1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
|
#!/usr/bin/python3
# SPDX-License-Identifier: GPL-2.0-or-later
# Copyright (C) 2022, Ideas on Board Oy
#
# Generate color space conversion table coefficients with configurable
# fixed-point precision
import argparse
import enum
import sys
encodings = {
'rec601': [
[ 0.299, 0.587, 0.114 ],
[ -0.299 / 1.772, -0.587 / 1.772, 0.886 / 1.772 ],
[ 0.701 / 1.402, -0.587 / 1.402, -0.114 / 1.402 ]
],
'rec709': [
[ 0.2126, 0.7152, 0.0722 ],
[ -0.2126 / 1.8556, -0.7152 / 1.8556, 0.9278 / 1.8556 ],
[ 0.7874 / 1.5748, -0.7152 / 1.5748, -0.0722 / 1.5748 ]
],
'rec2020': [
[ 0.2627, 0.6780, 0.0593 ],
[ -0.2627 / 1.8814, -0.6780 / 1.8814, 0.9407 / 1.8814 ],
[ 0.7373 / 1.4746, -0.6780 / 1.4746, -0.0593 / 1.4746 ],
],
'smpte240m': [
[ 0.2122, 0.7013, 0.0865 ],
[ -0.2122 / 1.8270, -0.7013 / 1.8270, 0.9135 / 1.8270 ],
[ 0.7878 / 1.5756, -0.7013 / 1.5756, -0.0865 / 1.5756 ],
],
}
class Precision(object):
def __init__(self, precision):
if precision[0].upper() != 'Q':
raise RuntimeError(f'Invalid precision `{precision}`')
prec = precision[1:].split('.')
if len(prec) != 2:
raise RuntimeError(f'Invalid precision `{precision}`')
self.__prec = [int(v) for v in prec]
@property
def integer(self):
return self.__prec[0]
@property
def fractional(self):
return self.__prec[1]
@property
def total(self):
# Add 1 for the sign bit
return self.__prec[0] + self.__prec[1] + 1
class Quantization(enum.Enum):
FULL = 0
LIMITED = 1
def scale_coeff(coeff, quantization, luma, precision):
"""Scale a coefficient to the output range dictated by the quantization and
the precision.
Parameters
----------
coeff : float
The CSC matrix coefficient to scale
quantization : Quantization
The quantization, either FULL or LIMITED
luma : bool
True if the coefficient corresponds to a luma value, False otherwise
precision : int
The desired precision for the scaled coefficient as a number of
fractional bits
"""
# Assume the input range is 8 bits. The output range is set by the
# quantization and differs between luma and chrome components for limited
# range.
in_range = 255 - 0
if quantization == Quantization.FULL:
out_range = 255 - 0
elif luma:
out_range = 235 - 16
else:
out_range = 240 - 16
return coeff * out_range / in_range * (1 << precision)
def round_array(values):
"""Round a list of signed floating point values to the closest integer while
preserving the (rounded) value of the sum of all elements.
"""
# Calculate the rounding error as the difference between the rounded sum of
# values and the sum of rounded values. This is by definition an integer
# (positive or negative), which indicates how many values will need to be
# 'flipped' to the opposite rounding.
rounded_values = [round(value) for value in values]
sum_values = round(sum(values))
sum_error = sum_values - sum(rounded_values)
if sum_error == 0:
return rounded_values
# The next step is to distribute the error among the values, in a way that
# will minimize the relative error introduced in individual values. We
# extend the values list with the rounded value and original index for each
# element, and sort by rounding error. Then we modify the elements with the
# highest or lowest error, depending on whether the sum error is negative
# or positive.
values = [[value, round(value), index] for index, value in enumerate(values)]
values.sort(key=lambda v: v[1] - v[0])
# It could also be argued that the key for the sort order should not be the
# absolute rouding error but the relative error, as the impact of identical
# rounding errors will differ for coefficients with widely different values.
# This is a topic for further research.
#
# values.sort(key=lambda v: (v[1] - v[0]) / abs(v[0]))
if sum_error > 0:
for i in range(sum_error):
values[i][1] += 1
else:
for i in range(-sum_error):
values[len(values) - i - 1][1] -= 1
# Finally, sort back by index, make sure the total rounding error is now 0,
# and return the rounded values.
values.sort(key=lambda v: v[2])
values = [value[1] for value in values]
assert(sum(values) == sum_values)
return values
def main(argv):
# Parse command line arguments.
parser = argparse.ArgumentParser(
description='Generate color space conversion table coefficients with '
'configurable fixed-point precision.'
)
parser.add_argument('--precision', '-p', default='Q1.7',
help='The output fixed point precision in Q notation (sign bit excluded)')
parser.add_argument('--quantization', '-q', choices=['full', 'limited'],
default='limited', help='Quantization range')
parser.add_argument('encoding', choices=encodings.keys(), help='YCbCr encoding')
args = parser.parse_args(argv[1:])
try:
precision = Precision(args.precision)
except Exception:
print(f'Invalid precision `{args.precision}`')
return 1
encoding = encodings[args.encoding]
quantization = Quantization[args.quantization.upper()]
# Scale and round the encoding coefficients based on the precision and
# quantization range.
luma = True
scaled_coeffs = []
for line in encoding:
line = [scale_coeff(coeff, quantization, luma, precision.fractional) for coeff in line]
scaled_coeffs.append(line)
luma = False
rounded_coeffs = []
for line in scaled_coeffs:
line = round_array(line)
# Convert coefficients to the number of bits selected by the precision.
# Negative values will be turned into positive integers using 2's
# complement.
line = [coeff & ((1 << precision.total) - 1) for coeff in line]
rounded_coeffs.append(line)
# Print the result as C code.
nbits = 1 << (precision.total - 1).bit_length()
nbytes = nbits // 4
print(f'static const u{nbits} rgb2yuv_{args.encoding}_{quantization.name.lower()}_coeffs[] = {{')
for line in rounded_coeffs:
line = [f'0x{coeff:0{nbytes}x}' for coeff in line]
print(f'\t{", ".join(line)},')
print('};')
return 0
if __name__ == '__main__':
sys.exit(main(sys.argv))
|
