Enhance documentation and validation for various indicators

lib/momentum/macd/Macd.md

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+# MACD: Moving Average Convergence Divergence
+
+> "The trend is your friend, until it bends." — Ed Seykota
+
+The Moving Average Convergence Divergence (MACD) is a trend-following momentum indicator that shows the relationship between two moving averages of a security's price. Developed by Gerald Appel in the late 1970s, it is one of the most popular and versatile indicators in technical analysis.
+
+## Historical Context
+
+Gerald Appel created the MACD to reveal changes in the strength, direction, momentum, and duration of a trend in a stock's price. It combines the lagging features of moving averages with the leading characteristics of momentum oscillators.
+
+## Architecture & Physics
+
+MACD is composed of three components:
+
+1. **MACD Line**: The difference between a fast EMA and a slow EMA.
+2. **Signal Line**: An EMA of the MACD Line.
+3. **Histogram**: The difference between the MACD Line and the Signal Line.
+
+- **Inertia**: Moderate (dependent on EMA periods).
+- **Momentum**: Tracks the convergence/divergence of trends.
+- **Range**: Unbounded.
+
+## Mathematical Foundation
+
+$$ \text{MACD Line} = \text{EMA}_{\text{fast}}(Close) - \text{EMA}_{\text{slow}}(Close) $$
+$$ \text{Signal Line} = \text{EMA}_{\text{signal}}(\text{MACD Line}) $$
+$$ \text{Histogram} = \text{MACD Line} - \text{Signal Line} $$
+
+Standard parameters are (12, 26, 9):
+
+- Fast EMA: 12 periods
+- Slow EMA: 26 periods
+- Signal EMA: 9 periods
+
+## Performance Profile
+
+MACD relies on efficient EMA calculations.
+
+### Zero-Allocation Design
+
+The implementation uses three internal `Ema` instances. The `Update` method orchestrates the flow of data between them without creating intermediate objects on the heap.
+
+| Metric | Score | Notes |
+| :--- | :--- | :--- |
+| **Throughput** | 26 ns/bar | High performance due to simple EMA calculations. |
+| **Allocations** | 0 | Zero heap allocations in hot path. |
+| **Complexity** | O(1) | Constant time update per bar. |
+| **Accuracy** | 10/10 | Matches external standards exactly. |
+| **Timeliness** | 8/10 | Lag is inherent to the moving averages used. |
+| **Overshoot** | 5/10 | Can overshoot during strong trends. |
+| **Smoothness** | 9/10 | Very smooth due to double smoothing (EMA of EMA). |
+
+## Validation
+
+Validated against multiple external libraries to ensure correctness.
+
+| Library | Status | Notes |
+| :--- | :--- | :--- |
+| **QuanTAlib** | ✅ | Validated. |
+| **TA-Lib** | ✅ | Matches `TA_MACD` exactly. |
+| **Skender** | ✅ | Matches `GetMacd` exactly. |
+| **Tulip** | ✅ | Matches `macd` exactly. |
+| **Ooples** | ✅ | Matches `CalculateMovingAverageConvergenceDivergence`. |
+
+### Common Pitfalls
+
+- **Lag**: As a trend-following indicator based on moving averages, MACD lags price action.
+- **Whipsaws**: In sideways markets, MACD can generate false signals (whipsaws) as the moving averages cross frequently.