DOOM-3-BFG/neo/renderer/jpeg-6/jquant2.cpp

/*
 * 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 */