Decimal Precision, Query Validation, and Wrap-Up

1. Introduction: The Final Polish of Recursive CTEs

When working with recursive Common Table Expressions (CTEs) in SQL—particularly for multi-step compounding logic such as salary hikes over sequential promotions—getting the mathematical logic right is only half the battle. The second half involves data type consistency, decimal precision control, and output validation. This chapter covers the final adjustments needed to turn a raw recursive calculation into a production-ready, clean reporting query.

2. Reviewing the Recursive Step and Multiplication Fix

In our recursive CTE, we track an employee's salary progression by joining the anchor/recursive member with a promotion history table. A common pitfall during rapid query construction is mixing up additive operations with multiplicative scaling factors when calculating percentages.

Naive Addition vs. Correct Multiplicative Scaling

If an employee receives a 20% promotion increase, we cannot simply add + 0.2 or misapply parentheses. We need the current salary to scale by 1 + (percent_increase / 100).

-- Naive / Incorrect approach (mixing addition signs incorrectly)
-- r.current_salary + (p.percent_increase) -- leads to incorrect flat additions

-- Correct Multiplicative Scaling Approach:
-- If percent_increase is 20, we do: (100 + 20) / 100 = 1.2
-- So: current_salary * (1.2)

Step-by-Step Evolution of the Recursive Query

3. Fixing Arithmetic Operators and Debugging Output

During live execution, a minor operator typo can skew financial figures or break type compatibility across the UNION ALL boundary separating the anchor member from the recursive member.

Code Comparison: Before and After Fix

-- BEFORE: Flawed arithmetic logic causing unexpected scaling
SELECT 
    r.id, 
    r.name, 
    r.initial_salary, 
    r.current_salary + (p.percent_increase) AS current_salary, -- Bug: Added percentage directly
    r.promo_id + 1 AS promo_id
FROM r_cte r
JOIN promos p ON r.id = p.emp_id AND r.promo_id + 1 = p.promo_id;

-- AFTER: Correct multiplicative compounding logic
SELECT 
    r.id, 
    r.name, 
    r.initial_salary, 
    r.current_salary * (1.0 + p.percent_increase / 100.0) AS current_salary, -- Fixed: Multiplicative growth
    r.promo_id + 1 AS promo_id
FROM r_cte r
JOIN promos p ON r.id = p.emp_id AND r.promo_id + 1 = p.promo_id;

4. Enforcing Data Type Consistency for UNION ALL

Recursive CTEs rely on a UNION ALL operator combining the initial anchor query with the recursive query. SQL engines strictly require that corresponding columns across both parts of a UNION share compatible data types. If fractional calculations introduce varying floating-point representations, the engine may throw type mismatch errors.

The Explicit Casting Strategy

To guarantee stable data types and clean output presentation (e.g., restricted to one decimal place), we use the CAST() function.

-- Casting current_salary explicitly to decimal(6, 1) in both anchor and recursive select clauses
CAST(initial_salary AS DECIMAL(6, 1)) AS current_salary
-- and
CAST(r.current_salary * (1.0 + p.percent_increase / 100.0) AS DECIMAL(6, 1)) AS current_salary

Note: DECIMAL(6, 1) allocates a total of 6 digits of precision, with exactly 1 digit reserved for the fractional decimal portion. This prevents floating-point drift and standardizes currency/percentage displays.

5. Query Validation: Tracing Employee Progression

After applying the arithmetic fix and decimal casting, executing the query against sample data yields clean, predictable compounding steps.

Example Walkthrough: Employee Alice

1. Initial State (Promo ID 0): Alice starts with an initial salary of 50,000.0.
2. First Promotion (Promo ID 1): A 10% increase is applied:

3. Second Promotion (Promo ID 2): A subsequent 20% increase is applied to the new base:

Other employee records also reflect precise fractional outcomes (e.g., Charlie showing .5 fractional values, David showing .3), validating that our DECIMAL(6, 1) constraint is operating correctly across all rows.

6. Extracting the Latest Salary: MAX() vs. ROW_NUMBER()

Once the recursive CTE has generated every historical salary state for every promotion tier per employee, our final objective is to isolate only the latest (current) salary.

Choosing the Right Aggregation Strategy

Depending on business rules and data guarantees, developers can use two primary patterns to fetch the latest record:

| Strategy | SQL Implementation | Assumptions & Constraints | | :--- | MAX(current_salary) | Assumes salaries always increase over time. If a salary decrease or demotion is possible, MAX() will return an incorrect peak rather than chronological latest. | | Window Function | ROW_NUMBER() OVER (PARTITION BY id ORDER BY promo_id DESC) | Safest approach; explicitly orders records by promotion sequence date/ID regardless of whether values go up or down. |

Final Aggregation Query (Assuming Strictly Increasing Salaries)

SELECT 
    id, 
    name, 
    initial_salary, 
    MAX(current_salary) AS current_salary
FROM r_cte
GROUP BY id, name, initial_salary;

7. Alternative Approaches: Exponential and Logarithmic Math

While recursive CTEs offer an intuitive, row-by-row procedural simulation of compounding interest and sequential salary hikes, advanced SQL optimization sometimes leverages mathematical shortcuts.

Conceptually: Compound growth formulas can be calculated directly in a single mathematical pass using exponential ($e^x$) and logarithmic ($\ln$) functions if all percentage increments follow uniform algebraic properties, bypassing iterative recursion loops entirely. While recursive CTEs remain superior for handling variable conditional logic per step, exploring math functions provides a robust alternative for high-performance analytics.

Summary and Key Takeaways

• Multiplicative Scaling: Always multiply current values by scaling factors like (1.0 + rate / 100.0) rather than attempting additive percentage adjustments.
• UNION ALL Type Safety: Ensure data types match strictly between the anchor member and recursive member of a CTE to avoid implicit conversion errors.
• Precision Control: Use CAST(expression AS DECIMAL(p, s)) to enforce consistent decimal formatting and prevent floating-point display artifacts.
• Validation Discipline: Always trace sample records (e.g., Alice, Charlie, David) step-by-step through intermediate iterations before writing final aggregation wrappers.
• Aggregation Caveats: MAX(salary) is safe for finding latest values only if salaries strictly increase; use window functions (ROW_NUMBER) when downward adjustments or demotions are possible.
• Alternative Mathematics: Complex iterative growth problems can sometimes be refactored using exponential and logarithmic SQL functions for performance optimization.