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RGB->Indexed quantizer version 3.0 (the rest of the commit started a year 

2002-02-10  Adam D. Moss  <adam@gimp.org>

	* app/core/gimpimage-convert.[ch]:
	RGB->Indexed quantizer version 3.0 (the rest of the commit started
	a year ago -- whoops).  Divide colours within CIE L*a*b* space using
	CPercep module (cpercep.[ch]), colour-match and dither likewise,
	change the underlying box selection criteria and division point
	logic, bump luminance precision upwards, etc. etc.

	* app/core/cpercep.[ch] (new files): utility module used by
	quantizer for quantifying perceptual colour distances

	* app/core/gimpimage-convert-data.h (new file): move the big
	static data arrays out of gimpimage-convert.c

	* app/core/gimpimage-convert-fsdither.h: static-ify data

	* app/core/Makefile.am: add cpercep.[ch] and gimpimage-convert-data.h
This commit is contained in:
Adam D. Moss 2002-02-10 18:33:16 +00:00 committed by Adam D. Moss
parent ceed8eae4e
commit ee4115a86e
10 changed files with 2501 additions and 475 deletions
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19
ChangeLog
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@ -1,3 +1,22 @@
2002-02-10 Adam D. Moss <adam@gimp.org>
* app/core/gimpimage-convert.[ch]:
RGB->Indexed quantizer version 3.0 (the rest of the commit started
a year ago -- whoops). Divide colours within CIE L*a*b* space using
CPercep module (cpercep.[ch]), colour-match and dither likewise,
change the underlying box selection criteria and division point
logic, bump luminance precision upwards, etc. etc.
* app/core/cpercep.[ch] (new files): utility module used by
quantizer for quantifying perceptual colour distances
* app/core/gimpimage-convert-data.h (new file): move the big
static data arrays out of gimpimage-convert.c
* app/core/gimpimage-convert-fsdither.h: static-ify data
* app/core/Makefile.am: add cpercep.[ch] and gimpimage-convert-data.h
2002-02-10 Michael Natterer <mitch@gimp.org>
* app/undo.c: removed #if 0'ed old display update hackery. Don't

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app/base/cpercep.c Normal file
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/*
Copyright (C) 1999-2002 Adam D. Moss (the "Author"). All Rights Reserved.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is fur-
nished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FIT-
NESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHOR BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CON-
NECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Except as contained in this notice, the name of the Author of the
Software shall not be used in advertising or otherwise to promote the sale,
use or other dealings in this Software without prior written authorization
from the Author.
*/
/*
cpercep.c: The CPercep Functions v0.9: 2002-02-10
Adam D. Moss: adam@gimp.org <http://www.foxbox.org/adam/code/cpercep/>
This code module concerns itself with conversion from a hard-coded
RGB colour space (sRGB by default) to CIE L*a*b* and back again with
(primarily) precision and (secondarily) speed, oriented largely
towards the purposes of quantifying the PERCEPTUAL difference between
two arbitrary RGB colours with a minimum of fuss.
Motivation One: The author is disheartened at the amount of graphics
processing software around which uses weighted or non-weighted
Euclidean distance between co-ordinates within a (poorly-defined) RGB
space as the basis of what should really be an estimate of perceptual
difference to the human eye. Certainly it's fast to do it that way,
but please think carefully about whether your particular application
should be tolerating sloppy results for the sake of real-time response.
Motivation Two: Lack of tested, re-usable and free code available
for this purpose. The difficulty in finding something similar to
CPercep with a free license motivated this project; I hope that this
code also serves to illustrate how to perform the
R'G'B'->XYZ->L*a*b*->XYZ->R'G'B' transformation correctly since I
was distressed to note how many of the equations and code snippets
on the net were omitting the reverse transform and/or were using
incorrectly-derived or just plain wrong constants.
TODO: document functions, rename erroneously-named arguments
*/
#include <stdlib.h>
#include <math.h>
/* defines:
SANITY: emits warnings when passed non-sane colours (and usually
corrects them) -- useful when debugging.
APPROX: speeds up the conversion from RGB to the colourspace by
assuming that the RGB values passed in are integral and definitely
in the range 0->255
SRGB: assumes that the RGB values being passed in (and out) are
destined for an sRGB-alike display device (a typical modern monitor)
-- if you change this then you'll probably want to change ASSUMED_GAMMA,
the phosphor colours and the white point definition.
*/
/*#define SANITY*/
#define APPROX
#define SRGB
#ifdef SANITY
/* for fprintf */
#include <stdio.h>
#endif
#include "cpercep.h"
#ifdef SRGB
#define ASSUMED_GAMMA (2.2F)
#else
/*#define ASSUMED_GAMMA (2.591F)*/
#define ASSUMED_GAMMA (2.2F)
#endif
#define REV_GAMMA ((1.0F / ASSUMED_GAMMA))
/* define characteristics of the source RGB space (and the space
within which we try to behave linearly). */
/* Phosphor colours: */
/* sRGB/HDTV phosphor colours */
static const double pxr = 0.64F;
static const double pyr = 0.33F;
static const double pxg = 0.30F;
static const double pyg = 0.60F;
static const double pxb = 0.15F;
static const double pyb = 0.06F;
/* White point: */
/* D65 (6500K) (recommended but not a common display default) */
static const double lxn = 0.312713F;
static const double lyn = 0.329016F;
/* D50 (5000K) */
/*static const double lxn = 0.3457F; */
/*static const double lyn = 0.3585F; */
/* D55 (5500K) */
/*static const double lxn = 0.3324F; */
/*static const double lyn = 0.3474F; */
/* D93 (9300K) (a common monitor default, but poor colour reproduction) */
/* static const double lxn = 0.2848F; */
/* static const double lyn = 0.2932F; */
/* illum E (normalized) */
/*static const double lxn = 1.0/3.0F; */
/*static const double lyn = 1.0/3.0F; */
/* illum C (average sunlight) */
/*static const double lxn = 0.3101F; */
/*static const double lyn = 0.3162F; */
/* illum B (direct sunlight) */
/*static const double lxn = 0.3484F; */
/*static const double lyn = 0.3516F; */
/* illum A (tungsten lamp) */
/*static const double lxn = 0.4476F; */
/*static const double lyn = 0.4074F; */
static const double LRAMP = 7.99959199F;
static double xnn, znn;
static double powtable[256];
#define CLAMP(x,l,u) ((x)<(l)?(l):((x)>(u)?(u):(x)))
static void
init_powtable(const double gamma)
{
int i;
#ifndef SRGB
/* pure gamma function */
for (i=0; i<256; i++)
{
powtable[i] = pow((i)/255.0F, gamma);
}
#else
/* sRGB gamma curve */
for (i=0; i<11 /* 0.03928 * 255 */; i++)
{
powtable[i] = (i) / (255.0F * 12.92F);
}
for (; i<256; i++)
{
powtable[i] = pow( (((i) / 255.0F) + 0.055F) / 1.055F, 2.4F);
}
#endif
}
typedef double CMatrix[3][3];
typedef double CVector[3];
static CMatrix Mrgb_to_xyz, Mxyz_to_rgb;
static int
Minvert (const CMatrix src, CMatrix dest)
{
double det;
dest[0][0] = src[1][1] * src[2][2] - src[1][2] * src[2][1];
dest[0][1] = src[0][2] * src[2][1] - src[0][1] * src[2][2];
dest[0][2] = src[0][1] * src[1][2] - src[0][2] * src[1][1];
dest[1][0] = src[1][2] * src[2][0] - src[1][0] * src[2][2];
dest[1][1] = src[0][0] * src[2][2] - src[0][2] * src[2][0];
dest[1][2] = src[0][2] * src[1][0] - src[0][0] * src[1][2];
dest[2][0] = src[1][0] * src[2][1] - src[1][1] * src[2][0];
dest[2][1] = src[0][1] * src[2][0] - src[0][0] * src[2][1];
dest[2][2] = src[0][0] * src[1][1] - src[0][1] * src[1][0];
det =
src[0][0] * dest[0][0] +
src[0][1] * dest[1][0] +
src[0][2] * dest[2][0];
if (det <= 0.0F)
{
#ifdef SANITY
fprintf(stderr, "\n\007 XXXX det: %f\n", det);
#endif
return 0;
}
dest[0][0] /= det;
dest[0][1] /= det;
dest[0][2] /= det;
dest[1][0] /= det;
dest[1][1] /= det;
dest[1][2] /= det;
dest[2][0] /= det;
dest[2][1] /= det;
dest[2][2] /= det;
return 1;
}
static void
rgbxyzrgb_init(void)
{
init_powtable (ASSUMED_GAMMA);
xnn = lxn / lyn;
/* ynn taken as 1.0 */
znn = (1.0F - (lxn + lyn)) / lyn;
{
CMatrix MRC, MRCi;
double C1,C2,C3;
MRC[0][0] = pxr;
MRC[0][1] = pxg;
MRC[0][2] = pxb;
MRC[1][0] = pyr;
MRC[1][1] = pyg;
MRC[1][2] = pyb;
MRC[2][0] = 1.0F - (pxr + pyr);
MRC[2][1] = 1.0F - (pxg + pyg);
MRC[2][2] = 1.0F - (pxb + pyb);
Minvert (MRC, MRCi);
C1 = MRCi[0][0]*xnn + MRCi[0][1] + MRCi[0][2]*znn;
C2 = MRCi[1][0]*xnn + MRCi[1][1] + MRCi[1][2]*znn;
C3 = MRCi[2][0]*xnn + MRCi[2][1] + MRCi[2][2]*znn;
Mrgb_to_xyz[0][0] = MRC[0][0] * C1;
Mrgb_to_xyz[0][1] = MRC[0][1] * C2;
Mrgb_to_xyz[0][2] = MRC[0][2] * C3;
Mrgb_to_xyz[1][0] = MRC[1][0] * C1;
Mrgb_to_xyz[1][1] = MRC[1][1] * C2;
Mrgb_to_xyz[1][2] = MRC[1][2] * C3;
Mrgb_to_xyz[2][0] = MRC[2][0] * C1;
Mrgb_to_xyz[2][1] = MRC[2][1] * C2;
Mrgb_to_xyz[2][2] = MRC[2][2] * C3;
Minvert (Mrgb_to_xyz, Mxyz_to_rgb);
}
}
static void
xyz_to_rgb (double *inx_outr,
double *iny_outg,
double *inz_outb)
{
const double x = *inx_outr;
const double y = *iny_outg;
const double z = *inz_outb;
*inx_outr = Mxyz_to_rgb[0][0]*x + Mxyz_to_rgb[0][1]*y + Mxyz_to_rgb[0][2]*z;
*iny_outg = Mxyz_to_rgb[1][0]*x + Mxyz_to_rgb[1][1]*y + Mxyz_to_rgb[1][2]*z;
*inz_outb = Mxyz_to_rgb[2][0]*x + Mxyz_to_rgb[2][1]*y + Mxyz_to_rgb[2][2]*z;
}
static void
rgb_to_xyz (double *inr_outx,
double *ing_outy,
double *inb_outz)
{
const double r = *inr_outx;
const double g = *ing_outy;
const double b = *inb_outz;
*inr_outx = Mrgb_to_xyz[0][0]*r + Mrgb_to_xyz[0][1]*g + Mrgb_to_xyz[0][2]*b;
*ing_outy = Mrgb_to_xyz[1][0]*r + Mrgb_to_xyz[1][1]*g + Mrgb_to_xyz[1][2]*b;
*inb_outz = Mrgb_to_xyz[2][0]*r + Mrgb_to_xyz[2][1]*g + Mrgb_to_xyz[2][2]*b;
}
/* call this before using the CPercep function */
void
init_conversions(void)
{
rgbxyzrgb_init();
}
const static inline double
ffunc(const double t)
{
if (t > 0.008856F)
{
return (cbrt(t));
}
else
{
return (7.787F * t + 16.0F/116.0F);
}
}
const static inline double
ffunc_inv(const double t)
{
if (t > 0.206893F)
{
return (t * t * t);
}
else
{
return ((t - 16.0F/116.0F) / 7.787F);
}
}
static void
xyz_to_lab (double *inx,
double *iny,
double *inz)
{
double L,a,b;
double ffuncY;
const double X = *inx;
const double Y = *iny;
const double Z = *inz;
if (Y > 0.0F)
{
if (Y > 0.008856F)
{
L = (116.0F * cbrt(Y)) - 16.0F;
}
else
{
L = (Y * 903.3F);
}
#ifdef SANITY
if (L < 0.0F)
{
fprintf(stderr, " <eek1>%f \007",(float)L);
}
if (L > 100.0F)
{
fprintf(stderr, " <eek2>%f \007",(float)L);
}
#endif
}
else
{
L = 0.0;
}
ffuncY = ffunc(Y);
a = 500.0F * (ffunc(X/xnn) - ffuncY);
b = 200.0F * (ffuncY - ffunc(Z/znn));
*inx = L;
*iny = a;
*inz = b;
}
static void
lab_to_xyz (double *inl,
double *ina,
double *inb)
{
double X,Y,Z;
double P;
const double L = *inl;
const double a = *ina;
const double b = *inb;
if (L > LRAMP)
{
P = Y = (L + 16.0F) / 116.0F;
Y = Y * Y * Y;
}
else
{
Y = L / 903.3F;
P = 7.787F * Y + 16.0F/116.0F;
}
X = (P + a / 500.0F);
X = xnn * ffunc_inv(X);
Z = (P - b / 200.0F);
Z = znn * ffunc_inv(Z);
#ifdef SANITY
if (X<-0.00000F)
{
if (X<-0.0001F)
fprintf(stderr,"{badX %f {%f,%f,%f}}",X,L,a,b);
X = 0.0F;
}
if (Y<-0.00000F)
{
if (Y<-0.0001F)
fprintf(stderr,"{badY %f}",Y);
Y = 0.0F;
}
if (Z<-0.00000F)
{
if (Z<-0.1F)
fprintf(stderr,"{badZ %f}",Z);
Z = 0.0F;
}
#endif
*inl = X;
*ina = Y;
*inb = Z;
}
void
rgb_to_space (double inr, double ing, double inb,
double* outr, double* outg, double* outb)
{
#ifdef APPROX
#ifdef SANITY
/* ADM extra sanity */
if ((inr) > 255.0F ||
(ing) > 255.0F ||
(inb) > 255.0F ||
(inr) < -0.0F ||
(ing) < -0.0F ||
(inb) < -0.0F
)
abort();
#endif /* SANITY */
inr = powtable[(int)inr];
ing = powtable[(int)ing];
inb = powtable[(int)inb];
#else
#ifdef SRGB
/* sRGB gamma curve */
if (inr <= (0.03928F * 255.0F))
inr = inr / (255.0F * 12.92F);
else
inr = pow( (inr + (0.055F * 255.0F)) / (1.055F * 255.0F), 2.4F);
if (ing <= (0.03928F * 255.0F))
ing = ing / (255.0F * 12.92F);
else
ing = pow( (ing + (0.055F * 255.0F)) / (1.055F * 255.0F), 2.4F);
if (inb <= (0.03928F * 255.0F))
inb = inb / (255.0F * 12.92F);
else
inb = pow( (inb + (0.055F * 255.0F)) / (1.055F * 255.0F), 2.4F);
#else
/* pure gamma function */
inr = pow((inr)/255.0F, ASSUMED_GAMMA);
ing = pow((ing)/255.0F, ASSUMED_GAMMA);
inb = pow((inb)/255.0F, ASSUMED_GAMMA);
#endif /* SRGB */
#endif /* APPROX */
#ifdef SANITY
/* ADM extra sanity */
if ((inr) > 1.0F ||
(ing) > 1.0F ||
(inb) > 1.0F ||
(inr) < 0.0F ||
(ing) < 0.0F ||
(inb) < 0.0F
)
{
fprintf(stderr, "%%");
/* abort(); */
}
#endif /* SANITY */
rgb_to_xyz(&inr, &ing, &inb);
#ifdef SANITY
if (inr < 0.0F || ing < 0.0F || inb < 0.0F)
{
fprintf(stderr," [BAD2 XYZ: %f,%f,%f]\007 ",
inr,ing,inb);
}
#endif /* SANITY */
xyz_to_lab(&inr, &ing, &inb);
*outr = inr;
*outg = ing;
*outb = inb;
}
void
space_to_rgb (double inr, double ing, double inb,
double* outr, double* outg, double* outb)
{
lab_to_xyz(&inr, &ing, &inb);
#ifdef SANITY
if (inr<-0.0F || ing<-0.0F || inb<-0.0F)
{
fprintf(stderr," [BAD1 XYZ: %f,%f,%f]\007 ",
inr,ing,inb);
}
#endif
xyz_to_rgb(&inr, &ing, &inb);
/* yes, essential. :( */
inr = CLAMP(inr,0.0F,1.0F);
ing = CLAMP(ing,0.0F,1.0F);
inb = CLAMP(inb,0.0F,1.0F);
#ifdef SRGB
if (inr <= 0.0030402477F)
inr = inr * (12.92F * 255.0F);
else
inr = pow(inr, 1.0F/2.4F) * (1.055F * 255.0F) - (0.055F * 255.0F);
if (ing <= 0.0030402477F)
ing = ing * (12.92F * 255.0F);
else
ing = pow(ing, 1.0F/2.4F) * (1.055F * 255.0F) - (0.055F * 255.0F);
if (inb <= 0.0030402477F)
inb = inb * (12.92F * 255.0F);
else
inb = pow(inb, 1.0F/2.4F) * (1.055F * 255.0F) - (0.055F * 255.0F);
#else
inr = 255.0F * pow(inr, REV_GAMMA);
ing = 255.0F * pow(ing, REV_GAMMA);
inb = 255.0F * pow(inb, REV_GAMMA);
#endif
*outr = inr;
*outg = ing;
*outb = inb;
}
#if 0
/* EXPERIMENTAL SECTION */
const double
xscaler(const double start, const double end,
const double me, const double him)
{
return start + ((end-start) * him) / (me + him);
}
void
mix_colours (const double L1, const double a1, const double b1,
const double L2, const double a2, const double b2,
double *rtnL, double *rtna, double *rtnb,
double mass1, double mass2)
{
double w1, w2;
#if 0
*rtnL = xscaler (L1, L2, mass1, mass2);
*rtna = xscaler (a1, a2, mass1, mass2);
*rtnb = xscaler (b1, b2, mass1, mass2);
#else
#if 1
w1 = mass1 * L1;
w2 = mass2 * L2;
#else
w1 = mass1 * (L1*L1*L1);
w2 = mass2 * (L2*L2*L2);
#endif
*rtnL = xscaler (L1, L2, mass1, mass2);
if (w1 <= 0.0 &&
w2 <= 0.0)
{
*rtna =
*rtnb = 0.0;
#ifdef SANITY
/* fprintf(stderr, "\007OUCH. "); */
#endif
}
else
{
*rtna = xscaler(a1, a2, w1, w2);
*rtnb = xscaler(b1, b2, w1, w2);
}
#endif
}
#endif /* EXPERIMENTAL SECTION */

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#ifndef __CPERCEP_H__
#define __CPERCEP_H__
/*
Copyright (C) 1997-2002 Adam D. Moss (the "Author"). All Rights Reserved.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is fur-
nished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FIT-
NESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHOR BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CON-
NECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Except as contained in this notice, the name of the Author of the
Software shall not be used in advertising or otherwise to promote the sale,
use or other dealings in this Software without prior written authorization
from the Author.
*/
/*
cpercep.c: The CPercep Functions v0.9: 2002-02-10
Adam D. Moss: adam@gimp.org <http://www.foxbox.org/adam/code/cpercep/>
TODO: document functions, rename erroneously-named arguments
*/
void
init_conversions(void);
void
rgb_to_space (double inr, double ing, double inb,
double* outr, double* outg, double* outb);
void
space_to_rgb (double inr, double ing, double inb,
double* outr, double* outg, double* outb);
/* This is in the header so that it can potentially be inlined. */
static const double
distance_space (const double L1, const double a1, const double b1,
const double L2, const double a2, const double b2)
{
const double Ld = L1 - L2;
const double ad = a1 - a2;
const double bd = b1 - b2;
return (Ld*Ld + ad*ad + bd*bd);
}
/* EXPERIMENTAL */
#if 0
void
mix_colours (const double L1, const double a1, const double b1,
const double L2, const double a2, const double b2,
double *rtnL, double *rtna, double *rtnb,
double mass1, double mass2);
/* util function */
const double
xscaler(const double start, const double end,
const double me, const double him);
#define MF(L) ((L)<=0.0 ? 0.0 : 1.0)
#endif /* EXPERIMENTAL */
#endif /* __CPERCEP_H__ */

3
app/core/Makefile.am
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@ -18,6 +18,8 @@ noinst_LIBRARIES = libappcore.a
libappcore_a_sources = @STRIP_BEGIN@ \
core-enums.h \
core-types.h \
cpercep.c \
cpercep.h \
gimp.c \
gimp.h \
gimpbrush.c \
@ -82,6 +84,7 @@ libappcore_a_sources = @STRIP_BEGIN@ \
gimpimage-convert.c \
gimpimage-convert.h \
gimpimage-convert-fsdither.h \
gimpimage-convert-data.h \
gimpimage-crop.c \
gimpimage-crop.h \
gimpimage-duplicate.c \

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/*
Copyright (C) 1999-2002 Adam D. Moss (the "Author"). All Rights Reserved.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is fur-
nished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FIT-
NESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHOR BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CON-
NECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Except as contained in this notice, the name of the Author of the
Software shall not be used in advertising or otherwise to promote the sale,
use or other dealings in this Software without prior written authorization
from the Author.
*/
/*
cpercep.c: The CPercep Functions v0.9: 2002-02-10
Adam D. Moss: adam@gimp.org <http://www.foxbox.org/adam/code/cpercep/>
This code module concerns itself with conversion from a hard-coded
RGB colour space (sRGB by default) to CIE L*a*b* and back again with
(primarily) precision and (secondarily) speed, oriented largely
towards the purposes of quantifying the PERCEPTUAL difference between
two arbitrary RGB colours with a minimum of fuss.
Motivation One: The author is disheartened at the amount of graphics
processing software around which uses weighted or non-weighted
Euclidean distance between co-ordinates within a (poorly-defined) RGB
space as the basis of what should really be an estimate of perceptual
difference to the human eye. Certainly it's fast to do it that way,
but please think carefully about whether your particular application
should be tolerating sloppy results for the sake of real-time response.
Motivation Two: Lack of tested, re-usable and free code available
for this purpose. The difficulty in finding something similar to
CPercep with a free license motivated this project; I hope that this
code also serves to illustrate how to perform the
R'G'B'->XYZ->L*a*b*->XYZ->R'G'B' transformation correctly since I
was distressed to note how many of the equations and code snippets
on the net were omitting the reverse transform and/or were using
incorrectly-derived or just plain wrong constants.
TODO: document functions, rename erroneously-named arguments
*/
#include <stdlib.h>
#include <math.h>
/* defines:
SANITY: emits warnings when passed non-sane colours (and usually
corrects them) -- useful when debugging.
APPROX: speeds up the conversion from RGB to the colourspace by
assuming that the RGB values passed in are integral and definitely
in the range 0->255
SRGB: assumes that the RGB values being passed in (and out) are
destined for an sRGB-alike display device (a typical modern monitor)
-- if you change this then you'll probably want to change ASSUMED_GAMMA,
the phosphor colours and the white point definition.
*/
/*#define SANITY*/
#define APPROX
#define SRGB
#ifdef SANITY
/* for fprintf */
#include <stdio.h>
#endif
#include "cpercep.h"
#ifdef SRGB
#define ASSUMED_GAMMA (2.2F)
#else
/*#define ASSUMED_GAMMA (2.591F)*/
#define ASSUMED_GAMMA (2.2F)
#endif
#define REV_GAMMA ((1.0F / ASSUMED_GAMMA))
/* define characteristics of the source RGB space (and the space
within which we try to behave linearly). */
/* Phosphor colours: */
/* sRGB/HDTV phosphor colours */
static const double pxr = 0.64F;
static const double pyr = 0.33F;
static const double pxg = 0.30F;
static const double pyg = 0.60F;
static const double pxb = 0.15F;
static const double pyb = 0.06F;
/* White point: */
/* D65 (6500K) (recommended but not a common display default) */
static const double lxn = 0.312713F;
static const double lyn = 0.329016F;
/* D50 (5000K) */
/*static const double lxn = 0.3457F; */
/*static const double lyn = 0.3585F; */
/* D55 (5500K) */
/*static const double lxn = 0.3324F; */
/*static const double lyn = 0.3474F; */
/* D93 (9300K) (a common monitor default, but poor colour reproduction) */
/* static const double lxn = 0.2848F; */
/* static const double lyn = 0.2932F; */
/* illum E (normalized) */
/*static const double lxn = 1.0/3.0F; */
/*static const double lyn = 1.0/3.0F; */
/* illum C (average sunlight) */
/*static const double lxn = 0.3101F; */
/*static const double lyn = 0.3162F; */
/* illum B (direct sunlight) */
/*static const double lxn = 0.3484F; */
/*static const double lyn = 0.3516F; */
/* illum A (tungsten lamp) */
/*static const double lxn = 0.4476F; */
/*static const double lyn = 0.4074F; */
static const double LRAMP = 7.99959199F;
static double xnn, znn;
static double powtable[256];
#define CLAMP(x,l,u) ((x)<(l)?(l):((x)>(u)?(u):(x)))
static void
init_powtable(const double gamma)
{
int i;
#ifndef SRGB
/* pure gamma function */
for (i=0; i<256; i++)
{
powtable[i] = pow((i)/255.0F, gamma);
}
#else
/* sRGB gamma curve */
for (i=0; i<11 /* 0.03928 * 255 */; i++)
{
powtable[i] = (i) / (255.0F * 12.92F);
}
for (; i<256; i++)
{
powtable[i] = pow( (((i) / 255.0F) + 0.055F) / 1.055F, 2.4F);
}
#endif
}
typedef double CMatrix[3][3];
typedef double CVector[3];
static CMatrix Mrgb_to_xyz, Mxyz_to_rgb;
static int
Minvert (const CMatrix src, CMatrix dest)
{
double det;
dest[0][0] = src[1][1] * src[2][2] - src[1][2] * src[2][1];
dest[0][1] = src[0][2] * src[2][1] - src[0][1] * src[2][2];
dest[0][2] = src[0][1] * src[1][2] - src[0][2] * src[1][1];
dest[1][0] = src[1][2] * src[2][0] - src[1][0] * src[2][2];
dest[1][1] = src[0][0] * src[2][2] - src[0][2] * src[2][0];
dest[1][2] = src[0][2] * src[1][0] - src[0][0] * src[1][2];
dest[2][0] = src[1][0] * src[2][1] - src[1][1] * src[2][0];
dest[2][1] = src[0][1] * src[2][0] - src[0][0] * src[2][1];
dest[2][2] = src[0][0] * src[1][1] - src[0][1] * src[1][0];
det =
src[0][0] * dest[0][0] +
src[0][1] * dest[1][0] +
src[0][2] * dest[2][0];
if (det <= 0.0F)
{
#ifdef SANITY
fprintf(stderr, "\n\007 XXXX det: %f\n", det);
#endif
return 0;
}
dest[0][0] /= det;
dest[0][1] /= det;
dest[0][2] /= det;
dest[1][0] /= det;
dest[1][1] /= det;
dest[1][2] /= det;
dest[2][0] /= det;
dest[2][1] /= det;
dest[2][2] /= det;
return 1;
}
static void
rgbxyzrgb_init(void)
{
init_powtable (ASSUMED_GAMMA);
xnn = lxn / lyn;
/* ynn taken as 1.0 */
znn = (1.0F - (lxn + lyn)) / lyn;
{
CMatrix MRC, MRCi;
double C1,C2,C3;
MRC[0][0] = pxr;
MRC[0][1] = pxg;
MRC[0][2] = pxb;
MRC[1][0] = pyr;
MRC[1][1] = pyg;
MRC[1][2] = pyb;
MRC[2][0] = 1.0F - (pxr + pyr);
MRC[2][1] = 1.0F - (pxg + pyg);
MRC[2][2] = 1.0F - (pxb + pyb);
Minvert (MRC, MRCi);
C1 = MRCi[0][0]*xnn + MRCi[0][1] + MRCi[0][2]*znn;
C2 = MRCi[1][0]*xnn + MRCi[1][1] + MRCi[1][2]*znn;
C3 = MRCi[2][0]*xnn + MRCi[2][1] + MRCi[2][2]*znn;
Mrgb_to_xyz[0][0] = MRC[0][0] * C1;
Mrgb_to_xyz[0][1] = MRC[0][1] * C2;
Mrgb_to_xyz[0][2] = MRC[0][2] * C3;
Mrgb_to_xyz[1][0] = MRC[1][0] * C1;
Mrgb_to_xyz[1][1] = MRC[1][1] * C2;
Mrgb_to_xyz[1][2] = MRC[1][2] * C3;
Mrgb_to_xyz[2][0] = MRC[2][0] * C1;
Mrgb_to_xyz[2][1] = MRC[2][1] * C2;
Mrgb_to_xyz[2][2] = MRC[2][2] * C3;
Minvert (Mrgb_to_xyz, Mxyz_to_rgb);
}
}
static void
xyz_to_rgb (double *inx_outr,
double *iny_outg,
double *inz_outb)
{
const double x = *inx_outr;
const double y = *iny_outg;
const double z = *inz_outb;
*inx_outr = Mxyz_to_rgb[0][0]*x + Mxyz_to_rgb[0][1]*y + Mxyz_to_rgb[0][2]*z;
*iny_outg = Mxyz_to_rgb[1][0]*x + Mxyz_to_rgb[1][1]*y + Mxyz_to_rgb[1][2]*z;
*inz_outb = Mxyz_to_rgb[2][0]*x + Mxyz_to_rgb[2][1]*y + Mxyz_to_rgb[2][2]*z;
}
static void
rgb_to_xyz (double *inr_outx,
double *ing_outy,
double *inb_outz)
{
const double r = *inr_outx;
const double g = *ing_outy;
const double b = *inb_outz;
*inr_outx = Mrgb_to_xyz[0][0]*r + Mrgb_to_xyz[0][1]*g + Mrgb_to_xyz[0][2]*b;
*ing_outy = Mrgb_to_xyz[1][0]*r + Mrgb_to_xyz[1][1]*g + Mrgb_to_xyz[1][2]*b;
*inb_outz = Mrgb_to_xyz[2][0]*r + Mrgb_to_xyz[2][1]*g + Mrgb_to_xyz[2][2]*b;
}
/* call this before using the CPercep function */
void
init_conversions(void)
{
rgbxyzrgb_init();
}
const static inline double
ffunc(const double t)
{
if (t > 0.008856F)
{
return (cbrt(t));
}
else
{
return (7.787F * t + 16.0F/116.0F);
}
}
const static inline double
ffunc_inv(const double t)
{
if (t > 0.206893F)
{
return (t * t * t);
}
else
{
return ((t - 16.0F/116.0F) / 7.787F);
}
}
static void
xyz_to_lab (double *inx,
double *iny,
double *inz)
{
double L,a,b;
double ffuncY;
const double X = *inx;
const double Y = *iny;
const double Z = *inz;
if (Y > 0.0F)
{
if (Y > 0.008856F)
{
L = (116.0F * cbrt(Y)) - 16.0F;
}
else
{
L = (Y * 903.3F);
}
#ifdef SANITY
if (L < 0.0F)
{
fprintf(stderr, " <eek1>%f \007",(float)L);
}
if (L > 100.0F)
{
fprintf(stderr, " <eek2>%f \007",(float)L);
}
#endif
}
else
{
L = 0.0;
}
ffuncY = ffunc(Y);
a = 500.0F * (ffunc(X/xnn) - ffuncY);
b = 200.0F * (ffuncY - ffunc(Z/znn));
*inx = L;
*iny = a;
*inz = b;
}
static void
lab_to_xyz (double *inl,
double *ina,
double *inb)
{
double X,Y,Z;
double P;
const double L = *inl;
const double a = *ina;
const double b = *inb;
if (L > LRAMP)
{
P = Y = (L + 16.0F) / 116.0F;
Y = Y * Y * Y;
}
else
{
Y = L / 903.3F;
P = 7.787F * Y + 16.0F/116.0F;
}
X = (P + a / 500.0F);
X = xnn * ffunc_inv(X);
Z = (P - b / 200.0F);
Z = znn * ffunc_inv(Z);
#ifdef SANITY
if (X<-0.00000F)
{
if (X<-0.0001F)
fprintf(stderr,"{badX %f {%f,%f,%f}}",X,L,a,b);
X = 0.0F;
}
if (Y<-0.00000F)
{
if (Y<-0.0001F)
fprintf(stderr,"{badY %f}",Y);
Y = 0.0F;
}
if (Z<-0.00000F)
{
if (Z<-0.1F)
fprintf(stderr,"{badZ %f}",Z);
Z = 0.0F;
}
#endif
*inl = X;
*ina = Y;
*inb = Z;
}
void
rgb_to_space (double inr, double ing, double inb,
double* outr, double* outg, double* outb)
{
#ifdef APPROX
#ifdef SANITY
/* ADM extra sanity */
if ((inr) > 255.0F ||
(ing) > 255.0F ||
(inb) > 255.0F ||
(inr) < -0.0F ||
(ing) < -0.0F ||
(inb) < -0.0F
)
abort();
#endif /* SANITY */
inr = powtable[(int)inr];
ing = powtable[(int)ing];
inb = powtable[(int)inb];
#else
#ifdef SRGB
/* sRGB gamma curve */
if (inr <= (0.03928F * 255.0F))
inr = inr / (255.0F * 12.92F);
else
inr = pow( (inr + (0.055F * 255.0F)) / (1.055F * 255.0F), 2.4F);
if (ing <= (0.03928F * 255.0F))
ing = ing / (255.0F * 12.92F);
else
ing = pow( (ing + (0.055F * 255.0F)) / (1.055F * 255.0F), 2.4F);
if (inb <= (0.03928F * 255.0F))
inb = inb / (255.0F * 12.92F);
else
inb = pow( (inb + (0.055F * 255.0F)) / (1.055F * 255.0F), 2.4F);
#else
/* pure gamma function */
inr = pow((inr)/255.0F, ASSUMED_GAMMA);
ing = pow((ing)/255.0F, ASSUMED_GAMMA);
inb = pow((inb)/255.0F, ASSUMED_GAMMA);
#endif /* SRGB */
#endif /* APPROX */
#ifdef SANITY
/* ADM extra sanity */
if ((inr) > 1.0F ||
(ing) > 1.0F ||
(inb) > 1.0F ||
(inr) < 0.0F ||
(ing) < 0.0F ||
(inb) < 0.0F
)
{
fprintf(stderr, "%%");
/* abort(); */
}
#endif /* SANITY */
rgb_to_xyz(&inr, &ing, &inb);
#ifdef SANITY
if (inr < 0.0F || ing < 0.0F || inb < 0.0F)
{
fprintf(stderr," [BAD2 XYZ: %f,%f,%f]\007 ",
inr,ing,inb);
}
#endif /* SANITY */
xyz_to_lab(&inr, &ing, &inb);
*outr = inr;
*outg = ing;
*outb = inb;
}
void
space_to_rgb (double inr, double ing, double inb,
double* outr, double* outg, double* outb)
{
lab_to_xyz(&inr, &ing, &inb);
#ifdef SANITY
if (inr<-0.0F || ing<-0.0F || inb<-0.0F)
{
fprintf(stderr," [BAD1 XYZ: %f,%f,%f]\007 ",
inr,ing,inb);
}
#endif
xyz_to_rgb(&inr, &ing, &inb);
/* yes, essential. :( */
inr = CLAMP(inr,0.0F,1.0F);
ing = CLAMP(ing,0.0F,1.0F);
inb = CLAMP(inb,0.0F,1.0F);
#ifdef SRGB
if (inr <= 0.0030402477F)
inr = inr * (12.92F * 255.0F);
else
inr = pow(inr, 1.0F/2.4F) * (1.055F * 255.0F) - (0.055F * 255.0F);
if (ing <= 0.0030402477F)
ing = ing * (12.92F * 255.0F);
else
ing = pow(ing, 1.0F/2.4F) * (1.055F * 255.0F) - (0.055F * 255.0F);
if (inb <= 0.0030402477F)
inb = inb * (12.92F * 255.0F);
else
inb = pow(inb, 1.0F/2.4F) * (1.055F * 255.0F) - (0.055F * 255.0F);
#else
inr = 255.0F * pow(inr, REV_GAMMA);
ing = 255.0F * pow(ing, REV_GAMMA);
inb = 255.0F * pow(inb, REV_GAMMA);
#endif
*outr = inr;
*outg = ing;
*outb = inb;
}
#if 0
/* EXPERIMENTAL SECTION */
const double
xscaler(const double start, const double end,
const double me, const double him)
{
return start + ((end-start) * him) / (me + him);
}
void
mix_colours (const double L1, const double a1, const double b1,
const double L2, const double a2, const double b2,
double *rtnL, double *rtna, double *rtnb,
double mass1, double mass2)
{
double w1, w2;
#if 0
*rtnL = xscaler (L1, L2, mass1, mass2);
*rtna = xscaler (a1, a2, mass1, mass2);
*rtnb = xscaler (b1, b2, mass1, mass2);
#else
#if 1
w1 = mass1 * L1;
w2 = mass2 * L2;
#else
w1 = mass1 * (L1*L1*L1);
w2 = mass2 * (L2*L2*L2);
#endif
*rtnL = xscaler (L1, L2, mass1, mass2);
if (w1 <= 0.0 &&
w2 <= 0.0)
{
*rtna =
*rtnb = 0.0;
#ifdef SANITY
/* fprintf(stderr, "\007OUCH. "); */
#endif
}
else
{
*rtna = xscaler(a1, a2, w1, w2);
*rtnb = xscaler(b1, b2, w1, w2);
}
#endif
}
#endif /* EXPERIMENTAL SECTION */

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#ifndef __CPERCEP_H__
#define __CPERCEP_H__
/*
Copyright (C) 1997-2002 Adam D. Moss (the "Author"). All Rights Reserved.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is fur-
nished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FIT-
NESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHOR BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CON-
NECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Except as contained in this notice, the name of the Author of the
Software shall not be used in advertising or otherwise to promote the sale,
use or other dealings in this Software without prior written authorization
from the Author.
*/
/*
cpercep.c: The CPercep Functions v0.9: 2002-02-10
Adam D. Moss: adam@gimp.org <http://www.foxbox.org/adam/code/cpercep/>
TODO: document functions, rename erroneously-named arguments
*/
void
init_conversions(void);
void
rgb_to_space (double inr, double ing, double inb,
double* outr, double* outg, double* outb);
void
space_to_rgb (double inr, double ing, double inb,
double* outr, double* outg, double* outb);
/* This is in the header so that it can potentially be inlined. */
static const double
distance_space (const double L1, const double a1, const double b1,
const double L2, const double a2, const double b2)
{
const double Ld = L1 - L2;
const double ad = a1 - a2;
const double bd = b1 - b2;
return (Ld*Ld + ad*ad + bd*bd);
}
/* EXPERIMENTAL */
#if 0
void
mix_colours (const double L1, const double a1, const double b1,
const double L2, const double a2, const double b2,
double *rtnL, double *rtna, double *rtnb,
double mass1, double mass2);
/* util function */
const double
xscaler(const double start, const double end,
const double me, const double him);
#define MF(L) ((L)<=0.0 ? 0.0 : 1.0)
#endif /* EXPERIMENTAL */
#endif /* __CPERCEP_H__ */

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/* The GIMP -- an image manipulation program
* Copyright (C) 1995 Spencer Kimball and Peter Mattis
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/* Misc data definitions used by the convert.c code module. Moved
out here simply to unclutter convert.c, mostly. */
#ifndef __CONVERT_DATA_H__
#define __CONVERT_DATA_H__
#include <glib.h>
/* 'web safe' palette. */
static const guchar webpal[] =
{
255,255,255,255,255,204,255,255,153,255,255,102,255,255,51,255,255,0,255,
204,255,255,204,204,255,204,153,255,204,102,255,204,51,255,204,0,255,153,
255,255,153,204,255,153,153,255,153,102,255,153,51,255,153,0,255,102,255,
255,102,204,255,102,153,255,102,102,255,102,51,255,102,0,255,51,255,255,
51,204,255,51,153,255,51,102,255,51,51,255,51,0,255,0,255,255,0,
204,255,0,153,255,0,102,255,0,51,255,0,0,204,255,255,204,255,204,
204,255,153,204,255,102,204,255,51,204,255,0,204,204,255,204,204,204,204,
204,153,204,204,102,204,204,51,204,204,0,204,153,255,204,153,204,204,153,
153,204,153,102,204,153,51,204,153,0,204,102,255,204,102,204,204,102,153,
204,102,102,204,102,51,204,102,0,204,51,255,204,51,204,204,51,153,204,
51,102,204,51,51,204,51,0,204,0,255,204,0,204,204,0,153,204,0,
102,204,0,51,204,0,0,153,255,255,153,255,204,153,255,153,153,255,102,
153,255,51,153,255,0,153,204,255,153,204,204,153,204,153,153,204,102,153,
204,51,153,204,0,153,153,255,153,153,204,153,153,153,153,153,102,153,153,
51,153,153,0,153,102,255,153,102,204,153,102,153,153,102,102,153,102,51,
153,102,0,153,51,255,153,51,204,153,51,153,153,51,102,153,51,51,153,
51,0,153,0,255,153,0,204,153,0,153,153,0,102,153,0,51,153,0,
0,102,255,255,102,255,204,102,255,153,102,255,102,102,255,51,102,255,0,
102,204,255,102,204,204,102,204,153,102,204,102,102,204,51,102,204,0,102,
153,255,102,153,204,102,153,153,102,153,102,102,153,51,102,153,0,102,102,
255,102,102,204,102,102,153,102,102,102,102,102,51,102,102,0,102,51,255,
102,51,204,102,51,153,102,51,102,102,51,51,102,51,0,102,0,255,102,
0,204,102,0,153,102,0,102,102,0,51,102,0,0,51,255,255,51,255,
204,51,255,153,51,255,102,51,255,51,51,255,0,51,204,255,51,204,204,
51,204,153,51,204,102,51,204,51,51,204,0,51,153,255,51,153,204,51,
153,153,51,153,102,51,153,51,51,153,0,51,102,255,51,102,204,51,102,
153,51,102,102,51,102,51,51,102,0,51,51,255,51,51,204,51,51,153,
51,51,102,51,51,51,51,51,0,51,0,255,51,0,204,51,0,153,51,
0,102,51,0,51,51,0,0,0,255,255,0,255,204,0,255,153,0,255,
102,0,255,51,0,255,0,0,204,255,0,204,204,0,204,153,0,204,102,
0,204,51,0,204,0,0,153,255,0,153,204,0,153,153,0,153,102,0,
153,51,0,153,0,0,102,255,0,102,204,0,102,153,0,102,102,0,102,
51,0,102,0,0,51,255,0,51,204,0,51,153,0,51,102,0,51,51,
0,51,0,0,0,255,0,0,204,0,0,153,0,0,102,0,0,51,0,0,0
};
/* Note: convert.c code currently makes assumptions about some of the
below defines, so small fixes are needed if they change... */
#define DM_WIDTH 128
#define DM_WIDTHMASK 127
#define DM_WIDTH_SHIFT 7
#define DM_HEIGHT 128
#define DM_HEIGHTMASK 127
/* This dither table was generated by Raph Levien using patented
technology (US Patent 5,276,535). The dither table itself is in the
public domain. */
static const guchar DM[128][128] =
{
{ 0, 41, 23, 5, 17, 39, 7, 15, 62, 23, 40, 51, 31, 47, 9, 32, 52, 27, 57, 25, 6, 61, 27, 52, 37, 7, 40, 63, 18, 36, 10, 42, 25, 62, 45, 34, 20, 42, 37, 14, 35, 29, 50, 10, 61, 2, 40, 8, 37, 12, 58, 22, 5, 41, 10, 39, 0, 60, 11, 46, 2, 55, 38, 17, 36, 59, 13, 54, 37, 56, 8, 29, 16, 13, 63, 22, 41, 55, 7, 20, 49, 14, 23, 55, 37, 23, 19, 36, 15, 49, 23, 63, 30, 14, 38, 27, 53, 13, 22, 41, 19, 31, 7, 19, 50, 30, 49, 16, 3, 32, 56, 40, 29, 34, 8, 48, 19, 45, 4, 51, 12, 46, 35, 49, 16, 42, 12, 62 },
{ 30, 57, 36, 54, 47, 34, 52, 27, 43, 4, 28, 7, 17, 36, 62, 13, 44, 7, 18, 48, 33, 21, 44, 14, 30, 47, 12, 33, 5, 55, 31, 58, 13, 30, 4, 17, 52, 10, 60, 26, 46, 0, 39, 27, 42, 22, 47, 25, 60, 32, 9, 38, 48, 17, 59, 30, 49, 18, 34, 25, 51, 19, 5, 48, 21, 8, 28, 46, 1, 32, 41, 19, 54, 47, 37, 18, 28, 11, 44, 30, 39, 56, 2, 33, 8, 42, 61, 28, 58, 8, 46, 9, 41, 4, 58, 7, 21, 48, 59, 10, 52, 14, 42, 57, 12, 25, 7, 53, 42, 24, 11, 50, 17, 59, 42, 2, 36, 60, 32, 17, 63, 29, 21, 7, 59, 32, 24, 39 },
{ 22, 8, 16, 32, 3, 25, 13, 57, 18, 45, 58, 39, 55, 20, 5, 42, 23, 34, 63, 1, 51, 10, 58, 4, 60, 23, 53, 27, 44, 21, 3, 48, 8, 50, 43, 54, 27, 32, 5, 55, 21, 58, 12, 53, 6, 36, 14, 50, 17, 29, 53, 15, 24, 52, 7, 36, 13, 42, 4, 53, 9, 35, 61, 26, 56, 32, 49, 15, 62, 23, 6, 60, 2, 31, 4, 48, 58, 38, 15, 61, 5, 25, 47, 28, 50, 15, 7, 40, 3, 32, 33, 52, 25, 50, 35, 42, 61, 3, 28, 36, 23, 63, 4, 33, 46, 62, 36, 23, 60, 6, 54, 28, 4, 37, 23, 55, 25, 8, 42, 54, 14, 6, 56, 38, 19, 52, 4, 46 },
{ 48, 53, 43, 12, 45, 63, 30, 37, 9, 34, 21, 1, 25, 47, 29, 58, 3, 54, 15, 39, 29, 17, 38, 35, 20, 43, 1, 49, 15, 59, 29, 39, 22, 35, 16, 23, 1, 47, 39, 18, 8, 44, 25, 31, 57, 19, 63, 4, 45, 3, 42, 61, 1, 31, 45, 20, 57, 29, 62, 21, 32, 41, 14, 44, 3, 39, 5, 34, 10, 43, 51, 35, 23, 52, 40, 10, 21, 1, 53, 18, 51, 43, 12, 62, 18, 54, 26, 51, 20, 57, 14, 1, 62, 16, 11, 18, 32, 39, 17, 44, 1, 48, 26, 37, 18, 2, 51, 14, 28, 45, 35, 18, 57, 13, 47, 11, 51, 20, 2, 39, 31, 47, 25, 1, 50, 11, 60, 7 },
{ 18, 28, 1, 56, 21, 10, 51, 2, 46, 54, 14, 61, 11, 50, 13, 38, 19, 31, 45, 9, 55, 24, 47, 5, 54, 9, 62, 11, 35, 8, 51, 14, 57, 6, 63, 40, 58, 14, 51, 28, 62, 34, 15, 48, 1, 41, 30, 35, 55, 21, 34, 11, 49, 37, 8, 52, 4, 23, 15, 43, 1, 58, 11, 23, 53, 16, 55, 26, 58, 18, 27, 12, 45, 14, 25, 63, 42, 33, 27, 35, 9, 31, 21, 38, 1, 44, 34, 12, 48, 38, 21, 44, 29, 47, 26, 53, 1, 46, 54, 8, 59, 29, 11, 55, 22, 41, 33, 20, 39, 1, 48, 9, 44, 32, 5, 62, 29, 44, 57, 23, 10, 58, 34, 43, 15, 37, 26, 33 },
{ 51, 38, 59, 24, 35, 42, 19, 60, 5, 32, 41, 26, 43, 33, 7, 53, 48, 11, 59, 23, 42, 2, 61, 30, 16, 40, 32, 24, 56, 41, 19, 33, 37, 26, 47, 9, 31, 22, 2, 45, 9, 54, 4, 37, 21, 52, 11, 23, 7, 57, 16, 25, 55, 18, 63, 27, 46, 39, 56, 10, 50, 37, 29, 47, 19, 63, 24, 9, 46, 2, 39, 60, 9, 57, 30, 7, 49, 11, 59, 3, 45, 57, 5, 60, 29, 22, 5, 60, 30, 9, 59, 18, 40, 6, 57, 36, 30, 12, 24, 34, 15, 40, 52, 6, 49, 9, 58, 4, 63, 12, 26, 61, 22, 53, 38, 16, 35, 14, 28, 50, 42, 17, 5, 28, 62, 20, 54, 12 },
{ 26, 6, 31, 15, 49, 6, 38, 27, 22, 49, 16, 56, 2, 62, 30, 21, 0, 36, 28, 6, 49, 32, 13, 52, 26, 50, 19, 46, 3, 26, 62, 0, 53, 12, 29, 3, 53, 41, 60, 24, 38, 13, 58, 16, 43, 9, 59, 39, 46, 28, 44, 40, 2, 33, 13, 41, 16, 6, 47, 31, 26, 17, 57, 6, 38, 0, 42, 36, 29, 52, 20, 31, 48, 0, 34, 56, 20, 36, 23, 54, 14, 41, 24, 37, 10, 55, 46, 25, 16, 45, 36, 4, 55, 23, 15, 8, 50, 62, 5, 56, 44, 20, 13, 28, 59, 31, 24, 47, 31, 52, 37, 17, 40, 0, 26, 49, 3, 60, 7, 33, 0, 61, 53, 40, 8, 45, 2, 41 },
{ 16, 63, 43, 4, 61, 24, 56, 13, 53, 8, 36, 12, 24, 41, 16, 46, 60, 26, 52, 39, 14, 57, 21, 37, 0, 45, 7, 59, 38, 17, 43, 10, 45, 20, 61, 43, 19, 11, 33, 17, 50, 32, 23, 61, 28, 49, 26, 0, 18, 51, 5, 60, 22, 58, 29, 0, 59, 34, 19, 62, 3, 52, 7, 44, 30, 59, 13, 50, 15, 62, 7, 17, 38, 22, 44, 15, 40, 4, 47, 28, 33, 17, 49, 16, 51, 40, 10, 56, 0, 53, 13, 49, 28, 38, 60, 21, 43, 19, 37, 27, 3, 51, 34, 39, 0, 45, 15, 43, 10, 21, 3, 55, 8, 33, 59, 10, 41, 18, 52, 24, 46, 20, 30, 13, 58, 22, 36, 57 },
{ 50, 34, 11, 47, 29, 17, 44, 0, 33, 63, 28, 46, 52, 5, 57, 10, 42, 18, 4, 63, 20, 8, 44, 10, 56, 34, 14, 29, 5, 54, 23, 59, 32, 49, 7, 34, 49, 27, 56, 0, 42, 7, 46, 3, 40, 6, 54, 32, 62, 13, 36, 10, 47, 8, 35, 49, 24, 51, 12, 40, 22, 35, 60, 12, 22, 51, 33, 4, 40, 25, 43, 55, 5, 54, 12, 61, 26, 51, 8, 62, 0, 53, 7, 63, 2, 32, 19, 34, 42, 24, 31, 63, 2, 10, 45, 33, 0, 48, 9, 61, 22, 47, 8, 62, 18, 56, 7, 54, 27, 57, 46, 30, 50, 19, 45, 30, 56, 36, 22, 47, 11, 38, 3, 51, 32, 48, 18, 9 },
{ 0, 21, 40, 19, 52, 9, 37, 48, 20, 40, 3, 18, 27, 38, 35, 22, 31, 56, 13, 35, 46, 28, 60, 40, 27, 18, 61, 50, 41, 30, 7, 36, 2, 25, 16, 57, 5, 15, 47, 29, 55, 19, 30, 52, 15, 34, 20, 12, 43, 30, 20, 54, 25, 44, 53, 12, 38, 5, 55, 27, 48, 15, 33, 27, 45, 8, 19, 28, 56, 11, 33, 49, 18, 36, 29, 2, 45, 16, 39, 19, 31, 43, 27, 35, 20, 52, 26, 6, 61, 11, 41, 17, 29, 51, 20, 56, 25, 32, 41, 17, 53, 31, 25, 14, 42, 23, 35, 16, 38, 6, 34, 12, 15, 62, 6, 21, 13, 1, 63, 9, 55, 27, 43, 25, 14, 4, 31, 55 },
{ 44, 29, 61, 2, 35, 58, 26, 15, 60, 10, 51, 59, 14, 55, 8, 50, 2, 44, 25, 51, 1, 33, 16, 4, 48, 36, 2, 21, 12, 57, 48, 13, 51, 55, 40, 28, 37, 62, 8, 39, 12, 63, 36, 10, 59, 24, 56, 47, 9, 50, 41, 1, 32, 17, 6, 21, 61, 30, 9, 43, 1, 54, 41, 2, 54, 37, 48, 61, 1, 46, 21, 3, 58, 24, 50, 32, 60, 10, 57, 25, 46, 12, 59, 4, 45, 13, 57, 47, 27, 39, 5, 58, 47, 14, 35, 4, 52, 13, 60, 6, 36, 10, 45, 55, 4, 50, 29, 2, 61, 50, 25, 58, 44, 24, 36, 42, 54, 28, 40, 32, 16, 56, 6, 62, 46, 39, 60, 23 },
{ 7, 48, 14, 54, 23, 40, 4, 45, 30, 22, 42, 32, 1, 44, 20, 29, 58, 8, 37, 19, 41, 54, 24, 58, 9, 53, 25, 46, 34, 16, 23, 38, 27, 11, 18, 1, 52, 21, 35, 22, 48, 5, 25, 45, 18, 38, 2, 27, 35, 4, 57, 15, 62, 39, 57, 28, 42, 16, 36, 60, 24, 18, 10, 63, 20, 5, 16, 23, 37, 14, 59, 27, 41, 8, 13, 42, 21, 35, 6, 50, 3, 38, 15, 48, 30, 39, 17, 3, 49, 14, 53, 33, 24, 7, 61, 44, 11, 39, 23, 49, 19, 58, 1, 32, 36, 12, 60, 41, 20, 13, 41, 4, 39, 1, 48, 8, 18, 51, 14, 44, 5, 37, 21, 34, 1, 26, 10, 37 },
{ 53, 36, 27, 9, 50, 12, 32, 55, 2, 57, 7, 17, 48, 34, 63, 15, 40, 26, 62, 11, 49, 6, 31, 39, 22, 42, 6, 63, 1, 39, 60, 4, 42, 61, 32, 45, 24, 44, 2, 60, 16, 41, 53, 1, 33, 61, 49, 17, 63, 23, 45, 26, 33, 3, 23, 46, 2, 50, 20, 4, 45, 34, 49, 30, 39, 58, 44, 31, 53, 34, 6, 52, 30, 47, 63, 1, 53, 22, 42, 31, 58, 23, 54, 22, 61, 8, 36, 59, 22, 35, 21, 1, 55, 40, 27, 16, 30, 54, 2, 29, 43, 16, 39, 63, 21, 46, 26, 10, 48, 32, 19, 53, 30, 56, 26, 60, 33, 4, 61, 23, 49, 59, 15, 53, 19, 58, 42, 16 },
{ 20, 5, 59, 46, 25, 62, 7, 19, 43, 25, 37, 61, 11, 24, 4, 54, 12, 52, 3, 32, 17, 61, 12, 47, 15, 55, 18, 31, 53, 28, 9, 50, 21, 6, 55, 9, 58, 14, 54, 26, 33, 7, 31, 58, 13, 21, 8, 42, 29, 6, 37, 11, 48, 52, 14, 60, 11, 39, 56, 32, 14, 58, 7, 26, 17, 4, 42, 8, 11, 47, 19, 38, 10, 17, 26, 37, 9, 55, 28, 13, 18, 40, 6, 33, 1, 43, 25, 11, 51, 7, 62, 43, 18, 37, 3, 57, 45, 9, 38, 58, 5, 52, 27, 7, 17, 53, 5, 57, 37, 2, 63, 9, 22, 15, 11, 38, 25, 45, 35, 0, 28, 10, 41, 30, 50, 8, 31, 57 },
{ 49, 33, 16, 38, 1, 42, 51, 34, 53, 14, 28, 49, 30, 56, 36, 23, 43, 20, 38, 56, 22, 45, 28, 0, 62, 35, 26, 44, 11, 19, 52, 35, 44, 15, 30, 38, 10, 31, 40, 4, 46, 50, 20, 40, 27, 44, 51, 14, 56, 53, 19, 59, 7, 29, 41, 19, 35, 25, 8, 52, 22, 44, 13, 53, 50, 32, 61, 24, 56, 25, 63, 0, 45, 57, 33, 59, 16, 46, 4, 62, 50, 11, 60, 37, 52, 19, 55, 29, 37, 46, 13, 26, 48, 10, 50, 34, 21, 63, 26, 13, 42, 33, 22, 55, 35, 28, 43, 15, 24, 51, 27, 34, 46, 49, 58, 3, 52, 9, 57, 19, 48, 55, 3, 35, 12, 45, 24, 3 },
{ 41, 11, 56, 28, 18, 31, 22, 10, 37, 6, 47, 13, 3, 41, 9, 46, 0, 48, 29, 6, 34, 10, 55, 37, 20, 8, 49, 3, 41, 59, 14, 25, 0, 63, 19, 47, 27, 51, 17, 57, 23, 10, 61, 6, 54, 3, 38, 31, 0, 22, 34, 43, 20, 55, 31, 0, 49, 63, 29, 38, 3, 62, 28, 40, 0, 22, 14, 35, 2, 48, 15, 43, 23, 14, 3, 29, 49, 20, 39, 34, 0, 44, 29, 9, 15, 47, 5, 42, 0, 31, 58, 5, 31, 61, 23, 15, 0, 47, 19, 50, 24, 3, 59, 11, 44, 0, 31, 59, 6, 42, 17, 60, 0, 39, 20, 31, 43, 17, 29, 40, 12, 25, 60, 22, 52, 15, 63, 29 },
{ 20, 52, 8, 44, 62, 4, 59, 49, 17, 63, 21, 39, 60, 18, 52, 27, 33, 59, 14, 51, 59, 43, 24, 5, 51, 30, 57, 17, 32, 5, 37, 56, 48, 34, 42, 3, 60, 5, 36, 13, 43, 37, 18, 34, 25, 12, 59, 24, 47, 36, 11, 50, 3, 38, 9, 58, 16, 5, 43, 18, 47, 10, 37, 18, 59, 46, 29, 52, 40, 12, 34, 28, 56, 36, 53, 7, 43, 8, 24, 52, 26, 17, 56, 43, 24, 32, 63, 20, 57, 16, 22, 52, 36, 8, 41, 56, 29, 32, 54, 7, 35, 57, 14, 48, 20, 62, 13, 39, 53, 29, 8, 45, 13, 29, 7, 61, 14, 54, 6, 63, 38, 32, 18, 43, 2, 39, 6, 47 },
{ 0, 58, 23, 35, 13, 46, 12, 39, 0, 31, 55, 24, 5, 35, 15, 61, 17, 5, 39, 25, 18, 2, 50, 33, 41, 13, 39, 23, 62, 46, 29, 12, 22, 8, 56, 25, 20, 49, 32, 62, 0, 56, 11, 46, 63, 42, 9, 16, 55, 5, 60, 15, 62, 26, 45, 21, 36, 51, 13, 57, 31, 24, 55, 6, 35, 9, 57, 5, 20, 60, 7, 51, 5, 19, 40, 25, 61, 32, 56, 12, 36, 48, 21, 2, 58, 12, 39, 28, 9, 50, 40, 12, 44, 18, 25, 49, 6, 38, 11, 62, 18, 46, 30, 9, 40, 25, 49, 19, 10, 36, 55, 22, 33, 52, 41, 18, 37, 27, 49, 21, 2, 46, 7, 53, 33, 61, 27, 35 },
{ 41, 31, 5, 39, 51, 26, 33, 57, 27, 41, 9, 44, 54, 29, 48, 7, 44, 36, 57, 10, 31, 63, 16, 45, 11, 60, 1, 47, 7, 20, 43, 3, 58, 36, 13, 52, 39, 7, 15, 28, 22, 48, 30, 21, 1, 29, 49, 44, 27, 17, 40, 30, 24, 42, 12, 53, 33, 7, 47, 20, 1, 42, 11, 49, 25, 43, 17, 32, 45, 27, 41, 21, 31, 62, 11, 49, 2, 15, 42, 5, 63, 7, 41, 27, 49, 6, 54, 23, 46, 34, 2, 28, 54, 3, 59, 12, 46, 17, 42, 28, 40, 1, 37, 51, 5, 55, 2, 34, 47, 16, 3, 62, 47, 5, 23, 56, 1, 44, 12, 34, 51, 16, 57, 11, 25, 17, 54, 13 },
{ 60, 26, 55, 18, 3, 60, 20, 6, 52, 15, 50, 19, 32, 11, 23, 53, 26, 21, 1, 47, 42, 27, 8, 58, 21, 27, 53, 36, 26, 54, 31, 50, 17, 30, 45, 1, 29, 59, 44, 53, 41, 4, 35, 58, 51, 19, 32, 4, 52, 34, 48, 8, 51, 5, 56, 2, 25, 61, 27, 38, 54, 27, 62, 21, 51, 1, 39, 62, 10, 50, 1, 58, 13, 47, 38, 18, 35, 54, 22, 51, 30, 19, 59, 34, 14, 32, 44, 4, 60, 15, 52, 62, 20, 43, 30, 35, 21, 60, 4, 52, 12, 24, 61, 18, 30, 42, 23, 61, 25, 50, 27, 38, 11, 59, 12, 35, 50, 30, 59, 24, 8, 42, 28, 37, 48, 9, 44, 21 },
{ 10, 47, 15, 50, 30, 43, 8, 45, 29, 2, 36, 59, 1, 58, 41, 3, 63, 31, 54, 20, 13, 55, 35, 38, 4, 44, 15, 9, 61, 2, 14, 38, 61, 10, 23, 54, 18, 12, 24, 2, 14, 55, 16, 8, 38, 14, 41, 60, 10, 23, 1, 58, 32, 17, 28, 37, 41, 15, 3, 60, 15, 33, 4, 36, 16, 59, 28, 14, 23, 55, 37, 18, 44, 28, 2, 57, 30, 10, 27, 46, 14, 38, 3, 53, 21, 61, 17, 35, 10, 41, 26, 7, 33, 9, 57, 1, 53, 37, 26, 20, 56, 48, 9, 33, 58, 16, 37, 7, 45, 1, 57, 15, 32, 26, 42, 23, 7, 20, 4, 54, 31, 62, 22, 1, 59, 30, 4, 51 },
{ 36, 2, 38, 11, 24, 36, 54, 22, 62, 47, 25, 8, 28, 45, 16, 38, 12, 43, 9, 37, 49, 3, 23, 52, 18, 30, 50, 33, 19, 42, 49, 26, 6, 40, 47, 35, 63, 38, 50, 33, 60, 26, 36, 47, 24, 57, 6, 26, 39, 63, 19, 44, 14, 46, 61, 9, 50, 30, 45, 23, 10, 50, 44, 8, 31, 54, 6, 46, 36, 4, 30, 54, 8, 52, 22, 41, 4, 60, 40, 0, 58, 24, 45, 10, 37, 1, 48, 30, 56, 17, 38, 48, 24, 47, 19, 39, 14, 8, 45, 32, 2, 34, 27, 44, 4, 52, 11, 56, 31, 21, 40, 19, 44, 51, 2, 63, 46, 58, 36, 43, 14, 5, 50, 38, 14, 56, 40, 23 },
{ 61, 46, 32, 63, 54, 1, 14, 34, 12, 40, 18, 49, 37, 10, 61, 30, 51, 24, 60, 7, 29, 40, 62, 11, 46, 58, 6, 56, 24, 10, 34, 52, 21, 59, 16, 3, 27, 5, 20, 46, 9, 40, 7, 62, 2, 30, 53, 15, 48, 10, 28, 35, 54, 6, 21, 34, 18, 55, 7, 40, 57, 19, 26, 60, 41, 13, 24, 51, 19, 61, 9, 25, 34, 15, 63, 11, 45, 17, 20, 47, 33, 8, 31, 62, 43, 26, 53, 7, 24, 59, 0, 13, 55, 4, 62, 27, 51, 31, 63, 15, 58, 7, 54, 14, 46, 22, 28, 43, 12, 63, 8, 54, 5, 17, 39, 33, 15, 10, 27, 17, 47, 34, 19, 45, 27, 12, 33, 17 },
{ 5, 28, 21, 7, 17, 48, 42, 58, 23, 4, 63, 14, 55, 21, 34, 5, 19, 0, 45, 17, 52, 15, 25, 32, 0, 22, 40, 13, 45, 62, 18, 0, 43, 11, 33, 55, 30, 42, 57, 19, 51, 31, 22, 43, 18, 45, 34, 0, 43, 31, 56, 3, 23, 40, 59, 0, 44, 13, 48, 35, 2, 32, 46, 0, 21, 48, 35, 3, 40, 32, 43, 59, 0, 48, 33, 26, 53, 36, 55, 12, 51, 16, 55, 5, 18, 29, 11, 39, 51, 19, 45, 31, 42, 21, 35, 6, 22, 47, 10, 38, 23, 50, 20, 36, 0, 60, 38, 4, 50, 35, 48, 34, 24, 57, 9, 53, 28, 48, 61, 0, 56, 24, 53, 3, 63, 6, 42, 57 },
{ 13, 53, 45, 40, 58, 27, 6, 16, 38, 51, 33, 30, 43, 2, 47, 56, 40, 50, 33, 57, 27, 5, 47, 42, 60, 36, 16, 54, 28, 4, 37, 57, 28, 51, 22, 8, 45, 14, 6, 39, 0, 54, 11, 59, 28, 12, 50, 21, 61, 13, 19, 38, 49, 11, 25, 37, 58, 29, 22, 63, 14, 56, 12, 53, 30, 63, 9, 57, 26, 12, 47, 16, 23, 39, 50, 6, 31, 2, 25, 6, 28, 41, 36, 22, 50, 57, 42, 3, 34, 8, 28, 61, 11, 50, 16, 54, 41, 0, 55, 43, 5, 29, 41, 63, 25, 16, 53, 18, 26, 10, 21, 0, 61, 30, 41, 22, 3, 38, 20, 39, 29, 8, 41, 16, 36, 52, 22, 19 },
{ 55, 34, 0, 25, 10, 32, 56, 44, 28, 0, 57, 7, 26, 53, 23, 8, 13, 35, 22, 12, 36, 60, 20, 8, 14, 29, 48, 2, 41, 49, 23, 13, 39, 7, 48, 58, 25, 53, 34, 62, 28, 16, 48, 4, 37, 56, 27, 5, 36, 52, 46, 7, 62, 33, 52, 11, 17, 53, 5, 28, 41, 24, 38, 17, 5, 39, 20, 45, 15, 56, 5, 38, 60, 8, 14, 57, 21, 48, 62, 39, 59, 13, 1, 60, 9, 32, 16, 63, 44, 25, 52, 15, 36, 2, 60, 29, 12, 33, 25, 17, 59, 45, 13, 8, 49, 32, 6, 40, 59, 29, 45, 37, 13, 47, 6, 55, 30, 45, 9, 52, 13, 59, 25, 47, 32, 1, 49, 30 },
{ 9, 39, 14, 61, 49, 37, 3, 20, 50, 13, 41, 19, 46, 17, 38, 59, 28, 62, 4, 44, 54, 1, 34, 51, 55, 7, 63, 32, 21, 8, 56, 31, 62, 19, 36, 1, 41, 17, 24, 12, 42, 35, 25, 52, 20, 8, 44, 59, 25, 2, 22, 42, 16, 29, 4, 46, 20, 36, 43, 9, 51, 8, 49, 26, 58, 33, 54, 1, 37, 29, 52, 20, 27, 45, 19, 35, 42, 16, 10, 32, 20, 49, 46, 27, 40, 4, 47, 22, 13, 55, 4, 47, 26, 44, 23, 40, 58, 19, 48, 13, 31, 2, 57, 34, 42, 19, 61, 32, 14, 55, 5, 51, 26, 19, 58, 16, 49, 14, 62, 5, 33, 44, 21, 7, 60, 26, 11, 41 },
{ 62, 24, 47, 29, 8, 19, 53, 11, 60, 24, 32, 61, 4, 55, 31, 2, 49, 16, 39, 9, 31, 24, 43, 17, 26, 38, 11, 25, 58, 43, 12, 35, 3, 46, 15, 32, 63, 4, 49, 56, 2, 60, 10, 32, 63, 17, 39, 12, 55, 30, 57, 9, 48, 55, 39, 24, 60, 2, 58, 31, 19, 61, 34, 3, 42, 11, 22, 46, 7, 61, 10, 42, 3, 55, 32, 1, 58, 28, 44, 54, 4, 34, 23, 15, 56, 20, 37, 58, 6, 30, 38, 18, 63, 9, 32, 5, 51, 3, 62, 37, 52, 18, 39, 23, 3, 51, 9, 47, 1, 23, 43, 15, 60, 35, 11, 40, 1, 36, 31, 26, 57, 2, 37, 54, 18, 44, 58, 16 },
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{ 0, 56, 8, 53, 14, 31, 61, 20, 55, 28, 62, 18, 35, 60, 25, 57, 7, 23, 39, 54, 47, 17, 43, 0, 40, 59, 29, 2, 56, 10, 37, 5, 43, 11, 29, 52, 1, 23, 54, 41, 59, 30, 55, 1, 62, 15, 33, 4, 43, 10, 47, 39, 1, 31, 40, 60, 49, 33, 7, 55, 26, 50, 31, 61, 8, 18, 21, 32, 44, 1, 25, 47, 18, 36, 30, 23, 59, 7, 40, 59, 27, 19, 38, 32, 44, 54, 40, 17, 38, 60, 27, 6, 35, 55, 10, 14, 44, 5, 50, 17, 38, 26, 42, 50, 18, 3, 44, 52, 2, 49, 7, 52, 15, 46, 62, 39, 55, 10, 31, 48, 3, 58, 33, 18, 61, 34, 13, 59 },
{ 39, 27, 63, 20, 35, 41, 4, 45, 26, 5, 38, 13, 44, 2, 50, 17, 37, 52, 2, 13, 28, 58, 24, 51, 21, 8, 34, 48, 27, 42, 18, 51, 31, 56, 5, 36, 38, 44, 4, 17, 26, 11, 38, 23, 42, 8, 56, 39, 24, 51, 5, 56, 21, 59, 14, 6, 18, 42, 22, 35, 16, 37, 3, 25, 39, 46, 63, 5, 50, 17, 58, 8, 55, 3, 50, 12, 43, 17, 47, 2, 51, 9, 62, 12, 1, 35, 13, 50, 1, 37, 12, 51, 19, 29, 46, 59, 22, 58, 33, 45, 22, 60, 10, 32, 61, 39, 8, 33, 25, 36, 20, 60, 38, 4, 21, 5, 28, 45, 12, 18, 42, 11, 49, 1, 27, 40, 6, 30 },
{ 24, 16, 42, 1, 50, 10, 48, 17, 33, 43, 24, 48, 21, 55, 31, 42, 10, 21, 63, 35, 49, 6, 33, 13, 41, 53, 10, 20, 60, 6, 53, 26, 12, 41, 22, 60, 14, 28, 63, 33, 49, 3, 45, 16, 48, 26, 14, 46, 18, 30, 35, 26, 8, 50, 29, 51, 25, 57, 12, 47, 53, 9, 62, 20, 54, 2, 36, 15, 40, 28, 33, 13, 38, 24, 46, 1, 29, 56, 33, 20, 44, 24, 41, 26, 57, 20, 63, 8, 30, 55, 5, 41, 62, 8, 34, 2, 37, 10, 19, 6, 37, 1, 53, 23, 5, 27, 58, 22, 43, 12, 50, 26, 9, 34, 54, 32, 49, 1, 59, 37, 22, 46, 25, 36, 51, 15, 54, 46 },
{ 52, 7, 45, 33, 26, 58, 14, 60, 7, 54, 3, 58, 8, 34, 14, 5, 59, 30, 18, 44, 8, 22, 48, 62, 3, 26, 55, 38, 23, 16, 39, 1, 62, 24, 49, 9, 53, 19, 46, 7, 19, 60, 31, 58, 2, 34, 53, 7, 59, 2, 62, 42, 46, 19, 36, 11, 44, 4, 38, 28, 1, 43, 32, 51, 12, 29, 56, 22, 52, 2, 62, 49, 22, 60, 14, 35, 63, 5, 25, 57, 14, 53, 4, 46, 18, 31, 42, 22, 47, 20, 58, 31, 16, 43, 23, 54, 30, 42, 52, 57, 29, 49, 30, 13, 45, 48, 16, 55, 6, 63, 1, 44, 14, 58, 19, 47, 15, 24, 51, 34, 6, 55, 5, 63, 20, 41, 21, 9 },
{ 30, 62, 18, 55, 5, 23, 39, 29, 49, 30, 15, 36, 28, 46, 60, 25, 39, 46, 4, 32, 61, 40, 15, 30, 36, 45, 14, 2, 49, 33, 57, 45, 18, 32, 3, 45, 30, 2, 35, 52, 40, 27, 13, 21, 38, 63, 20, 28, 37, 23, 16, 10, 13, 55, 2, 62, 21, 32, 60, 17, 58, 23, 5, 40, 16, 48, 7, 45, 10, 26, 43, 19, 6, 31, 52, 21, 39, 16, 48, 9, 37, 28, 36, 55, 7, 48, 3, 59, 15, 45, 25, 1, 53, 13, 47, 7, 62, 15, 4, 25, 12, 41, 18, 60, 38, 11, 34, 19, 39, 31, 29, 56, 23, 42, 3, 27, 60, 41, 8, 16, 61, 29, 43, 9, 32, 2, 60, 34 },
{ 3, 38, 13, 37, 52, 44, 2, 19, 12, 42, 63, 19, 40, 1, 20, 50, 12, 55, 15, 56, 27, 1, 54, 11, 57, 18, 32, 63, 44, 4, 29, 13, 37, 61, 35, 16, 42, 57, 12, 22, 6, 55, 43, 10, 50, 5, 44, 11, 48, 52, 34, 58, 28, 41, 38, 30, 7, 52, 11, 49, 30, 14, 45, 27, 59, 34, 21, 38, 32, 58, 11, 36, 56, 42, 9, 41, 3, 54, 31, 42, 0, 60, 16, 11, 39, 24, 52, 33, 6, 36, 10, 40, 32, 60, 26, 20, 39, 28, 47, 34, 63, 8, 54, 3, 24, 56, 0, 51, 13, 47, 16, 40, 7, 35, 52, 11, 36, 4, 57, 30, 39, 13, 18, 50, 58, 28, 12, 48 },
{ 57, 24, 49, 21, 10, 31, 61, 36, 56, 0, 22, 53, 11, 56, 32, 7, 36, 27, 41, 9, 46, 19, 34, 42, 25, 7, 50, 9, 28, 21, 54, 8, 50, 7, 27, 59, 10, 25, 48, 62, 37, 0, 33, 58, 25, 18, 32, 61, 0, 15, 45, 5, 50, 3, 23, 55, 47, 17, 40, 6, 60, 34, 53, 8, 41, 0, 61, 13, 54, 4, 46, 28, 0, 17, 48, 27, 58, 13, 23, 61, 33, 21, 50, 30, 62, 8, 14, 29, 56, 27, 61, 49, 17, 2, 44, 11, 51, 0, 59, 17, 40, 20, 32, 47, 36, 21, 42, 28, 60, 4, 54, 10, 59, 17, 30, 62, 21, 43, 26, 48, 0, 56, 36, 25, 8, 44, 39, 17 },
{ 10, 42, 4, 59, 27, 47, 8, 23, 51, 32, 45, 6, 37, 26, 48, 43, 62, 0, 21, 53, 38, 12, 51, 5, 60, 47, 24, 37, 59, 15, 35, 47, 22, 55, 0, 50, 21, 40, 6, 29, 15, 52, 24, 8, 41, 55, 13, 29, 40, 56, 24, 31, 19, 33, 61, 15, 0, 35, 24, 42, 21, 2, 19, 57, 24, 15, 30, 50, 20, 25, 40, 16, 57, 34, 61, 8, 29, 45, 6, 49, 11, 47, 2, 44, 19, 57, 38, 50, 12, 42, 21, 4, 35, 52, 28, 56, 23, 36, 13, 45, 4, 52, 27, 14, 6, 62, 9, 45, 21, 37, 25, 46, 33, 49, 0, 44, 7, 53, 13, 19, 53, 31, 3, 47, 15, 56, 22, 51 },
{ 35, 28, 53, 32, 1, 16, 54, 40, 9, 17, 25, 58, 14, 59, 3, 22, 16, 51, 31, 5, 23, 58, 28, 17, 35, 20, 0, 42, 11, 52, 3, 31, 41, 17, 43, 13, 32, 54, 18, 60, 32, 45, 17, 49, 2, 36, 51, 22, 7, 36, 9, 63, 48, 12, 46, 26, 43, 28, 63, 13, 48, 37, 51, 33, 5, 47, 55, 9, 42, 63, 7, 51, 24, 12, 37, 19, 55, 34, 18, 38, 15, 28, 54, 34, 5, 43, 22, 0, 48, 14, 54, 24, 58, 9, 38, 5, 32, 55, 21, 30, 49, 9, 59, 43, 30, 51, 35, 26, 7, 53, 2, 22, 14, 27, 57, 18, 38, 24, 33, 45, 10, 41, 20, 60, 37, 5, 32, 0 },
{ 63, 19, 15, 40, 62, 35, 14, 28, 46, 61, 4, 49, 35, 10, 29, 54, 33, 8, 45, 62, 37, 1, 43, 55, 10, 52, 61, 30, 19, 40, 25, 62, 11, 38, 27, 58, 36, 3, 46, 8, 39, 4, 62, 28, 47, 20, 4, 54, 47, 27, 43, 1, 21, 38, 8, 58, 10, 54, 4, 56, 9, 26, 12, 39, 60, 27, 18, 37, 1, 31, 35, 5, 45, 50, 2, 43, 26, 1, 59, 23, 56, 40, 7, 26, 58, 17, 32, 63, 25, 39, 7, 31, 45, 19, 63, 15, 48, 8, 37, 61, 16, 34, 1, 56, 18, 3, 15, 58, 49, 32, 63, 41, 55, 5, 40, 22, 50, 6, 59, 2, 63, 23, 52, 11, 26, 61, 44, 23 },
{ 11, 56, 46, 6, 22, 43, 58, 3, 34, 21, 38, 30, 18, 44, 52, 13, 41, 57, 17, 28, 14, 49, 25, 7, 33, 39, 26, 6, 56, 48, 1, 20, 56, 5, 46, 9, 19, 51, 30, 25, 56, 21, 35, 14, 57, 42, 16, 33, 10, 57, 17, 59, 41, 25, 53, 37, 20, 40, 30, 18, 31, 62, 44, 22, 3, 44, 11, 48, 23, 53, 18, 60, 29, 22, 62, 15, 53, 47, 10, 41, 3, 19, 52, 36, 13, 46, 10, 35, 3, 61, 41, 16, 1, 50, 26, 42, 18, 46, 2, 25, 54, 20, 39, 23, 47, 31, 41, 12, 38, 17, 8, 19, 31, 48, 12, 61, 9, 54, 29, 35, 15, 38, 6, 43, 34, 14, 7, 47 },
{ 39, 2, 33, 26, 53, 8, 18, 50, 41, 12, 53, 1, 63, 24, 19, 39, 2, 24, 47, 10, 60, 38, 19, 63, 48, 4, 15, 45, 32, 14, 60, 36, 29, 53, 23, 63, 34, 12, 61, 1, 43, 11, 53, 30, 1, 26, 60, 45, 23, 39, 3, 29, 12, 50, 4, 16, 51, 3, 45, 36, 50, 1, 16, 54, 35, 14, 57, 30, 58, 9, 46, 14, 41, 10, 32, 38, 4, 30, 21, 51, 32, 63, 25, 1, 60, 27, 53, 18, 51, 22, 28, 55, 34, 12, 40, 3, 60, 29, 57, 41, 6, 44, 11, 53, 8, 61, 24, 57, 1, 28, 44, 59, 36, 3, 34, 25, 41, 31, 16, 44, 22, 47, 28, 58, 1, 49, 54, 29 },
{ 58, 25, 50, 13, 38, 30, 60, 24, 6, 57, 27, 42, 9, 45, 6, 61, 30, 50, 4, 34, 29, 3, 46, 13, 22, 42, 58, 28, 9, 39, 23, 44, 7, 15, 44, 2, 40, 15, 47, 41, 23, 37, 7, 59, 38, 11, 34, 6, 62, 14, 52, 35, 55, 19, 32, 61, 33, 24, 57, 6, 22, 59, 29, 7, 49, 25, 40, 3, 17, 39, 27, 52, 0, 55, 16, 57, 24, 61, 36, 6, 29, 12, 48, 39, 20, 44, 6, 40, 33, 5, 48, 10, 57, 36, 22, 51, 33, 9, 24, 12, 62, 29, 50, 35, 14, 43, 5, 33, 47, 52, 13, 23, 10, 51, 56, 16, 46, 1, 49, 4, 61, 9, 52, 18, 31, 21, 36, 17 },
{ 19, 42, 9, 48, 2, 44, 11, 37, 48, 20, 33, 16, 55, 35, 49, 15, 37, 20, 59, 16, 53, 22, 56, 31, 50, 11, 34, 54, 16, 51, 4, 49, 33, 53, 21, 28, 56, 24, 31, 9, 52, 16, 48, 24, 44, 13, 51, 20, 31, 49, 18, 6, 34, 2, 44, 14, 47, 8, 15, 43, 13, 41, 33, 52, 20, 61, 7, 51, 34, 62, 4, 20, 36, 33, 43, 8, 46, 13, 53, 17, 45, 42, 9, 31, 52, 11, 30, 56, 13, 59, 17, 44, 27, 6, 62, 11, 43, 17, 49, 38, 26, 2, 16, 27, 58, 21, 54, 18, 26, 5, 35, 61, 43, 27, 7, 39, 14, 58, 37, 55, 20, 33, 13, 40, 62, 10, 55, 5 },
{ 51, 14, 61, 29, 59, 20, 55, 31, 0, 49, 11, 60, 3, 26, 22, 56, 0, 40, 12, 43, 41, 8, 36, 0, 17, 57, 24, 2, 46, 26, 61, 18, 0, 38, 12, 59, 6, 49, 3, 57, 19, 63, 5, 33, 18, 54, 28, 56, 0, 43, 26, 46, 63, 27, 56, 22, 27, 54, 38, 28, 63, 24, 10, 45, 0, 31, 42, 21, 12, 25, 44, 49, 59, 6, 26, 50, 3, 34, 27, 59, 0, 35, 62, 16, 4, 58, 47, 0, 43, 24, 37, 2, 54, 20, 46, 31, 0, 56, 34, 5, 55, 45, 60, 37, 0, 40, 10, 38, 63, 46, 15, 20, 0, 53, 21, 62, 30, 11, 24, 27, 40, 0, 57, 26, 3, 45, 27, 35 },
};
#endif /* __CONVERT_DATA_H__ */

10
app/core/gimpimage-convert-fsdither.h
View File

@ -27,7 +27,7 @@
*/
const short range_array[] = {
static const short range_array[] = {
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
@ -133,7 +133,7 @@ const short range_array[] = {
255, 255, 255, 255, 255,
};
const short floyd_steinberg_error1[] = {
static const short floyd_steinberg_error1[] = {
-223, -223, -222, -222, -221, -221, -220, -220, -220, -219,
-219, -218, -218, -217, -217, -217, -216, -216, -215, -215,
-214, -214, -213, -213, -213, -212, -212, -211, -211, -210,
@ -239,7 +239,7 @@ const short floyd_steinberg_error1[] = {
222, 223, 223, 224, 224,
};
const short floyd_steinberg_error2[] = {
static const short floyd_steinberg_error2[] = {
-95, -95, -95, -95, -95, -94, -94, -94, -94, -94,
-93, -93, -93, -93, -93, -93, -92, -92, -92, -92,
-92, -91, -91, -91, -91, -91, -90, -90, -90, -90,
@ -345,7 +345,7 @@ const short floyd_steinberg_error2[] = {
95, 95, 95, 96, 96,
};
const short floyd_steinberg_error3[] = {
static const short floyd_steinberg_error3[] = {
-159, -159, -159, -158, -158, -158, -157, -157, -157, -156,
-156, -156, -155, -155, -155, -155, -154, -154, -154, -153,
-153, -153, -152, -152, -152, -151, -151, -151, -150, -150,
@ -451,7 +451,7 @@ const short floyd_steinberg_error3[] = {
159, 159, 159, 160, 160,
};
const short floyd_steinberg_error4[] = {
static const short floyd_steinberg_error4[] = {
-34, -33, -33, -33, -33, -33, -34, -33, -32, -33,
-33, -33, -33, -33, -32, -31, -33, -32, -32, -32,
-32, -32, -33, -32, -31, -32, -32, -32, -32, -32,

1224
app/core/gimpimage-convert.c
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File diff suppressed because it is too large Load Diff

2
app/core/gimpimage-convert.h
View File

@ -26,7 +26,7 @@
void gimp_image_convert (GimpImage *gimage,
GimpImageBaseType new_type,
/* The following params used only for
* new_type == INDEXED
* new_type == GIMP_INDEXED
*/
gint num_cols,
ConvertDitherType dither,