#fixed #math #numeric

nightly no-std fp

Fast & safe fixed-point arithmetic via compile-time checks

2 unstable releases

0.3.0 May 24, 2024
0.2.0 May 23, 2024
0.1.0 Jan 23, 2017

#488 in Embedded development

24 downloads per month

MIT license

30KB
451 lines

This is a Rust crate providing fixed-point arithmetic with statically verified overflow safety and bit shift correctness, and zero runtime overhead.

Please note: this crate requires nightly Rust, for the generic_const_exprs feature. In addition, this is an "alpha" release with incomplete documentation and incomplete test coverage. The fixed package provides a widely-used, production-ready option for fixed-point arithmetic -- although it does not provide compile-time overflow safety, nor the guarantee of zero runtime overhead.

Fixed-point arithmetic represents fractional values as integers with an implicit bit shift. For example, the decimal number 2.375 (in base 2: 10.011) could be represented in fixed-point as the integer 0b10011 (decimal 19) with an implicit bit shift of 3. It is typically the programmer's responsibility to keep track of all the bit shifts used in a program, ensure they are consistent with each other, and avoid any overflows during arithmetic operations.

In contrast, floating-point numbers automatically adjust the "bit shift" (i.e. the exponent) to provide the largest possible resolution which will not overflow. They are easy to use, and they do the right thing most of the time. However, they can cause subtle rounding bugs which are famously difficult to identify and prevent. In the immortal words of Professor Gerald Sussman, "Nothing brings fear to my heart more than a floating-point number."

This crate uses the Rust type system to provide fixed-point numbers with compile-time bit shift checking and overflow protection. Each fixed-point type has two const generic parameters, one describing the bit shift and one describing the maximum number of bits which could be nonzero. Each arithmetic operation is implemented with an output type which correctly reflects the bits and shift of the result. For example, the result of multiplying a 10-bit number (shifted by 2) and a 12-bit number (shifted by 3) is a 22-bit number (shifted by 5).

The fp::Num trait represents any fixed-point number stored as an integer, and the generic structs fp::X??<const BITS: u32, const SHIFT: i32> implement the fp::Num trait for each width and shift of fixed-point number which could be represented by the integer type x??. Arithmetic operations on the fixed-point types are guaranteed to provide correctness and overflow safety with zero runtime overhead.

No runtime deps