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_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.mode == 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.mode == 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]: k_r.reverse()
 102                 if SVSHAPE.invxyz[2]: j_r.reverse()
 103                 hz2 = halfsize // 2 # zero stops reversing 1-item lists
 104                 # if you *really* want to do the in-place swapping manually,
 105                 # this allows you to do it.  good luck...
 106                 if SVSHAPE.mode == 0b01 and not inplace_mode:
 107                     print ("swap mode")
 108                     jr = j_r[:hz2]
 109                 print ("xform jr", jr)
 110                 for jl, jh in zip(j, jr):   # loop over 1st order dimension
 111                     z_end = jl == j[-1]
 112                     # now depending on MODE return the index
 113                     if SVSHAPE.skip in [0b00, 0b10]:
 114                         result = ri[ji[jl]]        # lower half
 115                     elif SVSHAPE.skip in [0b01, 0b11]:
 116                         result = ri[ji[jh]] # upper half, reverse order
 117                     loopends = (z_end |
 118                                ((y_end and z_end)<<1) |
 119                                 ((y_end and x_end and z_end)<<2))
 120
 121                     yield result + SVSHAPE.offset, loopends
 122
 123                 # now in-place swap
 124                 if SVSHAPE.mode == 0b01 and inplace_mode:
 125                     for ci, (jl, jh) in enumerate(zip(j[:hz2], jr[:hz2])):
 126                         jlh = jl+halfsize
 127                         #print ("inplace swap", jh, jlh)
 128                         tmp1, tmp2 = ji[jlh], ji[jh]
 129                         ji[jlh], ji[jh] = tmp2, tmp1
 130
 131
 132 def pprint_schedule(schedule, n):
 133     size = 2
 134     idx = 0
 135     while size <= n:
 136         halfsize = size // 2
 137         tablestep = n // size
 138         print ("size %d halfsize %d tablestep %d" % \
 139                 (size, halfsize, tablestep))
 140         for i in range(0, n, size):
 141             prefix = "i %d\t" % i
 142             for j in range(i, i + halfsize):
 143                 (jl, je), (jh, he) = schedule[idx]
 144                 print ("  %-3d\t%s j=%-2d jh=%-2d "
 145                         "j[jl=%-2d] j[jh=%-2d]" % \
 146                                 (idx, prefix, j, j+halfsize,
 147                                       jl, jh,
 148                                 ),
 149                                 "end", bin(je)[2:], bin(je)[2:])
 150                 idx += 1
 151         size *= 2
 152
 153 # totally cool *in-place* DCT algorithm using yield REMAPs
 154 def transform2(vec):
 155
 156     # Initialization
 157     n = len(vec)
 158     print ()
 159     print ("transform2", n)
 160     levels = n.bit_length() - 1
 161
 162     # reference (read/write) the in-place data in *reverse-bit-order*
 163     ri = list(range(n))
 164     ri = [ri[reverse_bits(i, levels)] for i in range(n)]
 165
 166     # and pretend we LDed data in half-swapped *and* bit-reversed order as well
 167     # TODO: merge these two
 168     vec = halfrev2(vec, False)
 169     vec = [vec[ri[i]] for i in range(n)]
 170
 171     # create a cos table: not strictly necessary but here for illustrative
 172     # purposes, to demonstrate the point that it really *is* iterative.
 173     # this table could be cached and used multiple times rather than
 174     # computed every time.
 175     ctable = []
 176     size = n
 177     VL = 0
 178     while size >= 2:
 179         halfsize = size // 2
 180         for i in range(n//size):
 181             for ci in range(halfsize):
 182                 ctable.append((math.cos((ci + 0.5) * math.pi / size) * 2.0))
 183                 VL += 1
 184         size //= 2
 185
 186     ################
 187     # INNER butterfly
 188     ################
 189     xdim = n
 190     ydim = 0
 191     zdim = 0
 192
 193     # set up an SVSHAPE
 194     class SVSHAPE:
 195         pass
 196     # j schedule
 197     SVSHAPE0 = SVSHAPE()
 198     SVSHAPE0.lims = [xdim, ydim, zdim]
 199     SVSHAPE0.order = [0,1,2]  # experiment with different permutations, here
 200     SVSHAPE0.mode = 0b01
 201     SVSHAPE0.skip = 0b00
 202     SVSHAPE0.offset = 0       # experiment with different offset, here
 203     SVSHAPE0.invxyz = [1,0,0] # inversion if desired
 204     # j+halfstep schedule
 205     SVSHAPE1 = SVSHAPE()
 206     SVSHAPE1.lims = [xdim, ydim, zdim]
 207     SVSHAPE1.order = [0,1,2]  # experiment with different permutations, here
 208     SVSHAPE1.mode = 0b01
 209     SVSHAPE1.skip = 0b01
 210     SVSHAPE1.offset = 0       # experiment with different offset, here
 211     SVSHAPE1.invxyz = [1,0,0] # inversion if desired
 212
 213     # enumerate over the iterator function, getting new indices
 214     i0 = iterate_dct_butterfly_indices(SVSHAPE0)
 215     i1 = iterate_dct_butterfly_indices(SVSHAPE1)
 216     for k, ((jl, jle), (jh, jhe)) in enumerate(zip(i0, i1)):
 217         if k >= VL:
 218             break
 219         t1, t2 = vec[jl], vec[jh]
 220         coeff = ctable[k]
 221         vec[jl] = t1 + t2
 222         vec[jh] = (t1 - t2) * (1/coeff)
 223         print ("coeff", size, i, "ci", ci,
 224                 "jl", jl, "jh", jh,
 225                "i/n", (ci+0.5)/size, coeff, vec[jl],
 226                                             vec[jh])
 227
 228     print("transform2 pre-itersum", vec)
 229
 230     # now things are in the right order for the outer butterfly.
 231     n = len(vec)
 232     size = n // 2
 233     while size >= 2:
 234         halfsize = size // 2
 235         ir = list(range(0, halfsize))
 236         print ("itersum", halfsize, size, ir)
 237         for i in ir:
 238             jr = list(range(i+halfsize, i+n-halfsize, size))
 239             print ("itersum    jr", i+halfsize, i+size, jr)
 240             for jh in jr:
 241                 vec[jh] += vec[jh+size]
 242                 print ("    itersum", size, i, jh, jh+size)
 243         size //= 2
 244
 245     print("transform2 result", vec)
 246
 247     return vec
 248
 249
 250 def demo():
 251     # set the dimension sizes here
 252     xdim = 8
 253     ydim = 0 # not needed
 254     zdim = 0 # again, not needed
 255
 256     # set total. err don't know how to calculate how many there are...
 257     # do it manually for now
 258     VL = 0
 259     size = 2
 260     n = xdim
 261     while size <= n:
 262         halfsize = size // 2
 263         tablestep = n // size
 264         for i in range(0, n, size):
 265             for j in range(i, i + halfsize):
 266                 VL += 1
 267         size *= 2
 268
 269     ################
 270     # INNER butterfly
 271     ################
 272
 273     # set up an SVSHAPE
 274     class SVSHAPE:
 275         pass
 276     # j schedule
 277     SVSHAPE0 = SVSHAPE()
 278     SVSHAPE0.lims = [xdim, ydim, zdim]
 279     SVSHAPE0.order = [0,1,2]  # experiment with different permutations, here
 280     SVSHAPE0.mode = 0b01
 281     SVSHAPE0.skip = 0b00
 282     SVSHAPE0.offset = 0       # experiment with different offset, here
 283     SVSHAPE0.invxyz = [0,0,0] # inversion if desired
 284     # j+halfstep schedule
 285     SVSHAPE1 = SVSHAPE()
 286     SVSHAPE1.lims = [xdim, ydim, zdim]
 287     SVSHAPE1.order = [0,1,2]  # experiment with different permutations, here
 288     SVSHAPE1.mode = 0b01
 289     SVSHAPE1.skip = 0b01
 290     SVSHAPE1.offset = 0       # experiment with different offset, here
 291     SVSHAPE1.invxyz = [0,0,0] # inversion if desired
 292
 293     # enumerate over the iterator function, getting new indices
 294     schedule = []
 295     i0 = iterate_dct_butterfly_indices(SVSHAPE0)
 296     i1 = iterate_dct_butterfly_indices(SVSHAPE1)
 297     for idx, (jl, jh) in enumerate(zip(i0, i1)):
 298         if idx >= VL:
 299             break
 300         schedule.append((jl, jh))
 301
 302     # ok now pretty-print the results, with some debug output
 303     print ("inner butterfly")
 304     pprint_schedule(schedule, n)
 305     print ("")
 306
 307     ################
 308     # outer butterfly
 309     ################
 310
 311     # j schedule
 312     SVSHAPE0 = SVSHAPE()
 313     SVSHAPE0.lims = [xdim, ydim, zdim]
 314     SVSHAPE0.order = [0,1,2]  # experiment with different permutations, here
 315     SVSHAPE0.mode = 0b10
 316     SVSHAPE0.skip = 0b00
 317     SVSHAPE0.offset = 0       # experiment with different offset, here
 318     SVSHAPE0.invxyz = [1,0,0] # inversion if desired
 319     # j+halfstep schedule
 320     SVSHAPE1 = SVSHAPE()
 321     SVSHAPE1.lims = [xdim, ydim, zdim]
 322     SVSHAPE1.order = [0,1,2]  # experiment with different permutations, here
 323     SVSHAPE1.mode = 0b10
 324     SVSHAPE1.skip = 0b01
 325     SVSHAPE1.offset = 0       # experiment with different offset, here
 326     SVSHAPE1.invxyz = [1,0,0] # inversion if desired
 327
 328     # enumerate over the iterator function, getting new indices
 329     schedule = []
 330     i0 = iterate_dct_butterfly_indices(SVSHAPE0)
 331     i1 = iterate_dct_butterfly_indices(SVSHAPE1)
 332     for idx, (jl, jh) in enumerate(zip(i0, i1)):
 333         if idx >= VL:
 334             break
 335         schedule.append((jl, jh))
 336
 337     # ok now pretty-print the results, with some debug output
 338     print ("outer butterfly")
 339     pprint_schedule(schedule, n)
 340
 341 # run the demo
 342 if __name__ == '__main__':
 343     demo()