Source: https://guthlabs.ai/docs/instruments/amdahl-s-law-parallel-speedup-calculator/implementation/

instrument implementation / implementation-contract

# Amdahl's Law / Parallel Speedup Calculator implementation

A source-bound implementation contract for Amdahl's Law / Parallel Speedup Calculator; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t6-062

**Effect**: Computation or source lookup only

## Input and validation requirements

N=0 produces an undefined Amdahl result unless explicitly rejected, and an unlabelled p=80 can be interpreted either as 80% or as the invalid fraction 80, producing radically different results.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "law": "Amdahl",
    "p": 0.75,
    "sampled_N": [
      1,
      2,
      4,
      8
    ]
  },
  "expected_outputs": {
    "sampled_points": [
      {
        "N": 1,
        "speedup": 1
      },
      {
        "N": 2,
        "speedup": 1.6
      },
      {
        "N": 4,
        "speedup": 2.285714285714286
      },
      {
        "N": 8,
        "speedup": 2.909090909090909
      }
    ],
    "curve_features": {
      "domain": "N>=1",
      "at_N_1": "S(1)=1",
      "monotonicity": "strictly increasing for N>=1",
      "concavity": "concave down",
      "asymptote": "S approaches 4 as N approaches infinity",
      "finite_positive_roots": "none"
    }
  },
  "working": "Amdahl with p=0.75 gives serial fraction 1-p=0.25. N=1: denominator=0.25+0.75/1=1, so S=1/1=1. N=2: denominator=0.25+0.75/2=0.25+0.375=0.625, so S=1/0.625=1.6. N=4: denominator=0.25+0.75/4=0.25+0.1875=0.4375=7/16, so S=1/(7/16)=16/7=2.285714285714286. N=8: denominator=0.25+0.75/8=0.25+0.09375=0.34375=11/32, so S=1/(11/32)=32/11=2.909090909090909. As N increases, p/N approaches 0, so S approaches 1/(1-p)=1/0.25=4."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/amdahl-s-law-parallel-speedup-calculator/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/amdahl-s-law-parallel-speedup-calculator/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/amdahl-s-law-parallel-speedup-calculator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche6/tranche6-results.json`