Emulating Double-Precision Arithmetic with Float Pairs

Question:

An embedded hardware system with limited floating-point precision requires the emulation of double-precision arithmetic using single-precision floats. Specifically, a 64-bit double-precision addition and comparison are needed.

Addition:

The addition process raises complexities in determining the base and carry detection mechanism. What approach should be used, and how can the carry be handled?

Comparison:

The comparison operation can be implemented using lexicographic ordering.

Background:

The objective is to obtain additional significant digits rather than extending the exponent range.

Answer:

Double-Float Emulation

Double-float or float-float is a technique that utilizes pairs of single-precision numbers to simulate double-precision precision. While this provides enhanced precision, it comes at the expense of reduced exponent range.

Recommended Resources

For further guidance on double-float emulation, refer to these technical papers:

• [Implementation of float-float operators on graphics hardware](https://hal.archives-ouvertes.fr/hal-00021443)
• [Extended-Precision Floating-Point Numbers for GPU Computation](http://andrewthall.org/papers/df64_qf128.pdf)

These papers provide insights into adapting float-float techniques to various platforms, including embedded systems.