1#!/usr/bin/python
2
3'''
4Copyright 2013 Google Inc.
5
6Use of this source code is governed by a BSD-style license that can be
7found in the LICENSE file.
8'''
9
10import math
11import pprint
12
13def withinStdDev(n):
14  """Returns the percent of samples within n std deviations of the normal."""
15  return math.erf(n / math.sqrt(2))
16
17def withinStdDevRange(a, b):
18  """Returns the percent of samples within the std deviation range a, b"""
19  if b < a:
20    return 0;
21
22  if a < 0:
23    if b < 0:
24      return (withinStdDev(-a) - withinStdDev(-b)) / 2;
25    else:
26      return (withinStdDev(-a) + withinStdDev(b)) / 2;
27  else:
28    return (withinStdDev(b) - withinStdDev(a)) / 2;
29
30
31#We have a bunch of smudged samples which represent the average coverage of a range.
32#We have a 'center' which may not line up with those samples.
33#From the 'center' we want to make a normal approximation where '5' sample width out we're at '3' std deviations.
34#The first and last samples may not be fully covered.
35
36#This is the sub-sample shift for each set of FIR coefficients (the centers of the lcds in the samples)
37#Each subpxl takes up 1/3 of a pixel, so they are centered at x=(i/n+1/2n), or 1/6, 3/6, 5/6 of a pixel.
38#Each sample takes up 1/4 of a pixel, so the results fall at (x*4)%1, or 2/3, 0, 1/3 of a sample.
39samples_per_pixel = 4
40subpxls_per_pixel = 3
41#sample_offsets is (frac, int) in sample units.
42sample_offsets = [math.modf((float(subpxl_index)/subpxls_per_pixel + 1.0/(2.0*subpxls_per_pixel))*samples_per_pixel) for subpxl_index in range(subpxls_per_pixel)]
43
44#How many samples to consider to the left and right of the subpxl center.
45sample_units_width = 5
46
47#The std deviation at sample_units_width.
48std_dev_max = 3
49
50#The target sum is in some fixed point representation.
51#Values larger the 1 in fixed point simulate ink spread.
52target_sum = 0x110
53
54for sample_offset, sample_align in sample_offsets:
55  coeffs = []
56  coeffs_rounded = []
57
58  #We start at sample_offset - sample_units_width
59  current_sample_left = sample_offset - sample_units_width
60  current_std_dev_left = -std_dev_max
61
62  done = False
63  while not done:
64    current_sample_right = math.floor(current_sample_left + 1)
65    if current_sample_right > sample_offset + sample_units_width:
66      done = True
67      current_sample_right = sample_offset + sample_units_width
68    current_std_dev_right = current_std_dev_left + ((current_sample_right - current_sample_left) / sample_units_width) * std_dev_max
69
70    coverage = withinStdDevRange(current_std_dev_left, current_std_dev_right)
71    coeffs.append(coverage * target_sum)
72    coeffs_rounded.append(int(round(coverage * target_sum)))
73
74    current_sample_left = current_sample_right
75    current_std_dev_left = current_std_dev_right
76
77  # Now we have the numbers we want, but our rounding needs to add up to target_sum.
78  delta = 0
79  coeffs_rounded_sum = sum(coeffs_rounded)
80  if coeffs_rounded_sum > target_sum:
81    # The coeffs add up to too much. Subtract 1 from the ones which were rounded up the most.
82    delta = -1
83
84  if coeffs_rounded_sum < target_sum:
85    # The coeffs add up to too little. Add 1 to the ones which were rounded down the most.
86    delta = 1
87
88  if delta:
89    print "Initial sum is 0x%0.2X, adjusting." % (coeffs_rounded_sum,)
90    coeff_diff = [(coeff_rounded - coeff) * delta
91                  for coeff, coeff_rounded in zip(coeffs, coeffs_rounded)]
92
93    class IndexTracker:
94      def __init__(self, index, item):
95        self.index = index
96        self.item = item
97      def __lt__(self, other):
98        return self.item < other.item
99      def __repr__(self):
100        return "arr[%d] == %s" % (self.index, repr(self.item))
101
102    coeff_pkg = [IndexTracker(i, diff) for i, diff in enumerate(coeff_diff)]
103    coeff_pkg.sort()
104
105    # num_elements_to_force_round had better be < (2 * sample_units_width + 1) or
106    # * our math was wildy wrong
107    # * an awful lot of the curve is out side our sample
108    # either is pretty bad, and probably means the results will not be useful.
109    num_elements_to_force_round = abs(coeffs_rounded_sum - target_sum)
110    for i in xrange(num_elements_to_force_round):
111      print "Adding %d to index %d to force round %f." % (delta, coeff_pkg[i].index, coeffs[coeff_pkg[i].index])
112      coeffs_rounded[coeff_pkg[i].index] += delta
113
114  print "Prepending %d 0x00 for allignment." % (sample_align,)
115  coeffs_rounded_aligned = ([0] * int(sample_align)) + coeffs_rounded
116
117  print ', '.join(["0x%0.2X" % coeff_rounded for coeff_rounded in coeffs_rounded_aligned])
118  print sum(coeffs), hex(sum(coeffs_rounded))
119  print
120