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Tremendously improve img2twit.cpp: only compute the new error around the 

updated pixel, compute bit allocation at runtime, weight operations in
order to try usual "winners" more often, increase RGB allocation size.

git-svn-id: file:///srv/caca.zoy.org/var/lib/svn/libpipi/trunk@3520 92316355-f0b4-4df1-b90c-862c8a59935f
master
sam vor 15 Jahren
Ursprung
8bf0131c9f
Commit
1779efba6b
1 geänderte Dateien mit 276 neuen und 104 gelöschten Zeilen
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  1. +276
    -104
      examples/img2twit.cpp

+ 276
- 104
examples/img2twit.cpp Datei anzeigen

@@ -11,15 +11,51 @@

#include <pipi.h>

#define TOTAL_POINTS 138
/*
* User-definable settings.
*/

/* The maximum message length */
#define MAX_MSG_LEN 140

/* The number of characters at disposal */
//#define NUM_CHARACTERS 0x7fffffff // The sky's the limit
//#define NUM_CHARACTERS 1111998 // Full valid Unicode set
//#define NUM_CHARACTERS 100507 // Full graphic Unicode
#define NUM_CHARACTERS 32768 // Chinese characters
//#define NUM_CHARACTERS 127 // ASCII

/* The maximum image size we want to support */
#define MAX_W 4000
#define MAX_H 4000

/* How does the algorithm work: one point per cell, or two */
#define POINTS_PER_CELL 2

#define RANGE_X 16
#define RANGE_Y 16
#define RANGE_R 5
#define RANGE_G 5
#define RANGE_B 5
#define RANGE_S 1
/* The range value for point parameters: X Y, red/green/blue, "strength"
* Tested values (on Mona Lisa) are:
* 16 16 5 5 5 2 -> 0.06511725914
* 16 16 6 7 6 1 -> 0.05731491348 *
* 16 16 7 6 6 1 -> 0.06450513783
* 14 14 7 7 6 1 -> 0.0637207893
* 19 19 6 6 5 1 -> 0.06801999094 */
static unsigned int RANGE_X = 16;
static unsigned int RANGE_Y = 16;
static unsigned int RANGE_R = 6;
static unsigned int RANGE_G = 6;
static unsigned int RANGE_B = 6;
static unsigned int RANGE_S = 1;

/*
* These values are computed at runtime
*/

static float TOTAL_BITS;
static float HEADER_BITS;
static float DATA_BITS;
static float POINT_BITS;

static unsigned int TOTAL_CELLS;

#define RANGE_SY (RANGE_S*RANGE_Y)
#define RANGE_SYX (RANGE_S*RANGE_Y*RANGE_X)
@@ -32,7 +68,7 @@ typedef CGAL::Delaunay_triangulation_2<K> Delaunay_triangulation;
typedef std::vector<std::pair<K::Point_2, K::FT> > Point_coordinate_vector;

/* Global aspect ratio */
static int dw, dh;
static unsigned int dw, dh;

/* Global point encoding */
static uint32_t points[1024];
@@ -48,19 +84,24 @@ static unsigned int det_rand(unsigned int mod)
return ((unsigned)(next / 65536) % 32768) % mod;
}

static inline int float2int(float val, int range)
static inline int range2int(float val, int range)
{
int ret = (int)(val * ((float)range - 0.0001));
return ret < 0 ? 0 : ret > range - 1? range - 1 : ret;
return ret < 0 ? 0 : ret > range - 1 ? range - 1 : ret;
}

static inline float int2float(int val, int range)
static inline float int2midrange(int val, int range)
{
return (float)(1 + 2 * val) / (float)(2 * range);
}

static inline uint32_t set_point(int index, float x, float y, float r,
float g, float b, float s)
static inline float int2fullrange(int val, int range)
{
return range > 1 ? (float)val / (float)(range - 1) : 0.0;
}

static inline void set_point(int index, float x, float y, float r,
float g, float b, float s)
{
int dx = (index / POINTS_PER_CELL) % dw;
int dy = (index / POINTS_PER_CELL) / dw;
@@ -68,14 +109,14 @@ static inline uint32_t set_point(int index, float x, float y, float r,
float fx = (x - dx * RANGE_X) / RANGE_X;
float fy = (y - dy * RANGE_Y) / RANGE_Y;

int is = float2int(s, RANGE_S);
int is = range2int(s, RANGE_S);

int ix = float2int(fx, RANGE_X);
int iy = float2int(fy, RANGE_Y);
int ix = range2int(fx, RANGE_X);
int iy = range2int(fy, RANGE_Y);

int ir = float2int(r, RANGE_R);
int ig = float2int(g, RANGE_G);
int ib = float2int(b, RANGE_B);
int ir = range2int(r, RANGE_R);
int ig = range2int(g, RANGE_G);
int ib = range2int(b, RANGE_B);

points[index] = is + RANGE_S * (iy + RANGE_Y * (ix + RANGE_X *
(ib + RANGE_B * (ig + (RANGE_R * ir)))));
@@ -89,19 +130,17 @@ static inline void get_point(int index, float *x, float *y, float *r,
unsigned int dx = (index / POINTS_PER_CELL) % dw;
unsigned int dy = (index / POINTS_PER_CELL) / dw;

float fs = int2float(pt % RANGE_S, RANGE_S); pt /= RANGE_S;
*s = int2fullrange(pt % RANGE_S, RANGE_S); pt /= RANGE_S;

*s = fs < 0.5 ? 0.0 : 1.0;

float fy = int2float(pt % RANGE_Y, RANGE_Y); pt /= RANGE_Y;
float fx = int2float(pt % RANGE_X, RANGE_X); pt /= RANGE_X;
float fy = int2midrange(pt % RANGE_Y, RANGE_Y); pt /= RANGE_Y;
float fx = int2midrange(pt % RANGE_X, RANGE_X); pt /= RANGE_X;

*x = (fx + dx) * RANGE_X;
*y = (fy + dy) * RANGE_Y;

*b = int2float(pt % RANGE_R, RANGE_R); pt /= RANGE_R;
*g = int2float(pt % RANGE_G, RANGE_G); pt /= RANGE_G;
*r = int2float(pt % RANGE_B, RANGE_B); pt /= RANGE_B;
*b = int2midrange(pt % RANGE_R, RANGE_R); pt /= RANGE_R;
*g = int2midrange(pt % RANGE_G, RANGE_G); pt /= RANGE_G;
*r = int2midrange(pt % RANGE_B, RANGE_B); pt /= RANGE_B;
}

static inline float clip(float x, int modulo)
@@ -114,11 +153,33 @@ static inline float clip(float x, int modulo)
static void add_point(float x, float y, float r, float g, float b, float s)
{
set_point(npoints, x, y, r, g, b, s);
get_point(npoints, &x, &y, &r, &g, &b, &s);
npoints++;
}

#define MAX_OPS 15
static void add_random_point()
{
points[npoints] = det_rand(RANGE_SYXRGB);
npoints++;
}

#define NB_OPS 20

static uint8_t rand_op(void)
{
uint8_t x = det_rand(NB_OPS);

/* Randomly ignore statistically less efficient ops */
if(x == 0)
return rand_op();
if(x == 1 && (RANGE_S == 1 || det_rand(2)))
return rand_op();
if(x <= 5 && det_rand(2))
return rand_op();
//if((x < 10 || x > 15) && !det_rand(4)) /* Favour colour changes */
// return rand_op();

return x;
}

static uint32_t apply_op(uint8_t op, uint32_t val)
{
@@ -127,61 +188,72 @@ static uint32_t apply_op(uint8_t op, uint32_t val)
switch(op)
{
case 0: /* Flip strength value */
case 1:
/* Statistics show that this helps often, but does not reduce
* the error significantly. */
return val ^ 1;
case 1: /* Move up; if impossible, down */
case 2: /* Move up; if impossible, down */
rem = val % RANGE_S;
ext = (val / RANGE_S) % RANGE_Y;
ext = ext > 0 ? ext - 1 : ext + 1;
return (val / RANGE_SY * RANGE_Y + ext) * RANGE_S + rem;
case 2: /* Move down; if impossible, up */
case 3: /* Move down; if impossible, up */
rem = val % RANGE_S;
ext = (val / RANGE_S) % RANGE_Y;
ext = ext < RANGE_Y - 1 ? ext + 1 : ext - 1;
return (val / RANGE_SY * RANGE_Y + ext) * RANGE_S + rem;
case 3: /* Move left; if impossible, right */
case 4: /* Move left; if impossible, right */
rem = val % RANGE_SY;
ext = (val / RANGE_SY) % RANGE_X;
ext = ext > 0 ? ext - 1 : ext + 1;
return (val / RANGE_SYX * RANGE_X + ext) * RANGE_SY + rem;
case 4: /* Move left; if impossible, right */
case 5: /* Move left; if impossible, right */
rem = val % RANGE_SY;
ext = (val / RANGE_SY) % RANGE_X;
ext = ext < RANGE_X - 1 ? ext + 1 : ext - 1;
return (val / RANGE_SYX * RANGE_X + ext) * RANGE_SY + rem;
case 5: /* Corner 1 */
return apply_op(1, apply_op(3, val));
case 6: /* Corner 2 */
return apply_op(1, apply_op(4, val));
case 7: /* Corner 3 */
case 6: /* Corner 1 */
return apply_op(2, apply_op(4, val));
case 8: /* Corner 4 */
return apply_op(2, apply_op(3, val));
case 9: /* R-- (or R++) */
case 7: /* Corner 2 */
return apply_op(2, apply_op(5, val));
case 8: /* Corner 3 */
return apply_op(3, apply_op(5, val));
case 9: /* Corner 4 */
return apply_op(3, apply_op(4, val));
case 16: /* Double up */
return apply_op(2, apply_op(2, val));
case 17: /* Double down */
return apply_op(3, apply_op(3, val));
case 18: /* Double left */
return apply_op(4, apply_op(4, val));
case 19: /* Double right */
return apply_op(5, apply_op(5, val));
case 10: /* R-- (or R++) */
rem = val % RANGE_SYX;
ext = (val / RANGE_SYX) % RANGE_R;
ext = ext > 0 ? ext - 1 : ext + 1;
return (val / RANGE_SYXR * RANGE_R + ext) * RANGE_SYX + rem;
case 10: /* R++ (or R--) */
case 11: /* R++ (or R--) */
rem = val % RANGE_SYX;
ext = (val / RANGE_SYX) % RANGE_R;
ext = ext < RANGE_R - 1 ? ext + 1 : ext - 1;
return (val / RANGE_SYXR * RANGE_R + ext) * RANGE_SYX + rem;
case 11: /* G-- (or G++) */
case 12: /* G-- (or G++) */
rem = val % RANGE_SYXR;
ext = (val / RANGE_SYXR) % RANGE_G;
ext = ext > 0 ? ext - 1 : ext + 1;
return (val / RANGE_SYXRG * RANGE_G + ext) * RANGE_SYXR + rem;
case 12: /* G++ (or G--) */
case 13: /* G++ (or G--) */
rem = val % RANGE_SYXR;
ext = (val / RANGE_SYXR) % RANGE_G;
ext = ext < RANGE_G - 1 ? ext + 1 : ext - 1;
return (val / RANGE_SYXRG * RANGE_G + ext) * RANGE_SYXR + rem;
case 13: /* B-- (or B++) */
case 14: /* B-- (or B++) */
rem = val % RANGE_SYXRG;
ext = (val / RANGE_SYXRG) % RANGE_B;
ext = ext > 0 ? ext - 1 : ext + 1;
return ext * RANGE_SYXRG + rem;
case 14: /* B++ (or B--) */
case 15: /* B++ (or B--) */
rem = val % RANGE_SYXRG;
ext = (val / RANGE_SYXRG) % RANGE_B;
ext = ext < RANGE_B - 1 ? ext + 1 : ext - 1;
@@ -211,16 +283,16 @@ static uint32_t apply_op(uint8_t op, uint32_t val)

static void render(pipi_image_t *dst, int rx, int ry, int rw, int rh)
{
uint8_t lookup[TOTAL_POINTS / POINTS_PER_CELL * RANGE_X * RANGE_Y];
uint8_t lookup[TOTAL_CELLS * RANGE_X * RANGE_Y];
pipi_pixels_t *p = pipi_get_pixels(dst, PIPI_PIXELS_RGBA_F32);
float *data = (float *)p->pixels;
float fx, fy, fr, fg, fb, fs;
int i, x, y;

memset(lookup, 0, sizeof(lookup));
dt.clear();
for(i = 0; i < npoints; i++)
{
float fx, fy, fr, fg, fb, fs;
get_point(i, &fx, &fy, &fr, &fg, &fb, &fs);
lookup[(int)fx + dw * RANGE_X * (int)fy] = i; /* Keep link to point */
dt.insert(K::Point_2(fx, fy));
@@ -236,9 +308,6 @@ static void render(pipi_image_t *dst, int rx, int ry, int rw, int rh)
{
for(x = rx; x < rx + rw; x++)
{
int i1 = 0, i2 = 0, i3 = 0;
float d1 = 1000000, d2 = 0, d3 = 0;

K::Point_2 m(x, y);
Point_coordinate_vector coords;
CGAL::Triple<
@@ -252,8 +321,10 @@ static void render(pipi_image_t *dst, int rx, int ry, int rw, int rh)
Point_coordinate_vector::iterator it;
for(it = coords.begin(); it != coords.end(); ++it)
{
float fx = (*it).first.x();
float fy = (*it).first.y();
float fx, fy, fr, fg, fb, fs;

fx = (*it).first.x();
fy = (*it).first.y();

if(fx < 0 || fy < 0 || fx > p->w - 1 || fy > p->h - 1)
continue;
@@ -262,10 +333,10 @@ static void render(pipi_image_t *dst, int rx, int ry, int rw, int rh)

get_point(index, &fx, &fy, &fr, &fg, &fb, &fs);

float k = (*it).second;
if(fs > 0.5) k = pow(k, 1.2);
else k = pow(k, 0.8);
//float k = (*it).second * (1.0f + fs);
//float k = pow((*it).second * (1.0 + fs), 1.2);
float k = (*it).second * (1.00f + fs);
//float k = (*it).second * (0.60f + fs);
//float k = pow((*it).second, (1.0f + fs));

r += k * fr;
g += k * fg;
@@ -287,18 +358,17 @@ static void analyse(pipi_image_t *src)
{
pipi_pixels_t *p = pipi_get_pixels(src, PIPI_PIXELS_RGBA_F32);
float *data = (float *)p->pixels;
int i;

for(int dy = 0; dy < dh; dy++)
for(int dx = 0; dx < dw; dx++)
for(unsigned int dy = 0; dy < dh; dy++)
for(unsigned int dx = 0; dx < dw; dx++)
{
float min = 1.1f, max = -0.1f;
float total = 0.0;
int xmin = 0, xmax = 0, ymin = 0, ymax = 0;
int npixels = 0;

for(int iy = RANGE_Y * dy; iy < RANGE_Y * (dy + 1); iy++)
for(int ix = RANGE_X * dx; ix < RANGE_X * (dx + 1); ix++)
for(unsigned int iy = RANGE_Y * dy; iy < RANGE_Y * (dy + 1); iy++)
for(unsigned int ix = RANGE_X * dx; ix < RANGE_X * (dx + 1); ix++)
{
float lum = 0.0f;

@@ -330,41 +400,70 @@ static void analyse(pipi_image_t *src)

if(total < min + (max - min) / 4)
wmin = 1.0, wmax = 0.0;
else if(total < min + (max - min) / 4 * 2)
wmin = 0.0, wmax = 0.0;
else if(total < min + (max - min) / 4 * 3)
wmin = 0.0, wmax = 0.0;
else
wmin = 0.0, wmax = 1.0;

//wmin = wmax = 1.0;
//if(total < min + (max - min) /3 )
//if((dx + dy) & 1)
{
#if 0
add_random_point();
add_random_point();
#else
#if POINTS_PER_CELL == 1
if(total < min + (max - min) / 2)
{
#endif
add_point(xmin, ymin,
data[4 * (xmin + ymin * p->w) + 0],
data[4 * (xmin + ymin * p->w) + 1],
data[4 * (xmin + ymin * p->w) + 2],
wmin);
}
//else
{
#if POINTS_PER_CELL == 1
}
else
{
#endif
add_point(xmax, ymax,
data[4 * (xmax + ymax * p->w) + 0],
data[4 * (xmax + ymax * p->w) + 1],
data[4 * (xmax + ymax * p->w) + 2],
wmax);
}
#if POINTS_PER_CELL == 1
}
#endif
#endif
}
}

int main(int argc, char *argv[])
{
int opstats[2 * MAX_OPS];
int opstats[2 * NB_OPS];
pipi_image_t *src, *tmp, *dst;
double error = 1.0;
int width, height, ret = 0;

/* Compute bit allocation */
fprintf(stderr, "Available characters: %i\n", NUM_CHARACTERS);
fprintf(stderr, "Maximum message size: %i\n", MAX_MSG_LEN);
TOTAL_BITS = MAX_MSG_LEN * logf(NUM_CHARACTERS) / logf(2);
fprintf(stderr, "Available bits: %f\n", TOTAL_BITS);
fprintf(stderr, "Maximum image resolution: %ix%i\n", MAX_W, MAX_H);
HEADER_BITS = logf(MAX_W * MAX_H) / logf(2);
fprintf(stderr, "Header bits: %f\n", HEADER_BITS);
DATA_BITS = TOTAL_BITS - HEADER_BITS;
fprintf(stderr, "Bits available for data: %f\n", DATA_BITS);
#if POINTS_PER_CELL == 1
POINT_BITS = logf(RANGE_SYXRGB) / logf(2);
#else
float coord_bits = logf((RANGE_Y * RANGE_X) * (RANGE_Y * RANGE_X + 1) / 2);
float other_bits = logf(RANGE_R * RANGE_G * RANGE_B * RANGE_S);
POINT_BITS = (coord_bits + 2 * other_bits) / logf(2);
#endif
fprintf(stderr, "Cell bits: %f\n", POINT_BITS);
TOTAL_CELLS = (int)(DATA_BITS / POINT_BITS);
fprintf(stderr, "Available cells: %i\n", TOTAL_CELLS);
fprintf(stderr, "Wasted bits: %f\n", DATA_BITS - POINT_BITS * TOTAL_CELLS);

/* Load image */
pipi_set_gamma(1.0);
src = pipi_load(argv[1]);
@@ -372,23 +471,33 @@ int main(int argc, char *argv[])
height = pipi_get_image_height(src);

/* Compute best w/h ratio */
dw = 1;
for(int i = 1; i <= TOTAL_POINTS / POINTS_PER_CELL; i++)
dw = 1; dh = TOTAL_CELLS;
for(unsigned int i = 1; i <= TOTAL_CELLS; i++)
{
int j = TOTAL_CELLS / i;

float r = (float)width / (float)height;
float ir = (float)i / (float)(TOTAL_POINTS / POINTS_PER_CELL / i);
float dwr = (float)dw / (float)(TOTAL_POINTS / POINTS_PER_CELL / dw);
float ir = (float)i / (float)j;
float dwr = (float)dw / (float)dh;

if(fabs(logf(r / ir)) < fabs(logf(r / dwr)))
{
dw = i;
dh = TOTAL_CELLS / dw;
}
}
dh = TOTAL_POINTS / POINTS_PER_CELL / dw;
fprintf(stderr, "Chosen image ratio: %i:%i\n", dw, dh);
while((dh + 1) * dw <= TOTAL_CELLS) dh++;
while(dw * (dh + 1) <= TOTAL_CELLS) dw++;
fprintf(stderr, "Chosen image ratio: %i:%i (wasting %i point cells)\n",
dw, dh, TOTAL_CELLS - dw * dh);
fprintf(stderr, "Total wasted bits: %f\n",
DATA_BITS - POINT_BITS * dw * dh);

/* Resize and filter image to better state */
tmp = pipi_resize(src, dw * RANGE_X, dh * RANGE_Y);
pipi_free(src);
src = pipi_median_ext(tmp, 2, 2);
src = pipi_median_ext(tmp, 1, 1);
pipi_free(tmp);

/* Analyse image */
analyse(src);
@@ -401,32 +510,92 @@ int main(int argc, char *argv[])
fprintf(stderr, "Distance: %2.10g\n", error);

memset(opstats, 0, sizeof(opstats));
for(int iter = 0, failures = 0; /*failures < 200 &&*/ iter < 3000; iter++)
for(int iter = 0, stuck = 0, failures = 0, success = 0;
/*stuck < 5 && */iter < 10000;
iter++)
{
uint32_t oldval;
if(failures > 500)
{
stuck++;
failures = 0;
}

pipi_image_t *scrap = pipi_copy(tmp);

/* Choose a point at random */
int pt = det_rand(npoints);
oldval = points[pt];
uint32_t oldval = points[pt];

/* Compute the affected image zone */
float fx, fy, fr, fg, fb, fs;
get_point(pt, &fx, &fy, &fr, &fg, &fb, &fs);
int zonex = (int)fx / RANGE_X - 1;
int zoney = (int)fy / RANGE_Y - 1;
int zonew = 3;
int zoneh = 3;
if(zonex < 0) { zonex = 0; zonew--; }
if(zoney < 0) { zoney = 0; zoneh--; }
if(zonex + zonew >= (int)dw) { zonew--; }
if(zoney + zoneh >= (int)dh) { zoneh--; }

/* Choose random operations and measure their effect */
uint8_t op1 = rand_op();
//uint8_t op2 = rand_op();

uint32_t candidates[3];
double besterr = error + 1.0;
int bestop = -1;
candidates[0] = apply_op(op1, oldval);
//candidates[1] = apply_op(op2, oldval);
//candidates[2] = apply_op(op1, apply_op(op2, oldval));

for(int i = 0; i < 1; i++)
//for(int i = 0; i < 3; i++)
{
if(oldval == candidates[i])
continue;

/* Apply a random operation and measure its effect */
uint8_t op = det_rand(MAX_OPS);
points[pt] = apply_op(op, oldval);
render(scrap, 0, 0, dw * RANGE_X, dh * RANGE_Y);
points[pt] = candidates[i];

opstats[op * 2]++;
render(scrap, zonex * RANGE_X, zoney * RANGE_Y,
zonew * RANGE_X, zoneh * RANGE_Y);

double newerr = pipi_measure_rmsd(src, scrap);
if(newerr < error)
double newerr = pipi_measure_rmsd(src, scrap);
if(newerr < besterr)
{
besterr = newerr;
bestop = i;
}
}

opstats[op1 * 2]++;
//opstats[op2 * 2]++;

if(besterr < error)
{
points[pt] = candidates[bestop];
/* Redraw image if the last check wasn't the best one */
if(bestop != 2)
render(scrap, zonex * RANGE_X, zoney * RANGE_Y,
zonew * RANGE_X, zoneh * RANGE_Y);

pipi_free(tmp);
tmp = scrap;
error = newerr;
fprintf(stderr, "%06i %2.010g after op%i(%i)\n",
iter, error, op, pt);
opstats[op * 2 + 1]++;
//fprintf(stderr, "%08i %2.010g %2.010g after op%i(%i)\n",
// iter, besterr - error, error, op1, pt);
fprintf(stderr, "%08i -.%08i %2.010g after op%i(%i)\n", iter,
(int)((error - besterr) * 100000000), error, op1, pt);
error = besterr;
opstats[op1 * 2 + 1]++;
//opstats[op2 * 2 + 1]++;
failures = 0;
success++;

/* Save image! */
//char buf[128];
//sprintf(buf, "twit%08i.bmp", success);
//if((success % 10) == 0)
// pipi_save(tmp, buf);
}
else
{
@@ -436,16 +605,19 @@ int main(int argc, char *argv[])
}
}

fprintf(stderr, "operation: ");
for(int i = 0; i < MAX_OPS; i++)
fprintf(stderr, "%3i ", i);
fprintf(stderr, "\nattempts: ");
for(int i = 0; i < MAX_OPS; i++)
fprintf(stderr, "%3i ", opstats[i * 2]);
fprintf(stderr, "\nsuccesses: ");
for(int i = 0; i < MAX_OPS; i++)
fprintf(stderr, "%3i ", opstats[i * 2 + 1]);
fprintf(stderr, "\n");
for(int j = 0; j < 2; j++)
{
fprintf(stderr, "operation: ");
for(int i = NB_OPS / 2 * j; i < NB_OPS / 2 * (j + 1); i++)
fprintf(stderr, "%4i ", i);
fprintf(stderr, "\nattempts: ");
for(int i = NB_OPS / 2 * j; i < NB_OPS / 2 * (j + 1); i++)
fprintf(stderr, "%4i ", opstats[i * 2]);
fprintf(stderr, "\nsuccesses: ");
for(int i = NB_OPS / 2 * j; i < NB_OPS / 2 * (j + 1); i++)
fprintf(stderr, "%4i ", opstats[i * 2 + 1]);
fprintf(stderr, "\n");
}

fprintf(stderr, "Distance: %2.10g\n", error);



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