Implementation and Synthesis of Math Library Functions

• Main Authors: Briggs, Ian, Lad, Yash, Panchekha, Pavel
• Format: Journal Article
• Language: English
• Published: 02-11-2023
• Subjects: Computer Science - Programming Languages
• DOI: 10.48550/arxiv.2311.01515

Achieving speed and accuracy for math library functions like exp, sin, and
log is difficult. This is because low-level implementation languages like C do
not help math library developers catch mathematical errors, build
implementations incrementally, or separate high-level and low-level decision
making. This ultimately puts development of such functions out of reach for all
but the most experienced experts. To address this, we introduce MegaLibm, a
domain-specific language for implementing, testing, and tuning math library
implementations. MegaLibm is safe, modular, and tunable. Implementations in
MegaLibm can automatically detect mathematical mistakes like sign flips via
semantic wellformedness checks, and components like range reductions can be
implemented in a modular, composable way, simplifying implementations. Once the
high-level algorithm is done, tuning parameters like working precisions and
evaluation schemes can be adjusted through orthogonal tuning parameters to
achieve the desired speed and accuracy. MegaLibm also enables math library
developers to work interactively, compiling, testing, and tuning their
implementations and invoking tools like Sollya and type-directed synthesis to
complete components and synthesize entire implementations. MegaLibm can express
8 state-of-the-art math library implementations with comparable speed and
accuracy to the original C code, and can synthesize 5 variations and 3
from-scratch implementations with minimal guidance.