PhD Thesis

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« Compilation and optimizations for variable precision floating-Point arithmetic: from language and libraries to code generation ».

Author: T. Trevisan Jost
Advisor: F. Pétrot
Co-advisor: A. Cohen, C. Fabre
These de Doctorat Université Grenoble Alpes
Speciality: Micro et Nano Electronique
Defense: July 02 2021


The emerging number format named UNUMs – an abbreviation for universal numbers – claims to provide several key improvements over the current floating point formats IEEE-754, like (1) information about the exactness of a number or variable size format, reducing memory footprint. If those promises are interesting, they nevertheless have a number of limitations. E.g. the variable size format requires an internal normalization within an operator and rounding will have to take place, because the operators' internal memory is necessary limited. Striking a good trade-off between UNUM's promises and limitations requires a greater interaction and integration between UNUMs operators' and the compiler. A compiler implementing a UNUM-aware language can, e.g., make dedicated analyses of potential parallelism to steer the hardware modules implementing the operators. Its goal will be to organize the flow of computations that may depend on metainformation on the intermediate results, such as size of mantissa or a UNUM's exactness' range. The goal of the project is to propose a hardware/software interface between UNUM binary programs and their hardware implementation. This usually includes the set of registers that stores intermediate value and the list of instructions that trigger operations.