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0xPolygonMiden · Oct 17, 2024 · 891bb1c · 891bb1c
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diff --git a/design/stack/main.html b/design/stack/main.html
@@ -258,7 +258,7 @@ <h1 id="operand-stack"><a class="header" href="#operand-stack">Operand stack</a>
 </ul>
 <h2 id="stack-representation"><a class="header" href="#stack-representation">Stack representation</a></h2>
 <p>The VM allocates <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">19</span></span></span></span> trace columns for the stack. The layout of the columns is illustrated below.</p>
-<p><img src="../../assets/design/stack/trace_layout.png" alt="" /></p>
+<p><img src="../../assets/design/stack/trace_layout.png" alt="trace_layout" /></p>
 <p>The meaning of the above columns is as follows:</p>
 <ul>
 <li><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">...</span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">15</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> are the columns representing the top <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">16</span></span></span></span> slots of the stack.</li>
@@ -269,7 +269,7 @@ <h2 id="stack-representation"><a class="header" href="#stack-representation">Sta
 <h3 id="overflow-table"><a class="header" href="#overflow-table">Overflow table</a></h3>
 <p>To keep track of the data which doesn't fit into the top <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">16</span></span></span></span> stack slots, we'll use an overflow table. This will be a <a href="../lookups/multiset.html#virtual-tables">virtual table</a>. To represent this table, we'll use a single auxiliary column <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>.</p>
 <p>The table itself can be thought of as having 3 columns as illustrated below.</p>
-<p><img src="../../assets/design/stack/overflow_table_layout.png" alt="" /></p>
+<p><img src="../../assets/design/stack/overflow_table_layout.png" alt="overflow_table_layout" /></p>
 <p>The meaning of the columns is as follows:</p>
 <ul>
 <li>Column <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7651em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> contains row address. Every address in the table must be unique.</li>
@@ -291,16 +291,16 @@ <h3 id="overflow-table"><a class="header" href="#overflow-table">Overflow table<
 <p>How these are enforced will be described a bit later.</p>
 <h2 id="right-shift"><a class="header" href="#right-shift">Right shift</a></h2>
 <p>If an operation adds data to the stack, we say that the operation caused a right shift. For example, <code>PUSH</code> and <code>DUP</code> operations cause a right shift. Graphically, this looks like so:</p>
-<p><img src="../../assets/design/stack/stack_right_shift.png" alt="" /></p>
+<p><img src="../../assets/design/stack/stack_right_shift.png" alt="stack_right_shift" /></p>
 <p>Here, we pushed value <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">17</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> onto the stack. All other values on the stack are shifted by one slot to the right and the stack depth increases by <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span>. There is not enough space at the top of the stack for all <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">17</span></span></span></span> values, thus, <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> needs to be moved to the overflow table.</p>
 <p>To do this, we need to rely on another column: <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>. This is a system column which keeps track of the current VM cycle. The value in this column is simply incremented by <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> with every step.</p>
 <p>The row we want to add to the overflow table is defined by tuple <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">0</span><span class="mclose">)</span></span></span></span>, and after it is added, the table would look like so:</p>
-<p><img src="../../assets/design/stack/stack_overflow_table_post_1_right_shift.png" alt="" /></p>
+<p><img src="../../assets/design/stack/stack_overflow_table_post_1_right_shift.png" alt="stack_overflow_table_post_1_right_shift" /></p>
 <p>The reason we use VM clock cycle as row address is that the clock cycle is guaranteed to be unique, and thus, the same row can not be added to the table twice.</p>
 <p>Let's push another item onto the stack:</p>
-<p><img src="../../assets/design/stack/stack_overflow_push_2nd_item.png" alt="" /></p>
+<p><img src="../../assets/design/stack/stack_overflow_push_2nd_item.png" alt="stack_overflow_push_2nd_item" /></p>
 <p>Again, as we push <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">18</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> onto the stack, all items on the stack are shifted to the right, and now <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> needs to be moved to the overflow table. The tuple we want to insert into the table now is <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">)</span></span></span></span>. After the operation, the overflow table will look like so:</p>
-<p><img src="../../assets/design/stack/stack_overflow_table_post_2_right_shift.png" alt="" /></p>
+<p><img src="../../assets/design/stack/stack_overflow_table_post_2_right_shift.png" alt="stack_overflow_table_post_2_right_shift" /></p>
 <p>Notice that <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7651em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> for row which contains value <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> points back to the row with address <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span></span></span></span>.</p>
 <p>Overall, during a right shift we do the following:</p>
 <ul>
@@ -312,7 +312,7 @@ <h2 id="right-shift"><a class="header" href="#right-shift">Right shift</a></h2>
 <p>Also, as mentioned previously, the prover sets values in <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> non-deterministically to <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2902em;vertical-align:-0.4451em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight">16</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>.</p>
 <h2 id="left-shift"><a class="header" href="#left-shift">Left shift</a></h2>
 <p>If an operation removes an item from the stack, we say that the operation caused a left shift. For example, a <code>DROP</code> operation causes a left shift. Assuming the stack is in the state we left it at the end of the previous section, graphically, this looks like so:</p>
-<p><img src="../../assets/design/stack/stack_1st_left_shift.png" alt="" /></p>
+<p><img src="../../assets/design/stack/stack_1st_left_shift.png" alt="stack_1st_left_shift" /></p>
 <p>Overall, during the left shift we do the following:</p>
 <ul>
 <li>When stack depth is greater than <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">16</span></span></span></span>: