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_costable_indices(SVSHAPE):
  47     # get indices to iterate over, in the required order
  48     n = SVSHAPE.lims[0]
  49     mode = SVSHAPE.lims[1]
  50     print ("inner costable", mode)
  51     # creating lists of indices to iterate over in each dimension
  52     # has to be done dynamically, because it depends on the size
  53     # first, the size-based loop (which can be done statically)
  54     x_r = []
  55     size = 2
  56     while size <= n:
  57         x_r.append(size)
  58         size *= 2
  59     # invert order if requested
  60     if SVSHAPE.invxyz[0]:
  61         x_r.reverse()
  62
  63     if len(x_r) == 0:
  64         return
  65
  66     #print ("ri", ri)
  67     #print ("ji", ji)
  68
  69     # start an infinite (wrapping) loop
  70     skip = 0
  71     z_end = 1 # doesn't exist in this, only 2 loops
  72     k = 0
  73     while True:
  74         for size in x_r:           # loop over 3rd order dimension (size)
  75             x_end = size == x_r[-1]
  76             # y_r schedule depends on size
  77             halfsize = size // 2
  78             y_r = []
  79             for i in range(0, n, size):
  80                 y_r.append(i)
  81             # invert if requested
  82             if SVSHAPE.invxyz[1]: y_r.reverse()
  83             # two lists of half-range indices, e.g. j 0123, jr 7654
  84             j = list(range(0, halfsize))
  85             # invert if requested
  86             if SVSHAPE.invxyz[2]: j_r.reverse()
  87             #print ("xform jr", jr)
  88             # loop over 1st order dimension
  89             for ci, jl in enumerate(j):
  90                 y_end = jl == j[-1]
  91                 # now depending on MODE return the index.  inner butterfly
  92                 if SVSHAPE.skip == 0b00: # in [0b00, 0b10]:
  93                     result = k  # offset into COS table
  94                 elif SVSHAPE.skip == 0b10: #
  95                     result = ci # coefficient helper
  96                 elif SVSHAPE.skip == 0b11: #
  97                     result = size # coefficient helper
  98                 loopends = (z_end |
  99                            ((y_end and z_end)<<1) |
 100                             ((y_end and x_end and z_end)<<2))
 101
 102                 yield result + SVSHAPE.offset, loopends
 103                 k += 1
 104
 105 # python "yield" can be iterated. use this to make it clear how
 106 # the indices are generated by using natural-looking nested loops
 107 def iterate_dct_inner_butterfly_indices(SVSHAPE):
 108     # get indices to iterate over, in the required order
 109     n = SVSHAPE.lims[0]
 110     mode = SVSHAPE.lims[1]
 111     #print ("inner butterfly", mode)
 112     # creating lists of indices to iterate over in each dimension
 113     # has to be done dynamically, because it depends on the size
 114     # first, the size-based loop (which can be done statically)
 115     x_r = []
 116     size = 2
 117     while size <= n:
 118         x_r.append(size)
 119         size *= 2
 120     # invert order if requested
 121     if SVSHAPE.invxyz[0]:
 122         x_r.reverse()
 123
 124     if len(x_r) == 0:
 125         return
 126
 127     # reference (read/write) the in-place data in *reverse-bit-order*
 128     ri = list(range(n))
 129     if SVSHAPE.submode2 == 0b01:
 130         levels = n.bit_length() - 1
 131         ri = [ri[reverse_bits(i, levels)] for i in range(n)]
 132
 133     # reference list for not needing to do data-swaps, just swap what
 134     # *indices* are referenced (two levels of indirection at the moment)
 135     # pre-reverse the data-swap list so that it *ends up* in the order 0123..
 136     ji = list(range(n))
 137     inplace_mode = SVSHAPE.submode2 == 0b01
 138     #                     and SVSHAPE.skip not in [0b10, 0b11]
 139     if inplace_mode:
 140         #print ("inplace mode")
 141         ji = halfrev2(ji, True)
 142
 143     #print ("ri", ri)
 144     #print ("ji", ji)
 145
 146     # start an infinite (wrapping) loop
 147     skip = 0
 148     while True:
 149         for size in x_r:           # loop over 3rd order dimension (size)
 150             x_end = size == x_r[-1]
 151             # y_r schedule depends on size
 152             halfsize = size // 2
 153             y_r = []
 154             for i in range(0, n, size):
 155                 y_r.append(i)
 156             # invert if requested
 157             if SVSHAPE.invxyz[1]: y_r.reverse()
 158             for i in y_r:       # loop over 2nd order dimension
 159                 y_end = i == y_r[-1]
 160                 # two lists of half-range indices, e.g. j 0123, jr 7654
 161                 j = list(range(i, i + halfsize))
 162                 jr = list(range(i+halfsize, i + size))
 163                 jr.reverse()
 164                 # invert if requested
 165                 if SVSHAPE.invxyz[2]: j_r.reverse()
 166                 hz2 = halfsize // 2 # zero stops reversing 1-item lists
 167                 # if you *really* want to do the in-place swapping manually,
 168                 # this allows you to do it.  good luck...
 169                 if SVSHAPE.submode2 == 0b01 and not inplace_mode:
 170                     #print ("swap mode")
 171                     jr = j_r[:hz2]
 172                 #print ("xform jr", jr)
 173                 # loop over 1st order dimension
 174                 for ci, (jl, jh) in enumerate(zip(j, jr)):
 175                     z_end = jl == j[-1]
 176                     # now depending on MODE return the index.  inner butterfly
 177                     if SVSHAPE.skip == 0b00: # in [0b00, 0b10]:
 178                         result = ri[ji[jl]]        # lower half
 179                     elif SVSHAPE.skip == 0b01: # in [0b01, 0b11]:
 180                         result = ri[ji[jh]] # upper half, reverse order
 181                     elif SVSHAPE.skip == 0b10: #
 182                         result = ci # coefficient helper
 183                     elif SVSHAPE.skip == 0b11: #
 184                         result = size # coefficient helper
 185                     loopends = (z_end |
 186                                ((y_end and z_end)<<1) |
 187                                 ((y_end and x_end and z_end)<<2))
 188
 189                     yield result + SVSHAPE.offset, loopends
 190
 191                 # now in-place swap
 192                 if inplace_mode:
 193                     for ci, (jl, jh) in enumerate(zip(j[:hz2], jr[:hz2])):
 194                         jlh = jl+halfsize
 195                         #print ("inplace swap", jh, jlh)
 196                         tmp1, tmp2 = ji[jlh], ji[jh]
 197                         ji[jlh], ji[jh] = tmp2, tmp1
 198
 199
 200 # python "yield" can be iterated. use this to make it clear how
 201 # the indices are generated by using natural-looking nested loops
 202 def iterate_dct_outer_butterfly_indices(SVSHAPE):
 203     # get indices to iterate over, in the required order
 204     n = SVSHAPE.lims[0]
 205     mode = SVSHAPE.lims[1]
 206     # createing lists of indices to iterate over in each dimension
 207     # has to be done dynamically, because it depends on the size
 208     # first, the size-based loop (which can be done statically)
 209     x_r = []
 210     size = n // 2
 211     while size >= 2:
 212         x_r.append(size)
 213         size //= 2
 214     # invert order if requested
 215     if SVSHAPE.invxyz[0]:
 216         x_r.reverse()
 217
 218     if len(x_r) == 0:
 219         return
 220
 221     #print ("outer butterfly")
 222
 223     # reference (read/write) the in-place data in *reverse-bit-order*
 224     ri = list(range(n))
 225     if SVSHAPE.submode2 == 0b11:
 226         levels = n.bit_length() - 1
 227         ri = [ri[reverse_bits(i, levels)] for i in range(n)]
 228
 229     # reference list for not needing to do data-swaps, just swap what
 230     # *indices* are referenced (two levels of indirection at the moment)
 231     # pre-reverse the data-swap list so that it *ends up* in the order 0123..
 232     ji = list(range(n))
 233     inplace_mode = False # need the space... SVSHAPE.skip in [0b10, 0b11]
 234     if inplace_mode:
 235         #print ("inplace mode", SVSHAPE.skip)
 236         ji = halfrev2(ji, True)
 237
 238     #print ("ri", ri)
 239     #print ("ji", ji)
 240
 241     # start an infinite (wrapping) loop
 242     skip = 0
 243     k = 0
 244     k_start = 0
 245     while True:
 246         for size in x_r:           # loop over 3rd order dimension (size)
 247             halfsize = size//2
 248             x_end = size == x_r[-1]
 249             y_r = list(range(0, halfsize))
 250             #print ("itersum", halfsize, size, y_r)
 251             # invert if requested
 252             if SVSHAPE.invxyz[1]: y_r.reverse()
 253             for i in y_r:       # loop over 2nd order dimension
 254                 y_end = i == y_r[-1]
 255                 # one list to create iterative-sum schedule
 256                 jr = list(range(i+halfsize, i+n-halfsize, size))
 257                 #print ("itersum     jr", i+halfsize, i+size, jr)
 258                 # invert if requested
 259                 if SVSHAPE.invxyz[2]: j_r.reverse()
 260                 hz2 = halfsize // 2 # zero stops reversing 1-item lists
 261                 k = k_start
 262                 for ci, jh in enumerate(jr):   # loop over 1st order dimension
 263                     z_end = jh == jr[-1]
 264                     #print ("     itersum", size, i, jh, jh+size)
 265                     if mode == 4:
 266                         # COS table pre-generated mode
 267                         if SVSHAPE.skip == 0b00: # in [0b00, 0b10]:
 268                             result = ri[ji[jh]]        # lower half
 269                         elif SVSHAPE.skip == 0b01: # in [0b01, 0b11]:
 270                             result = ri[ji[jh+size]] # upper half
 271                         elif SVSHAPE.skip == 0b10: #
 272                             result = k # cos table offset
 273                     else:
 274                         # COS table generated on-demand ("Vertical-First") mode
 275                         if SVSHAPE.skip == 0b00: # in [0b00, 0b10]:
 276                             result = ri[ji[jh]]        # lower half
 277                         elif SVSHAPE.skip == 0b01: # in [0b01, 0b11]:
 278                             result = ri[ji[jh+size]] # upper half
 279                         elif SVSHAPE.skip == 0b10: #
 280                             result = ci # coefficient helper
 281                         elif SVSHAPE.skip == 0b11: #
 282                             result = size # coefficient helper
 283                     loopends = (z_end |
 284                                ((y_end and z_end)<<1) |
 285                                 ((y_end and x_end and z_end)<<2))
 286
 287                     yield result + SVSHAPE.offset, loopends
 288                     k += 1
 289
 290                 # now in-place swap
 291                 if SVSHAPE.submode2 == 0b11 and inplace_mode:
 292                     j = list(range(i, i + halfsize))
 293                     jr = list(range(i+halfsize, i + size))
 294                     jr.reverse()
 295                     for ci, (jl, jh) in enumerate(zip(j[:hz2], jr[:hz2])):
 296                         jlh = jl+halfsize
 297                         #print ("inplace swap", jh, jlh)
 298                         tmp1, tmp2 = ji[jlh], ji[jh]
 299                         ji[jlh], ji[jh] = tmp2, tmp1
 300
 301             # new k_start point for cos tables( runs inside x_r loop NOT i loop)
 302             k_start += halfsize
 303
 304
 305 def pprint_schedule(schedule, n):
 306     size = 2
 307     idx = 0
 308     while size <= n:
 309         halfsize = size // 2
 310         tablestep = n // size
 311         print ("size %d halfsize %d tablestep %d" % \
 312                 (size, halfsize, tablestep))
 313         for i in range(0, n, size):
 314             prefix = "i %d\t" % i
 315             for j in range(i, i + halfsize):
 316                 (jl, je), (jh, he) = schedule[idx]
 317                 print ("  %-3d\t%s j=%-2d jh=%-2d "
 318                         "j[jl=%-2d] j[jh=%-2d]" % \
 319                                 (idx, prefix, j, j+halfsize,
 320                                       jl, jh,
 321                                 ),
 322                                 "end", bin(je)[2:], bin(je)[2:])
 323                 idx += 1
 324         size *= 2
 325
 326 def pprint_schedule_outer(schedule, n):
 327     size = 2
 328     idx = 0
 329     while size <= n//2:
 330         halfsize = size // 2
 331         tablestep = n // size
 332         print ("size %d halfsize %d tablestep %d" % \
 333                 (size, halfsize, tablestep))
 334         y_r = list(range(0, halfsize))
 335         for i in y_r:
 336             prefix = "i %d\t" % i
 337             jr = list(range(i+halfsize, i+n-halfsize, size))
 338             for j in jr:
 339                 (jl, je), (jh, he) = schedule[idx]
 340                 print ("  %-3d\t%s j=%-2d jh=%-2d "
 341                         "j[jl=%-2d] j[jh=%-2d]" % \
 342                                 (idx, prefix, j, j+halfsize,
 343                                       jl, jh,
 344                                 ),
 345                                 "end", bin(je)[2:], bin(je)[2:])
 346                 idx += 1
 347         size *= 2
 348
 349
 350 # totally cool *in-place* DCT algorithm using yield REMAPs
 351 def transform2(vec):
 352
 353     # Initialization
 354     n = len(vec)
 355     print ()
 356     print ("transform2", n)
 357     levels = n.bit_length() - 1
 358
 359     # set up dims
 360     xdim = n
 361
 362     # reference (read/write) the in-place data in *reverse-bit-order*
 363     ri = list(range(n))
 364     ri = [ri[reverse_bits(i, levels)] for i in range(n)]
 365
 366     # and pretend we LDed data in half-swapped *and* bit-reversed order as well
 367     # TODO: merge these two
 368     vec = halfrev2(vec, False)
 369     vec = [vec[ri[i]] for i in range(n)]
 370
 371     # create a cos table: not strictly necessary but here for illustrative
 372     # purposes, to demonstrate the point that it really *is* iterative.
 373     # this table could be cached and used multiple times rather than
 374     # computed every time.
 375     ctable = []
 376     size = n
 377     while size >= 2:
 378         halfsize = size // 2
 379         for ci in range(halfsize):
 380             coeff = (math.cos((ci + 0.5) * math.pi / size) * 2.0)
 381             ctable.append(coeff)
 382             print ("coeff", size,  "ci", ci, "k", len(ctable)-1,
 383                    "i/n", (ci+0.5)/size, coeff)
 384         size //= 2
 385
 386     # set up an SVSHAPE
 387     class SVSHAPE:
 388         pass
 389     # ci schedule
 390     SVSHAPE0 = SVSHAPE()
 391     SVSHAPE0.lims = [xdim, 4, 0]
 392     SVSHAPE0.mode = 0b01
 393     SVSHAPE0.submode2 = 0b01
 394     SVSHAPE0.skip = 0b10
 395     SVSHAPE0.offset = 0       # experiment with different offset, here
 396     SVSHAPE0.invxyz = [1,0,0] # inversion if desired
 397     # size schedule
 398     SVSHAPE1 = SVSHAPE()
 399     SVSHAPE1.lims = [xdim, 4, 0]
 400     SVSHAPE1.mode = 0b01
 401     SVSHAPE1.submode2 = 0b01
 402     SVSHAPE1.skip = 0b11
 403     SVSHAPE1.offset = 0       # experiment with different offset, here
 404     SVSHAPE1.invxyz = [1,0,0] # inversion if desired
 405     # k schedule
 406     SVSHAPE2 = SVSHAPE()
 407     SVSHAPE2.lims = [xdim, 4, 0]
 408     SVSHAPE2.mode = 0b01
 409     SVSHAPE2.submode2 = 0b01
 410     SVSHAPE2.skip = 0b00
 411     SVSHAPE2.offset = 0       # experiment with different offset, here
 412     SVSHAPE2.invxyz = [1,0,0] # inversion if desired
 413
 414     # enumerate over the iterator function, getting new indices
 415     i0 = iterate_dct_inner_costable_indices(SVSHAPE0)
 416     i1 = iterate_dct_inner_costable_indices(SVSHAPE1)
 417     i2 = iterate_dct_inner_costable_indices(SVSHAPE2)
 418     for ((ci, cie), (size, sze), (k, ke)) in \
 419                 zip(i0, i1, i2):
 420         print ("xform2 cos", ci, size, k)
 421         coeff = (math.cos((ci + 0.5) * math.pi / size) * 2.0)
 422         assert coeff == ctable[k]
 423         print ("coeff", size,  "ci", ci, "k", k,
 424                "i/n", (ci+0.5)/size, coeff,
 425                 "end", bin(cie), bin(sze), bin(ke))
 426         if cie == 0b111: # all loops end
 427             break
 428
 429     ################
 430     # INNER butterfly
 431     ################
 432
 433     # j schedule
 434     SVSHAPE0 = SVSHAPE()
 435     SVSHAPE0.lims = [xdim, 0b000001, 0]
 436     SVSHAPE0.mode = 0b01
 437     SVSHAPE0.submode2 = 0b01
 438     SVSHAPE0.skip = 0b00
 439     SVSHAPE0.offset = 0       # experiment with different offset, here
 440     SVSHAPE0.invxyz = [1,0,0] # inversion if desired
 441     # j+halfstep schedule
 442     SVSHAPE1 = SVSHAPE()
 443     SVSHAPE1.lims = [xdim, 0b000001, 0]
 444     SVSHAPE1.mode = 0b01
 445     SVSHAPE1.submode2 = 0b01
 446     SVSHAPE1.skip = 0b01
 447     SVSHAPE1.offset = 0       # experiment with different offset, here
 448     SVSHAPE1.invxyz = [1,0,0] # inversion if desired
 449     # ci schedule
 450     SVSHAPE2 = SVSHAPE()
 451     SVSHAPE2.lims = [xdim, 0b000001, 0]
 452     SVSHAPE2.mode = 0b01
 453     SVSHAPE2.submode2 = 0b01
 454     SVSHAPE2.skip = 0b10
 455     SVSHAPE2.offset = 0       # experiment with different offset, here
 456     SVSHAPE2.invxyz = [1,0,0] # inversion if desired
 457     # size schedule
 458     SVSHAPE3 = SVSHAPE()
 459     SVSHAPE3.lims = [xdim, 0b000001, 0]
 460     SVSHAPE3.mode = 0b01
 461     SVSHAPE3.submode2 = 0b01
 462     SVSHAPE3.skip = 0b11
 463     SVSHAPE3.offset = 0       # experiment with different offset, here
 464     SVSHAPE3.invxyz = [1,0,0] # inversion if desired
 465
 466     # enumerate over the iterator function, getting new indices
 467     i0 = iterate_dct_inner_butterfly_indices(SVSHAPE0)
 468     i1 = iterate_dct_inner_butterfly_indices(SVSHAPE1)
 469     i2 = iterate_dct_inner_butterfly_indices(SVSHAPE2)
 470     i3 = iterate_dct_inner_butterfly_indices(SVSHAPE3)
 471     for k, ((jl, jle), (jh, jhe), (ci, cie), (size, sze)) in \
 472                 enumerate(zip(i0, i1, i2, i3)):
 473         t1, t2 = vec[jl], vec[jh]
 474         print ("xform2", jl, jh, ci, size)
 475         coeff = (math.cos((ci + 0.5) * math.pi / size) * 2.0)
 476         #assert coeff == ctable[k]
 477         vec[jl] = t1 + t2
 478         vec[jh] = (t1 - t2) * (1/coeff)
 479         print ("coeff", size, "ci", ci,
 480                 "jl", jl, "jh", jh,
 481                "i/n", (ci+0.5)/size, coeff, vec[jl],
 482                                             vec[jh],
 483                 "end", bin(jle), bin(jhe))
 484         if jle == 0b111: # all loops end
 485             break
 486
 487     print("transform2 pre-itersum", vec)
 488
 489     # now things are in the right order for the outer butterfly.
 490
 491     # j schedule
 492     SVSHAPE0 = SVSHAPE()
 493     SVSHAPE0.lims = [xdim, 0b0000010, 0]
 494     SVSHAPE0.submode2 = 0b100
 495     SVSHAPE0.mode = 0b01
 496     SVSHAPE0.skip = 0b00
 497     SVSHAPE0.offset = 0       # experiment with different offset, here
 498     SVSHAPE0.invxyz = [0,0,0] # inversion if desired
 499     # j+halfstep schedule
 500     SVSHAPE1 = SVSHAPE()
 501     SVSHAPE1.lims = [xdim, 0b0000010, 0]
 502     SVSHAPE1.mode = 0b01
 503     SVSHAPE1.submode2 = 0b100
 504     SVSHAPE1.skip = 0b01
 505     SVSHAPE1.offset = 0       # experiment with different offset, here
 506     SVSHAPE1.invxyz = [0,0,0] # inversion if desired
 507
 508     # enumerate over the iterator function, getting new indices
 509     i0 = iterate_dct_outer_butterfly_indices(SVSHAPE0)
 510     i1 = iterate_dct_outer_butterfly_indices(SVSHAPE1)
 511     for k, ((jl, jle), (jh, jhe)) in enumerate(zip(i0, i1)):
 512         print ("itersum    jr", jl, jh,
 513                 "end", bin(jle), bin(jhe))
 514         vec[jl] += vec[jh]
 515         size //= 2
 516         if jle == 0b111: # all loops end
 517             break
 518
 519     print("transform2 result", vec)
 520
 521     return vec
 522
 523
 524 def demo():
 525     # set the dimension sizes here
 526     n = 8
 527     xdim = n
 528     ydim = 0 # not needed
 529     zdim = 0 # again, not needed
 530
 531
 532     ################
 533     # INNER butterfly
 534     ################
 535
 536     # set up an SVSHAPE
 537     class SVSHAPE:
 538         pass
 539     # j schedule
 540     SVSHAPE0 = SVSHAPE()
 541     SVSHAPE0.lims = [xdim, 0b000001, zdim]
 542     SVSHAPE0.submode2 = 0b010
 543     SVSHAPE0.mode = 0b01
 544     SVSHAPE0.skip = 0b00
 545     SVSHAPE0.offset = 0       # experiment with different offset, here
 546     SVSHAPE0.invxyz = [0,0,0] # inversion if desired
 547     # j+halfstep schedule
 548     SVSHAPE1 = SVSHAPE()
 549     SVSHAPE1.lims = [xdim, 0b000001, zdim]
 550     SVSHAPE1.submode2 = 0b010
 551     SVSHAPE1.mode = 0b01
 552     SVSHAPE1.skip = 0b01
 553     SVSHAPE1.offset = 0       # experiment with different offset, here
 554     SVSHAPE1.invxyz = [0,0,0] # inversion if desired
 555
 556     # enumerate over the iterator function, getting new indices
 557     schedule = []
 558     i0 = iterate_dct_inner_butterfly_indices(SVSHAPE0)
 559     i1 = iterate_dct_inner_butterfly_indices(SVSHAPE1)
 560     for idx, (jl, jh) in enumerate(zip(i0, i1)):
 561         schedule.append((jl, jh))
 562         if jl[1] == 0b111: # end
 563             break
 564
 565     # ok now pretty-print the results, with some debug output
 566     print ("inner butterfly")
 567     pprint_schedule(schedule, n)
 568     print ("")
 569
 570     ################
 571     # outer butterfly
 572     ################
 573
 574     # j schedule
 575     SVSHAPE0 = SVSHAPE()
 576     SVSHAPE0.lims = [xdim, 0b000010, zdim]
 577     SVSHAPE0.mode = 0b01
 578     SVSHAPE0.submode2 = 0b100
 579     SVSHAPE0.skip = 0b10
 580     SVSHAPE0.offset = 0       # experiment with different offset, here
 581     SVSHAPE0.invxyz = [1,0,0] # inversion if desired
 582     # j+halfstep schedule
 583     SVSHAPE1 = SVSHAPE()
 584     SVSHAPE1.lims = [xdim, 0b000010, zdim]
 585     SVSHAPE1.mode = 0b01
 586     SVSHAPE1.submode2 = 0b100
 587     SVSHAPE1.skip = 0b11
 588     SVSHAPE1.offset = 0       # experiment with different offset, here
 589     SVSHAPE1.invxyz = [1,0,0] # inversion if desired
 590
 591     # enumerate over the iterator function, getting new indices
 592     schedule = []
 593     i0 = iterate_dct_outer_butterfly_indices(SVSHAPE0)
 594     i1 = iterate_dct_outer_butterfly_indices(SVSHAPE1)
 595     for idx, (jl, jh) in enumerate(zip(i0, i1)):
 596         schedule.append((jl, jh))
 597         if jl[1] == 0b111: # end
 598             break
 599
 600     # ok now pretty-print the results, with some debug output
 601     print ("outer butterfly")
 602     pprint_schedule_outer(schedule, n)
 603
 604 # run the demo
 605 if __name__ == '__main__':
 606     demo()