This project is archived and will be replaced with xmath. Someday.
Fix32 is a collection of highly optimized fixed-point mathematical functions for embedded systems. These functions operate on 32-bit fixed-point numbers, whose format, with rare exceptions, may vary from Q1 to Q31. To utilize all the features of a target CPU and achieve faster execution speeds and smaller memory footprint, all the functions are written in an assembly language.
Simply put, this software library is aimed at those who want to perform fast and precise non-integer calculations on devices lacking a FPU. But even with a presence of FPU, this library may still be useful, as most of the library functions are considerably faster than standard floating-point alternatives. In addition, 32-bit signed fixed-point numbers have more significant digits than single-precision floating-point numbers.
The header file contains a brief description of each function. If you have already know what fixed-point numbers are, this should be enough. Otherwise, it is a good idea to read up on them a little bit, so you can understand the basic principles and terminology. For more information about the execution time and accuracy, as well as the other implementation details of a certain function, you may refer to the comments in the corresponding source file.
The library does not require any initialization or configuration routines. Simply download the latest precompiled static library file for the required CPU architecture and add it to your project. To manually build the library, use one of the makefiles in the project root. Each makefile contains recipes to build both the debug and release version of the library for a particular CPU architecture. For more information on the build process and used tools, see the contents of the makefiles.
As stated in the description, this is a tried and tested cross platform fixed point maths library. It is written in the C programming language, so it will work considerably slower and will take up more space in memory. Another major drawback is that this library supports only Q16 fixed-point format, while the current library supports a full range of formats starting from Q1 and ending with Q31.
The advantage of the libfixmath library is that it includes several functions that are not (yet) implemented in the current library. These are the tangent function, a few inverse trigonometric functions, and a set of basic saturated arithmetic functions.
The CMSIS DSP software library is a collection of common signal processing functions for use on Cortex-M based devices. Just like the previous library, it is also written in C language. So it will perform slower and will occupy more space in memory, especially because it uses a larger lookup tables.
One more drawback is that the CMSIS DSP library supports only two fixed-point formats, namely the Q15 and Q31. A set of supported mathematical functions is also very poor and includes only the sine, cosine, and square root function. There are other functions, but they are designed to work with vector values or complex numbers.
The Texas Instruments IQmath Library is a collection of highly-optimized and high-precision mathematical functions. Like its counterpart, it is writen in assembly language and supports a full range of fixed-point formats starting from Q1 and ending with Q31. Furthermore, the library provides a large set of functions, including those that are absent in the current library. These are the tangent function, several inverse trigonometric functions, and the exponent function.
Despite these advantages, many functions in the IQmath library tend to be a few cycles slower and little less accurate than their counterparts from the current library. Also, the IQmath library uses a larger lookup tables, which significantly increases the size of the library.
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The library functions do not check their inputs. A function will silently return an undefined value if you violate the requirements given in the function description. This is not a defect but a conscious design choice to increase the library performance. Thus, all the passed values should be checked in a higher software level.
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Since the lowest negative two's complement 32-bit signed integer does not have its positive counterpart, some of the library functions may not work properly if you specify this value.
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All cycle counts are based on a system with zero wait states, yet the real systems usually have memory with more than zero wait states. In such cases the execution times can increase by several times. Also, time measurements do not include the function call overhead.
If you find a bug, ensure this bug was not already submitted by searching on the issue tracker. If it is not, be sure to include a meaningful title, clear description, and a code sample demonstrating the incorrect behavior.
If you wrote a patch that fixes a bug — feel free to send a pull request with this patch. Ensure the pull request description clearly describes the problem and solution. Include the relevant issue number if applicable.
In the case if you intend to add a new feature or change existing one, you can submit a new issue on the issue tracker or send me an email to discuss the proposed changes.
This is free and unencumbered software released into the public domain. For more information, see the LICENSE file.