为何IEEE754二进制格式标准中roundTiesToAway舍入模式为可选？

Great question! Let’s unpack the reasoning behind this distinction between binary and decimal formats in the IEEE 754-2008 standard.

First, let’s recap the relevant standard language for context:

根据《IEEE浮点运算标准（2008）》第4.3.3节：本标准的实现必须提供roundTiesToEven及三种定向舍入属性；十进制格式实现必须提供roundTiesToAway作为用户可选舍入方向属性，但二进制格式实现无需提供该属性。

Here’s why the standard draws this line:

• Binary floating-point prioritizes implementation efficiency and common use cases
  In binary, ties (values exactly halfway between two representable numbers) are rare and follow a strict pattern—they only occur when the discarded fraction is exactly 1/2 of the least significant bit. The required roundTiesToEven mode is trivial to implement in hardware: you just check if the least significant bit of the target value is even (keep it) or odd (round up). This mode already minimizes cumulative rounding bias effectively for most scientific, engineering, and general computing tasks.
  Adding roundTiesToAway would require extra logic, but since it’s rarely needed in binary contexts, making it optional lets hardware designers optimize for performance and die size—critical factors for processors that rely heavily on binary floating-point operations.

• Decimal floating-point is built for user-centric and financial use cases
  Decimal formats are designed for scenarios where rounding behavior needs to match human intuition, like financial calculations or user-facing displays. roundTiesToAway (what most people call "round half up") is the expected behavior here—think 2.5 rounding to 3, -2.5 rounding to -3. Ties are far more common and impactful in decimal, so the standard mandates that decimal implementations offer roundTiesToAway as an option to meet the needs of these real-world applications.

• Historical design legacy
  Binary floating-point was the foundation of the original IEEE 754 standard, and roundTiesToEven was chosen as the default for its balance of bias reduction and implementation simplicity. Decimal support was added later in the 2008 revision, and the authors explicitly designed it to address gaps in the binary standard for commercial use cases—hence the requirement for roundTiesToAway as an optional feature.

内容的提问来源于stack exchange，提问作者Arma6815