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    <p>I'll try to provide an answer that allows you to build a generic tree, without recursion, based only on the tree height provided as a generic at compile time. The code itself looks a bit tricky for my taste; however, the principles behind the solution are straigthforward. Here's an outline of the solution:</p> <ul> <li>Imagine your nodes will be placed on a grid, with dimensions V=TREE_HEIGHT+1 and H=2**TREE_HEIGHT (see the ASCII-gram below). Then, all you need is an algorithm to populate the grid with nodes, and to make the right input and output connections.</li> <li>To connect one level of the tree to the next, you can use a bidimensional array of size TREE_HEIGHT x 2**TREE_HEIGHT (see line 63 in the code example below).</li> <li>To instantiate the nodes, use two nested loops (<code>for-generate</code> in VHDL, see lines 68-69). You will not populate all nodes; for a given row at depth=<em>i</em>, only 2**(i-1) nodes are needed (line 71).</li> <li>You can instantiate different entities for internal and leaf nodes. Just check whether the current value of <em>i</em> equals TREE_HEIGHT (lines 74 and 84).</li> <li>Finally, you just need to connect the layers of the tree. The arithmetic is a bit tricky, but once you get it right you're done (lines 78-80).</li> <li>Count on your synthesis tool to remove the unused wires.</li> </ul> <p>Here's a poor rendition of the "grid" for HEIGHT=2:</p> <pre><code> j = 1 j = 2 j = 3 j = 4 +---------------+---------------+---------------+---------------+ i = 1 | Root Node | (empty) | (empty) | (empty) | +---------------+---------------+---------------+---------------+ i = 2 | Internal Node | Internal Node | (empty) | (empty) | +---------------+---------------+---------------+---------------+ i = 3 | Internal Node | Internal Node | Internal Node | Internal Node | +---------------+---------------+---------------+---------------+ </code></pre> <p>Here's the code example:</p> <pre><code>/* 1 */ package tree_types_pkg is /* 2 */ -- define a data type for the input and output values at each node /* 3 */ subtype tree_data_type is integer range 0 to 255; /* 4 */ -- define a vector type to propagate the output of a tree level to the next /* 5 */ type layer_to_layer_channel_type is array (natural range &lt;&gt;) of tree_data_type; /* 6 */ end; /* 7 */ -------------------------------------------------------------------------------- /* 8 */ use work.tree_types_pkg.all; /* 9 */ /* 10 */ entity internal_node is /* 11 */ generic ( /* 12 */ TREE_HEIGHT: integer := 3 /* 13 */ ); /* 14 */ port ( /* 15 */ x: in integer range 1 to 2**TREE_HEIGHT; /* 16 */ y: in integer range 1 to TREE_HEIGHT; /* 17 */ input: in tree_data_type; /* 18 */ output_left: out tree_data_type; /* 19 */ output_right: out tree_data_type /* 20 */ ); /* 21 */ end; /* 22 */ /* 23 */ architecture rtl of internal_node is begin /* 24 */ -- perform some calculation at the node /* 25 */ output_left &lt;= input + x * y; /* 26 */ output_right &lt;= input - x * y; /* 27 */ end; /* 28 */ -------------------------------------------------------------------------------- /* 29 */ use work.tree_types_pkg.all; /* 20 */ /* 31 */ entity leaf_node is /* 32 */ generic ( /* 33 */ TREE_HEIGHT: integer := 3 /* 34 */ ); /* 35 */ port ( /* 36 */ x: in integer range 1 to 2**TREE_HEIGHT; /* 37 */ y: in integer range 1 to TREE_HEIGHT; /* 38 */ input: in tree_data_type; /* 39 */ output: out tree_data_type /* 30 */ ); /* 41 */ end; /* 42 */ /* 43 */ architecture rtl of leaf_node is begin /* 44 */ -- perform some calculation at the node /* 45 */ output &lt;= input + x * y; /* 46 */ end; /* 47 */ -------------------------------------------------------------------------------- /* 48 */ use work.tree_types_pkg.all; /* 49 */ /* 50 */ entity dirtybit_binary_tree is /* 51 */ generic ( /* 52 */ TREE_HEIGHT: integer := 4 /* 53 */ ); /* 54 */ port ( /* 55 */ tree_input: in tree_data_type; /* 56 */ tree_outputs: out layer_to_layer_channel_type(1 to 2**TREE_HEIGHT) /* 57 */ ); /* 58 */ end; /* 59 */ /* 60 */ architecture behavior of dirtybit_binary_tree is /* 61 */ constant LEAF_NODES_COUNT: integer := 2**TREE_HEIGHT; /* 62 */ type channel_array_type is array (natural range &lt;&gt;) of layer_to_layer_channel_type; /* 63 */ signal connections: channel_array_type(1 to TREE_HEIGHT)(1 to LEAF_NODES_COUNT); /* 64 */ begin /* 65 */ /* 66 */ connections(1)(1) &lt;= tree_input; /* 67 */ /* 68 */ grid_y: for i in 1 to TREE_HEIGHT generate /* 69 */ grid_x: for j in 1 to LEAF_NODES_COUNT generate /* 70 */ /* 71 */ instantiate_nodes: if j &lt;= 2**(i-1) generate /* 72 */ /* 73 */ internal_nodes: if (i /= TREE_HEIGHT) generate /* 74 */ internal_node: entity work.internal_node /* 75 */ generic map (TREE_HEIGHT =&gt; TREE_HEIGHT) /* 76 */ port map ( /* 77 */ x =&gt; j, /* 78 */ y =&gt; i, /* 79 */ input =&gt; connections(i)(j), /* 80 */ output_left =&gt; connections(i+1)((j-1)*i+1), /* 81 */ output_right =&gt; connections(i+1)((j-1)*i+2) /* 82 */ ); /* 83 */ end generate; /* 84 */ /* 85 */ leaf_nodes: if (i = TREE_HEIGHT) generate /* 86 */ leaf_node: entity work.leaf_node /* 87 */ generic map (TREE_HEIGHT =&gt; TREE_HEIGHT) /* 88 */ port map ( /* 89 */ x =&gt; j, /* 90 */ y =&gt; i, /* 91 */ input =&gt; connections(i)(j), /* 92 */ output =&gt; tree_outputs(j) /* 93 */ ); /* 94 */ end generate; /* 95 */ /* 96 */ end generate; /* 97 */ /* 98 */ end generate; /* 99 */ end generate; /* 100 */ /* 101 */ end; </code></pre> <p>Finally, here's what the synthesized circuit looks like on Quartus 12.1 (RTL Viewer):</p> <p><img src="https://i.stack.imgur.com/TMtfV.png" alt="Tree circuit on Quartus RTL Viewer"></p>
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