src/openpower/decoder/isa/fastdctlee.py

   1 #
   2 # Fast discrete cosine transform algorithms (Python)
   3 #
   4 # Copyright (c) 2020 Project Nayuki. (MIT License)
   5 # https://www.nayuki.io/page/fast-discrete-cosine-transform-algorithms
   6 #
   7 # Permission is hereby granted, free of charge, to any person obtaining a copy of
   8 # this software and associated documentation files (the "Software"), to deal in
   9 # the Software without restriction, including without limitation the rights to
  10 # use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
  11 # the Software, and to permit persons to whom the Software is furnished to do so,
  12 # subject to the following conditions:
  13 # - The above copyright notice and this permission notice shall be included in
  14 #   all copies or substantial portions of the Software.
  15 # - The Software is provided "as is", without warranty of any kind, express or
  16 #   implied, including but not limited to the warranties of merchantability,
  17 #   fitness for a particular purpose and noninfringement. In no event shall the
  18 #   authors or copyright holders be liable for any claim, damages or other
  19 #   liability, whether in an action of contract, tort or otherwise, arising from,
  20 #   out of or in connection with the Software or the use or other dealings in the
  21 #   Software.
  22 #
  23
  24 import math
  25
  26
  27 # DCT type II, unscaled. Algorithm by Byeong Gi Lee, 1984.
  28 # See: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.118.3056&rep=rep1&type=pdf#page=34
  29 def transform(vector):
  30     n = len(vector)
  31     if n == 1:
  32         return list(vector)
  33     elif n == 0 or n % 2 != 0:
  34         raise ValueError()
  35     else:
  36         half = n // 2
  37         alpha = [(vector[i] + vector[-(i + 1)]) for i in range(half)]
  38         beta  = [(vector[i] - vector[-(i + 1)]) /
  39                  (math.cos((i + 0.5) * math.pi / n) * 2.0)
  40                     for i in range(half)]
  41         alpha = transform(alpha)
  42         beta  = transform(beta )
  43         result = []
  44         for i in range(half - 1):
  45             result.append(alpha[i])
  46             result.append(beta[i] + beta[i + 1])
  47         result.append(alpha[-1])
  48         result.append(beta [-1])
  49         return result
  50
  51
  52 # DCT type III, unscaled. Algorithm by Byeong Gi Lee, 1984.
  53 # See: https://www.nayuki.io/res/fast-discrete-cosine-transform-algorithms/lee-new-algo-discrete-cosine-transform.pdf
  54 def inverse_transform(vector, root=True, indent=0):
  55     idt = "   " * indent
  56     if root:
  57         vector = list(vector)
  58         vector[0] /= 2
  59     n = len(vector)
  60     if n == 1:
  61         return vector, [0]
  62     elif n == 0 or n % 2 != 0:
  63         raise ValueError()
  64     else:
  65         half = n // 2
  66         alpha = [vector[0]]
  67         beta  = [vector[1]]
  68         for i in range(2, n, 2):
  69             alpha.append(vector[i])
  70             beta.append(vector[i - 1] + vector[i + 1])
  71         print (idt, "n", n, "alpha 0", end=" ")
  72         for i in range(2, n, 2):
  73             print (i, end=" ")
  74         print ("beta 1", end=" ")
  75         for i in range(2, n, 2):
  76             print ("%d+%d" % (i-1, i+1), end=" ")
  77         print()
  78         inverse_transform(alpha, False, indent+1)
  79         inverse_transform(beta , False, indent+1)
  80         for i in range(half):
  81             x = alpha[i]
  82             y = beta[i] / (math.cos((i + 0.5) * math.pi / n) * 2)
  83             vector[i] = x + y
  84             vector[-(i + 1)] = x - y
  85             print (idt, " v[%d] = alpha[%d]+beta[%d]" % (i, i, i))
  86             print (idt, " v[%d] = alpha[%d]-beta[%d]" % (n-i-1, i, i))
  87         return vector
  88
  89
  90 def inverse_transform2(vector, root=True):
  91     n = len(vector)
  92     if root:
  93         vector = list(vector)
  94     if n == 1:
  95         return vector
  96     elif n == 0 or n % 2 != 0:
  97         raise ValueError()
  98     else:
  99         half = n // 2
 100         alpha = [0]
 101         beta  = [1]
 102         for i in range(2, n, 2):
 103             alpha.append(i)
 104             beta.append(("add", i - 1, i + 1))
 105         inverse_transform2(alpha, False)
 106         inverse_transform2(beta , False)
 107         for i in range(half):
 108             x = alpha[i]
 109             y = ("cos", beta[i], i)
 110             vector[i] = ("add", x, y)
 111             vector[-(i + 1)] = ("sub", x, y)
 112         return vector
 113
 114
 115 if __name__ == '__main__':
 116     vector = range(8)
 117     ops = inverse_transform(vector)
 118     print (ops)