algorithm-design

Algorithm Design

Overview

System requirements and architecture often identify modules whose behavior is inherently algorithmic: a PID temperature controller, a low-pass filter chain for sensor data, a touch calibration routine, an FFT-based fault detector. These modules cannot be specified by interface alone — you need to define the math, the parameters, the precision, the convergence guarantees.

This skill takes algorithm-relevant requirements and the system architecture as input and produces a quantified algorithm design document. It answers the "how does this module compute?" question that architecture-design leaves for the spec author. Every parameter is traced to a requirement. Every precision, latency, and memory claim is backed by a number with units. Every hardware-dependent assumption is explicit — and if the hardware spec does not yet provide the needed characteristic, the design flags it rather than guessing.

When to Use

• System requirements contain quantitative algorithmic needs (e.g., "filter settling time ≤ 10ms", "PID overshoot ≤ 5%", "calibration accuracy ±1 LSB")
• The architecture document identifies modules whose core responsibility is computation, not just data plumbing (signal processing blocks, control loops, estimation/calibration, transforms)
• A downstream skill (spec-authoring) detects that a module in the architecture decomposition has algorithm behavior described only by the module name ("Touch Calibration Module") with no math, no parameters, no convergence criteria
• Adding a new algorithm to an existing system (new sensor processing pipeline, new control strategy)
• An algorithm behavior depends on hardware characteristics that must be verified before implementation (ADC noise floor, DAC settling time, sensor response curve)

When NOT to use: The module is purely data plumbing (reads a register, writes a buffer, translates a protocol) — use architecture-design interface definitions. The algorithm is a standard library call with no design decisions (e.g., memcpy, crc32, arm_biquad_cascade_df1_f32). Algorithm requirements do not yet exist — run requirements-decompose first. The module's algorithm is already fully specified with quantified parameters traced to requirements.