inv_cmap.c

/*
 * This software is copyrighted as noted below.  It may be freely copied,
 * modified, and redistributed, provided that the copyright notice is
 * preserved on all copies.
 *
 * There is no warranty or other guarantee of fitness for this software,
 * it is provided solely "as is".  Bug reports or fixes may be sent
 * to the author, who may or may not act on them as he desires.
 *
 * You may not include this software in a program or other software product
 * without supplying the source, or without informing the end-user that the
 * source is available for no extra charge.
 *
 * If you modify this software, you should include a notice giving the
 * name of the person performing the modification, the date of modification,
 * and the reason for such modification.
 */
/*
 * inv_cmap.c - Compute an inverse colormap.
 *
 * Author:	Spencer W. Thomas
 * 		EECS Dept.
 * 		University of Michigan
 * Date:	Thu Sep 20 1990
 * Copyright (c) 1990, University of Michigan
 *
 * $Id$
 */

#include <math.h>
#include <stdio.h>

#ifndef NO_INV_CMAP_TRACKING

#ifdef DEBUG
static int cred, cgreen, cblue;
static int red, green;
static unsigned char *zrgbp;
#endif
static int bcenter, gcenter, rcenter;
static long gdist, rdist, cdist;
static long cbinc, cginc, crinc;
static unsigned long *gdp, *rdp, *cdp;
static unsigned char *grgbp, *rrgbp, *crgbp;
static int gstride, rstride;
static long x, xsqr, colormax;
static int cindex;
#ifdef INSTRUMENT_IT
static long outercount = 0, innercount = 0;
#endif

#ifdef USE_PROTOTYPES
static void maxfill( unsigned long *, long );
static int redloop( void );
static int greenloop( int );
static int blueloop( int );
#else
static void maxfill();
static int redloop();
static int greenloop();
static int blueloop();
#endif


/*****************************************************************
 * TAG( inv_cmap )
 *
 * Compute an inverse colormap efficiently.
 * Inputs:
 * 	colors:		Number of colors in the forward colormap.
 * 	colormap:	The forward colormap.
 * 	bits:		Number of quantization bits.  The inverse
 * 			colormap will have (2^bits)^3 entries.
 * 	dist_buf:	An array of (2^bits)^3 long integers to be
 * 			used as scratch space.
 * Outputs:
 * 	rgbmap:		The output inverse colormap.  The entry
 * 			rgbmap[(r<<(2*bits)) + (g<<bits) + b]
 * 			is the colormap entry that is closest to the
 * 			(quantized) color (r,g,b).
 * Assumptions:
 * 	Quantization is performed by right shift (low order bits are
 * 	truncated).  Thus, the distance to a quantized color is
 * 	actually measured to the color at the center of the cell
 * 	(i.e., to r+.5, g+.5, b+.5, if (r,g,b) is a quantized color).
 * Algorithm:
 * 	Uses a "distance buffer" algorithm:
 * 	The distance from each representative in the forward color map
 * 	to each point in the rgb space is computed.  If it is less
 * 	than the distance currently stored in dist_buf, then the
 * 	corresponding entry in rgbmap is replaced with the current
 * 	representative (and the dist_buf entry is replaced with the
 * 	new distance).
 *
 * 	The distance computation uses an efficient incremental formulation.
 *
 * 	Distances are computed "outward" from each color.  If the
 * 	colors are evenly distributed in color space, the expected
 * 	number of cells visited for color I is N^3/I.
 * 	Thus, the complexity of the algorithm is O(log(K) N^3),
 * 	where K = colors, and N = 2^bits.
 */

/*
 * Here's the idea:  scan from the "center" of each cell "out"
 * until we hit the "edge" of the cell -- that is, the point
 * at which some other color is closer -- and stop.  In 1-D,
 * this is simple:
 * 	for i := here to max do
 * 		if closer then buffer[i] = this color
 * 		else break
 * 	repeat above loop with i := here-1 to min by -1
 *
 * In 2-D, it's trickier, because along a "scan-line", the
 * region might start "after" the "center" point.  A picture
 * might clarify:
 *		 |    ...
 *               | ...	.
 *              ...    	.
 *           ... |      .
 *          .    +     	.
 *           .          .
 *            .         .
 *             .........
 *
 * The + marks the "center" of the above region.  On the top 2
 * lines, the region "begins" to the right of the "center".
 *
 * Thus, we need a loop like this:
 * 	detect := false
 * 	for i := here to max do
 * 		if closer then
 * 			buffer[..., i] := this color
 * 			if !detect then
 * 				here = i
 * 				detect = true
 * 		else
 * 			if detect then
 * 				break
 *
 * Repeat the above loop with i := here-1 to min by -1.  Note that
 * the "detect" value should not be reinitialized.  If it was
 * "true", and center is not inside the cell, then none of the
 * cell lies to the left and this loop should exit
 * immediately.
 *
 * The outer loops are similar, except that the "closer" test
 * is replaced by a call to the "next in" loop; its "detect"
 * value serves as the test.  (No assignment to the buffer is
 * done, either.)
 *
 * Each time an outer loop starts, the "here", "min", and
 * "max" values of the next inner loop should be
 * re-initialized to the center of the cell, 0, and cube size,
 * respectively.  Otherwise, these values will carry over from
 * one "call" to the inner loop to the next.  This tracks the
 * edges of the cell and minimizes the number of
 * "unproductive" comparisons that must be made.
 *
 * Finally, the inner-most loop can have the "if !detect"
 * optimized out of it by splitting it into two loops: one
 * that finds the first color value on the scan line that is
 * in this cell, and a second that fills the cell until
 * another one is closer:
 *  	if !detect then	    {needed for "down" loop}
 * 	    for i := here to max do
 * 		if closer then
 * 			buffer[..., i] := this color
 * 			detect := true
 * 			break
 *	for i := i+1 to max do
 *		if closer then
 * 			buffer[..., i] := this color
 * 		else
 * 			break
 *
 * In this implementation, each level will require the
 * following variables.  Variables labelled (l) are local to each
 * procedure.  The ? should be replaced with r, g, or b:
 *  	cdist:	    	The distance at the starting point.
 * 	?center:	The value of this component of the color
 *  	c?inc:	    	The initial increment at the ?center position.
 * 	?stride:	The amount to add to the buffer
 * 			pointers (dp and rgbp) to get to the
 * 			"next row".
 * 	min(l):		The "low edge" of the cell, init to 0
 * 	max(l):		The "high edge" of the cell, init to
 * 			colormax-1
 * 	detect(l):    	True if this row has changed some
 * 	    	    	buffer entries.
 *  	i(l): 	    	The index for this row.
 *  	?xx:	    	The accumulated increment value.
 *
 *  	here(l):    	The starting index for this color.  The
 *  	    	    	following variables are associated with here,
 *  	    	    	in the sense that they must be updated if here
 *  	    	    	is changed.
 *  	?dist:	    	The current distance for this level.  The
 *  	    	    	value of dist from the previous level (g or r,
 *  	    	    	for level b or g) initializes dist on this
 *  	    	    	level.  Thus gdist is associated with here(b)).
 *  	?inc:	    	The initial increment for the row.
 *  	?dp:	    	Pointer into the distance buffer.  The value
 *  	    	    	from the previous level initializes this level.
 *  	?rgbp:	    	Pointer into the rgb buffer.  The value
 *  	    	    	from the previous level initializes this level.
 *
 * The blue and green levels modify 'here-associated' variables (dp,
 * rgbp, dist) on the green and red levels, respectively, when here is
 * changed.
 */

void
inv_cmap( colors, colormap, bits, dist_buf, rgbmap )
int colors, bits;
unsigned char *colormap[3], *rgbmap;
unsigned long *dist_buf;
{
    int nbits = 8 - bits;

    colormax = 1 << bits;
    x = 1 << nbits;
    xsqr = 1 << (2 * nbits);

    /* Compute "strides" for accessing the arrays. */
    gstride = colormax;
    rstride = colormax * colormax;

#ifdef INSTRUMENT_IT
	outercount = 0;
	innercount = 0;
#endif
    maxfill( dist_buf, colormax );

    for ( cindex = 0; cindex < colors; cindex++ )
    {
	/*
	 * Distance formula is
	 * (red - map[0])^2 + (green - map[1])^2 + (blue - map[2])^2
	 *
	 * Because of quantization, we will measure from the center of
	 * each quantized "cube", so blue distance is
	 * 	(blue + x/2 - map[2])^2,
	 * where x = 2^(8 - bits).
	 * The step size is x, so the blue increment is
	 * 	2*x*blue - 2*x*map[2] + 2*x^2
	 *
	 * Now, b in the code below is actually blue/x, so our
	 * increment will be 2*(b*x^2 + x^2 - x*map[2]).  For
	 * efficiency, we will maintain this quantity in a separate variable
	 * that will be updated incrementally by adding 2*x^2 each time.
	 */
	/* The initial position is the cell containing the colormap
	 * entry.  We get this by quantizing the colormap values.
	 */
	rcenter = colormap[0][cindex] >> nbits;
	gcenter = colormap[1][cindex] >> nbits;
	bcenter = colormap[2][cindex] >> nbits;
#ifdef DEBUG
	cred = colormap[0][cindex];
	cgreen = colormap[1][cindex];
	cblue = colormap[2][cindex];
	fprintf( stderr, "---Starting %d: %d,%d,%d -> %d,%d,%d\n",
		 cindex, cred, cgreen, cblue,
		 rcenter, gcenter, bcenter );
	zrgbp = rgbmap;
#endif

	rdist = colormap[0][cindex] - (rcenter * x + x/2);
	gdist = colormap[1][cindex] - (gcenter * x + x/2);
	cdist = colormap[2][cindex] - (bcenter * x + x/2);
	cdist = rdist*rdist + gdist*gdist + cdist*cdist;

	crinc = 2 * ((rcenter + 1) * xsqr - (colormap[0][cindex] * x));
	cginc = 2 * ((gcenter + 1) * xsqr - (colormap[1][cindex] * x));
	cbinc = 2 * ((bcenter + 1) * xsqr - (colormap[2][cindex] * x));

	/* Array starting points. */
	cdp = dist_buf + rcenter * rstride + gcenter * gstride + bcenter;
	crgbp = rgbmap + rcenter * rstride + gcenter * gstride + bcenter;

	(void)redloop();
    }
#ifdef INSTRUMENT_IT
    fprintf( stderr, "K = %d, N = %d, outer count = %ld, inner count = %ld\n",
	     colors, colormax, outercount, innercount );
#endif
}

/* redloop -- loop up and down from red center. */
static int
redloop()
{
    int detect;
    int r;
    int first;
    long txsqr = xsqr + xsqr;
    static long rxx;

    detect = 0;

    /* Basic loop up. */
    for ( r = rcenter, rdist = cdist, rxx = crinc,
	  rdp = cdp, rrgbp = crgbp, first = 1;
	  r < colormax;
	  r++, rdp += rstride, rrgbp += rstride,
	  rdist += rxx, rxx += txsqr, first = 0 )
    {
#ifdef DEBUG
	red = r;
#endif
	if ( greenloop( first ) )
	    detect = 1;
	else if ( detect )
	    break;
    }

    /* Basic loop down. */
    for ( r = rcenter - 1, rxx = crinc - txsqr, rdist = cdist - rxx,
	  rdp = cdp - rstride, rrgbp = crgbp - rstride, first = 1;
	  r >= 0;
	  r--, rdp -= rstride, rrgbp -= rstride,
	  rxx -= txsqr, rdist -= rxx, first = 0 )
    {
#ifdef DEBUG
	red = r;
#endif
	if ( greenloop( first ) )
	    detect = 1;
	else if ( detect )
	    break;
    }

    return detect;
}

/* greenloop -- loop up and down from green center. */
static int
greenloop( restart )
int restart;
{
    int detect;
    int g;
    int first;
    long txsqr = xsqr + xsqr;
    static int here, min, max;
#ifdef MINMAX_TRACK
    static int prevmax, prevmin;
    int thismax, thismin;
#endif
    static long ginc, gxx, gcdist;	/* "gc" variables maintain correct */
    static unsigned long *gcdp;		/*  values for bcenter position, */
    static unsigned char *gcrgbp;	/*  despite modifications by blueloop */
					/*  to gdist, gdp, grgbp. */

    if ( restart )
    {
	here = gcenter;
	min = 0;
	max = colormax - 1;
	ginc = cginc;
#ifdef MINMAX_TRACK
	prevmax = 0;
	prevmin = colormax;
#endif
    }

#ifdef MINMAX_TRACK
    thismin = min;
    thismax = max;
#endif
    detect = 0;

    /* Basic loop up. */
    for ( g = here, gcdist = gdist = rdist, gxx = ginc,
	  gcdp = gdp = rdp, gcrgbp = grgbp = rrgbp, first = 1;
	  g <= max;
	  g++, gdp += gstride, gcdp += gstride, grgbp += gstride, gcrgbp += gstride,
	  gdist += gxx, gcdist += gxx, gxx += txsqr, first = 0 )
    {
#ifdef DEBUG
	green = g;
#endif
	if ( blueloop( first ) )
	{
	    if ( !detect )
	    {
		/* Remember here and associated data! */
		if ( g > here )
		{
		    here = g;
		    rdp = gcdp;
		    rrgbp = gcrgbp;
		    rdist = gcdist;
		    ginc = gxx;
#ifdef MINMAX_TRACK
		    thismin = here;
#endif
#ifdef DEBUG
		    fprintf( stderr, "===Adjusting green here up at %d,%d\n",
			     red, here );
#endif
		}
		detect = 1;
	    }
	}
	else if ( detect )
	{
#ifdef MINMAX_TRACK
	    thismax = g - 1;
#endif
	    break;
	}
    }

    /* Basic loop down. */
    for ( g = here - 1, gxx = ginc - txsqr, gcdist = gdist = rdist - gxx,
	  gcdp = gdp = rdp - gstride, gcrgbp = grgbp = rrgbp - gstride,
	  first = 1;
	  g >= min;
	  g--, gdp -= gstride, gcdp -= gstride, grgbp -= gstride, gcrgbp -= gstride,
	  gxx -= txsqr, gdist -= gxx, gcdist -= gxx, first = 0 )
    {
#ifdef DEBUG
	green = g;
#endif
	if ( blueloop( first ) )
	{
	    if ( !detect )
	    {
		/* Remember here! */
		here = g;
		rdp = gcdp;
		rrgbp = gcrgbp;
		rdist = gcdist;
		ginc = gxx;
#ifdef MINMAX_TRACK
		thismax = here;
#endif
#ifdef DEBUG
		fprintf( stderr, "===Adjusting green here down at %d,%d\n",
			 red, here );
#endif
		detect = 1;
	    }
	}
	else if ( detect )
	{
#ifdef MINMAX_TRACK
	    thismin = g + 1;
#endif
	    break;
	}
    }

#ifdef MINMAX_TRACK
    /* If we saw something, update the edge trackers.  For now, only
     * tracks edges that are "shrinking" (min increasing, max
     * decreasing.
     */
    if ( detect )
    {
	if ( thismax < prevmax )
	    max = thismax;

	prevmax = thismax;

	if ( thismin > prevmin )
	    min = thismin;

	prevmin = thismin;
    }
#endif

    return detect;
}

/* blueloop -- loop up and down from blue center. */
static int
blueloop( restart )
int restart;
{
    int detect;
    register unsigned long *dp;
    register unsigned char *rgbp;
    register unsigned long bdist;
    register long bxx;
    register int b, i = cindex;
    register long txsqr = xsqr + xsqr;
    register int lim;
    static int here, min, max;
#ifdef MINMAX_TRACK
    static int prevmin, prevmax;
    int thismin, thismax;
#ifdef DMIN_DMAX_TRACK
    static int dmin, dmax;
#endif /* DMIN_DMAX_TRACK */
#endif /* MINMAX_TRACK */
    static long binc;
#ifdef DEBUG
    long dist, tdist;
#endif

    if ( restart )
    {
	here = bcenter;
	min = 0;
	max = colormax - 1;
	binc = cbinc;
#ifdef MINMAX_TRACK
	prevmin = colormax;
	prevmax = 0;
#ifdef DMIN_DMAX_TRACK
	dmin = 0;
	dmax = 0;
#endif /* DMIN_DMAX_TRACK */
#endif /* MINMAX_TRACK */
    }

    detect = 0;
#ifdef MINMAX_TRACK
    thismin = min;
    thismax = max;
#endif
#ifdef DEBUG
    tdist = cred - red * x - x/2;
    dist = tdist*tdist;
    tdist = cgreen - green * x - x/2;
    dist += tdist*tdist;
    tdist = cblue - here * x - x/2;
    dist += tdist*tdist;
    if ( gdist != dist )
	fprintf( stderr, "*** At %d,%d,%d; dist = %ld != gdist = %ld\n",
		 red, green, here, dist, gdist );
    if ( grgbp != zrgbp + red*rstride + green*gstride + here )
	fprintf( stderr, "*** At %d,%d,%d: buffer pointer is at %d,%d,%d\n",
		 red, green, here,
		 (grgbp - zrgbp) / rstride,
		 ((grgbp - zrgbp) % rstride) / gstride,
		 (grgbp - zrgbp) % gstride );
#endif /* DEBUG */

    /* Basic loop up. */
    /* First loop just finds first applicable cell. */
    for ( b = here, bdist = gdist, bxx = binc, dp = gdp, rgbp = grgbp, lim = max;
	  b <= lim;
	  b++, dp++, rgbp++,
	  bdist += bxx, bxx += txsqr )
    {
#ifdef INSTRUMENT_IT
	outercount++;
#endif
	if ( *dp > bdist )
	{
	    /* Remember new 'here' and associated data! */
	    if ( b > here )
	    {
		here = b;
		gdp = dp;
		grgbp = rgbp;
		gdist = bdist;
		binc = bxx;
#ifdef MINMAX_TRACK
		thismin = here;
#endif
#ifdef DEBUG
		fprintf( stderr, "===Adjusting blue here up at %d,%d,%d\n",
			 red, green, here );

		tdist = cred - red * x - x/2;
		dist = tdist*tdist;
		tdist = cgreen - green * x - x/2;
		dist += tdist*tdist;
		tdist = cblue - here * x - x/2;
		dist += tdist*tdist;
		if ( gdist != dist )
		    fprintf( stderr,
	     "*** Adjusting here up at %d,%d,%d; dist = %ld != gdist = %ld\n",
			     red, green, here, dist, gdist );
#endif /* DEBUG */
	    }
	    detect = 1;
#ifdef INSTRUMENT_IT
	    outercount--;
#endif
	    break;
	}
    }
    /* Second loop fills in a run of closer cells. */
    for ( ;
	  b <= lim;
	  b++, dp++, rgbp++,
	  bdist += bxx, bxx += txsqr )
    {
#ifdef INSTRUMENT_IT
	outercount++;
#endif
	if ( *dp > bdist )
	{
#ifdef INSTRUMENT_IT
	    innercount++;
#endif
	    *dp = bdist;
	    *rgbp = i;
	}
	else
	{
#ifdef MINMAX_TRACK
	    thismax = b - 1;
#endif
	    break;
	}
    }
#ifdef DEBUG
    tdist = cred - red * x - x/2;
    dist = tdist*tdist;
    tdist = cgreen - green * x - x/2;
    dist += tdist*tdist;
    tdist = cblue - b * x - x/2;
    dist += tdist*tdist;
    if ( bdist != dist )
	fprintf( stderr,
		 "*** After up loop at %d,%d,%d; dist = %ld != bdist = %ld\n",
		 red, green, b, dist, bdist );
#endif /* DEBUG */

    /* Basic loop down. */
    /* Do initializations here, since the 'find' loop might not get
     * executed.
     */
    lim = min;
    b = here - 1;
    bxx = binc - txsqr;
    bdist = gdist - bxx;
    dp = gdp - 1;
    rgbp = grgbp - 1;
    /* The 'find' loop is executed only if we didn't already find
     * something.
     */
    if ( !detect )
	for ( ;
	      b >= lim;
	      b--, dp--, rgbp--,
	      bxx -= txsqr, bdist -= bxx )
	{
#ifdef INSTRUMENT_IT
	    outercount++;
#endif
	    if ( *dp > bdist )
	    {
		/* Remember here! */
		/* No test for b against here necessary because b <
		 * here by definition.
		 */
		here = b;
		gdp = dp;
		grgbp = rgbp;
		gdist = bdist;
		binc = bxx;
#ifdef MINMAX_TRACK
		thismax = here;
#endif
		detect = 1;
#ifdef DEBUG
		fprintf( stderr, "===Adjusting blue here down at %d,%d,%d\n",
			 red, green, here );
		tdist = cred - red * x - x/2;
		dist = tdist*tdist;
		tdist = cgreen - green * x - x/2;
		dist += tdist*tdist;
		tdist = cblue - here * x - x/2;
		dist += tdist*tdist;
		if ( gdist != dist )
		    fprintf( stderr,
	     "*** Adjusting here down at %d,%d,%d; dist = %ld != gdist = %ld\n",
			     red, green, here, dist, gdist );
#endif /* DEBUG */
#ifdef INSTRUMENT_IT
		outercount--;
#endif
		break;
	    }
	}
    /* The 'update' loop. */
    for ( ;
	  b >= lim;
	  b--, dp--, rgbp--,
	  bxx -= txsqr, bdist -= bxx )
    {
#ifdef INSTRUMENT_IT
	outercount++;
#endif
	if ( *dp > bdist )
	{
#ifdef INSTRUMENT_IT
	    innercount++;
#endif
	    *dp = bdist;
	    *rgbp = i;
	}
	else
	{
#ifdef MINMAX_TRACK
	    thismin = b + 1;
#endif
	    break;
	}
    }

#ifdef DEBUG
    tdist = cred - red * x - x/2;
    dist = tdist*tdist;
    tdist = cgreen - green * x - x/2;
    dist += tdist*tdist;
    tdist = cblue - b * x - x/2;
    dist += tdist*tdist;
    if ( bdist != dist )
	fprintf( stderr,
		 "*** After down loop at %d,%d,%d; dist = %ld != bdist = %ld\n",
		 red, green, b, dist, bdist );
#endif /* DEBUG */

	/* If we saw something, update the edge trackers. */
#ifdef MINMAX_TRACK
    if ( detect )
    {
#ifdef DMIN_DMAX_TRACK
	/* Predictively track.  Not clear this is a win. */
	/* If there was a previous line, update the dmin/dmax values. */
	if ( prevmax >= prevmin )
	{
	    if ( thismin > 0 )
		dmin = thismin - prevmin - 1;
	    else
		dmin = 0;
	    if ( thismax < colormax - 1 )
		dmax = thismax - prevmax + 1;
	    else
		dmax = 0;
	    /* Update the min and max values by the differences. */
	    max = thismax + dmax;
	    if ( max >= colormax )
		max = colormax - 1;
	    min = thismin + dmin;
	    if ( min < 0 )
		min = 0;
	}
#else /* !DMIN_DMAX_TRACK */
	/* Only tracks edges that are "shrinking" (min increasing, max
	 * decreasing.
	 */
	if ( thismax < prevmax )
	    max = thismax;

	if ( thismin > prevmin )
	    min = thismin;
#endif /* DMIN_DMAX_TRACK */

	/* Remember the min and max values. */
	prevmax = thismax;
	prevmin = thismin;
    }
#endif /* MINMAX_TRACK */

    return detect;
}

static void
maxfill( buffer, side )
unsigned long *buffer;
long side;
{
    register unsigned long maxv = ~0L;
    register long i;
    register unsigned long *bp;

    for ( i = colormax * colormax * colormax, bp = buffer;
	  i > 0;
	  i--, bp++ )
	*bp = maxv;
}

#else /* !NO_INV_CMAP_TRACKING */
/*****************************************************************
 * TAG( inv_cmap )
 *
 * Compute an inverse colormap efficiently.
 * Inputs:
 * 	colors:		Number of colors in the forward colormap.
 * 	colormap:	The forward colormap.
 * 	bits:		Number of quantization bits.  The inverse
 * 			colormap will have (2^bits)^3 entries.
 * 	dist_buf:	An array of (2^bits)^3 long integers to be
 * 			used as scratch space.
 * Outputs:
 * 	rgbmap:		The output inverse colormap.  The entry
 * 			rgbmap[(r<<(2*bits)) + (g<<bits) + b]
 * 			is the colormap entry that is closest to the
 * 			(quantized) color (r,g,b).
 * Assumptions:
 * 	Quantization is performed by right shift (low order bits are
 * 	truncated).  Thus, the distance to a quantized color is
 * 	actually measured to the color at the center of the cell
 * 	(i.e., to r+.5, g+.5, b+.5, if (r,g,b) is a quantized color).
 * Algorithm:
 * 	Uses a "distance buffer" algorithm:
 * 	The distance from each representative in the forward color map
 * 	to each point in the rgb space is computed.  If it is less
 * 	than the distance currently stored in dist_buf, then the
 * 	corresponding entry in rgbmap is replaced with the current
 * 	representative (and the dist_buf entry is replaced with the
 * 	new distance).
 *
 * 	The distance computation uses an efficient incremental formulation.
 *
 * 	Right now, distances are computed for all entries in the rgb
 * 	space.  Thus, the complexity of the algorithm is O(K N^3),
 * 	where K = colors, and N = 2^bits.
 */
void
inv_cmap( colors, colormap, bits, dist_buf, rgbmap )
int colors, bits;
unsigned char *colormap[3], *rgbmap;
unsigned long *dist_buf;
{
    register unsigned long *dp;
    register unsigned char *rgbp;
    register long bdist, bxx;
    register int b, i;
    int nbits = 8 - bits;
    register int colormax = 1 << bits;
    register long xsqr = 1 << (2 * nbits);
    int x = 1 << nbits;
    int rinc, ginc, binc, r, g;
    long rdist, gdist, rxx, gxx;
#ifdef INSTRUMENT_IT
    long outercount = 0, innercount = 0;
#endif

    for ( i = 0; i < colors; i++ )
    {
	/*
	 * Distance formula is
	 * (red - map[0])^2 + (green - map[1])^2 + (blue - map[2])^2
	 *
	 * Because of quantization, we will measure from the center of
	 * each quantized "cube", so blue distance is
	 * 	(blue + x/2 - map[2])^2,
	 * where x = 2^(8 - bits).
	 * The step size is x, so the blue increment is
	 * 	2*x*blue - 2*x*map[2] + 2*x^2
	 *
	 * Now, b in the code below is actually blue/x, so our
	 * increment will be 2*x*x*b + (2*x^2 - 2*x*map[2]).  For
	 * efficiency, we will maintain this quantity in a separate variable
	 * that will be updated incrementally by adding 2*x^2 each time.
	 */
	rdist = colormap[0][i] - x/2;
	gdist = colormap[1][i] - x/2;
	bdist = colormap[2][i] - x/2;
	rdist = rdist*rdist + gdist*gdist + bdist*bdist;

	rinc = 2 * (xsqr - (colormap[0][i] << nbits));
	ginc = 2 * (xsqr - (colormap[1][i] << nbits));
	binc = 2 * (xsqr - (colormap[2][i] << nbits));
	dp = dist_buf;
	rgbp = rgbmap;
	for ( r = 0, rxx = rinc;
	      r < colormax;
	      rdist += rxx, r++, rxx += xsqr + xsqr )
	    for ( g = 0, gdist = rdist, gxx = ginc;
		  g < colormax;
		  gdist += gxx, g++, gxx += xsqr + xsqr )
		for ( b = 0, bdist = gdist, bxx = binc;
		      b < colormax;
		      bdist += bxx, b++, dp++, rgbp++,
		      bxx += xsqr + xsqr )
		{
#ifdef INSTRUMENT_IT
		    outercount++;
#endif
		    if ( i == 0 || *dp > bdist )
		    {
#ifdef INSTRUMENT_IT
			innercount++;
#endif
			*dp = bdist;
			*rgbp = i;
		    }
		}
    }
#ifdef INSTRUMENT_IT
    fprintf( stderr, "K = %d, N = %d, outer count = %ld, inner count = %ld\n",
	     colors, colormax, outercount, innercount );
#endif
}

#endif /* NO_INV_CMAP_TRACKING */