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;
  register 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.
 */
{