src/openpower/decoder/isa/remap_dct_yield.py

   1 # DCT "REMAP" scheduler
   2 #
   3 # Modifications made to create an in-place iterative DCT:
   4 # Copyright (c) 2021 Luke Kenneth Casson Leighton <lkcl@lkcl.net>
   5 #
   6 # SPDX: LGPLv3+
   7 #
   8 # Original fastdctlee.py by Nayuki:
   9 # Copyright (c) 2020 Project Nayuki. (MIT License)
  10 # https://www.nayuki.io/page/fast-discrete-cosine-transform-algorithms
  11
  12 import math
  13
  14 # bits of the integer 'val'.
  15 def reverse_bits(val, width):
  16     result = 0
  17     for _ in range(width):
  18         result = (result << 1) | (val & 1)
  19         val >>= 1
  20     return result
  21
  22
  23 # iterative version of [recursively-applied] half-rev.
  24 # relies on the list lengths being power-of-two and the fact
  25 # that bit-inversion of a list of binary numbers is the same
  26 # as reversing the order of the list
  27 # this version is dead easy to implement in hardware.
  28 # a big surprise is that the half-reversal can be done with
  29 # such a simple XOR. the inverse operation is slightly trickier
  30 def halfrev2(vec, pre_rev=True):
  31     res = []
  32     for i in range(len(vec)):
  33         if pre_rev:
  34             res.append(i ^ (i>>1))
  35         else:
  36             ri = i
  37             bl = i.bit_length()
  38             for ji in range(1, bl):
  39                 ri ^= (i >> ji)
  40             res.append(vec[ri])
  41     return res
  42
  43
  44 # python "yield" can be iterated. use this to make it clear how
  45 # the indices are generated by using natural-looking nested loops
  46 def iterate_dct_inner_butterfly_indices(SVSHAPE):
  47     # get indices to iterate over, in the required order
  48     n = SVSHAPE.lims[0]
  49     # createing lists of indices to iterate over in each dimension
  50     # has to be done dynamically, because it depends on the size
  51     # first, the size-based loop (which can be done statically)
  52     x_r = []
  53     size = 2
  54     while size <= n:
  55         x_r.append(size)
  56         size *= 2
  57     # invert order if requested
  58     if SVSHAPE.invxyz[0]:
  59         x_r.reverse()
  60
  61     if len(x_r) == 0:
  62         return
  63
  64     # reference (read/write) the in-place data in *reverse-bit-order*
  65     ri = list(range(n))
  66     if SVSHAPE.submode2 == 0b01:
  67         levels = n.bit_length() - 1
  68         ri = [ri[reverse_bits(i, levels)] for i in range(n)]
  69
  70     # reference list for not needing to do data-swaps, just swap what
  71     # *indices* are referenced (two levels of indirection at the moment)
  72     # pre-reverse the data-swap list so that it *ends up* in the order 0123..
  73     ji = list(range(n))
  74     inplace_mode = SVSHAPE.submode2 == 0b01 and SVSHAPE.skip not in [0b10, 0b11]
  75     if inplace_mode:
  76         #print ("inplace mode")
  77         ji = halfrev2(ji, True)
  78
  79     #print ("ri", ri)
  80     #print ("ji", ji)
  81
  82     # start an infinite (wrapping) loop
  83     skip = 0
  84     while True:
  85         for size in x_r:           # loop over 3rd order dimension (size)
  86             x_end = size == x_r[-1]
  87             # y_r schedule depends on size
  88             halfsize = size // 2
  89             y_r = []
  90             for i in range(0, n, size):
  91                 y_r.append(i)
  92             # invert if requested
  93             if SVSHAPE.invxyz[1]: y_r.reverse()
  94             for i in y_r:       # loop over 2nd order dimension
  95                 y_end = i == y_r[-1]
  96                 # two lists of half-range indices, e.g. j 0123, jr 7654
  97                 j = list(range(i, i + halfsize))
  98                 jr = list(range(i+halfsize, i + size))
  99                 jr.reverse()
 100                 # invert if requested
 101                 if SVSHAPE.invxyz[2]: j_r.reverse()
 102                 hz2 = halfsize // 2 # zero stops reversing 1-item lists
 103                 # if you *really* want to do the in-place swapping manually,
 104                 # this allows you to do it.  good luck...
 105                 if SVSHAPE.submode2 == 0b01 and not inplace_mode:
 106                     #print ("swap mode")
 107                     jr = j_r[:hz2]
 108                 #print ("xform jr", jr)
 109                 for jl, jh in zip(j, jr):   # loop over 1st order dimension
 110                     z_end = jl == j[-1]
 111                     # now depending on MODE return the index.  inner butterfly
 112                     if SVSHAPE.skip in [0b00, 0b10]:
 113                         result = ri[ji[jl]]        # lower half
 114                     elif SVSHAPE.skip in [0b01, 0b11]:
 115                         result = ri[ji[jh]] # upper half, reverse order
 116                     loopends = (z_end |
 117                                ((y_end and z_end)<<1) |
 118                                 ((y_end and x_end and z_end)<<2))
 119
 120                     yield result + SVSHAPE.offset, loopends
 121
 122                 # now in-place swap
 123                 if inplace_mode:
 124                     for ci, (jl, jh) in enumerate(zip(j[:hz2], jr[:hz2])):
 125                         jlh = jl+halfsize
 126                         #print ("inplace swap", jh, jlh)
 127                         tmp1, tmp2 = ji[jlh], ji[jh]
 128                         ji[jlh], ji[jh] = tmp2, tmp1
 129
 130
 131 # python "yield" can be iterated. use this to make it clear how
 132 # the indices are generated by using natural-looking nested loops
 133 def iterate_dct_outer_butterfly_indices(SVSHAPE):
 134     # get indices to iterate over, in the required order
 135     n = SVSHAPE.lims[0]
 136     # createing lists of indices to iterate over in each dimension
 137     # has to be done dynamically, because it depends on the size
 138     # first, the size-based loop (which can be done statically)
 139     x_r = []
 140     size = n // 2
 141     while size >= 2:
 142         x_r.append(size)
 143         size //= 2
 144     # invert order if requested
 145     if SVSHAPE.invxyz[0]:
 146         x_r.reverse()
 147
 148     if len(x_r) == 0:
 149         return
 150
 151     #print ("outer butterfly")
 152
 153     # reference (read/write) the in-place data in *reverse-bit-order*
 154     ri = list(range(n))
 155     if SVSHAPE.submode2 == 0b11:
 156         levels = n.bit_length() - 1
 157         ri = [ri[reverse_bits(i, levels)] for i in range(n)]
 158
 159     # reference list for not needing to do data-swaps, just swap what
 160     # *indices* are referenced (two levels of indirection at the moment)
 161     # pre-reverse the data-swap list so that it *ends up* in the order 0123..
 162     ji = list(range(n))
 163     inplace_mode = SVSHAPE.skip in [0b10, 0b11]
 164     if inplace_mode:
 165         #print ("inplace mode", SVSHAPE.skip)
 166         ji = halfrev2(ji, True)
 167
 168     #print ("ri", ri)
 169     #print ("ji", ji)
 170
 171     # start an infinite (wrapping) loop
 172     skip = 0
 173     while True:
 174         for size in x_r:           # loop over 3rd order dimension (size)
 175             halfsize = size//2
 176             x_end = size == x_r[-1]
 177             y_r = list(range(0, halfsize))
 178             #print ("itersum", halfsize, size, y_r)
 179             # invert if requested
 180             if SVSHAPE.invxyz[1]: y_r.reverse()
 181             for i in y_r:       # loop over 2nd order dimension
 182                 y_end = i == y_r[-1]
 183                 # one list to create iterative-sum schedule
 184                 jr = list(range(i+halfsize, i+n-halfsize, size))
 185                 #print ("itersum     jr", i+halfsize, i+size, jr)
 186                 # invert if requested
 187                 if SVSHAPE.invxyz[2]: j_r.reverse()
 188                 hz2 = halfsize // 2 # zero stops reversing 1-item lists
 189                 for jh in jr:   # loop over 1st order dimension
 190                     z_end = jh == jr[-1]
 191                     #print ("     itersum", size, i, jh, jh+size)
 192                     if SVSHAPE.skip in [0b00, 0b10]:
 193                         result = ri[ji[jh]]        # lower half
 194                     elif SVSHAPE.skip in [0b01, 0b11]:
 195                         result = ri[ji[jh+size]] # upper half
 196                     loopends = (z_end |
 197                                ((y_end and z_end)<<1) |
 198                                 ((y_end and x_end and z_end)<<2))
 199
 200                     yield result + SVSHAPE.offset, loopends
 201
 202                 # now in-place swap
 203                 if SVSHAPE.submode2 == 0b11 and inplace_mode:
 204                     j = list(range(i, i + halfsize))
 205                     jr = list(range(i+halfsize, i + size))
 206                     jr.reverse()
 207                     for ci, (jl, jh) in enumerate(zip(j[:hz2], jr[:hz2])):
 208                         jlh = jl+halfsize
 209                         #print ("inplace swap", jh, jlh)
 210                         tmp1, tmp2 = ji[jlh], ji[jh]
 211                         ji[jlh], ji[jh] = tmp2, tmp1
 212
 213
 214 def pprint_schedule(schedule, n):
 215     size = 2
 216     idx = 0
 217     while size <= n:
 218         halfsize = size // 2
 219         tablestep = n // size
 220         print ("size %d halfsize %d tablestep %d" % \
 221                 (size, halfsize, tablestep))
 222         for i in range(0, n, size):
 223             prefix = "i %d\t" % i
 224             for j in range(i, i + halfsize):
 225                 (jl, je), (jh, he) = schedule[idx]
 226                 print ("  %-3d\t%s j=%-2d jh=%-2d "
 227                         "j[jl=%-2d] j[jh=%-2d]" % \
 228                                 (idx, prefix, j, j+halfsize,
 229                                       jl, jh,
 230                                 ),
 231                                 "end", bin(je)[2:], bin(je)[2:])
 232                 idx += 1
 233         size *= 2
 234
 235 def pprint_schedule_outer(schedule, n):
 236     size = 2
 237     idx = 0
 238     while size <= n//2:
 239         halfsize = size // 2
 240         tablestep = n // size
 241         print ("size %d halfsize %d tablestep %d" % \
 242                 (size, halfsize, tablestep))
 243         y_r = list(range(0, halfsize))
 244         for i in y_r:
 245             prefix = "i %d\t" % i
 246             jr = list(range(i+halfsize, i+n-halfsize, size))
 247             for j in jr:
 248                 (jl, je), (jh, he) = schedule[idx]
 249                 print ("  %-3d\t%s j=%-2d jh=%-2d "
 250                         "j[jl=%-2d] j[jh=%-2d]" % \
 251                                 (idx, prefix, j, j+halfsize,
 252                                       jl, jh,
 253                                 ),
 254                                 "end", bin(je)[2:], bin(je)[2:])
 255                 idx += 1
 256         size *= 2
 257
 258
 259 # totally cool *in-place* DCT algorithm using yield REMAPs
 260 def transform2(vec):
 261
 262     # Initialization
 263     n = len(vec)
 264     print ()
 265     print ("transform2", n)
 266     levels = n.bit_length() - 1
 267
 268     # reference (read/write) the in-place data in *reverse-bit-order*
 269     ri = list(range(n))
 270     ri = [ri[reverse_bits(i, levels)] for i in range(n)]
 271
 272     # and pretend we LDed data in half-swapped *and* bit-reversed order as well
 273     # TODO: merge these two
 274     vec = halfrev2(vec, False)
 275     vec = [vec[ri[i]] for i in range(n)]
 276
 277     # create a cos table: not strictly necessary but here for illustrative
 278     # purposes, to demonstrate the point that it really *is* iterative.
 279     # this table could be cached and used multiple times rather than
 280     # computed every time.
 281     ctable = []
 282     size = n
 283     while size >= 2:
 284         halfsize = size // 2
 285         for i in range(n//size):
 286             for ci in range(halfsize):
 287                 ctable.append((math.cos((ci + 0.5) * math.pi / size) * 2.0))
 288         size //= 2
 289
 290     ################
 291     # INNER butterfly
 292     ################
 293     xdim = n
 294     ydim = 0
 295     zdim = 0
 296
 297     # set up an SVSHAPE
 298     class SVSHAPE:
 299         pass
 300     # j schedule
 301     SVSHAPE0 = SVSHAPE()
 302     SVSHAPE0.lims = [xdim, ydim, zdim]
 303     SVSHAPE0.order = [0,1,2]  # experiment with different permutations, here
 304     SVSHAPE0.mode = 0b01
 305     SVSHAPE0.submode2 = 0b01
 306     SVSHAPE0.skip = 0b00
 307     SVSHAPE0.offset = 0       # experiment with different offset, here
 308     SVSHAPE0.invxyz = [1,0,0] # inversion if desired
 309     # j+halfstep schedule
 310     SVSHAPE1 = SVSHAPE()
 311     SVSHAPE1.lims = [xdim, ydim, zdim]
 312     SVSHAPE1.order = [0,1,2]  # experiment with different permutations, here
 313     SVSHAPE1.mode = 0b01
 314     SVSHAPE1.submode2 = 0b01
 315     SVSHAPE1.skip = 0b01
 316     SVSHAPE1.offset = 0       # experiment with different offset, here
 317     SVSHAPE1.invxyz = [1,0,0] # inversion if desired
 318
 319     # enumerate over the iterator function, getting new indices
 320     i0 = iterate_dct_inner_butterfly_indices(SVSHAPE0)
 321     i1 = iterate_dct_inner_butterfly_indices(SVSHAPE1)
 322     for k, ((jl, jle), (jh, jhe)) in enumerate(zip(i0, i1)):
 323         t1, t2 = vec[jl], vec[jh]
 324         coeff = ctable[k]
 325         vec[jl] = t1 + t2
 326         vec[jh] = (t1 - t2) * (1/coeff)
 327         print ("coeff", size, i, "ci", ci,
 328                 "jl", jl, "jh", jh,
 329                "i/n", (ci+0.5)/size, coeff, vec[jl],
 330                                             vec[jh],
 331                 "end", bin(jle), bin(jhe))
 332         if jle == 0b111: # all loops end
 333             break
 334
 335     print("transform2 pre-itersum", vec)
 336
 337     # now things are in the right order for the outer butterfly.
 338
 339     # j schedule
 340     SVSHAPE0 = SVSHAPE()
 341     SVSHAPE0.lims = [xdim, ydim, zdim]
 342     SVSHAPE0.submode2 = 0b100
 343     SVSHAPE0.mode = 0b01
 344     SVSHAPE0.skip = 0b00
 345     SVSHAPE0.offset = 0       # experiment with different offset, here
 346     SVSHAPE0.invxyz = [0,0,0] # inversion if desired
 347     # j+halfstep schedule
 348     SVSHAPE1 = SVSHAPE()
 349     SVSHAPE1.lims = [xdim, ydim, zdim]
 350     SVSHAPE1.mode = 0b01
 351     SVSHAPE1.submode2 = 0b100
 352     SVSHAPE1.skip = 0b01
 353     SVSHAPE1.offset = 0       # experiment with different offset, here
 354     SVSHAPE1.invxyz = [0,0,0] # inversion if desired
 355
 356     # enumerate over the iterator function, getting new indices
 357     i0 = iterate_dct_outer_butterfly_indices(SVSHAPE0)
 358     i1 = iterate_dct_outer_butterfly_indices(SVSHAPE1)
 359     for k, ((jl, jle), (jh, jhe)) in enumerate(zip(i0, i1)):
 360         print ("itersum    jr", jl, jh,
 361                 "end", bin(jle), bin(jhe))
 362         vec[jl] += vec[jh]
 363         size //= 2
 364         if jle == 0b111: # all loops end
 365             break
 366
 367     print("transform2 result", vec)
 368
 369     return vec
 370
 371
 372 def demo():
 373     # set the dimension sizes here
 374     n = 8
 375     xdim = n
 376     ydim = 0 # not needed
 377     zdim = 0 # again, not needed
 378
 379
 380     ################
 381     # INNER butterfly
 382     ################
 383
 384     # set up an SVSHAPE
 385     class SVSHAPE:
 386         pass
 387     # j schedule
 388     SVSHAPE0 = SVSHAPE()
 389     SVSHAPE0.lims = [xdim, ydim, zdim]
 390     SVSHAPE0.submode2 = 0b010
 391     SVSHAPE0.mode = 0b01
 392     SVSHAPE0.skip = 0b00
 393     SVSHAPE0.offset = 0       # experiment with different offset, here
 394     SVSHAPE0.invxyz = [0,0,0] # inversion if desired
 395     # j+halfstep schedule
 396     SVSHAPE1 = SVSHAPE()
 397     SVSHAPE1.lims = [xdim, ydim, zdim]
 398     SVSHAPE1.submode2 = 0b010
 399     SVSHAPE1.mode = 0b01
 400     SVSHAPE1.skip = 0b01
 401     SVSHAPE1.offset = 0       # experiment with different offset, here
 402     SVSHAPE1.invxyz = [0,0,0] # inversion if desired
 403
 404     # enumerate over the iterator function, getting new indices
 405     schedule = []
 406     i0 = iterate_dct_inner_butterfly_indices(SVSHAPE0)
 407     i1 = iterate_dct_inner_butterfly_indices(SVSHAPE1)
 408     for idx, (jl, jh) in enumerate(zip(i0, i1)):
 409         schedule.append((jl, jh))
 410         if jl[1] == 0b111: # end
 411             break
 412
 413     # ok now pretty-print the results, with some debug output
 414     print ("inner butterfly")
 415     pprint_schedule(schedule, n)
 416     print ("")
 417
 418     ################
 419     # outer butterfly
 420     ################
 421
 422     # j schedule
 423     SVSHAPE0 = SVSHAPE()
 424     SVSHAPE0.lims = [xdim, ydim, zdim]
 425     SVSHAPE0.mode = 0b10
 426     SVSHAPE0.submode2 = 0b100
 427     SVSHAPE0.skip = 0b10
 428     SVSHAPE0.offset = 0       # experiment with different offset, here
 429     SVSHAPE0.invxyz = [1,0,0] # inversion if desired
 430     # j+halfstep schedule
 431     SVSHAPE1 = SVSHAPE()
 432     SVSHAPE1.lims = [xdim, ydim, zdim]
 433     SVSHAPE1.mode = 0b10
 434     SVSHAPE1.submode2 = 0b100
 435     SVSHAPE1.skip = 0b11
 436     SVSHAPE1.offset = 0       # experiment with different offset, here
 437     SVSHAPE1.invxyz = [1,0,0] # inversion if desired
 438
 439     # enumerate over the iterator function, getting new indices
 440     schedule = []
 441     i0 = iterate_dct_outer_butterfly_indices(SVSHAPE0)
 442     i1 = iterate_dct_outer_butterfly_indices(SVSHAPE1)
 443     for idx, (jl, jh) in enumerate(zip(i0, i1)):
 444         schedule.append((jl, jh))
 445         if jl[1] == 0b111: # end
 446             break
 447
 448     # ok now pretty-print the results, with some debug output
 449     print ("outer butterfly")
 450     pprint_schedule_outer(schedule, n)
 451
 452 # run the demo
 453 if __name__ == '__main__':
 454     demo()