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, reverse=True):
 133
 134     vec = deepcopy(vec)
 135     # Initialization
 136     n = len(vec)
 137     print ("transform2", n)
 138     levels = n.bit_length() - 1
 139
 140     # reference (read/write) the in-place data in *reverse-bit-order*
 141     if reverse:
 142         ri = range(n)
 143         ri = [ri[reverse_bits(i, levels)] for i in range(n)]
 144
 145     size = n
 146     while size >= 2:
 147         halfsize = size // 2
 148         tablestep = n // size
 149         ir = list(range(0, n, size))
 150         print ("  xform", size, ir)
 151         for i in ir:
 152             k = 0
 153             j = list(range(i, i + halfsize))
 154             jr = list(range(i+halfsize, i + size))
 155             jr.reverse()
 156             print ("  xform jr", j, jr)
 157             vec2 = deepcopy(vec)
 158             for ci, (jl, jh) in enumerate(zip(j, jr)):
 159                 t1, t2 = vec[jl], vec[jh]
 160                 coeff = (math.cos((ci + 0.5) * math.pi / size) * 2.0)
 161                 vec2[jl] = t1 + t2
 162                 vec2[jl+halfsize] = (t1 - t2) * (1/coeff)
 163                 print ("coeff", size, i, k, "jl", jl, "jh", jh,
 164                        "i/n", (k+0.5)/size, coeff, vec[jl], vec[jh])
 165                 k += tablestep
 166             vec = vec2
 167         size //= 2
 168
 169     print("transform2 pre-itersum", vec)
 170     # Copy with bit-reversed permutation
 171
 172     print("transform2 intermediate", vec)
 173
 174     n = len(vec)
 175     size = n // 2
 176     while size >= 2:
 177         halfsize = size // 2
 178         ir = list(range(0, halfsize))
 179         #ir.reverse()
 180         print ("itersum", halfsize, size, ir)
 181         for i in ir:
 182             jr = list(range(i+halfsize, i+n-halfsize, size))
 183             print ("itersum    jr", i+halfsize, i+size, jr)
 184             for jh in jr:
 185                 vec[ri[jh]] += vec[ri[jh+size]]
 186                 print ("    itersum", size, i, jh, jh+size)
 187         size //= 2
 188
 189     if reverse:
 190         vec = [vec[reverse_bits(i, levels)] for i in range(n)]
 191
 192     print("transform2 result", vec)
 193
 194     return vec
 195
 196
 197 # DCT type III, unscaled. Algorithm by Byeong Gi Lee, 1984.
 198 # See: https://www.nayuki.io/res/fast-discrete-cosine-transform-algorithms/lee-new-algo-discrete-cosine-transform.pdf
 199 def inverse_transform(vector, root=True, indent=0):
 200     idt = "   " * indent
 201     if root:
 202         vector = list(vector)
 203         vector[0] /= 2
 204     n = len(vector)
 205     if n == 1:
 206         return vector, [0]
 207     elif n == 0 or n % 2 != 0:
 208         raise ValueError()
 209     else:
 210         half = n // 2
 211         alpha = [vector[0]]
 212         beta  = [vector[1]]
 213         for i in range(2, n, 2):
 214             alpha.append(vector[i])
 215             beta.append(vector[i - 1] + vector[i + 1])
 216         print (idt, "n", n, "alpha 0", end=" ")
 217         for i in range(2, n, 2):
 218             print (i, end=" ")
 219         print ("beta 1", end=" ")
 220         for i in range(2, n, 2):
 221             print ("%d+%d" % (i-1, i+1), end=" ")
 222         print()
 223         inverse_transform(alpha, False, indent+1)
 224         inverse_transform(beta , False, indent+1)
 225         for i in range(half):
 226             x = alpha[i]
 227             y = beta[i] / (math.cos((i + 0.5) * math.pi / n) * 2)
 228             vector[i] = x + y
 229             vector[-(i + 1)] = x - y
 230             print (idt, " v[%d] = alpha[%d]+beta[%d]" % (i, i, i))
 231             print (idt, " v[%d] = alpha[%d]-beta[%d]" % (n-i-1, i, i))
 232         return vector
 233
 234
 235 def inverse_transform2(vector, root=True):
 236     n = len(vector)
 237     if root:
 238         vector = list(vector)
 239     if n == 1:
 240         return vector
 241     elif n == 0 or n % 2 != 0:
 242         raise ValueError()
 243     else:
 244         half = n // 2
 245         alpha = [0]
 246         beta  = [1]
 247         for i in range(2, n, 2):
 248             alpha.append(i)
 249             beta.append(("add", i - 1, i + 1))
 250         inverse_transform2(alpha, False)
 251         inverse_transform2(beta , False)
 252         for i in range(half):
 253             x = alpha[i]
 254             y = ("cos", beta[i], i)
 255             vector[i] = ("add", x, y)
 256             vector[-(i + 1)] = ("sub", x, y)
 257         return vector
 258
 259
 260 def failllll_transform2(block):
 261     N = len(block)
 262     cos = [0.0] * (N>>1)
 263
 264     front = deepcopy(block)
 265     back = deepcopy(block)
 266
 267     step = 1
 268     j = N *2
 269     half_N = N
 270     prev_half_N = N
 271
 272     while j > 1: #// Cycle of iterations Input Butterfly
 273         half_N = half_N >> 1
 274         current_PI_half_By_N = (math.pi / 2) / prev_half_N
 275         current_PI_By_N = 0.0
 276         step_Phase = current_PI_half_By_N * 2.0
 277         print ("n", N, "cos", end=" ")
 278         for i in range(half_N):
 279             #Precompute Cosine's coefficients
 280             a = current_PI_By_N + current_PI_half_By_N
 281             print (i, a / (math.pi), math.cos(a) * 2, end=" ")
 282             cos[i] = 0.5 / math.cos(a)
 283             current_PI_By_N += step_Phase
 284         print()
 285         k = 0
 286         for x in range(step):
 287             for i in range(half_N):
 288                 shift = k + prev_half_N - i - 1
 289                 back[k + i]          = front[k + i] + front[shift]
 290                 back[k + half_N + i] = (front[k + i] - front[shift]) * cos[i]
 291                 print ("xf coeff", N, j, i, x, "k/kh", k+i, k+half_N+i)
 292             k += prev_half_N
 293         temp = front
 294         front = back
 295         back = temp
 296         j = j >> 1
 297         step = step << 1
 298         prev_half_N = half_N
 299
 300     half_N = 2
 301     prev_half_N = 2
 302     j = 2
 303
 304     print("xform intermediate", front)
 305
 306     while j < N: # Cycle of Out ButterFly
 307         k = 0
 308         print ("out", j, N, step, half_N)
 309         for x in range(step):
 310             for i in range(half_N - 1):
 311                 back[k + (i << 1)] = front[k + i]
 312                 back[k + (i << 1) + 1] = (front[k + half_N + i] +
 313                                           front[k + half_N + i + 1])
 314                 print ("  out", j, x, i, "k", k,
 315                                 "k+i<<1", k+(i<<1), "hh1", k+half_N+i)
 316             back[k + ((half_N - 1) << 1)] = front[k + half_N - 1]
 317             back[k + (half_N << 1) - 1] = front[k + (half_N << 1) - 1]
 318             k += prev_half_N
 319
 320         temp = front
 321         front = back
 322         back = temp
 323         j = j << 1
 324         step = step >> 1
 325         half_N = prev_half_N
 326         prev_half_N = prev_half_N << 1
 327
 328     for i in range(N):
 329         block[i] = front[i] #// Unload DCT coefficients
 330     dN = 2.0
 331     #block[0] = block[0] / dN #// Compute DC.
 332
 333     print("transform2 result", block)
 334     return block
 335
 336
 337 def itersum_explore(vector, indent=0):
 338     idt = "   " * indent
 339     n = len(vector)
 340     if n == 1:
 341         return list(vector)
 342     elif n == 0 or n % 2 != 0:
 343         raise ValueError()
 344     else:
 345         half = n // 2
 346         alpha = [0] * half
 347         beta = [0] * half
 348         for i in range(half):
 349             t1, t2 = vector[i], vector[i+half]
 350             alpha[i] = t1
 351             beta[i] = t2
 352         alpha = itersum_explore(alpha, indent+1)
 353         beta  = itersum_explore(beta , indent+1)
 354         result = [0] * n
 355         for i in range(half):
 356             result[i*2] = alpha[i]
 357             result[i*2+1] = beta[i]
 358         print(idt, "iter-merge", result)
 359         for i in range(half - 1):
 360             result[i*2+1] = ("add", result[i*2+1], result[i*2+3])
 361         print(idt, "iter-result", result)
 362         return result
 363
 364
 365 def itersum_explore2(vec, indent=0):
 366     n = len(vec)
 367     size = n // 2
 368     while size >= 2:
 369         halfsize = size // 2
 370         ir = list(range(0, halfsize))
 371         #ir.reverse()
 372         print ("itersum", halfsize, size, ir)
 373         for i in ir:
 374             jr = list(range(i+halfsize, i+n-halfsize, size))
 375             print ("itersum    jr", i+halfsize, i+size, jr)
 376             for jh in jr:
 377                 vec[jh] = ("add", vec[jh], vec[jh+size])
 378                 print ("    itersum", size, i, jh, jh+size)
 379         size //= 2
 380
 381     #if reverse:
 382     #    vec = [vec[reverse_bits(i, levels)] for i in range(n)]
 383
 384     return vec
 385
 386 if __name__ == '__main__':
 387     n = 16
 388     vec = list(range(n))
 389     levels = n.bit_length() - 1
 390     vec = [vec[reverse_bits(i, levels)] for i in range(n)]
 391     ops = itersum_explore(vec)
 392     #ops = [ops[reverse_bits(i, levels)] for i in range(n)]
 393     for i, x in enumerate(ops):
 394         print (i, x)
 395
 396     n = 16
 397     vec = list(range(n))
 398     levels = n.bit_length() - 1
 399     #vec = [vec[reverse_bits(i, levels)] for i in range(n)]
 400     ops = itersum_explore2(vec)
 401     for i, x in enumerate(ops):
 402         print (i, x)