DNG lossy details - I found out

Question

Dear reader,
my first step was to create color-filter-array dng files, but in lack of knowledge about windows development and the superior dng specs (missing free available TIFF/EP standard I found out later), I developed based on libtiff (see Listing 1 )
It uses IEC-sRGB XYZ->RGB color matrix.
Then I used Adobe DNG Converter 8.2 to get DNG lossy. There I found out that almost always in the opcodes (see Listing2) (extracted with tiffdump -m300 -o offset lossy.dng | perl Listing2.pl ) (for availbale subifd-offsets, do tiffdump | grep -i ifd )
there is following transformation:
linear = 0.0625*perceptual + 0.9375*perceptual³
(reverse function:
sub perceptual {
    my $linear=shift;
    my $y=$linear;
    my $term=(360*$y +sqrt(5)*sqrt(1+25920*$y**2))**(1/3);
    return
        -(    1 /
            (5**(1/3)*$term)
        +
        $term /
        5**(2/3)
    )/3;
... or something with shrinked range to match tighter range of input values (than 0..1).
So, assuming 12 bit linear raw, you get an 1:1 mapping near zero (4 bits lost from 12 to 8 bit, but *16 due tue perceptual() transformation, and a 1:46 mapping near one (4 bits lost = /16, additional factor 2,8 approx due to differentiation of linear = ... ( see above ) ).
The afterwards jpeg compression uses no subsampling and these quantization tables:
qtable 0: 2 2 2 2 3 4 5 6 2 2 2 2 3 4 5 6 2 2 2 2 4 5 7 9 2 2 2 4 5 7 9 12 3 3 4 5 8 10 12 12 4 4 5 7 10 12 12 12 5 5 7 9 12 12 12 12 6 6 9 12 12 12 12 12
qtable 1: 3 3 5 9 13 15 15 15 3 4 6 10 14 12 12 12 5 6 9 14 12 12 12 12 9 10 14 12 12 12 12 12 13 14 12 12 12 12 12 12 15 12 12 12 12 12 12 12 15 12 12 12 12 12 12 12 15 12 12 12 12 12 12 12
Perhaps this coud clear some things.
Kind regards,
Listing 1:
/* CameraProfile - erforderl? */
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include "tiffio.h"
#include <math.h>
#define TRUE -1
/* siehe http://www.remotesensing.org/libtiff/addingtags.html */
/* siehe auch http://www.opensource.apple.com/source/tcl/tcl-87/tcl_ext/tkimg/tkimg/libtiff/tools/tiffse t.c */
static const TIFFFieldInfo xtiffFieldInfo[] = {
    { 33421, -1,-1, TIFF_SHORT,    FIELD_CUSTOM, TRUE, TRUE, "CFARepeatPatternDim" },
    { 33422, -1,-1, TIFF_BYTE,    FIELD_CUSTOM, TRUE, TRUE, "CFAPattern" },
    { 50706,  4, 4, TIFF_BYTE,    FIELD_CUSTOM, TRUE, TRUE, "DNG_Version" },
    { 50708, -1,-1, TIFF_ASCII,    FIELD_CUSTOM, TRUE, TRUE, "DNG_UniqueCameraModel" },
    { 50721, -1,-1, TIFF_FLOAT, FIELD_CUSTOM, TRUE, TRUE, "ColorMatrix1" }
#define    N(a)    (sizeof (a) / sizeof (a[0]))
uint16_t quant16(double x) { return (int)(65535*x+0.5); }
/* Quote from Wikipedia:
The numerical values below match those in the official sRGB specification (IEC 61966-2-1:1999) and differ slightly from those in a publication by sRGB's creators.[2] Note that these linear values are not the final result.
[2] Michael Stokes, Matthew Anderson, Srinivasan Chandrasekar, Ricardo Motta (November 5, 1996). "A Standard Default Color Space for the Internet – sRGB, Version 1.10". http://www.w3.org/Graphics/Color/sRGB
float iec61966_2_1_1999_XYZ_to_sRGB_D50[]={
3.2406, -1.5372, -0.4986,
-0.9689,  1.8758,  0.0415,
0.0557, -0.2040,  1.0570};
int main(int argc, char **argv)
    uint8_t ver[]={1,4,0,0};
    int16_t repeat[]={2,2};
    uint8_t pattern[]={0,1,1,2};
    int width=2048, height=4096, format;
    uint16_t *cfa_row;
    double minc[3]={ 9e99, 9e99, 9e99};
    double maxc[3]={-9e99,-9e99,-9e99};
    double xx,yy,d;
    int x,y, c;
    double v;
    FILE *fw;
    TIFF* tif = TIFFOpen("out.dng", "w");
    cfa_row = malloc(width *16/8);
    /* Install the extended Tag field info */
    TIFFMergeFieldInfo(tif, xtiffFieldInfo, N(xtiffFieldInfo));
    TIFFSetField(tif, TIFFTAG_IMAGEWIDTH,  width);
    TIFFSetField(tif, TIFFTAG_IMAGELENGTH, height);
    TIFFSetField(tif, TIFFTAG_BITSPERSAMPLE, 16);
    TIFFSetField(tif, TIFFTAG_SUBFILETYPE, 0);
    TIFFSetField(tif, TIFFTAG_ORIENTATION, ORIENTATION_TOPLEFT);
    TIFFSetField(tif, TIFFTAG_PHOTOMETRIC, 32803);
    TIFFSetField(tif, 33421, 2, repeat); /* obwohl immer 2, muss oben -1 stehen sonst speicherfehler*/
    TIFFSetField(tif, 33422, 4, pattern);
    TIFFSetField(tif, 50706, ver); /* aber hier nicht -1 ?! */
    TIFFSetField(tif, 50708, "dng.c");
    TIFFSetField(tif, 50721, 3*3, iec61966_2_1_1999_XYZ_to_sRGB_D50);
    for(y=0; y<height; y++) {
        d=yy=1.0*(y/2)/((height-1)/2);
        for(x=0; x<width; x++) {
            xx=1.0*(x/2)/((width-1)/2);
            c=1;
            if(x%2==0 && y%2==0) c=0;
            if(x%2==1 && y%2==1) c=2;
            v=0;
            if(x==0) { printf("yy=%f  d=%f\n",yy,d); }
            switch(c) {
                case 0: v=65535.0*d; break;
                case 1: v=65535.0*d; break;
                case 2: v=65535.0*d; break;
            cfa_row[x]=(uint16_t)(v+0.5);
            if(v<minc[c]) minc[c]=v;
            if(v>maxc[c]) maxc[c]=v;
        TIFFWriteScanline(tif, cfa_row, y, 0);
    TIFFClose(tif);
    for(c=0; c<3; c++) {
        printf("%f..%f\n", minc[c], maxc[c]);
    return 0;
Listing2:
#!/usr/bin/perl
use strict;
$|++;
# big-endian!
# tiffdump -m 300 -o 63248 DSC_1572.dng |perl opcodes.pl
#51009 (0xc741) UNDEFINED (7) 256<00 00 00 0x3 00 00 00 0x8 0x1 0x3 00 00 00 00 00 00 00 00 00 0x44 00 00 00 00 00 00 00 00 00 00 0x4 0x60 00 00 0x6 0x90 00 00 00 00 00 00 00 0x1 00 00 00 0x1 00 00 00 0x1 00 00 00 0x3 00 00 00 00 00 00 00 00 0x3f 0x6e 0x54 0x1e 0x54 0x1e 0x54 0x1e 00 00 00 00 00 00 00 00 0x3f 0xac 0x6e 0xdc 0x6e 0xdc 0x6e 0xdc 00 00 00 0x8 0x1 0x3 00 00 00 00 00 00 00 00 00 0x44 00 00 00 00 00 00 00 00 00 00 0x4 0x60 00 00 0x6 0x90 00 00 00 0x1 00 00 00 0x1 00 00 00 0x1 00 00 00 0x1 00 00 00 0x3 00 00 00 00 00 00 00 00 0x3f 0x79 0xc9 0x19 0xc9 0x19 0xc9 0x1a 00 00 00 00 00 00 00 00 0x3f 0xb8 0x2c 0x88 0x2c 0x88 0x2c 0x88 00 00 00 0x8 0x1 0x3 00 00 00 00 00 00 00 00 00 0x44 00 00 00 00 00 00 00 00 00 00 0x4 0x60 00 00 0x6 0x90 00 00 00 0x2 00 00 00 0x1 00 00 00 0x1 00 00 00 0x1 00 00 00 0x3 00 00 00 00 00 00 00 00 0x3f 0x6e 0xc 0x1e 0xc 0x1e 0xc 0x1e 00 00 00 00 00 00 00 00 0x3f 0xac 0x2b 0x5c 0x2b 0x5c 0x2b 0x5c>
my @plot;
sub op {
    my $s=shift;
    my $opcodeId=unpack "N", substr($s,0,4);
    my @ver=unpack "CCCC", substr($s,4,4);
    my $flags=unpack "N",  substr($s,8,4);
    my $vsize=unpack "N",  substr($s,12,4);
    print "$opcodeId - v".join(".",@ver)." flags=$flags vsize=$vsize\n";
    $s=substr($s,16);
    print "   ";
    if($opcodeId==8) {
        my @v=unpack(("N"x9), substr($s,0,4*9));
        $s=substr($s,4*9);
        print join(", ", @v);
        my $degree=$v[$#v]; # 0..degree
        print " degree=$degree ";
        my @coeff=unpack(("d>"x($degree+1)), substr($s,0,($degree+1)*8));
        $s=substr($s,($degree+1)*8);
        my $out="";
        for(my $c=0; $c<=$degree; $c++) {
            if($coeff[$c]==0) { next; }
            $out.=sprintf "%+g*x**$c", $coeff[$c];
        print $out;
        push @plot, $out;
    else {
        die "$opcodeId ?\n";
    print "\n";
    return $s;
sub pre_op {
    my $s=shift;
    $s=~s/0x//g;
    $s=join("", map { chr(hex($_)) } split / +/, $s);
    my $n=unpack "N", substr($s,0,4);
    print "$n opcodes\n";
    $s=substr($s,4);
    for(my $i=0; $i<$n; $i++) {
        $s=op($s);
while(<>) {
    chomp;
    if($_=~/^510(08|09|22)\b/) {
        if($_=~/<([^>]*)>/) {
            pre_op($1);
    elsif($_=~/^50712/) { print "LinearizationTable\n"; }
    elsif($_=~/^5071[34567]/) { print "Black/WhiteLevel\n"; }
print join(", ", @plot)."\n";

Answer 1

You can get back 3.6 here: http://www.mozilla.com/en-US/firefox/all-older.html