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# cython: infer_types=True
# cython: profile=False
# cython: boundscheck=False
# cython: wraparound=False
cimport cython
import numpy as np
from libc.stdlib cimport malloc, free
cimport common
import screen as screen_py
# TODO: use a cdef class
# C representation of dither_pattern.DitherPattern data, for efficient access.
cdef struct Dither:
float* pattern # Flattened dither pattern
int x_shape
int y_shape
int x_origin
int y_origin
# Compute left-hand bounding box for dithering at horizontal position x.
cdef inline int dither_bounds_xl(Dither *dither, int x) nogil:
cdef int el = max(dither.x_origin - x, 0)
cdef int xl = x - dither.x_origin + el
return xl
#Compute right-hand bounding box for dithering at horizontal position x.
cdef inline int dither_bounds_xr(Dither *dither, int x_res, int x) nogil:
cdef int er = min(dither.x_shape, x_res - x)
cdef int xr = x - dither.x_origin + er
return xr
# Compute upper bounding box for dithering at vertical position y.
cdef inline int dither_bounds_yt(Dither *dither, int y) nogil:
cdef int et = max(dither.y_origin - y, 0)
cdef int yt = y - dither.y_origin + et
return yt
# Compute lower bounding box for dithering at vertical position y.
cdef inline int dither_bounds_yb(Dither *dither, int y_res, int y) nogil:
cdef int eb = min(dither.y_shape, y_res - y)
cdef int yb = y - dither.y_origin + eb
return yb
cdef inline unsigned char shift_pixel_window(
unsigned char last_pixels,
unsigned int next_pixels,
unsigned char shift_right_by,
unsigned char window_width) nogil:
"""Right-shift a sliding window of n pixels to incorporate new pixels.
last_pixels: n-bit value representing n pixels from left up to current position (MSB = current pixel).
next_pixels: n-bit value representing n pixels to right of current position (LSB = pixel to right)
shift_right_by: how many pixels of next_pixels to shift into the sliding window
window_width: how many pixels to maintain in the sliding window (must be <= 8)
Returns: n-bit value representing shifted pixel window
cdef unsigned char window_mask = 0xff >> (8 - window_width)
cdef unsigned int shifted_next_pixels
if window_width > shift_right_by:
shifted_next_pixels = next_pixels << (window_width - shift_right_by)
shifted_next_pixels = next_pixels >> (shift_right_by - window_width)
return ((last_pixels >> shift_right_by) | shifted_next_pixels) & window_mask
# Given a byte to store on the hi-res screen, compute the sequence of 560-resolution pixels that will be displayed.
# Hi-res graphics works like this:
# - Each of the low 7 bits in screen_byte results in enabling or disabling two sequential 560-resolution pixels.
# - pixel screen order is from LSB to MSB
# - if bit 8 (the "palette bit) is set then the 14-pixel sequence is shifted one position to the right, and the
# left-most pixel is filled in by duplicating the right-most pixel controlled by the previous screen byte (i.e. bit 7)
# - this gives a 15 or 14 pixel sequence depending on whether or not the palette bit is set.
cdef unsigned int compute_fat_pixels(unsigned int screen_byte, unsigned char last_pixels) nogil:
cdef int i, bit, fat_bit
cdef unsigned int result = 0
for i in range(7):
bit = (screen_byte >> i) & 0b1
fat_bit = bit << 1 | bit
result |= (fat_bit) << (2 * i)
if screen_byte & 0x80:
# Palette bit shifts to the right
result <<= 1
result |= (last_pixels >> 7)
return result
# Context parametrizes the differences between DHGR and HGR image optimization
cdef struct Context:
# How many bit positions to lookahead when optimizing
unsigned char bit_lookahead
# How many screen pixels produced by bit_lookahead. This is 1:1 for DHGR but for HGR 8 bits in memory produce
# 14 or 15 screen pixels (see compute_fat_pixels above)
unsigned char pixel_lookahead
# HGR has a NTSC phase shift relative to DHGR which rotates the effective mappings from screen pixels to colours
unsigned char phase_shift
# Non-zero for HGR optimization
unsigned char is_hgr
# Look ahead a number of pixels and compute choice for next pixel with lowest total squared error after dithering.
# Args:
# dither: error diffusion pattern to apply
# palette_rgb: matrix of all n-bit colour palette RGB values
# image_rgb: RGB image in the process of dithering
# x: current horizontal screen position
# y: current vertical screen position
# options_nbit: matrix of (2**lookahead, lookahead) possible n-bit colour choices at positions x .. x + lookahead
# lookahead: how many horizontal pixels to look ahead
# distances: matrix of (24-bit RGB, n-bit palette) perceptual colour distances
# x_res: horizontal screen resolution
# Returns: index from 0 .. 2**lookahead into options_nbit representing best available choice for position (x,y)
cdef int dither_lookahead(Dither* dither, unsigned char palette_depth, float[:, :, ::1] palette_cam16,
float[:, :, ::1] palette_rgb, float[:, :, ::1] image_rgb, int x, int y, unsigned char last_pixels,
int x_res, float[:,::1] rgb_to_cam16ucs, Context context) nogil:
cdef int candidate, next_pixels, i, j
cdef float[3] quant_error
cdef int best
cdef float best_error = 2**31-1
cdef float total_error
cdef unsigned char current_pixels
cdef int phase
cdef common.float3 lah_cam16ucs
cdef float[3] cam
# Don't bother dithering past the lookahead horizon or edge of screen.
cdef int xxr = min(x + context.pixel_lookahead, x_res)
cdef int lah_shape1 = xxr - x
cdef int lah_shape2 = 3
# TODO: try again with memoryview - does it actually have overhead here?
cdef float *lah_image_rgb = <float *> malloc(lah_shape1 * lah_shape2 * sizeof(float))
# For each 2**lookahead possibilities for the on/off state of the next lookahead pixels, apply error diffusion
# and compute the total squared error to the source image. Since we only have two possible colours for each
# given pixel (dependent on the state already chosen for pixels to the left), we need to look beyond local minima.
# i.e. it might be better to make a sub-optimal choice for this pixel if it allows access to much better pixel
# colours at later positions.
for candidate in range(1 << context.bit_lookahead):
# Working copy of input pixels
for i in range(xxr - x):
for j in range(3):
lah_image_rgb[i * lah_shape2 + j] = image_rgb[y, x+i, j]
total_error = 0
if context.is_hgr:
# A HGR screen byte controls 14 or 15 screen pixels
next_pixels = compute_fat_pixels(candidate, last_pixels)
# DHGR pixels are 1:1 with memory bits
next_pixels = candidate
# Apply dithering to lookahead horizon or edge of screen
for i in range(xxr - x):
xl = dither_bounds_xl(dither, i)
xr = dither_bounds_xr(dither, xxr - x, i)
phase = (x + i + context.phase_shift) % 4
current_pixels = shift_pixel_window(
last_pixels, next_pixels=next_pixels, shift_right_by=i+1, window_width=palette_depth)
# We don't update the input at position x (since we've already chosen fixed outputs), but we do propagate
# quantization errors to positions >x so we can compensate for how good/bad these choices were. i.e. the
# current_pixels choices are fixed, but we can still distribute quantization error from having made these
# choices, in order to compute the total error.
for j in range(3):
quant_error[j] = lah_image_rgb[i * lah_shape2 + j] - palette_rgb[current_pixels, phase, j]
apply_one_line(dither, xl, xr, i, lah_image_rgb, lah_shape2, quant_error)
# Accumulate error distance from pixel colour to target colour in CAM16UCS colour space
lah_cam16ucs = common.convert_rgb_to_cam16ucs(
rgb_to_cam16ucs, lah_image_rgb[i*lah_shape2], lah_image_rgb[i*lah_shape2+1],
for j in range(3):
cam[j] = palette_cam16[current_pixels, phase, j]
total_error += common.colour_distance_squared(lah_cam16ucs.data, cam)
if total_error >= best_error:
# No need to continue
if total_error < best_error:
best_error = total_error
best = candidate
return best
# Perform error diffusion to a single image row.
# Args:
# dither: dither pattern to apply
# xl: lower x bounding box
# xr: upper x bounding box
# x: starting horizontal position to apply error diffusion
# image: array of shape (image_shape1, 3) representing RGB pixel data for a single image line, to be mutated.
# image_shape1: horizontal dimension of image
# quant_error: RGB quantization error to be diffused
cdef inline void apply_one_line(Dither* dither, int xl, int xr, int x, float[] image, int image_shape1,
float[] quant_error) noexcept nogil:
cdef int i, j
cdef float error_fraction
for i in range(xl, xr):
error_fraction = dither.pattern[i - x + dither.x_origin]
for j in range(3):
image[i * image_shape1 + j] = common.clip(image[i * image_shape1 + j] + error_fraction * quant_error[j], 0, 1)
# Perform error diffusion across multiple image rows.
# Args:
# dither: dither pattern to apply
# x_res: horizontal image resolution
# y_res: vertical image resolution
# x: starting horizontal position to apply error diffusion
# y: starting vertical position to apply error diffusion
# image: RGB pixel data, to be mutated
# quant_error: RGB quantization error to be diffused
cdef void apply(Dither* dither, int x_res, int y_res, int x, int y, float[:,:,::1] image, float[] quant_error) noexcept nogil:
cdef int i, j, k
cdef int yt = dither_bounds_yt(dither, y)
cdef int yb = dither_bounds_yb(dither, y_res, y)
cdef int xl = dither_bounds_xl(dither, x)
cdef int xr = dither_bounds_xr(dither, x_res, x)
cdef float error_fraction
for i in range(yt, yb):
for j in range(xl, xr):
error_fraction = dither.pattern[(i - y) * dither.x_shape + j - x + dither.x_origin]
for k in range(3):
image[i,j,k] = common.clip(image[i,j,k] + error_fraction * quant_error[k], 0, 1)
cdef image_nbit_to_bitmap(
(unsigned char)[:, ::1] image_nbit, unsigned int x_res, unsigned int y_res, unsigned char palette_depth):
cdef unsigned int x, y
bitmap = np.zeros((y_res, x_res), dtype=bool)
for y in range(y_res):
for x in range(x_res):
# MSB of each array element is the pixel state at (x, y)
bitmap[y, x] = image_nbit[y, x] >> (palette_depth - 1)
return bitmap
# Dither a source image
# Args:
# screen: screen.Screen object
# image_rgb: input RGB image
# dither: dither_pattern.DitherPattern to apply during dithering
# lookahead: how many x positions to look ahead to optimize colour choices
# verbose: whether to output progress during image conversion
# Returns: tuple of n-bit output image array and RGB output image array
def dither_image(
screen, float[:, :, ::1] image_rgb, dither, int lookahead, unsigned char verbose, float[:, ::1] rgb_to_cam16ucs):
cdef int y, x
cdef unsigned char i, j, pixels_nbit, phase
cdef float[3] quant_error
cdef unsigned char output_pixel_nbit
cdef unsigned int next_pixels
cdef float[3] output_pixel_rgb
# Hoist some python attribute accesses into C variables for efficient access during the main loop
cdef int yres = screen.Y_RES
cdef int xres = screen.X_RES
# TODO: convert this instead of storing on palette?
cdef float[:, :, ::1] palette_cam16 = np.zeros((len(screen.palette.CAM16UCS), 4, 3), dtype=np.float32)
for pixels_nbit, phase in screen.palette.CAM16UCS.keys():
for i in range(3):
palette_cam16[pixels_nbit, phase, i] = screen.palette.CAM16UCS[pixels_nbit, phase][i]
cdef float[:, :, ::1] palette_rgb = np.zeros((len(screen.palette.RGB), 4, 3), dtype=np.float32)
for pixels_nbit, phase in screen.palette.RGB.keys():
for i in range(3):
palette_rgb[pixels_nbit, phase, i] = screen.palette.RGB[pixels_nbit, phase][i] / 255
cdef Dither cdither
cdither.y_shape = dither.PATTERN.shape[0]
cdither.x_shape = dither.PATTERN.shape[1]
cdither.y_origin = dither.ORIGIN[0]
cdither.x_origin = dither.ORIGIN[1]
# TODO: should be just as efficient to use a memoryview?
cdither.pattern = <float *> malloc(cdither.x_shape * cdither.y_shape * sizeof(float))
for i in range(cdither.y_shape):
for j in range(cdither.x_shape):
cdither.pattern[i * cdither.x_shape + j] = dither.PATTERN[i, j]
cdef unsigned char palette_depth = screen.palette.PALETTE_DEPTH
# The nbit image representation contains the trailing n dot values as an n-bit value with MSB representing the
# current pixel. This choice (cf LSB) is slightly awkward but matches the DHGR behaviour that bit positions in
# screen memory map LSB to MSB from L to R. The value of n is chosen by the palette depth, i.e. how many trailing
# dot positions are used to determine the colour of a given pixel.
cdef (unsigned char)[:, ::1] image_nbit = np.empty((image_rgb.shape[0], image_rgb.shape[1]), dtype=np.uint8)
cdef Context context
if screen.MODE == screen_py.Mode.HI_RES:
context.is_hgr = 1
context.bit_lookahead = 8
context.pixel_lookahead = 15
# HGR and DHGR have a timing phase shift which rotates the effective mappings from screen dots to colours
context.phase_shift = 3
context.is_hgr = 0
context.bit_lookahead = lookahead
context.pixel_lookahead = lookahead
context.phase_shift = 0
cdef (unsigned char)[:, ::1] linear_bytemap = np.zeros((192, 40), dtype=np.uint8)
# After performing lookahead, move ahead this many pixels at once.
cdef int apply_batch_size
if context.is_hgr:
# For HGR we have to apply an entire screen byte at a time, which controls 14 or 15 pixels (see
# compute_fat_pixels above). This is because the high bit shifts this entire group of 14 pixels at once,
# so we have to make a single decision about whether or not to enable it.
apply_batch_size = 14
# For DHGR we can choose each pixel state independently, so we get better results if we apply one pixel at
# a time.
apply_batch_size = 1
for y in range(yres):
if verbose:
print("%d/%d" % (y, yres))
output_pixel_nbit = 0
for x in range(xres):
if x % apply_batch_size == 0:
# Compute all possible 2**N choices of n-bit pixel colours for positions x .. x + lookahead
# Apply error diffusion for each of these 2**N choices, and compute which produces the closest match
# to the source image over the succeeding N pixels
next_pixels = dither_lookahead(
&cdither, palette_depth, palette_cam16, palette_rgb, image_rgb, x, y, output_pixel_nbit, xres,
rgb_to_cam16ucs, context)
if context.is_hgr:
linear_bytemap[y, x // 14] = next_pixels
next_pixels = compute_fat_pixels(next_pixels, output_pixel_nbit)
# Apply best choice for next 1 pixel
output_pixel_nbit = shift_pixel_window(
output_pixel_nbit, next_pixels, shift_right_by=x % apply_batch_size + 1, window_width=palette_depth)
# Apply error diffusion from chosen output pixel value
for i in range(3):
output_pixel_rgb[i] = palette_rgb[output_pixel_nbit, x % 4, i]
quant_error[i] = image_rgb[y,x,i] - output_pixel_rgb[i]
apply(&cdither, xres, yres, x, y, image_rgb, quant_error)
# Update image with our chosen image pixel
image_nbit[y, x] = output_pixel_nbit
for i in range(3):
image_rgb[y, x, i] = output_pixel_rgb[i]
return image_nbit_to_bitmap(image_nbit, xres, yres, palette_depth), linear_bytemap