Description
Shift a cycle/phase coordinate with exact integer intermediates.
Conversion direction matters for reciprocal and logarithmic quantities. Frequencies, periods, phase coordinates and reference ratios use explicit origins, sign policies and denominator units, rather than a single ordinary length or time multiplier.
Shift a cycle/phase coordinate with exact integer intermediates.
When to use this tool
Use Phase Cycle Index Offset when converting the stated reciprocal, angular, phase or logarithmic convention.
How to use the tool and how it works
- Enter cycleIndex, offset, phasesPerCycle, phaseIndex. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read shiftedCycleDecimal, shiftedPhase. Use the output convention below.
Shift a cycle/phase coordinate with exact integer intermediates. Require positive whole phasesPerCycle and phaseIndex in [0,period); combine cycle*period+phase+offset using BigInt, then return floor-style cycle quotient as decimal text and nonnegative phase.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| cycleIndex | Cycle Index | Required. Safe integer. |
| offset | Offset | Required. Safe integer. |
| phasesPerCycle | Phases Per Cycle | Required. Safe integer; minimum 1. |
| phaseIndex | Phase Index | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| shiftedCycleDecimal | Exact signed decimal cycle quotient using floor-style division. | Required. Text; maximum UTF-16 length 8192. |
| shiftedPhase | Nonnegative remainder below phasesPerCycle. | Required. Safe integer. |
{
"input": {
"cycleIndex": 2,
"offset": 3,
"phasesPerCycle": 4,
"phaseIndex": 2
},
"output": {
"shiftedCycleDecimal": "3",
"shiftedPhase": 1
}
}Limitations and assumptions
- Numeric inputs still obey their contracts; cycle output is exact text and no calendar or physical period is inferred.
- 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
Use the complete unit and origin definitions, and distinguish a coordinate conversion from a density Jacobian or a physical measurement.
References
Similar or alternative tools
- Fictional Calendar Cycle Phase Token
Return a fictional calendar's cycle and nonnegative phase.
- Discrete Mode Frequency Fold
Fold an integer mode into a signed sampled frequency.