QuanTAlib/lib/trends_FIR/sma/Sma.md

SMA: Simple Moving Average

The vanilla ice cream of technical analysis. Boring, ubiquitous, and the only thing your grandfather and your high-frequency trading bot agree on.

Property	Value
Category	Trend (FIR MA)
Inputs	Source (close)
Parameters	period
Outputs	Single series (Sma)
Output range	Tracks input
Warmup	period bars
PineScript	sma.pine
Signature	sma_signature

• The Simple Moving Average (SMA) is the unweighted arithmetic mean of the last N data points.
• Similar: EMA, WMA | 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.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

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.

Sum_{new} = Sum_{old} - Value_{oldest} + Value_{new} SMA = \frac{Sum_{new}}{N}

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.

Mathematical Foundation

1. The Mean

SMA_t = \frac{1}{N} \sum_{i=0}^{N-1} P_{t-i}

Performance Profile

Operation Count (Streaming Mode, O(1) Running Sum)

Operation	Count	Cost (cycles)	Subtotal
SUB (Sum - oldest)	1	1	1
ADD (Sum + newest)	1	1	1
DIV (Sum / N)	1	15	15
Total (hot)	3	—	~17 cycles

Every 1000 bars, a resync recalculates the sum to prevent drift:

Operation	Count	Cost (cycles)	Subtotal
ADD (N values)	N	1	N
DIV (Sum / N)	1	15	15
Resync cost	N+1	—	~N+15 cycles

Amortized cost: ~17 + (N+15)/1000 ≈ ~17 cycles/bar for typical use.

Batch Mode (SIMD Analysis)

SMA batch processing is highly vectorizable using running sum + prefix sum techniques:

Operation	Scalar Ops	SIMD Ops (AVX2)	Speedup
Initial N-sum	N	N/8	8×
Running update (per bar)	3	~1	~3×
Division	1	1/8 (batched)	8×

For 512 bars:

Mode	Cycles/bar	Total	Notes
Scalar streaming	~17	~8,700	O(1) per bar
SIMD batch	~3	~1,500	Vectorized running sum
Improvement	5.8×	—	Batch wins for large N

Quality Metrics

Metric	Score	Notes
Accuracy	10/10	Exact arithmetic mean
Timeliness	3/10	Significant lag (~N/2 bars)
Overshoot	10/10	Never overshoots input range
Smoothness	5/10	Smooth but susceptible to drop-off jumps

Benchmark Results

Metric	Value	Notes
Throughput	~100M bars/sec	SIMD batch mode
Allocations	0 bytes	Zero-allocation in hot paths
Complexity	O(1)	Constant time regardless of period N
State Size	8 + 8N bytes	Sum + RingBuffer

Validation

Library	Status	Notes
TA-Lib	✅	Matches TA_SMA exactly.
Skender	✅	Matches GetSma exactly.
Tulip	✅	Matches sma exactly.
Ooples	✅	Matches CalculateSimpleMovingAverage.