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]: x_r.reverse()
  59
  60     if len(x_r) == 0:
  61         return
  62
  63     # reference (read/write) the in-place data in *reverse-bit-order*
  64     ri = list(range(n))
  65     ri = [ri[reverse_bits(i, levels)] for i in range(n)]
  66
  67     # reference list for not needing to do data-swaps, just swap what
  68     # *indices* are referenced (two levels of indirection at the moment)
  69     # pre-reverse the data-swap list so that it *ends up* in the order 0123..
  70     ji = list(range(n))
  71     inplace_mode = SVSHAPE.skip not in [0b10, 0b11]
  72     if inplace_mode:
  73         ji = halfrev2(ji, True)
  74
  75     # start an infinite (wrapping) loop
  76     skip = 0
  77     while True:
  78         for size in x_r:           # loop over 3rd order dimension (size)
  79             x_end = size == x_r[-1]
  80             # y_r schedule depends on size
  81             halfsize = size // 2
  82             y_r = []
  83             for i in range(0, n, size):
  84                 y_r.append(i)
  85             # invert if requested
  86             if SVSHAPE.invxyz[1]: y_r.reverse()
  87             for i in y_r:       # loop over 2nd order dimension
  88                 y_end = i == y_r[-1]
  89                 k_r = []
  90                 j_r = []
  91                 k = 0
  92                 for j in range(i, i+halfsize):
  93                     k_r.append(k)
  94                     j_r.append(j)
  95                 # invert if requested
  96                 if SVSHAPE.invxyz[2]: k_r.reverse()
  97                 if SVSHAPE.invxyz[2]: j_r.reverse()
  98                 hz2 = halfsize // 2 # zero stops reversing 1-item lists
  99                 # if you *really* want to do the in-place swapping manually,
 100                 # this allows you to do it.  good luck...
 101                 if not inplace_mode:
 102                     jr = j_r[:hz2]
 103                 for j in j_r:   # loop over 1st order dimension
 104                     z_end = j == j_r[-1]
 105                     # now depending on MODE return the index
 106                     if SVSHAPE.skip in [0b00, 0b10]:
 107                         result = ri[ji[j]]        # lower half
 108                     elif SVSHAPE.skip in [0b01, 0b11]:
 109                         result = ri[ji[size-j-1]] # upper half, reverse order
 110                     loopends = (z_end |
 111                                ((y_end and z_end)<<1) |
 112                                 ((y_end and x_end and z_end)<<2))
 113
 114                     yield result + SVSHAPE.offset, loopends
 115
 116                 # now in-place swap
 117                 if inplace_mode:
 118                     for ci, (jl, jh) in enumerate(zip(j[:hz2], jr[:hz2])):
 119                         jlh = jl+halfsize
 120                         tmp1, tmp2 = ji[jlh], ji[jh]
 121                         ji[jlh], ji[jh] = tmp2, tmp1
 122
 123
 124 # totally cool *in-place* DCT algorithm
 125 def transform2(vec):
 126
 127     # Initialization
 128     n = len(vec)
 129     levels = n.bit_length() - 1
 130
 131     # and pretend we LDed data in half-swapped *and* bit-reversed order as well
 132     # TODO: merge these two
 133     vec = halfrev2(vec, False)
 134     vec = [vec[ri[i]] for i in range(n)]
 135
 136     # start the inner butterfly
 137     size = n
 138     while size >= 2:
 139         halfsize = size // 2
 140         tablestep = n // size
 141         ir = list(range(0, n, size))
 142         for i in ir:
 143             # two lists of half-range indices, e.g. j 0123, jr 7654
 144             j = list(range(i, i + halfsize))
 145             jr = list(range(i+halfsize, i + size))
 146             jr.reverse()
 147             for ci, (jl, jh) in enumerate(zip(j, jr)):
 148                 vec[ri[ji[jl]]] = t1 + t2
 149                 vec[ri[ji[jh]]] = (t1 - t2) * (1/coeff)
 150             hz2 = halfsize // 2 # can be zero which stops reversing 1-item lists
 151             for ci, (jl, jh) in enumerate(zip(j[:hz2], jr[:hz2])):
 152                 jlh = jl+halfsize
 153                 tmp1, tmp2 = ji[jlh], ji[jh]
 154                 ji[jlh], ji[jh] = tmp2, tmp1
 155         size //= 2
 156
 157 def dct_outer_butterfly(SVSHAPE):
 158     n = len(vec)
 159     size = n // 2
 160     while size >= 2:
 161         halfsize = size // 2
 162         ir = list(range(0, halfsize))
 163         print ("itersum", halfsize, size, ir)
 164         for i in ir:
 165             jr = list(range(i+halfsize, i+n-halfsize, size))
 166             print ("itersum    jr", i+halfsize, i+size, jr)
 167             for jh in jr:
 168                 vec[jh] += vec[jh+size]
 169                 print ("    itersum", size, i, jh, jh+size)
 170         size //= 2
 171
 172     return vec
 173