Okay. I took your spec and coded this slow and labourious implementation and applied it to the bytes 0 .. 255:

#! perl -slw
use strict;
use Data::Dump qw[ pp ];

my %map;

for my $i ( 0 .. 255 ) {
    my @Q;
    my @D = split '', unpack 'b8', chr $i;
    $Q[ 0 ] = $D[ 0 ];
    $Q[ 1 ] = $D[ 1 ] ^ $Q[ 0 ];
    $Q[ 2 ] = $D[ 2 ] ^ $Q[ 1 ];
    $Q[ 3 ] = $D[ 3 ] ^ $Q[ 2 ];
    $Q[ 4 ] = $D[ 4 ] ^ $Q[ 3 ];
    $Q[ 5 ] = $D[ 5 ] ^ $Q[ 4 ];
    $Q[ 6 ] = $D[ 6 ] ^ $Q[ 5 ];
    $Q[ 7 ] = $D[ 7 ] ^ $Q[ 6 ];
    my $outb = ord pack 'b8', "@Q";
    $map{ $i } = $outb;
}

pp \%map;
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And it produced this output:

That's a byte to byte mapping table. I then used that to build the translation table I posted.

A couple of points I don't understand about Re^7: encoding hdmi video byte.

First, in the statement
    my $outb = ord pack 'b8',"@Q";
will not  "@Q" interpolate the array with spaces between the elements of  @Q and so give an oddball result (i.e., only 16 unique values) since a space (ASCII space == 0x20) is packed by b as a 0 bit and half the elements of  @Q will be ignored?
I.e., shouldn't it be
    my $outb = ord pack 'b8',join '', @Q;
instead?

The other point I don't understand is that I took the OP statement

Data byte D(0:7) encode this to make 9bit data q_m(0:8)
q_m[0] = D(0);
q_m(1) = q_m(0) XOR D(1);
q_m(2) = q_m(1) XOR D(2);
q_m(3) = q_m(2) XOR D(3);
q_m(4) = q_m(3) XOR D(4);
q_m(5) = q_m(4) XOR D(5);
q_m(6) = q_m(5) XOR D(6);
q_m(7) = q_m(6) XOR D(7);
q_m(8) = 1;
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to be pseudo-code, and to be the equivalent (on a byte-for-byte basis) of

$q_m_byte = (0x100 | ($D_byte ^ (0xff & ($q_m_byte << 1))));
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with a  $q_m_byte 'byte' of 9 bits always ending up with its bit-8 set, and bit-7 of the original value of  $q_m_byte always being lost.

But

$Q[ 0 ] = $D[ 0 ];
$Q[ 1 ] = $D[ 1 ] ^ $Q[ 0 ];
$Q[ 2 ] = $D[ 2 ] ^ $Q[ 1 ];
$Q[ 3 ] = $D[ 3 ] ^ $Q[ 2 ];
...
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seems to be the equivalent of

$Q[ 0 ] = $D[ 0 ];
$Q[ 1 ] = $D[ 1 ] ^ $D[ 0 ];
$Q[ 2 ] = $D[ 2 ] ^ $D[ 1 ] ^ $D[ 0 ];
$Q[ 3 ] = $D[ 3 ] ^ $D[ 2 ] ^ $D[ 1 ] ^ $D[ 0 ];
...
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which is very different.

You're right on the "@Q" part. Dumb mistake. With that corrected, the mapping makes a lot more sense.

As for the right interpretation of the spec, I guess you'll have to ask the OP. I believe, (with the "deliberate" error:) and constant 9th bit excepted), I coded a direct implementation of the spec. If the spec is wrong, or my interpretation of it is wrong, then the OP will have to correct it.

The main point was to answer the OPs question of the best way to perform the mapping efficiently, and that is tr/// with the appropriate translation strings. On a gig of data, doing 10 x 100MB tr///s, (or even 1 x 1GB if he has the memory), is going to beat performing half a dozens boolean operations on every byte, hands down.

---

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority".

In the absence of evidence, opinion is indistinguishable from prejudice.

"I'd rather go naked than blow up my ass"

Hi AnomalousMonk, Here is the quote from my req... "...the LSb of the output (Q[0] = D[0]) matches the LSb of the input. With the starting value established, the remaining 7bits of the output (9th bit always 1) is derived from sequential XORing of each bit of the input with the previously derived bit...." Therefore i coded it this way. In a very simple way. pls let me know if it is clear now. Also i was looking for some input to make my code smaller/smarter than it is now.

my %map;

for my $i ( 0 .. 255 ) {
    my @Q = qw(0 0 0 0 0 0 0 0 0);
    my $result;
    #Step 1 : $Q[0] = D[0]
    $Q[0] = ($i & 0x01);

    #Step 2 : $Q[1] = D[1] ^ $Q[0]
    $Q[1] = (($i & 0x02) ^ ($Q[0] << 1));

    #Step 3 : $Q[2] = D[2] ^ $Q[1]
    $Q[2] = ($i & 0x04) ^ ($Q[1] << 1);

    #Step 4 : $Q[3] = D[3] ^ $Q[2]
    $Q[3] = ($i & 0x08) ^ ($Q[2] << 1);

    #Step 5 : $Q[4] = D[4] ^ $Q[3]
    $Q[4] = ($i & 0x10) ^ ($Q[3] << 1);

    #Step 6 : $Q[5] = D[5] ^ $Q[4]
    $Q[5] = ($i & 0x20) ^ ($Q[4] << 1);

    #Step 7 : $Q[6] = D[6] ^ $Q[5]
    $Q[6] = ($i & 0x40) ^ ($Q[5] << 1);

    #Step 8 : $Q[7] = D[7] ^ $Q[6]
    $Q[7] = ($i & 0x80) ^ ($Q[6] << 1);

    #Step 9 : $Q[8] = 1
    $Q[8] = 0x100;

    $result = ($Q[0] | $Q[1] | $Q[2] | $Q[3] | $Q[4] | $Q[5] | $Q[6] |
+ $Q[7] | $Q[8]);
    $map{ $i } = $result;
    #print "$result ";
}

pp \%map;
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Thanks a lot! Mr. BrowserUK.... that is really a ery big help !!!!

Just to clarify, is the proper interpretation of your OP that of Re^7: encoding hdmi video byte, or is it more like

Data byte D(0:7) encode this to make 9bit data q_m(0:8)
new      previous
bit of   bit of
q_m(0) =            D(0);
q_m(1) = q_m(0) XOR D(1);
q_m(2) = q_m(1) XOR D(2);
q_m(3) = q_m(2) XOR D(3);
q_m(4) = q_m(3) XOR D(4);
q_m(5) = q_m(4) XOR D(5);
q_m(6) = q_m(5) XOR D(6);
q_m(7) = q_m(6) XOR D(7);
q_m(8) =            1;
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