diff --git a/ceno_zkvm/src/instructions/riscv/mul.rs b/ceno_zkvm/src/instructions/riscv/mul.rs
index 185503741..44d54b6a5 100644
--- a/ceno_zkvm/src/instructions/riscv/mul.rs
+++ b/ceno_zkvm/src/instructions/riscv/mul.rs
@@ -443,9 +443,7 @@ impl<E: ExtensionField> Signed<E> {
             lkm,
             *val.as_u16_limbs().last().unwrap() as u64,
         )?;
-        let signed_val = val.as_u32() as i32;
-
-        Ok(signed_val)
+        Ok(i32::from(val))
     }
 }
 
diff --git a/ceno_zkvm/src/uint.rs b/ceno_zkvm/src/uint.rs
index 0220cd0f3..ed2fcd4b2 100644
--- a/ceno_zkvm/src/uint.rs
+++ b/ceno_zkvm/src/uint.rs
@@ -607,6 +607,30 @@ pub struct Value<'a, T: Into<u64> + From<u32> + Copy + Default> {
     pub limbs: Cow<'a, [u16]>,
 }
 
+impl<'a, T: Into<u64> + From<u32> + Copy + Default> From<&'a Value<'a, T>> for &'a [u16] {
+    fn from(v: &'a Value<'a, T>) -> Self {
+        v.as_u16_limbs()
+    }
+}
+
+impl<'a, T: Into<u64> + From<u32> + Copy + Default> From<&Value<'a, T>> for u64 {
+    fn from(v: &Value<'a, T>) -> Self {
+        v.as_u64()
+    }
+}
+
+impl<'a, T: Into<u64> + From<u32> + Copy + Default> From<&Value<'a, T>> for u32 {
+    fn from(v: &Value<'a, T>) -> Self {
+        v.as_u32()
+    }
+}
+
+impl<'a, T: Into<u64> + From<u32> + Copy + Default> From<&Value<'a, T>> for i32 {
+    fn from(v: &Value<'a, T>) -> Self {
+        v.as_i32()
+    }
+}
+
 // TODO generalize to support non 16 bit limbs
 // TODO optimize api with fixed size array
 impl<'a, T: Into<u64> + From<u32> + Copy + Default> Value<'a, T> {
@@ -617,10 +641,7 @@ impl<'a, T: Into<u64> + From<u32> + Copy + Default> Value<'a, T> {
     const LIMBS: usize = (Self::M + 15) / 16;
 
     pub fn new(val: T, lkm: &mut LkMultiplicity) -> Self {
-        let uint = Value::<T> {
-            val,
-            limbs: Cow::Owned(Self::split_to_u16(val)),
-        };
+        let uint = Self::new_unchecked(val);
         Self::assert_u16(&uint.limbs, lkm);
         uint
     }
@@ -685,6 +706,11 @@ impl<'a, T: Into<u64> + From<u32> + Copy + Default> Value<'a, T> {
         self.as_u64() as u32
     }
 
+    /// Convert the limbs to an i32 value
+    pub fn as_i32(&self) -> i32 {
+        self.as_u32() as i32
+    }
+
     pub fn u16_fields<F: SmallField>(&self) -> Vec<F> {
         self.limbs.iter().map(|v| F::from(*v as u64)).collect_vec()
     }
diff --git a/mpcs/src/sum_check/classic/coeff.rs b/mpcs/src/sum_check/classic/coeff.rs
index 36d5390a6..10d5c1c20 100644
--- a/mpcs/src/sum_check/classic/coeff.rs
+++ b/mpcs/src/sum_check/classic/coeff.rs
@@ -49,7 +49,7 @@ impl<E: ExtensionField> ClassicSumCheckRoundMessage<E> for Coefficients<E> {
     }
 
     fn sum(&self) -> E {
-        self[..].iter().sum()
+        self[0] + self[..].iter().sum::<E>()
     }
 
     fn evaluate(&self, _: &Self::Auxiliary, challenge: &E) -> E {