Nios II Custom Instruction User Guide

ID 683242
Date 4/27/2020
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5.3. Rounding Schemes

When the exact result of a floating point operation cannot be exactly represented as a floating point value, it must be rounded.

The IEEE 754-2008 standard defines the default rounding mode to be “Round-to-Nearest RoundTiesToEven”. In the IEEE 754-1985 standard, this is called “Round-to-Nearest-Even”. Both standards also define additional rounding modes called “Round-to-Zero”, “Round-to-Negative-Infinity”, and “Round-to-Positive-Infinity”. The IEEE 754-2008 standard introduced a new optional rounding mode called “Round-to-Nearest RoundTiesAway”.

The FPH2 operations either support Nearest Rounding (RoundTiesAway), Truncation Rounding, or Faithful Rounding. The type of rounding is a function of the operation and is specified in Table 4-2. Because the software emulation library (used when floating point hardware is not available) and FPH1 implement Round-to-Nearest RoundTiesToEven, there can be differences in the results between FPH2 and these other solutions.