assisting
> >> on
> >> >>> >>> >> this topic
> >> >>> >>> >>
> >> >>> >>> >> https://github.com/evegard/pngview/blob/master/huffman.c#L54
> >> >>> >>> >>
> >> >>> >>> >> And a fork of the putty version with dynamic huffman coding:
> >> >>> >>> >>
> >> http://rc.quest.com/viewvc/putty/trunk/halibut/deflate.c?diff_format=s&revision=2&view=markup
> >> >>> >>> >>
> >> >>> >>> >> Or just generally googling some of the code from the RFC:
> >> >>> >>> >>
> >> https://www.google.com/search?q=next_code%5Blen%5D%2B%2B%3B&oq=next_code%5Blen%5D%2B%2B%3B&aqs=chrome..69i57.387j0j7&sourceid=chrome&es_sm=93&ie=UTF-8#q=next_code%5Blen%5D%2B%2B%3B&start=20
> >> >>> >>> >>
> >> >>> >>> >>
> >> >>> >>> >> Using the code from
> >> >>> >>> >> http://www.jsoftware.com/jwiki/Essays/Huffman%20Coding, I got
> >> stuck
> >> >>> >>> >> trying to match a simple example to the binary tree in the RFC:
> >> >>> >>> >>
> >> >>> >>> >> From the RFC:
> >> >>> >>> >>
> >> >>> >>> >> /\ Symbol Code
> >> >>> >>> >> 0 1 ------ ----
> >> >>> >>> >> / \ A 00
> >> >>> >>> >> /\ B B 1
> >> >>> >>> >> 0 1 C 011
> >> >>> >>> >> / \ D 010
> >> >>> >>> >> A /\
> >> >>> >>> >> 0 1
> >> >>> >>> >> / \
> >> >>> >>> >> D C
> >> >>> >>> >>
> >> >>> >>> >>
> >> >>> >>> >>
> >> >>> >>> >> (4#1) hcodes 'ABCD'
> >> >>> >>> >> ┌───┬───┬───┬───┐
> >> >>> >>> >> │0 0│0 1│1 0│1 1│
> >> >>> >>> >> └───┴───┴───┴───┘
> >> >>> >>> >>
> >> >>> >>> >> Per the RFC, ideally that should match this?
> >> '00';'1';'011';'010'
> >> >>> >>> >>
> >> >>> >>> >>
> >> >>> >>> >> From there, it seems like a pretty straightforward exercise to
> >> >>> >>> >> transliterate the C code from the RFC into J code to recode the
> >> >>> >>> >> example to:
> >> >>> >>> >>
> >> >>> >>> >>
> >> >>> >>> >> Symbol Code
> >> >>> >>> >> ------ ----
> >> >>> >>> >> A 10
> >> >>> >>> >> B 0
> >> >>> >>> >> C 110
> >> >>> >>> >> D 111
> >> >>> >>> >>
> >> >>> >>> >>
> >> >>> >>> >> I would probably start with a looping construct like what's in
> >> the RFC
> >> >>> >>> >> and then figure out a more J way to do it, but first I would
> >> need to
> >> >>> >>> >> figure out how to create the binary tree in that initial format.
> >> >>> >>> >>
> >> >>> >>> >> On Wed, Sep 10, 2014 at 7:41 PM, bill lam <[email protected]>
> >> wrote:
> >> >>> >>> >>> Thanks Joe,
> >> >>> >>> >>> putty only use zlib static huffman for encoding so that it
> >> does not build
> >> >>> >>> >>> any huffman dictionary table.
> >> >>> >>> >>>
> >> >>> >>> >>> The zlib static huffman code does not care about individual
> >> symbol's
> >> >>> >>> >>> frequency, it just encode 0 to 286 into bits, see section
> >> 3.2.6.
> >> >>> >>> >>> On Sep 11, 2014 1:26 AM, "Joe Bogner" <[email protected]>
> >> wrote:
> >> >>> >>> >>>
> >> >>> >>> >>>> You've already likely considered this, but if it were me I
> >> would compare
> >> >>> >>> >>>> results to a working implementation. The one from putty seems
> >> pretty clean
> >> >>> >>> >>>> and standalone:
> >> >>> >>> >>>>
> >> https://raw.githubusercontent.com/grumpydev/PortablePuTTY/master/SSHZLIB.C
> >> >>> >>> >>>> . I was able to compile it on windows no problem and I assume
> >> it'd be fine
> >> >>> >>> >>>> on linux as well.
> >> >>> >>> >>>>
> >> >>> >>> >>>> On Wed, Sep 10, 2014 at 1:00 PM, Raul Miller <
> >> [email protected]>
> >> >>> >>> >>>> wrote:
> >> >>> >>> >>>>
> >> >>> >>> >>>> > I think the use of the term "consecutive" rather than
> >> "sequential" is
> >> >>> >>> >>>> > telling.
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > The described algorithm is: compute the huffman code
> >> lengths:
> >> >>> >>> >>>> > #@>F1 hcodes A1
> >> >>> >>> >>>> > 1 3 7 7 6 6 6 6 6 6 6 2
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > Then assign ascending huffman codes first in length order
> >> and then
> >> >>> >>> >>>> > within codes of the same length.
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > Taken literally, that might be something like this:
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > H=: 4 :0
> >> >>> >>> >>>> > L=.#@> x hcodes y
> >> >>> >>> >>>> > U=.~.L
> >> >>> >>> >>>> > ;<@(({.{.U e.~i.&.<:@{.)<@:+"1-@{.{."1 #:@i.@#)/.~L
> >> >>> >>> >>>> > )
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > ":@>F1 H A1
> >> >>> >>> >>>> > 0
> >> >>> >>> >>>> > 1 1 0
> >> >>> >>> >>>> > 1 1 1 0 0 1 0
> >> >>> >>> >>>> > 1 1 1 0 0 1 1
> >> >>> >>> >>>> > 1 1 1 0 0 0
> >> >>> >>> >>>> > 1 1 1 0 0 1
> >> >>> >>> >>>> > 1 1 1 0 1 0
> >> >>> >>> >>>> > 1 1 1 0 1 1
> >> >>> >>> >>>> > 1 1 1 1 0 0
> >> >>> >>> >>>> > 1 1 1 1 0 1
> >> >>> >>> >>>> > 1 1 1 1 1 0
> >> >>> >>> >>>> > 1 0
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > But is this correct? Is it actually safe to leave the
> >> results like
> >> >>> >>> >>>> > this - with all codes of the same length being consecutive
> >> to each
> >> >>> >>> >>>> > other?
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > F (hcodes -:&:(#@>) H) A
> >> >>> >>> >>>> > 0
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > No.
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > So... "consecutive" must refer only to the values used and
> >> not their
> >> >>> >>> >>>> > order within the result.
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > Perhaps something like this:
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > deflatecodes=:4 :0
> >> >>> >>> >>>> > L=.#@> x hcodes y
> >> >>> >>> >>>> > U=.~.L
> >> >>> >>> >>>> > R=. ;<@(({.{.U e.~i.&.<:@{.)<@:+"1-@{.{."1 #:@i.@#)/.~L
> >> >>> >>> >>>> > R/:;(</. i.@#)L
> >> >>> >>> >>>> > )
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > F (hcodes -:&:(#@>) deflatecodes) A
> >> >>> >>> >>>> > 1
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > There should be a better way of doing this, but this should
> >> at least
> >> >>> >>> >>>> > get you started.
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > Thanks,
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > --
> >> >>> >>> >>>> > Raul
> >> >>> >>> >>>> >
> >> >>> >>> >>>> >
> >> >>> >>> >>>> > On Wed, Sep 10, 2014 at 10:45 AM, bill lam <
> >> [email protected]> wrote:
> >> >>> >>> >>>> > > For huffman coding used in zlib:
> >> >>> >>> >>>> > > https://www.ietf.org/rfc/rfc1951.txt section 3.2.2.
> >> >>> >>> >>>> > >
> >> >>> >>> >>>> > > The Huffman codes used for each alphabet in the "deflate"
> >> >>> >>> >>>> > > format have two additional rules:
> >> >>> >>> >>>> > >
> >> >>> >>> >>>> > > * All codes of a given bit length have lexicographically
> >> >>> >>> >>>> > > consecutive values, in the same order as the symbols
> >> >>> >>> >>>> > > they represent;
> >> >>> >>> >>>> > >
> >> >>> >>> >>>> > > * Shorter codes lexicographically precede longer codes.
> >> >>> >>> >>>> > > I tried jwiki hcodes in
> >> >>> >>> >>>> > > I try Roger's essay
> >> >>> >>> >>>> > > http://www.jsoftware.com/jwiki/Essays/Huffman%20Coding
> >> >>> >>> >>>> > >
> >> >>> >>> >>>> > > hc=: 4 : 0
> >> >>> >>> >>>> > > if. 1=#x do. y
> >> >>> >>> >>>> > > else. ((i{x),+/j{x) hc (i{y),<j{y [ i=. (i.#x) -. j=.
> >> 2{./:x end.
> >> >>> >>> >>>> > > )
> >> >>> >>> >>>> > >
> >> >>> >>> >>>> > > hcodes=: 4 : 0
> >> >>> >>> >>>> > > assert. x -:&$ y NB. weights and words have
> >> same shape
> >> >>> >>> >>>> > > assert. (0<:x) *. 1=#$x NB. weights are non-negative
> >> >>> >>> >>>> > > assert. 1 >: L.y NB. words are boxed not more
> >> than once
> >> >>> >>> >>>> > > w=. ,&.> y NB. standardized words
> >> >>> >>> >>>> > > assert. w -: ~.w NB. words are unique
> >> >>> >>> >>>> > > t=. 0 {:: x hc w NB. minimal weight binary tree
> >> >>> >>> >>>> > > ((< S: 0 t) i. w) { <@(1&=)@; S: 1 {:: t
> >> >>> >>> >>>> > > )
> >> >>> >>> >>>> > >
> >> >>> >>> >>>> > > but the coding produced is malformed for zlib. eg,
> >> >>> >>> >>>> > > this is what I ran into trouble
> >> >>> >>> >>>> > >
> >> >>> >>> >>>> > > f1=: 1 256 17 1 1 9 1
> >> >>> >>> >>>> > > f2=: 2 1 0 1 255 0 1536
> >> >>> >>> >>>> > > F=: ,/(f1#f2)
> >> >>> >>> >>>> > > A=: i.286
> >> >>> >>> >>>> > >
> >> >>> >>> >>>> > > F hcodes A
> >> >>> >>> >>>> > >
> >> >>> >>> >>>> > > Or a shorter example
> >> >>> >>> >>>> > >
> >> >>> >>> >>>> > > A1=: i.12
> >> >>> >>> >>>> > > F1=: 2 1 0 0 0 0 0 0 0 0 0 1
> >> >>> >>> >>>> > >
> >> >>> >>> >>>> > > F1 hcodes A1
> >> >>> >>> >>>> > >
> >> >>> >>> >>>> > > Any idea?
> >> >>> >>> >>>> > >
> >> >>> >>> >>>> > > --
> >> >>> >>> >>>> > > regards,
> >> >>> >>> >>>> > > ====================================================
> >> >>> >>> >>>> > > GPG key 1024D/4434BAB3 2008-08-24
> >> >>> >>> >>>> > > gpg --keyserver subkeys.pgp.net --recv-keys 4434BAB3
> >> >>> >>> >>>> > > gpg --keyserver subkeys.pgp.net --armor --export 4434BAB3
> >> >>> >>> >>>> > >
> >> ----------------------------------------------------------------------
> >> >>> >>> >>>> > > For information about J forums see
> >> http://www.jsoftware.com/forums.htm
> >> >>> >>> >>>> >
> >> ----------------------------------------------------------------------
> >> >>> >>> >>>> > For information about J forums see
> >> http://www.jsoftware.com/forums.htm
> >> >>> >>> >>>> >
> >> >>> >>> >>>>
> >> ----------------------------------------------------------------------
> >> >>> >>> >>>> For information about J forums see
> >> http://www.jsoftware.com/forums.htm
> >> >>> >>> >>>>
> >> >>> >>> >>>
> >> ----------------------------------------------------------------------
> >> >>> >>> >>> For information about J forums see
> >> http://www.jsoftware.com/forums.htm
> >> >>> >>> >>
> >> ----------------------------------------------------------------------
> >> >>> >>> >> For information about J forums see
> >> http://www.jsoftware.com/forums.htm
> >> >>> >>> >
> >> ----------------------------------------------------------------------
> >> >>> >>> > For information about J forums see
> >> http://www.jsoftware.com/forums.htm
> >> >>> >>>
> >> ----------------------------------------------------------------------
> >> >>> >>> For information about J forums see
> >> http://www.jsoftware.com/forums.htm
> >> >>> >>
> >> >>> >> --
> >> >>> >> regards,
> >> >>> >> ====================================================
> >> >>> >> GPG key 1024D/4434BAB3 2008-08-24
> >> >>> >> gpg --keyserver subkeys.pgp.net --recv-keys 4434BAB3
> >> >>> >> gpg --keyserver subkeys.pgp.net --armor --export 4434BAB3
> >> >>> >>
> >> ----------------------------------------------------------------------
> >> >>> >> For information about J forums see
> >> http://www.jsoftware.com/forums.htm
> >> >>> ----------------------------------------------------------------------
> >> >>> For information about J forums see http://www.jsoftware.com/forums.htm
> >> >>
> >> >> --
> >> >> regards,
> >> >> ====================================================
> >> >> GPG key 1024D/4434BAB3 2008-08-24
> >> >> gpg --keyserver subkeys.pgp.net --recv-keys 4434BAB3
> >> >> gpg --keyserver subkeys.pgp.net --armor --export 4434BAB3
> >> >> ----------------------------------------------------------------------
> >> >> For information about J forums see http://www.jsoftware.com/forums.htm
> >> > ----------------------------------------------------------------------
> >> > For information about J forums see http://www.jsoftware.com/forums.htm
> >> ----------------------------------------------------------------------
> >> For information about J forums see http://www.jsoftware.com/forums.htm
> > ----------------------------------------------------------------------
> > For information about J forums see http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
--
regards,
====================================================
GPG key 1024D/4434BAB3 2008-08-24
gpg --keyserver subkeys.pgp.net --recv-keys 4434BAB3
gpg --keyserver subkeys.pgp.net --armor --export 4434BAB3
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
