- **Similar:** [EMA](../../trends_IIR/ema/ema.md), [WMA](../wma/wma.md) | **Complementary:** ATR for Keltner-style bands | **Trading note:** Simple Moving Average; equal-weight FIR filter. Most basic and widely used MA. Foundation of many composite indicators.
The Simple Moving Average (SMA) is the unweighted arithmetic mean of the last $N$ data points. It acts as a low-pass filter, smoothing out high-frequency noise to reveal the underlying trend. While conceptually simple, efficient implementation on modern hardware requires careful attention to memory access patterns and vectorization.
## Historical Context
The concept of a moving average dates back to 1901 (R.H. Hooker) for smoothing weather data, but it became a staple of financial analysis in the mid-20th century. It is the baseline against which all other averages are compared.
## Architecture & Physics
The naive implementation of SMA sums $N$ numbers at every step, resulting in $O(N)$ complexity. QuanTAlib uses an optimized $O(1)$ approach.
### O(1) Running Sum
A running `Sum` and a `RingBuffer` of history are maintained.
This ensures that calculating an SMA(200) takes the exact same time as an SMA(10).
### Drift Correction
Floating-point addition is not associative. Repeatedly adding and subtracting values from a running sum introduces cumulative error (drift) over millions of ticks. QuanTAlib implements a periodic **Resync** mechanism (every 1000 ticks) that recalculates the sum from scratch to ensure precision remains within `1e-9` of the true mean.
### SIMD Optimization
For batch processing of large datasets, `Sma.Batch` utilizes `System.Runtime.Intrinsics` (AVX2/AVX-512) to process multiple data points in parallel, significantly outperforming scalar loops.
