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Precompute the edit distance between the 8-bit (2-pixel) and 12-bit

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(3-pixel) sequences that may be modified when storing bytes to the
DHGR display.

This relies on producing an efficient linear representation of the
DHGR framebuffer in terms of a packed 28-bit representation of (Aux,
Main, Aux, Main) screen bytes.
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kris 2019-06-13 22:58:10 +01:00
parent b33b730bfa
commit 494503aa88
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transcoder/edit_distance.pickle Normal file
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transcoder/make_data_tables.py Normal file
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import functools
import pickle
from typing import Iterable
import numpy as np
import weighted_levenshtein
import palette
# The DHGR display encodes 7 pixels across interleaved 4-byte sequences
# of AUX and MAIN memory, as follows:
#
# PBBBAAAA PDDCCCCB PFEEEEDD PGGGGFFF
# Aux N Main N Aux N+1 Main N+1 (N even)
#
# Where A..G are the pixels, and P represents the (unused) palette bit.
#
# This layout makes more sense when written as a (little-endian) 32-bit integer:
#
# 33222222222211111111110000000000 <- bit pos in uint32
# 10987654321098765432109876543210
# PGGGGFFFPFEEEEDDPDDCCCCBPBBBAAAA
#
# i.e. apart from the palette bits this is a linear ordering of pixels,
# when read from LSB to MSB (i.e. right-to-left). i.e. the screen layout order
# of bits is opposite to the usual binary representation ordering.
#
# If we now look at the effect of storing a byte in each of the 4
# byte-offset positions within this uint32,
#
# PGGGGFFFPFEEEEDDPDDCCCCBPBBBAAAA
# 33333333222222221111111100000000
#
# We see that these byte offsets cause changes to the following pixels:
#
# 0: A B
# 1: B C D
# 2: D E F
# 3: F G
#
# i.e. DHGR byte stores to offsets 0 and 3 result in changing one 8-bit value
# (2 DHGR pixels) into another; offsets 1 and 3 result in changing one 12-bit
# value (3 DHGR pixels).
#
# We can simplify things by stripping out the palette bit and packing
# down to a 28-bit integer representation:
#
# 33222222222211111111110000000000 <- bit pos in uint32
# 10987654321098765432109876543210
#
# 0000GGGGFFFFEEEEDDDDCCCCBBBBAAAA <- pixel A..G
# 3210321032103210321032103210 <- bit pos in A..G pixel
#
# 3333333222222211111110000000 <- byte offset 0.3
#
# With this representation, we can precompute an edit distance for the
# pixel changes resulting from all possible DHGR byte stores.
#
# We further encode these (source, target) -> distance mappings by
# concatenating source and target into 16- or 24-bit values. This is
# efficient to work with in the video transcoder.
#
# Since we are enumerating all such 16- or 24-bit values, these can be packed
# contiguously into an array whose index is the (source, target) pair and
# the value is the edit distance.
PIXEL_CHARS = "0123456789ABCDEF"
def pixel_char(i: int) -> str:
return PIXEL_CHARS[i]
@functools.lru_cache(None)
def pixel_string(pixels: Iterable[palette.DHGRColours]) -> str:
return "".join(pixel_char(p.value) for p in pixels)
@functools.lru_cache(None)
def pixels_influenced_by_byte_index(
pixels: Iterable[palette.DHGRColours],
idx: int) -> Iterable[palette.DHGRColours]:
"""Return subset of pixels that are influenced by given byte index (0..4)"""
start, end = {
0: (0, 1),
1: (1, 3),
2: (3, 5),
3: (5, 6)
}[idx]
return pixels[start:end + 1]
# Don't even consider insertions and deletions into the string, they don't
# make sense for comparing pixel strings
insert_costs = np.ones(128, dtype=np.float64) * 100000
delete_costs = np.ones(128, dtype=np.float64) * 100000
# Smallest substitution value is ~20 from palette.diff_matrix, i.e.
# we always prefer to transpose 2 pixels rather than substituting colours.
transpose_costs = np.ones((128, 128), dtype=np.float64) * 10
substitute_costs = np.zeros((128, 128), dtype=np.float64)
# Substitution costs to use when evaluating other potential offsets at which
# to store a content byte. We penalize more harshly for introducing
# errors that alter pixel colours, since these tend to be very
# noticeable as visual noise.
error_substitute_costs = np.zeros((128, 128), dtype=np.float64)
def make_substitute_costs():
# Penalty for changing colour
for i, c in enumerate(PIXEL_CHARS):
for j, d in enumerate(PIXEL_CHARS):
cost = palette.diff_matrix[i, j]
substitute_costs[(ord(c), ord(d))] = cost # / 20
substitute_costs[(ord(d), ord(c))] = cost # / 20
error_substitute_costs[(ord(c), ord(d))] = 5 * cost # / 4
error_substitute_costs[(ord(d), ord(c))] = 5 * cost # / 4
make_substitute_costs()
@functools.lru_cache(None)
def edit_distance(a, b, error: bool):
res = weighted_levenshtein.dam_lev(
a, b,
insert_costs=insert_costs,
delete_costs=delete_costs,
substitute_costs=error_substitute_costs if error else substitute_costs,
)
assert res == 0 or (1 <= res < 2 ** 16), res
return res
@functools.lru_cache(None)
def int28_to_pixels(int28):
return tuple(
palette.DHGRColours(
(int28 & (0b1111 << (4 * i))) >> (4 * i)) for i in range(7)
)
# TODO: these duplicates byte_mask32/byte_shift from DHGRBitmap
# Map n-bit int into 32-bit masked value
def map_int8_to_mask32_0(int8):
assert 0 <= int8 < 2 ** 8, int8
return int8
def map_int12_to_mask32_1(int12):
assert 0 <= int12 < 2 ** 12, int12
return int12 << 4
def map_int12_to_mask32_2(int12):
assert 0 <= int12 < 2 ** 12, int12
return int12 << 12
def map_int8_to_mask32_3(int8):
assert 0 <= int8 < 2 ** 8, int8
return int8 << 20
def make_edit_distance():
edit = [
np.zeros(shape=(2 ** 16), dtype=np.int16),
np.zeros(shape=(2 ** 24), dtype=np.int16),
np.zeros(shape=(2 ** 24), dtype=np.int16),
np.zeros(shape=(2 ** 16), dtype=np.int16),
]
for i in range(2 ** 8):
print(i)
for j in range(2 ** 8):
pair = (i << 8) + j
first = map_int8_to_mask32_0(i)
second = map_int8_to_mask32_0(j)
first_pixels = pixels_influenced_by_byte_index(
pixel_string(int28_to_pixels(first)), 0)
second_pixels = pixels_influenced_by_byte_index(
pixel_string(int28_to_pixels(second)), 0)
edit[0][pair] = edit_distance(first_pixels, second_pixels,
error=False)
first = map_int8_to_mask32_3(i)
second = map_int8_to_mask32_3(j)
first_pixels = pixels_influenced_by_byte_index(
pixel_string(int28_to_pixels(first)), 3)
second_pixels = pixels_influenced_by_byte_index(
pixel_string(int28_to_pixels(second)), 3)
edit[3][pair] = edit_distance(first_pixels, second_pixels,
error=False)
for i in range(2 ** 12):
print(i)
for j in range(2 ** 12):
pair = (i << 12) + j
first = map_int12_to_mask32_1(i)
second = map_int12_to_mask32_1(j)
first_pixels = pixels_influenced_by_byte_index(
pixel_string(int28_to_pixels(first)), 1)
second_pixels = pixels_influenced_by_byte_index(
pixel_string(int28_to_pixels(second)), 1)
edit[1][pair] = edit_distance(first_pixels, second_pixels,
error=False)
first = map_int12_to_mask32_2(i)
second = map_int12_to_mask32_2(j)
first_pixels = pixels_influenced_by_byte_index(
pixel_string(int28_to_pixels(first)), 2)
second_pixels = pixels_influenced_by_byte_index(
pixel_string(int28_to_pixels(second)), 2)
edit[2][pair] = edit_distance(first_pixels, second_pixels,
error=False)
return edit
def main():
edit = make_edit_distance()
# TODO: error distance matrices
with open("transcoder/edit_distance.pickle", "wb") as out:
pickle.dump(
edit, out, protocol=pickle.HIGHEST_PROTOCOL)
if __name__ == "__main__":
main()

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transcoder/make_data_tables_test.py Normal file
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import unittest
from colours import DHGRColours
import make_data_tables
class TestMakeDataTables(unittest.TestCase):
def test_pixel_string(self):
pixels = (DHGRColours.BLACK, DHGRColours.WHITE, DHGRColours.ORANGE)
self.assertEqual("0FC", make_data_tables.pixel_string(pixels))
def test_pixels_influenced_by_byte_index(self):
pixels = (
DHGRColours.ORANGE,
DHGRColours.GREEN,
DHGRColours.BLACK,
DHGRColours.BLACK,
DHGRColours.BLACK,
DHGRColours.BLACK,
DHGRColours.BLACK,
)
self.assertEqual(
(DHGRColours.ORANGE, DHGRColours.GREEN),
make_data_tables.pixels_influenced_by_byte_index(pixels, 0)
)
pixels = (
DHGRColours.BLACK,
DHGRColours.BROWN,
DHGRColours.YELLOW,
DHGRColours.GREY1,
DHGRColours.BLACK,
DHGRColours.BLACK,
DHGRColours.BLACK,
)
self.assertEqual(
(DHGRColours.BROWN, DHGRColours.YELLOW, DHGRColours.GREY1),
make_data_tables.pixels_influenced_by_byte_index(pixels, 1)
)
def test_int28_to_pixels(self):
self.assertEqual(
(
DHGRColours.BLACK,
DHGRColours.BLACK,
DHGRColours.YELLOW,
DHGRColours.BLACK,
DHGRColours.BLACK,
DHGRColours.BLACK,
DHGRColours.BLACK,
),
tuple(
make_data_tables.int28_to_pixels(
0b00000000000000000000111000000000)
)
)
self.assertEqual(
(
DHGRColours.BLACK,
DHGRColours.WHITE,
DHGRColours.BLACK,
DHGRColours.WHITE,
DHGRColours.BLACK,
DHGRColours.WHITE,
DHGRColours.BLACK,
),
tuple(
make_data_tables.int28_to_pixels(
0b0000111100001111000011110000)
)
)
def test_map_to_mask32(self):
byte_mask32 = [
# 33222222222211111111110000000000 <- bit pos in uint32
# 10987654321098765432109876543210
# 0000GGGGFFFFEEEEDDDDCCCCBBBBAAAA <- pixel A..G
# 3210321032103210321032103210 <- bit pos in A..G pixel
0b00000000000000000000000011111111, # byte 0 influences A,B
0b00000000000000001111111111110000, # byte 1 influences B,C,D
0b00000000111111111111000000000000, # byte 2 influences D,E,F
0b00001111111100000000000000000000, # byte 3 influences F,G
]
int8_max = 2 ** 8 - 1
int12_max = 2 ** 12 - 1
self.assertEqual(
make_data_tables.map_int8_to_mask32_0(int8_max), byte_mask32[0])
self.assertEqual(
make_data_tables.map_int12_to_mask32_1(int12_max), byte_mask32[1])
self.assertEqual(
make_data_tables.map_int12_to_mask32_2(int12_max), byte_mask32[2])
self.assertEqual(
make_data_tables.map_int8_to_mask32_3(int8_max), byte_mask32[3])
if __name__ == '__main__':
unittest.main()