Funko sources as released by Rotacak.HEADmaster

1 files changed, 1310 insertions, 0 deletions

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+/*
+ * jquant2.c
+ *
+ * Copyright (C) 1991-1995, 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 UINT16 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 INT16 FSERROR;		/* 16 bits should be enough */
+typedef int LOCFSERROR;		/* use 'int' for calculation temps */
+#else
+typedef INT32 FSERROR;		/* may need more than 16 bits */
+typedef INT32 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 */
+
+  boolean needs_zeroed;		/* TRUE if next pass must zero histogram */
+
+  /* Variables for Floyd-Steinberg dithering */
+  FSERRPTR fserrors;		/* accumulated errors */
+  boolean 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 output_buf, int num_rows)
+{
+  my_cquantize_ptr cquantize = (my_cquantize_ptr) cinfo->cquantize;
+  register JSAMPROW ptr;
+  register histptr histp;
+  register 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 */
+  INT32 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 */
+{
+  register boxptr boxp;
+  register int i;
+  register 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 */
+{
+  register boxptr boxp;
+  register int i;
+  register INT32 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;
+  INT32 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;
+  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.
+ */
+{
+  int numcolors = cinfo->actual_number_of_colors;
+  int maxc0, maxc1, maxc2;
+  int centerc0, centerc1, centerc2;
+  int i, x, ncolors;
+  INT32 minmaxdist, min_dist, max_dist, tdist;
+  INT32 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;
+  register INT32 * bptr;	/* pointer into bestdist[] array */
+  JSAMPLE * cptr;		/* pointer into bestcolor[] array */
+  INT32 dist0, dist1;		/* initial distance values */
+  register INT32 dist2;		/* current distance in inner loop */
+  INT32 xx0, xx1;		/* distance increments */
+  register INT32 xx2;
+  INT32 inc0, inc1, inc2;	/* initial values for increments */
+  /* This array holds the distance to the nearest-so-far color for each cell */
+  INT32 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;
+  register JSAMPLE * cptr;	/* pointer into bestcolor[] array */
+  register 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;
+  register JSAMPROW inptr, outptr;
+  register histptr cachep;
+  register 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;
+  register 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 */
+  register 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 */
+      { register 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.
+       */
+      { register 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 cinfo)
+{
+  /* no work */
+}
+
+
+/*
+ * Initialize for each processing pass.
+ */
+
+METHODDEF void
+start_pass_2_quant (j_decompress_ptr cinfo, boolean 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 */