Cyclic List Phase Remainder Tool

Description

Subtract origin from index using exact integers and reduce modulo positive length into phase in [0, length).

An index map tracks where one item lands after a structural list operation. Zero-based element positions differ from boundary cursors, and missing destinations need a sentinel.

Subtract origin from index using exact integers and reduce modulo positive length into phase in [0, length).

When to use this tool

Use Cyclic List Phase Remainder when you need one item's position under an explicit list transformation.

How to use the tool and how it works

Enter index, origin, length. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read phase. Use the output convention below.

Subtract origin from index using exact integers and reduce modulo positive length into phase in [0, length).^[1]

Input field	Meaning and units	Accepted input
index	Zero-based position or diagnostic index under the calculation above; inspect any sentinel policy.	Required. Safe integer.
origin	Origin	Required. Safe integer.
length	Length, count, or code length under the stated domain and unit convention.	Required. Safe integer; minimum 1.

Output field	Interpretation	Returned shape
phase	Phase	Required. Safe integer.

json

{
  "input": {
    "index": 12,
    "origin": 3,
    "length": 5
  },
  "output": {
    "phase": 4
  }
}

Limitations and assumptions

This is a cyclic phase relative to a supplied origin, not an observed traversal count.
Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Apply the operation to a small representative list when checking a consuming language's indexing and slicing semantics.

References

Calculation and input contract: list/cyclic-list-phase-remainder — tool.io

Similar or alternative tools

List Offset Wrap Index
Add signed index and offset using exact integers, then use floor division by positive length to return a nonnegative wrappedIndex and signed turns.
List Rotation Selected Index Preimage
Subtract shift from the valid selected destination and reduce modulo positive length for source.