Random Saturating Counter Input Trace

Description

Draw independent uniform bounded integer increments and saturate each result to explicit inclusive endpoints; not uniform over final states or hardware fault behavior.

A random construction is defined by its sampling support: positions, permutations, complete tilings, proposal sequences or another explicit set. Uniform choices at one stage do not necessarily make final visible outcomes uniform. A replay seed gives a deterministic sequence; equal values can hide different sampled positions. These tools are for reproducible synthetic examples rather than cryptographic entropy.

Draw independent uniform bounded integer increments and saturate each result to explicit inclusive endpoints; not uniform over final states or hardware fault behavior.

When to use this tool

Use this tool to draw independent uniform bounded integer increments and saturate each result to explicit inclusive endpoints; not uniform over final states or hardware fault behavior.

How to use the tool and how it works

Enter initial, minimum, maximum, steps, stepMinimum, stepMaximum, seed using the definitions below.
Run the operation. Resolve input-format errors before interpreting an output.
Read result.seed, result.increments, result.states, using the stated boundary, ordering, sign and absence conventions.

Draw independent inclusive integer increments, start with initial and clamp every proposed state to [minimum,maximum]. Return proposals as increments and all states including the initial value.^[1]

Input field	Meaning and units	Accepted input
initial	Initial integer state within the explicitly supplied counter/walk bounds.	Finite safe integer satisfying the stated bounds.
minimum	Inclusive integer state lower bound within ±1,000,000.	Finite safe integer satisfying the stated bounds.
maximum	Inclusive integer state upper bound within ±1,000,000. It must be at least minimum; a reflecting walk requires it to be strictly greater.	Finite safe integer satisfying the stated bounds.
steps	Number of transitions, integer 1–127; the states output includes the initial state as well.	Finite safe integer satisfying the stated bounds.
stepMinimum	Inclusive minimum increment, integer within ±1,000,000.	Finite safe integer satisfying the stated bounds.
stepMaximum	Inclusive maximum increment, at least stepMinimum and no greater than 1,000,000.	Finite safe integer satisfying the stated bounds.
seed	Nonblank replay seed, at most 256 UTF-16 code units; an injected source overrides seeded draws.	Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply.

Output field	Interpretation
result	Object containing the fields below.
result.seed	Original supplied seed string; injected-source replay additionally requires that source’s state.
result.increments	Proposed signed increments in generated order.
result.states	State sequence including the initial coordinate followed by every transition.

json

{
  "input": {
    "initial": 1,
    "minimum": 0,
    "maximum": 3,
    "steps": 3,
    "stepMinimum": -1,
    "stepMaximum": 1,
    "seed": "batch56"
  },
  "output": {
    "result": {
      "seed": "batch56",
      "increments": [
        0,
        1,
        1
      ],
      "states": [
        1,
        1,
        2,
        3
      ]
    }
  }
}

Limitations and assumptions

Counter bounds/increments are within ±1,000,000; steps is 1–127. Clamping accumulates probability at boundaries and does not yield uniform states.
A nonblank seed of at most 256 UTF-16 code units is required. With ordinary use the seed initializes one deterministic advancing source; an application-injected random source takes precedence and the seed alone then cannot replay the result. Uniformity statements assume independent uniform source draws in [0,1). Source calls are bounded and degenerate injected sources can fail a rejection budget. This is not cryptographically secure.
Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
Ordinary numeric outputs must be finite and within safe-integer magnitude. Exact large lengths/counts use decimal strings. Original record indexes and code-unit positions are zero-based; span ends are exclusive unless stated otherwise.

Alternative or Complementary methods

Choose a generator whose support matches the intended experiment and retain source-position provenance. Use a separate statistically justified process model or cryptographic source where those properties matter.

References

Tool behavior and example: Random Saturating Counter Input Trace — tool.io

Similar or alternative tools

Random Wrapping Counter Input Trace
Draw independent uniform bounded integer increments and wrap each result in the explicit inclusive integer range; not uniform over final states or hardware fault behavior.
Random Block Order Permutation
Uniform whole-block position permutation preserving internal order and duplicate display labels.