RNS-APAL™ is the world’s first arbitrary precision arithmetic library based entirely on the Residue Number System (RNS) — a bold departure from traditional carry-based computation. Unlike conventional libraries like GMP or MPFR that rely on fixed-radix systems and digit-to-digit carry propagation, RNS-APAL™ performs all arithmetic without carry, using an entirely modular approach. The result: a cleaner, parallel-friendly, and profoundly different kind of number crunching.
Key Features:
Arbitrary precision integer and fractional arithmetic, fully in RNS
True fixed-point and sliding-point math, performed without ever converting back to binary
No carry chains — ever. Calculations remain modular from start to finish
Fractional multiplication, division, and iteration with carry-free, high-precision performance
Built-in tools for educational insight, debugging, and RNS code modeling
Why It Matters
RNS-APAL isn’t just another math library — it’s a new computational paradigm. For the first time, researchers and developers can explore general-purpose computation in a carry-free environment. This opens doors to:
Breakthroughs in parallel processing
More efficient hardware-software co-design
Re-imagined algorithms for AI, cryptography, signal processing, and numerical simulation
Modular Computation: A New Field of Arithmetic
MaiTRIX introduces the term modular computation to describe this evolving domain — an area made possible by decades of RNS research and now unlocked by RNS-APAL™. Whether you’re an engineer, a mathematician, or a curious researcher, this library is your hands-on gateway into a new world of carry-free, modular arithmetic.
Try It Yourself
RNS-APAL™ is open to the public, providing source code, worked examples, and routines that bring RNS theory to life. Dive in, explore its structure, and reimagine what digital arithmetic can be. Download it here.
Note: RNS-APAL is copyrighted source code that is free to use by academics, researchers and private individuals. The new release has been licensed under the Creative Commons license CC BY-NC-SA. This license allows users to remix, adapt, and build upon our work non-commercially, as long as the users credit us and license their new creations under the identical terms.
Our software is a source code library reflecting fundamental research and is published compliant to Section §734.7, §734.8 & §734.10 of the U.S. EAR export rules and is therefore available for public dissemination. However, the download of our software does not provide a commercial license, please contact MaiTRIX for a license allowing commercial use. Commercial use of RNS-APAL includes the use of the software to develop RNS based ALU and CPU technology.