Binary Round To Even Increment Decision Tool

Description

Return a round-to-nearest-even increment decision.

Fixed-width arithmetic can wrap, saturate, shift in sign bits or expose discarded bits. Carry, borrow and signed overflow describe different conditions; a local rounding decision or guard/sticky triplet is one part of an arithmetic operation rather than a complete floating-point result.

Return a round-to-nearest-even increment decision.

When to use this tool

Use Binary Round To Even Increment Decision when evaluating the stated shift, arithmetic flag or rounding convention.

How to use the tool and how it works

Enter leastSignificant, guard, round, sticky. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read increment, tie. Inspect increment, tie before interpreting the associated values.

Return a round-to-nearest-even increment decision. increment = guard AND (round OR sticky OR leastSignificant), tie = guard AND not round AND not sticky.^[1]

Input field	Meaning and units	Accepted input
leastSignificant	Least Significant	Required. Boolean.
guard	Guard	Required. Boolean.
round	Round	Required. Boolean.
sticky	Sticky	Required. Boolean.

Output field	Interpretation	Returned shape
increment	guard AND (round OR sticky OR leastSignificant); applies to retained significand magnitude.	Required. Boolean.
tie	Tie	Required. Boolean.

json

{
  "input": {
    "leastSignificant": true,
    "guard": true,
    "round": false,
    "sticky": false
  },
  "output": {
    "increment": true,
    "tie": true
  }
}

Limitations and assumptions

Inputs describe the magnitude-significand rounding context; no full floating-point value, overflow or signed rounding operation is implemented.
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.

Alternative or Complementary methods

Use a complete arithmetic operation with explicit width, signedness, overflow and rounding policy; keep exact integer text when values exceed ordinary numeric precision.

References

Calculation and input contract: bitwise/binary-round-to-even-increment-decision — tool.io

Similar or alternative tools

Binary Sticky Round Guard Triplet
Split discarded bits into guard, round and sticky flags.
Bitword Offset Binary To Unsigned Tool
Compute bitword offset binary to unsigned from explicit bounded inputs.