diff --git a/evm/src/cpu/kernel/asm/core/jumpdest_analysis.asm b/evm/src/cpu/kernel/asm/core/jumpdest_analysis.asm
index aed6c186..c197fb6a 100644
--- a/evm/src/cpu/kernel/asm/core/jumpdest_analysis.asm
+++ b/evm/src/cpu/kernel/asm/core/jumpdest_analysis.asm
@@ -2,7 +2,7 @@
 // for the given context's code.
 // Pre stack: init_pos, ctx, final_pos, retdest
 // Post stack: (empty)
-global verify_path_and_write_table:
+global verify_path_and_write_jumpdest_table:
 loop:
     // stack: i, ctx, final_pos, retdest
     DUP3 DUP2 EQ // i == final_pos
@@ -10,7 +10,7 @@ loop:
     DUP3 DUP2 GT // i > final_pos
     %jumpi(proof_not_ok)
 
-    // stack: i, ctx, code_len, retdest
+     // stack: i, ctx, final_pos, retdest
     %stack (i, ctx) -> (ctx, i, i, ctx)
     ADD // combine context and offset to make an address (SEGMENT_CODE == 0)
     MLOAD_GENERAL
@@ -124,7 +124,7 @@ global write_table_if_jumpdest:
     SWAP2 DUP1
     // stack: proof_prefix_addr, proof_prefix_addr, ctx, jumpdest
     ISZERO
-    %jumpi(verify_path_and_write_table)
+    %jumpi(verify_path_and_write_jumpdest_table)
 
 
     // stack: proof_prefix_addr, ctx, jumpdest, retdest
@@ -266,7 +266,7 @@ global write_table_if_jumpdest:
     %add_const(32)
 
     // check the remaining path
-    %jump(verify_path_and_write_table)
+    %jump(verify_path_and_write_jumpdest_table)
 return:
     // stack: proof_prefix_addr, jumpdest, ctx, retdest
     %pop3
diff --git a/evm/src/generation/mod.rs b/evm/src/generation/mod.rs
index 238011d8..e14de9b9 100644
--- a/evm/src/generation/mod.rs
+++ b/evm/src/generation/mod.rs
@@ -379,7 +379,7 @@ fn simulate_cpu_between_labels_and_get_user_jumps<F: Field>(
                 state.registers.program_counter,
             ))) else {
                 log::debug!(
-                    "Simulated CPU halted after {} cycles",
+                    "Simulated CPU for jumpdest analysis halted after {} cycles",
                     state.traces.clock() - initial_clock
                 );
                 return Some(jumpdest_addresses);
@@ -395,7 +395,7 @@ fn simulate_cpu_between_labels_and_get_user_jumps<F: Field>(
                 // Avoid deeper calls to abort
                 let Ok(jumpdest) = u256_to_usize(state.registers.stack_top) else {
                     log::debug!(
-                        "Simulated CPU halted after {} cycles",
+                        "Simulated CPU for jumpdest analysis halted after {} cycles",
                         state.traces.clock() - initial_clock
                     );
                     return Some(jumpdest_addresses);
@@ -416,7 +416,7 @@ fn simulate_cpu_between_labels_and_get_user_jumps<F: Field>(
             }
             if halt || transition(state).is_err() {
                 log::debug!(
-                    "Simulated CPU halted after {} cycles",
+                    "Simulated CPU for jumpdest analysis halted after {} cycles",
                     state.traces.clock() - initial_clock
                 );
                 return Some(jumpdest_addresses);
diff --git a/evm/src/generation/prover_input.rs b/evm/src/generation/prover_input.rs
index 97177a8c..ccec9c45 100644
--- a/evm/src/generation/prover_input.rs
+++ b/evm/src/generation/prover_input.rs
@@ -240,6 +240,7 @@ impl<F: Field> GenerationState<F> {
         }
     }
 
+    /// Generate the either the next used jump address or the the proof for the last jump address.
     fn run_jumpdest_table(&mut self, input_fn: &ProverInputFn) -> Result<U256, ProgramError> {
         match input_fn.0[1].as_str() {
             "next_address" => self.run_next_jumpdest_table_address(),
@@ -293,6 +294,7 @@ impl<F: Field> GenerationState<F> {
 }
 
 impl<F: Field> GenerationState<F> {
+    /// Simulate the user's code and store all the jump addresses with their respective contexts.
     fn generate_jumpdest_proofs(&mut self) -> Result<(), ProgramError> {
         let checkpoint = self.checkpoint();
         let memory = self.memory.clone();
@@ -322,6 +324,8 @@ impl<F: Field> GenerationState<F> {
         Ok(())
     }
 
+    /// Given a HashMap containing the contexts and the jumpdest addresses, compute their respective proofs,
+    /// by calling `get_proofs_and_jumpdests`
     pub(crate) fn set_proofs_and_jumpdests(
         &mut self,
         jumpdest_table: HashMap<usize, std::collections::BTreeSet<usize>>,
diff --git a/evm/src/util.rs b/evm/src/util.rs
index ee2d9607..f4d80859 100644
--- a/evm/src/util.rs
+++ b/evm/src/util.rs
@@ -70,17 +70,17 @@ pub(crate) fn u256_to_u64<F: Field>(u256: U256) -> Result<(F, F), ProgramError>
     ))
 }
 
-/// Safe conversion from U256 to u8, which errors in case of overflow instead of panicking.
-pub(crate) fn u256_to_u8(u256: U256) -> Result<u8, ProgramError> {
-    u256.try_into().map_err(|_| ProgramError::IntegerTooLarge)
-}
-
 /// Safe alternative to `U256::as_usize()`, which errors in case of overflow instead of panicking.
 pub(crate) fn u256_to_usize(u256: U256) -> Result<usize, ProgramError> {
     u256.try_into().map_err(|_| ProgramError::IntegerTooLarge)
 }
 
-/// Converts a `U256` to a `bool`, erroring in case of overlow instead of panicking.
+/// Converts a `U256` to a `u8`, erroring in case of overflow instead of panicking.
+pub(crate) fn u256_to_u8(u256: U256) -> Result<u8, ProgramError> {
+    u256.try_into().map_err(|_| ProgramError::IntegerTooLarge)
+}
+
+/// Converts a `U256` to a `bool`, erroring in case of overflow instead of panicking.
 pub(crate) fn u256_to_bool(u256: U256) -> Result<bool, ProgramError> {
     if u256 == U256::zero() {
         Ok(false)