Mixed Radix Previous Digits
Advance a mixed-radix tuple backward by one in most-significant-first lexicographic order, returning null rather than wrapping at boundaries.
Description
Advance a mixed-radix tuple backward by one in most-significant-first lexicographic order, returning null rather than wrapping at boundaries.
A mixed-radix predecessor is subtraction by one in a positional system whose bases can differ by digit.
When to use this tool
Advance a mixed-radix tuple backward by one in most-significant-first lexicographic order, returning null rather than wrapping at boundaries.
- Prepare the supplied digits, radices fields for this operation.
- Compare the complete example with the representation used by your own input before carrying the result into another step.
How to use the tool and how it works
- Enter digits, radices. Use the exact text syntax, units and index conventions explained below.
- Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
- Read result.digits. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Validate aligned digits/radices, with positive radices and each digit in range. Encode the digits left-to-right, subtract one and decode if nonnegative; otherwise return null.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| digits | digits. | List of finite numbers; at most 128 entries |
| radices | radices. | List of finite numbers; at most 128 entries |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.digits | The digits list in the ordering and representation described above. |
{
"input": {
"digits": [
0,
2
],
"radices": [
2,
3
]
},
"output": {
"result": {
"digits": [
0,
1
]
}
}
}Limitations and assumptions
- The rightmost digit changes fastest. There is no wraparound before the all-zero vector.
- All declared input fields are required and unexpected top-level fields are rejected. Numbers must be finite; lists are limited to 128 entries and ordinary text fields to 8,192 UTF-16 code units, with tighter limits where stated.
- JSON text inputs must parse within bounded nesting and size limits. Numeric outputs outside the safe finite range are rejected; large exact integer results use decimal strings. Indexes and half-open spans are zero-based unless a rank is explicitly described as one-based.
Alternative or Complementary methods
Retain the universe size, subset size and ordering convention with a rank. Use rank/unrank pairs from the same convention and distinguish subset masks from lexicographic indexes.
References
Similar or alternative tools
- Mixed Radix Next Digits
Advance a mixed-radix tuple forward by one in most-significant-first lexicographic order, returning null rather than wrapping at boundaries.
- Mixed Radix Digit Decoder
Decode a zero-based exact integer index into mixed-radix digits most-significant lane first; out-of-range indexes do not wrap.