3d_gpu/architecture/dynamic_simd/add.mdwn

   1 # Partitioned Add
   2
   3 this principle also applies to subtract and negate (-)
   4
   5 the basic principle is: the partition bits, when inverted, can actually
   6 be inserted into an (expanded) add, and, if the bit is set, it has
   7 the side-effect of "rolling through" the carry bit of the MSB from
   8 the previous partition.
   9
  10 this is a really neat trick, basically, that allows the use of a
  11 straight "add" (DSP in an FPGA, add in a simulator) where
  12 otherwise it would be extraordinarily complex, CPU-intensive
  13 and take up large resources.
  14
  15     partition:     P    P    P    P     (4 bits)
  16     a        : .... .... .... .... .... (32 bits)
  17     b        : .... .... .... .... .... (32 bits)
  18     exp-a    : ....P....P....P....P.... (32+4 bits, P=1 if no partition)
  19     exp-b    : ....0....0....0....0.... (32 bits plus 4 zeros)
  20     exp-o    : ....xN...xN...xN...xN... (32+4 bits - x to be discarded)
  21     o        : .... N... N... N... N... (32 bits - x ignored, N is carry-over)
  22
  23 new version:
  24
  25     partition:      p    p    p    p      (4 bits)
  26     carry-in :           c    c    c    c (4 bits)
  27     C = c & P:           C    C    C    c (4 bits)
  28     a        :  AAAA AAAA AAAA AAAA AAAA  (32 bits)
  29     b        :  BBBB BBBB BBBB BBBB BBBB  (32 bits)
  30     exp-a    : 0AAAApAAAACAAAACAAAACAAAAc (32+4 bits, P=1 if no partition)
  31     exp-b    : 0BBBB0BBBBCBBBBCBBBBCBBBBc (32 bits plus 4 zeros)
  32     exp-o    : o....oN...oN...oN...oN...x (32+4 bits - x to be discarded)
  33     o        :  .... N... N... N... N... (32 bits - x ignored, N is carry-over)
  34     carry-out:      o    o    o    o      (4 bits)
  35
  36 the new version
  37
  38 * brings in the carry-in (C) bits which, in combination with
  39   the Partition bits, are ANDed to create "C & p".
  40 * C is positioned twice (in both A and B) intermediates, which
  41   has the effect of preserving carry-out, yet only performing a
  42   carry-over if the carry-in bit (c) is set and this is part of
  43   a partition
  44 * o (carry-out) must be "cascaded" down to the relevant partition
  45   start-point.  this can be done with a Mux-cascade.
  46