perf: Combine constraints of illegal num_words

The constraints prohibiting an illegal value for `NumberOfWords` are mutually exclusive. More importantly, the set of all the constraints has Hamming weight 1. This implies they can safely (and soundly) be summed.
TritonVM · Jun 10, 2024 · d74e10a · d74e10a
1 parent 6ff8500
commit d74e10a
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diff --git a/specification/src/arithmetization-overview.md b/specification/src/arithmetization-overview.md
@@ -34,7 +34,7 @@ Before automatic degree lowering:
 | table name                                     | #initial | #consistency | #transition | #terminal | max degree |
 |:-----------------------------------------------|---------:|-------------:|------------:|----------:|-----------:|
 | [ProgramTable](program-table.md)               |        6 |            4 |          10 |         2 |          4 |
-| [ProcessorTable](processor-table.md)           |       29 |           10 |          49 |         1 |         19 |
+| [ProcessorTable](processor-table.md)           |       29 |           10 |          41 |         1 |         19 |
 | [OpStackTable](operational-stack-table.md)     |        3 |            0 |           5 |         0 |          4 |
 | [RamTable](random-access-memory-table.md)      |        7 |            0 |          12 |         1 |          5 |
 | [JumpStackTable](jump-stack-table.md)          |        6 |            0 |           6 |         0 |          4 |
@@ -43,14 +43,14 @@ Before automatic degree lowering:
 | [LookupTable](lookup-table.md)                 |        3 |            1 |           4 |         1 |          3 |
 | [U32Table](u32-table.md)                       |        1 |           15 |          22 |         2 |         12 |
 | [Grand Cross-Table Argument](table-linking.md) |        0 |            0 |           0 |        14 |          1 |
-| **TOTAL**                                      |   **79** |       **76** |     **158** |    **23** |     **19** |
+| **TOTAL**                                      |   **79** |       **76** |     **150** |    **23** |     **19** |
 
 After automatically lowering degree to 4:
 
 | table name                                     | #initial | #consistency | #transition | #terminal |
 |:-----------------------------------------------|---------:|-------------:|------------:|----------:|
 | [ProgramTable](program-table.md)               |        6 |            4 |          10 |         2 |
-| [ProcessorTable](processor-table.md)           |       31 |           10 |         227 |         1 |
+| [ProcessorTable](processor-table.md)           |       31 |           10 |         219 |         1 |
 | [OpStackTable](operational-stack-table.md)     |        3 |            0 |           5 |         0 |
 | [RamTable](random-access-memory-table.md)      |        7 |            0 |          13 |         1 |
 | [JumpStackTable](jump-stack-table.md)          |        6 |            0 |           6 |         0 |
@@ -59,7 +59,7 @@ After automatically lowering degree to 4:
 | [LookupTable](lookup-table.md)                 |        3 |            1 |           4 |         1 |
 | [U32Table](u32-table.md)                       |        1 |           26 |          34 |         2 |
 | [Grand Cross-Table Argument](table-linking.md) |        0 |            0 |           0 |        14 |
-| **TOTAL**                                      |   **81** |       **94** |     **386** |    **23** |
+| **TOTAL**                                      |   **81** |       **94** |     **378** |    **23** |
 <!-- auto-gen info stop constraints_overview -->
 
 
@@ -71,5 +71,5 @@ In order to gauge the runtime cost for this step, the following table provides e
 <!-- auto-gen info start tasm_air_evaluation_cost -->
 | Processor | Op Stack |   RAM |
 |----------:|---------:|------:|
-|     35689 |    66327 | 23592 |
+|     35207 |    65377 | 23220 |
 <!-- auto-gen info stop tasm_air_evaluation_cost -->
diff --git a/triton-vm/src/table/processor_table.rs b/triton-vm/src/table/processor_table.rs
@@ -2720,9 +2720,10 @@ impl ExtProcessorTable {
     fn prohibit_any_illegal_number_of_words(
         circuit_builder: &ConstraintCircuitBuilder<DualRowIndicator>,
     ) -> Vec<ConstraintCircuitMonad<DualRowIndicator>> {
-        NumberOfWords::illegal_values()
+        vec![NumberOfWords::illegal_values()
             .map(|n| Self::indicator_polynomial(circuit_builder, n))
-            .to_vec()
+            .into_iter()
+            .sum()]
     }
 
     fn log_derivative_accumulates_clk_next(