refactor: refactor scale cast numerical utils (#722)

Please be sure to look over the pull request guidelines here:
https://github.com/spaceandtimelabs/sxt-proof-of-sql/blob/main/CONTRIBUTING.md#submit-pr.

# Please go through the following checklist
- [ ] The PR title and commit messages adhere to guidelines here:
https://github.com/spaceandtimelabs/sxt-proof-of-sql/blob/main/CONTRIBUTING.md.
In particular `!` is used if and only if at least one breaking change
has been introduced.
- [ ] I have run the ci check script with `source
scripts/run_ci_checks.sh`.
- [ ] I have run the clean commit check script with `source
scripts/check_commits.sh`, and the commit history is certified to follow
clean commit guidelines as described here:
https://github.com/spaceandtimelabs/sxt-proof-of-sql/blob/main/COMMIT_GUIDELINES.md
- [ ] The latest changes from `main` have been incorporated to this PR
by simple rebase if possible, if not, then conflicts are resolved
appropriately.

# Rationale for this change

<!--
Why are you proposing this change? If this is already explained clearly
in the linked issue then this section is not needed.
Explaining clearly why changes are proposed helps reviewers understand
your changes and offer better suggestions for fixes.

 Example:
 Add `NestedLoopJoinExec`.
 Closes #345.

Since we added `HashJoinExec` in #323 it has been possible to do
provable inner joins. However performance is not satisfactory in some
cases. Hence we need to fix the problem by implement
`NestedLoopJoinExec` and speed up the code
 for `HashJoinExec`.
-->

# What changes are included in this PR?

<!--
There is no need to duplicate the description in the ticket here but it
is sometimes worth providing a summary of the individual changes in this
PR.

Example:
- Add `NestedLoopJoinExec`.
- Speed up `HashJoinExec`.
- Route joins to `NestedLoopJoinExec` if the outer input is sufficiently
small.
-->

# Are these changes tested?
<!--
We typically require tests for all PRs in order to:
1. Prevent the code from being accidentally broken by subsequent changes
2. Serve as another way to document the expected behavior of the code

If tests are not included in your PR, please explain why (for example,
are they covered by existing tests)?

Example:
Yes.
-->

Author: stuarttimwhite

crates/proof-of-sql/src/base/database/column_type_operation.rs

@@ -233,7 +233,7 @@ pub fn try_cast_types(from: ColumnType, to: ColumnType) -> ColumnOperationResult
 /// Casting can only be supported if the resulting data type is a superset of the input data type.
 /// For example Deciaml(6,1) can be cast to Decimal(7,1), but not vice versa.
 #[expect(clippy::missing_panics_doc)]
-pub fn try_scale_cast_types(from: ColumnType, to: ColumnType) -> ColumnOperationResult<()> {
+pub fn try_decimal_scale_cast_types(from: ColumnType, to: ColumnType) -> ColumnOperationResult<()> {
     match (from, to) {
         (
             ColumnType::TinyInt
@@ -1003,6 +1003,7 @@ mod test {
         ));
     }
 
+    #[expect(clippy::too_many_lines)]
     #[test]
     fn we_can_properly_determine_if_types_are_scale_castable() {
         for from in [
@@ -1016,84 +1017,118 @@ mod test {
             let from_precision = Precision::new(from.precision_value().unwrap()).unwrap();
             let two_prec = Precision::new(2).unwrap();
             let forty_prec = Precision::new(40).unwrap();
-            try_scale_cast_types(from, ColumnType::Decimal75(two_prec, 0)).unwrap_err();
-            try_scale_cast_types(from, ColumnType::Decimal75(two_prec, -1)).unwrap_err();
-            try_scale_cast_types(from, ColumnType::Decimal75(two_prec, 1)).unwrap_err();
-            try_scale_cast_types(from, ColumnType::Decimal75(from_precision, 0)).unwrap();
-            try_scale_cast_types(from, ColumnType::Decimal75(from_precision, -1)).unwrap_err();
-            try_scale_cast_types(from, ColumnType::Decimal75(from_precision, 1)).unwrap_err();
-            try_scale_cast_types(from, ColumnType::Decimal75(forty_prec, 0)).unwrap();
-            try_scale_cast_types(from, ColumnType::Decimal75(forty_prec, -1)).unwrap_err();
-            try_scale_cast_types(from, ColumnType::Decimal75(forty_prec, 1)).unwrap();
+            try_decimal_scale_cast_types(from, ColumnType::Decimal75(two_prec, 0)).unwrap_err();
+            try_decimal_scale_cast_types(from, ColumnType::Decimal75(two_prec, -1)).unwrap_err();
+            try_decimal_scale_cast_types(from, ColumnType::Decimal75(two_prec, 1)).unwrap_err();
+            try_decimal_scale_cast_types(from, ColumnType::Decimal75(from_precision, 0)).unwrap();
+            try_decimal_scale_cast_types(from, ColumnType::Decimal75(from_precision, -1))
+                .unwrap_err();
+            try_decimal_scale_cast_types(from, ColumnType::Decimal75(from_precision, 1))
+                .unwrap_err();
+            try_decimal_scale_cast_types(from, ColumnType::Decimal75(forty_prec, 0)).unwrap();
+            try_decimal_scale_cast_types(from, ColumnType::Decimal75(forty_prec, -1)).unwrap_err();
+            try_decimal_scale_cast_types(from, ColumnType::Decimal75(forty_prec, 1)).unwrap();
         }
 
         let twenty_prec = Precision::new(20).unwrap();
 
         // from_with_negative_scale
         let neg_scale = ColumnType::Decimal75(twenty_prec, -3);
 
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_prec, -4)).unwrap_err();
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_prec, -3)).unwrap();
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_prec, -2)).unwrap_err();
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_prec, 0)).unwrap_err();
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_prec, 1)).unwrap_err();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_prec, -4))
+            .unwrap_err();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_prec, -3)).unwrap();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_prec, -2))
+            .unwrap_err();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_prec, 0)).unwrap_err();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_prec, 1)).unwrap_err();
 
         let nineteen_prec = Precision::new(19).unwrap();
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(nineteen_prec, -4)).unwrap_err();
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(nineteen_prec, -3)).unwrap_err();
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(nineteen_prec, -2)).unwrap_err();
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(nineteen_prec, 0)).unwrap_err();
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(nineteen_prec, 1)).unwrap_err();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(nineteen_prec, -4))
+            .unwrap_err();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(nineteen_prec, -3))
+            .unwrap_err();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(nineteen_prec, -2))
+            .unwrap_err();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(nineteen_prec, 0))
+            .unwrap_err();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(nineteen_prec, 1))
+            .unwrap_err();
 
         let twenty_one_prec = Precision::new(21).unwrap();
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_one_prec, -4)).unwrap_err();
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_one_prec, -3)).unwrap();
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_one_prec, -2)).unwrap();
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_one_prec, 0)).unwrap_err();
-        try_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_one_prec, 1)).unwrap_err();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_one_prec, -4))
+            .unwrap_err();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_one_prec, -3))
+            .unwrap();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_one_prec, -2))
+            .unwrap();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_one_prec, 0))
+            .unwrap_err();
+        try_decimal_scale_cast_types(neg_scale, ColumnType::Decimal75(twenty_one_prec, 1))
+            .unwrap_err();
 
         // from_with_zero_scale
         let zero_scale = ColumnType::Decimal75(twenty_prec, 0);
 
-        try_scale_cast_types(zero_scale, ColumnType::Decimal75(twenty_prec, -1)).unwrap_err();
-        try_scale_cast_types(zero_scale, ColumnType::Decimal75(twenty_prec, 0)).unwrap();
-        try_scale_cast_types(zero_scale, ColumnType::Decimal75(twenty_prec, 1)).unwrap_err();
-
-        try_scale_cast_types(zero_scale, ColumnType::Decimal75(nineteen_prec, -1)).unwrap_err();
-        try_scale_cast_types(zero_scale, ColumnType::Decimal75(nineteen_prec, 0)).unwrap_err();
-        try_scale_cast_types(zero_scale, ColumnType::Decimal75(nineteen_prec, 1)).unwrap_err();
-        try_scale_cast_types(zero_scale, ColumnType::Decimal75(nineteen_prec, 2)).unwrap_err();
-
-        try_scale_cast_types(zero_scale, ColumnType::Decimal75(twenty_one_prec, -1)).unwrap_err();
-        try_scale_cast_types(zero_scale, ColumnType::Decimal75(twenty_one_prec, 0)).unwrap();
-        try_scale_cast_types(zero_scale, ColumnType::Decimal75(twenty_one_prec, 1)).unwrap();
-        try_scale_cast_types(zero_scale, ColumnType::Decimal75(twenty_one_prec, 2)).unwrap_err();
+        try_decimal_scale_cast_types(zero_scale, ColumnType::Decimal75(twenty_prec, -1))
+            .unwrap_err();
+        try_decimal_scale_cast_types(zero_scale, ColumnType::Decimal75(twenty_prec, 0)).unwrap();
+        try_decimal_scale_cast_types(zero_scale, ColumnType::Decimal75(twenty_prec, 1))
+            .unwrap_err();
+
+        try_decimal_scale_cast_types(zero_scale, ColumnType::Decimal75(nineteen_prec, -1))
+            .unwrap_err();
+        try_decimal_scale_cast_types(zero_scale, ColumnType::Decimal75(nineteen_prec, 0))
+            .unwrap_err();
+        try_decimal_scale_cast_types(zero_scale, ColumnType::Decimal75(nineteen_prec, 1))
+            .unwrap_err();
+        try_decimal_scale_cast_types(zero_scale, ColumnType::Decimal75(nineteen_prec, 2))
+            .unwrap_err();
+
+        try_decimal_scale_cast_types(zero_scale, ColumnType::Decimal75(twenty_one_prec, -1))
+            .unwrap_err();
+        try_decimal_scale_cast_types(zero_scale, ColumnType::Decimal75(twenty_one_prec, 0))
+            .unwrap();
+        try_decimal_scale_cast_types(zero_scale, ColumnType::Decimal75(twenty_one_prec, 1))
+            .unwrap();
+        try_decimal_scale_cast_types(zero_scale, ColumnType::Decimal75(twenty_one_prec, 2))
+            .unwrap_err();
 
         // from_with_positive_scale
         let pos_scale = ColumnType::Decimal75(twenty_prec, 3);
 
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_prec, -1)).unwrap_err();
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_prec, 0)).unwrap_err();
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_prec, 2)).unwrap_err();
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_prec, 3)).unwrap();
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_prec, 4)).unwrap_err();
-
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(nineteen_prec, -1)).unwrap_err();
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(nineteen_prec, 0)).unwrap_err();
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(nineteen_prec, 2)).unwrap_err();
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(nineteen_prec, 3)).unwrap_err();
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(nineteen_prec, 4)).unwrap_err();
-
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_one_prec, -1)).unwrap_err();
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_one_prec, 0)).unwrap_err();
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_one_prec, 2)).unwrap_err();
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_one_prec, 3)).unwrap();
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_one_prec, 4)).unwrap();
-        try_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_one_prec, 5)).unwrap_err();
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_prec, -1))
+            .unwrap_err();
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_prec, 0)).unwrap_err();
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_prec, 2)).unwrap_err();
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_prec, 3)).unwrap();
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_prec, 4)).unwrap_err();
+
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(nineteen_prec, -1))
+            .unwrap_err();
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(nineteen_prec, 0))
+            .unwrap_err();
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(nineteen_prec, 2))
+            .unwrap_err();
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(nineteen_prec, 3))
+            .unwrap_err();
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(nineteen_prec, 4))
+            .unwrap_err();
+
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_one_prec, -1))
+            .unwrap_err();
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_one_prec, 0))
+            .unwrap_err();
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_one_prec, 2))
+            .unwrap_err();
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_one_prec, 3)).unwrap();
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_one_prec, 4)).unwrap();
+        try_decimal_scale_cast_types(pos_scale, ColumnType::Decimal75(twenty_one_prec, 5))
+            .unwrap_err();
     }
 
     #[test]
     fn we_cannot_scale_cast_nonsense_pairings() {
-        try_scale_cast_types(ColumnType::Int128, ColumnType::Boolean).unwrap_err();
+        try_decimal_scale_cast_types(ColumnType::Int128, ColumnType::Boolean).unwrap_err();
     }
 }

crates/proof-of-sql/src/base/database/mod.rs

@@ -14,8 +14,8 @@ mod slice_decimal_operation;
 
 mod column_type_operation;
 pub use column_type_operation::{
-    try_add_subtract_column_types, try_cast_types, try_divide_column_types,
-    try_multiply_column_types, try_scale_cast_types,
+    try_add_subtract_column_types, try_cast_types, try_decimal_scale_cast_types,
+    try_divide_column_types, try_multiply_column_types,
 };
 
 mod column_arithmetic_operation;