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