Stable Summation and Mean Calculation

Install and import#

npm install fintech-algorithms

import { stableSummationAndMeanCalculation } from "fintech-algorithms/foundations/statistical-computing-and-reproducibility/stable-summation-and-mean-calculation";

Signature#

stableSummationAndMeanCalculation(input)

Adds a list twice, once straight left to right and once carrying a running compensation term, so the two totals can be put side by side.

Parameters#

Returns#

D00Output

naiveSum is the plain running total, stableSum the compensated one, stableMean that compensated total divided by the observation count, and difference the compensated total minus the naive one.

Errors#

• When values is absent, empty, or holds a non-finite number — throws RangeError

Complexity: time O(n), space O(n).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

{
  "values": [10000000000000000, 1, -10000000000000000, 3],
  "floatingValue": 0.1,
  "maxSafeMagnitude": 1.7976931348623157e+308,
  "window": 3,
  "rawValues": [1, null, 2, "bad", 3],
  "invalidPolicy": "drop-and-report",
  "seed": 42,
  "sampleCount": 5,
  "leftVector": [
    {
      "index": "A",
      "value": 1
    },
    {
      "index": "B",
      "value": 2
    }
  ],
  "rightVector": [
    {
      "index": "B",
      "value": 20
    },
    {
      "index": "C",
      "value": 30
    }
  ],
  "train": [10, 12, 14, 16],
  "test": [18, 20],
  "actual": [1, 2.0000001, 3],
  "expected": [1, 2, 3]
}

Showing 14 of 18 fields.

Call#

stableSummationAndMeanCalculation(input)

Returns#

object with 2 fields: naiveSum, stableSum

{
  "naiveSum": 3,
  "stableSum": 4
}

Diagrams#

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

• Floating-Point Arithmetic — IEEE 754-2019
• math.fsum — Python Documentation
• Random Sampling — NumPy Documentation
• Common Pitfalls and Recommended Practices — scikit-learn
• Historical-example decision

The rest of the Statistical Computing and Reproducibility family#

• Floating-Point Representation, Overflow, and UnderflowInspects one double-precision number: whether it is finite, how large one representable step at its magnitude is, and whether s…
• Stable Online Variance and Welford's AlgorithmRuns Welford's single-pass update to produce the mean and sample variance without ever accumulating a sum of raw squares.
• Batch, Rolling, and Streaming Statistic EquivalenceComputes the same fixed-window mean two ways, by re-averaging each window slice and by a running add-and-drop sum, then checks …
• Missing, Infinite, Invalid, and Unsupported-State PoliciesScreens a mixed raw list down to the entries that are genuinely finite numbers and reports how many were turned away.
• Pseudorandom Numbers, Seeds, and ReproducibilityDraws a run of unit-interval numbers from a seeded linear congruential generator, so the same seed always replays the same stream.
• Vectorization, Index Alignment, and Shape SafetyInner-joins two labelled vectors on their index field and reports what each side lost in the process.
• Leakage-Free Fitting, Scaling, and PreprocessingFits a standardizing centre and scale on the training split alone, then applies that one transform to both splits.
• Fixtures, Numerical Tolerances, and Property TestsCompares an actual vector against an expected one under an absolute tolerance, the way a fixture check does.
• Reproducible Analysis, Metadata, and Audit TrailsSerializes a run's inputs, method, version and seed into a deterministic JSON string and fingerprints it with a 32-bit FNV-1a h…