In the last of def_code (,. i.@#)c /: o has a bug in that the index of non-zero I.0~:y instead of i@# should be stitched. Thanks. On Sep 12, 2014 12:25 PM, "Raul Miller" <[email protected]> wrote:
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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
