Description
Choose a uniform fixed-cardinality bit-position subset without replacement, returning ascending selected positions; no arbitrary rejection loop.
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.
Choose a uniform fixed-cardinality bit-position subset without replacement, returning ascending selected positions; no arbitrary rejection loop.
When to use this tool
Use this tool to choose a uniform fixed-cardinality bit-position subset without replacement, returning ascending selected positions; no arbitrary rejection loop.
How to use the tool and how it works
- Enter width, ones, seed using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.seed, result.positions, result.mask, using the stated boundary, ordering, sign and absence conventions.
Choose ones distinct positions uniformly from width, sort their indexes and create a text mask with exactly those positions set to one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| width | Integer width, 1–128, in the positions/cells described above. | Finite safe integer satisfying the stated bounds. |
| ones | Exact number of set positions, from 1 through width. | 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.positions | Sorted distinct selected/flipped/set positions. |
| result.mask | Left-to-right 0/1 text mask of the requested width. |
{
"input": {
"width": 4,
"ones": 2,
"seed": "batch56"
},
"output": {
"result": {
"seed": "batch56",
"positions": [
2,
3
],
"mask": "0011"
}
}
}Limitations and assumptions
- width is 1–128 and ones is 1–width. Uniformity concerns fixed-popcount masks, not all binary strings.
- 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
Similar or alternative tools
- Random Contiguous Bit Burst Mask
Choose one uniform nonwrapping contiguous positive bit burst start; the mask is left-to-right text, not an encoded integer.
- Random Exact Deletion Index Mask
Choose a uniform exact-size deletion index subset, retaining source positions and one-is-deleted mask; does not edit payload data.