    /*
     * jquant2.c
     *
     * Copyright (C) 1991-1996, Thomas G. Lane.
     * This file is part of the Independent JPEG Group's software.
     * For conditions of distribution and use, see the accompanying README file.
     *
     * This file contains 2-pass color quantization (color mapping) routines.
     * These routines provide selection of a custom color map for an image,
     * followed by mapping of the image to that color map, with optional
     * Floyd-Steinberg dithering.
     * It is also possible to use just the second pass to map to an arbitrary
     * externally-given color map.
     *
     * Note: ordered dithering is not supported, since there isn't any fast
     * way to compute intercolor distances; it's unclear that ordered dither's
     * fundamental assumptions even hold with an irregularly spaced color map.
     */

    #define JPEG_INTERNALS
    #include "jinclude.h"
    #include "jpeglib.h"

    #ifdef QUANT_2PASS_SUPPORTED

    /*
     * This module implements the well-known Heckbert paradigm for color
     * quantization.  Most of the ideas used here can be traced back to
     * Heckbert's seminal paper
     *   Heckbert, Paul.  "Color Image Quantization for Frame Buffer Display",
     *   Proc. SIGGRAPH '82, Computer Graphics v.16 #3 (July 1982), pp 297-304.
     *
     * In the first pass over the image, we accumulate a histogram showing the
     * usage count of each possible color.  To keep the histogram to a reasonable
     * size, we reduce the precision of the input; typical practice is to retain
     * 5 or 6 bits per color, so that 8 or 4 different input values are counted
     * in the same histogram cell.
     *
     * Next, the color-selection step begins with a box representing the whole
     * color space, and repeatedly splits the "largest" remaining box until we
     * have as many boxes as desired colors.  Then the mean color in each
     * remaining box becomes one of the possible output colors.
     *
     * The second pass over the image maps each input pixel to the closest output
     * color (optionally after applying a Floyd-Steinberg dithering correction).
     * This mapping is logically trivial, but making it go fast enough requires
     * considerable care.
     *
     * Heckbert-style quantizers vary a good deal in their policies for choosing
     * the "largest" box and deciding where to cut it.  The particular policies
     * used here have proved out well in experimental comparisons, but better ones
     * may yet be found.
     *
     * In earlier versions of the IJG code, this module quantized in YCbCr color
     * space, processing the raw upsampled data without a color conversion step.
     * This allowed the color conversion math to be done only once per colormap
     * entry, not once per pixel.  However, that optimization precluded other
     * useful optimizations (such as merging color conversion with upsampling)
     * and it also interfered with desired capabilities such as quantizing to an
     * externally-supplied colormap.  We have therefore abandoned that approach.
     * The present code works in the post-conversion color space, typically RGB.
     *
     * To improve the visual quality of the results, we actually work in scaled
     * RGB space, giving G distances more weight than R, and R in turn more than
     * B.  To do everything in integer math, we must use integer scale factors.
     * The 2/3/1 scale factors used here correspond loosely to the relative
     * weights of the colors in the NTSC grayscale equation.
     * If you want to use this code to quantize a non-RGB color space, you'll
     * probably need to change these scale factors.
     */

    #define R_SCALE 2		/* scale R distances by this much */
    #define G_SCALE 3		/* scale G distances by this much */
    #define B_SCALE 1		/* and B by this much */

    /* Relabel R/G/B as components 0/1/2, respecting the RGB ordering defined
     * in jmorecfg.h.  As the code stands, it will do the right thing for R,G,B
     * and B,G,R orders.  If you define some other weird order in jmorecfg.h,
     * you'll get compile errors until you extend this logic.  In that case
     * you'll probably want to tweak the histogram sizes too.
     */

    #if RGB_RED == 0
    #define C0_SCALE R_SCALE
    #endif
    #if RGB_BLUE == 0
    #define C0_SCALE B_SCALE
    #endif
    #if RGB_GREEN == 1
    #define C1_SCALE G_SCALE
    #endif
    #if RGB_RED == 2
    #define C2_SCALE R_SCALE
    #endif
    #if RGB_BLUE == 2
    #define C2_SCALE B_SCALE
    #endif

    /*
     * First we have the histogram data structure and routines for creating it.
     *
     * The number of bits of precision can be adjusted by changing these symbols.
     * We recommend keeping 6 bits for G and 5 each for R and B.
     * If you have plenty of memory and cycles, 6 bits all around gives marginally
     * better results; if you are short of memory, 5 bits all around will save
     * some space but degrade the results.
     * To maintain a fully accurate histogram, we'd need to allocate a "long"
     * (preferably unsigned long) for each cell.  In practice this is overkill;
     * we can get by with 16 bits per cell.  Few of the cell counts will overflow,
     * and clamping those that do overflow to the maximum value will give close-
     * enough results.  This reduces the recommended histogram size from 256Kb
     * to 128Kb, which is a useful savings on PC-class machines.
     * (In the second pass the histogram space is re-used for pixel mapping data;
     * in that capacity, each cell must be able to store zero to the number of
     * desired colors.  16 bits/cell is plenty for that too.)
     * Since the JPEG code is intended to run in small memory model on 80x86
     * machines, we can't just allocate the histogram in one chunk.  Instead
     * of a true 3-D array, we use a row of pointers to 2-D arrays.  Each
     * pointer corresponds to a C0 value (typically 2^5 = 32 pointers) and
     * each 2-D array has 2^6*2^5 = 2048 or 2^6*2^6 = 4096 entries.  Note that
     * on 80x86 machines, the pointer row is in near memory but the actual
     * arrays are in far memory (same arrangement as we use for image arrays).
     */

    #define MAXNUMCOLORS  (MAXJSAMPLE+1) /* maximum size of colormap */

    /* These will do the right thing for either R,G,B or B,G,R color order,
     * but you may not like the results for other color orders.
     */
    #define HIST_C0_BITS  5		/* bits of precision in R/B histogram */
    #define HIST_C1_BITS  6		/* bits of precision in G histogram */
    #define HIST_C2_BITS  5		/* bits of precision in B/R histogram */

    /* Number of elements along histogram axes. */
    #define HIST_C0_ELEMS  (1<<HIST_C0_BITS)
    #define HIST_C1_ELEMS  (1<<HIST_C1_BITS)
    #define HIST_C2_ELEMS  (1<<HIST_C2_BITS)

    /* These are the amounts to shift an input value to get a histogram index. */
    #define C0_SHIFT  (BITS_IN_JSAMPLE-HIST_C0_BITS)
    #define C1_SHIFT  (BITS_IN_JSAMPLE-HIST_C1_BITS)
    #define C2_SHIFT  (BITS_IN_JSAMPLE-HIST_C2_BITS)

    typedef unsigned short histcell;	/* histogram cell; prefer an unsigned type */

    typedef histcell FAR * histptr;	/* for pointers to histogram cells */

    typedef histcell hist1d[HIST_C2_ELEMS]; /* typedefs for the array */
    typedef hist1d FAR * hist2d;	/* type for the 2nd-level pointers */
    typedef hist2d * hist3d;	/* type for top-level pointer */

    /* Declarations for Floyd-Steinberg dithering.
     *
     * Errors are accumulated into the array fserrors[], at a resolution of
     * 1/16th of a pixel count.  The error at a given pixel is propagated
     * to its not-yet-processed neighbors using the standard F-S fractions,
     *		...	(here)	7/16
     *		3/16	5/16	1/16
     * We work left-to-right on even rows, right-to-left on odd rows.
     *
     * We can get away with a single array (holding one row's worth of errors)
     * by using it to store the current row's errors at pixel columns not yet
     * processed, but the next row's errors at columns already processed.  We
     * need only a few extra variables to hold the errors immediately around the
     * current column.  (If we are lucky, those variables are in registers, but
     * even if not, they're probably cheaper to access than array elements are.)
     *
     * The fserrors[] array has (#columns + 2) entries; the extra entry at
     * each end saves us from special-casing the first and last pixels.
     * Each entry is three values long, one value for each color component.
     *
     * Note: on a wide image, we might not have enough room in a PC's near data
     * segment to hold the error array; so it is allocated with alloc_large.
     */

    #if BITS_IN_JSAMPLE == 8
    typedef short FSERROR;		/* 16 bits should be enough */
    typedef int LOCFSERROR;		/* use 'int' for calculation temps */
    #else
    typedef long FSERROR;		/* may need more than 16 bits */
    typedef long LOCFSERROR;	/* be sure calculation temps are big enough */
    #endif

    typedef FSERROR FAR *FSERRPTR;	/* pointer to error array (in FAR storage!) */

    /* Private subobject */

    typedef struct {
      struct jpeg_color_quantizer pub; /* public fields */

      /* Space for the eventually created colormap is stashed here */
      JSAMPARRAY sv_colormap;	/* colormap allocated at init time */
      int desired;			/* desired # of colors = size of colormap */

      /* Variables for accumulating image statistics */
      hist3d histogram;		/* pointer to the histogram */

      int needs_zeroed;		/* TRUE if next pass must zero histogram */

      /* Variables for Floyd-Steinberg dithering */
      FSERRPTR fserrors;		/* accumulated errors */
      int on_odd_row;		/* flag to remember which row we are on */
      int * error_limiter;		/* table for clamping the applied error */
    } my_cquantizer;

    typedef my_cquantizer * my_cquantize_ptr;

    /*
     * Prescan some rows of pixels.
     * In this module the prescan simply updates the histogram, which has been
     * initialized to zeroes by start_pass.
     * An output_buf parameter is required by the method signature, but no data
     * is actually output (in fact the buffer controller is probably passing a
     * NULL pointer).
     */

    METHODDEF(void)
    prescan_quantize (j_decompress_ptr cinfo, JSAMPARRAY input_buf,
    		  JSAMPARRAY , int num_rows)
    {
      my_cquantize_ptr cquantize = (my_cquantize_ptr) cinfo->cquantize;
      JSAMPROW ptr;
      histptr histp;
      hist3d histogram = cquantize->histogram;
      int row;
      JDIMENSION col;
      JDIMENSION width = cinfo->output_width;

      for (row = 0; row < num_rows; row++) {
        ptr = input_buf[row];
        for (col = width; col > 0; col--) {
          /* get pixel value and index into the histogram */
          histp = & histogram[GETJSAMPLE(ptr[0]) >> C0_SHIFT]
    			 [GETJSAMPLE(ptr[1]) >> C1_SHIFT]
    			 [GETJSAMPLE(ptr[2]) >> C2_SHIFT];
          /* increment, check for overflow and undo increment if so. */
          if (++(*histp) <= 0)
    	(*histp)--;
          ptr += 3;
        }
      }
    }

    /*
     * Next we have the really interesting routines: selection of a colormap
     * given the completed histogram.
     * These routines work with a list of "boxes", each representing a rectangular
     * subset of the input color space (to histogram precision).
     */

    typedef struct {
      /* The bounds of the box (inclusive); expressed as histogram indexes */
      int c0min, c0max;
      int c1min, c1max;
      int c2min, c2max;
      /* The volume (actually 2-norm) of the box */
      long volume;
      /* The number of nonzero histogram cells within this box */
      long colorcount;
    } box;

    typedef box * boxptr;

    LOCAL(boxptr)
    find_biggest_color_pop (boxptr boxlist, int numboxes)
    /* Find the splittable box with the largest color population */
    /* Returns NULL if no splittable boxes remain */
    {
      boxptr boxp;
      int i;
      long maxc = 0;
      boxptr which = NULL;

      for (i = 0, boxp = boxlist; i < numboxes; i++, boxp++) {
        if (boxp->colorcount > maxc && boxp->volume > 0) {
          which = boxp;
          maxc = boxp->colorcount;
        }
      }
      return which;
    }

    LOCAL(boxptr)
    find_biggest_volume (boxptr boxlist, int numboxes)
    /* Find the splittable box with the largest (scaled) volume */
    /* Returns NULL if no splittable boxes remain */
    {
      boxptr boxp;
      int i;
      long maxv = 0;
      boxptr which = NULL;

      for (i = 0, boxp = boxlist; i < numboxes; i++, boxp++) {
        if (boxp->volume > maxv) {
          which = boxp;
          maxv = boxp->volume;
        }
      }
      return which;
    }

    LOCAL(void)
    update_box (j_decompress_ptr cinfo, boxptr boxp)
    /* Shrink the min/max bounds of a box to enclose only nonzero elements, */
    /* and recompute its volume and population */
    {
      my_cquantize_ptr cquantize = (my_cquantize_ptr) cinfo->cquantize;
      hist3d histogram = cquantize->histogram;
      histptr histp;
      int c0,c1,c2;
      int c0min,c0max,c1min,c1max,c2min,c2max;
      long dist0,dist1,dist2;
      long ccount;

      c0min = boxp->c0min;  c0max = boxp->c0max;
      c1min = boxp->c1min;  c1max = boxp->c1max;
      c2min = boxp->c2min;  c2max = boxp->c2max;

      if (c0max > c0min)
        for (c0 = c0min; c0 <= c0max; c0++)
          for (c1 = c1min; c1 <= c1max; c1++) {
    	histp = & histogram[c0][c1][c2min];
    	for (c2 = c2min; c2 <= c2max; c2++)
    	  if (*histp++ != 0) {
    	    boxp->c0min = c0min = c0;
    	    goto have_c0min;
    	  }
          }
     have_c0min:
      if (c0max > c0min)
        for (c0 = c0max; c0 >= c0min; c0--)
          for (c1 = c1min; c1 <= c1max; c1++) {
    	histp = & histogram[c0][c1][c2min];
    	for (c2 = c2min; c2 <= c2max; c2++)
    	  if (*histp++ != 0) {
    	    boxp->c0max = c0max = c0;
    	    goto have_c0max;
    	  }
          }
     have_c0max:
      if (c1max > c1min)
        for (c1 = c1min; c1 <= c1max; c1++)
          for (c0 = c0min; c0 <= c0max; c0++) {
    	histp = & histogram[c0][c1][c2min];
    	for (c2 = c2min; c2 <= c2max; c2++)
    	  if (*histp++ != 0) {
    	    boxp->c1min = c1min = c1;
    	    goto have_c1min;
    	  }
          }
     have_c1min:
      if (c1max > c1min)
        for (c1 = c1max; c1 >= c1min; c1--)
          for (c0 = c0min; c0 <= c0max; c0++) {
    	histp = & histogram[c0][c1][c2min];
    	for (c2 = c2min; c2 <= c2max; c2++)
    	  if (*histp++ != 0) {
    	    boxp->c1max = c1max = c1;
    	    goto have_c1max;
    	  }
          }
     have_c1max:
      if (c2max > c2min)
        for (c2 = c2min; c2 <= c2max; c2++)
          for (c0 = c0min; c0 <= c0max; c0++) {
    	histp = & histogram[c0][c1min][c2];
    	for (c1 = c1min; c1 <= c1max; c1++, histp += HIST_C2_ELEMS)
    	  if (*histp != 0) {
    	    boxp->c2min = c2min = c2;
    	    goto have_c2min;
    	  }
          }
     have_c2min:
      if (c2max > c2min)
        for (c2 = c2max; c2 >= c2min; c2--)
          for (c0 = c0min; c0 <= c0max; c0++) {
    	histp = & histogram[c0][c1min][c2];
    	for (c1 = c1min; c1 <= c1max; c1++, histp += HIST_C2_ELEMS)
    	  if (*histp != 0) {
    	    boxp->c2max = c2max = c2;
    	    goto have_c2max;
    	  }
          }
     have_c2max:

      /* Update box volume.
       * We use 2-norm rather than real volume here; this biases the method
       * against making long narrow boxes, and it has the side benefit that
       * a box is splittable iff norm > 0.
       * Since the differences are expressed in histogram-cell units,
       * we have to shift back to JSAMPLE units to get consistent distances;
       * after which, we scale according to the selected distance scale factors.
       */
      dist0 = ((c0max - c0min) << C0_SHIFT) * C0_SCALE;
      dist1 = ((c1max - c1min) << C1_SHIFT) * C1_SCALE;
      dist2 = ((c2max - c2min) << C2_SHIFT) * C2_SCALE;
      boxp->volume = dist0*dist0 + dist1*dist1 + dist2*dist2;

      /* Now scan remaining volume of box and compute population */
      ccount = 0;
      for (c0 = c0min; c0 <= c0max; c0++)
        for (c1 = c1min; c1 <= c1max; c1++) {
          histp = & histogram[c0][c1][c2min];
          for (c2 = c2min; c2 <= c2max; c2++, histp++)
    	if (*histp != 0) {
    	  ccount++;
    	}
        }
      boxp->colorcount = ccount;
    }

    LOCAL(int)
    median_cut (j_decompress_ptr cinfo, boxptr boxlist, int numboxes,
    	    int desired_colors)
    /* Repeatedly select and split the largest box until we have enough boxes */
    {
      int n,lb;
      int c0,c1,c2,cmax;
      boxptr b1,b2;

      while (numboxes < desired_colors) {
        /* Select box to split.
         * Current algorithm: by population for first half, then by volume.
         */
        if (numboxes*2 <= desired_colors) {
          b1 = find_biggest_color_pop(boxlist, numboxes);
        } else {
          b1 = find_biggest_volume(boxlist, numboxes);
        }
        if (b1 == NULL)		/* no splittable boxes left! */
          break;
        b2 = &boxlist[numboxes];	/* where new box will go */
        /* Copy the color bounds to the new box. */
        b2->c0max = b1->c0max; b2->c1max = b1->c1max; b2->c2max = b1->c2max;
        b2->c0min = b1->c0min; b2->c1min = b1->c1min; b2->c2min = b1->c2min;
        /* Choose which axis to split the box on.
         * Current algorithm: longest scaled axis.
         * See notes in update_box about scaling distances.
         */
        c0 = ((b1->c0max - b1->c0min) << C0_SHIFT) * C0_SCALE;
        c1 = ((b1->c1max - b1->c1min) << C1_SHIFT) * C1_SCALE;
        c2 = ((b1->c2max - b1->c2min) << C2_SHIFT) * C2_SCALE;
        /* We want to break any ties in favor of green, then red, blue last.
         * This code does the right thing for R,G,B or B,G,R color orders only.
         */
    #if RGB_RED == 0
        cmax = c1; n = 1;
        if (c0 > cmax) { cmax = c0; n = 0; }
        if (c2 > cmax) { n = 2; }
    #else
        cmax = c1; n = 1;
        if (c2 > cmax) { cmax = c2; n = 2; }
        if (c0 > cmax) { n = 0; }
    #endif
        /* Choose split point along selected axis, and update box bounds.
         * Current algorithm: split at halfway point.
         * (Since the box has been shrunk to minimum volume,
         * any split will produce two nonempty subboxes.)
         * Note that lb value is max for lower box, so must be < old max.
         */
        switch (n) {
        case 0:
          lb = (b1->c0max + b1->c0min) / 2;
          b1->c0max = lb;
          b2->c0min = lb+1;
          break;
        case 1:
          lb = (b1->c1max + b1->c1min) / 2;
          b1->c1max = lb;
          b2->c1min = lb+1;
          break;
        case 2:
          lb = (b1->c2max + b1->c2min) / 2;
          b1->c2max = lb;
          b2->c2min = lb+1;
          break;
        }
        /* Update stats for boxes */
        update_box(cinfo, b1);
        update_box(cinfo, b2);
        numboxes++;
      }
      return numboxes;
    }

    LOCAL(void)
    compute_color (j_decompress_ptr cinfo, boxptr boxp, int icolor)
    /* Compute representative color for a box, put it in colormap[icolor] */
    {
      /* Current algorithm: mean weighted by pixels (not colors) */
      /* Note it is important to get the rounding correct! */
      my_cquantize_ptr cquantize = (my_cquantize_ptr) cinfo->cquantize;
      hist3d histogram = cquantize->histogram;
      histptr histp;
      int c0,c1,c2;
      int c0min,c0max,c1min,c1max,c2min,c2max;
      long count;
      long total = 0;
      long c0total = 0;
      long c1total = 0;
      long c2total = 0;

      c0min = boxp->c0min;  c0max = boxp->c0max;
      c1min = boxp->c1min;  c1max = boxp->c1max;
      c2min = boxp->c2min;  c2max = boxp->c2max;

      for (c0 = c0min; c0 <= c0max; c0++)
        for (c1 = c1min; c1 <= c1max; c1++) {
          histp = & histogram[c0][c1][c2min];
          for (c2 = c2min; c2 <= c2max; c2++) {
    	if ((count = *histp++) != 0) {
    	  total += count;
    	  c0total += ((c0 << C0_SHIFT) + ((1<<C0_SHIFT)>>1)) * count;
    	  c1total += ((c1 << C1_SHIFT) + ((1<<C1_SHIFT)>>1)) * count;
    	  c2total += ((c2 << C2_SHIFT) + ((1<<C2_SHIFT)>>1)) * count;
    	}
          }
        }

      cinfo->colormap[0][icolor] = (JSAMPLE) ((c0total + (total>>1)) / total);
      cinfo->colormap[1][icolor] = (JSAMPLE) ((c1total + (total>>1)) / total);
      cinfo->colormap[2][icolor] = (JSAMPLE) ((c2total + (total>>1)) / total);
    }

    LOCAL(void)
    select_colors (j_decompress_ptr cinfo, int desired_colors)
    /* Master routine for color selection */
    {
      boxptr boxlist;
      int numboxes;
      int i;

      /* Allocate workspace for box list */
      boxlist = (boxptr) (*cinfo->mem->alloc_small)
        ((j_common_ptr) cinfo, JPOOL_IMAGE, desired_colors * SIZEOF(box));
      /* Initialize one box containing whole space */
      numboxes = 1;
      boxlist[0].c0min = 0;
      boxlist[0].c0max = MAXJSAMPLE >> C0_SHIFT;
      boxlist[0].c1min = 0;
      boxlist[0].c1max = MAXJSAMPLE >> C1_SHIFT;
      boxlist[0].c2min = 0;
      boxlist[0].c2max = MAXJSAMPLE >> C2_SHIFT;
      /* Shrink it to actually-used volume and set its statistics */
      update_box(cinfo, & boxlist[0]);
      /* Perform median-cut to produce final box list */
      numboxes = median_cut(cinfo, boxlist, numboxes, desired_colors);
      /* Compute the representative color for each box, fill colormap */
      for (i = 0; i < numboxes; i++)
        compute_color(cinfo, & boxlist[i], i);
      cinfo->actual_number_of_colors = numboxes;
      TRACEMS1(cinfo, 1, JTRC_QUANT_SELECTED, numboxes);
    }

    /*
     * These routines are concerned with the time-critical task of mapping input
     * colors to the nearest color in the selected colormap.
     *
     * We re-use the histogram space as an "inverse color map", essentially a
     * cache for the results of nearest-color searches.  All colors within a
     * histogram cell will be mapped to the same colormap entry, namely the one
     * closest to the cell's center.  This may not be quite the closest entry to
     * the actual input color, but it's almost as good.  A zero in the cache
     * indicates we haven't found the nearest color for that cell yet; the array
     * is cleared to zeroes before starting the mapping pass.  When we find the
     * nearest color for a cell, its colormap index plus one is recorded in the
     * cache for future use.  The pass2 scanning routines call fill_inverse_cmap
     * when they need to use an unfilled entry in the cache.
     *
     * Our method of efficiently finding nearest colors is based on the "locally
     * sorted search" idea described by Heckbert and on the incremental distance
     * calculation described by Spencer W. Thomas in chapter III.1 of Graphics
     * Gems II (James Arvo, ed.  Academic Press, 1991).  Thomas points out that
     * the distances from a given colormap entry to each cell of the histogram can
     * be computed quickly using an incremental method: the differences between
     * distances to adjacent cells themselves differ by a constant.  This allows a
     * fairly fast implementation of the "brute force" approach of computing the
     * distance from every colormap entry to every histogram cell.  Unfortunately,
     * it needs a work array to hold the best-distance-so-far for each histogram
     * cell (because the inner loop has to be over cells, not colormap entries).
     * The work array elements have to be INT32s, so the work array would need
     * 256Kb at our recommended precision.  This is not feasible in DOS machines.
     *
     * To get around these problems, we apply Thomas' method to compute the
     * nearest colors for only the cells within a small subbox of the histogram.
     * The work array need be only as big as the subbox, so the memory usage
     * problem is solved.  Furthermore, we need not fill subboxes that are never
     * referenced in pass2; many images use only part of the color gamut, so a
     * fair amount of work is saved.  An additional advantage of this
     * approach is that we can apply Heckbert's locality criterion to quickly
     * eliminate colormap entries that are far away from the subbox; typically
     * three-fourths of the colormap entries are rejected by Heckbert's criterion,
     * and we need not compute their distances to individual cells in the subbox.
     * The speed of this approach is heavily influenced by the subbox size: too
     * small means too much overhead, too big loses because Heckbert's criterion
     * can't eliminate as many colormap entries.  Empirically the best subbox
     * size seems to be about 1/512th of the histogram (1/8th in each direction).
     *
     * Thomas' article also describes a refined method which is asymptotically
     * faster than the brute-force method, but it is also far more complex and
     * cannot efficiently be applied to small subboxes.  It is therefore not
     * useful for programs intended to be portable to DOS machines.  On machines
     * with plenty of memory, filling the whole histogram in one shot with Thomas'
     * refined method might be faster than the present code --- but then again,
     * it might not be any faster, and it's certainly more complicated.
     */

    /* log2(histogram cells in update box) for each axis; this can be adjusted */
    #define BOX_C0_LOG  (HIST_C0_BITS-3)
    #define BOX_C1_LOG  (HIST_C1_BITS-3)
    #define BOX_C2_LOG  (HIST_C2_BITS-3)

    #define BOX_C0_ELEMS  (1<<BOX_C0_LOG) /* # of hist cells in update box */
    #define BOX_C1_ELEMS  (1<<BOX_C1_LOG)
    #define BOX_C2_ELEMS  (1<<BOX_C2_LOG)

    #define BOX_C0_SHIFT  (C0_SHIFT + BOX_C0_LOG)
    #define BOX_C1_SHIFT  (C1_SHIFT + BOX_C1_LOG)
    #define BOX_C2_SHIFT  (C2_SHIFT + BOX_C2_LOG)

    /*
     * The next three routines implement inverse colormap filling.  They could
     * all be folded into one big routine, but splitting them up this way saves
     * some stack space (the mindist[] and bestdist[] arrays need not coexist)
     * and may allow some compilers to produce better code by registerizing more
     * inner-loop variables.
     */

    LOCAL(int)
    find_nearby_colors (j_decompress_ptr cinfo, int minc0, int minc1, int minc2,
    		    JSAMPLE colorlist[])
    /* Locate the colormap entries close enough to an update box to be candidates
     * for the nearest entry to some cell(s) in the update box.  The update box
     * is specified by the center coordinates of its first cell.  The number of
     * candidate colormap entries is returned, and their colormap indexes are
     * placed in colorlist[].
     * This routine uses Heckbert's "locally sorted search" criterion to select
     * the colors that need further consideration.
     */
    {
      int numcolors = cinfo->actual_number_of_colors;
      int maxc0, maxc1, maxc2;
      int centerc0, centerc1, centerc2;
      int i, x, ncolors;
      long minmaxdist, min_dist, max_dist, tdist;
      long mindist[MAXNUMCOLORS];	/* min distance to colormap entry i */

      /* Compute true coordinates of update box's upper corner and center.
       * Actually we compute the coordinates of the center of the upper-corner
       * histogram cell, which are the upper bounds of the volume we care about.
       * Note that since ">>" rounds down, the "center" values may be closer to
       * min than to max; hence comparisons to them must be "<=", not "<".
       */
      maxc0 = minc0 + ((1 << BOX_C0_SHIFT) - (1 << C0_SHIFT));
      centerc0 = (minc0 + maxc0) >> 1;
      maxc1 = minc1 + ((1 << BOX_C1_SHIFT) - (1 << C1_SHIFT));
      centerc1 = (minc1 + maxc1) >> 1;
      maxc2 = minc2 + ((1 << BOX_C2_SHIFT) - (1 << C2_SHIFT));
      centerc2 = (minc2 + maxc2) >> 1;

      /* For each color in colormap, find:
       *  1. its minimum squared-distance to any point in the update box
       *     (zero if color is within update box);
       *  2. its maximum squared-distance to any point in the update box.
       * Both of these can be found by considering only the corners of the box.
       * We save the minimum distance for each color in mindist[];
       * only the smallest maximum distance is of interest.
       */
      minmaxdist = 0x7FFFFFFFL;

      for (i = 0; i < numcolors; i++) {
        /* We compute the squared-c0-distance term, then add in the other two. */
        x = GETJSAMPLE(cinfo->colormap[0][i]);
        if (x < minc0) {
          tdist = (x - minc0) * C0_SCALE;
          min_dist = tdist*tdist;
          tdist = (x - maxc0) * C0_SCALE;
          max_dist = tdist*tdist;
        } else if (x > maxc0) {
          tdist = (x - maxc0) * C0_SCALE;
          min_dist = tdist*tdist;
          tdist = (x - minc0) * C0_SCALE;
          max_dist = tdist*tdist;
        } else {
          /* within cell range so no contribution to min_dist */
          min_dist = 0;
          if (x <= centerc0) {
    	tdist = (x - maxc0) * C0_SCALE;
    	max_dist = tdist*tdist;
          } else {
    	tdist = (x - minc0) * C0_SCALE;
    	max_dist = tdist*tdist;
          }
        }

        x = GETJSAMPLE(cinfo->colormap[1][i]);
        if (x < minc1) {
          tdist = (x - minc1) * C1_SCALE;
          min_dist += tdist*tdist;
          tdist = (x - maxc1) * C1_SCALE;
          max_dist += tdist*tdist;
        } else if (x > maxc1) {
          tdist = (x - maxc1) * C1_SCALE;
          min_dist += tdist*tdist;
          tdist = (x - minc1) * C1_SCALE;
          max_dist += tdist*tdist;
        } else {
          /* within cell range so no contribution to min_dist */
          if (x <= centerc1) {
    	tdist = (x - maxc1) * C1_SCALE;
    	max_dist += tdist*tdist;
          } else {
    	tdist = (x - minc1) * C1_SCALE;
    	max_dist += tdist*tdist;
          }
        }

        x = GETJSAMPLE(cinfo->colormap[2][i]);
        if (x < minc2) {
          tdist = (x - minc2) * C2_SCALE;
          min_dist += tdist*tdist;
          tdist = (x - maxc2) * C2_SCALE;
          max_dist += tdist*tdist;
        } else if (x > maxc2) {
          tdist = (x - maxc2) * C2_SCALE;
          min_dist += tdist*tdist;
          tdist = (x - minc2) * C2_SCALE;
          max_dist += tdist*tdist;
        } else {
          /* within cell range so no contribution to min_dist */
          if (x <= centerc2) {
    	tdist = (x - maxc2) * C2_SCALE;
    	max_dist += tdist*tdist;
          } else {
    	tdist = (x - minc2) * C2_SCALE;
    	max_dist += tdist*tdist;
          }
        }

        mindist[i] = min_dist;	/* save away the results */
        if (max_dist < minmaxdist)
          minmaxdist = max_dist;
      }

      /* Now we know that no cell in the update box is more than minmaxdist
       * away from some colormap entry.  Therefore, only colors that are
       * within minmaxdist of some part of the box need be considered.
       */
      ncolors = 0;
      for (i = 0; i < numcolors; i++) {
        if (mindist[i] <= minmaxdist)
          colorlist[ncolors++] = (JSAMPLE) i;
      }
      return ncolors;
    }

    LOCAL(void)
    find_best_colors (j_decompress_ptr cinfo, int minc0, int minc1, int minc2,
    		  int numcolors, JSAMPLE colorlist[], JSAMPLE bestcolor[])
    /* Find the closest colormap entry for each cell in the update box,
     * given the list of candidate colors prepared by find_nearby_colors.
     * Return the indexes of the closest entries in the bestcolor[] array.
     * This routine uses Thomas' incremental distance calculation method to
     * find the distance from a colormap entry to successive cells in the box.
     */
    {
      int ic0, ic1, ic2;
      int i, icolor;
      long * bptr;	/* pointer into bestdist[] array */
      JSAMPLE * cptr;		/* pointer into bestcolor[] array */
      long dist0, dist1;		/* initial distance values */
      long dist2;		/* current distance in inner loop */
      long xx0, xx1;		/* distance increments */
      long xx2;
      long inc0, inc1, inc2;	/* initial values for increments */
      /* This array holds the distance to the nearest-so-far color for each cell */
      long bestdist[BOX_C0_ELEMS * BOX_C1_ELEMS * BOX_C2_ELEMS];

      /* Initialize best-distance for each cell of the update box */
      bptr = bestdist;
      for (i = BOX_C0_ELEMS*BOX_C1_ELEMS*BOX_C2_ELEMS-1; i >= 0; i--)
        *bptr++ = 0x7FFFFFFFL;

      /* For each color selected by find_nearby_colors,
       * compute its distance to the center of each cell in the box.
       * If that's less than best-so-far, update best distance and color number.
       */

      /* Nominal steps between cell centers ("x" in Thomas article) */
    #define STEP_C0  ((1 << C0_SHIFT) * C0_SCALE)
    #define STEP_C1  ((1 << C1_SHIFT) * C1_SCALE)
    #define STEP_C2  ((1 << C2_SHIFT) * C2_SCALE)

      for (i = 0; i < numcolors; i++) {
        icolor = GETJSAMPLE(colorlist[i]);
        /* Compute (square of) distance from minc0/c1/c2 to this color */
        inc0 = (minc0 - GETJSAMPLE(cinfo->colormap[0][icolor])) * C0_SCALE;
        dist0 = inc0*inc0;
        inc1 = (minc1 - GETJSAMPLE(cinfo->colormap[1][icolor])) * C1_SCALE;
        dist0 += inc1*inc1;
        inc2 = (minc2 - GETJSAMPLE(cinfo->colormap[2][icolor])) * C2_SCALE;
        dist0 += inc2*inc2;
        /* Form the initial difference increments */
        inc0 = inc0 * (2 * STEP_C0) + STEP_C0 * STEP_C0;
        inc1 = inc1 * (2 * STEP_C1) + STEP_C1 * STEP_C1;
        inc2 = inc2 * (2 * STEP_C2) + STEP_C2 * STEP_C2;
        /* Now loop over all cells in box, updating distance per Thomas method */
        bptr = bestdist;
        cptr = bestcolor;
        xx0 = inc0;
        for (ic0 = BOX_C0_ELEMS-1; ic0 >= 0; ic0--) {
          dist1 = dist0;
          xx1 = inc1;
          for (ic1 = BOX_C1_ELEMS-1; ic1 >= 0; ic1--) {
    	dist2 = dist1;
    	xx2 = inc2;
    	for (ic2 = BOX_C2_ELEMS-1; ic2 >= 0; ic2--) {
    	  if (dist2 < *bptr) {
    	    *bptr = dist2;
    	    *cptr = (JSAMPLE) icolor;
    	  }
    	  dist2 += xx2;
    	  xx2 += 2 * STEP_C2 * STEP_C2;
    	  bptr++;
    	  cptr++;
    	}
    	dist1 += xx1;
    	xx1 += 2 * STEP_C1 * STEP_C1;
          }
          dist0 += xx0;
          xx0 += 2 * STEP_C0 * STEP_C0;
        }
      }
    }

    LOCAL(void)
    fill_inverse_cmap (j_decompress_ptr cinfo, int c0, int c1, int c2)
    /* Fill the inverse-colormap entries in the update box that contains */
    /* histogram cell c0/c1/c2.  (Only that one cell MUST be filled, but */
    /* we can fill as many others as we wish.) */
    {
      my_cquantize_ptr cquantize = (my_cquantize_ptr) cinfo->cquantize;
      hist3d histogram = cquantize->histogram;
      int minc0, minc1, minc2;	/* lower left corner of update box */
      int ic0, ic1, ic2;
      JSAMPLE * cptr;	/* pointer into bestcolor[] array */
      histptr cachep;	/* pointer into main cache array */
      /* This array lists the candidate colormap indexes. */
      JSAMPLE colorlist[MAXNUMCOLORS];
      int numcolors;		/* number of candidate colors */
      /* This array holds the actually closest colormap index for each cell. */
      JSAMPLE bestcolor[BOX_C0_ELEMS * BOX_C1_ELEMS * BOX_C2_ELEMS];

      /* Convert cell coordinates to update box ID */
      c0 >>= BOX_C0_LOG;
      c1 >>= BOX_C1_LOG;
      c2 >>= BOX_C2_LOG;

      /* Compute true coordinates of update box's origin corner.
       * Actually we compute the coordinates of the center of the corner
       * histogram cell, which are the lower bounds of the volume we care about.
       */
      minc0 = (c0 << BOX_C0_SHIFT) + ((1 << C0_SHIFT) >> 1);
      minc1 = (c1 << BOX_C1_SHIFT) + ((1 << C1_SHIFT) >> 1);
      minc2 = (c2 << BOX_C2_SHIFT) + ((1 << C2_SHIFT) >> 1);

      /* Determine which colormap entries are close enough to be candidates
       * for the nearest entry to some cell in the update box.
       */
      numcolors = find_nearby_colors(cinfo, minc0, minc1, minc2, colorlist);

      /* Determine the actually nearest colors. */
      find_best_colors(cinfo, minc0, minc1, minc2, numcolors, colorlist,
    		   bestcolor);

      /* Save the best color numbers (plus 1) in the main cache array */
      c0 <<= BOX_C0_LOG;		/* convert ID back to base cell indexes */
      c1 <<= BOX_C1_LOG;
      c2 <<= BOX_C2_LOG;
      cptr = bestcolor;
      for (ic0 = 0; ic0 < BOX_C0_ELEMS; ic0++) {
        for (ic1 = 0; ic1 < BOX_C1_ELEMS; ic1++) {
          cachep = & histogram[c0+ic0][c1+ic1][c2];
          for (ic2 = 0; ic2 < BOX_C2_ELEMS; ic2++) {
    	*cachep++ = (histcell) (GETJSAMPLE(*cptr++) + 1);
          }
        }
      }
    }

    /*
     * Map some rows of pixels to the output colormapped representation.
     */

    METHODDEF(void)
    pass2_no_dither (j_decompress_ptr cinfo,
    		 JSAMPARRAY input_buf, JSAMPARRAY output_buf, int num_rows)
    /* This version performs no dithering */
    {
      my_cquantize_ptr cquantize = (my_cquantize_ptr) cinfo->cquantize;
      hist3d histogram = cquantize->histogram;
      JSAMPROW inptr, outptr;
      histptr cachep;
      int c0, c1, c2;
      int row;
      JDIMENSION col;
      JDIMENSION width = cinfo->output_width;

      for (row = 0; row < num_rows; row++) {
        inptr = input_buf[row];
        outptr = output_buf[row];
        for (col = width; col > 0; col--) {
          /* get pixel value and index into the cache */
          c0 = GETJSAMPLE(*inptr++) >> C0_SHIFT;
          c1 = GETJSAMPLE(*inptr++) >> C1_SHIFT;
          c2 = GETJSAMPLE(*inptr++) >> C2_SHIFT;
          cachep = & histogram[c0][c1][c2];
          /* If we have not seen this color before, find nearest colormap entry */
          /* and update the cache */
          if (*cachep == 0)
    	fill_inverse_cmap(cinfo, c0,c1,c2);
          /* Now emit the colormap index for this cell */
          *outptr++ = (JSAMPLE) (*cachep - 1);
        }
      }
    }

    METHODDEF(void)
    pass2_fs_dither (j_decompress_ptr cinfo,
    		 JSAMPARRAY input_buf, JSAMPARRAY output_buf, int num_rows)
    /* This version performs Floyd-Steinberg dithering */
    {
      my_cquantize_ptr cquantize = (my_cquantize_ptr) cinfo->cquantize;
      hist3d histogram = cquantize->histogram;
      LOCFSERROR cur0, cur1, cur2;	/* current error or pixel value */
      LOCFSERROR belowerr0, belowerr1, belowerr2; /* error for pixel below cur */
      LOCFSERROR bpreverr0, bpreverr1, bpreverr2; /* error for below/prev col */
      FSERRPTR errorptr;	/* => fserrors[] at column before current */
      JSAMPROW inptr;		/* => current input pixel */
      JSAMPROW outptr;		/* => current output pixel */
      histptr cachep;
      int dir;			/* +1 or -1 depending on direction */
      int dir3;			/* 3*dir, for advancing inptr & errorptr */
      int row;
      JDIMENSION col;
      JDIMENSION width = cinfo->output_width;
      JSAMPLE *range_limit = cinfo->sample_range_limit;
      int *error_limit = cquantize->error_limiter;
      JSAMPROW colormap0 = cinfo->colormap[0];
      JSAMPROW colormap1 = cinfo->colormap[1];
      JSAMPROW colormap2 = cinfo->colormap[2];
      SHIFT_TEMPS

      for (row = 0; row < num_rows; row++) {
        inptr = input_buf[row];
        outptr = output_buf[row];
        if (cquantize->on_odd_row) {
          /* work right to left in this row */
          inptr += (width-1) * 3;	/* so point to rightmost pixel */
          outptr += width-1;
          dir = -1;
          dir3 = -3;
          errorptr = cquantize->fserrors + (width+1)*3; /* => entry after last column */
          cquantize->on_odd_row = FALSE; /* flip for next time */
        } else {
          /* work left to right in this row */
          dir = 1;
          dir3 = 3;
          errorptr = cquantize->fserrors; /* => entry before first real column */
          cquantize->on_odd_row = TRUE; /* flip for next time */
        }
        /* Preset error values: no error propagated to first pixel from left */
        cur0 = cur1 = cur2 = 0;
        /* and no error propagated to row below yet */
        belowerr0 = belowerr1 = belowerr2 = 0;
        bpreverr0 = bpreverr1 = bpreverr2 = 0;

        for (col = width; col > 0; col--) {
          /* curN holds the error propagated from the previous pixel on the
           * current line.  Add the error propagated from the previous line
           * to form the complete error correction term for this pixel, and
           * round the error term (which is expressed * 16) to an integer.
           * RIGHT_SHIFT rounds towards minus infinity, so adding 8 is correct
           * for either sign of the error value.
           * Note: errorptr points to *previous* column's array entry.
           */
          cur0 = RIGHT_SHIFT(cur0 + errorptr[dir3+0] + 8, 4);
          cur1 = RIGHT_SHIFT(cur1 + errorptr[dir3+1] + 8, 4);
          cur2 = RIGHT_SHIFT(cur2 + errorptr[dir3+2] + 8, 4);
          /* Limit the error using transfer function set by init_error_limit.
           * See comments with init_error_limit for rationale.
           */
          cur0 = error_limit[cur0];
          cur1 = error_limit[cur1];
          cur2 = error_limit[cur2];
          /* Form pixel value + error, and range-limit to 0..MAXJSAMPLE.
           * The maximum error is +- MAXJSAMPLE (or less with error limiting);
           * this sets the required size of the range_limit array.
           */
          cur0 += GETJSAMPLE(inptr[0]);
          cur1 += GETJSAMPLE(inptr[1]);
          cur2 += GETJSAMPLE(inptr[2]);
          cur0 = GETJSAMPLE(range_limit[cur0]);
          cur1 = GETJSAMPLE(range_limit[cur1]);
          cur2 = GETJSAMPLE(range_limit[cur2]);
          /* Index into the cache with adjusted pixel value */
          cachep = & histogram[cur0>>C0_SHIFT][cur1>>C1_SHIFT][cur2>>C2_SHIFT];
          /* If we have not seen this color before, find nearest colormap */
          /* entry and update the cache */
          if (*cachep == 0)
    	fill_inverse_cmap(cinfo, cur0>>C0_SHIFT,cur1>>C1_SHIFT,cur2>>C2_SHIFT);
          /* Now emit the colormap index for this cell */
          { int pixcode = *cachep - 1;
    	*outptr = (JSAMPLE) pixcode;
    	/* Compute representation error for this pixel */
    	cur0 -= GETJSAMPLE(colormap0[pixcode]);
    	cur1 -= GETJSAMPLE(colormap1[pixcode]);
    	cur2 -= GETJSAMPLE(colormap2[pixcode]);
          }
          /* Compute error fractions to be propagated to adjacent pixels.
           * Add these into the running sums, and simultaneously shift the
           * next-line error sums left by 1 column.
           */
          { LOCFSERROR bnexterr, delta;

    	bnexterr = cur0;	/* Process component 0 */
    	delta = cur0 * 2;
    	cur0 += delta;		/* form error * 3 */
    	errorptr[0] = (FSERROR) (bpreverr0 + cur0);
    	cur0 += delta;		/* form error * 5 */
    	bpreverr0 = belowerr0 + cur0;
    	belowerr0 = bnexterr;
    	cur0 += delta;		/* form error * 7 */
    	bnexterr = cur1;	/* Process component 1 */
    	delta = cur1 * 2;
    	cur1 += delta;		/* form error * 3 */
    	errorptr[1] = (FSERROR) (bpreverr1 + cur1);
    	cur1 += delta;		/* form error * 5 */
    	bpreverr1 = belowerr1 + cur1;
    	belowerr1 = bnexterr;
    	cur1 += delta;		/* form error * 7 */
    	bnexterr = cur2;	/* Process component 2 */
    	delta = cur2 * 2;
    	cur2 += delta;		/* form error * 3 */
    	errorptr[2] = (FSERROR) (bpreverr2 + cur2);
    	cur2 += delta;		/* form error * 5 */
    	bpreverr2 = belowerr2 + cur2;
    	belowerr2 = bnexterr;
    	cur2 += delta;		/* form error * 7 */
          }
          /* At this point curN contains the 7/16 error value to be propagated
           * to the next pixel on the current line, and all the errors for the
           * next line have been shifted over.  We are therefore ready to move on.
           */
          inptr += dir3;		/* Advance pixel pointers to next column */
          outptr += dir;
          errorptr += dir3;		/* advance errorptr to current column */
        }
        /* Post-loop cleanup: we must unload the final error values into the
         * final fserrors[] entry.  Note we need not unload belowerrN because
         * it is for the dummy column before or after the actual array.
         */
        errorptr[0] = (FSERROR) bpreverr0; /* unload prev errs into array */
        errorptr[1] = (FSERROR) bpreverr1;
        errorptr[2] = (FSERROR) bpreverr2;
      }
    }

    /*
     * Initialize the error-limiting transfer function (lookup table).
     * The raw F-S error computation can potentially compute error values of up to
     * +- MAXJSAMPLE.  But we want the maximum correction applied to a pixel to be
     * much less, otherwise obviously wrong pixels will be created.  (Typical
     * effects include weird fringes at color-area boundaries, isolated bright
     * pixels in a dark area, etc.)  The standard advice for avoiding this problem
     * is to ensure that the "corners" of the color cube are allocated as output
     * colors; then repeated errors in the same direction cannot cause cascading
     * error buildup.  However, that only prevents the error from getting
     * completely out of hand; Aaron Giles reports that error limiting improves
     * the results even with corner colors allocated.
     * A simple clamping of the error values to about +- MAXJSAMPLE/8 works pretty
     * well, but the smoother transfer function used below is even better.  Thanks
     * to Aaron Giles for this idea.
     */

    LOCAL(void)
    init_error_limit (j_decompress_ptr cinfo)
    /* Allocate and fill in the error_limiter table */
    {
      my_cquantize_ptr cquantize = (my_cquantize_ptr) cinfo->cquantize;
      int * table;
      int in, out;

      table = (int *) (*cinfo->mem->alloc_small)
        ((j_common_ptr) cinfo, JPOOL_IMAGE, (MAXJSAMPLE*2+1) * SIZEOF(int));
      table += MAXJSAMPLE;		/* so can index -MAXJSAMPLE .. +MAXJSAMPLE */
      cquantize->error_limiter = table;

    #define STEPSIZE ((MAXJSAMPLE+1)/16)
      /* Map errors 1:1 up to +- MAXJSAMPLE/16 */
      out = 0;
      for (in = 0; in < STEPSIZE; in++, out++) {
        table[in] = out; table[-in] = -out;
      }
      /* Map errors 1:2 up to +- 3*MAXJSAMPLE/16 */
      for (; in < STEPSIZE*3; in++, out += (in&1) ? 0 : 1) {
        table[in] = out; table[-in] = -out;
      }
      /* Clamp the rest to final out value (which is (MAXJSAMPLE+1)/8) */
      for (; in <= MAXJSAMPLE; in++) {
        table[in] = out; table[-in] = -out;
      }
    #undef STEPSIZE
    }

    /*
     * Finish up at the end of each pass.
     */

    METHODDEF(void)
    finish_pass1 (j_decompress_ptr cinfo)
    {
      my_cquantize_ptr cquantize = (my_cquantize_ptr) cinfo->cquantize;

      /* Select the representative colors and fill in cinfo->colormap */
      cinfo->colormap = cquantize->sv_colormap;
      select_colors(cinfo, cquantize->desired);
      /* Force next pass to zero the color index table */
      cquantize->needs_zeroed = TRUE;
    }

    METHODDEF(void)
    finish_pass2 (j_decompress_ptr )
    {
      /* no work */
    }

    /*
     * Initialize for each processing pass.
     */

    METHODDEF(void)
    start_pass_2_quant (j_decompress_ptr cinfo, int is_pre_scan)
    {
      my_cquantize_ptr cquantize = (my_cquantize_ptr) cinfo->cquantize;
      hist3d histogram = cquantize->histogram;
      int i;

      /* Only F-S dithering or no dithering is supported. */
      /* If user asks for ordered dither, give him F-S. */
      if (cinfo->dither_mode != JDITHER_NONE)
        cinfo->dither_mode = JDITHER_FS;

      if (is_pre_scan) {
        /* Set up method pointers */
        cquantize->pub.color_quantize = prescan_quantize;
        cquantize->pub.finish_pass = finish_pass1;
        cquantize->needs_zeroed = TRUE; /* Always zero histogram */
      } else {
        /* Set up method pointers */
        if (cinfo->dither_mode == JDITHER_FS)
          cquantize->pub.color_quantize = pass2_fs_dither;
        else
          cquantize->pub.color_quantize = pass2_no_dither;
        cquantize->pub.finish_pass = finish_pass2;

        /* Make sure color count is acceptable */
        i = cinfo->actual_number_of_colors;
        if (i < 1)
          ERREXIT1(cinfo, JERR_QUANT_FEW_COLORS, 1);
        if (i > MAXNUMCOLORS)
          ERREXIT1(cinfo, JERR_QUANT_MANY_COLORS, MAXNUMCOLORS);

        if (cinfo->dither_mode == JDITHER_FS) {
          size_t arraysize = (size_t) ((cinfo->output_width + 2) *
    				   (3 * SIZEOF(FSERROR)));
          /* Allocate Floyd-Steinberg workspace if we didn't already. */
          if (cquantize->fserrors == NULL)
    	cquantize->fserrors = (FSERRPTR) (*cinfo->mem->alloc_large)
    	  ((j_common_ptr) cinfo, JPOOL_IMAGE, arraysize);
          /* Initialize the propagated errors to zero. */
          jzero_far((void FAR *) cquantize->fserrors, arraysize);
          /* Make the error-limit table if we didn't already. */
          if (cquantize->error_limiter == NULL)
    	init_error_limit(cinfo);
          cquantize->on_odd_row = FALSE;
        }

      }
      /* Zero the histogram or inverse color map, if necessary */
      if (cquantize->needs_zeroed) {
        for (i = 0; i < HIST_C0_ELEMS; i++) {
          jzero_far((void FAR *) histogram[i],
    		HIST_C1_ELEMS*HIST_C2_ELEMS * SIZEOF(histcell));
        }
        cquantize->needs_zeroed = FALSE;
      }
    }

    /*
     * Switch to a new external colormap between output passes.
     */

    METHODDEF(void)
    new_color_map_2_quant (j_decompress_ptr cinfo)
    {
      my_cquantize_ptr cquantize = (my_cquantize_ptr) cinfo->cquantize;

      /* Reset the inverse color map */
      cquantize->needs_zeroed = TRUE;
    }

    /*
     * Module initialization routine for 2-pass color quantization.
     */

    GLOBAL(void)
    jinit_2pass_quantizer (j_decompress_ptr cinfo)
    {
      my_cquantize_ptr cquantize;
      int i;

      cquantize = (my_cquantize_ptr)
        (*cinfo->mem->alloc_small) ((j_common_ptr) cinfo, JPOOL_IMAGE,
    				SIZEOF(my_cquantizer));
      cinfo->cquantize = (struct jpeg_color_quantizer *) cquantize;
      cquantize->pub.start_pass = start_pass_2_quant;
      cquantize->pub.new_color_map = new_color_map_2_quant;
      cquantize->fserrors = NULL;	/* flag optional arrays not allocated */
      cquantize->error_limiter = NULL;

      /* Make sure jdmaster didn't give me a case I can't handle */
      if (cinfo->out_color_components != 3)
        ERREXIT(cinfo, JERR_NOTIMPL);

      /* Allocate the histogram/inverse colormap storage */
      cquantize->histogram = (hist3d) (*cinfo->mem->alloc_small)
        ((j_common_ptr) cinfo, JPOOL_IMAGE, HIST_C0_ELEMS * SIZEOF(hist2d));
      for (i = 0; i < HIST_C0_ELEMS; i++) {
        cquantize->histogram[i] = (hist2d) (*cinfo->mem->alloc_large)
          ((j_common_ptr) cinfo, JPOOL_IMAGE,
           HIST_C1_ELEMS*HIST_C2_ELEMS * SIZEOF(histcell));
      }
      cquantize->needs_zeroed = TRUE; /* histogram is garbage now */

      /* Allocate storage for the completed colormap, if required.
       * We do this now since it is FAR storage and may affect
       * the memory manager's space calculations.
       */
      if (cinfo->enable_2pass_quant) {
        /* Make sure color count is acceptable */
        int desired = cinfo->desired_number_of_colors;
        /* Lower bound on # of colors ... somewhat arbitrary as long as > 0 */
        if (desired < 8)
          ERREXIT1(cinfo, JERR_QUANT_FEW_COLORS, 8);
        /* Make sure colormap indexes can be represented by JSAMPLEs */
        if (desired > MAXNUMCOLORS)
          ERREXIT1(cinfo, JERR_QUANT_MANY_COLORS, MAXNUMCOLORS);
        cquantize->sv_colormap = (*cinfo->mem->alloc_sarray)
          ((j_common_ptr) cinfo,JPOOL_IMAGE, (JDIMENSION) desired, (JDIMENSION) 3);
        cquantize->desired = desired;
      } else
        cquantize->sv_colormap = NULL;

      /* Only F-S dithering or no dithering is supported. */
      /* If user asks for ordered dither, give him F-S. */
      if (cinfo->dither_mode != JDITHER_NONE)
        cinfo->dither_mode = JDITHER_FS;

      /* Allocate Floyd-Steinberg workspace if necessary.
       * This isn't really needed until pass 2, but again it is FAR storage.
       * Although we will cope with a later change in dither_mode,
       * we do not promise to honor max_memory_to_use if dither_mode changes.
       */
      if (cinfo->dither_mode == JDITHER_FS) {
        cquantize->fserrors = (FSERRPTR) (*cinfo->mem->alloc_large)
          ((j_common_ptr) cinfo, JPOOL_IMAGE,
           (size_t) ((cinfo->output_width + 2) * (3 * SIZEOF(FSERROR))));
        /* Might as well create the error-limiting table too. */
        init_error_limit(cinfo);
      }
    }

    #endif /* QUANT_2PASS_SUPPORTED */