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.