diff --git a/emulator/src/state.rs b/emulator/src/state.rs
index b8f30de1..58e0afe5 100644
--- a/emulator/src/state.rs
+++ b/emulator/src/state.rs
@@ -573,7 +573,7 @@ impl InstrumentedState {
                 log::debug!("input: {:?}", vec);
                 assert_eq!(a0 % 4, 0, "hint read address not aligned to 4 bytes");
                 if a1 >= 1 {
-                    self.state.cycle += (a1 as u64 + 31) / 32;
+                    self.state.cycle += (a1 as u64).div_ceil(32);
                 }
                 for i in (0..a1).step_by(4) {
                     // Get each byte in the chunk
diff --git a/prover/examples/Cargo.toml b/prover/examples/Cargo.toml
index f9c50110..a8d6efb0 100644
--- a/prover/examples/Cargo.toml
+++ b/prover/examples/Cargo.toml
@@ -2,7 +2,7 @@
 members = [
   "revme/host",
   "sha2-rust/host",
-  "sha2-precompile/host",
+  "sha2-composition/host",
   "sha2-go/host",
   "keccak/host",
   "split-seg",
diff --git a/prover/examples/README.md b/prover/examples/README.md
index 401fde5e..4770fa00 100644
--- a/prover/examples/README.md
+++ b/prover/examples/README.md
@@ -76,15 +76,15 @@ RUST_LOG=info JSON_PATH=../../../../emulator/test-vectors/test.json SEG_OUTPUT=/
 
 ```
 
-## Prove precompile code
+## Prove composition code
 * Build the sha2-rust (**new**)
 ```
 cd prover/examples/sha2-rust/host
 cargo check
 ```
 
-* Build and run the sha2-precompile (**new**)
+* Build and run the sha2-composition (**new**)
 ```
-cd ../../sha2-precompile/host
+cd ../../sha2-composition/host
 RUST_LOG=info PRECOMPILE_PATH=../../sha2-rust/guest/elf/mips-zkm-zkvm-elf SEG_OUTPUT=/tmp/output cargo run --release
 ```
diff --git a/prover/examples/sha2-precompile/guest/Cargo.lock b/prover/examples/sha2-composition/guest/Cargo.lock
similarity index 100%
rename from prover/examples/sha2-precompile/guest/Cargo.lock
rename to prover/examples/sha2-composition/guest/Cargo.lock
diff --git a/prover/examples/sha2-precompile/guest/Cargo.toml b/prover/examples/sha2-composition/guest/Cargo.toml
similarity index 100%
rename from prover/examples/sha2-precompile/guest/Cargo.toml
rename to prover/examples/sha2-composition/guest/Cargo.toml
diff --git a/prover/examples/sha2-precompile/guest/src/main.rs b/prover/examples/sha2-composition/guest/src/main.rs
similarity index 100%
rename from prover/examples/sha2-precompile/guest/src/main.rs
rename to prover/examples/sha2-composition/guest/src/main.rs
diff --git a/prover/examples/sha2-precompile/host/Cargo.toml b/prover/examples/sha2-composition/host/Cargo.toml
similarity index 95%
rename from prover/examples/sha2-precompile/host/Cargo.toml
rename to prover/examples/sha2-composition/host/Cargo.toml
index e5e78bd2..ac4d8df6 100644
--- a/prover/examples/sha2-precompile/host/Cargo.toml
+++ b/prover/examples/sha2-composition/host/Cargo.toml
@@ -1,5 +1,5 @@
 [package]
-name = "precompile-host"
+name = "composition-host"
 version = { workspace = true }
 edition = { workspace = true }
 publish = false
diff --git a/prover/examples/sha2-precompile/host/build.rs b/prover/examples/sha2-composition/host/build.rs
similarity index 100%
rename from prover/examples/sha2-precompile/host/build.rs
rename to prover/examples/sha2-composition/host/build.rs
diff --git a/prover/examples/sha2-precompile/host/src/main.rs b/prover/examples/sha2-composition/host/src/main.rs
similarity index 100%
rename from prover/examples/sha2-precompile/host/src/main.rs
rename to prover/examples/sha2-composition/host/src/main.rs
diff --git a/prover/src/cpu/cpu_stark.rs b/prover/src/cpu/cpu_stark.rs
index de688cb3..01d625d5 100644
--- a/prover/src/cpu/cpu_stark.rs
+++ b/prover/src/cpu/cpu_stark.rs
@@ -1,5 +1,5 @@
 use std::borrow::Borrow;
-use std::iter::repeat;
+use std::iter::repeat_n;
 use std::marker::PhantomData;
 
 use itertools::Itertools;
@@ -167,7 +167,7 @@ pub fn ctl_data_code_memory<F: Field>() -> Vec<Column<F>> {
     cols.push(Column::le_bits(base));
 
     // High limbs of the value are all zero.
-    cols.extend(repeat(Column::constant(F::ZERO)).take(VALUE_LIMBS - 1));
+    cols.extend(repeat_n(Column::constant(F::ZERO), VALUE_LIMBS - 1));
 
     cols.push(mem_time_and_channel(MEM_CODE_CHANNEL_IDX));
 
diff --git a/runtime/precompiles/src/io.rs b/runtime/precompiles/src/io.rs
index 335b7d4f..10c519db 100644
--- a/runtime/precompiles/src/io.rs
+++ b/runtime/precompiles/src/io.rs
@@ -38,7 +38,7 @@ impl std::io::Write for SyscallWriter {
 pub fn read_vec() -> Vec<u8> {
     let len = unsafe { syscall_hint_len() };
     // Round up to the nearest multiple of 4 so that the memory allocated is in whole words
-    let capacity = (len + 3) / 4 * 4;
+    let capacity = len.div_ceil(4);
 
     // Allocate a buffer of the required length that is 4 byte aligned
     let layout = Layout::from_size_align(capacity, 4).expect("vec is too large");