/*

 * jquant2.c

 *

 * Copyright (C) 1991-1996, 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;

	}