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/*
 * jquant2.c
 *
 * Copyright (C) 1991-1996, Thomas G. Lane.
 * Modified 2011 by Guido Vollbeding.
 * 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;