Two-Level-Multiplier

This repository contains source code for a VHDL implementation of the high-precision integer multiplication algorithm proposed in the paper "Leveraging a Novel Two-Level Priority Encoder for High-Precision Integer Multiplication." All components are generalized such that only generics need modified to adapt the hardware to different bit precisions.

Files

• For implementation and on-board testing, all files in /src and subdirectories are required.
  • Technically, not all of the small encoder components in /src/Base Encoders are needed depending on bit precision, but if you are switching between bit precisions it is recommended to simply import all of them, as priority_encoder_generic will only instantiate the necessary components.
  • To adjust for different bit precisions, modify the generics in the top-level file.
  • Constraint files for Digilent Basys 3 and Nexys A7-100T FPGA development boards are located in /src/XCVR. For other devices, adapt these constraints appropriately.
  • For uneven multipliers, slight modification is necessary to mk8_container_multiplier_####.vhd and mk8_apex_####.vhd to set the generic from the top-level file instead of dividing the top-level G_total_bits by 2 to get G_n and G_m.
• For synthesis and simulation only, the files in /src/XCVR are not required. Everything else is as stated above.
• The 'Software Simulator' folder contains a high-level simulation of the multiplication algorithm, written in Kotlin. You can also test it easily online on Kotlin Playground here: https://pl.kotl.in/j2RgjnehS.
• The 'Output Postprocessor' folder contains a Kotlin program useful for managing the input and output of an FPGA board running the VHDL code. For instance, removing non-digit characters like spaces or commas.
• Note: the code provided implements our serial transceiver, which can be found here.

Other

The following resources are useful when testing the hardware:

• Random 256-Bit Number Generator (similar generators are also available for higher input lengths)
• High Precision Base Converter
• Big Number Calculator (Warning: truncates past ~4096-bit operands)

Example

Below is an illustrative example with a small input size of our algorithm and the first two cycles of the hardware.