It refered to A and F (not A1 and F1) in my first email. I sent you an email off-list that included attachments.
Ср, 10 сен 2014, Raul Miller написал(а): > Something is wrong here: > > $bits > 286 > (0=bits)-:0=F1 > 0 > +/0=F1 > 9 > +/0=bits > 26 > > 0 bits should mean that that symbol is not represented. > > But there are only 9 such symbols in F1. > > -- > Raul > > On Wed, Sep 10, 2014 at 11:09 PM, bill lam <[email protected]> wrote: > > I guess the description of the algorithm itself is correct, but > > it does not mention how to get the bits of each symbol. The bit > > lengths for classic and zlib huffman can be different. > > > > for testing, the bits for A from libz.so are > > > > ":&>_10<\bits > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 11 11 10 10 10 10 11 > > 11 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 10 10 10 > > 10 10 10 10 10 10 10 0 0 0 > > 0 0 0 0 0 0 0 0 0 0 > > 0 0 0 0 10 2 0 0 0 0 > > 0 0 0 0 0 1 > > > > this is the huffman dictionary stored in zlib stream and the actual > > huffman codes are computed using the algorithm mentioned during decoding. > > > > Ср, 10 сен 2014, Raul Miller написал(а): > >> I agree that there should not be any 2s. > >> > >> However, I think this means that there's something wrong with the > >> description of the algorithm, or at least my understanding of it. > >> > >> I'll need some time to digest this. > >> > >> Thanks, > >> > >> -- > >> Raul > >> > >> On Wed, Sep 10, 2014 at 9:39 PM, bill lam <[email protected]> wrote: > >> > pardon me of forgetting telling another cavaet. > >> > zlib huffman code is suboptimal so that bit length of code > >> > for each symbol can be longer than that in classic huffman. > >> > eg in my orignal data. > >> > > >> > 10{. ":@>F deflatecodes2 A > >> > 1 1 0 0 0 0 0 0 0 0 > >> > 1 1 1 1 1 1 1 1 1 1 0 > >> > 1 1 1 1 1 1 1 1 1 1 1 > >> > 1 1 1 1 1 1 1 1 1 2 0 > >> > 1 1 1 1 1 1 1 1 1 2 1 > >> > 1 1 1 1 1 1 1 1 2 1 0 > >> > 1 1 0 0 0 0 0 0 0 1 > >> > 1 1 0 0 0 0 0 0 1 0 > >> > 1 1 0 0 0 0 0 0 1 1 > >> > 1 1 0 0 0 0 0 1 0 0 > >> > > >> > there shouldn't be any 2's. It needs to increase bit length of > >> > some code. > >> > > >> > Ср, 10 сен 2014, Raul Miller написал(а): > >> >> Oops, sorry about that. > >> >> > >> >> Try it this way: > >> >> > >> >> deflatecodes2=:4 :0 > >> >> L=. #@> x hcodes y > >> >> U=. 0,~.L > >> >> R=. ;<@(({. >./@(>#])&U #1:)@{. <@:+"1-@{.{."1 #:@i.@#)/.~L > >> >> R/:;(</. i.@#)L > >> >> ) > >> >> > >> >> ":@>F1 deflatecodes2 A1 > >> >> 0 > >> >> 1 1 0 > >> >> 1 1 1 1 1 1 0 > >> >> 1 1 1 1 1 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 > >> >> > >> >> Thanks, > >> >> > >> >> -- > >> >> Raul > >> >> > >> >> > >> >> On Wed, Sep 10, 2014 at 7:26 PM, bill lam <[email protected]> wrote: > >> >> > for zlib, all huffman code of the same bit length are in sequential, > >> >> > starting with a code an 0 bit in the end (even number), and no gaps > >> >> > in the > >> >> > block (consecutive). the symbols of these block represented are > >> >> > sequential > >> >> > but not consecutive (possibly gaps). So the zlib huffman code is > >> >> > slightly > >> >> > less efficient than the original huffman code but the advantage is > >> >> > simpler > >> >> > to store the table, just the bits used. section 3.2.6 gives an > >> >> > example of > >> >> > such table. > >> >> > > >> >> > deflatecodes can satisfy the 2 rules _but_ its result is invalid > >> >> > because > >> >> > huffman code is a prefix coding. > >> >> > > >> >> > ,.F1 ( deflatecodes) 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 │ > >> >> > └─────────────┘ > >> >> > 7 bit 1110010 is a prefix of 6 bit 111001 and this is illegal. > >> >> > Instead 7 bit code block should start with > >> >> > #.inv 2b11100 + 7 > >> >> > 1 1 1 1 1 1 0 > >> >> > because there are 6 symbols in the 6 bit code. (algorithm given in > >> >> > section > >> >> > 3.2.2). > >> >> > > >> >> > Any idea to fix deflatecodes so that it can give valid huffman codes? > >> >> > Thanks. > >> >> > On Sep 11, 2014 1:01 AM, "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 > >> > > >> > -- > >> > 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 -- 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
