Square Root

$\sqrt{x} \text{ for } x \geq 0$

Computes the principal square root of each value. A compression tool that reduces the scale of extreme values while preserving order.

Input	Output
0	0
4	2
100	10
10,000	100

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Input Constraint

⚠️ Important: Input values must be non-negative (≥ 0). Negative numbers have no real square root, so a negative input produces a null output at that position — the math is never faked with a substitute value.

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The Compression Effect

Square root compresses large values more than small ones:

Original	√ Result	Compression
1	1	1:1
100	10	10:1
10,000	100	100:1
1,000,000	1,000	1000:1

This makes data with extreme outliers (like volume or market cap) more manageable for comparison and analysis.

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Practical Example: Volume Normalization

Trading volume varies by orders of magnitude across assets. Square root makes comparison meaningful:

Stock Type	Raw Volume	√ Volume
Small-cap	100,000	316
Mid-cap	1,000,000	1,000
Large-cap	100,000,000	10,000

Now “2× average volume” has comparable significance across all asset sizes.

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SQRT vs. POW(0.5)

Mathematically equivalent, but SQRT:

• Enforces non-negative input constraint
• Is semantically clearer for square root operations

Use POW with exponent 0.5 if you need more flexibility (e.g., variable exponents).

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Related Modules

• POW — General exponentiation (use exponent 2 to reverse SQRT)
• ABS — Ensure non-negative input before SQRT
• DIV — Alternative normalization (ratio-based)

Transform	Compression	Best For
√x	Moderate	Volume, counts, moderate outliers
log(x)	Strong	Price ratios, returns, extreme outliers

Use square root when you want to reduce scale without completely flattening the data.

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Missing Data

When an input position is missing (null) — for example, a stock series has no bar on a weekend or holiday — the output at that same position is null. Values are never invented to fill a gap: every non-null output is the true square root of a real datapoint.

In live mode, the module returns exactly one datapoint — the most recent position — and it may be null when no bar exists at that moment (e.g., a weekend tick on a market-hours series). That gap is correct, not an error.

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Handling Negative Inputs

A negative value is a real datapoint whose square root simply does not exist — distinct from missing data, where no datapoint exists at all. Both surface as null in the output, but they mean different things:

• Missing input → null: there was no bar to compute from
• Negative input → null: there was a bar, but the math is undefined for it

If your data may contain negative values, pre-process with the ABS module to make inputs non-negative.

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Quick Reference

Input	Output
0	0
1	1
4	2
9	3
2.25	1.5
1,000,000	1,000