CORDIC Abs APFX

A free way to implement a CORDIC-based Complex Absolute Value 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 also can be used to approximate the module of a complex. It is also useful for microcontrollers or microprocessors lacking floating-point units, as such multiplications can consume a noticeable amount of CPU cycles.

Indeed, |z| = sqrt(x² + y²) = |exp(-j*angle(z)) * z|, thus the module of z is the absolute value of the real part of its rotated version. So, ... CORDIC!

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

This repository defines one working CORDIC-based Absolute Value units class, CCordicAbs.

Test suite and dependencies

The Catch2 test framework has been used in conjunction with CTest to provides unit tests.

• Has been tested successfully compiled with:
  • GNU GCC 6.2 (Xilinx bundled version), 6.5, 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.

License and copyright

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.