diff --git a/crates/proof-of-sql/src/sql/proof_exprs/comparison_util.rs b/crates/proof-of-sql/src/sql/proof_exprs/comparison_util.rs
index bec516cb7..25aea3c8e 100644
--- a/crates/proof-of-sql/src/sql/proof_exprs/comparison_util.rs
+++ b/crates/proof-of-sql/src/sql/proof_exprs/comparison_util.rs
@@ -1,15 +1,15 @@
 use crate::{
     base::{
-        database::{Column, ColumnarValue},
+        database::{Column, ColumnarValue, LiteralValue},
         if_rayon,
         math::decimal::{DecimalError, Precision},
-        scalar::Scalar,
+        scalar::{Scalar, ScalarExt},
     },
     sql::parse::{type_check_binary_operation, ConversionError, ConversionResult},
 };
 use alloc::string::ToString;
 use bumpalo::Bump;
-use core::cmp;
+use core::cmp::{max, Ordering};
 use proof_of_sql_parser::intermediate_ast::BinaryOperator;
 #[cfg(feature = "rayon")]
 use rayon::iter::{IndexedParallelIterator, IntoParallelRefMutIterator, ParallelIterator};
@@ -31,6 +31,70 @@ fn unchecked_subtract_impl<'a, S: Scalar>(
     Ok(result)
 }
 
+#[allow(
+    clippy::missing_panics_doc,
+    reason = "precision and scale are validated prior to calling this function, ensuring no panic occurs"
+)]
+/// Scale LHS and RHS to the same scale if at least one of them is decimal
+/// and take the difference. This function is used for comparisons.
+#[allow(clippy::cast_sign_loss)]
+pub fn scale_and_subtract_literal<S: Scalar>(
+    lhs: LiteralValue<S>,
+    rhs: LiteralValue<S>,
+    lhs_scale: i8,
+    rhs_scale: i8,
+    is_equal: bool,
+) -> ConversionResult<S> {
+    let lhs_type = lhs.column_type();
+    let rhs_type = rhs.column_type();
+    let operator = if is_equal {
+        BinaryOperator::Equal
+    } else {
+        BinaryOperator::LessThanOrEqual
+    };
+    if !type_check_binary_operation(&lhs_type, &rhs_type, operator) {
+        return Err(ConversionError::DataTypeMismatch {
+            left_type: lhs_type.to_string(),
+            right_type: rhs_type.to_string(),
+        });
+    }
+    let max_scale = max(lhs_scale, rhs_scale);
+    let lhs_upscale = max_scale - lhs_scale;
+    let rhs_upscale = max_scale - rhs_scale;
+    // Only check precision overflow issues if at least one side is decimal
+    if max_scale != 0 {
+        let lhs_precision_value = lhs_type
+            .precision_value()
+            .expect("If scale is set, precision must be set");
+        let rhs_precision_value = rhs_type
+            .precision_value()
+            .expect("If scale is set, precision must be set");
+        let max_precision_value = max(
+            lhs_precision_value + (max_scale - lhs_scale) as u8,
+            rhs_precision_value + (max_scale - rhs_scale) as u8,
+        );
+        // Check if the precision is valid
+        let _max_precision = Precision::new(max_precision_value).map_err(|_| {
+            ConversionError::DecimalConversionError {
+                source: DecimalError::InvalidPrecision {
+                    error: max_precision_value.to_string(),
+                },
+            }
+        })?;
+    }
+    match lhs_scale.cmp(&rhs_scale) {
+        Ordering::Less => {
+            let upscale_factor = S::pow10(rhs_upscale as u8);
+            Ok(lhs.to_scalar() * upscale_factor - rhs.to_scalar())
+        }
+        Ordering::Equal => Ok(lhs.to_scalar() - rhs.to_scalar()),
+        Ordering::Greater => {
+            let upscale_factor = S::pow10(lhs_upscale as u8);
+            Ok(lhs.to_scalar() - rhs.to_scalar() * upscale_factor)
+        }
+    }
+}
+
 #[allow(
     clippy::missing_panics_doc,
     reason = "precision and scale are validated prior to calling this function, ensuring no panic occurs"
@@ -67,7 +131,7 @@ pub(crate) fn scale_and_subtract<'a, S: Scalar>(
             right_type: rhs_type.to_string(),
         });
     }
-    let max_scale = cmp::max(lhs_scale, rhs_scale);
+    let max_scale = max(lhs_scale, rhs_scale);
     let lhs_upscale = max_scale - lhs_scale;
     let rhs_upscale = max_scale - rhs_scale;
     // Only check precision overflow issues if at least one side is decimal
@@ -78,7 +142,7 @@ pub(crate) fn scale_and_subtract<'a, S: Scalar>(
         let rhs_precision_value = rhs_type
             .precision_value()
             .expect("If scale is set, precision must be set");
-        let max_precision_value = cmp::max(
+        let max_precision_value = max(
             lhs_precision_value + (max_scale - lhs_scale) as u8,
             rhs_precision_value + (max_scale - rhs_scale) as u8,
         );
@@ -98,3 +162,47 @@ pub(crate) fn scale_and_subtract<'a, S: Scalar>(
         lhs_len,
     )
 }
+
+#[allow(clippy::cast_sign_loss)]
+#[allow(dead_code)]
+pub(crate) fn scale_and_subtract_columnar_value<'a, S: Scalar>(
+    alloc: &'a Bump,
+    lhs: ColumnarValue<'a, S>,
+    rhs: ColumnarValue<'a, S>,
+    lhs_scale: i8,
+    rhs_scale: i8,
+    is_equal: bool,
+) -> ConversionResult<ColumnarValue<'a, S>> {
+    match (lhs, rhs) {
+        (ColumnarValue::Column(lhs), ColumnarValue::Column(rhs)) => {
+            Ok(ColumnarValue::Column(Column::Scalar(scale_and_subtract(
+                alloc, lhs, rhs, lhs_scale, rhs_scale, is_equal,
+            )?)))
+        }
+        (ColumnarValue::Literal(lhs), ColumnarValue::Column(rhs)) => {
+            Ok(ColumnarValue::Column(Column::Scalar(scale_and_subtract(
+                alloc,
+                Column::from_literal_with_length(&lhs, rhs.len(), alloc),
+                rhs,
+                lhs_scale,
+                rhs_scale,
+                is_equal,
+            )?)))
+        }
+        (ColumnarValue::Column(lhs), ColumnarValue::Literal(rhs)) => {
+            Ok(ColumnarValue::Column(Column::Scalar(scale_and_subtract(
+                alloc,
+                lhs,
+                Column::from_literal_with_length(&rhs, lhs.len(), alloc),
+                lhs_scale,
+                rhs_scale,
+                is_equal,
+            )?)))
+        }
+        (ColumnarValue::Literal(lhs), ColumnarValue::Literal(rhs)) => {
+            Ok(ColumnarValue::Literal(LiteralValue::Scalar(
+                scale_and_subtract_literal(lhs, rhs, lhs_scale, rhs_scale, is_equal)?,
+            )))
+        }
+    }
+}
diff --git a/crates/proof-of-sql/src/sql/proof_exprs/numerical_util.rs b/crates/proof-of-sql/src/sql/proof_exprs/numerical_util.rs
index a96f3aae0..116454b21 100644
--- a/crates/proof-of-sql/src/sql/proof_exprs/numerical_util.rs
+++ b/crates/proof-of-sql/src/sql/proof_exprs/numerical_util.rs
@@ -1,8 +1,35 @@
 use crate::base::{
-    database::{Column, ColumnarValue},
+    database::{Column, ColumnarValue, LiteralValue},
     scalar::{Scalar, ScalarExt},
 };
 use bumpalo::Bump;
+use core::cmp::Ordering;
+
+/// Add or subtract two literals together.
+pub(crate) fn add_subtract_literals<S: Scalar>(
+    lhs: LiteralValue<S>,
+    rhs: LiteralValue<S>,
+    lhs_scale: i8,
+    rhs_scale: i8,
+    is_subtract: bool,
+) -> S {
+    let (lhs_scaled, rhs_scaled) = match lhs_scale.cmp(&rhs_scale) {
+        Ordering::Less => {
+            let scaling_factor = S::pow10((rhs_scale - lhs_scale) as u8);
+            (lhs.to_scalar() * scaling_factor, rhs.to_scalar())
+        }
+        Ordering::Equal => (lhs.to_scalar(), rhs.to_scalar()),
+        Ordering::Greater => {
+            let scaling_factor = S::pow10((lhs_scale - rhs_scale) as u8);
+            (lhs.to_scalar(), rhs.to_scalar() * scaling_factor)
+        }
+    };
+    if is_subtract {
+        lhs_scaled - rhs_scaled
+    } else {
+        lhs_scaled + rhs_scaled
+    }
+}
 
 #[allow(
     clippy::missing_panics_doc,
@@ -37,6 +64,7 @@ pub(crate) fn add_subtract_columns<'a, S: Scalar>(
 }
 
 /// Add or subtract two [`ColumnarValues`] together.
+#[allow(dead_code)]
 pub(crate) fn add_subtract_columnar_values<'a, S: Scalar>(
     lhs: ColumnarValue<'a, S>,
     rhs: ColumnarValue<'a, S>,
@@ -47,41 +75,43 @@ pub(crate) fn add_subtract_columnar_values<'a, S: Scalar>(
 ) -> ColumnarValue<'a, S> {
     match (lhs, rhs) {
         (ColumnarValue::Column(lhs), ColumnarValue::Column(rhs)) => {
-            ColumnarValue::Column(add_subtract_columns(lhs, rhs, lhs_scale, rhs_scale, alloc, is_subtract))
+            ColumnarValue::Column(Column::Scalar(add_subtract_columns(
+                lhs,
+                rhs,
+                lhs_scale,
+                rhs_scale,
+                alloc,
+                is_subtract,
+            )))
         }
         (ColumnarValue::Literal(lhs), ColumnarValue::Column(rhs)) => {
-            let lhs_len = rhs.len();
-            let lhs_scalar = lhs.to_scalar_with_scaling(lhs_scale);
-            let result = alloc.alloc_slice_fill_with(lhs_len, |i| {
-                if is_subtract {
-                    lhs_scalar - rhs.scalar_at(i).unwrap()
-                } else {
-                    lhs_scalar + rhs.scalar_at(i).unwrap()
-                }
-            });
-            ColumnarValue::Column(result)
+            ColumnarValue::Column(Column::Scalar(add_subtract_columns(
+                Column::from_literal_with_length(&lhs, rhs.len(), alloc),
+                rhs,
+                lhs_scale,
+                rhs_scale,
+                alloc,
+                is_subtract,
+            )))
         }
-        (ColumnarValue::Column(lhs), ColumnarValue::Scalar(rhs)) => {
-            let rhs_len = lhs.len();
-            let rhs_scalar = rhs.to_scalar_with_scaling(rhs_scale);
-            let result = alloc.alloc_slice_fill_with(rhs_len, |i| {
-                if is_subtract {
-                    lhs.scalar_at(i).unwrap() - rhs_scalar
-                } else {
-                    lhs.scalar_at(i).unwrap() + rhs_scalar
-                }
-            });
-            ColumnarValue::Column(result)
+        (ColumnarValue::Column(lhs), ColumnarValue::Literal(rhs)) => {
+            ColumnarValue::Column(Column::Scalar(add_subtract_columns(
+                lhs,
+                Column::from_literal_with_length(&rhs, lhs.len(), alloc),
+                lhs_scale,
+                rhs_scale,
+                alloc,
+                is_subtract,
+            )))
         }
-        (ColumnarValue::Scalar(lhs), ColumnarValue::Scalar(rhs)) => {
-            let lhs_scalar = lhs.to_scalar_with_scaling(lhs_scale);
-            let rhs_scalar = rhs.to_scalar_with_scaling(rhs_scale);
-            let result = if is_subtract {
-                lhs_scalar - rhs_scalar
-            } else {
-                lhs_scalar + rhs_scalar
-            };
-            ColumnarValue::Scalar(result)
+        (ColumnarValue::Literal(lhs), ColumnarValue::Literal(rhs)) => {
+            ColumnarValue::Literal(LiteralValue::Scalar(add_subtract_literals(
+                lhs,
+                rhs,
+                lhs_scale,
+                rhs_scale,
+                is_subtract,
+            )))
         }
     }
 }
@@ -105,7 +135,34 @@ pub(crate) fn multiply_columns<'a, S: Scalar>(
     })
 }
 
-
+#[allow(dead_code)]
+pub(crate) fn multiply_columnar_values<'a, S: Scalar>(
+    lhs: &ColumnarValue<'a, S>,
+    rhs: &ColumnarValue<'a, S>,
+    alloc: &'a Bump,
+) -> ColumnarValue<'a, S> {
+    match (lhs, rhs) {
+        (ColumnarValue::Column(lhs), ColumnarValue::Column(rhs)) => {
+            ColumnarValue::Column(Column::Scalar(multiply_columns(lhs, rhs, alloc)))
+        }
+        (ColumnarValue::Literal(lhs), ColumnarValue::Column(rhs)) => {
+            let lhs_scalar = lhs.to_scalar();
+            let result =
+                alloc.alloc_slice_fill_with(rhs.len(), |i| lhs_scalar * rhs.scalar_at(i).unwrap());
+            ColumnarValue::Column(Column::Scalar(result))
+        }
+        (ColumnarValue::Column(lhs), ColumnarValue::Literal(rhs)) => {
+            let rhs_scalar = rhs.to_scalar();
+            let result =
+                alloc.alloc_slice_fill_with(lhs.len(), |i| lhs.scalar_at(i).unwrap() * rhs_scalar);
+            ColumnarValue::Column(Column::Scalar(result))
+        }
+        (ColumnarValue::Literal(lhs), ColumnarValue::Literal(rhs)) => {
+            let result = lhs.to_scalar() * rhs.to_scalar();
+            ColumnarValue::Literal(LiteralValue::Scalar(result))
+        }
+    }
+}
 
 #[allow(
     clippy::missing_panics_doc,