LibFi - A fixed-point arithmetic library.

What is LibFi?

LibFi is a binary fixed-point arithmetic library for C++, focusing on flexibility and correctness. It is intended to be used for modeling hardware systems. LibFi is template-based and is a header-only library.

Unlike most other C++ fixed-point libraries, the word length in Fi does not have to be a power of two, and the overflow behavior and rounding mode are customizable.

This is a header-only library so you include ./fi/Fixed.hpp, and any applicable overflow handlers and rounding modes from ./fi/overflow and ./fi/rounding.

Here is an example of multiplying 8-bit, signed fixed-point numbers with 4 fractional bits:

#include "fi/Fixed.hpp"
#include "fi/overflow/Wrap.hpp"

#include <iostream>

int main(int argc, char* argv[]) {

  Fi::Fixed<8, 4, Fi::SIGNED> a("3.14");
  Fi::Fixed<8, 4, Fi::SIGNED> b("1.14");

  std::cout << a*b << std::endl;

  return 0;

}

Documentation

LibFi is documented using Doxygen. To build the documentation, you need Doxygen. In the library's root directory, run doxygen. The documentation will be available in doc/html/index.html.

Quick Reference

The Fi::Fixed<TOTAL_WIDTH, FRACTION_WIDTH, SIGNEDNESS, OVERFLOW, ROUNDING> datatype accepts five parameters:

Parameter	Description	Required
TOTAL_WIDTH	Total number of bits in binary representation, including the sign for signed types.	Yes
FRACTION_WIDTH	Number of fractional bits.	Yes
SIGNEDNESS	Fi::SIGNED for signed values; Fi::UNSIGNED for unsigned values.	Yes
OVERFLOW	Behavior when a number overflows the range representable using the selected quantization parameters. See below for valid options.	No (Default: Fi::Throw)
ROUNDING	Behavior when a number is not representable using the selected quantization parameters. See below for valid options.	No (Default: Fi::Fix)

Rounding

Mode	Description
Fi::Classic	Round to nearest representable value. Ties are rounded away from zero.
Fi::Ceil	Round towards positive infinity.
Fi::Floor	Round towards negative infinity.
Fi::Fix	Round towards zero.
Fi::NearEven	Round to nearest representable value. Ties are rounded towards an LSB of 0.
Fi::NearOdd	Round to nearest representable value. Ties are rounded towards an LSB of 1.

Overflow

Mode	Description
Fi::Saturate	Saturate value to maximum or minimum value allowed by selected quantization parameters.
Fi::Wrap	Wrap the value around when overflow occurs.
Fi::Throw	When overflow occurs, throw a Fi::PositiveOverflow or a Fi::NegativeOverflow exception, depending on the direction of the overflow.
Fi::Undefined	The behavior of overflow is undefined. Use when execution speed is more important than results.

Tests

Nightly test build results are available on the following page.

Supported Platforms

Tests are run on the following platforms:

• 64-bit Linux using GCC.
• 64-bit Linux using Clang.

The master branch always contains code which passes all the tests on the supported platforms.

External References

• MATLAB Fixed-Point Designer Toolbox
• C++ Binary Fixed-Point Arithmetic Library Proposal

Changelog

• 2013-07-02 v1.0: First public release of LibFi.