A template to implement a CORDIC-based rotation with bit accurate fixed-point number representation.
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CORDIC Rotate APFX

A free way to implement a CORDIC-based rotation using HLS, with bit-accurate precision.

Goal

CORDIC (COordinate Rotation DIgital Computer) is an efficient way to implement hardware complex rotations (e.g. z * exp(jw), with z = x + jy a complex and w a real angle). It is also useful for microcontrollers or microprocessors lacking floating-point units, as such multiplications can consume a noticeable amount of CPU cycles.

This implementation in C++14 (-std=c++14) is suitable for hardware simulation and (with the right lib's and a few tweaks) for synthesis.

This repository mainly hosts CCordicRotateHalfPiRom, CORDIC-based rotation units which rely on a ROM. Currently, It ranges from 2 to 7 stages, and the word length is a template. It depends on ROM generators, each one producing a ROM table which contains control signals for each CORDIC stage, depending on the input angle. There are generators:

  • A true constexpr one, that is entirely processed by the compiler.
  • A Monte-Carlo one, that is evaluated at runtime and can be used to produced ROM-headers, suitable for Autoconf/CMake header generations.

Only rotations of pi and pi/2 are currently supported, but support for any pi/2^k can be easily added.

CCordicRotate is an unfinished template that would implement a smart CORDIC, which can work without a ROM.

Test suite and dependencies

The Catch2 test framework has been used in conjunction with CTest to provides unit tests. The GitHub mirror of the repository also make use of GitHub Actions and Docker as a CI/CD solution.

  • Has been tested successfully compiled with:
    • GNU GCC 9.4, 10.1, 10.2 and 11.2,
    • LLVM Clang 12.0 and 13.0,
  • Uses Catch v2.13.7,
  • Depends on Xilinx HLS arbitrary precision types, available as FOSS here provided by Xilinx or here patched by myself. Note: Xilinx also provides proprietary versions of those headers, suitable for synthesis and implementation, bundled with their products.

Copyright 2022 Camille "DrasLorus" Monière.

This program is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

A copy of the license is available here in Markdown or here in plain text.