DOOM-3-BFG

jquant2.cpp (54356B)

---

 /*
  * 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 */