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 <table>
  18     <tr class="text-right">
  19         <th scope="row" class="text-left">Bit #</th>
  20         <td>63&#8288;&hellip;&#8288;56</td>
  21         <td>55&#8288;&hellip;&#8288;48</td>
  22         <td>47&#8288;&hellip;&#8288;40</td>
  23         <td>39&#8288;&hellip;&#8288;32</td>
  24         <td>31&#8288;&hellip;&#8288;24</td>
  25         <td>23&#8288;&hellip;&#8288;16</td>
  26         <td>15&#8288;&hellip;&#8288;8</td>
  27         <td>7&#8288;&hellip;&#8288;0</td>
  28     </tr>
  29     <tr class="text-right">
  30         <th scope="row" class="text-left">ElWid: 8-bit</th>
  31         <td><code>a[56:64]</code></td>
  32         <td><code>a[48:56]</code></td>
  33         <td><code>a[40:48]</code></td>
  34         <td><code>a[32:40]</code></td>
  35         <td><code>a[24:32]</code></td>
  36         <td><code>a[16:24]</code></td>
  37         <td><code>a[8:16]</code></td>
  38         <td><code>a[0:8]</code></td>
  39     </tr>
  40     <tr class="text-right">
  41         <th scope="row" class="text-left">ElWid: 16-bit</th>
  42         <td colspan="2"><code>a[48:64]</code></td>
  43         <td colspan="2"><code>a[32:48]</code></td>
  44         <td colspan="2"><code>a[16:32]</code></td>
  45         <td colspan="2"><code>a[0:16]</code></td>
  46     </tr>
  47     <tr class="text-right">
  48         <th scope="row" class="text-left">ElWid: 32-bit</th>
  49         <td colspan="4"><code>a[32:64]</code></td>
  50         <td colspan="4"><code>a[0:32]</code></td>
  51     </tr>
  52     <tr class="text-right">
  53         <th scope="row" class="text-left">ElWid: 64-bit</th>
  54         <td colspan="8"><code>a[0:64]</code></td>
  55     </tr>
  56 </table>
  57
  58 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:
  59
  60 ## `b`'s Elements:
  61
  62 <table>
  63     <tr class="text-right">
  64         <th scope="row" class="text-left">Bit #</th>
  65         <td>23&#8288;&hellip;&#8288;21</td>
  66         <td>20&#8288;&hellip;&#8288;18</td>
  67         <td>17&#8288;&hellip;&#8288;15</td>
  68         <td>14&#8288;&hellip;&#8288;12</td>
  69         <td>11&#8288;&hellip;&#8288;9</td>
  70         <td>8&#8288;&hellip;&#8288;6</td>
  71         <td>5&#8288;&hellip;&#8288;3</td>
  72         <td>2&#8288;&hellip;&#8288;0</td>
  73     </tr>
  74     <tr class="text-right">
  75         <th scope="row" class="text-left">ElWid: 8-bit</th>
  76         <td><code>b[21:24]</code></td>
  77         <td><code>b[18:21]</code></td>
  78         <td><code>b[15:18]</code></td>
  79         <td><code>b[12:15]</code></td>
  80         <td><code>b[9:12]</code></td>
  81         <td><code>b[6:9]</code></td>
  82         <td><code>b[3:6]</code></td>
  83         <td><code>b[0:3]</code></td>
  84     </tr>
  85     <tr class="text-right">
  86         <th scope="row" class="text-left">ElWid: 16-bit</th>
  87         <td class="text-center"><i>Padding</i></td>
  88         <td><code>b[18:21]</code></td>
  89         <td class="text-center"><i>Padding</i></td>
  90         <td><code>b[12:15]</code></td>
  91         <td class="text-center"><i>Padding</i></td>
  92         <td><code>b[6:9]</code></td>
  93         <td class="text-center"><i>Padding</i></td>
  94         <td><code>b[0:3]</code></td>
  95     </tr>
  96     <tr class="text-right">
  97         <th scope="row" class="text-left">ElWid: 32-bit</th>
  98         <td colspan="3" class="text-center"><i>Padding</i></td>
  99         <td><code>b[12:15]</code></td>
 100         <td colspan="3" class="text-center"><i>Padding</i></td>
 101         <td><code>b[0:3]</code></td>
 102     </tr>
 103     <tr class="text-right">
 104         <th scope="row" class="text-left">ElWid: 64-bit</th>
 105         <td colspan="7" class="text-center"><i>Padding</i></td>
 106         <td><code>b[0:3]</code></td>
 107     </tr>
 108 </table>
 109
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