Floor Division

Floor Division divides two values and rounds down to the nearest integer—always toward negative infinity.

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The Formula

$$Q_i = \left\lfloor \frac{A_i}{B_i} \right\rfloor$$

Where:

• $A$ = First Value (numerator)
• $B$ = Second Value (denominator)
• $\lfloor \cdot \rfloor$ = Floor function (round down toward −∞)

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Floor vs. Regular Division

Expression	Regular Division	Floor Division
7 ÷ 3	2.333...	2
10 ÷ 4	2.5	2
−7 ÷ 3	−2.333...	−3
−10 ÷ −4	2.5	2

Key insight: Floor division rounds toward negative infinity, not toward zero. This means −7 ÷ 3 = −3 (not −2).

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Worked Example

Calculating how many complete lots can be purchased:

Available Capital	Lot Size	Floor Division	Interpretation
10,000	3,000	3	Can buy 3 complete lots
10,000	4,000	2	Can buy 2 complete lots
10,000	7,000	1	Can buy 1 complete lot
5,500	2,000	2	Can buy 2 complete lots (remainder 1,500)

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Practical Applications

1. Lot Sizing and Position Calculation

When determining how many shares or contracts to trade:

Position Size = Floor(Capital Available ÷ Price per Unit)

This ensures you never attempt to buy fractional units that aren't tradeable.

2. Time Bucketing

Grouping data into discrete time periods:

Hourly Bucket = Floor(Minutes Since Start ÷ 60)
Weekly Bucket = Floor(Days Since Start ÷ 7)

3. Price Level Discretization

Rounding prices to tick sizes or round numbers:

Tick Level = Floor(Price ÷ Tick Size)

4. Ratio Thresholds

Counting how many times one value "fits into" another:

Multiplier = Floor(Target ÷ Baseline)

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Edge Cases

Situation	Result	Notes
Division by zero	null	The math is undefined — no value is invented
Both values zero	null	Same undefined-math rule
Negative numerator	Rounds down (toward −∞)	−7 ÷ 3 = −3
Negative denominator	Standard floor behavior	7 ÷ −3 = −3
Very large values	Valid integer result	May lose precision for extremely large numbers
Decimal inputs	Treated as real numbers	Floor applies after division

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Missing Data

• If either input is missing (null) at a position — a data gap or a closed-market day — the quotient is null at that same position. The math is never faked with substitute values.
• Division by zero is different from missing data: both inputs exist, but the result is mathematically undefined — the output is also null at that position.
• In live execution the module returns exactly one datapoint: the newest one, which is null when it cannot be determined.

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Key Takeaways

Property	Value
Output Type	Integer (whole number), or null when undeterminable
Rounding Direction	Always toward −∞
Zero Division	Returns null (undefined math)
Missing Inputs	Return null at the same position
Best for	Lot sizing, bucketing, discretization

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Further Reading

• Floor and Ceiling Functions — Mathematical foundation
• Python Floor Division — Implementation reference