3d_gpu/architecture/dynamic_simd/slice.mdwn

   1 # Dynamic Partitioned Slice (`SimdSlice`)
   2
   3 In order to match the semantics of nmigen's `Slice` class, `SimdSlice` has to have each element of the result have
   4 exactly the same `Shape` as the result of slicing the input `SimdSignal`'s corresponding element.
   5
   6 ## Example code:
   7
   8 ```python
   9 a_s = SimdSignal(...)
  10 a = a_s.sig # shorthand to make table smaller
  11 b_s = a_s[3:6]
  12 b = b_s.sig # shorthand to make table smaller
  13 ```
  14
  15 ## `a`'s Elements:
  16
  17 (TODO 1: shrink to only 4 partitions.  TODO 2: convert to markdown)
  18
  19 <table>
  20     <tr class="text-right">
  21         <th scope="row" class="text-left">Bit #</th>
  22         <td>63&#8288;&hellip;&#8288;56</td>
  23         <td>55&#8288;&hellip;&#8288;48</td>
  24         <td>47&#8288;&hellip;&#8288;40</td>
  25         <td>39&#8288;&hellip;&#8288;32</td>
  26         <td>31&#8288;&hellip;&#8288;24</td>
  27         <td>23&#8288;&hellip;&#8288;16</td>
  28         <td>15&#8288;&hellip;&#8288;8</td>
  29         <td>7&#8288;&hellip;&#8288;0</td>
  30     </tr>
  31     <tr class="text-right">
  32         <th scope="row" class="text-left">ElWid: 8-bit</th>
  33         <td><code>a[56:64]</code></td>
  34         <td><code>a[48:56]</code></td>
  35         <td><code>a[40:48]</code></td>
  36         <td><code>a[32:40]</code></td>
  37         <td><code>a[24:32]</code></td>
  38         <td><code>a[16:24]</code></td>
  39         <td><code>a[8:16]</code></td>
  40         <td><code>a[0:8]</code></td>
  41     </tr>
  42     <tr class="text-right">
  43         <th scope="row" class="text-left">ElWid: 16-bit</th>
  44         <td colspan="2"><code>a[48:64]</code></td>
  45         <td colspan="2"><code>a[32:48]</code></td>
  46         <td colspan="2"><code>a[16:32]</code></td>
  47         <td colspan="2"><code>a[0:16]</code></td>
  48     </tr>
  49     <tr class="text-right">
  50         <th scope="row" class="text-left">ElWid: 32-bit</th>
  51         <td colspan="4"><code>a[32:64]</code></td>
  52         <td colspan="4"><code>a[0:32]</code></td>
  53     </tr>
  54     <tr class="text-right">
  55         <th scope="row" class="text-left">ElWid: 64-bit</th>
  56         <td colspan="8"><code>a[0:64]</code></td>
  57     </tr>
  58 </table>
  59
  60 So, slicing bits `3:6` of a 32-bit element of `a` must, because we have to match nmigen, produce a 3-bit element, which might seem like no problem, however, slicing bits `3:6` of a 16-bit element of a 64-bit `SimdSignal` must *also* produce a 3-bit element, so, in order to get a `SimdSignal` where *all* elements are 3-bit elements, as required by `SimdSlice`'s output, we have to introduce padding:
  61
  62 ## `b`'s Elements:
  63
  64 (TODO 1: shrink to only 4 partitions.  TODO 2: convert to markdown)
  65
  66 <table>
  67     <tr class="text-right">
  68         <th scope="row" class="text-left">Bit #</th>
  69         <td>23&#8288;&hellip;&#8288;21</td>
  70         <td>20&#8288;&hellip;&#8288;18</td>
  71         <td>17&#8288;&hellip;&#8288;15</td>
  72         <td>14&#8288;&hellip;&#8288;12</td>
  73         <td>11&#8288;&hellip;&#8288;9</td>
  74         <td>8&#8288;&hellip;&#8288;6</td>
  75         <td>5&#8288;&hellip;&#8288;3</td>
  76         <td>2&#8288;&hellip;&#8288;0</td>
  77     </tr>
  78     <tr class="text-right">
  79         <th scope="row" class="text-left">ElWid: 8-bit</th>
  80         <td><code>b[21:24]</code></td>
  81         <td><code>b[18:21]</code></td>
  82         <td><code>b[15:18]</code></td>
  83         <td><code>b[12:15]</code></td>
  84         <td><code>b[9:12]</code></td>
  85         <td><code>b[6:9]</code></td>
  86         <td><code>b[3:6]</code></td>
  87         <td><code>b[0:3]</code></td>
  88     </tr>
  89     <tr class="text-right">
  90         <th scope="row" class="text-left">ElWid: 16-bit</th>
  91         <td class="text-center"><i>Padding</i></td>
  92         <td><code>b[18:21]</code></td>
  93         <td class="text-center"><i>Padding</i></td>
  94         <td><code>b[12:15]</code></td>
  95         <td class="text-center"><i>Padding</i></td>
  96         <td><code>b[6:9]</code></td>
  97         <td class="text-center"><i>Padding</i></td>
  98         <td><code>b[0:3]</code></td>
  99     </tr>
 100     <tr class="text-right">
 101         <th scope="row" class="text-left">ElWid: 32-bit</th>
 102         <td colspan="3" class="text-center"><i>Padding</i></td>
 103         <td><code>b[12:15]</code></td>
 104         <td colspan="3" class="text-center"><i>Padding</i></td>
 105         <td><code>b[0:3]</code></td>
 106     </tr>
 107     <tr class="text-right">
 108         <th scope="row" class="text-left">ElWid: 64-bit</th>
 109         <td colspan="7" class="text-center"><i>Padding</i></td>
 110         <td><code>b[0:3]</code></td>
 111     </tr>
 112 </table>
 113
 114 <style>
 115     /* duplicated from bootstrap so text editors can see it
 116         -- ignored by ikiwiki */
 117     .text-left {
 118         text-align: left !important
 119     }
 120
 121     .text-right {
 122         text-align: right !important
 123     }
 124
 125     .text-center {
 126         text-align: center !important
 127     }
 128 </style>
 129
 130 # Partitioned SIMD Design implications
 131
 132 Slice is the very first of the entire suite of sub-modules of Partitioned
 133 SimdSignal that requires (and propagates) fixed element widths.  All other
 134 sub-modules have up until this point been a fixed *overall* width where the
 135 element widths adapt to completely fill the entire underlying Signal.
 136
 137 Given that this new width context is then passed through to other SimdSignals,
 138 the entire SimdSignal suite has to adapt to this change in requirements.
 139 It is however not as big an adaptation as it first seems, because ultimately
 140 SimdSignals use PartitionPoints (and a PartType) to decide what to do.
 141 Illustrating that SimdSignal uses PartitionPoints to make its decisions
 142 at the low level, an add example using `b` and a new SimdSignal `c` of
 143 an overall 8-bit width (with fixed element widths of size 2):
 144
 145 (TODO: add an example of how this would then do e.g. an add (to another
 146 SimdSignal of only 8 bits in length or so - all element widths being
 147 2 in all partitions, but having the exact same PartitionPoints)
 148
 149 Questions raised by the add example:
 150
 151 * after performing a Slice, which creates an entirely new
 152   (padded) set of PartitionPoints, where does c's PartitionPoints
 153   come from?
 154 * how should a SimdSignal that does not contain the same
 155   padding be add()ed to a Slice()d SimdSignal that does *not*
 156   contain padding, having a completely different set of PartitionPoints?
 157 * what happens when a fixed element width Slice()d source `b` is
 158   add()ed to a fixed *overall* width SimdSignal of width 8 that
 159   permits variable-length (max available space) elements?
 160
 161 Illustrating the case of adding a SimdSignal with padding to one that
 162 does not:
 163
 164 (TODO: add a second example of how this would then do e.g. an add (to another
 165 SimdSignal of only 8 bits in length or so, but having a **different**
 166 style of PartitionPoints, with no padding this time)
 167
 168 Illustrating the case where a Sliced (fixed element width) SimdSignal
 169 is added to one which has variable-length elements that take up the
 170 entirety of the partition (overall fixed width):
 171
 172 (TODO: third example)