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 from copy import deepcopy
  26
  27 # bits of the integer 'val'.
  28 def reverse_bits(val, width):
  29     result = 0
  30     for _ in range(width):
  31         result = (result << 1) | (val & 1)
  32         val >>= 1
  33     return result
  34
  35
  36 # DCT type II, unscaled. Algorithm by Byeong Gi Lee, 1984.
  37 # See: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.118.3056&rep=rep1&type=pdf#page=34
  38 def transform(vector, indent=0):
  39     idt = "   " * indent
  40     n = len(vector)
  41     if n == 1:
  42         return list(vector)
  43     elif n == 0 or n % 2 != 0:
  44         raise ValueError()
  45     else:
  46         half = n // 2
  47         alpha = [(vector[i] + vector[-(i + 1)]) for i in range(half)]
  48         beta  = [(vector[i] - vector[-(i + 1)]) /
  49                  (math.cos((i + 0.5) * math.pi / n) * 2.0)
  50                     for i in range(half)]
  51         alpha = transform(alpha)
  52         beta  = transform(beta )
  53         result = []
  54         for i in range(half - 1):
  55             result.append(alpha[i])
  56             result.append(beta[i] + beta[i + 1])
  57         result.append(alpha[-1])
  58         result.append(beta [-1])
  59         return result
  60
  61
  62 def transform(vector, indent=0):
  63     idt = "   " * indent
  64     n = len(vector)
  65     if n == 1:
  66         return list(vector)
  67     elif n == 0 or n % 2 != 0:
  68         raise ValueError()
  69     else:
  70         half = n // 2
  71         alpha = [0] * half
  72         beta = [0] * half
  73         print (idt, "xf", vector)
  74         print (idt, "coeff", n, "->", end=" ")
  75         for i in range(half):
  76             t1, t2 = vector[i], vector[n-i-1]
  77             k = (math.cos((i + 0.5) * math.pi / n) * 2.0)
  78             print (i, n-i-1, "i/n", (i+0.5)/n, ":", k, end= " ")
  79             alpha[i] = t1 + t2
  80             beta[i] = (t1 - t2) * (1/k)
  81         print ()
  82         print (idt, "n", n, "alpha", end=" ")
  83         for i in range(0, n, 2):
  84             print (i, i//2, alpha[i//2], end=" ")
  85         print()
  86         print (idt, "n", n, "beta", end=" ")
  87         for i in range(0, n, 2):
  88             print (i, beta[i//2], end=" ")
  89         print()
  90         alpha = transform(alpha, indent+1)
  91         beta  = transform(beta , indent+1)
  92         result = [0] * n
  93         for i in range(half):
  94             result[i*2] = alpha[i]
  95             result[i*2+1] = beta[i]
  96         print(idt, "merge", result)
  97         for i in range(half - 1):
  98             result[i*2+1] += result[i*2+3]
  99         print(idt, "result", result)
 100         return result
 101
 102
 103 def transform_itersum(vector, indent=0):
 104     idt = "   " * indent
 105     n = len(vector)
 106     if n == 1:
 107         return list(vector)
 108     elif n == 0 or n % 2 != 0:
 109         raise ValueError()
 110     else:
 111         half = n // 2
 112         alpha = [0] * half
 113         beta = [0] * half
 114         for i in range(half):
 115             t1, t2 = vector[i], vector[i+half]
 116             alpha[i] = t1
 117             beta[i] = t2
 118         alpha = transform_itersum(alpha, indent+1)
 119         beta  = transform_itersum(beta , indent+1)
 120         result = [0] * n
 121         for i in range(half):
 122             result[i*2] = alpha[i]
 123             result[i*2+1] = beta[i]
 124         print(idt, "iter-merge", result)
 125         for i in range(half - 1):
 126             result[i*2+1] += result[i*2+3]
 127         print(idt, "iter-result", result)
 128         return result
 129
 130
 131
 132 def transform2(vec):
 133
 134     vec = deepcopy(vec)
 135     # Initialization
 136     n = len(vec)
 137     print ()
 138     print ("transform2", n)
 139     levels = n.bit_length() - 1
 140
 141     # reference (read/write) the in-place data in *reverse-bit-order*
 142     ri = list(range(n))
 143     ri = [ri[reverse_bits(i, levels)] for i in range(n)]
 144
 145     # and pretend we LDed the data in bit-reversed order as well
 146     vec = [vec[reverse_bits(i, levels)] for i in range(n)]
 147
 148     size = n
 149     while size >= 2:
 150         halfsize = size // 2
 151         tablestep = n // size
 152         ir = list(range(0, n, size))
 153         print ("  xform", size, ir)
 154         for i in ir:
 155             k = 0
 156             j = list(range(i, i + halfsize))
 157             jr = list(range(i+halfsize, i + size))
 158             jr.reverse()
 159             print ("  xform jr", j, jr)
 160             for ci, (jl, jh) in enumerate(zip(j, jr)):
 161                 t1, t2 = vec[ri[jl]], vec[ri[jh]]
 162                 coeff = (math.cos((ci + 0.5) * math.pi / size) * 2.0)
 163                 # normally DCT would use jl+halfsize not jh, here.
 164                 # to be able to work in-place, the idea is to perform a
 165                 # swap afterwards.  however actually we swap the *indices*
 166                 vec[ri[jl]] = t1 + t2
 167                 vec[ri[jh]] = (t1 - t2) * (1/coeff)
 168                 print ("coeff", size, i, k, "jl", jl, "jh", jh,
 169                        "i/n", (k+0.5)/size, coeff, vec[ri[jl]], vec[ri[jh]])
 170                 k += tablestep
 171             # instead of using jl+halfsize, perform a swap here.
 172             # use half of j/jr because actually jl+halfsize = reverse(j)
 173             # actually: swap the *indices*... not the actual data.
 174             # incredibly... bizarrely... this works *without* having
 175             # to do anything else.
 176             hz2 = halfsize // 2 # can be zero which stops reversing 1-item lists
 177             for ci, (jl, jh) in enumerate(zip(j[:hz2], jr[:hz2])):
 178                 tmp = ri[jl+halfsize]
 179                 ri[jl+halfsize] = ri[jh]
 180                 ri[jh] = tmp
 181                 print ("     swap", size, i, ri[jl+halfsize], ri[jh])
 182         size //= 2
 183
 184     print("post-swapped", ri)
 185     print("transform2 pre-itersum", vec)
 186
 187     n = len(vec)
 188     size = n // 2
 189     while size >= 2:
 190         halfsize = size // 2
 191         ir = list(range(0, halfsize))
 192         print ("itersum", halfsize, size, ir)
 193         for i in ir:
 194             jr = list(range(i+halfsize, i+n-halfsize, size))
 195             print ("itersum    jr", i+halfsize, i+size, jr)
 196             for jh in jr:
 197                 vec[jh] += vec[jh+size]
 198                 print ("    itersum", size, i, jh, jh+size)
 199         size //= 2
 200
 201     print("transform2 result", vec)
 202
 203     return vec
 204
 205
 206 # DCT type III, unscaled. Algorithm by Byeong Gi Lee, 1984.
 207 # See: https://www.nayuki.io/res/fast-discrete-cosine-transform-algorithms/lee-new-algo-discrete-cosine-transform.pdf
 208 def inverse_transform(vector, root=True, indent=0):
 209     idt = "   " * indent
 210     if root:
 211         vector = list(vector)
 212         vector[0] /= 2
 213     n = len(vector)
 214     if n == 1:
 215         return vector, [0]
 216     elif n == 0 or n % 2 != 0:
 217         raise ValueError()
 218     else:
 219         half = n // 2
 220         alpha = [vector[0]]
 221         beta  = [vector[1]]
 222         for i in range(2, n, 2):
 223             alpha.append(vector[i])
 224             beta.append(vector[i - 1] + vector[i + 1])
 225         print (idt, "n", n, "alpha 0", end=" ")
 226         for i in range(2, n, 2):
 227             print (i, end=" ")
 228         print ("beta 1", end=" ")
 229         for i in range(2, n, 2):
 230             print ("%d+%d" % (i-1, i+1), end=" ")
 231         print()
 232         inverse_transform(alpha, False, indent+1)
 233         inverse_transform(beta , False, indent+1)
 234         for i in range(half):
 235             x = alpha[i]
 236             y = beta[i] / (math.cos((i + 0.5) * math.pi / n) * 2)
 237             vector[i] = x + y
 238             vector[-(i + 1)] = x - y
 239             print (idt, " v[%d] = alpha[%d]+beta[%d]" % (i, i, i))
 240             print (idt, " v[%d] = alpha[%d]-beta[%d]" % (n-i-1, i, i))
 241         return vector
 242
 243
 244 def inverse_transform2(vector, root=True):
 245     n = len(vector)
 246     if root:
 247         vector = list(vector)
 248     if n == 1:
 249         return vector
 250     elif n == 0 or n % 2 != 0:
 251         raise ValueError()
 252     else:
 253         half = n // 2
 254         alpha = [0]
 255         beta  = [1]
 256         for i in range(2, n, 2):
 257             alpha.append(i)
 258             beta.append(("add", i - 1, i + 1))
 259         inverse_transform2(alpha, False)
 260         inverse_transform2(beta , False)
 261         for i in range(half):
 262             x = alpha[i]
 263             y = ("cos", beta[i], i)
 264             vector[i] = ("add", x, y)
 265             vector[-(i + 1)] = ("sub", x, y)
 266         return vector
 267
 268
 269 def itersum_explore(vector, indent=0):
 270     idt = "   " * indent
 271     n = len(vector)
 272     if n == 1:
 273         return list(vector)
 274     elif n == 0 or n % 2 != 0:
 275         raise ValueError()
 276     else:
 277         half = n // 2
 278         alpha = [0] * half
 279         beta = [0] * half
 280         for i in range(half):
 281             t1, t2 = vector[i], vector[i+half]
 282             alpha[i] = t1
 283             beta[i] = t2
 284         alpha = itersum_explore(alpha, indent+1)
 285         beta  = itersum_explore(beta , indent+1)
 286         result = [0] * n
 287         for i in range(half):
 288             result[i*2] = alpha[i]
 289             result[i*2+1] = beta[i]
 290         print(idt, "iter-merge", result)
 291         for i in range(half - 1):
 292             result[i*2+1] = ("add", result[i*2+1], result[i*2+3])
 293         print(idt, "iter-result", result)
 294         return result
 295
 296
 297 def itersum_explore2(vec, indent=0):
 298     n = len(vec)
 299     size = n // 2
 300     while size >= 2:
 301         halfsize = size // 2
 302         ir = list(range(0, halfsize))
 303         #ir.reverse()
 304         print ("itersum", halfsize, size, ir)
 305         for i in ir:
 306             jr = list(range(i+halfsize, i+n-halfsize, size))
 307             print ("itersum    jr", i+halfsize, i+size, jr)
 308             for jh in jr:
 309                 vec[jh] = ("add", vec[jh], vec[jh+size])
 310                 print ("    itersum", size, i, jh, jh+size)
 311         size //= 2
 312
 313     #if reverse:
 314     #    vec = [vec[reverse_bits(i, levels)] for i in range(n)]
 315
 316     return vec
 317
 318 if __name__ == '__main__':
 319     n = 16
 320     vec = list(range(n))
 321     levels = n.bit_length() - 1
 322     vec = [vec[reverse_bits(i, levels)] for i in range(n)]
 323     ops = itersum_explore(vec)
 324     #ops = [ops[reverse_bits(i, levels)] for i in range(n)]
 325     for i, x in enumerate(ops):
 326         print (i, x)
 327
 328     n = 16
 329     vec = list(range(n))
 330     levels = n.bit_length() - 1
 331     #vec = [vec[reverse_bits(i, levels)] for i in range(n)]
 332     ops = itersum_explore2(vec)
 333     for i, x in enumerate(ops):
 334         print (i, x)