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lib/numerics/slope/Slope.md
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# SLOPE: First Derivative (Velocity)
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Numeric |
| **Inputs** | Source (close) |
| **Parameters** | None |
| **Outputs** | Single series (SLOPE) |
| **Output range** | Varies (see docs) |
| **Warmup** | `2` bars |
### TL;DR
- SLOPE measures the instantaneous rate of change—the velocity of a time series.
- No configurable parameters; computation is stateless per bar.
- Output range: Varies (see docs).
- Requires `2` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "The simplest measure of change reveals the most: is it going up, or going down?"
SLOPE measures the instantaneous rate of change—the velocity of a time series. As the first derivative, it answers the fundamental question: how fast is the value changing right now? A positive slope means ascending; negative means descending; zero means flat. This O(1) streaming implementation uses SIMD optimization for batch calculations and handles bar corrections via state rollback.