A Comparison of Posit and IEEE 754 Floating-Point Arithmetic That Accounts for Exception Handling
John Gustafson
National University of Singapore, SG
ABSTRACT
The posit number format has advantages over the decades-old IEEE 754 Standard floating-point standard in many dimensions: Accuracy, dynamic range, simplicity, bitwise reproducibility, resiliency, and resistance to side-channel security attacks. In making comparisons, it is essential to distinguish between an IEEE 754 Standard implementation that handles all the exceptions in hardware, and one that either ignores the exceptions of the Standard or handles them with software or microcode that take hundreds of clock cycles to execute. Ignoring the exceptions quickly leads to egregious problems such as different values comparing as equal; handling exceptions with microcode creates massive data-dependency on timing that permits side-channel attacks like the well-known Spectre and Meltdown security weaknesses. Many microprocessors, such as current x86 architectures, use the exception-trapping approach for exceptions such as denormalized floats, which makes them unsuitable for secure use. Posit arithmetic provides data-independent and fast execution times with less complexity than a data-independent IEEE 754 float environment for the same data size.
