On 02.10.2013 11:28, Vladimir 'φ-coder/phcoder' Serbinenko wrote: > On 02.10.2013 08:57, Melki Christian (consultant) wrote: >> Limited usefullness. I've used a lot of PNG's in GRUB lately and can't think >> of a reason why I would use either. >> Maybe paletted 8-bit (if-that’s what you meant?) to save space.. > 8-bit palette is an easy one. The tricky one is 4-/2-/1-bit palettes > (16-/4-/2-color) since then PNG packs several pixels in a single byte. > Usefulness of it to compress image is debatable since although it saves > space by itself, it messes with filter and huffman. Narrow PNG part is easy, small, doesn't affect performance of other supported types and surely useful, so I committed this part. >> but adam7? It's still going to be loaded as a bitmap. >> If I had some web png's and was to lazy to pass them through a converter... > The compatibility is the idea. Or if editor used by artist defaults to > adam7 and doesn't have an option (at least not easily accessible one) to > change this behaviour Remaining (adam7) attached. However this increases pnd.mod by 27% (from 8776 to 11192). I don't know of performance of adam7 compared to normal png. Complexity involved is not easy either. Any more opinions?
=== modified file 'grub-core/video/readers/png.c'
--- grub-core/video/readers/png.c 2013-10-02 11:22:56 +0000
+++ grub-core/video/readers/png.c 2013-10-02 11:54:07 +0000
@@ -31,7 +31,6 @@
enum
{
- PNG_COLOR_TYPE_GRAY = 0,
PNG_COLOR_MASK_PALETTE = 1,
PNG_COLOR_MASK_COLOR = 2,
PNG_COLOR_MASK_ALPHA = 4,
@@ -40,8 +39,11 @@
#define PNG_COMPRESSION_BASE 0
-#define PNG_INTERLACE_NONE 0
-#define PNG_INTERLACE_ADAM7 1
+enum
+ {
+ PNG_INTERLACE_NONE = 0,
+ PNG_INTERLACE_ADAM7 = 1
+ };
#define PNG_FILTER_TYPE_BASE 0
@@ -88,6 +90,28 @@
int num_values, max_length;
};
+struct interlace_stage
+{
+ int start_x, start_y;
+ int log_step_x, log_step_y;
+};
+
+static struct interlace_stage interleave_none[] =
+ {
+ { 0, 0, 0, 0 }
+ };
+
+static struct interlace_stage interleave_adam7[] =
+ {
+ { 0, 0, 3, 3 },
+ { 4, 0, 3, 3 },
+ { 0, 4, 2, 3 },
+ { 2, 0, 2, 2 },
+ { 0, 2, 1, 2 },
+ { 1, 0, 1, 1 },
+ { 0, 1, 0, 1 }
+ };
+
struct grub_png_data
{
grub_file_t file;
@@ -99,7 +123,8 @@
int image_width, image_height, bpp, is_16bit;
int raw_bytes, is_gray, is_alpha, is_palette;
- int row_bytes, color_bits;
+ int row_bytes, row_bytes_i, row_bytes_i2, color_bits;
+ int skip;
grub_uint8_t *image_data;
int inside_idat, idat_remain;
@@ -120,9 +145,15 @@
grub_uint8_t slide[WSIZE];
int wp;
- grub_uint8_t *cur_rgb;
+ grub_uint8_t *cur_rgb, *rgb0;
int cur_column, cur_filter, first_line;
+ int cur_component;
+
+ struct interlace_stage *cur_interleave;
+ int n_interleave;
+
+ int is_adam7;
};
static grub_uint32_t
@@ -246,6 +277,7 @@
int color_type;
int color_bits;
enum grub_video_blit_format blt;
+ grub_uint8_t interleave;
data->image_width = grub_png_get_dword (data);
data->image_height = grub_png_get_dword (data);
@@ -283,7 +315,8 @@
}
if ((color_bits != 8) && (color_bits != 16)
- && (color_bits != 4
+ && ((color_bits != 4 && color_bits != 2
+ && color_bits != 1)
|| !(data->is_gray || data->is_palette)))
return grub_error (GRUB_ERR_BAD_FILE_TYPE,
"png: bit depth must be 8 or 16");
@@ -304,6 +337,9 @@
if (data->color_bits <= 4)
data->row_bytes = (data->image_width * data->color_bits + 7) / 8;
+ if (data->is_adam7 && data->color_bits <= 4)
+ data->row_bytes += 16;
+
#ifndef GRUB_CPU_WORDS_BIGENDIAN
if (data->is_16bit || data->is_gray || data->is_palette)
#endif
@@ -312,21 +348,16 @@
if (grub_errno)
return grub_errno;
- data->cur_rgb = data->image_data;
+ data->rgb0 = data->image_data;
}
#ifndef GRUB_CPU_WORDS_BIGENDIAN
else
{
data->image_data = 0;
- data->cur_rgb = (*data->bitmap)->data;
+ data->rgb0 = (*data->bitmap)->data;
}
#endif
- data->raw_bytes = data->image_height * (data->row_bytes + 1);
-
- data->cur_column = 0;
- data->first_line = 1;
-
if (grub_png_get_byte (data) != PNG_COMPRESSION_BASE)
return grub_error (GRUB_ERR_BAD_FILE_TYPE,
"png: compression method not supported");
@@ -335,9 +366,22 @@
return grub_error (GRUB_ERR_BAD_FILE_TYPE,
"png: filter method not supported");
- if (grub_png_get_byte (data) != PNG_INTERLACE_NONE)
- return grub_error (GRUB_ERR_BAD_FILE_TYPE,
- "png: interlace method not supported");
+ interleave = grub_png_get_byte (data);
+ switch (interleave)
+ {
+ case PNG_INTERLACE_NONE:
+ data->cur_interleave = interleave_none - 1;
+ data->n_interleave = ARRAY_SIZE (interleave_none);
+ break;
+ case PNG_INTERLACE_ADAM7:
+ data->cur_interleave = interleave_adam7 - 1;
+ data->n_interleave = ARRAY_SIZE (interleave_adam7);
+ data->is_adam7 = 1;
+ break;
+ default:
+ return grub_error (GRUB_ERR_BAD_FILE_TYPE,
+ "png: interlace method not supported");
+ }
/* Skip crc checksum. */
grub_png_get_dword (data);
@@ -576,24 +620,85 @@
static grub_err_t
grub_png_output_byte (struct grub_png_data *data, grub_uint8_t n)
{
- if (--data->raw_bytes < 0)
+ while (data->raw_bytes == 0 && data->n_interleave)
+ {
+ int rows_i, cols_i;
+ data->cur_interleave++;
+
+ data->cur_rgb = data->rgb0;
+
+ if (data->image_width <= data->cur_interleave->start_x)
+ rows_i = 0;
+ else
+ rows_i = ((data->image_width - data->cur_interleave->start_x - 1)
+ >> data->cur_interleave->log_step_x) + 1;
+
+ if (data->image_height <= data->cur_interleave->start_y)
+ cols_i = 0;
+ else
+ cols_i = ((data->image_height - data->cur_interleave->start_y - 1)
+ >> data->cur_interleave->log_step_y) + 1;
+ if (data->color_bits <= 4)
+ {
+ data->row_bytes_i = (rows_i * data->color_bits + 7) / 8;
+ data->skip = ((1 << data->cur_interleave->log_step_x) - 1);
+ data->cur_rgb += data->cur_interleave->start_x;
+ }
+ else
+ {
+ data->row_bytes_i = rows_i * data->bpp;
+
+ data->skip = ((1 << data->cur_interleave->log_step_x) - 1) * data->bpp;
+ data->cur_rgb += data->cur_interleave->start_x * data->bpp;
+ }
+
+ data->row_bytes_i2 = data->row_bytes_i
+ + data->skip * (data->row_bytes_i / data->bpp);
+
+ data->raw_bytes = cols_i * (data->row_bytes_i + 1);
+
+ data->cur_column = 0;
+ data->cur_filter = 0;
+ data->first_line = 1;
+ data->cur_component = 0;
+ data->cur_rgb += data->cur_interleave->start_y * data->row_bytes;
+ data->n_interleave--;
+ grub_printf ("{%d}",n);
+ }
+
+ data->raw_bytes--;
+
+ if (data->raw_bytes < 0)
return grub_error (GRUB_ERR_BAD_FILE_TYPE, "image size overflown");
if (data->cur_column == 0)
{
+ grub_printf ("<%d>",n);
if (n >= PNG_FILTER_VALUE_LAST)
- return grub_error (GRUB_ERR_BAD_FILE_TYPE, "invalid filter value");
+ return grub_error (GRUB_ERR_BAD_FILE_TYPE, "invalid filter value %d", n);
data->cur_filter = n;
+ if (!data->first_line)
+ data->cur_rgb += (1 << data->cur_interleave->log_step_y)
+ * data->row_bytes - data->row_bytes_i2;
}
else
- *data->cur_rgb++ = n;
+ {
+ *data->cur_rgb++ = n;
+ data->cur_component++;
+ if (data->cur_component == data->bpp)
+ {
+ data->cur_component = 0;
+ data->cur_rgb += data->skip;
+ }
+ }
data->cur_column++;
- if (data->cur_column == data->row_bytes + 1)
+
+ if (data->cur_column == data->row_bytes_i + 1)
{
grub_uint8_t *blank_line = NULL;
- grub_uint8_t *cur = data->cur_rgb - data->row_bytes;
+ grub_uint8_t *cur = data->cur_rgb - data->row_bytes_i2;
grub_uint8_t *left = cur;
grub_uint8_t *up;
@@ -606,71 +711,109 @@
up = blank_line;
}
else
- up = cur - data->row_bytes;
+ up = cur - (data->row_bytes << data->cur_interleave->log_step_y);
switch (data->cur_filter)
{
case PNG_FILTER_VALUE_SUB:
{
- int i;
+ int i, j;
- cur += data->bpp;
- for (i = data->bpp; i < data->row_bytes; i++, cur++, left++)
- *cur += *left;
+ cur += data->bpp + data->skip;
+ for (i = data->bpp; i < data->row_bytes; )
+ {
+ for (j = 0; j < data->bpp; j++)
+ {
+ *cur += *left;
+ i++, cur++, left++;
+ }
+ i += data->skip;
+ cur += data->skip;
+ left += data->skip;
+ }
break;
}
case PNG_FILTER_VALUE_UP:
{
- int i;
-
- for (i = 0; i < data->row_bytes; i++, cur++, up++)
- *cur += *up;
-
+ int i, j;
+
+ for (i = 0; i < data->row_bytes; )
+ {
+ for (j = 0; j < data->bpp; j++)
+ {
+ *cur += *up;
+ i++, cur++, up++;
+ }
+ i += data->skip;
+ cur += data->skip;
+ up += data->skip;
+ }
break;
}
case PNG_FILTER_VALUE_AVG:
{
- int i;
+ int i, j;
for (i = 0; i < data->bpp; i++, cur++, up++)
*cur += *up >> 1;
- for (; i < data->row_bytes; i++, cur++, up++, left++)
- *cur += ((int) *up + (int) *left) >> 1;
+ i += data->skip;
+ cur += data->skip;
+ up += data->skip;
+
+ for (; i < data->row_bytes; )
+ {
+ for (j = 0; j < data->bpp; j++)
+ {
+ *cur += ((int) *up + (int) *left) >> 1;
+ i++, cur++, up++, left++;
+ }
+ i+= data->skip, cur+= data->skip, up+= data->skip, left+= data->skip;
+ }
break;
}
case PNG_FILTER_VALUE_PAETH:
{
- int i;
+ int i, j;
grub_uint8_t *upper_left = up;
for (i = 0; i < data->bpp; i++, cur++, up++)
*cur += *up;
- for (; i < data->row_bytes; i++, cur++, up++, left++, upper_left++)
+ i += data->skip;
+ cur += data->skip;
+ up += data->skip;
+
+ for (; i < data->row_bytes; )
{
- int a, b, c, pa, pb, pc;
-
- a = *left;
- b = *up;
- c = *upper_left;
-
- pa = b - c;
- pb = a - c;
- pc = pa + pb;
-
- if (pa < 0)
- pa = -pa;
-
- if (pb < 0)
- pb = -pb;
-
- if (pc < 0)
- pc = -pc;
-
- *cur += ((pa <= pb) && (pa <= pc)) ? a : (pb <= pc) ? b : c;
+ for (j = 0; j < data->bpp; j++)
+ {
+ int a, b, c, pa, pb, pc;
+
+ a = *left;
+ b = *up;
+ c = *upper_left;
+
+ pa = b - c;
+ pb = a - c;
+ pc = pa + pb;
+
+ if (pa < 0)
+ pa = -pa;
+
+ if (pb < 0)
+ pb = -pb;
+
+ if (pc < 0)
+ pc = -pc;
+
+ *cur += ((pa <= pb) && (pa <= pc)) ? a : (pb <= pc) ? b : c;
+ i++, cur++, up++, left++, upper_left++;
+ }
+ i+=data->skip, cur+=data->skip, up+=data->skip;
+ left+=data->skip, upper_left+=data->skip;
}
}
}
@@ -815,6 +958,8 @@
static const grub_uint8_t png_magic[8] =
{ 0x89, 0x50, 0x4e, 0x47, 0xd, 0xa, 0x1a, 0x0a };
+#include "png_adam7.c"
+
static void
grub_png_convert_image (struct grub_png_data *data)
{
@@ -845,7 +990,7 @@
if (data->color_bits <= 4)
{
grub_uint8_t palette[16][3];
- grub_uint8_t *d1c, *d2c;
+ grub_uint8_t *dc;
int shift;
int mask = (1 << data->color_bits) - 1;
int j;
@@ -859,28 +1004,88 @@
}
else
grub_memcpy (palette, data->palette, 16 * 3);
- d1c = d1;
- d2c = d2;
- for (j = 0; j < data->image_height; j++, d1c += data->image_width * 3,
- d2c += data->row_bytes)
+ dc = d2;
+ /* Our algorithms work on bytes in case of color depth <= 4.
+ Usually it's no problem as PNG specs does the same. However
+ Adam7 always works on pixels, so we need this additional shuffling.
+ */
+ if (data->is_adam7)
{
- d1 = d1c;
- d2 = d2c;
- shift = 8 - data->color_bits;
- for (i = 0; i < data->image_width; i++, d1 += 3)
- {
- grub_uint8_t col = (d2[0] >> shift) & mask;
- d1[R3] = data->palette[col][2];
- d1[G3] = data->palette[col][1];
- d1[B3] = data->palette[col][0];
- shift -= data->color_bits;
- if (shift < 0)
- {
- d2++;
- shift += 8;
- }
- }
+ int klen = 16;
+ if (data->color_bits == 2)
+ klen = 32;
+ if (data->color_bits == 1)
+ klen = 64;
+ for (j = 0; j < data->image_height; j++,
+ dc += data->row_bytes)
+ if (j & 1)
+ {
+ d2 = dc;
+ shift = 8 - data->color_bits;
+ for (i = 0; i < data->image_width;
+ i++, d1 += 3)
+ {
+ grub_uint8_t col = (d2[0] >> shift) & mask;
+ d1[R3] = data->palette[col][2];
+ d1[G3] = data->palette[col][1];
+ d1[B3] = data->palette[col][0];
+ shift -= data->color_bits;
+ if (shift < 0)
+ {
+ d2++;
+ shift += 8;
+ }
+ }
+ }
+ else
+ {
+ const grub_uint8_t (*remap)[2] = NULL;
+ int k;
+
+ if (data->color_bits == 4)
+ remap = adam7_remap_4bit[(j & 7) >> 1];
+ if (data->color_bits == 2)
+ remap = adam7_remap_2bit[(j & 7) >> 1];
+ if (data->color_bits == 1)
+ remap = adam7_remap_1bit[(j & 7) >> 1];
+ d2 = dc;
+ for (i = 0, k = 0; i < data->image_width;
+ i++, d1 += 3)
+ {
+ grub_uint8_t col = (d2[remap[k][0]] >> remap[k][1]) & mask;
+ d1[R3] = data->palette[col][2];
+ d1[G3] = data->palette[col][1];
+ d1[B3] = data->palette[col][0];
+ k++;
+ if (k == klen)
+ {
+ d2 += 8;
+ k = 0;
+ }
+ }
+ }
}
+ else
+ for (j = 0; j < data->image_height; j++)
+ {
+ d2 = dc;
+ dc += data->row_bytes;
+ shift = 8 - data->color_bits;
+ for (i = 0; i < data->image_width;
+ i++, d1 += 3)
+ {
+ grub_uint8_t col = (d2[0] >> shift) & mask;
+ d1[R3] = data->palette[col][2];
+ d1[G3] = data->palette[col][1];
+ d1[B3] = data->palette[col][0];
+ shift -= data->color_bits;
+ if (shift < 0)
+ {
+ d2++;
+ shift += 8;
+ }
+ }
+ }
return;
}
=== added file 'grub-core/video/readers/png_adam7.c'
--- grub-core/video/readers/png_adam7.c 1970-01-01 00:00:00 +0000
+++ grub-core/video/readers/png_adam7.c 2013-10-02 09:39:56 +0000
@@ -0,0 +1,91 @@
+static const grub_uint8_t adam7_remap_4bit[4][16][2] =
+ {
+ { { 0, 4 }, { 1, 4 }, { 2, 4 }, { 1, 0 }, { 4, 4 }, { 3, 4 },
+ { 2, 0 }, { 3, 0 }, { 0, 0 }, { 5, 4 }, { 6, 4 }, { 5, 0 },
+ { 4, 0 }, { 7, 4 }, { 6, 0 }, { 7, 0 }, },
+ { { 0, 4 }, { 1, 4 }, { 0, 0 }, { 1, 0 }, { 2, 4 }, { 3, 4 },
+ { 2, 0 }, { 3, 0 }, { 4, 4 }, { 5, 4 }, { 4, 0 }, { 5, 0 },
+ { 6, 4 }, { 7, 4 }, { 6, 0 }, { 7, 0 }, },
+ { { 0, 4 }, { 1, 4 }, { 2, 4 }, { 1, 0 }, { 0, 0 }, { 3, 4 },
+ { 2, 0 }, { 3, 0 }, { 4, 4 }, { 5, 4 }, { 6, 4 }, { 5, 0 },
+ { 4, 0 }, { 7, 4 }, { 6, 0 }, { 7, 0 }, },
+ { { 0, 4 }, { 1, 4 }, { 0, 0 }, { 1, 0 }, { 2, 4 }, { 3, 4 },
+ { 2, 0 }, { 3, 0 }, { 4, 4 }, { 5, 4 }, { 4, 0 }, { 5, 0 },
+ { 6, 4 }, { 7, 4 }, { 6, 0 }, { 7, 0 }, },
+ };
+
+static const grub_uint8_t adam7_remap_2bit[4][32][2] =
+ {
+ { { 0, 6 }, { 1, 6 }, { 2, 6 }, { 1, 4 }, { 4, 6 }, { 1, 2 },
+ { 2, 4 }, { 1, 0 }, { 0, 4 }, { 3, 6 }, { 2, 2 }, { 3, 4 },
+ { 4, 4 }, { 3, 2 }, { 2, 0 }, { 3, 0 }, { 0, 2 }, { 5, 6 },
+ { 6, 6 }, { 5, 4 }, { 4, 2 }, { 5, 2 }, { 6, 4 }, { 5, 0 },
+ { 0, 0 }, { 7, 6 }, { 6, 2 }, { 7, 4 }, { 4, 0 }, { 7, 2 },
+ { 6, 0 }, { 7, 0 }, },
+ { { 0, 6 }, { 1, 6 }, { 0, 4 }, { 1, 4 }, { 0, 2 }, { 1, 2 },
+ { 0, 0 }, { 1, 0 }, { 2, 6 }, { 3, 6 }, { 2, 4 }, { 3, 4 },
+ { 2, 2 }, { 3, 2 }, { 2, 0 }, { 3, 0 }, { 4, 6 }, { 5, 6 },
+ { 4, 4 }, { 5, 4 }, { 4, 2 }, { 5, 2 }, { 4, 0 }, { 5, 0 },
+ { 6, 6 }, { 7, 6 }, { 6, 4 }, { 7, 4 }, { 6, 2 }, { 7, 2 },
+ { 6, 0 }, { 7, 0 }, },
+ { { 0, 6 }, { 1, 6 }, { 2, 6 }, { 1, 4 }, { 0, 4 }, { 1, 2 },
+ { 2, 4 }, { 1, 0 }, { 0, 2 }, { 3, 6 }, { 2, 2 }, { 3, 4 },
+ { 0, 0 }, { 3, 2 }, { 2, 0 }, { 3, 0 }, { 4, 6 }, { 5, 6 },
+ { 6, 6 }, { 5, 4 }, { 4, 4 }, { 5, 2 }, { 6, 4 }, { 5, 0 },
+ { 4, 2 }, { 7, 6 }, { 6, 2 }, { 7, 4 }, { 4, 0 }, { 7, 2 },
+ { 6, 0 }, { 7, 0 }, },
+ { { 0, 6 }, { 1, 6 }, { 0, 4 }, { 1, 4 }, { 0, 2 }, { 1, 2 },
+ { 0, 0 }, { 1, 0 }, { 2, 6 }, { 3, 6 }, { 2, 4 }, { 3, 4 },
+ { 2, 2 }, { 3, 2 }, { 2, 0 }, { 3, 0 }, { 4, 6 }, { 5, 6 },
+ { 4, 4 }, { 5, 4 }, { 4, 2 }, { 5, 2 }, { 4, 0 }, { 5, 0 },
+ { 6, 6 }, { 7, 6 }, { 6, 4 }, { 7, 4 }, { 6, 2 }, { 7, 2 },
+ { 6, 0 }, { 7, 0 }, },
+ };
+
+static const grub_uint8_t adam7_remap_1bit[4][64][2] =
+ {
+ { { 0, 7 }, { 1, 7 }, { 2, 7 }, { 1, 6 }, { 4, 7 }, { 1, 5 },
+ { 2, 6 }, { 1, 4 }, { 0, 6 }, { 1, 3 }, { 2, 5 }, { 1, 2 },
+ { 4, 6 }, { 1, 1 }, { 2, 4 }, { 1, 0 }, { 0, 5 }, { 3, 7 },
+ { 2, 3 }, { 3, 6 }, { 4, 5 }, { 3, 5 }, { 2, 2 }, { 3, 4 },
+ { 0, 4 }, { 3, 3 }, { 2, 1 }, { 3, 2 }, { 4, 4 }, { 3, 1 },
+ { 2, 0 }, { 3, 0 }, { 0, 3 }, { 5, 7 }, { 6, 7 }, { 5, 6 },
+ { 4, 3 }, { 5, 5 }, { 6, 6 }, { 5, 4 }, { 0, 2 }, { 5, 3 },
+ { 6, 5 }, { 5, 2 }, { 4, 2 }, { 5, 1 }, { 6, 4 }, { 5, 0 },
+ { 0, 1 }, { 7, 7 }, { 6, 3 }, { 7, 6 }, { 4, 1 }, { 7, 5 },
+ { 6, 2 }, { 7, 4 }, { 0, 0 }, { 7, 3 }, { 6, 1 }, { 7, 2 },
+ { 4, 0 }, { 7, 1 }, { 6, 0 }, { 7, 0 }, },
+ { { 0, 7 }, { 1, 7 }, { 0, 6 }, { 1, 6 }, { 0, 5 }, { 1, 5 },
+ { 0, 4 }, { 1, 4 }, { 0, 3 }, { 1, 3 }, { 0, 2 }, { 1, 2 },
+ { 0, 1 }, { 1, 1 }, { 0, 0 }, { 1, 0 }, { 2, 7 }, { 3, 7 },
+ { 2, 6 }, { 3, 6 }, { 2, 5 }, { 3, 5 }, { 2, 4 }, { 3, 4 },
+ { 2, 3 }, { 3, 3 }, { 2, 2 }, { 3, 2 }, { 2, 1 }, { 3, 1 },
+ { 2, 0 }, { 3, 0 }, { 4, 7 }, { 5, 7 }, { 4, 6 }, { 5, 6 },
+ { 4, 5 }, { 5, 5 }, { 4, 4 }, { 5, 4 }, { 4, 3 }, { 5, 3 },
+ { 4, 2 }, { 5, 2 }, { 4, 1 }, { 5, 1 }, { 4, 0 }, { 5, 0 },
+ { 6, 7 }, { 7, 7 }, { 6, 6 }, { 7, 6 }, { 6, 5 }, { 7, 5 },
+ { 6, 4 }, { 7, 4 }, { 6, 3 }, { 7, 3 }, { 6, 2 }, { 7, 2 },
+ { 6, 1 }, { 7, 1 }, { 6, 0 }, { 7, 0 }, },
+ { { 0, 7 }, { 1, 7 }, { 2, 7 }, { 1, 6 }, { 0, 6 }, { 1, 5 },
+ { 2, 6 }, { 1, 4 }, { 0, 5 }, { 1, 3 }, { 2, 5 }, { 1, 2 },
+ { 0, 4 }, { 1, 1 }, { 2, 4 }, { 1, 0 }, { 0, 3 }, { 3, 7 },
+ { 2, 3 }, { 3, 6 }, { 0, 2 }, { 3, 5 }, { 2, 2 }, { 3, 4 },
+ { 0, 1 }, { 3, 3 }, { 2, 1 }, { 3, 2 }, { 0, 0 }, { 3, 1 },
+ { 2, 0 }, { 3, 0 }, { 4, 7 }, { 5, 7 }, { 6, 7 }, { 5, 6 },
+ { 4, 6 }, { 5, 5 }, { 6, 6 }, { 5, 4 }, { 4, 5 }, { 5, 3 },
+ { 6, 5 }, { 5, 2 }, { 4, 4 }, { 5, 1 }, { 6, 4 }, { 5, 0 },
+ { 4, 3 }, { 7, 7 }, { 6, 3 }, { 7, 6 }, { 4, 2 }, { 7, 5 },
+ { 6, 2 }, { 7, 4 }, { 4, 1 }, { 7, 3 }, { 6, 1 }, { 7, 2 },
+ { 4, 0 }, { 7, 1 }, { 6, 0 }, { 7, 0 }, },
+ { { 0, 7 }, { 1, 7 }, { 0, 6 }, { 1, 6 }, { 0, 5 }, { 1, 5 },
+ { 0, 4 }, { 1, 4 }, { 0, 3 }, { 1, 3 }, { 0, 2 }, { 1, 2 },
+ { 0, 1 }, { 1, 1 }, { 0, 0 }, { 1, 0 }, { 2, 7 }, { 3, 7 },
+ { 2, 6 }, { 3, 6 }, { 2, 5 }, { 3, 5 }, { 2, 4 }, { 3, 4 },
+ { 2, 3 }, { 3, 3 }, { 2, 2 }, { 3, 2 }, { 2, 1 }, { 3, 1 },
+ { 2, 0 }, { 3, 0 }, { 4, 7 }, { 5, 7 }, { 4, 6 }, { 5, 6 },
+ { 4, 5 }, { 5, 5 }, { 4, 4 }, { 5, 4 }, { 4, 3 }, { 5, 3 },
+ { 4, 2 }, { 5, 2 }, { 4, 1 }, { 5, 1 }, { 4, 0 }, { 5, 0 },
+ { 6, 7 }, { 7, 7 }, { 6, 6 }, { 7, 6 }, { 6, 5 }, { 7, 5 },
+ { 6, 4 }, { 7, 4 }, { 6, 3 }, { 7, 3 }, { 6, 2 }, { 7, 2 },
+ { 6, 1 }, { 7, 1 }, { 6, 0 }, { 7, 0 }, },
+ };
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